DOC TOR A L T H E S I S
Department of Engineering Sciences and Mathematics
Division of Energy Science
Luleå University of Technology 2015
Kai Yang On Harmonic Emission, Propagation and Aggregation in Wind Power Plants
ISSN 1402-1544
ISBN 978-91-7583-260-9 (print)
ISBN 978-91-7583-261-6 (pdf)
On Harmonic Emission, Propagation and
Aggregation in Wind Power Plants
Kai Yang
Thesis for the degree of Doctor of Philosophy
On Harmonic Emission, Propagation
and Aggregation in Wind Power Plants
Kai Yang
Electric Power Engineering
Division of Energy Engineering
Department of Engineering Sciences and Mathematics
Luleå University of Technology
Skellefteå, Sweden
On Harmonic Emission, Propagation and Aggregation in
Wind Power Plants
Kai Yang
This thesis has been prepared using LATEX.
c Kai Yang, 2015.
Copyright All rights reserved.
Doctoral Thesis
Department of Engineering Sciences and Mathematics
Luleå University of Technology
Electric Power Engineering
Department of Engineering Sciences and Mathematics
Luleå University of Technology
SE-931 87 Skellefteå, Sweden
Phone: +46 (0)920 49 10 00
Author e-mail: [email protected]
Printed by Luleå University of Technology, Graphic Production 2015
ISSN
ISBN
ISSN 1402-1544
Printed by Universitetstryckeriet
ISBN 978-91-7583-260-9 (print)
Luleå, Sweden, March 2015
ISBN 978-91-7583-261-6 (pdf)
Luleå 2015
www.ltu.se
Nothing is softer or more ﬂexible than water,
yet nothing can resist it.
—Lao Tzu
Abstract
The increasing use of wind energy is a global trend as part of the overall transition to a more
sustainable energy system. By using modern technologies, the wind energy is converted into
electric power which is transported to the consumers by means of the electric power system. The
use of these technologies, in the meantime, plays a signiﬁcant role in maintaining power quality in
the electric power system; including positive as well as negative impacts. This thesis emphasises
on harmonic distortion within a wind power plant (WPP), for a wind turbine and for the plant
level.
The harmonic study presented in this thesis has been based on ﬁeld measurements at a few
diﬀerent individual wind turbines and at a second location in one WPP. In general, the levels of
harmonic distortion as percentage of the turbine and WPP ratings are low. Among the frequency
components, even harmonics and especially interharmonics are present at levels comparable with
the levels of characteristic harmonics. The measurements show that both harmonics and interharmonics vary strongly with time. Interharmonics further show a strong dependence on the active
power production of the turbine, while characteristic harmonics are independent on the power
production. The even harmonics and interharmonics may excite any resonance in the collection
grid or in the external grid.
The origin of interharmonic emission due to power converters has been veriﬁed through a series of measurements over a two-week period. The interharmonic emission originates from the
diﬀerence between the generator-side frequency and the power system frequency. A series of
interharmonic frequencies are produced and they vary in accordance with the generator-side frequency. Both these interharmonic frequencies and the magnitudes are related to each other, and
the theoretical relations have been conﬁrmed through the measurements.
The harmonic propagation in a collection grid has been studied by using transfer functions.
Without the need to know the harmonic sources, the characteristics of harmonic propagations are
quantiﬁed through transfer functions. The method has been used to estimate the total harmonic
level in a WPP, by combining knowledge of the transfer function with information from harmonic
emission of the individual wind turbines. The harmonic aggregation of the emission from the
individual turbines towards the point of connection (PoC) has been studied as well. From the
studies it was found that interharmonics show a stronger cancellation compared to harmonics,
especially compared to lower-order harmonics.
According to the object of interest and the harmonic propagation, a distinction has been
made between primary and secondary emission. A more detailed classiﬁcation of the diﬀerent
propagations within a WPP has been proposed. A systematic approach for harmonic studies
in association with WPPs has resulted from this. The harmonic voltages and currents at any
location are obtained as the superposition of the contribution from diﬀerent emission sources
to this speciﬁc location. This location can be either within the WPP or in the external grid.
The studies presented conclude that all the contributions should be included to get a reasonable
overview of the harmonic distortion in the WPP.
Keywords: Renewable energy, electric power system, wind power, power quality, power system
harmonics, harmonic aggregation.
i
Acknowledgments
The work within this research project has been undertaken in the Electric Power Engineering
group at Luleå University of Technology, Skellefteå campus. The work has been funded by Elforsk
AB through the VindForsk program and by Skellefteå Kraft AB. The ﬁnancial supports are greatly
acknowledged.
Sincere thanks to the many people who helped and supported me during my PhD study. My
deepest thanks to my supervisor professor Math Bollen for his patient guidance and inspiration.
My deepest gratitude to his excellent supervision, and external impact beyond the academic work.
Also, many thanks to my co-supervisor Dr. Anders Larsson for the helpful discussions and a lot
of help in my study, even during his personal time.
Many thanks to my colleagues at Luleå University of Technology in Skellefteå, and all local
and external colleagues within the Electric Power Engineering group. I especially appreciate the
friendly work environment within the group. A special thanks to Mats Walhberg, who is also with
Skellefteå Kraft AB, for helping me with measurements for my study.
Last but not the least, I would like to thank my parents, my sister and my brother for their
unwavering support and patience. To them, I dedicate this thesis.
Kai Yang
Skellefteå, March 2015
iii
iv
List of Publications
The thesis is based on the following publications:
Paper A
K. Yang, M.H.J. Bollen, E.A. Larsson and M. Wahlberg, “Measurements of Harmonic Emission
versus Active Power from Wind Turbines”, Electric Power Systems Research, vol.108, pp. 304
314, 2014. doi:http://dx.doi.org/10.1016/j.epsr.2013.11.025.
Paper B
K. Yang, M.H.J. Bollen and E.A. Larsson, “Aggregation and Ampliﬁcation of Wind-Turbine
Harmonic Emission in A Wind Park”, IEEE Transactions on Power Delivery (in press), 2014.
doi:10.1109/TPWRD.2014.2326692.
Paper C
K. Yang, M.H.J. Bollen, H. Amaris and C. Alvarez, “Decompositions of Harmonic Propagation
in A Wind Power Plant”, revision submitted to Electric Power Systems Research, 2015.
Paper D
K. Yang and M.H.J. Bollen, “Interharmonic Currents from A Type-IV Wind Energy Conversion
System”, submitted to Electric Power Systems Research, 2015.
Paper E
K. Yang and M.H.J. Bollen, “A Systematic Approach for Studying the Propagation of Harmonics
in Wind Power Plants”, submitted to IEEE Transactions on Power Delivery, 2015.
Paper F
K. Yang, M.H. Bollen, E. A. Larsson and M. Wahlberg, “A Statistic Study of Harmonics and Interharmonics at A Modern Wind-Turbine”, in Proceedings of International Conference on Harmonics
and Quality of Power (ICHQP), Bucharest, 2014.
Paper G
K. Yang, M.H.J. Bollen and E.A. Larsson, “Wind Power Harmonic Aggregation of Multiple Turbines in Power Bins”, in Proceedings of International Conference on Harmonics and Quality of
Power (ICHQP), Bucharest, 2014.
Other publications by the author:
K. Yang, M.H.J. Bollen and M. Wahlberg, “A Comparison Study of Harmonic Emission Measurements in Four Windparks”, in Proceedings of The 2011 IEEE Power & Energy Society General
Meeting, Detroit, July 2011.
M.H.J. Bollen, S. Cundeva, S.K. Rönnberg, M. Wahlberg, K. Yang and L.Z. Yao, “A Wind Park
v
Emitting Characteristic and Non-Characteristic Harmonics”, in Proceedings of 14th International
Power Electronics and Motion Control Conference (EPE/PEMC), Ohrid Macedonia, September
2010.
K. Yang, M.H.J. Bollen and M. Wahlberg, “Characteristic and Non-Characteristic Harmonics from
Windparks”, in Proceedings of 21st International Conference Electricity Distribution (CIRED),
Frankfurt, June 2011.
K. Yang, M.H.J. Bollen and L.Z. Yao, “Theoretical Emission Study of Windpark Grids: Emission
Propagation between Windpark and Grid”, in Proceedings of 11th International Conference on
Electrical Power Quality and Utilization (EPQU), Lisbon, Oct. 2011.
K. Yang, M.H.J. Bollen and M. Wahlberg, “Comparison of Harmonic Emissions at Two Nodes in
A Windpark”, In Proceedings of 15th IEEE International Conference on Harmonics and Quality
of Power (ICHQP), Hongkong, 2012.
M.H.J. Bollen, S. Cundeva, N. Etherden and K. Yang, “Considering the Needs of the Customer
in the Electricity Network of the Future”, in Proceedings of The 7th Conference on Sustainable
Development of Energy, Water and Environment Systems (SDEWES), 2012.
M.H.J. Bollen, N. Etherden, K. Yang and G. W. Chang, “Continuity of Supply and Voltage Quality
in the Electricity Network of the Future”, in Proceedings of 15th IEEE International Conference
on Harmonics and Quality of Power (ICHQP), Hongkong, 2012.
K. Yang, M.H.J. Bollen and M. Wahlberg, “Measurements at Two diﬀerent Nodes of A Windpark”,
in Proceedings of 2012 IEEE Power & Energy Society General Meeting, Piscataway, NJ: IEEE,
2012.
K. Yang, M.H.J. Bollen and M. Wahlberg, “Measurements of Four-Windpark Harmonic Emissions in Northern Sweden”, in Proceedings of Tenth Nordic Conference on Electricity Distribution
System Management and Development (NORDAC), Helsinki, 2012.
U. Axelsson, A. Holm, M.H.J. Bollen and K. Yang, “Propagation of Harmonic Emission from
the Turbines through the Collection Grid to the Public Grid”, in Proceedings of International
Workshop on Large-Scale Integration of Wind Power into Power Systems, Lisbon Portugal, Nov.
2012.
K. Yang and M.H.J. Bollen, “Spread of Harmonic Emission from a Windpark”, Luleå University
of Technology, technical report, January 2012.
K. Yang, “Wind-Turbine Harmonic Emissions and Propagation through A Wind Farm”, Licentiate
thesis, Luleå University of Technology, May 2012.
S. Cundeva, M.H.J. Bollen and K. Yang, “Distortion Levels in the Grid due to Windpower Integration”, MAKO Cigre, Sep., Ohrid, Macedonia, 2013.
vi
K. Yang, S. Cundeva, M.H.J. Bollen and M. Wahlberg, “Harmonic Aspects of Wind-Power Installations”, in Proceedings of International Conference on Applied Electromagnetics ,Niš, Serbia,
Sep. 2013.
M.H.J. Bollen and K. Yang, “Harmonic aspects of wind power integration”, Journal of modern
power systems and clean energy, July 2013.
K. Yang, S. Cundeva, M.H.J. Bollen and M. Wahlberg, “Harmonic emission study of individual
wind turbines and a wind park”, in Renewable Energy & Power Quality Journal, 2013.
M.H.J. Bollen and K. Yang, “Harmonics Another Aspect of the Interaction between Wind-Power
Installations and the Grid”, in Proceeding of CIRED 2013: 22nd International Conference and
Exhibition on Electricity Distribution, Stockholm, 2013.
U. Axelsson, A. Holm, M.H.J. Bollen and K. Yang, “Propagation of Harmonic Emission from the
Turbines through the Collection Grid to the Public Grid”, in Proceedings of22nd International
Conference and Exhibition on Electricity Distribution, CIRED 2013, Stockholm, 2013.
S. Rönnberg, K. Yang, M. Bollen and A.G. Castro, “Waveform Distortion A Comparison of
Photovoltaic and Wind Power”, in Proceedings of International Conference on Harmonics and
Quality of Power (ICHQP), Cordoba Spain, 2014.
J. Meyer, M. Bollen, H. Amaris, A.M. Blanco1, A.G. Castro, J. Desmet, M. Klatt, L
. Kocewiak,
S. Rönnberg and K. Yang, “Future Work on Harmonics Some Expert Opinions Part I Wind and
Solar Power”, in Proceedings of International Conference on Harmonics and Quality of Power
(ICHQP), Bucharest, 2014.
J. Meyer, M. Bollen, H. Amaris, A.M. Blanco1, A.G. Castro, J. Desmet, M. Klatt, L
. Kocewiak,
S. Rönnberg and K. Yang, “Future Work on Harmonics Some Expert Opinions Part II Supraharmonics, Standards and Measurements”, in Proceedings of International Conference on Harmonics
and Quality of Power (ICHQP), Bucharest, 2014.
K. Yang, S. Cundeva, M.H.J. Bollen and M. Wahlberg, “Measurements of Harmonic and Interharmonic Emission from Wind Power Systems”, ISSN 1068-3712, Journal of Russian Electrical
c
Engineering, 2014, Vol.85, No.12, pp.769-776. Allerton
Press, Inc., 2014.
K. Yang and M.H.J. Bollen, “Wind Power Harmonic Emission versus Active-Power Production”,
in Proceedings of 11th Nordic Conference on Electricity Distribution System Management and
Development (NORDAC), Stockholm, Sep. 2014.
vii
viii
Contents
Abstract
i
Acknowledgments
iii
List of publications
v
Contents
ix
Abbreviations
xiii
Part I: Introduction
1
1 Introduction
1.1 Background . . . . . . . . . . . . . . . . . . . . .
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . .
1.3 Scope of the Thesis . . . . . . . . . . . . . . . . .
1.4 Approach . . . . . . . . . . . . . . . . . . . . . .
1.4.1 Measurement . . . . . . . . . . . . . . . .
1.4.2 Simple Conversion Model and Veriﬁcation
1.4.3 Simulation . . . . . . . . . . . . . . . . . .
1.5 Contributions . . . . . . . . . . . . . . . . . . . .
1.6 Structure of the Thesis . . . . . . . . . . . . . . .
1.7 Appended Papers . . . . . . . . . . . . . . . . . .
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Part II: Basic of Wind Power and Power Quality
2 Wind Power Conversion Systems
2.1 Wind Power Source . . . . . . . . . . . . . .
2.2 Technics of Wind Power Conversion . . . . .
2.2.1 Wind Power Extraction . . . . . . .
2.2.2 Turbine Type and Conversion System
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3 Basics of Power Quality
3.1 Deﬁnition . . . . . . . . . . . . . .
3.2 Power Quality Parameters . . . . .
3.3 Origin of Wind Power Quality . . .
3.3.1 Origin from the Network . .
3.3.2 Origin from the Turbine . .
3.3.3 Voltage Fluctuation . . . . .
3.3.4 Harmonics . . . . . . . . . .
3.3.5 Basic of Harmonic Analysis
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Part III: Wind Power Harmonics and Propagations
15
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18
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21
4 Overview of Related Work
4.1 Harmonic Measurements . . . . . . . . . . . . . .
4.1.1 Harmonic Levels of Wind Power . . . . . .
4.1.2 Harmonics as a Function of Output-Power
4.1.3 Wind Power Interharmonics . . . . . . . .
4.1.4 Wind Power Harmonic Variations . . . . .
4.2 Harmonic Simulations . . . . . . . . . . . . . . .
4.2.1 Harmonic Source Modeling . . . . . . . . .
4.2.2 Component Modeling . . . . . . . . . . . .
4.2.3 Harmonic Simulation . . . . . . . . . . . .
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5 Time-Varying Harmonics
5.1 Harmonic Measurements . . . . . . . . . . . . . .
5.1.1 Measurement Object . . . . . . . . . . . .
5.2 Wind Power Harmonic Representation . . . . . .
5.2.1 Average Spectrum . . . . . . . . . . . . .
5.2.2 Spectrum as a Function of Time . . . . . .
5.2.3 Statistical Representations . . . . . . . . .
5.2.4 Individual Turbine and Wind Power Plant
5.3 Emission versus Active-Power . . . . . . . . . . .
5.3.1 THD and TID . . . . . . . . . . . . . . . .
5.3.2 Individual Subgroups . . . . . . . . . . . .
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6 Origin of Interharmonics from Wind Turbines
6.1 Wind Power Frequency Conversion . . . . . . . . . . .
6.1.1 Frequency Conversion . . . . . . . . . . . . . .
6.1.2 Emission versus Active-Power . . . . . . . . . .
6.1.3 Ratio between Related Interharmonic Currents .
6.2 Measurement . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Correlation of Harmonic Distortion . . . . . . .
6.2.2 Emission versus Active-Power . . . . . . . . . .
6.2.3 Voltage vs. Current . . . . . . . . . . . . . . . .
6.2.4 Current vs. Current . . . . . . . . . . . . . . .
6.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . .
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41
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51
x
6.3.1
Discussions on Type 3 Turbine . . . . . . . . . . . . . . . . . . . . . . . . .
7 Harmonic Propagation and Aggregation in WPP
7.1 Complex Current . . . . . . . . . . . . . . . . . . .
7.1.1 Transformation of Complex Current . . . . .
7.1.2 Measurements of Complex Harmonics . . . .
7.1.3 Statistics of Harmonic Magnitude and Phase
7.1.4 Test of Uniformity . . . . . . . . . . . . . .
7.2 Harmonic Propagation and Transfer Function . . .
7.2.1 Harmonic Contributions . . . . . . . . . . .
7.2.2 Quantifying Harmonic Propagation . . . . .
7.2.3 Overall Transfers . . . . . . . . . . . . . . .
7.3 Harmonic Aggregation . . . . . . . . . . . . . . . .
7.3.1 Aggregation of Harmonic Propagations . . .
7.3.2 Case Study of Turbine Aggregation . . . . .
7.3.3 Case Study of Total Aggregation . . . . . .
7.4 Discussion . . . . . . . . . . . . . . . . . . . . . . .
7.4.1 Primary and Secondary Emission . . . . . .
7.4.2 Aggregation in Measurements . . . . . . . .
7.4.3 Uncertainty of Damping . . . . . . . . . . .
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Part IV: Discussions and Conclusions
51
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71
8 Discussion
8.1 Measurement Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.1 Error Origins . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.2 Distortion Level versus Power and Relations between Frequencies
8.1.3 Spectrum Leakage . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 Impacts of Components in Collection Grid . . . . . . . . . . . . . . . . .
8.3 Secondary Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.4 Generalization of the Results . . . . . . . . . . . . . . . . . . . . . . . . .
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9 Conclusion and Future Work
9.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.1.1 Harmonic Emission from Individual Wind Turbines . .
9.1.2 Primary and Secondary Emission . . . . . . . . . . . .
9.1.3 Harmonic Propagation . . . . . . . . . . . . . . . . . .
9.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.1 Frequency Resolution of Measurement . . . . . . . . .
9.2.2 High Voltage Measurement . . . . . . . . . . . . . . . .
9.2.3 Distinguish between Primary and Secondary Emission .
9.2.4 Type 3 Wind Turbine . . . . . . . . . . . . . . . . . . .
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83
xi
Part V: Publications
91
Paper A: Measurements of Harmonic Emission versus Active Power from Wind
Turbines
A1
Paper B: Aggregation and Ampliﬁcation of Wind-Turbine Harmonic Emission in
A Wind Park
B1
Paper C: Decompositions of Harmonic Propagation in A Wind Power Plant
C1
Paper D: Interharmonic Currents from A Type-IV Wind Energy Conversion System
D1
Paper E: A Systematic Approach for Studying the Propagation of Harmonics in
Wind Power Plants
E1
Paper F: A Statistic Study of Harmonics and Interharmonics at A Modern WindTurbine
F1
Paper G: Wind Power Harmonic Aggregation of Multiple Turbines in Power Bins G1
xii
Abbreviations and acronyms
CT
DFAG
DSO
FFT
H
IG
IGBT
IH
GSC
PDF
PLL
PoC
PWM
RSC
STATCOM
THD
TID
TSO
VSC
VT
WPCS
WPP
WT
WTG
Current Transformer
Doubly Fed Asynchronous Generator
Distribution System Operator
Fast Fourier Transform
Harmonic
Induction Generator
Insulated Gate Bipolar Transistor
Interharmonic
Grid-Side Converter
Probability Density Function
Phase-Locked-Loop
Point of Connection
Pulse-Width Modulation
Rotor-Side Converter
Static Synchronous Compensator
Total Harmonic Distortion
Total interharmonic Distortion
Transmission System Operator
Voltage Source Converter
Voltage Transformer
Wind Power Conversion System
Wind Power Plant
Wind Turbine
Wind Turbine Generator
xiii
Part I:
Introduction
1
Chapter
1
Introduction
1.1
Background
The demand of energy is steadily growing worldwide [1]. Simultaneously there is a broad understanding worldwide for the need to substantially reduce the greenhouse gas emission. Among
various approaches, the use of sustainable energy provides an eﬀective solution that oﬀers a huge
potential towards the future energy vision. The ambitious target to make use of sustainable energy
has been renewed by several countries. Among types of sustainable energy, wind power oﬀers a
globally huge potential of renewable energy.
In addition to the role of reduction of greenhouse gas emission, wind power contributes with free
primary energy into the electric power systems and creates job opportunities in many countries.
The installed capacity of wind power tends to increase annually despite ﬂuctuations due to energy
policies, among others, in diﬀerent countries; and the cumulative installed capacity is continually
and steadily increasing worldwide [2].
Onshore wind power is developing rapidly due to a relatively low cost and easier installing
compared to oﬀshore wind power. The relatively slow development of oﬀshore wind power is due
to the substantial cost compared to a conventional power and the diﬃculty of installing oﬀshore
wind power. However there are a number of advantages compared to onshore wind power, e.g.
a relatively stable and larger source of wind. The amount of investment in oﬀshore wind power
tends to increase in many countries. Additionally both costs of onshore and oﬀshore wind power
continue to drop dramatically.
1.2
Motivation
The increasing demand of renewable energy, such as wind power and solar power, into power
systems is a technical challenge. Unlike conventional power (hydro power, fossil-fuel based power),
the source of wind power, in the form of kinetic energy of wind movements, is varying with time.
The variation of wind speed (and thus wind power production) takes place over a large range of
timescales from seconds to annual [3–5]. Wind power production is not only varying, it is also
diﬃcult to predict. Consequently it provides a challenge for the planning and operation of the
power system.
Accompanied with the diﬃculty of wind-speed prediction, the integration of the intermittent
wind power into power systems is another challenge. To satisfy integration requirements (e.g. a
3
4
INTRODUCTION
sinusoidal current waveform at the power system frequency), a varying wind speed requires the
use of power electronics which convert as much energy from the wind as possible into electric
power at the right frequency and magnitude for the grid [6–13]. Next to power electronics other
technologies are needed as well.
The conversion of energy from the wind into electric power makes use of wind power source,
at the same time it brings new challenges to power systems, for example:
• the planning of power system operation;
• the stability of power systems with injecting a large amount of intermittent wind power;
• possible environmental problems (e.g. land use, wildlife and habitat, public health and
community);
• and issues related to the way in which the wind turbines impact the grid diﬀerently than
conventional production units.
Among the latter challenge, the power quality is an important one. It concerns the gridintegration requirements (e.g. voltage and frequency within their permissible range and an acceptable level of distortion), and impacts of wind power installations on power systems as well as
interactions with other equipment [14–16].
An ideal supply of electric power has a sinusoidal voltage and current waveform at the power
system frequency (50 or 60 Hz, the former is used throughout this thesis). In practice both voltage
and current deviate from the ideal waveform. One of those deviations is referred to as harmonic
distortion [17–20]: harmonic distortion is the phenomenon that a waveform deviates from the
ideal waveform and can be decomposed into sinusoidal waveforms at other frequencies rather
than the power system frequency. Transmission system operators (TSO) and distribution system
operators (DSO) set limits regarding the power quality in their power systems [21–25]. Also wind
turbine manufactures attempt to lower the distortion originating from turbines, e.g. by means of
ﬁlters [6, 7, 13, 26].
In a power system, the knowledge of waveform distortion that originates either from a wind
turbine, from the whole wind power plant (WPP, synonyms: wind park, wind farm) or from the
external grid is of help to identify the contributions of waveform distortion from diﬀerent locations.
To a WPP owner it is helpful for the grid integration under the regulations; to a TSO or a DSO
it is of interest to limit the distortion at the point of connection (PoC). As well in the technical
viewpoint it helps to eliminate the distortion in a power system.
1.3
Scope of the Thesis
This thesis covers methods and models to perform harmonic studies of wind power installations
in a systematic way. Three levels of harmonic study are included: the harmonic distortion at
individual wind turbines; the harmonic distortion at the PoC of a WPP; and the systematic
estimation of the harmonic distortion in a WPP as a part of the power system.
Waveform distortion, throughout the thesis, is deﬁned as the presence of frequency components
other than at the power system frequency. This term used in the thesis concerns components not
only at integer multiples of the power system frequency (harmonics), but also those at non-integer
multiples (interharmonics).
1.4. APPROACH
5
The harmonic study based on ﬁeld measurements has been performed at the MV-side of turbine
transformers for individual turbines and at the collection grid side of the substation transformer
for a WPP. Field measurements at individual turbine terminals (LV-side of turbine transformers)
have not been performed as part of this thesis. Measurements have been performed for frequencies
up to 6.4 kHz, but most of the studies covers only the frequency range up to 2 kHz. Most of
the measurements gave a 5 Hz frequency resolution and statistical methods have been applied
for the analysis of the data. These measurements at individual turbines were performed over a
period between one and four weeks, so as to include all operational states from idle to full-power
production.
The harmonic emission has been studied for a few variable-speed wind turbines, of Type 3 and
Type 4 [27]. The other types of wind turbine are not included in this study.
Simulations with a detailed harmonic model of a wind turbine, e.g. including a wind turbine
control algorithm, are not in the scope of this thesis.
1.4
Approach
Three types of studies are used and developed as part of this thesis: novel analysis methods on
extended sets of voltage and current measurements; simpliﬁed simulation models applied to new
phenomena; simulations for wind power installations, with measurements as input. These three
types are described in more detail in the forthcoming sections.
1.4.1
Measurement
The harmonic characteristics of wind power installations have been studied by analysing measurements in actual wind-power installations. The measurements were obtained using a standard
power quality monitor that complies with the standards IEC 61000-4-7 [28] and IEC 61000-430 [29]. Two types of data have been obtained by these monitors: harmonic and interharmonic
subgroups over 10-minute windows, and 10-cycle voltage and current waveforms every 10 minutes.
The latter provides a possibility for various ways of analysis.
The ﬁeld measurements have been performed over a period up to a few weeks, which covers
all operational states (diﬀerent output power) of individual wind turbines. Also the simultaneous
measurements at the PoC of certain WPPs cover all operational states. This amount of data
enables studies on the time-varying and frequency-varying harmonics of individual turbines. The
relation between the harmonic distortion and the operational states has been studied. The data
has been further used as input data in harmonic simulations.
1.4.2
Simple Conversion Model and Veriﬁcation
A model of the power conversion system with a Type IV turbine has been used to explain the observed interharmonics. The model reveals the origin of interharmonics, relations between diﬀerent
frequency components and the relations with the active-power production. The models have been
veriﬁed using a novel way of analysing data from long-term ﬁeld measurements.
6
INTRODUCTION
1.4.3
Simulation
Harmonic propagation (synonyms: harmonic ﬂow, harmonic transfer, harmonic penetration)
within wind power installations has been studied as a part of the electric power system. The
harmonic propagation has been studied. The impact of components anywhere in the system has
been considered in harmonic propagation in a systematic way.
As part of the study of harmonic propagation, harmonic aggregation has been studied. The
aggregation has been studied using the statistical properties of harmonic emission from individual
wind turbines as a base. Due to the time-varying harmonics, average aggregation is presented
instead of the aggregation at each moment.
The harmonic propagation has been studied by using a set of transfer functions in frequency
domain (voltage transfer, current transfer, transfer impedance and transfer admittance) and applying these to a harmonic model of the collection grid. The simulation has been performed in
combination with measurements obtained over a period up to a few weeks.
This approach, using transfer functions, enables a study and quantiﬁcation of the properties of
the harmonic propagation and the impact of the collection grid on the emission from the WPP as
a whole, without knowledge of the emission by individual harmonic sources. Two models for the
collection grid have been used to illustrate the systematic approach: one with the existing software
DIgSILENT PowerFactory, the other with a simpliﬁed circuit-theory model and the calculations
being performed in Matlab. The resulting trends of harmonic propagation, are the same for the
two models, despite the strong diﬀerences in model detail.
A method for the contributions of harmonic propagation has been developed in the thesis.
These decompositions are used as base for a systematic harmonic study in a network, with multiple
harmonic sources.
Again because of the time-varying harmonics, statistical methods should be used. A MonteCarlo Simulation has been applied to obtain average values of the harmonic emission. Except for
estimating the harmonic distortion at an individual node, the proposed systematic approach can
also be used to evaluate the contribution to the harmonic distortion by certain individual sources
or groups of harmonic sources.
1.5
Contributions
This thesis presents the development of systematic methods for harmonic studies of wind power
installations. This includes: the harmonic emission at individual turbines, the impact of the
collection grid, the emission from the WPP. The main contributions of the thesis are summarized
in the following points:
• Characterization of wind power emission. [Paper A and Paper F]: The characterization of
harmonic emission at individual wind turbines has been performed from ﬁeld measurements
obtained over a period of one to four weeks. The emission of individual wind turbines
contains a low level of (integer) harmonics in relation with the fundamental. However,
even harmonics and interharmonics are signiﬁcant compared to the characteristic harmonics.
Detailed emission spectra vary between turbines, but overall patterns are similar. Variations
of harmonic emission with active-power production have been studied. The trends for the
latter are divided into three groups: characteristic harmonics (plus the 3rd harmonic) present
random variation in magnitude versus output power and a large spread even for the same
1.5. CONTRIBUTIONS
7
output power; non-characteristic harmonics present various trends; certain interharmonics,
especially the ones with the highest emission, present a strong increase with increasing
output power.
• Interharmonic conversion by power electronics. [Paper D]: It is shown that the time-varying
frequency of the generator-side waveform results in a number of frequency components on
the grid-side of the converter with time-varing frequency and magnitude. Relations are
obtained between the generator-side and grid-side frequencies. It is also shown that these
frequency components are strongly correlated to the active-power production.
• Analysis of time-varying interharmonics [Paper D]: a method has been developed to analyse time varying interharmonics coming from a frequency converter. By using correlations
between magnitudes of the components at diﬀerent frequencies, detailed information about
the interharmonics can be obtained despite the limited frequency resolution used.
• Distributions of complex harmonics and interharmonics. [Paper B and Paper G]: The complex current harmonics present three types of distributions in the complex plane: characteristic harmonics (plus the 3rd harmonic) present a non-round scatter plots that is oﬀset from
the origin; non-characteristic harmonics present a round scatter plot that is oﬀset from the
origin; and interharmonics present a round scatter plot centered on the origin.
• Aggregation of harmonics and interharmonics. [Paper B and Paper G]: The harmonic emission at the PoC of a WPP presents diﬀerent levels of aggregation: cancellation is small at
harmonic frequencies, especially for low-order harmonics (lower than H 15); while cancellation at interharmonic frequencies is high, and following the square-root rule. The aggregation
is strongly related to the distribution of the complex harmonics.
• Harmonic transfer functions. [Paper B and Paper C]: The harmonic transfer functions, voltage and current transfer functions, transfer impedance and transfer admittance, are used
to study the harmonic propagation through the collection grid of a WPP. Depending on
the type of a harmonic source and the type of the studied emission (voltage or current), a
suitable transfer function is chosen. Ampliﬁcation and attenuation are quantiﬁed by means
of the transfer functions.
• Harmonic classiﬁcations. [Paper E]: Contributions from various sources to the harmonic
distortion at a speciﬁc location have been classiﬁed into two main groups: primary emission
and secondary emission. Depending on harmonic sources and diﬀerent types of propagation,
the harmonic contributions have been further classiﬁed into seven types of propagation
especially for a WPP.
• Systematic approach. [Paper E]: The harmonic distortion at a certain node is the result of
contributions from all harmonic sources connected to the grid. The harmonic distortion
at any node in a WPP can be estimated using the proposed systematic approach: adding
the harmonic contributions at a node that have propagated from all harmonic sources, with
suitable transfer functions. The harmonic emission from certain individual source or groups
of sources can be estimated with the help of the proposed systematic approach.
8
1.6
INTRODUCTION
Structure of the Thesis
Chapter 1 introduces the background, motivation, scope, approach and contribution of the thesis.
Chapter 2 presents the basics of wind power and energy conversion system. Chapter 3 presents the
basic of power quality in relation to wind power. Chapter 4 gives an overview of related research in
the ﬁeld. Chapter 5 presents the harmonic distortion with ﬁeld measurements. Chapter 6 presents
the origin of interharmonics. Chapter 7 the harmonic propagation and aggregation. The discussion
is presented in Chapter 8 and the conclusion in Chapter 9.
Part V includes the appended papers in the thesis, as listed in Section 1.7.
1.7
Appended Papers
Paper A
K. Yang, M.H.J. Bollen, E.A. Larsson and M. Wahlberg, “Measurements of Harmonic Emission
versus Active Power from Wind Turbines”, Electric Power Systems Research, vol.108, pp. 304
314, 2014. doi:http://dx.doi.org/10.1016/j.epsr.2013.11.025.
Paper B
K. Yang, M.H.J. Bollen and E.A. Larsson, “Aggregation and Ampliﬁcation of Wind-Turbine
Harmonic Emission in A Wind Park”, IEEE Transactions on Power Delivery (in press), 2014.
doi:10.1109/TPWRD.2014.2326692.
Paper C
K. Yang, M.H.J. Bollen, H. Amaris and C. Alvarez, “Decompositions of Harmonic Propagation
in A Wind Power Plant”, revision submitted to Electric Power Systems Research, 2015.
Paper D
K. Yang and M.H.J. Bollen, “Interharmonic Currents from A Type-IV Wind Energy Conversion
System”, submitted to Electric Power Systems Research, 2015.
Paper E
K. Yang and M.H.J. Bollen, “A Systematic Approach for Studying the Propagation of Harmonics
in Wind Power Plants”, submitted to IEEE Transactions on Power Delivery, 2015.
Paper F
K. Yang, M.H.J. Bollen, E. A. Larsson and M. Wahlberg, “A Statistic Study of Harmonics and
Interharmonics at A Modern Wind-Turbine”, in Proceedings of International Conference on Harmonics and Quality of Power (ICHQP), Bucharest, 2014.
Paper G
K. Yang, M.H.J. Bollen and E.A. Larsson, “Wind Power Harmonic Aggregation of Multiple Turbines in Power Bins”, in Proceedings of International Conference on Harmonics and Quality of
Power (ICHQP), Bucharest, 2014.
Part II:
Basic of Wind Power and Power Quality
9
Chapter
2
Wind Power Conversion Systems
2.1
Wind Power Source
The wind power source varies with time due to variations of the wind speed. Those variation take
place in a timescale ranging from seconds to annual. An analysis of the power spectrum shows a
number of peaks: “turbulence peak” up to minutes, “diurnal peak” about 12 hours and “synoptic
peak” up to 10 days (originally presented in [30] and cited in [3, 31]).
A short timescale variation in wind speed is diﬃcult to predict. Whereas the wind speed
presents annual and seasonal variations [3,26,31]. The movement of wind is mainly due to a global
circulation pattern driven by the sun and by the earth’s rotation: Coriolis eﬀect, the geographic
and temperature diﬀerences between day and night side of the earth as well as between the poles
and the tropical areas.
The wind speed increases logarithmically with height, as a result higher towers give more wind
power. The turbulence of wind close to the ground is due to the impacts of forests, buildings,
mountains and other frictions. At a higher altitude the wind speed not only increases but also
shows less turbulence.
In an early stage of planning a WPP, the choice of a location (siting) concerns the evaluation
of the annual condition of wind source. An estimation of the wind source is needed, e.g. by means
of a wind rose approach or by means of a histogram approach. The data of wind source is used to
estimate the amount of wind energy that can be converted into electric energy. The estimation
method is similar for either an onshore siting or an oﬀshore siting, as one of the important issues
of WPP planning. An oﬀshore location normally has higher wind energy potential and a more
stable wind source than an onshore location.
The installing of an onshore WPP meets diﬀerent diﬃculties compared with that of an oﬀshore
WPP. Sites suitable for oﬀshore WPP are normally owned by the state; while onshore lands are
often owned by multiple owners. There might be diﬃculties to install a WPP when considering
the views of the diﬀerent stakeholders. Next to issues such as environmental problems, the power
transmission to the public grid, is also important in the planning.
2.2
Technics of Wind Power Conversion
Wind energy is converted to electric power by means of wind turbines, which are generally categorized/or divided in two groups: the horizontal axis wind turbine and the vertical axis wind
11
12
WIND POWER CONVERSION SYSTEMS
turbine. A horizontal axis turbine has the blades rotating on an axis parallel to the ground;
while a vertical axis turbine has the blades rotating on an axis perpendicular to the ground. The
horizontal axis turbine is most common, and is the type of turbine studied throughout the thesis.
2.2.1
Wind Power Extraction
The mechanical power in the form of movement of air drives the rotation of the wind turbine
blades. The study of its mechanical property is called blade aerodynamics [31]. The principle of
an aerodynamic designed shape of blade is that, the air ﬂow makes a force diﬀerence on two sides
of the blade. According to the aerodynamics, the pressure of one side is higher than the other
side due to the diﬀerence of the ﬂowing speeds. The pressure diﬀerence results in a force, which
is equivalently represented by a lift force and a drag force. The lift force is much larger than the
drag force, and lifts the blades (the drive of the blade rotation). With the momentum theory, the
torque of rotating blades is obtained by the drive of the wind ﬂowing. In principle a maximum
of 16/27 kinetic energy from the wind can be extracted according to the theory of the Betz limit.
Modern variable-speed wind turbines are designed to approach as close as possible this maximum
power for diﬀerent rotational speed at diﬀerent wind speed. In order to achieve this, the rotational
speed has to be adjusted to the wind speed.
The mechanical torque on the turbine axis drives the rotation of the turbine generator. The
power curve of a wind turbine indicates how much output electric power will be produced at
diﬀerent wind speeds. A too low wind speed will not generate enough power to move the blades
and overcome the losses; while a too high wind speed may damage turbine components. Technically
a power curve, which is identiﬁed by a wind turbine, is set with a cut-in and a cut-out speed for
the operation of a wind turbine.
For instance, the operational wind speed is normally from 4 to 25 m/s, which indicates that
the cut-in speed is at 4 m/s and cut-out speed at 25 m/s. In the power curve, there is another
important wind speed and that is the point where the wind turbine reaches its rated power. For
instance a wind turbine reaches the rated power at about 12 m/s. Until the wind turbine operates
at the rated power, the turbine output is constant. The pitch system reacts when a rated power is
reached and when the wind speed is higher than 12 m/s; the angle of the blades (which impacts the
lift force) is controlled to maintain the turbine operating at the rated power. The maximum power
from the wind is not extracted in this case. Too low or too high wind speed, beyond the cut-in
and cut-out speeds, will make a wind turbine to stop generating. Also other power regulations
are applied in the operation of wind turbines.
2.2.2
Turbine Type and Conversion System
Due to the variations of the wind speed, modern wind turbines are equipped with power electronics
to extract as much power as possible over a range of wind speed. There are ﬁve types of wind
turbines according to the IEEE classiﬁcation [27]. Type 1 is ﬁxed speed and has a squirrel-cage
induction generator (SCIG) connected directly to the step-up transformer. Type 2 is a turbine
with limited variable speed, using a wound rotor induction generator (including a variable resistor
in the rotor circuit) connected directly to the step-up transformer. Type 5 is a turbine with
full variable speed with a mechanical torque converter between the rotors low-speed shaft and
the generators high-speed shaft controlling the synchronous-generator speed to be equal to the
electrical synchronous speed. The other two types (Type 3 and Type 4) are modern turbines that
2.2. TECHNICS OF WIND POWER CONVERSION
13
are commonly installed and used, as shown in Figure 2.1. They are considered throughout this
thesis.
Figure 2.1: Wind turbine types: Type 3 and Type 4.
The two types are also called variable-speed generators, which the conﬁgurations are presented:
• Type 3: also called doubly-feed asynchronous generator (DFAG); a gear box converts the
rotation speed of blades to an suitable speed for the wound rotor induction generator; the
generator stator is connected to the grid through the turbine transformer; a partial-scale
frequency converter through the turbine transformer is connected to the generator rotor and
provides up to 30% power of the stator in both directions; this type allows for a narrow
range (both above and below synchronous speed by up to 50%) variable speed control;
• Type 4: a broad range variable speed generator, or a turbine with full-power converter; a gear
box is optional for the type; without a gear box, the direct drive synchronous generator is
applied; the back to back converter handles the full power generated to the grid; the turbine
generator works over a larger range of rotational speed depending on the wind speed.
Both Type 3 and Type 4 wind turbines are equipped with a power-electronic converter and
these are prone to produce harmonic distortion. The harmonic distortion due to power electronics,
among other issues for wind power installations, is of interest in this thesis.
14
WIND POWER CONVERSION SYSTEMS
Chapter
3
Basics of Power Quality
3.1
Deﬁnition
There are various deﬁnitions of power quality from diﬀerent organizations and books: e.g. the
deﬁnition in the Institute of Electrical and Electronics Engineers (IEEE) dictionary, the deﬁnition
in the International Electrotechnical Commission (IEC) standard IEC 61000-4-30 [29], and the
deﬁnition in the power quality book by Dugan et al. [32]. The incomplete formulation from the
former two have been pointed out in [33], the deﬁnition of power quality “is related not to the
performance of equipment but to the possibility of measuring and quantifying the performance of
the power system”. Reference [32] deﬁnes the “power quality problem” as “any power problem
manifested in voltage, current, or frequency deviations that results in failure or misoperation of
customer equipment”. However in some cases, a power quality issue does not really cause a failure,
or does not reveal itself immediately. For instance, harmonic distortion may accelerate the aging
of electrical components; without causing an immediately failure or misoperation.
This thesis broadly follows the deﬁnition in the books [33,34]: “power quality is the combination
of voltage quality and current quality”. The voltage and current quality concerns deviations from
an ideal (sinusoidal) waveform, with a constant amplitude and a constant frequency equal to the
nominal values. The ideal current is further in phase with the voltage.
Any deviation of voltage or current from the ideal is a power quality disturbance. It can be a
voltage disturbance or a current disturbance. A voltage disturbance originates from the grid and
impacts customers or equipment, while a current disturbance originates from a customer or device
and aﬀects the network and/or other customers or devices. Another term “interference” is strictly
deﬁned as “the actual degradation of a device, equipment, or system caused by an electromagnetic
disturbance” [33]. The disturbance is the cause and the interference is the eﬀect. This thesis will
focus on disturbances, not on interference, within a WPP.
3.2
Power Quality Parameters
There are several parameters to quantify the power quality. Diﬀerent power-quality phenomena
can be distinguished:
• Interruption: the RMS voltage at the customer connection is close to zero (a typical threshold
value is 10% of the nominal voltage) during an interruption period; causes are lighting and
15
16
BASICS OF POWER QUALITY
storms, transformer outage, line outage, generator outage, etc.;
• voltage dips (sags) and voltage swells: a voltage dip (sag) is an RMS voltage below (typically)
90% of the nominal voltage (within a certain duration); a voltage swell is an RMS voltage
above (typically) 110% of the nominal voltage (within a certain duration); causes for a
voltage dip (sag) are lighting, and energizing of large loads; causes for a voltage swell are a
drop of large loads, unsymmetrical earth faults;
• harmonic distortion: a waveform is non-sinusoidal but periodic with a period of one cycle;
mathematically a distorted waveform is composed of waveforms of integer multiples of the
periodicity of the waveform; causes are due to a generator, a rectiﬁer, a converter and
inverters, etc.;
• commutation notches: a voltage change, with a duration much shorter than the AC period,
which appears on an AC voltage due to the commutation process in a converter; causes are
rectiﬁer loads, converters and inverters;
• frequency deviations: the voltage frequency deviates from the nominal frequency; causes are
load changes to isolated generators, a weak control of static converters, an outage of a large
generator;
• transients: a disturbance that lasts for a short duration such as a spike or surge in a power
line that intermittently fails; causes are lightning, power line feeder switching, capacitor
bank switching, etc.;
• voltage ﬂuctuation (ﬂicker eﬀect): a visual sensation produced by periodic ﬂuctuations in
light at rates ranging from a few cycles per second to a few tens of cycles per second; causes
are cycling of large loads, arc furnaces, blade passing, wind ﬂuctuations, etc.;
• voltage unbalance: phenomenon due to the diﬀerences between voltage deviations on the
various phases, at a point of a polyphase system, resulting from diﬀerences between the
phase currents or geometrical asymmetry in the line (IEC); causes are unsymmetrical loads,
unsymmetrical faults and unsymmetrical lines.
The main inﬂuence of a wind turbine on the voltage and current quality (as well as power
with the combination of the two types of quality) is voltage ﬂuctuations and harmonics from wind
turbines with power electronics [35].
3.3
Origin of Wind Power Quality
Power quality is of particular importance to wind turbines and wind power plants, especially
when an individual unit may be up to few MW feeding into a weak grid and with other customers
nearby. Issues of harmonic distortion for a variable-speed turbine that uses a power electronic
converter need careful consideration.
The origin of power quality issues for wind power generation is presented in [3, 31, 32]. As
an important participant of the network, wind power generation is one of the sources that may
cause power quality issue in the network. The power quality issues can either originate from the
network and impact the turbine or originate from the turbine and impact the network.
3.3. ORIGIN OF WIND POWER QUALITY
3.3.1
17
Origin from the Network
This section covers power quality issues that originate in the transmission or distribution networks
and impact or may impact wind power plants. Any equipment connected to an electricity network
is impacted by the voltage at its terminals. The transmission and distribution network, and
equipment connected to it, impact the voltage that wind turbines experience at their terminals:
• Voltage sags cause a ﬁxed-speed wind turbine to overspeed; this is not the case for the kind
of variable-speed wind turbines studied in this thesis;
• voltage swells are less common at the terminals of a wind turbine, and are therefore not a
major problem for wind turbines;
• harmonic voltage distortion leads to an increase of losses in the turbine generator and may
disturb the control systems and protection associated with the turbine; harmonic voltage
distortion may also adversely impact the harmonic current performance of power electronic
converters (as used in variable-speed wind turbines);
• unbalance of the network voltage increases losses and introduces torque ripples in a rotating
machine; it also causes power converters to inject unexpected harmonic currents to the
network unless special converter designs are used.
Since the studied object is wind power generation, the eﬀects from the network on the turbines
are considered to be external. Thus the issues originated from the network are referred to as
secondary power quality issues.
3.3.2
Origin from the Turbine
This section covers power quality issues that originate from wind turbines that may impact the
transmission or distribution networks. The current from a wind turbine impacts the voltage in
the transmission and distribution network to which it is connected:
• A variable-speed wind turbine using a power electronic converter injects harmonic currents
into the network;
• a possible unbalanced operation leads to negative-phase-sequence currents and in turn causes
a network voltage unbalance;
• the producing and absorbing of reactive power from a variable-speed wind turbine may cause
variations in the steady-state voltage;
• the voltage ﬂuctuations due to blades passing in from of the tower and other power ﬂuctuations may cause light ﬂuctuations;
• a ﬁxed-speed wind turbine may increase the network fault level; this can result in an improvement of the voltage quality;
• temporary over voltages may occur due to injection of power by the wind turbine in the MV
or LV grid.
18
BASICS OF POWER QUALITY
Similar to the secondary power quality issue, the issues originated from turbines (which are
internal) are called primary power quality issues.
Modern wind turbines are variable-speed wind turbines, they are currently the majority in the
market and they are the trend for the future wind power. The thesis therefore focuses on variable
speed wind turbines.
3.3.3
Voltage Fluctuation
Voltage ﬂuctuation (ﬂicker eﬀect) refers to fast voltage magnitude variations. Those fast voltage
magnitude variations, also know as “ﬂicker” cause variations in brightness for lamps and the
subsequent annoyance to customers [36]. The resulting light ﬂicker is more severe for incandescent
lamps than for most other types of lamps. There are however indications that also some modern
types of lamps, LED and CFL (compact ﬂuorescent lamp) are prone to ﬂicker in a similar way as
incandescent lamps.
Voltage ﬂuctuations produced by wind turbines are mainly due to variations in wind speed
resulting in power variations: wind gradients (wind shear), the tower shadow eﬀect [37, 38].
Fluctuations increase at higher wind speeds due to higher turbulence for a ﬁxed-speed wind
turbine; and it increases with the wind speed up to the rated wind speed for a variable-speed
wind turbine. The variable-speed system smoothes the power ﬂuctuation and thus the voltage
ﬂuctuation. Variable-speed wind turbines produce signiﬁcantly lower levels of ﬂuctuation than
ﬁxed-speed wind turbines.
The mitigation of ﬂuctuation needs auxiliary devices such as reactive power compensation or
energy storage equipment. The evaluation and measurement for wind turbine voltage ﬂuctuation
are speciﬁed in the standard IEC 61400-21 [39].
3.3.4
Harmonics
Unlike ﬁxed-speed wind turbines, variable-speed wind turbines contain power-electronic converters
that inject harmonic currents into the network; while ﬁxed-speed wind turbines, with power-factor
correction capacitors, create resonant circuits [31].
Modern variable-speed wind turbines use grid side voltage source converters. The commonly
equipped insulated gate bipolar transistors (IGBTs) switch at a few kHz to synthesize a sine wave
and reduce the level of low order harmonics. The harmonic currents originating at the switching
frequency are normally attenuated by a ﬁlter located between the turbine and the grid.
3.3.5
Basic of Harmonic Analysis
An ideal waveform is a sinusoidal waveform at the fundamental frequency, which is expressed as
(with current takes as an example) i(t) = I0 cos(2πf0 t + φ0 ), where t is the time, I0 the magnitude
of the waveform, f0 the fundamental frequency and φ0 the phase angle.
A distorted waveform can mathematically be written as the combination of the fundamental
sinusoidal waveform with sinusoidal waveforms at other frequencies:
i(t) =
∞
If cos(2πf t + φf )
f =0
where If is the magnitude of waveform at frequency f , φf the phase angle at frequency f .
(3.1)
3.3. ORIGIN OF WIND POWER QUALITY
19
Figure 3.1: Left ﬁgure: distorted three-phase current waveforms (in colors) at a wind turbine
compared to the ideal (in black) (50 Hz fundamental frequency); right ﬁgure: the
spectrum of the distorted waveform in phase A. Phase A in red, phase B in green and
phase C in blue (left ﬁgure).
The frequency f = 0 gives the DC current component. The current waveform is transformed
by Discrete Fourier Transform (DFT) into the frequency domain, after which the information
(magnitudes and phase angles) at each frequency becomes visible.
A measurement of waveform at a wind turbine in the power system and the processed spectrum
by FFT are shown in Figure 3.1.
The black waveforms in the left ﬁgure are the ideal waveforms at 50 Hz (fundamental frequency
of the power system). The colored lines are the distorted waveforms, being a combination of many
frequencies. The right ﬁgure is the spectrum of the waveform at phase A (the spectra of the other
two phases are not shown here). Only the magnitude spectrum is shown here; the phase angles
for the diﬀerent frequency components are not shown.
A distorted waveform is the combination of all harmonic components which are at integer
multiples of the fundamental frequency (e.g. 100 Hz or harmonic 2, 150 Hz or harmonic 3, 200 Hz or
harmonic 4), and all other components at non-integer frequencies which are called interharmonics.
When the waveform is distorted but periodic with the power-system frequency, no interharmonics
are present.
Among the harmonics, the harmonic orders h = 6n ± 1 with n a positive integer are the socalled characteristic harmonics of a six-pulse rectiﬁer, typically just referred to as “characteristic
harmonics”. Other harmonics, as well as interharmonics, are called non-characteristic harmonics.
20
BASICS OF POWER QUALITY
Part III:
Wind Power Harmonics and
Propagations
21
Chapter
4
Overview of Related Work
4.1
4.1.1
Harmonic Measurements
Harmonic Levels of Wind Power
The harmonic emission of wind power installations has been studied in a number of publications.
Papers [40–42] have studied harmonic currents at six variable-speed wind turbines, according to the
measurement instructions of the standards IEC 61000-4-7 and IEC 61400-21. At low-frequencies,
below 2 kHz, the characteristic harmonics are dominating for all the turbines. The emission of
two out of the six wind turbines has been studied up to 9 kHz; comparable emission levels as for
the low frequencies is shown to be present up to 5 kHz.
Paper [43] presents harmonic measurements at the point of connection of a WPP with 30 small
wind turbines (600 kW squirrel-cage, ﬁx-speed induction generators; Type 2). Two current spectra,
one at 18% of full power production and the other at 96% of full-power production, are shown.
The dominating harmonics are at the low-order characteristic harmonics 5-th and 7-th; the levels
(absolute value) of these two harmonics is the same for the two levels of power production. The
higher order harmonics from 21st to 41st are at levels comparable to the dominating harmonics.
The levels for this these higher order harmonics are higher at 96% production than that at 18%
production.
The integer harmonics presented in [44] are observed to be equal or even somewhat lower
compared to the interharmonics. The spectrum obtained from a 200-ms waveform is presented
for both voltage and current. The results show a comparable level of interharmonics as harmonics
in the frequency range up to 5 kHz. The spectrum obtained from an individual snapshot is not
enough to quantify the harmonic emission of a wind power installation, due to its string timevarying character. Longer term measurements are needed instead.
Other papers also present harmonic emission levels of wind turbines. Paper [45] presents an
example spectrum of turbine Enercon E-53 (800 kW) with all dominating harmonics (up to 20th
harmonic) below 0.5% of the rated current. It is mentioned in the paper that the turbine type
ENERCON WEC E-82 has even lower harmonic emission levels. Paper [46] presents one voltage
and one current spectrum of a DFAG wind turbine at the wind speed of 9.2 m/s. A broadband
component, especially for the voltage, is visible around 1 kHz. However it is not known from the
text whether the broadband is due to a noise-like emission or due to time-varying (in terms of
frequency and magnitude) emission.
23
24
4.1.2
OVERVIEW OF RELATED WORK
Harmonics as a Function of Output-Power
The standard IEC 61400-21 recommends that during a harmonic study the emission level are given
for diﬀerent levels of power production. The power production should be divided into 11 power
bins (e.g., power bin 10 with 5%-15% active power; power bin 20 with 15%-25% active power).
But several papers present individual harmonic levels (as well as THD) with reference to the power
production, instead of power bins.
Papers [40–42] show that the total harmonic current distortion (as a percentage of the rated
currents) of the six wind turbines is almost constant for diﬀerent output power. The 5th harmonic
of the six turbines is shown to be independent of output power.
The total harmonic distortion (THD) of the current and the 3rd, 5th and 7th harmonics (as a
percentage of the fundamental current) have been studied versus the output power (as a percentage
of the rated power) in [43]. The trend of the THD is presented to drop with the output power; the
5th and 7th harmonics are dominating but varying randomly with a clear diversity of magnitudes.
However the trend of the THD as a percentage of the rated current, instead of the fundamental
current, is shown to be more varying and irregular.
The voltage and current spectra for a DFAG at both low and high wind conditions are presented
in [44]. The change from the low to the high wind condition mainly results in the higher levels
of space harmonics (due to the non-homogeneous distribution of stator and rotor windings) that
originated from the induction generator. The level (in percent of the rating) of characteristic
harmonics, spectra originated from the rotor-side converter and the grid-side converter, remain
the same for diﬀerent wind condition.
The lack of detailed studies on all harmonic orders and interharmonics, as well as studies on
diﬀerent wind turbines, makes it diﬃcult to obtain information about the relation between power
production and harmonic distortion.
4.1.3
Wind Power Interharmonics
Due to the mechanical distributions of the stator and rotor windings, induction generators create
an air gap ﬂux which is not perfectly sinusoidal. The space harmonics are produced due to the
air gap ﬂux not being sinusoidal [47]. Thus certain interharmonic frequencies are related with
the air gap ﬂux in the induction generator. Besides the harmonics and interharmonics from the
rotor-side converter (RSC), also emission due to the grid-side converter (GSC) is present, which
has been theoretically introduced in [48–52].
The harmonic and interharmonic frequencies of a Type 3 variable-speed wind turbine have been
linked to the PWM switching frequency [44]. Simulation results and ﬁeld measurements with single
snapshots are presented in the paper. The presented space harmonics in the measurement (but
not in the simulation) and components at PWM switching frequencies in the simulation (but not
in the measurement) are not corresponding between the simulation and the measurement.
Papers [40–42] show that, the levels of interharmonics are comparable in magnitude to those
of the neighboring integer harmonics. Broadband emission is shown to be present around the
switching frequency (around 3 kHz) due to the PWM switching scheme.
Both paper [40] and paper [44] present harmonic emissions up to a few kHz, where the switching
frequencies are present. For a detailed analysis of the emission around the switching frequency, a
long time as well as a high frequency resolution are needed.
An analysis of the inﬂuence of harmonic voltages on the stator side of a DFAG on the harmonic
emission is studied through laboratory measurements in [53]. It is shown that grid supply harmonic
4.2. HARMONIC SIMULATIONS
25
voltages introduce harmonic and interharmonic currents, for the speciﬁc DFAG design.
4.1.4
Wind Power Harmonic Variations
The magnitudes of individual current harmonics are treated as random variables in [40, 41], and
several harmonics have been studied by means of probability density functions. In [40, 41] it
is concluded that: the 5-th harmonic is normally distributed; the 10-th is Weibull distributed;
and the 15-th is Rayleigh distributed. The Rayleigh approximation is generally valid for the
frequencies above 1 kHz. The phase-angle variation has been studied for both the low-order and
the high-order harmonics: the phase-angles of low-order harmonics tend to be synchronized to the
fundamental voltage waveform; and these of high-order harmonics vary randomly. Time-varying
interharmonics have not been studied in these papers.
In [43], the WPP harmonic currents at the orders: 3rd, 5th and 7th, have been studied in
several ways: the distributions of the harmonic vectors have been studied by mapping into x
and y axis; the distributions of harmonic magnitudes and phase-angles have been studied. Each
harmonic order is shown to be diﬀerent; the normaluniform distribution is concluded to be most
suitable for the studied orders. However other orders and even interharmonics have not been
studied.
4.2
Harmonic Simulations
The book [54] states in general that, the distortion in a wind power installation is signiﬁcant
especially when there is a resonance. Similar statements and examples are found in the books
[3, 6, 26].
Recommendations for a WPP design study are given by IEEE PES Wind Plant Collector
System Design Working Group [14]. Three stages are suggested for the study:
• stage 1, collect the measured background distortion at the point of interconnection (POI)
and the wind power generators;
• stage 2, establish the frequency-dependent models for the components in a WPP (turbine
transformers, collection grid cables and lines, shunt capacitors and reactors, substation transformers and an equivalent model of the transmission network);
• stage 3, estimate the harmonic distortion including the impact of resonances and further
adjust the WPP design to meet the relevant harmonic standards by possible ﬁlter designs
or parameter adjustments.
4.2.1
Harmonic Source Modeling
The model of time-varying harmonic sources and related discussions have been presented in papers [55–58], for the purpose of harmonic summation and propagation. Analytical expressions of
harmonic voltages and currents have been obtained for the case of unform or Gaussian distributions of complex value. A Monte-Carlo simulation is used to solve the statistical problem that
occurs when multiple time-varying sources are aggregated.
For non-stationary and time-varying harmonics in the power system, paper [59] establishes a
mixed (joint) stochastic vector process. According to this process the harmonics are decomposed
26
OVERVIEW OF RELATED WORK
into deterministic functions and Gaussian vectors. Similar work is presented in paper [60]. The
procedure of current harmonics injection has been presented based on a probabilistic model of the
harmonics and a model for the nonlinear load in the power system.
Papers [48, 61] present, besides wind power, several types of other interharmonic sources:
the interharmonics can for example be produced due to the power electronics connecting two AC
systems through a DC link. Interharmonics can be generated by a cycloconverter as well. Another
source of interharmonic components is due to time-varying loads. Interharmonics can also be due
to mechanical eﬀects, such as power ﬂuctuations and a mechanical torque. Finally interharmonics
can be produced by the rectiﬁer reaction with a non-linear load.
4.2.2
Component Modeling
A wind power plant consists of a number of components: wind turbines (with generators and
converters), cables and overhead lines, power transformers, etc. A number of publications present
models of such components that can be used for a harmonic study. In paper [62] the MV cables in
a frequency range 0 - 100 kHz have been studied with three models associated with the skin eﬀect:
a distributed parameter model, a Π model and a Γ equivalent circuit. The comparison between
the three models shows that the line impedances are almost the same in the frequency range 0 2.5 kHz; the resonance frequencies for the diﬀerent models are diﬀerent for a higher frequency. For
studies up to 2.5 kHz it is thus, according to [62], not needed to consider the distributed character
of medium-voltage cables.
Harmonic modelling of a power system with wind power generation has been performed in
paper [63]. The harmonic sources were modeled as current injections with diﬀerent amplitudes
for each frequency. The network was modeled by its positive, negative and zero-sequence (symmetrical) components. The asynchronous machines were modelled with series connected and
frequency-dependent resistance and reactance. Synchronous machines are modelled as series connected negative-sequence resistance and reactance. The transmission lines were modeled as a Π
model. Obvious levels of harmonic emission were observed due to the ﬁrst resonance frequency of
the system. However this high level of emission was visible only for the local MV network, not for
the HV system.
A number of works, [64–69], presents harmonic modeling of a power system with renewable
generation in diﬀerent network conﬁgurations, and in diﬀerent applications. Some papers model
the system impedances [70–72].
4.2.3
Harmonic Simulation
The aforementioned IEEE PES Wind Plant Collector System Design Working Group [37] also
gives recommendations on the modeling of components for harmonic studies. Harmonic sources
to be considered are the power system background harmonics and wind turbine generators (WTG).
Series resonances are due to series inductance and capacitance and excited by background harmonic voltages from the grid. The relatively small impedance at the series resonance frequency
results in high harmonic currents for frequency components present in the background voltage.
Parallel resonances amplify voltages and are associated with high values of impedance present in
the source impedance on the medium voltage side of the turbine transformer. When this parallel
resonance is excited by harmonic current sources of WTGs high levels of harmonic voltages occur.
The harmonic sources of wind turbine generators are diﬃcult to model, and are time-varying.
4.2. HARMONIC SIMULATIONS
27
The model of the harmonic emission requires accurate models for the sources with detailed system
harmonic impedance.
A study of harmonic resonance between an inverter and the grid has been performed in [65,66,
73]. The model used simpliﬁes the interaction between the current source inverter and the voltage
source that represents the grid. The frequency responses of the inverter output impedance and
the grid impedance are simulated up to 10 kHz. Harmonic resonances have been presented, and
passive and active damping methods have been discussed to reduce the resonance peaks.
The simulation of an existing distributed network with photovoltaic generation (equipped
with inverters) shows that high levels of current and voltage distortion occur at parallel and series
resonances [74].
Resonances due to the capacitance of cables and inductance of transformers are presented in
the papers [68,75]. Paper [68] performs a simulation study for an oﬀshore WPP with Type 3 wind
turbines. Parallel and series resonances are shown to occur at frequencies around a few hundred
Hz. Paper [75] presents resonances obtained from a system modeling. The paper also proposes
a damping method with cascaded notch-ﬁlter to limit the peak values at the lower frequency
resonances.
Additionally a patent presents a method to evaluate the harmonic distortion that excludes the
harmonic distortion from a wind turbine generator in [76].
By using the methods presented in [49, 50], a harmonic simulation has been performed in [63].
The magnitude and phase angle of harmonic impedances at the PoC of a WPP (MV-side) and
at the high voltage busbar (HV-side) have been studied with minimum and a maximum load.
The impacts of a load variation is visible at the MV-side, but not at the HV-side. The harmonic
ﬂow has been studied in the WPP using the second summation law of IEC 61000-3-6. The ﬁrst
resonance of the WPP gives an obvious rise in the voltage distortion at the MV-side but not at
the HV-side.
Paper [77] performs a study with an equivalent model for an oﬀshore WPP. Each section
of cable is modeled as a lumped π model, which connects the sending end voltage and current
with the receiving end voltage and current. The model of the collection grid is further reduced
mathematically to become an equivalent model. The harmonic distortion is next obtained using
this model.
Paper [78] performs a simulation of an oﬀshore WPP. It is shown that the background distortion
from the public grid has a large impact on both the voltage and current harmonic levels. The
study shows that both the emission from the wind turbines and the public grid need to be known.
The study presented in [78] shows that it is not possible to determine the emission coming from
the WPP.
28
OVERVIEW OF RELATED WORK
Chapter
5
Time-Varying Harmonics
5.1
5.1.1
Harmonic Measurements
Measurement Object
Measurements have been performed on the MV-side of a turbine transformer for an individual
wind turbine as shown in Figure 5.1, and at the collection grid side of a substation transformer
for a wind power plant (WPP).
Figure 5.1: Measuring point at an individual turbine.
A standard power quality (PQ) monitor, Dranetz-BMI Power Xplorer PX5, was connected
at the measurement point through conventional voltage and current transformers. The existing
Current Transformer (CT) is of 0.2 S class and has a turns ratio of 50:5. A general conventional
CT has been tested and stated with a suﬃcient accuracy at this voltage level for the frequency
range up to a few kHz, as presented in [17, 79, 80].
The PQ monitor, which implements a phase-locked loop (PLL), captures voltage and current waveforms of exactly 10-cycles (approximate 200 ms depending on the actual power system
frequency). The acquisition sampling frequency is 256 times the output frequency of PLL (approximately 12.8 kHz). Harmonic and interharmonic subgroups are obtained by aggregation every
10-minute according to IEC 61000-4-7 and IEC 61000-4-30. In the meantime, voltage and current
waveforms of 10 cycle duration are recorded once in every 10-minute interval. The spectra of these
10-cycle waveforms are obtained by applying a DFT with a rectangular window. The resulting
spectra are used for analysis. The resulting frequency resolution of the spectra is approximately
in 5 Hz resolution. Next to harmonic voltage and current the output active and reactive power is
aggregated over 10-minute intervals and recorded.
Harmonic measurements have been performed on the following three individual wind turbines:
29
30
TIME-VARYING HARMONICS
• Turbine I: This is a Type 3 wind turbine with a rated power of 2.5 MW. It is equipped
with a gearbox of multi-stage planetary plus one stage spur gear, a six-pole doubly-fed
asynchronous generator (DFAG). A partially rated converter is installed between the rotor
and line connection. It is designed as a DC voltage linked converter with IGBT technology.
The inverter generates a pulse-width modulated (PWM) voltage, while the stator generates
3 × 660 V/50 Hz voltage. The wind turbine is connected to the collection grid through one
medium-voltage (MV) transformer, which is housed in a separate transformer station beside
the turbine foundation. There are totally 14 such wind turbines within the WPP.
• Turbine II: The second wind turbine is also a DFAG (Type 3) wind turbine, with a rated
power of 2 MW. The turbine contains a hybrid gearbox with one planetary and two parallelshaft stages, a four-pole doubly-fed asynchronous generator with wound rotor, and a partial
rated converter. The converter consists of a rotor-side and a grid-side converter in back-toback conﬁguration [10]. By the use of the control schema, the rotor-side converter controls
the rotor current and the reactive power, whereas the grid-side converter controls the DClink voltage. Both converter units are equipped with IGBT switches. The output voltage is
690 V, and connected to the collection grid through a MV transformer (installed inside the
nacelle). There are 5 such turbines in the WPP.
• Turbine III: The third wind turbine is Type 4, with a full-power converter. The rated power
is 2 MW. The turbine is designed based on a gearless and direct drive on the synchronous
generator. The generated power is fed into the grid via a full rated converter, and further
to a grid side ﬁlter and a turbine transformer into the medium voltage level. The rotor
excitation current is fed by a DC-DC controller from the DC link of the power converter.
The inverters are self-commutated and the installed IGBTs pulse with variable switching
frequency [45,81]. The WPP in which the measurements were made consists of 12 such wind
turbines.
The rated voltage and current at the measurement location, as well as the duration of the
measurements, for the three turbines are listed in Table 5.1.
Turbine
No.
Turbine
I
Turbine
II
Turbine
III
Table 5.1: Summary of the measurements.
Generator
Turbine Measurement Point Measurement
type
type
current
voltage
duration
Asynchronous Type 3
66 A
22 kV
11 Days
double-fed
Asynchronous Type 3
36 A
32 kV
8 Days
double-fed
SYNC-RT
Type 4
116 A
10 kV
13 Days
The measurements on each wind turbine provide a set of data during one to two weeks, with
10-minute interval containing harmonic and interharmonic subgroups (voltage and current) up
to order 49, 10-cycle voltage and current waveforms, and the output active-power. The recorded
data covers all the operational states of the turbine from idle to full-rated power.
31
5.2. WIND POWER HARMONIC REPRESENTATION
5.2
5.2.1
Wind Power Harmonic Representation
Average Spectrum
The harmonic distortion of a wind power installation is time-varying. That means that one
spectrum obtained over a short period is not representative for the emission of the installation.
To represent the level of wind-power harmonic distortion, the “average spectrum” is used here.
The RMS value is taken over the absolute values of the spectrum components from all the 10cycle spectra obtained during the measurement period. The average spectra, with 5 Hz frequency
resolution, for the three turbines are shown in Figure 5.2.
0.15
Phase A − Turbine I
Phase B − Turbine I
Phase C − Turbine I
650Hz
0.1
0.05
0
0
Current (A)
0.2
500
1000
1500
2000
285Hz
0.15
2500
3000
Phase A − Turbine II
Phase B − Turbine II
Phase C − Turbine II
385Hz
0.1
0.05
0
0
0.4
500
1000
1500
2000
0.3
2500
3000
Phase A − Turbine III
Phase B − Turbine III
Phase C − Turbine III
280Hz
380Hz
0.2
0.1
0
0
500
1000
1500
Frequency (Hz)
2000
2500
3000
Figure 5.2: The average spectra (5 Hz frequency resolution) of the current for the three individual
wind turbines during a measurement period between 8 and 13 days.
The harmonic spectra diﬀer between the three wind turbines but some similarities can be
seen as well. In general the average spectrum of the three turbines presents a combination of
a broadband component and a number of narrowband components. These narrowband components are mainly centered at the integer harmonics. The characteristic harmonics are dominant
at frequencies below 500 Hz. The broadband component is slightly diﬀerent between the three
turbines: Turbine I (upper ﬁgure) presents a broadband component around the narrowband component that is centered at 650 Hz; Turbine II (middle ﬁgure) presents two dominating narrowband
components at frequencies 285 Hz and 385 Hz, with a combination of both narrowband and a
broadband components; Turbine III (bottom ﬁgure) presents two clear broadband components
around the frequencies 280 Hz and 380 Hz, next to the narrowband components at harmonic 5 and
7.
Note that the broadband components around 285 Hz and 385 Hz are obtained as the average
from a number of narrowband components that change in frequency and magnitude for the individual spectra. Each waveform gives a narrowband component with a frequency around the two
mentioned frequencies. The origin of these frequencies, among others, is discussed in Chapter 6.
Beside this behavior, the harmonic emission of individual wind turbines is characterized by
the following:
32
TIME-VARYING HARMONICS
• In general, despite diﬀerent voltage levels, the level of current harmonic distortion in percentage of the rated current is low, if compared to domestic devices (such as computers,
TVs, lamps) [82, 83];
• the non-characteristic harmonics and interharmonics reach levels that are comparale to the
levels of the characteristic harmonics; this behavior is diﬀerent from the behavior of generators without power electronics and from most loads connected to the grid; the levels of
interharmonics and non-characteristic harmonics are normally low in the grid;
• harmonic distortion is observed at a few kHz, which is in the switching frequency range; a
broadband component is present in the average spectrum;
• the obvious levels of interharmonics, even harmonics, as well as the emission at frequencies up
to a few kHz, are uncommon for devices connected to the public grid at these voltage levels;
wind turbines thus introduce new harmonic issues to the subtransmission and transmission
grid.
−0.5
Harmonic/interharmonic order
40
35
−1
30
25
−1.5
20
−2
15
10
−2.5
Active Power [pu]
5
1A
2
B 3 C
4
5
D 6
7
8
E9
10
11
1
0.5
F
0
0
2
G
4
6
Measurement duration [day]
H
8
10
Figure 5.3: Turbine I: Harmonic (H 2 - H 41) and interharmonic (IH 1.5 - IH 41.5) subgroups as a
function of time (upper plot), together with the active power production (lower plot).
Note: red represents the high emission, while blue represents the low emission.
5.2.2
Spectrum as a Function of Time
The subgroups of Turbine I during the 11-day period present large variations as shown in Figure 5.3. The upper ﬁgure presents the harmonic and interharmonic subgroups (in ampere). The
magnitude in logarithm with base 10 is represented with diﬀerent color, in which dark blue represents minimum emission level and dark red represents maximum emission level. The horizontal
axis is time in days, and the vertical axis is the harmonic (H) and interharmonic (IH) order up
33
5.2. WIND POWER HARMONIC REPRESENTATION
to 41.5. Each column of the color plot presents a spectrum with the harmonic and the interharmonic subgroups obtained from a 10-minute period. The lower ﬁgure presents the active-power
production over the corresponding 10-minute period.
The ﬁgure shows how the harmonic emission is varying over the measured period (in the
horizontal direction); simultaneously with the varying active-power production. The strongest
emission, shown in dark red spots, is present during periods with high active-power production.
The regions (durations in the upper ﬁgure) that are dominated with blue color correspond to
the idle states (marked F, G and H). In the regions G and H, there are broadband components
around H 13 lasting for several hours. These components are found to occur at about 50% power
production of the whole WPP, whereas the turbine at which the measurement was performed was
idle. The emission is caused by the voltage distortion from the terminal connected to the grid,
which is secondary emission (illustrated in Chapter 7) as described in [82, 83].
The harmonic emission during periods with active-power production is much higher than during
the idle states (the color suddenly changes from blue to orange and red in the ﬁgure). Especially
when the active-power production is near rated power as in regions A, B, C, D and E, the emission
get stronger at lower orders and in the broadband around H 13.
The spectrogram relating the harmonic current distortion with the power production at Turbine II during an 8-day measurement period is shown in Figure 5.4.
50
45
−0.5
Harmonic/interharmonic Order
40
−1
35
30
−1.5
25
−2
20
15
−2.5
10
5
−3
Active Power [pu]
1
2
3
A
4
5
B
6
C
7
1
D
F
0.5
E
G
0
0
1
2
3
4
5
Measurement duration [day]
6
7
Figure 5.4: Turbine II: Harmonic (H 2 - H 49) and interharmonic (IH 1.5 - IH 49.5) subgroups as a
function of time (upper plot), together with the active power production (lower plot).
Note: red represents the high emission, while blue represents the low emission.
The regions D, E, F and G in Figure 5.4 mark the idle state. The spectrogram during this state
mainly shows characteristic harmonics (plus H 3). At production states, the manifest emission
marked in red is present at orders below 10 and orders above 40. The regions A, B and C,
refer to production at about the full-power production, presenting stronger emission than other
34
TIME-VARYING HARMONICS
states. The strong emission in dark red is present at low-orders especially for IH 5 and IH 7,
as well as some higher order components. The characteristic harmonics H 5 and H 7 show less
visible change throughout the measurement period. It is necessarily pointed out that in the end
of regions A and C, the strongest emission continually shifts to lower orders, accompanying with
the decreasing power production. The trend that the strongest emission is shifting to a higher
order with increasing power production is also observed in the beginning of region A; the varying
orders of the strongest emission accompanying with the power ﬂuctuations in region B, as well as
during the ﬁrst two measuring days.
The spectrogram relating the harmonic current distortion with the power production at Turbine III during a 13-day measurement period is shown in Figure 5.5.
50
45
0
Harmonic/interharmonic Order
40
35
−0.5
30
25
−1
20
15
−1.5
10
5
−2
Active Power [pu]
2
4
6
A
8
10
12
1
0.5
B
C
0
0
2
4
6
8
Measurement duration [day]
10
12
Figure 5.5: Turbine III: Harmonic (H 2 - H 49) and interharmonic (IH 1.5 - IH 49.5) subgroups as a
function of time (upper plot), together with the active power production (lower plot).
Note: red represents the high emission, while blue represents the low emission.
The idle state corresponds to the regions B and C in Figure 5.5, which are dominated by blue.
The main emission at this state is present at orders lower than 15 (non-blue spots). The region
A is corresponds to about full-power production.
The emission variation with time is also clear at Turbine III. The characteristic harmonics are
almost constant during the measurement duration. They even maintain about the same level
during the idle state. During this state, the wind turbine is still connected to the collection grid,
and is impacted by the grid voltage.
Similarly as for the Type 3 turbines, the strongest emission shifts to a higher order at about
the full-power operational state. The main emission is visible at interharmonics IH 5, IH 7, IH 11
and IH 13, as well as other higher orders.
35
5.2. WIND POWER HARMONIC REPRESENTATION
5.2.3
Statistical Representations
Harmonic voltage [V]
To present the level of time-varying harmonic distortion, as illustrated in Section 5.2.2, statistical
approaches have been used by means of average spectra, 90-percentile, 95-percentile and 99percentile spectra, as shown in Figure 5.6 for voltage and current at phase-A. The spectra from
the statistical approaches have been obtained from the 10-cycle voltage and current waveforms
at Turbine II. The statistical value has been calculated from the number of components at each
frequency.
150
1150Hz
2300Hz
100
50
0
0
0.4
Harmonic current [A]
Average
90 percentile
95 percentile
99 percentile
1250Hz 1750Hz
350Hz
250Hz
500
1000
1500
2000
2500
285Hz
0.3
3000
Average
90 percentile
95 percentile
99 percentile
385Hz
0.2
0.1
0
0
500
1000
1500
2000
Frequency [Hz]
2500
3000
Figure 5.6: Average, 90-percentile, 95-percentile and 99-percentile spectra of voltage (upper ﬁgure)
and current (lower ﬁgure) from all 10-cycle waveforms at Turbine II phase-A. The
vertical scale is about 1% of rated voltage or current.
The statistical spectra are presented up to 3.5 kHz. Note that the zoomed plots by splitting
the frequency ranges in two sub-ﬁgures are found in Paper F of Part V.
The average, 90-percentile and 95-percentile spectra are all about the same level; while the
99-percentile spectrum presents a higher level of harmonic emission in certain frequency ranges.
Higher 99-percentile levels are observed at the broadband from 1.7 to 2.5 kHz for both voltage
and current spectra. A low-frequency broadband appears around IH 5 (around 285 Hz) and IH 7
(around 385 Hz) of the current spectrum. The diﬀerence between the 99-percentile and the others
(average, 90-percentile and 95-percentile) indicates that, high level of distortion occurs in shortduration peaks or is at least only present a short part of the time (between 1 and 5% of the time
to be more accurate).
In the frequency range below 500 Hz the voltage spectrum presents strong emission at the
characteristic harmonics H 5, and H 7. Next to this, two lower levels of broadband emission
around IH 5 and IH 7 are present. The current spectrum presents clear broadband components
around these interharmonics and around 85 Hz.
The voltage spectrum presents a higher level of characteristic harmonics than the broadband
components around 285 Hz and 385 Hz. This is opposite in the current spectrum. Since the voltage
36
TIME-VARYING HARMONICS
spectra are similar at both a turbine terminal and at the PoC of a WPP for the dominating
components, the broadband components in current spectrum are likely due to the wind turbine.
The frequency range of manifest emission from 1.7 to 2.5 kHz is suspected to be due to the PWM
switching.
5.2.4
Individual Turbine and Wind Power Plant
Voltage and Current
Simultaneously with the measurements at Turbine I, measurements have been performed at
the PoC of the WPP. There are 14 identical turbines in the WPP. The power is collected from
the turbines through 5 underground cables, which have a total length of about 8 km. During the
11-day measurement periods, 1587 spectra were obtained. The 95-percentile voltage and current
spectra are presented in Figure 5.7.
140
140
Phase A
Phase B
Phase C
120
100
Voltage [V]
Voltage [V]
100
80
60
80
60
40
40
20
20
0
2
Phase A
Phase B
Phase C
120
5
10
15
20
25
Harmonic Order
30
35
0
2
40
5
10
15
(a)
20
25
Harmonic Order
30
35
40
(b)
0.35
4.5
Phase A
Phase B
Phase C
0.3
Phase A
Phase B
Phase C
4
3.5
0.25
Current [A]
Current [A]
3
0.2
0.15
2.5
2
1.5
0.1
1
0.05
0
2
0.5
5
10
15
20
25
Harmonic Order
(c)
30
35
40
0
5
10
15
20
25
Harmonic Order
30
35
40
(d)
Figure 5.7: 95-percentile voltage and current spectra at Turbine I and at the point of connection of
the WPP. (a) 95-percentile voltage spectrum measured at Turbine I. (b) 95-percentile
voltage spectrum measured at the substation. (c) 95-percentile current spectrum
measured at Turbine I. (d) 95-percentile current spectrum at the substation.
All the spectra present a broadband component around H 13. The broadband is probably due
to the ampliﬁcation of the distortion in the wind power collection grid (this will be discussed
37
5.2. WIND POWER HARMONIC REPRESENTATION
further in Chapter 7). The cable capacitance, together with the grid inductance, results in a
resonance which is excited by the characteristic harmonic H 13 in the WPP.
The levels of voltage spectra are shown to be similar at Turbine I and at the PoC of the WPP.
The characteristic harmonics (5th, 7th, 11th and 13th) are most visible in the spectrum. The
similar levels of voltage distortion at the individual turbine terminals and the PoC of a WPP have
been observed also in Paper C.
There are diﬀerences in the current spectra between Turbine I and the PoC. Except for the
low-order narrowbands below H 10, the current spectrum at the PoC presents a smooth and decaying level above H 15, compared to the much more varying levels of Turbine I. This smooth level
of harmonic distortion at the PoC is the result of harmonic aggregation (presented in Chapter 7)
from all turbines.
THD and TID
The total harmonic distortion (THD) and total interharmonic distortion (TID) have been
recorded over every 10-minute window during the measurement period. The THD and TID are
the parameters to quantify the overall waveform distortion, which are calculated in this case from
the order 2 to 40. The deﬁnitions are found in IEC 61000-4-7 and IEC 61000-4-30. The variations
of current THD and TID during the 11-day measurement period are shown in Figure 5.8. Note
that, the values of Turbine I (black lines) are multiplied with 14 (the number of turbines in the
WPP) for a better comparison with the values at the substation (colored lines).
10
10
5
5
0
10
Current TID [A]
Current THD [A]
0
10
5
0
10
0
10
5
0
Day 1
5
5
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Time in Days
(a)
Day 8
Day 9
Day 10 Day 11
0
Day 1
Day 2
Day 3
Day 4
Day 5 Day 6 Day 7
Time in Days
Day 8
Day 9
Day 10 Day 11
(b)
Figure 5.8: The levels of THD and TID (in Ampere) varying with time. Red, green and blue lines
are the measured three phases at the substation, while the black lines are 14 times
that of the corresponding phases at Turbine I. (a) THD. (b) TID.
Turbine I was in the idle state during certain periods, as indicated by the almost zero values
(for the black lines). The THD and TID at the idle state are in accordance with the variations in
power shown in Figure 5.3. The values during this idle state are not comparable with those of the
substation (PoC), since there other turbines remaind operating.
In general, both THD and TID levels Turbine I times 14, are higher than the levels at the PoC.
Assuming that the THD and TID of Turbine I are representative for the average emission level of
all turbines, the conclusion is made that there is harmonic and interharmonic cancellation in the
collection grid of the WPP.
38
TIME-VARYING HARMONICS
The observation from the comparison of the THD (left ﬁgure) and the TID (right ﬁgure) leads
to the conclusion that: interharmonics aggregate more than harmonics. The larger diﬀerence
between the PoC and 14 times of Turbine I indicates a larger interharmonic cancellation. The
study of the phenomenon of harmonic and interharmonic aggregation (cancellation) is presented
in Chapter 7.
Individual Voltage versus Current
The harmonic voltage versus harmonic current at harmonic and interharmonic orders 12, 12.5,
13, 13.5, 14 and 14.5 (around the resonance frequency) are presented in Figure 5.9.
Harmonic/Interharmonic voltage verses current at the substation
180
160
160
140
120
100
80
60
12th
12.5th
13th
13.5th
14th
14.5th
40
20
0
0
0.05
0.1
0.15
0.2
0.25
Harmonic/Interharmonic current [A]
(a)
0.3
0.35
Harmonic/Interharmonic voltage [V]
Harmonic/Interharmonic voltage [V]
Harmonic/Interharmonic voltage verses current at the windturbine
180
140
120
100
80
60
12th
12.5th
13th
13.5th
14th
14.5th
40
20
0
0
1
2
3
4
Harmonic/Interharmonic current [A]
5
6
(b)
Figure 5.9: Voltage subgroup versus current subgroup at certain orders. (a) Voltage verses current
at orders 12, 12.5, 13, 13.5, 14 and 14.5 at Turbine I. (b) Voltage versus current of
orders 12, 12.5, 13, 13.5, 14 and 14.5 at the substation.
The scatter plots of voltage versus current contain diﬀerent frequencies (harmonic and interharmonic orders) that are marked with diﬀerent colors. For the substation (right ﬁgure), the slope
of the line-distributed scatter plots corresponds to the source impedance at the corresponding order seen at the substation looking towards the grid transformer. These lines are almost linear
with a similar slope. The small spread around the straight line might be due to variations in
background distortion. The small non-zero current for zero voltage is due to quantization noise
during the current measurement.
In general, the orders 12.5 and 13 have the highest emission among the six orders. Orders 14
and 14.5 show lower emission. They are somewhat outside of the peak value of the narrowband
shown in the spectra of Figure 5.7.
The harmonic voltage versus harmonic current with the same harmonic and interharmonic
orders at Turbine I are shown in the left ﬁgure. Diﬀerent from the substation, Turbine I has two
main linear distributions with two slopes, which are at operational and at idle states. Also these
distributions are less concentrated as the ones at the substation. The reason for this is that the
voltage is due to all 14 turbines, of which only one turbine has been measured. The origin of the
two slopes is discussed in Chapter 7.
39
5.3. EMISSION VERSUS ACTIVE-POWER
5.3
Emission versus Active-Power
5.3.1
THD and TID
The current THD and TID versus the active-power are presented for the three wind turbines
in Figure 5.10. The horizontal axis represents the active-power in per-unit. The vertical axis
represents the THD and TID in ampere.
0.5
0.5
Turbine I
0
0.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Turbine II
0
0
1
Current TID (A)
Current THD (A)
Turbine I
0
0.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Active Power [pu] (phase A)
0.8
0.9
1
Turbine II
0
1
1
0.5
0.5
Turbine III
Turbine III
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Active Power [pu] (phase A)
0.8
(a)
0.9
1
0
1
(b)
Figure 5.10: Total Harmonic Distortions (THD) and Total Interharmonic Distortion (TID) as a
function of active power in phase A. (a) THD verses active-power. (b) TID verses
active-power. Note the diﬀerent vertical scales.
The THDs at the three wind turbines show a slight diﬀerence in their relation between emission
and active-power production. Turbine I shows a slight increase; Turbine II shows a mild decrease
and Turbine III remains about the same. The magnitude diversity of both Turbine I and Turbine II
at certain production level is within a narrower range than that of Turbine III.
Diﬀerent from the THD, all the three turbines show a clear increase for the TID with activepower production. The trend is almost linear line but with a slight drop or ﬂuctuation at a certain
active-power level. The drop is at around 0.26 pu for turbine I (which is also visible for the THD).
There are multiple lines below 0.15 pu for Turbine II and a drop from 0.15 to 0.3 pu for Turbine III.
The TIDs have less diversity than the THDs.
5.3.2
Individual Subgroups
Certain typical individual harmonic and interharmonic subgroups have been plotted as a function
of the active-power production for the three individual wind turbines, as shown in Figure 5.11.
The emission patterns, from the various subgroups in the ﬁgure, diﬀer from order to order
and from turbine to turbine. However in general there is a diﬀerence between harmonics and
interharmonics: interharmonics tend to increase with power production (illustrated in Chapter 6).
The general trends of these subgroups as a function of the active-power are concluded into the
three patterns:
• Characteristic harmonics plus H 3: these harmonics are H 3, H 5, H 7, H 11 and H 13, which
show a similar pattern as H 5 or H 7 that are presented as a typical example in the ﬁgure; the
levels of these harmonic subgroups are not correlated with the active power; the subgroups
are within a wide magnitude range (or spread, diversity) as a function of power, without an
obvious trend.
40
TIME-VARYING HARMONICS
0.1
H3
0.1
0.05
0
0
0.2
0
0.5
1
H7
0.1
0
0.5
1
0.05
0.05
0
IH7
0
0.5
0.05
0
1
H12
0
0.5
1
IH12
0.2
0.1
0
0.10
0.5
0
1
0
0.5
0
0.5
1
0.05
H16
0.05
IH16
0
0
0.5
0
1
1
0.1
0.05
0
0.5
0
H19
0
1
0
Active Power in [pu] (phase A)
0.01
H3
0
0.5
0
1
0.1
IH3
0
0.5
0
1
0
0.10
0.5
1
IH6
0.5
1
IH32
0.2
0.05
IH5
H5
0
0.5
1
H6
0.1
0.05
0 x 10−3
50
0.5
0
0.040
0 x 10−3
50
1
H32
0.5
1
0
0.040
0.5
H36
0.02
0.05
0
0.02
0.1
IH3
Current Harmonic/Interharmonic subgroups (A)
Current Harmonic/Interharmonic subgroups (A)
0.2
1
IH36
0.02
IH19
0.5
0
1
0
0.5
0
1
0
Active Power in [pu] (phase A)
(a)
0.5
1
(b)
H3
Current Harmonic/Interharmonic subgroups (A)
0.2
0.05
IH3
0
0.20
0.5
0
1
H4
0
0.5
1
IH4
0.2
0.1
0.1
0
0.50
0.5
0
0.20
1
0.5
1
IH6
H6
0.1
0
0
0.5
0
1
0
0.5
0
0.030
0.5
1
0.5
0.2
0.1
IH7
0
0.030
0.5
H7
1
1
H22
0.02
0.01
0.02
0
0.5
0.01
1
0
Active Power in [pu] (phase A)
IH22
0.5
1
(c)
Figure 5.11: Individual Harmonic (H) and interharmonic (IH) subgroups as a function of activepower in Phase A. (a) Turbine I. (b) Turbine II. (c) Turbine III.
• Non-characteristic harmonics: the other harmonic orders present a narrower magnitude
variation (less magnitude diversity) as a function of power, and with various trends, e.g. H 4,
H 6 and H 8 (H 6 and H 12 are shown in the ﬁgure); some higher-order emission decreases with
the increasing power production, e.g. H 19, H 22 and H 36, and some with ﬂuctuations, e.g.
H 16 and H 19. Note that the emission level for higher-order components is low compared
to the emission level for lower-order components.
• Interharmonics: interharmonic subgroups present a stronger dependence on the active power
than the harmonic subgroups; there are several patterns observed: in general interharmonics
have a linear and increasing trend; a ﬂuctuation of emission around 0.3 pu active-power;
emission with two manifest linear trends associated with emission between the two linear
lines as a function of power (e.g. IH 4, IH 6 and IH 12, etc.); and some other irregular
patterns such as IH 32 and IH 36.
Chapter
6
Origin of Interharmonics from Wind Turbines
6.1
Wind Power Frequency Conversion
A power converter (or frequency converter) is an important component in variable-speed wind
turbines. It allows energy transfer between the two diﬀerent nominal frequencies on the generatorside and on the grid-side of the converter. A full-power converter (in a Type 4 turbine) enables the
power ﬂowing from the generator to the grid by ﬁrst rectifying and next inverting the generator
frequency. While a partial-scale frequency converter (in a Type 3 turbine) feeds the rotor-side
frequency and handles dual-direction power ﬂows (sub- and super-synchronous mode). For a
Type 3 turbine, the grid-side of the converter is coupled with the generator stator through a turbine
transformer (see Figure 2.1). This type of turbine is more complicated and will be discussed in
Section 6.3.1. The diagram of the power converter part in a Type 4 wind power conversion system
is shown in Figure 6.1.
Figure 6.1: Power converter in a Type 4 wind power conversion system.
The generator-side fundamental frequency, the input to the power converter, is f1 . This is
normally deviating from the power-system frequency f0 on the grid-side. The generator-side frequency varies depending on a wind speed and the turbine control strategy, which maximizes an
extraction of wind power. The grid-side frequency depends on the whole power system, and normally maintains around the nominal 50 Hz with very little deviation. The power-system frequency
is considered as constant in this thesis.
The AC-DC converter on the generator-side works as a rectiﬁer. A six-pulse rectiﬁer rectiﬁes
the three-phase AC voltage into a DC-bus voltage, which is consisting of a DC component and
a voltage ripple of frequency 6f1 . The DC-AC inverter, on the grid-side, is a voltage-source
converter (VSC) using pulse-width modulation (PWM). It inverts the DC-bus voltage into an
almost sinusoidal voltage waveform on the grid side.
41
42
ORIGIN OF INTERHARMONICS FROM WIND TURBINES
6.1.1
Frequency Conversion
Papers [48,52] introduce for the generation of interharmonics when two AC systems are connected
through a DC link. This work derives the relation of the two AC frequencies, and further analyzes
measurements during a long period.
The conversion from a frequency f1 to the frequency f0 introduces additional frequency components on the receiving end (the grid). These are determined by
• the number of pulses in the rectiﬁer;
• and the background voltage harmonics on the grid side.
The six-pulse rectiﬁcation results in a DC-bus voltage containing a ripple of 6 times the
generator-side frequency: 6f1 . The DC-bus voltage with ripple (and harmonics of the ripple
frequency) can be expressed as:
vDC (t) = V0 +
∞
V6k cos(6kω1 t + φ6k )
(6.1)
k=1
where vDC (t) the voltage waveform at the DC bus, as a function of time; V0 the DC component
magnitude; V6k , φ6k the amplitude and phase-angle of the component at frequency 6kf1 ; the radial
frequency ω1 = 2πf1 .
The conversion from the DC component to the power system frequency is implemented with
PWM [6, 7, 84]. The resulting waveform on the grid-side is regenerated mathematically by multiplication with cos(ω0 t) where ω0 = 2πf0 :
vAC (t) = V0 cos(ω0 t) +
= V0 cos(ω0 t) +
∞
k=1
∞
k=1
+
∞
V6k
k=1
2
V6k cos(6kω1 t + φ6k ) × cos(ω0 t)
V6k
cos((6kω1 + ω0 )t + φ6k )
2
(6.2)
cos((6kω1 − ω0 )t + φ6k )
Assume that the grid impedance is pure inductive and there is no background voltage distortion. At the AC output of the converter, the current is the ratio of the output voltage of the VSC
and the grid-side impedance. The output AC current is written as:
iAC (t) = I0 cos(ω0 t)
∞
V6k
cos((6kω1 + ω0 )t + φ6k )
+
2Z
6kω1 +ω0
k=1
+
∞
k=1
(6.3)
V6k
cos((6kω1 − ω0 )t + φ6k )
2Z6kω1 −ω0
here I0 is the current at power-system frequency; Z6kω1 ±ω0 the impedance at radian frequency
(6kω1 ± ω0 ) on the grid-side.
43
6.1. WIND POWER FREQUENCY CONVERSION
In addition to the above conversion into the power system frequency, the interaction with
characteristic harmonics of the power-system frequency also impacts the (inter)harmonic conversion through a converter. Instead of the conversion by the power-system frequency cos(ω0 t), the
characteristic harmonics cos((6n ± 1)ω0 t) will produce the frequencies ω+ = 6kω1 + (6n ± 1)ω0 and
ω− = 6kω1 − (6n ± 1)ω0 with the same schedule as in (6.2). Consequently the generated frequency
components due to both power-system frequency and its characteristic harmonics are written as:
iAC (t) = I0 cos(ω0 t) +
∞
I0 cos((6n ± 1)ω0 t)
n=1
+
∞ ∞
V6k
cos(6kω1 + (6n ± 1)ω0 )t + φ6k )
2Z
ω+
k=1 n=0
+
∞ ∞
V6k
cos(6kω1 − (6n ± 1)ω0 )t + φ6k )
2Z
ω−
k=1 n=0
(6.4)
The group of leading frequency components is deﬁned as:
k,n
= 6kf1 + (6n ± 1)f0
fleading
(6.5)
The group of lagging frequency components is deﬁned as:
k,n
flagging
= 6kf1 − (6n ± 1)f0
(6.6)
The resulting components are with a number of frequencies listed below (k = 1, 2, 3 and
k = 0, 1):
k=1:
k=2:
k=3:
6.1.2
6f1 ± f0
12f1 ± f0
18f1 ± f0
6f1 ± 5f0
12f1 ± 5f0
18f1 ± 5f0
6f1 ± 7f0
12f1 ± 7f0
18f1 ± 7f0
(6.7)
Emission versus Active-Power
For a symmetrical and sinusoidal voltage waveform on the generator-side and a six-pulse rectiﬁer,
the DC-bus voltage contains a voltage ripple with frequency 6f1 . The ripples are smoothed by
a capacitor C. The capacitor is charged when the voltage of the capacitor is lower than the
rectiﬁed AC-side voltage, with the charging time t1 ; then the capacitor will be discharging when
the rectiﬁed AC-side voltage drops below the capacitor voltage with the discharging time t2 . The
charging time t1 is much shorter than the discharging time t2 ; the discharging time is considered
equal to T /6 = 1/6f1 . The relation between voltage and current for a capacitor is:
i=C×
dv
dt
(6.8)
The current discharging the capacitor is a function of the active power P :
i=
P
VDC
(6.9)
44
ORIGIN OF INTERHARMONICS FROM WIND TURBINES
Thus the voltage drop during the discharging period is:
ΔV =
P
i
Δt =
C
VDC · C · 6f1
(6.10)
This voltage drop is the peak-to-peak amplitude of the voltage ripple. The VSC schedule
maintains the average voltage on the DC side the same as the AC output VDC = VAC . As from
(6.4) a harmonic current is a function of the DC current, the coeﬃcient α6kf1 ±(6n±1)f0 is used for
the relation between the amplitude of the frequency component at the ripple frequency and the
peak-to-peak amplitude of the ripple voltage:
I6kf1 ±(6n±1)f0 = α6kf1 ±(6n±1)f0 ×
P
6f1 CVDC
(6.11)
It indicates that the amplitude of the interharmonic current is proportional to the active-power.
The same expression also shows that the amplitude of the interharmonic currents becomes smaller
when a larger capacitor is used with the DC bus.
6.1.3
Ratio between Related Interharmonic Currents
As aforementioned, the wind power conversion system generates two groups of frequency components: the leading component group 6kf1 + f0 as in (6.5) and the lagging component group
6kf1 − f0 as in (6.6). The eﬀect of characteristic harmonics in the voltage is ignored, by setting
n = 0.
The interharmonic voltage at the VSC terminals for the leading and lagging components are
equal V6kf1 +f0 = V6kf1 −f0 as in (6.4). The impedance at frequency 6kf1 ± f0 , assuming a purely
inductive impedance, is written as:
Z6kf1 ±f0 = 2π(6kf1 ± f0 )L
(6.12)
The ratio of the magnitudes for the lagging and leading frequency component pair will be
inversely proportional to the ratio of the frequencies:
Rlagging,leading =
I6kf1 −f0
6k1 f1 + f0
=
I6k2 f1 +f0
6k2 f1 − f0
(6.13)
For instance, the ratio between a 285 Hz and a 385 Hz components will be
RI,285,385 =
I285
= 385/285 = 1.426
I385
(6.14)
A single ripple frequency at the DC side will give interharmonics at two frequencies (for certain
k and n) on the grid side, 100 Hz apart from each other. The voltages at the terminals of the VSC
will be the same for these two frequencies. The currents are limited by an inductance, which gives
an impedance linearly increasing with frequency. Hence the currents are not the same at the two
frequencies.
The ratio between the currents is the inverse of the ratio between the impedances, which is
the inverse of the ratio between the frequencies.
45
6.2. MEASUREMENT
6.2
Measurement
The measurements on the wind turbines, as presented in Chapter 5, are used to verify the model
introduced in Section 5.3. As a Type 4 turbine with full-power converter, Turbine III is chosen for
the veriﬁcation.
The measurements at Turbine III show that, the most frequent generator-side frequency, among
the varying frequencies (due to the varying-speed schema), is present at about f1 = 55.8 Hz.
Associated with the power-system frequency f0 = 50 Hz the resulting frequencies at the grid-side
with (6.7) are given in the Table 6.1, when n = 0.
Table 6.1: Resulting frequencies at the ﬁrst three orders with the generator-side frequency f1 =
55.8 Hz and grid-side frequency f0 = 50 Hz, when n = 0.
Order k leading component lagging component
1
385 Hz
285 Hz
2
720 Hz
620 Hz
3
1055 Hz
955 Hz
The two frequencies in the average spectrum, at the order k = 1, are clearly visible in Figure 5.2 (however the peak components in the measurements are at 280 and 380 Hz); broadband
components are around these frequencies. The frequencies at order k = 2 are not clearly visible;
however two broadband components are visible by zooming into the frequencies. The magnitudes
of the frequency components at the second order are much lower. That of a higher order is almost
not visible in the measurements.
6.2.1
Correlation of Harmonic Distortion
Section 6.1.1 explains that, the generator-side frequency f1 results in a series of frequencies that
are related to both f1 and the grid-side frequency f0 . The diﬀerent interharmonic frequencies are
not independent from each other but they always appear in groups. Although the frequencies
vary, there are certain relations between the frequencies within a group that do not vary.
The series of frequencies originated from the generator-side, with a constant f0 , have a relation
between each other as illustrated in Section 6.1.3. The pairs of frequencies, which are originated
from the generator-side, are listed between the following frequencies at low orders k = 1, 2 and
n = 0, 1:
• A: 6f1 − f0 and 6f1 + f0 ;
• B: 12f1 − f0 and 12f1 + f0 ;
• C: 6f1 ± f0 and 12f1 ± f0 ;
• D: 6f1 ± f0 and 6f1 − 5f0 ;
• E: 6f1 ± f0 and 6f1 − 7f0 ;
• F: 6f1 − 5f0 and 6f1 − 7f0 ;
46
ORIGIN OF INTERHARMONICS FROM WIND TURBINES
• G: 12f1 ± f0 and 6f1 − 5f0 ;
• H: 12f1 ± f0 and 6f1 − 7f0 .
Figure 6.2: Correlation coeﬃcient between each frequency (5 Hz resolution) at Turbine III. The
coeﬃcient ranges from -1 to 1, with the lowest correlation dark blue and highest dark
red.
The plot of correlation coeﬃcients between each (inter)harmonic current (in 5 Hz resolution)
have been shown for Turbine III, as in Figure 6.2. A positive unity correlation is represented in
dark red; while a negative correlation (around -0.4) is represented in dark blue.
The strong correlations occur between the aforementioned frequency pairs A to H, which are
marked in the ﬁgure. These correlations occur along straight lines. This is because of the variation
of the generator-side frequency f1 ; the pairs of both frequencies vary simultaneously with f1 . Each
dot of the strong correlation indicates an instantaneous generator-side frequency that links the
frequency pair. Since the analyzed spectra have a frequency resolution of 5 Hz, the eﬀect of
variation due to a very small change of power system frequency cannot be observed. Compared
to the impact of the generator-side frequency, that of the power system frequency can be ignored.
The main conclusion from the ﬁgure, especially from the linear lines, is that the harmonic
distortion at the wind turbine are originated from the generator-side frequency; and the frequencies
of strongest pair are simultaneously varying with f1 .
Note that, the two horizontal and two vertical blue areas indicate low (even negative) correlations if frequencies between H 5 and H 7 with any other frequencies. This phenomenon is probably
due to the schema of harmonic eliminations at the two characteristic harmonics in a wind turbine [17, 85]. The decreasing trends around H 5 and H 7 with the increasing (inter)harmonics at
other frequencies results in the low and even negative correlations.
47
6.2. MEASUREMENT
6.2.2
Emission versus Active-Power
The harmonic and interharmonic subgroups versus active-power production have been presented
in Section 5.3.2. The interharmonics present an increasing trend with an increasing active-power
production in general.
Here the interharmonic frequencies that resulted from the most-common generator-side frequency have been presented as a function of active-power (in per-unit) for Turbine II and Turbine III, as shown in Figure 6.3.
0.4
15 Hz
0.2
80 Hz
0.2
Harmonic/interharmonic curent [A]
0.1
0
1
0
0.2
0.4
0.6
0.8
1
285 Hz
0
0
0.2
0.6
0.5
0.4
0.6
0.8
1
0.6
0.8
1
0.6
0.8
1
385 Hz
0.4
0.2
0
0.1
0
0.2
0.4
0.6
0.8
620 Hz
0
0
0.2
0.1
0.05
0
1
0.4
720 Hz
0.05
0
0.2
0.4
0.6
0.8
0
1
0
0.2
Active power [pu]
0.4
Figure 6.3: Interharmonics (A) versus active-power production (per-unit) at the frequencies resulted by the most frequent generator-side frequency 55.8 Hz at Turbine III.
As presented in Section 6.1.2, harmonic distortion originated from the generator-side frequencycomponent is related with the active-power production. An increasing active-power results in a
higher level of interharmonic current.
The frequency components, 15 Hz, 80 Hz, 285 Hz, 385 Hz, 620 Hz and 720 Hz, are the results
of the generator-side frequency 55.8 Hz. Note that, the 15 Hz component is actually −15 Hz =
6f1 − 5f0 which is the same as a positive frequency, but shifted 180◦ in phase angle. There is
a clear increasing trend of interharmonic currents in accordance with an increasing active-power
production as shown in Figure 6.3. The scatter plots spread in a triangle area. The slope of the
triangle area is constant, which is determined by the parameters: power, frequency, capacitance
and the DC-voltage as in (6.11).
There are also a lot of dots that spread below the triangle slope. The dots on the triangle slope
are the emission when the generator is operating at the most common frequency of about 55.8 Hz.
When the generator-side frequency varies to another frequency, the resulted emission occurs at
a corresponding series of frequencies according to (6.11). In this case the present emission at
these studied frequencies is not following the formulation (6.11); the present emission is either a
leakage of the actual resulted component or caused by something else, which is spreading below
the triangle slope.
48
6.2.3
ORIGIN OF INTERHARMONICS FROM WIND TURBINES
Voltage vs. Current
The correlation coeﬃcient has been calculated between the measured voltage and current distortion at each frequency (with 5 Hz separation) at Turbine II, as shown in Figure 6.4.
285Hz
0.8
385Hz
720Hz
620Hz
0.6
0.4
Correlation Coefficient
0.2
0
−0.2
−0.4
0
100
200
300
400
500
600
700
800
900
1000
3000
3200
1
0.8
0.6
0.4
0.2
0
1000
1200
1400
1600
1800
2000 2200 2400
Frequency [Hz]
2600
2800
Figure 6.4: Correlation coeﬃcients of voltage and current emission up to 3200 Hz at Turbine II.
An unity correlation coeﬃcient means that there is a linear relation between the voltage and
the current, which a voltage increases with a current. A negative correlation coeﬃcient means that
the voltage increases with decreasing current. A zero correlation coeﬃcient means that voltage
and current are statistically independent.
The ﬁgure presents strong correlations between (inter)harmonic voltage and current components at 50 Hz, 85 Hz, 100 Hz, 285 Hz, 385 Hz, 620 Hz, 720 Hz, 850 Hz, 950 Hz, and several frequencies above 1000 Hz. Strong correlations are not only visible at the dominant interharmonic
frequencies (285, 385, 620 and 720 Hz) but also in a broadband around these frequencies. Negative correlation coeﬃcients are observed at the frequencies 400 Hz, 450 Hz, 500 Hz and at some
frequencies around 1500 Hz. Most other correlation coeﬃcients are around zero or positive.
The strong correlations occur at the interharmonic frequencies that occur from the connection
of two AC systems with diﬀerent frequency. These frequencies are normally not present in the
background voltage distortion. The injected current results in a voltage distortion linearly proportional in magnitude with the current distortion. Thus the voltages are strongly correlated with
the currents at these frequencies. Meanwhile those frequencies are varying according to the generator side frequency, which present broadband components around the most common frequencies
(285 Hz, 385 Hz, 620 Hz and 720 Hz).
49
6.2. MEASUREMENT
25
50
25
400 Hz
20
15
30
15
10
20
10
5
10
5
0
0
0.1
15
385 Hz
40
0.2
0
0.3
10
0
0.1
0.2
0.3
12
620 Hz
720 Hz
Voltage [V]
Voltage [V]
100 Hz
20
0
450 Hz
10
5
0
0.01
0.02
0.03
0.04
8
0
0
0.005
0.01
0.015
0.02
0.025
40
500 Hz
550 Hz
10
8
6
30
4
20
2
10
8
6
6
4
4
2
2
0
0
0
0.01
0.02
0.03
0
Current [A]
0.01
0.02
0
0.03
0
0.005
0.01
0
0.02
0
Current [A]
0.015
(a)
0.01
0.02
0.03
0.04
(b)
100
100
50
50
350 Hz
250 Hz
0
0
0.05
0.1
0.15
0.2
60
0.05
0.1
0.15
950 Hz
40
20
Voltage component [V]
0
60
40
0
0
850 Hz
0
0.005
0.01
0.015
20
0
0.02
0
0.002 0.004 0.006 0.008 0.01 0.012
200
1250 Hz
150
100
100
1150 Hz
0
0
0.01
0.02
0.03
30
0.04
0.05
1550 Hz
20
0
0
0.02
0.04
0.06
30
1650 Hz
20
10
0
50
10
0
0.005
0
0.01
0
2
4
6
8
−3
x 10
1750 Hz
30
100
20
50
0
10
0
0.01
0.02
0.03
0
0.04
0
0.002
Curent component [A]
1850 Hz
0.004
0.006
0.008
0.01
(c)
Figure 6.5: Scatter plots of voltage versus current distortion at individual frequencies at Turbine II.
(a) Positive correlation. (b) Negative correlation. (c) Linear correlation.
The correlations are divided into three types, based on the scatter plots shown in Figure 6.5:
• Positive correlations: the relatively strong positive correlation occurs at 285 Hz, 385 Hz,
620 Hz and 720 Hz as shown in Figure 6.5 (a), which are the resulted interharmonic components due to the generator-side frequency; the strong correlations are due to the converted
voltage interharmonics (from the two AC systems) and the resulted interharmonic currents;
• negative correlations: the strong negative correlation is present at 400 Hz, 450 Hz 500 Hz
and 550 Hz, which are shown in Figure 6.5 (b);
• linear correlations: the scatter plots of voltage and current are spreading along a linear
line; the frequencies of this type are 850 Hz, 950 Hz, 1150 Hz, 1250 Hz, 1550 Hz, 1650 Hz and
50
ORIGIN OF INTERHARMONICS FROM WIND TURBINES
1750 Hz. Among these frequencies, 250 Hz, 350 Hz and 1850 Hz present a strong correlation
coeﬃcient, and with a linear relation between voltage and current; The slope of the line
indicates the impedance value at the frequency being shown; at frequencies 250 Hz, 350 Hz,
1250 Hz and 1550 Hz the scatter plots are with multiple lines; the multiple slopes of the
multiple lines are due to diﬀerent impedances at the multiple operation states (e.g. idle
state).
The high correlation between voltage and current also indicates that there is high correlation
in emission between diﬀerent turbines. The correlation is also high for H 2, almost 0.8. Separate
studies are needed to ﬁnd out where this H 2 originates from.
6.2.4
Current vs. Current
The components of interharmonic frequencies that originated from the generator-side frequency
285 Hz, 385 Hz, 620 Hz and 720 Hz, are presented in Section 6.1.3, have been plotted as a function
with each other in Figure 6.6. Note that, each pair of interharmonics is from the same spectrum.
The low values (smaller than 0.02 A) of the clusters on the bottom left are probably quantisation
noise.
0.8
0.1
620 vs. 285
385 vs. 285
0.6
0.4
0.05
0.2
Interharmonic curent [A]
0
0
0.2
0.4
0.6
0.8
1
0
0
0.2
0.4
0.6
0.8
1
0.1
620 vs. 385
720 vs. 285
0.1
0.05
0.05
0
0
0.2
0.4
0.6
720 vs. 385
0.1
0.05
0
0.8
1
0
0.1
0
0.2
0.4
0.6
0.8
720 vs. 620
0.05
0
0.2
0.4
0
0.6
0
0.02
Interharmonic current [A]
0.04
0.06
0.08
0.1
Figure 6.6: Current versus current at individual frequencies, Turbine III. Note the diﬀerent scales.
In general, these individual currents have a strong correlation with each other, due to the same
origin. The strongest correlation is between the pair of 285 Hz and 385 Hz, and the pair of 620 Hz
and 720 Hz. These pairs are comprised of the leading and lagging frequency at the ﬁrst and second
order of k when n = 0.
Beyond the two pairs with strong correlation, other pairs present scatter plots that do show a
weak correlation only. It may be due to the reason that, the varying generator frequency results in
6.3. DISCUSSION
51
a larger variation of magnitude at a lower frequency than that at a higher frequency. For instance
for the pair of 720 Hz and 285 Hz, the 285 Hz component tends to increase when f1 is close to
55.8 Hz, while the increase of 720 Hz component remains small. Thus the scatter plots are biased
to x-axis, which is for 285 Hz component. Additionally, components of 720 Hz and 285 Hz do not
really form a pair with 100 Hz distance that are due to the same frequency at the DC bus voltage;
and the amplitude of the 720 Hz component is a lot smaller; the absolute spread is about the same
as for the 285 Hz component, but the relative spread is much higher.
6.3
6.3.1
Discussion
Discussions on Type 3 Turbine
A Type 3 turbine has a more complicated schema than a Type 4 turbine. Except the power
conversion from the generator-rotor to the grid-side, power can be converted from the grid side
to the generator rotor through the converter. On one hand, the generator rotor winding and
the stator winding impact each other; on the other hand, harmonic interactions can occur at the
coupling point on the grid-side of the converter. The converter also works at a diﬀerent frequency
from a Type 4 turbine. The origin of harmonic distortion from a Type 3 turbine needs a further
study.
The current spectrum of Turbine II presents harmonic emission with both similarities and
diﬀerences compared to Turbine III (see Figure 5.2). There are more diﬀerences found in the plot
of correlation coeﬃcients between each frequency as in Figure 6.7.
Figure 6.7: Correlation coeﬃcient between each frequency (5 Hz resolution) at Turbine II, similar
with Figure 6.2.
The diﬀerent phenomena of the Turbine II (compared to the Turbine III) are that: there are a
number of square regions with strong correlations between the frequencies at about 130 Hz, 300 Hz
52
ORIGIN OF INTERHARMONICS FROM WIND TURBINES
and 400 Hz. There are similar linear lines as in Figure 6.7, with one end of the lines connected to
the square regions.
0.15
0.15
15 Hz
0.2
0.4
0.6
0.8
0
1
0.1
0
0.2
Curent [A]
285 Hz
0.4
0.6
0.8
1
385 Hz
0.3
0.2
0.2
0.1
0.1
0
0.04
0
0.2
0.4
0.6
0.8
1
0
0.04
0
0.2
620 Hz
0.4
0.6
0.8
1
0
0.04
0
0.03
0.02
0.02
0.01
0.01
0
0
0.1
0.2
0.3
0
0.4
0
0.04
0.02
0
0.04
0.1
0.2
0.3
0.4
620 vs. 385
720 vs. 285
0.02
0
0.1
0.2
0.3
720 vs. 385
720 Hz
0.03
620 vs. 285
0.02
Interharmonic curent [A]
0.4
0
0.04
385 vs. 285
0.2
0.05
0.05
0
0.3
80 Hz
0.1
0.1
0
0.4
0
0.03
0.1
0.2
0.3
720 vs. 620
0.02
0.02
0.01
0
0.2
0.4
0.6
0.8
1
0
0.2
Active power [pu]
(a)
0
0.4
0.6
0.8
1
0
0.1
0.2
0
0.3
0
0.01
Interharmonic current [A]
0.02
0.03
(b)
Figure 6.8: (a) Interharmonics (A) versus active-power production (per-unit) at certain frequencies at Turbine II, compared to Figure 6.3. (b) Current versus current distortion at
individual frequencies, Turbine II, compared to Figure 6.6. Note the diﬀerent scales.
Compared to Turbine III (see ﬁgure 6.8 (a)), there is some diﬀerence in the scatter plots (frequencycomponents as a function of active-power): there are more points distributed around the triangle
slope in Turbine II than in Turbine III. The magnitude of the interharmonic current at the triangle slope is proportional to the output power at the corresponding frequency as in (6.11).
Those dots below the triangle slope are not at the frequent generator frequency (55.8 Hz). In
Figure 5.2, the broadband components of Turbine II around 285 and 385 Hz are within a narrower
frequency range, compared to that of Turbine III. The strong current correlations between the
studied frequency-components are shown in Figure 6.8 (b) for Turbine II.
Chapter
7
Harmonic Propagation and Aggregation in WPP
As was shown in Chapter 5 wind turbines generate waveform distortion, both harmonics and
interharmonics. This emission from the turbine causes harmonic voltages and currents in the rest
of the network. Furthermore, the background distortion due to other sources also impacts the
harmonic voltages and currents. The same holds for a WPP as a whole: voltages and currents
at the point of connection between the WPP and the public grid are due to sources inside of the
plant as well as due to sources outside of the plant. The transfer of harmonic emission from one
location to another is referred to here as harmonic propagation. The term propagation will be used
to refer to the appearance of harmonic voltages and current (or changes in existing levels) at a
certain location due to a harmonic voltage or current source at another location. The propagation
is strongly impacted by harmonic ampliﬁcation and attenuation in relation with resonances. This
chapter proposes a method for separating harmonic voltages and current at a certain location into
diﬀerent propagations or contributions from diﬀerent sources. The proposed method distinguishes
between the primary emission and secondary emission. This is the basic for a systematic approach
to study and simulate harmonic voltages and currents in and close to a WPP. When multiple
sources are present, the magnitude of the current due to all the sources together is less or equal
to the value when adding the magnitudes of the individual harmonic currents. This phenomenon
is called aggregation eﬀect or simply aggregation. The aggregation is due to diﬀerences in phase
angle between the harmonics from diﬀerent sources. In the terminology of this thesis: the larger
the diﬀerence between the two mentioned values, the more the aggregation.
Because of the importance of both magnitude and phase-angle in aggregation, the chapter
starts to present complex currents in ﬁeld measurements.
7.1
7.1.1
Complex Current
Transformation of Complex Current
A complex number can be expressed with real and imaginary parts, or in magnitude and phaseangle. The phase-angles of power system harmonics have been deﬁned in this thesis with reference
to the upward zero-crossing of the fundamental components of the corresponding phase-to-neutral
voltage. However, a waveform is not recorded from exactly this upward zero-crossing as a start of
the recording. Thus the complex harmonic is obtained from the DFT without a right phase-angle
reference. In this case, the transformation is needed of the obtained complex harmonic into a new
53
54
HARMONIC PROPAGATION AND AGGREGATION IN WPP
complex harmonic with the required reference. This transformation is presented in this section.
Consider an ideal voltage V (t) (at fundamental radian frequency ω0 ) as
V (t) = V0 sin(ω0 t + φ0 )
(7.1)
where V0 , φ0 are the fundamental frequency magnitude and phase-angle.
The phase angle used in the remainder of this chapter is the phase angle of the harmonic
voltage or current at the instant of the upward zero-crossing of the fundamental voltage. The
instant of the upward zero-crossing of the fundamental voltage is obtained from
ω0 t + φ0 = 0 or t = −
φ0
ω0
(7.2)
A distorted current at power-system frequency ω0 is expressed as
I(t) = I0 sin(ω0 t + φ0 ) +
∞
Ih sin(hω0 t + φh )
(7.3)
h=2
where I0 , φ0 are the fundamental magnitude and phase-angle of the fundamental frequency components; Ih , φh the magnitude and phase-angle at harmonic order h.
The phase angle of the harmonic current with new reference at order h is the diﬀerence between
the upward zero-crossing of the fundamental voltage and the phase with the old reference. The
phase angle for the new reference is obtained by substituting in equation (7.2):
φh = (hω0 t + φh ) − (ω0 t + φ0 )
= φh − hφ0
(7.4)
The complex harmonic rotates over an angle hφ0 compared to the upward zero-crossing of the
fundamental-frequency voltage. The modulus of the harmonic phase-angle after rotation can be
obtained in the range [0◦ , 360◦ ).
The transformation can also be represented in a diﬀerent way. Consider a harmonic current
complex number (obtained from (7.3)) at order h is Ih = Ireal + i × Iimag = |Ih |∠φh . According to
the phase angle reference, the transformed new vector in the reference complex plane reads as:
Ih = |Ih |∠(φh − hφ0 )
+ i × Iimag
= Ireal
(7.5)
where the two components of the new vector in the adjusted complex plane are obtained by the
transformation
cos(hφ0 ) − sin(hφ0 )
Iimag
] = [Ireal Iimag ]
(7.6)
[Ireal
sin(hφ0 ) cos(hφ0 )
The method is for any frequency, but not limited to integer harmonics. An equivalent harmonic
order can be written as h = ωω0 , where ω the radian frequency at an interested component and ω0
the power-system radian frequency.
55
7.1. COMPLEX CURRENT
100
0
800
60
600
40
H6
50
20
400
0
200
−100
−40
−100
0
100
200
H5
−400
300
−800 −600 −400 −200
0
200
H 11
100
100
50
0
0
−100
−300
−200
0
200
−50
0
−50
30
20
20
−50
0
20
H 17
50
10
0
100
0
−10
−20
H8
0
50
30
−30
−40
−20
0
20
20
H 10
20
10
10
0
50
H9
−60
−50
50
0
10
−40
−100
−200 −150 −100
0
−100
40
−20
−50
−200
H4
−80
150
H7
200
−50
−60
−200
H3
−300
Imaginary part of complex (inter)harmonic current [mA]
Imaginary part of complex (inter)harmonic current [mA]
−200
0
−20
0
0
0
−10
−10
−10
−50
−20
−20
−30
−30
−40
−20
H 13
−100
−100
−50
H 12
0
50
100
−30 −20 −10
Real part of complex (inter)harmonic current [mA]
0
10
20
−30
0
20
−20
−10
0
10
Real part of complex (inter)harmonic current [mA]
−20
(a)
20
30
(b)
50
500
IH 4
Imaginary part of complex (inter)harmonic current [mA]
0
−50
−50
IH 5
0
0
50
50
−500
−500
0
500
40
IH 6
IH 7
20
0
0
−20
−50
−50
150
0
−40
−40
50
100
100
50
50
0
0
−50
−50
−100
−150
−150 −100 −50
−20
0
20
150
285 Hz
40
385 Hz
−100
−150
0
50 100 150
−150 −100 −50
0
Real part of complex (inter)harmonic current [mA]
50
100
150
(c)
Figure 7.1: Scatter plots of complex currents for some typical frequencies (at phase A of Turbine II). (a) Characteristic harmonic (plus H 3) currents. (b) Non-characteristic harmonic (except H 3) currents. (c) Interharmonic currents. Note the diﬀerent scales.
7.1.2
Measurements of Complex Harmonics
A number of spectra (of the current for Turbine II) have been obtained from the measured 10cycle waveforms by applying the DFT, as explained in Chapter 5. The complex component at each
frequency has been transformed using the method presented in Section 7.1.1. The phase-A current
56
HARMONIC PROPAGATION AND AGGREGATION IN WPP
is chosen, thus with the upward zero-crossing of phase A-to-neutral voltage as the reference.
When plotting the complex harmonic currents for each frequency various patterns appear. In
general three types of patterns can be distinguished, the typical orders or frequencies for which
they occur have been presented in Figure 7.1.
• Characteristic harmonic (plus H 3) currents at integer harmonic orders H 3 (150 Hz), H 5
(250 Hz), H 7 (350 Hz), H 11 (550 Hz), H 13 (650 Hz), and H 17 (850 Hz). These complex
harmonics are distributed either along a line (H 3 and H 5) or along a curve (H 13), which
are oﬀset from the origin of the complex plane. Similar distributions are also observed for
other characteristic harmonics (not presented here).
• Non-characteristic harmonic (except H 3) currents at integer harmonic orders H 4 (200 Hz),
H 6 (300 Hz), H 8 (400 Hz), H 9 (450 Hz), H 10 (500 Hz) and H 12 (600 Hz). These complex
harmonics are centered on a point which is oﬀset from the origin of the complex plane. The
center point is diﬀerent for each harmonic. Note that, a small number of points clustered
around the origin represent the emission when the wind turbine is not producing any active
power. The other non-characteristic harmonics show a similar distribution as H 4. Additionally, harmonic orders higher than 20 present a center with less oﬀset from the origin.
• Interharmonic currents at centered interharmonic orders IH 4 (225 Hz), IH 5 (275 Hz), IH 6
(325 Hz), IH 7 (375 Hz), as well as components 285 Hz and 385 Hz. The scatter plots are
centered around the origin of the complex plane. The points in these scatter plots are
randomly distributed in the complex plane, which indicates a randomly distributed phaseangle. It is diﬀerent from the previous two types. The phase-angles of the interharmonics
are randomly distributed.
7.1.3
Statistics of Harmonic Magnitude and Phase Angle
Means and standard deviations of both magnitudes and phase-angles have been obtained from
the 1087 complex current values at each component of the 5 Hz frequency increment at Turbine II.
Next, the values for which the wind turbine was idle (or negative active power) have been removed
from the data set. Results are shown in Figure 7.2.
The main observations from Figure 7.2 are addressed and listed:
• The highest magnitude occurs for components at lower frequencies up to 400 Hz; means of
magnitude are high for integer harmonic orders and for interharmonics at 285 and 385 Hz.
The standard deviation of the magnitude is high, in several cases the standard deviation
exceeds the mean value.
• For many frequency components, including all interharmonic frequencies, the mean phase
angle is close to zero and the standard deviation
is close to 100◦ . For a uniform distribution
√
the values would be zero and 104◦ (360/ 12). This is another strong indication that the
phase angle is uniformly distributed for those frequencies.
• Both means and standard deviations of phase angles are diﬀerent from those of a uniform
distribution for most harmonics; especially for those at lower frequencies. Low standard
deviation is observed, e.g. harmonics 2, 3, 4, 6, 7, 10 and 11. This means that the complex
currents for those harmonics are found in a relatively small segment of the complex plane.
57
0.4
0.2
0.2
0.1
Mean Phase−Angle [Deg]
0
200
0
200
400
600
800
1000
1200
1400
1600
1800
0
2000
200
0
−200
100
0
200
400
600
800
1000 1200
Frequency [Hz]
1400
1600
1800
0
2000
Deviation Phase−Angle [Deg]Deviation Magnitude [A]
Mean Magnitude [A]
7.1. COMPLEX CURRENT
Figure 7.2: Means (red) and standard deviations (blue) of spectrum (component in 5 Hz increment) magnitudes and phase-angles. Note the diﬀerence in vertical scale between
mean and standard deviation in the upper plot.
Summarizing, a diﬀerence in distribution of the phase angle is observed for harmonics and
interharmonics, with the means and standard deviations for the phase angles of interharmonics
being close to those for a uniform distribution.
7.1.4
Test of Uniformity
The chi-square goodness-of-ﬁt test has been used to decide of distribution of the phase-angles of
complex currents is uniform at each frequency for Turbine II. This test has been performed on a 95
percent signiﬁcance level using the Matlab function chi2gof. The distribution is marked “uniform”
when the chi-square goodness-of-ﬁt test passes with the indicated signiﬁcance level; otherwise the
distribution is marked “non-uniform”. The uniform and non-uniform distributions are shown in
Figure 7.3.
Magnitude [A]
0.2
0.1
0.05
0
0.06
Magnitude [A]
Uniform
Non−Uniform
0.15
0
100
200
300
400
500
600
700
800
Uniform
Non−Uniform
0.04
0.02
0
1900
2000
2100
2200
2300
2400
Frequency [Hz]
2500
2600
2700
2800
Figure 7.3: Current magnitude spectrum (5 Hz increment) with uniform (marked with red dots)
and non-uniform (marked with blue stars) distributions of the phase-angles. Upper
ﬁgure: 0 - 800 Hz; lower ﬁgure: 1.9 - 2.8 kHz.
The red dots represent the frequency components with uniformly distributed phase-angles;
58
HARMONIC PROPAGATION AND AGGREGATION IN WPP
and the blue stars represent those with non-uniform distributions. The results show that: most
distributions of phase-angles for harmonics are non-uniform; these of many components below
100 Hz and around 500 Hz are also non-uniform; and those of interharmonics are in most cases
uniform.
The distribution of the phase-angle has a signiﬁcant impact on the aggregation of the emission
from individual turbines into the emission from a WPP, which will be studied in Section 7.3.
7.2
Harmonic Propagation and Transfer Function
The harmonic study in a wind power plant concerns multiple wind turbines, the collection grid,
and the public grid (either at transmission level or at distribution level) to which the plant is
connected. Harmonic distortion originates from diﬀerent sources: wind turbines, the background
harmonic distortion from the public grid (due to all other harmonic sources connected to the grid),
and any other harmonic sources in the collection grid (e.g. STATCOM).
At the terminal of a wind turbine, propagation of harmonic distortion is not only from this
turbine into the grid (to other turbines and the public grid), but also from other turbines to this
turbine and from the public grid to this turbine. The harmonic voltage and current at a certain
node is the result of the harmonic propagations from all sources to and from this node.
7.2.1
Harmonic Contributions
There are various harmonic sources in a power system, with propagation from any source to any
node in the network. Depending on the object studied, harmonic propagations with respect to
various harmonic sources in a power system can be divided in two groups: the primary emission
(P) and the secondary emission (S). A primary emission is the emission originated from the object
that is studied, e.g. the emission originated from one individual wind turbine when studying the
turbine emission. The secondary emission is the emission originated from anywhere else. To have
a harmonic study in a systematic approach, the diﬀerent contributions to harmonic voltages and
currents are classiﬁed according to their source and their propagation. The diﬀerent contributions
to the emission are illustrated with the example conﬁguration of a wind power plant (with ﬁve
turbines), as shown in Figure 7.4.
The detailed contributions to harmonic voltages and current, referring to Figure 7.4, are explained and listed in the following:
• P1: the primary emission from one wind turbine to the public grid; for instance the emission
(red arrow) from T1 to the public grid through the substation transformer as illustrated in
Figure 7.4 (a);
• P2: the primary emission from one wind turbine to another wind turbine in the collection grid; for instance the emission (blue arrow) from T1 to the other four turbines in
Figure 7.4 (a);
• P3: the total primary emission of a WPP; it is the sum of contributions of all wind turbines
to the primary emission of a whole WPP; for instance the emission (purple arrow) ﬂows
from the PoC to the public grid in Figure 7.4 (b);
59
7.2. HARMONIC PROPAGATION AND TRANSFER FUNCTION
• S1: the secondary emission from the public grid to a studied wind turbine; the emission (light
green arrow) ﬂows from the public grid to the ﬁve wind turbines as in the Figure 7.4 (b);
• S2: the secondary emission from another turbine to a studied wind turbine; this is the similar
propagation as P2 but seen from the viewpoint of the turbine at the receiving end; this is
not shown in the ﬁgure;
• S3: the secondary emission from the public grid to a WPP; the emission (dark green arrow)
ﬂows from the public grid to the PoC as shown in Figure 7.4 (b);
• S4: the overall secondary emission from all other turbines to a studied wind turbine; this is
the sum of all secondary emission S2 to the studied turbine; not shown in the ﬁgure.
(a)
(b)
Figure 7.4: A classiﬁcation of harmonic propagation in an example WPP with ﬁve wind turbines.
(a) Classiﬁcation of P1 and P2 (both from T1). (b) Classiﬁcation of P3, S1 and S3.
7.2.2
Quantifying Harmonic Propagation
In this chapter, voltage or transfer function, the transfer impedance and transfer admittance are
used for the quantiﬁcation of harmonic propagation in a network. The deﬁnitions of voltage or
current transfer function, transfer impedance and transfer admittance are given below.
Suppose a harmonic source at node A (as an input) and the resulting distortion at node B (as
an output) are of interest. The complex voltage and current at node A, as a function of frequency
A
A
B
B
f , are written as U f and I f ; and at node B they are U f and I f .
60
HARMONIC PROPAGATION AND AGGREGATION IN WPP
The transfer function is deﬁned as the (dimensionless) ratio of the output and the input, either
for voltage or current. The voltage transfer function is written as:
B
U
H f,A,B =
Uf
A
(7.7)
Uf
The current transfer function is written as:
B
I
H f,A,B =
If
A
(7.8)
If
The transfer impedance is deﬁned as the ratio of output voltage and input current with a unit
of Ω (Ohm):
B
Uf
Z f,A,B = A
(7.9)
If
As well the transfer admittance is deﬁned as the ratio of output current and input voltage with
a unit of S (Siemens) or 0 (Mho):
B
If
Y f,A,B = A
(7.10)
Uf
To study the harmonic voltage at the destination node, the formulae (7.7) and (7.9) can be
used; to study the harmonic current at the destination the formulae (7.8) and (7.10) can be used.
Furthermore, (7.7) and (7.10) are for a harmonic voltage input, while (7.8) and (7.9) are for a
harmonic current input. Depending on what type of harmonic source and the interested type of
output harmonic, any of the above combinations can be used.
7.2.3
Overall Transfers
For a WPP the term “overall transfer function” is deﬁned as the transfer function from all turbines
together to the node of interest, e.g. the PoC. The overall transfer function is obtained from all
the complex individual transfer functions with the inputs of complex voltages and currents. The
overall transfer function is not just a property of the network but it also includes properties of
the sources. Based on the distribution of the phase angle of the complex harmonic sources two
extreme aggregation cases are considered: with identical phase-angle for all emitting sources and
with uniformly-distributed phase-angles for all emitting sources. Both the phase shift of individual
transfer functions (from wind turbines) and the phase-angle diversity of harmonic sources result
in the cancellation of overall harmonic emission, which is the eﬀect of harmonic aggregation.
Harmonic aggregation is discussed in more detail in Section 7.3.
The overall transfer function, when assuming identical phase-angle, is obtained by summarizing
all the magnitudes of transfer functions and is written (in absolute value):
Hf,identical =
N
|H f,i |
i=1
where H f,i is the transfer function from the i-th turbine to the studied node.
(7.11)
61
7.3. HARMONIC AGGREGATION
The overall transfer function, when assuming uniformly-distributed phase-angles, is obtained
under the square-root-rule:
N
Hf,unif orm = |H f,i |2
(7.12)
i=1
The similar deﬁnitions have been made for the “overall transfer impedance” and “overall
transfer admittance”. The overall transfer impedance is deﬁned as:
Zf,identical =
N
|Z f,i |
(7.13)
i=1
Zf,unif orm
N
=
|Z f,i |2
(7.14)
i=1
The overall transfer admittance is deﬁned as:
Yf,identical =
N
|Y f,i |
(7.15)
i=1
Yf,overall
N
=
|Y
f,i |
2
(7.16)
i=1
7.3
7.3.1
Harmonic Aggregation
Aggregation of Harmonic Propagations
The harmonic distortion at certain node originates from propagations of all harmonic sources
in the network. For a WPP, the harmonic sources are mainly wind turbines, possible reactive
power compensation, nearby harmonic sources in the grid, and the power system background
distortion. In this section inside a WPP harmonic sources from wind turbines are considered, and
the background voltage distortion is considered on the public grid side.
When the harmonic sources and the transfer functions are known, the levels of harmonic
distortion can be obtained. When considering complex currents, the harmonic distortion at a
node L (at turbine terminals or PoC in this section) is the summation of the propagations from
all harmonic sources, which is written as:
grid
I f,L = U f
× Y f,grid,L +
N
H f,i,L × I f,i
(7.17)
i=1
grid
where U f is the background voltage distortion at the public grid, Y f,grid,L is the transfer admittance from the public grid to L, I f,i is the current harmonics at the i-th turbine, and H f,i,L is the
current transfer function from i-th turbine to L.
An individual wind turbine is assumed to be a current harmonic source in the study. A
measurement shows that the voltage spectrum at a turbine terminal is close to the voltage spectrum
62
HARMONIC PROPAGATION AND AGGREGATION IN WPP
at the PoC of the WPP; while the current spectrum of a turbine presents speciﬁed characteristics
[86]. Current emission is diﬀerent due to manufactures, models, turbine types, topologies, control
algorithms, etc. A turbine model is not the scope of this thesis, instead a current harmonic source
is used.
The harmonic currents at destinations in a WPP are studied in this thesis. The formulae (7.8)
and (7.10) are chosen in the chapter, due to harmonic current sources for the wind turbines and
the background voltage distortion from the public grid.
In many cases, not only the total harmonic distortion is of interest. The contributions from
certain harmonic sources are also of interest, e.g. the contribution of harmonic distortion from a
WPP, and the contribution from the background distortion. As a part of the total distortion in
(7.17), the harmonic distortion from the WPP to the public grid (the overall harmonic distortion
from all turbines to the PoC) is written as:
I f,grid =
N
H f,i,grid × I f,i
(7.18)
i=1
The contribution of the background harmonic distortion from the public grid to the PoC of
the WPP is written:
grid
I f,P oC = U f × Z f,grid,P oC
(7.19)
The harmonic aggregation happens naturally by the summation of all complex harmonic distortion. In other words, harmonic distortion has been cancelled due to diﬀerent phase angles of
contributions from all sources. The magnitude of the resulted harmonic distortion is never the
same as the sum of magnitudes from all contributions (with diﬀerent phase-angles). The extent of
harmonic aggregation (“aggregation factor” has been introduced in Section 7.3.2) is determined by
the diﬀerence between the total harmonic magnitude and the sum of contributions in magnitude
from harmonic sources. The larger the diﬀerence, the more the aggregation is.
The harmonic aggregation rule is set with a ﬁx “aggregation exponent” for four groups of
distortion in IEC 61000-3-6: low-order harmonics (H 2 - H 4), harmonics (H 5 - H 10), high order
harmonics (above H 10) and interharmonics. The harmonic aggregation has been presented in [87]
in a similar trend but in a diﬀerent way by using “aggregation factor”. An aggregation factor,
which is dimensionless, has been deﬁned as the ratio of the total emission and the sum of all
contributions of sources in magnitude. The aggregations are identiﬁed between each harmonic and
interharmonic order but in general they are grouped mainly into: harmonics (diﬀerence between
low-order and high-order) and interharmonics.
7.3.2
Case Study of Turbine Aggregation
A case study with ten-turbine WPP (as in Figure 7.5) from [88] has been performed for the
aggregation model.
The WPP consists of ten wind turbines, which are distributed uniformly over two feeders. On
each feeder, the distance between neighboring turbines is 320 m. A single substation transformer
with 110/30 kV, 30 MVA rating and 10% impedance (with an X/R ratio of 12), is connected to a
grid with a fault level of 800 MVA. The cable has a resistance of 0.13 Ω/km at 50 Hz, capacitance
of 0.25 μF/km and inductance of 0.356 mH/km.
The frequency-dependent circuit as in [89] is modeled: cables are represented by Π model with
f αc
frequency-dependent resistance (R(f ) = R50 × ( 50
) , with a damping exponent αc = 0.6); and
7.3. HARMONIC AGGREGATION
63
Figure 7.5: Case Study: A ten-turbine WPP conﬁguration.
transformer frequency-dependent resistance damping exponent αt = 1.0. The conﬁguration of the
WPP is symmetrical (for the upper and lower ﬁve turbines), thus the current transfer functions
(from medium voltage side of turbine transformer to the collection grid) are also symmetrical.
The equivalent model of the harmonic propagation from one wind turbine to the grid is shown
in Figure 7.6.
Figure 7.6: Equivalent circuit of the transfer from a single turbine to the public grid.
The details of Figure 7.6 are explained:
• C1 = 12 (l1 + l2 )C, the left-half cable capacitance according to the Π-circuit model (which
consists of left-half capacitance, resistance, inductance and right-half capacitance), which
involves the cables length l1 (from the turbine to the busbar) and l2 (rest of the cable
feeder);
• C2 = 12 l2 C, the right-half capacitance of cable of length l2 ;
• L2 = l2 L, the inductance of the cable of length l2 ;
• R2 = l2 R, the resistance of the cable of length l2 ;
• L3 = l1 L, the inductance of the cable of length l1 ;
• R3 = l1 R, the resistance of the cable of length l1 ;
• C3 = ( 21 l1 + 12 l3 )C, the right-half capacitance of the cable of length l1 and the left-half
capacitance of the other cable feeder;
• C4 = 12 l3 C, the right-half capacitance of the other cable feeder;
• L4 = l3 L, the inductance of the other cable feeder;
• R4 = l3 R, the resistance of the other cable feeder;
64
HARMONIC PROPAGATION AND AGGREGATION IN WPP
• L5 , the inductance of the transformer, any lines and cables on primary side of the transformer
and the inductance of the grid;
• R5 , the resistance of the transformer, any lines and cables on primary side of the transformer
and the resistance of the grid.
With the impedance Z12 replaces C1 , C2 , R2 and L2 ; and the impedance Z34 replaces C3 , C4
and L4 . The transfer function from the turbine to the grid Htg (ω) is obtained as a function of the
frequency ω:
Htg (ω) =
Z34
Z12
×
Z34 + jωL5 + R5 Z12 + (jωL3 + R3 ) +
Z34 ×(jωL5 +R5 )
Z34 +(jωL5 +R5 )
(7.20)
2
Input
Output 1.5
385Hz
285Hz
0.1
1
0.05
0
50
0.03
0.5
100
150
200
250
300
350
400
450
0.02
0.01
0
1300
0
500
0.3
Input
Output
0.2
0.1
1400
1500
1600
Frequency [Hz]
1700
1800
0
1900
Output Harmonics [A]
0.2
0.15
Output Harmonics [A]
Input Harmonics [A]
Input Harmonics [A]
The transfer functions present a parallel resonance at 1.585 kHz with maximum transfer of
16.49, for all the turbines. The transfer function is around unity below the resonance frequency
and decaying to zero above the resonance frequency.
The 1087 measured complex currents (frequency components in 5 Hz resolution) of Turbine II
are used as input to a stochastic model. The primary emission of individual turbines is obtained
randomly from the 1087 complex currents. The primary emission of the WPP is obtained by
applying the summation of the complex harmonic current, in a 5 Hz frequency increment.
The scenario has been repeated 100,000 times resulting in 100,000 complex currents. The
average spectrum (RMS spectrum) of these complex currents is obtained as the emission of the
WPP.
The average spectrum of the individual wind turbine (input) and the whole WPP (output)
from the Monte-Carlo Simulation have been presented in Figure 7.7. Note the factor of 10 (the
number of turbines) between the two scales.
Figure 7.7: Zoomed input average spectrum (blue lines and left vertical scale) and output average
spectrum (green lines and right vertical scale) at the collection grid after aggregation.
Upper ﬁgure: 50 Hz - 500 Hz; lower ﬁgure: 1.3 kHz - 1.9 kHz.
The spectrum at lower-order harmonics (upper ﬁgure) is about the same for an individual turbine as for the WPP (i.e. about a factor 10 higher for the WPP). The emission for interharmonics
is lower for the WPP as a whole than for the individual turbines. The emission around 1.55 kHz is
ampliﬁed for broadband and narrowband due to resonances in the collection grid. For frequencies
above about 1.75 kHz, the emission from the WPP is again smaller than ten times the emission
from one turbine.
65
7.3. HARMONIC AGGREGATION
The diﬀerence between the two levels in Figure 7.7 indicates an aggregation of harmonic distortion. In this thesis, the term “aggregation factor” is introduced to quantify the harmonic
aggregation (the collecting of units or parts in to a mass or a whole). The aggregation factor has
been deﬁned as the ratio of the emission from the WPP into the public grid and N times (the
number of turbines in the WPP) of the emission from an individual turbine, which the result is
shown in Figure 7.8.
15
Aggregation factor
10
5
0
0
500
1000
1
1500
2000
2500
3000
15
10
0.5
5
0
200
400
600
800
1300 1400 1500 1600 1700 1800
Frequency [Hz]
Figure 7.8: Aggregation factor (blue line, ratio of WPP emission and ten times of turbine emission)
and overall transfer function with identical phase-angle (solid red line) and uniform
phase-angle (solid green line).
The aggregation factor is obtained using the stochastic model, which is marked in blue line; the
aggregation factor with the “uniform phase angle” is marked with the green curve; the red curve
corresponds to “identical phase angle”. The diﬀerence in aggregation factor between interharmonics and harmonics up to about 1650 Hz, is clearly visible. For most interharmonic frequencies, the
uniform phase angle model is a good approximation.
The aggregation factor calculated from the stochastic model is between the results for identical
phase-angle (solid red line) and for uniform phase-angle (solid green line). The aggregation factor
of the interharmonic components is close to the transfer function with uniform phase-angle. The
aggregation factor for integer harmonics at lower frequencies is closer to the transfer function
with identical phase-angle. The lowest aggregation factor below the resonance√peak is obtained
at interharmonics in the low-frequency range. The value is around 0.316, or 1/ 10.
Thus the aggregation diﬀers for lower-order harmonics (mainly at characteristic harmonics),
higher-order harmonics and interharmonics.
The aggregation of harmonic distortion has been studied also for diﬀerent power bins, as in
Paper G. In general there is no signiﬁcant diﬀerence between diﬀerent power bins. With increasing
power production certain harmonics aggregate more, while others aggregate less. The aggregation
of interharmonics is however not impacted by the power production.
7.3.3
Case Study of Total Aggregation
Another case study has been presented in this section. The studied WPP is conﬁgured the same
as in Figure 7.4. As well the parameters of components are the same as in Section 7.3.2, with the
66
HARMONIC PROPAGATION AND AGGREGATION IN WPP
exceptions that: there are ﬁve wind turbines in this case study, and the distance between two
neighboring turbines is 1 km.
Additionally, the impedance on the turbine-side of the turbine transformer is modeled as a
series impedance representing the turbine-transformer (2.5 MVA, 6% leakage impedance) and a
series impedance representing the converter reactor (4 MVA, 10%). Only if a turbine is located at
the output node of a propagation, is it modelled as a ﬁnite impedance. Otherwise, the impedance
of the turbines is assumed to be inﬁnite.
Similar as the classiﬁcations of harmonic emission, a harmonic transfer is also speciﬁed with
primary or secondary transfer (transfer function, transfer impedance and transfer admittance),
which is determined by the object studied.
Harmonic sources considered in this case study are the current harmonic sources from wind
turbines, and the background voltage source from the public grid. The former is set with the
number of complex harmonic currents at Turbine II. The background voltage harmonic levels are
set equal to one third of the MV planning level in IEC 61000-3-6; one third of the compatibility
levels for interharmonics that at 0.2% of the fundamental voltage, according to IEC 61000-2-2.
The phase angles are assumed to be zero.
The average spectrum has been obtained, by using of Monte-Carlo Simulation, for the secondary emission from the public grid to all ﬁve turbines, the secondary emission from other four
turbines to T5 (as in Figure 7.4), and the total harmonic distortion at T5 due to all sources, as
shown in Figure 7.9.
3
Grid − T1, S1
Grid − T2, S1
Grid − T3, S1
Grid − T4, S1
Grid − T5, S1
2
1
0
0.1
500
1000
1500
2000
2500
Current [A]
T1/2/3/4 − T5, S2
0.05
0
3
500
1000
1500
2000
2500
Total Emission at T5
2
1
0
500
1000
1500
Frequency [Hz]
2000
2500
Figure 7.9: Upper ﬁgure: secondary emission from the public grid to the turbines (emission classiﬁcation: S1); middle ﬁgure: secondary emission from other turbines to T5 (emission
classiﬁcation: S2); lower ﬁgure: the total emission at T5 due to all the turbines and
the public grid.
In the upper ﬁgure, the harmonic distortion (secondary emission) from the public grid comprises of a smooth broadband with a resonance at around 1.3 kHz, and narrowband components
(at integer harmonic orders) with a dominating emission below 500 Hz. The dominating emission
is located at the lower-frequency narrowband components.
67
7.3. HARMONIC AGGREGATION
In the middle ﬁgure, the secondary emission from other turbines are mainly at low frequency
(below 500 Hz) emission with narrowband components at integer harmonics, and with manifest
narrowband components around the resonance (around 1.3 kHz). Compared to the emission from
the grid the emission from other turbines is very low, about one thirtieth of the former. This
is the case of harmonic aggregation between the secondary emission from other turbines to one
turbine.
In the lower ﬁgure, the total emission (primary and secondary) at T5 is dominating with the
low-frequency (below 500 Hz) narrowband components at integer harmonics from the public grid.
The resonance is visible in the spectrum, whereas it is low compared to that from the grid. Thus
the background distortion has an important impact on the harmonic distortion at a turbine. In
this case, the harmonic aggregation is between both the primary emission from the turbine, the
secondary emission from other turbines and the secondary emission from the public grid. The
aggregation is due to the summation as in (7.17), where the contribution from the public grid
is secondary emission, and except the studied turbine (primary emission) the contributions from
other turbines are secondary emission.
The contributions of harmonic distortion at the PoC of the WPP have been studied in a similar
way. The total harmonic emission at the PoC originates from all turbines and the public grid.
The harmonic emission contributed from all turbines, contributed from the public grid and the
total emission at the PoC are presented in Figure 7.10. Note that the vertical scale of the upper
ﬁgure is one tenth of those in the middle and lower ﬁgures.
1.5
T1/2/3/4/5 − Grid, P3
1
0.5
Current [A]
0
500
1000
1500
15
2000
2500
Grid − WP, S3
10
5
0
500
1000
1500
15
2000
2500
Total Emission at PCC
10
5
0
500
1000
1500
Frequency [Hz]
2000
2500
Figure 7.10: Upper ﬁgure: primary emission from all turbines to the public grid (emission classiﬁcation: P3); middle ﬁgure: secondary emission from the public grid to the WPP
(emission classiﬁcation: S3); lower ﬁgure: total emission at the PoC. Note the diﬀerence in vertical scale between the upper plot and the other two.
In Figure 7.10 the dominating emission from the turbines is present as narrowband components
below a few hundred Hz (integer harmonics mixed with a few interharmonics around IH 5 and
IH 7) and some narrowband components at the resonance frequency. The harmonic source from
the turbines excites the resonance at the broadband, and it results the manifest emission.
68
HARMONIC PROPAGATION AND AGGREGATION IN WPP
Unlike the distortion at T5, the harmonic contribution from the public grid can be found
mainly at the resonance frequency (around 1.3 kHz), with a broadband component and narrowband
components. The emission below 1 kHz and above 1.5 kHz is low compared to those around the
resonance frequency.
Consequently the total emission presents a dominant emission around the resonance frequency,
and a visible but low emission below 1 kHz. Conclusively the resonance in the WPP plays an
important role in the harmonic distortion. As well there is harmonic aggregation between the
primary emission from the WPP and the secondary emission from the public grid.
7.4
7.4.1
Discussion
Primary and Secondary Emission
Harmonic measurements in a WPP have been compared for the two locations: one at the PoC of
the WPP and the other is at one wind turbine. The comparison is shown in Figure 5.7.
The two upper ﬁgures present almost the same voltage spectrum, either at the individual
turbine or at the PoC. The voltage broadband around H 13 is dominant in the spectrum. It is due
to the ampliﬁcation of the collection grid in combination with the background voltage distortion.
This voltage ampliﬁcation is almost the same throughout the collection grid. This dominant
voltage distortion causes the harmonic currents as shown in the two lower ﬁgures. Consequently
the emission around H 13 is dominant by the secondary emission from the external grid.
Figure 5.9 (a) presents two linear lines of voltage versus current harmonics. The linear line
with a higher slope is at the idle states, which the presented voltage versus current is due to the
distortion from external (from the grid and other turbines). It indicates the secondary emission
to the studied turbine. The line of a lower slope is at the turbine operational state. At this
state, the measured harmonic distortion include both the primary emission from the turbine and
secondary emission from other turbines and the public grid. Figure 5.9 (b) presents both primary
and secondary emission.
7.4.2
Aggregation in Measurements
The 95-percentile levels of currents at one wind turbine and the WPP have been presented in
Figure 5.7 (c) and (d). Although measurements at the both locations are mixed with primary and
secondary emission, the ratio (aggregation factor as presented in Section 7.3.2) of the emission
(harmonics and interharmonics) at the PoC and 14 times the turbine is obtained and presented
in Figure 7.11.
69
7.4. DISCUSSION
X: 7
Y: 1.781
Aggregation factor
2
X: 11
Y: 2.071
1.5
X: 13.5
Y: 1.351
1
0.5
0
5
10
15
20
25
Harmonic Order
30
35
40
Figure 7.11: Aggregation factor (ratio) of wind power plant emission and 14 (the number of turbines in the WPP) times wind-turbine emission. Note that the ratio is obtained from
the 95-percentile values.
The measurements show that, aggregation factors at harmonic orders are higher than those of
interharmonic orders. This indicates again larger cancellation of interharmonics than harmonics.
Among these orders, H 7 and H 11 are manifest. Additionally the ampliﬁed orders around H 13 are
seen in a broadband, around the resonance frequency. The low aggregation factor of harmonics
and interharmonics above H 15 are manifest compared to the ampliﬁed broadband around H 13.
The phenomena are similar with the case study in Section 7.3.2.
7.4.3
Uncertainty of Damping
The harmonic study based on models with frequency-dependent resistance has been performed in
both matlab and PowerFactory DIgSILENT. The sensitivity study of cable frequency-dependent
exponent has been performed and the results are shown in Figure 7.12.
1
10
0
Impedance [Ω]
10
WT4
0.6
−1
10
WT90.6
WT40.8
WT9
0.8
−2
WT41.0
10
WT91.0
0
500
1000
1500
2000
Frequency [Hz]
2500
3000
3500
Figure 7.12: Sensitivity study of cable damping exponent αc at 0.6, 0.8 and 1.0 for a nine wind
turbines; impedance seen from wind turbine 4 (WT4) and 9 (WT9) into the grid
performed in PowerFactory DIgSILENT.
There are 9 wind turbines distributed on two feeders in the model, with wind turbine 4 (WT4)
and wind turbine 9 (WT9) at the ends of the two feeders. The impedances seen from the turbines
into the grid are shown with the cable damping exponents 0.6, 0.8 and 1.0.
70
HARMONIC PROPAGATION AND AGGREGATION IN WPP
It is shown that, the impedances at the peaks (parallel resonance and series resonance) are
diﬀerent with diﬀerent damping exponents, while others show no diﬀerence. The impacts would
be on the damping of a resonance.
The damping exponents αc = 0.4, αtrf = 0.8 give the magnitude of the ﬁrst resonance 30.53,
and the second 0.25. Using αc = 0.2, αtrf = 0.6 gives 56.86 and 0.7.
The uncertainty of damping will impact the contents of harmonic distortion at resonances.
A lower damping makes possible emission at a resonance point obvious and even dominating in
a spectrum. Whereas the impacts on a non-resonance point are not manifest, as shown in the
ﬁgure. An accurate systematic harmonic study requests the support of a detailed model for the
network property of harmonic ampliﬁcation and attenuation. Both the low-frequency emission and
the resonance point impact the total emission. The impact of the damping may only determine
whether the emission at the resonance point is dominating.
Part IV:
Discussions and Conclusions
71
Chapter
8
Discussion
8.1
Measurement Accuracy
Measurement errors are a natural part of all practical experiments and measurements. This thesis
is based on the analysis of ﬁeld measurements at wind power installations. It is therefore important
to consider the measurement error in the analysis as well as how this may impact the conclusions.
This section discusses the possible origins of measurement error and contains an estimation on
the size of the measurement error. A number of examples are discussed as part of this estimation.
8.1.1
Error Origins
Three types of measurement error can be distinguished with measurements of harmonic voltages
or currents:
• errors due to the instrument transformers (voltage and current transformers);
• errors due to the power quality monitor (a Dranetz instrument was used for most of the
measurements used in the thesis);
• errors due to the data processing (e.g. the FFT algorithm).
The frequency response of an instrument transformer is an important issue that limits the
accuracy. The power quality monitor used for the measurements in the thesis is designed with
an enough accurate frequency response up to a few kHz, complies with IEEE 1159, IEEE 519,
IEEE 1453, IEC 61000-4-30 Class A and EN50160. Anyhow, quantization noises may be a possible error. Additionally the data processing from a measurement setup may introduce things like
aliasing, spectra leakage.
Instrument transformer:
There are a number of references on testing of an instrument transformer. Tests presented in an
earlier paper [17,79,80], conclude that harmonic measurements with a normal current transformer
up to 10 kHz have an accuracy better than 3%. A few tests show however also that the frequency
responses are quite diﬀerent for diﬀerent brands of current transformers, for frequencies above
10 kHz. The harmonic study based on measurements in this thesis is mainly up to 2.5 kHz. It is
73
74
DISCUSSION
therefore concluded that the measurement error due to the instrument transformer is within an
acceptable range.
Noise level:
The term “noise level” concerns both thermal noise and quantization noise. Both of the noise
levels are time independent. They do not vary in relation with another parameter, e.g. in step
with active-power production. The noise level is therefore at most equal to the lowest levels of
measured emission. The discussion below is focused on the quantization noise.
Quantization noise (or quantization error) is introduced by the AD converter in the powerquality monitor. The quantization noise sets a limit on the detection of small levels of harmonic
voltages and currents. Under the assumption that quantization noise has a ﬂat spectrum, the high
levels in some broadband parts of the spectrum, cannot be quantization noise [90]. A number of
examples are to be discussed for the quantization noise in the following paragraphs.
In Figure 5.2, the averaged frequency-component presents a smooth broadband. For Turbine II
(middle ﬁgure), the emission levels in the band between 500 and 2000 Hz are very low. A similar
low level is also present in the frequency range of 2.7 to 3 kHz. Similar bands with low emission
are visible for Turbine III (lower ﬁgure). The observation that the broadband emission is limited
to certain bands (broadband but not covering the whole spectrum) clearly indicates that this is
unlikely to be due to quantization noise.
Similar phenomena are observed in Figure 5.3, Figure 5.4 and Figure 5.5. During the idle state
of the turbine the broadband emission is very low or not present at all (visible as a dark blue color
in the ﬁgure). The emission level visible as an orange color in operational states, compared to
the emission level as a dark blue color in the same duration, is unlikely to be due to quantization
noise.
In Figure 5.6, the 95- and 99-percentile values present an almost ﬂat broadband spectrum
(combined with narrowbands) in the frequency ranges between 500 to 1700 Hz and 2.7 to 3 kHz.
Compare to these low levels, the spectrum in the switching frequency range 1.7 to 2.5 kHz is
excluded to be quantization noise.
Figure 5.9 (a) shows low emission levels of harmonic voltages versus harmonic currents; almost
linear lines are visible below 0.05 A. The linear trend is clear for the line with the higher slope and
the scatter points are less spread from the linear line. An error (e.g. quantization noise) of the
low emission level of either voltage or current will make the scatter plots deviate from the linear
line.
More plots at individual (inter)harmonic orders in Figure 5.11 present less spread of current
emission as a function of active-power production, even at harmonic order up to 40. These trends
are obvious with certain patterns, but not visible with a noticeable error.
8.1.2
Distortion Level versus Power and Relations between Frequencies
Some of the measurements presented in Chapter 6 show strong correlations that cannot be explained if the observed harmonic levels would be merely measurement errors. An example of such
is the relation between interharmonics and active-power, as shown in Figure 6.3 and ﬁgure 6.8 (a).
The magnitude of interharmonics increases linearly with active-power. The linear relation exists
at diﬀerent frequencies, for example at 15 Hz but also at 720 Hz. The measurements also show a
strong correlation in magnitude between the 285 and 385 Hz components; and between the 620 and
720 Hz components. This strong correlation would not be visible if the interharmonic components
8.2. IMPACTS OF COMPONENTS IN COLLECTION GRID
75
would be strongly impacted by measurement noise and spectral leakage.
Another indication that noise levels are low, comes from the linear scatter plots of voltage
versus current at a number of frequencies, as shown in Figure 6.5. Voltages and currents are
obtained separately from diﬀerent instrument transformers (a VT and a CT). Noise is therefore
very unlikely to impact both voltage and current in the same way. The clear and strong correlation
of signals from two instruments conﬁrms the high enough measurement accuracy. Additionally the
linear trends are observed down to the mA level in current and down to the volt level in voltage.
The presence of linear lines of diﬀerent frequency pairs is the third indication in Chapter 6, as
shown in Figure 6.6 and ﬁgure 6.8 (b). The straight and less spread lines, which even from the mA
level to 0.03 A, are manifest in the ﬁgure.
The number of examples, among other analyzed results, indicate that the measurement errors
are low enough and the measurements are accurate enough to perform the harmonic analysis and
characterizations for distortion up to a few kHz.
8.1.3
Spectrum Leakage
The harmonic measurements have been performed based on 10-cycle waveforms with sampling
frequency of 256 samples per cycle. For a 50-Hz power-system frequency the sampling frequency
is 12.8 kHz. The corresponding frequency resolution, with a 200-ms window, is 5 Hz. The reason
for the sampling frequency being synchronized to the fundamental frequency is that this avoids
spectral leakage from the fundamental frequency to harmonic frequencies and between harmonic
frequencies. It does however not avoid spectral leakage to and from interharmonics.
Wikipedia states that “leakage caused by windowing is a relatively localized spreading of
frequency components, with often a blurring eﬀect”. Spectrum obtained from a sample by DFT
shows the value at each frequency-component in a certain frequency resolution. When an actual
sinusoid frequency lies in the component with the same frequency, its level is correctly represented;
otherwise there is spectral leakage. The presence of the level on other frequencies depends on the
window type and the frequency of the interharmonic component.
In the thesis spectral components are presented at each frequency component in 5 Hz step
with DFT. In the case that an interharmonic component is at frequency of one of the 5 Hzstep frequency, the accurate frequency and magnitude are observed in the processed spectrum;
otherwise if the interharmonic is at a frequency beyond any of the 5 Hz step frequency, the leakage
occurs; the actual component is not shown at the exact frequency but instead the side band of the
accurate component appears at nearby 5 Hz-step components. For example, the number of scatter
plots not on the triangle slope indicates the spectral leakage for Turbine III as in Figure 6.3.
Despite the leakage, Figure 6.2 and Figure 6.7 present the changing of the strong frequency
pairs.
8.2
Impacts of Components in Collection Grid
For a wind power plant, the ﬁrst resonance frequency can be approximated from the total capacitance and total inductance of the system. Other resonances occur at higher frequencies, where
parts of the capacitances and inductances determine the resonance frequency. The magnitude of
the transfer functions is inﬂuenced by the combination of all those resonances. Above the ﬁrst
resonance frequency, the ﬁrst resonance attenuates the transfer. At the higher resonance frequencies, the transfer function will contain a damping from the lower resonances together with an
76
DISCUSSION
ampliﬁcation from the actual resonances. The studies presented in this thesis show that the net
eﬀect is an attenuation of the transfer. From this it can be concluded that the ﬁrst resonance peak
is the most important one and that emission at frequencies a few times above the ﬁrst resonance
peak is normally less of a concern for the WPP as a whole.
The transfer functions used in the thesis are determined by the component capacitances, inductances and resistances. Beyond resonances, the transfer functions are much impacted by the
frequency-dependent resistance, which is the main cause of an attenuation. In general the higher
the frequency, the higher the resistance is. Consequently attenuation is stronger at higher frequencies.
The ampliﬁcation at the resonance frequency depends on the damping factor. Detailed modelling of a turbine equivalent circuit, a collection grid and the public grid, is needed for an accurate
harmonic estimation in a system due to the sensitivity of (inter)harmonic ampliﬁcation and attenuation. Additionally, resonances are an important issue for a wind power plant equipped with
cables, which are dominant with capacitance. Whereas a WPP equipped with overhead lines,
which are dominant with inductance, is supposed to have a higher resonance frequency that may
be attenuated a lot. A WPP with overhead lines is not considered in the thesis.
The damping exponent is an important parameter for a frequency-dependent resistance. The
parameter is determined by a number of issues, such as temperature, materials of a conductor,
cross-section of the conductor. Fortunately the attenuation is less impacted, except at the resonance point, up to a few kHz range as presented in Chapter 7 and Paper C.
8.3
Secondary Emission
The harmonic voltages and currents measured at the terminals of a wind turbine, which is connected to the power system, is the combination of primary emission from the turbine and secondary
emission from other turbines and from the external grid. The levels of primary and secondary
emission are determined by the harmonic sources and the properties of the network.
Due to the resonance in the WPP the voltage harmonics at Turbine I are excited at the resonance frequency, which causes the obvious secondary current emission. While resonances are not
observed for Turbine II and Turbine III, instead the observations are found with relatively high
levels of non-characteristic harmonics and interharmonics which are not observed in the background voltage distortion. Thus it is valid to input the measurements at Turbine II as a turbine
harmonic source in the simulation in Chapter 7.
On the other hand, the background voltage distortion in the public grid consists mainly of
low-order characteristic harmonics. Next to these low-order harmonics, interharmonics are present
which originate from the wind turbines, instead of from the public grid. The characteristic harmonics from the grid are dominating. They are present even when one turbine is idle.
8.4
Generalization of the Results
Despite that only a limited number of wind power plants have been measured and analyzed in this
thesis, the main conclusions hold generally. Similar general emission spectra for wind turbines are
shown in papers by other authors. Even harmonics and interharmonics are present in those spectra
at relatively high levels like in our measurements. Also components at switching frequencies are
visible in our as well as in other studies. Other studies show also that the emission is time varying,
8.4. GENERALIZATION OF THE RESULTS
77
like in this thesis. The speciﬁc details studied in this thesis have not been addressed by other
authors, so it cannot be known if they hold generally. But from the similarities of the spectra it
can be suspected that similar phenomena are expected there. To be sure about the generalization
of the results, similar detailed studies as presented in this thesis should be performed for other
wind turbines as well.
The interharmonics are produced due to the wind power conversion system, as studied in this
thesis. Associated with a possible resonance in a collection grid, these interharmonics may excite
the resonance if only at the same frequency. This is a concern for the wind power plant emission.
Additionally, except the impact of resonances in a collection grid, the aggregated harmonics and
interharmonics at the PoC are determined by the sources as well as the propagations. The proposed
systematic approach is a general way for the estimation of wind power harmonic emission.
The random phase angle holds for all harmonics and interharmonics (despite some diﬀerences)
at the three turbines, and similar results are partly seen from other papers. This in general
convinces the aggregation for a WPP. Interharmonics tend to be cancelled a lot within a collection
grid.
78
DISCUSSION
Chapter
9
Conclusion and Future Work
9.1
Conclusion
This thesis presents a study after wind power harmonic distortion by means of analysis of measurements, modelling, and simulations. The study has been performed for both harmonic distortion at
individual turbines and within a wind-power collection grid. The detailed ﬁndings are summarized
in the forthcoming sections.
9.1.1
Harmonic Emission from Individual Wind Turbines
Characterizations:
Three individual wind turbines, two turbines of Type 3 and one of Type 4, have been measured
during a period up to a few weeks. A large amount of data has been obtained and this data has
been the basis for a detailed analysis. Both individual spectra and statistical spectra (average
spectrum, 90-, 95- and 99-percentile spectrum) show that the harmonic distortion from a wind
turbine is time-varying, especially at certain frequencies. The main ﬁndings from the analysis of
the measurements are:
• the level of harmonic distortion is generally low, the levels of integer current harmonics are
low as a percentage of the rated current;
• the levels of even harmonics and interharmonics are comparable to the levels of characteristic
harmonics;
• interharmonics vary with time both in magnitude and frequency; for individual spectra,
narrowband components vary in magnitude and frequency; for average and other statistical
spectra, this shows up as a broadband component;
Relations with produced active-power:
The measurements have been used to study the level of harmonics and interharmonics as
a function of the produced active power. The total harmonic current distortion (expressed in
ampere) remains about the same as a function of the produced active power; whereas the total
interharmonic current distortion presents almost a linear increase with produced active power.
The individual harmonic and interharmonic subgroups versus produced active power show various
trends, however the following general trends have been observed:
79
80
CONCLUSION AND FUTURE WORK
• the characteristic harmonics (plus the third harmonic) are independent of the produced
active power, and with a higher diversity in magnitude (at a certain produced active power)
than other frequencies;
• other harmonics present various patterns and with a lower diversity in magnitude;
• the aforementioned interharmonics, at the related generator-side frequency, show a strong
and linear increase with the produced active power.
Harmonic conversion via power electronics:
The harmonic conversion schema via a power electronic converter has been explained. A novel
measurement analysis method has been applied to the measurement data for the veriﬁcation. The
conversion system generates a series of frequency components by converting the generator-side
frequency, which is normally diﬀerent from the power system frequency, to the power system
frequency. The correlations between frequency components have been presented as a color plot.
Strong correlations have been shown between certain frequency pairs that originate together from
the frequency conversion. It has also been shown that the interharmonic emission increases with
output power, exactly as predicted from the model.
9.1.2
Primary and Secondary Emission
Harmonic propagations:
Simulations have been performed to study the harmonic propagation within the collection grid
of a wind power plant. The study of harmonic distortion in a WPP has been performed based on
a separation between two contributions: the harmonic propagation in a WPP, and the distortion
levels of the harmonic sources. The former has been quantiﬁed by the transfer function, transfer
impedance and transfer admittance. Harmonic propagations are the product of a harmonic source
and its transfer to a destination.
A distinction is made between diﬀerent types of harmonic propagation. The main distinction is
between primary emission originated from the studied object, and secondary emission originated
from anywhere else. At a turbine, three components are present: primary emission from the
turbine; secondary emission from other turbines in the same WPP; and secondary emission from
the public grid. At the PoC of a WPP, the harmonic distortion consists of the aggregated primary
emission from all the turbines in the WPP and the secondary emission from the public grid.
In a systematic viewpoint, the mathematical expressions have been provided to estimate the
total emission at a node, and the emission from certain group of harmonic sources. The harmonic study with the systematic approach concludes that all harmonic contributions need to be
considered to get a complete picture of the harmonic voltages and currents in the WPP.
9.1.3
Harmonic Propagation
Aggregation:
The distributions of complex harmonic currents have been obtained, from the measurements.
In general, the phase-angles of harmonics are distributed non-uniformly, whereas those of interharmonics are distributed uniformly.
The simulations, combined with stochastic treatment (Monte-Carlo Simulation) of measurements, shows that the aggregation is diﬀerent for integer harmonics and interharmonics. Interharmonics present more aggregation than integer harmonics, following the square-root aggregation
9.2. FUTURE WORK
81
rule. A higher order integer harmonic tends to have more aggregation than a lower order integer
harmonic and for high frequencies (above 1 kHz) the aggregation becomes essentially the same for
harmonics and for interharmonics.
Simultaneous harmonic measurements have been performed at two locations in the mediumvoltage collection grid of a WPP, near a wind turbine and near the PoC. The aggregation observed
from the measurements presents a similar pattern as the result from the simulation: more aggregation at interharmonics than at harmonic frequencies, combined with the impact of a resonance.
Ampliﬁcation and Attenuation:
The harmonic distortion has been calculated by using transfer functions for a simpliﬁed WPP
harmonic model. The ampliﬁcation and attenuation of the propagation have been studied for a
WPP conﬁguration.
The ampliﬁcation is commonly caused by the main harmonic resonance in a WPP. For frequencies around the resonance frequency, the emission from the turbines will be ampliﬁed and the
total primary emission from the WPP may exceed the sum of the emission from the individual
turbines. For the kind of WPPs that were studied in this thesis, the resonance frequencies were in
the range from a few hundreds Hz to 3 kHz. For frequencies above the main resonance frequency,
the transfer function was shown to be substantially less than one, despite the presence of higher
order resonance frequencies. It can thus be concluded that primary emission from the turbines,
at frequencies well above the main resonance frequency, does not contribute much to the emission
from the WPP as a whole.
9.2
9.2.1
Future Work
Frequency Resolution of Measurement
There is an obvious presence of interharmonics in the emission from wind power installations.
Furthermore, the distortion, especially for interharmonics, varies with time, both in frequency
and magnitude. As the measurements are taken over 200-ms windows, the frequency resolution
is only 5 Hz. A higher frequency resolution would require a longer measurement window. The
interharmonics vary with time and may no longer be considered as constant in frequency and
magnitude over the whole measurement window. Frequency components obtained from a longer
window have lower magnitudes, which limits the visibility of the time-varying emission. A short
window can track a varying frequency and magnitude with higher time resolution, but it lowers
the frequency resolution. Future work is needed towards a harmonic measurement method that
gives both high frequency resolution and high time resolution.
9.2.2
High Voltage Measurement
More and more wind power plants are connected at transmission level. This requires studies,
including measurements, on the emission levels in the transmission grid. The harmonic emission
observed above 2 kHz is mainly due to the use of the active switching in the power electronic converters. This requires studies, including measurements, of the harmonic emission at frequencies
above 2 kHz. Combined, this shows that the study of harmonic emission at the higher voltage
levels and at higher frequencies is needed. However, it is a serious challenge to measure harmonic emission at high voltage and high frequency. Future work is needed towards an accurate
measurement method that makes this possible.
82
9.2.3
CONCLUSION AND FUTURE WORK
Distinguish between Primary and Secondary Emission
In this thesis, a simulation method has been presented to distinguish between primary and secondary emission. During measurements it is however often not possible to make this distinction.
This means that it can often not be decided if a high harmonic current is primary or secondary
emission, This in turn makes it diﬃcult to interpret the measurements and to use them in simulation studies. A method to determine the contribution to the harmonic distortion coming from
a wind turbine or from the public grid during measurements is of strong interest. Future work is
needed to develop such a method.
9.2.4
Type 3 Wind Turbine
Similar to Chapter 6, the study of origins of harmonic distortion is needed for a Type 3 wind
conversion system. The correlation plot as a tool for studying time-varying harmonics and interharmonics can be used, among others, for a study of a turbine conversion system of Type 3.
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Part V
Included Papers
91
Paper A
Measurements of Harmonic Emission versus Active Power
from Wind Turbines
K. Yang, M.H.J. Bollen, E.A. Larsson and M. Wahlberg
Published in Electric Power Systems Research
c
2014
Elsevier B.V.
A2
Electric Power Systems Research 108 (2014) 304–314
Contents lists available at ScienceDirect
Electric Power Systems Research
journal homepage: www.elsevier.com/locate/epsr
Measurements of harmonic emission versus active power from wind
turbines
Kai Yang a,∗ , Math H.J. Bollen a,b , E.O. Anders Larsson a , Mats Wahlberg a,c
a
b
c
Electric Power Engineering, Luleå University of Technology, 931 87 Skellefteå, Sweden
STRI AB, 771 80 Ludvika, Sweden
Skellefteå Kraft AB, 931 80 Skellefteå, Sweden
a r t i c l e
i n f o
Article history:
Received 10 June 2013
Received in revised form
26 November 2013
Accepted 29 November 2013
Available online 20 December 2013
Keywords:
Wind energy
Wind power generation
Power quality
Electromagnetic compatibility
Power conversion harmonics
Harmonic analysis
a b s t r a c t
This paper presents harmonic measurements from three individual wind turbines (2 and 2.5 MW size).
Both harmonics and interharmonics have been evaluated, especially with reference to variations in
the active-power production. The overall spectra reveal that emission components may occur at any
frequency and not only at odd harmonics. Interharmonics and even harmonics emitted from wind turbines are relatively high. Individual frequency components depend on the power production in different
ways: characteristic harmonics are independent of power; interharmonics show a strong correlation with
power; other harmonic and interharmonic components present various patterns. It is concluded that the
power production is not the only factor determining the current emission of a wind energy conversion
system.
© 2013 Elsevier B.V. All rights reserved.
1. Introduction
Modern wind turbines are commonly equipped with power
electronics, either with reduced-capacity power converters or fullcapacity power converters. Doubly-fed induction wind generators
equipped with reduced-capacity power converters are referred to
as type-3, and the wind turbines with full-capacity power converters as type-4 [1,2].
The use of power electronics produces waveform distortions
[3–7]. A waveform conversion from AC to DC, and then from DC
to AC is utilized in the schema of a power converter. The switching of converter involves waveform distortions in the output power
[4,8].
The potential consequences of high voltage and current distortion are discussed in various textbooks [9–11]. Waveform
distortion is however well regulated in most countries, through
compulsory or voluntary limits. The main concern for wind park
owners and network operators is to keep distortion levels below
those limits.
There are various power conversion schemes part of wind
energy conversion systems [5,8]. The output waveforms with distortions are determined by the switching schemes. To smooth the
∗ Corresponding author. Tel.: +46 736158980.
E-mail addresses: [email protected], epiphany [email protected] (K. Yang).
0378-7796/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.epsr.2013.11.025
generated harmonics, harmonic ﬁlters are used in the wind energy
conversion system [6,8]. The output distortions are thus dependent
on the detailed conﬁguration of the wind turbines.
The standard IEC 61400-21 [12] recommends measurement and
assessment of power quality characteristic of grid-connected wind
turbines with the measurement method speciﬁed in IEC 61000-4-7
[13]. IEC 61400-21 recommends that values of the individual current components (harmonics, interharmonics and higher frequency
components) and total harmonic current distortion are measured
within the active power bins 0, 10, 20, . . ., 100% of wind turbine
rated power. The highest value for each power bin is reported. From
a standardization viewpoint there are reasons for selecting one single value, the maximum value in this case. However, to quantify
the turbine emission, this is only of use when there are limited
variations of the emission within one power bin.
A study based on IEC 61400-21 has been performed on ﬁve wind
turbines [14]. The current total harmonic distortion is found independent on the output power. Also the ﬁfth harmonic is shown to
be independent of the active power for the ﬁve wind turbines. The
interharmonics and other harmonics have not been presented in
reference [14].
A number of 600 kW squirrel-cage induction generator wind
turbines have been tested according to IEC 61400-21 and
IEC 61000-4-7 on the medium voltage level [15]. The paper presents
an exponentially decreasing of current THD (in percent of fundamental current) with power output; the low order harmonics 3, 5
K. Yang et al. / Electric Power Systems Research 108 (2014) 304–314
and 7 (the dominant ones in THD) are presented without obvious
trend with power output.
The aim of this paper is to verify the ﬁndings from earlier papers
about the relation between active power production and harmonic
emission and to extend the study to other harmonics and interharmonics. For this, detailed measurements have been performed on
three modern wind turbines, with rating 2 or 2.5 MW. Especially
the signiﬁcant levels of interharmonics present in wind power
installations, which is much different from conventional installations, has been studied. The risk of the interharmonics and high
order harmonics exceeding the limit has been also studied in this
paper.
Section 2 describes the measurement setup used to obtain the
emission data from the three turbines. Section 3 presents the analysis of wind turbine spectra, whereas Section 4 studies the relation
between the emission and the active-power production. And the
paper is concluded in Section 5.
2. Measurement procedure
2.1. Measured objects
Three wind turbines, from different manufacturers and different
wind parks, have been measured. All three are 3-blade rotor with
horizontal axis, and upwind pitch turbine.
Turbine I: This is a type-3 wind turbine with a rated power
2.5 MW. It is equipped with a six-pole doubly-fed asynchronous
generator (DFIG). A partial rated converter is installed, and designed
as a DC voltage link converter with IGBT technology. The rotor
outputs a pulse-width modulated (PWM) voltage, while the stator
outputs 3 × 660 V/50 Hz voltage. The wind turbine is connected to
the collection grid through one medium-voltage (MV) transformer,
which is housed in a separate transformer station beside the turbine foundation. There are totally 14 such wind turbines within the
wind park.
Turbine II: The second wind turbine is also a DFIG type (type-3),
whereas the rated power is 2 MW. The turbine contains a four-pole
doubly-fed asynchronous generator with wound rotor, and a partial
rated converter. The output voltage is 690 V, and connected to the
collection grid through a medium voltage transformer (installed
inside the nacelle). There are 5 such turbines in the park.
Turbine III: The third wind turbine is type-4, with full-power
converter. The rated power is 2 MW. The turbine is designed based
on a gearless drive with synchronous generator. Power is fed into
the grid via a full rated converter, a grid side ﬁlter and a turbine
transformer to the medium voltage level. The inverters are self
commutated and pulse the installed IGBTs with variable switching
frequency [16].
2.2. Measurement setup
Measurements of the above three wind turbines have been performed at the MV side of the turbine transformers (Fig. 1). Both
voltage and current have been monitored and recorded using a
standard power quality monitor Dranetz-BMI Power Xplorer PX5.
Details at the measuring point are listed in Table 1.
305
Fig. 1. Power quality monitor position of an individual wind turbine measurement
within a wind park.
2.3. Measurement parameters
The three-phase voltage and current waveforms were recorded
by the monitor through the conventional voltage and current transformers at medium voltage, with a sufﬁcient accuracy for the
frequency range up to few kHz [17,18].
The waveform was continuously acquired with a sampling frequency of 256 times the power-system frequency (approximately
12.8 kHz) by the power quality monitor. The Discrete Fourier
Transform has been applied using a rectangular window of 10
cycles, which results in a 5 Hz frequency resolution. According to
IEC 61000-4-7 [13], the harmonic and interharmonic groups and
subgroups are obtained.
Harmonic subgroups Gsg,n and interharmonic subgroups Gisg,n at
order n are grouped as (for a 50 Hz system):
Gsg,n 2 =
1
Ck+1 2
(1)
i=−1
Gisg,n 2 =
8
Ck+i 2
(2)
i=2
where the harmonic subgroup Gsg,n is derived from the 3 Discrete
Fourier Transform (DFT) components Ck−1 , . . ., Ck+1 and the interharmonic subgroup Gisg,n is from the 7 DFT components Ck+2 , . . .,
Ck+8 , due to the 5 Hz resolution spectrum of 10 cycles of sampled
waveforms.
The harmonic and interharmonic subgroups, over each 10-cycle
window, are next aggregated into 10-min values. The 10-min value
is the RMS over all 10-cycle values within those 10 min. Details are
found in the standard, IEC 61000-4-30.
The grouping and aggregation according to the standard methods take place in the monitor. The user has only access to the
grouped and aggregated 10-min values. To allow more detailed
analysis, a 10-cycle snapshot of the voltage waveform, with a sample frequency of 12.8 kHz, is obtained every 10 min. The analysis
presented in this paper is partly based on the aggregated harmonic
and interharmonic subgroups and partly on the 200-ms snapshots.
2.4. Measurement accuracy
The average spectra, especially for Turbine I, show a broadband
spectrum as in Fig. 3 (will be shown later). This spectrum originally
raised the suspicion of being due to quantization noise. The spectra
Table 1
Measured objectives details (measure point current and voltage in nominal).
Turbine no.
Turbine I
Turbine II
Turbine III
Generator type
Asynchronous double-fed
Asynchronous double-fed
SYNC-RT
Turbine type
Type-3
Type-3
Type-4
Measure point
Measure duration
Current
Voltage
66 A
36 A
116 A
22 kV
32 kV
10 kV
11 days
8 days
13 days
K. Yang et al. / Electric Power Systems Research 108 (2014) 304–314
Current (A)
306
0.3
0.1
Current (A)
0
0
500
1000
1500
2000
0.3
2500
3000
25% Power, Phase A
25% Power, Phase B
25% Power, Phase C
0.2
0.1
0
Current (A)
Idle, Phase A
Idle, Phase B
Idle, Phase C
0.2
0
500
1000
0.3
1500
Frequency (Hz)
2000
1500
Frequency (Hz)
2000
2500
3000
Rated, Phase A
Rated, Phase B
Rated, Phase C
0.2
0.1
0
0
500
1000
2500
3000
Fig. 2. Spectra of Turbine I at zero, 25% and rated production.
shown in Fig. 3 have been obtained from the average of a number
of spectra obtained from the measurements.
The situation becomes different when looking at individual
spectra. A number of such individual spectra for low, medium and
high power production are plotted for Turbine I in Fig. 2. The spectra are derived from 200 ms current waveforms by Discrete Fourier
Transform (DFT) at roughly idle, 25% of rated and rated power production.
The top plot in Fig. 2 presents a spectrum with only a few apparent harmonics at certain narrowbands. The emission is much lower
than that of Fig. 3 (will be shown). As the level of quantization noise
would be rather independent of the active-power production, it is
concluded that the broadband spectrum in Fig. 3 is not due to quantization noise. This conclusion is also conﬁrmed and shown in Fig. 5
(will be shown later), where the blue areas represent low emission,
much lower than the level of the broadband. This is the same with
the other two turbines.
3. Wind turbine emission
3.1. Emission level
From the 200-ms windows, spectra with 5-Hz frequency resolution have been obtained. All those spectra, over the measurement
period of 8–13 days, have been used to calculate an average spectrum. The average spectra for the three turbines are shown in Fig. 3.
Note that this spectrum is obtained from the 10-cycle snapshots
and not from the 10-min grouped values.
The three turbines present a spectrum that is a combination of a broadband spectrum and a number of narrowbands.
The narrowbands are mainly centred around integer harmonics,
100 Hz, 150 Hz, 200 Hz and 250 Hz. Turbine I (upper sub-ﬁgure in
Fig. 3) presents a narrowband component centred at 650 Hz and a
broadband component covering neighbouring frequencies. Except
the narrowband emission at interger harmonics (e.g. 150 Hz and
0.15
Phase A − Turbine I
Phase B − Turbine I
Phase C − Turbine I
650Hz
0.1
0.05
0
0
Current (A)
0.2
500
1000
1500
2000
285Hz
0.15
2500
3000
Phase A − Turbine II
Phase B − Turbine II
Phase C − Turbine II
385Hz
0.1
0.05
0
0
0.4
500
1000
1500
2000
0.3
2500
3000
Phase A − Turbine III
Phase B − Turbine III
Phase C − Turbine III
280Hz
380Hz
0.2
0.1
0
0
500
1000
1500
Frequency (Hz)
2000
2500
3000
Fig. 3. The average spectra (5 Hz increment) of the three individual wind turbines during a measurement period between 8 and 13 days.
Interharmonic level (%) of IEEE 519 limit
Harmonic level (%) of IEEE 519 limit
K. Yang et al. / Electric Power Systems Research 108 (2014) 304–314
307
Turbine I
Turbine II
Turbine III
150
100
50
0
5
10
15
20
25
Harmonic order
30
35
40
35
40
350
Turbine I
Turbine II
Turbine III
300
250
200
150
100
50
0
5
10
15
20
25
Interharmonic order
30
Fig. 4. Upper ﬁgure: harmonic level (from harmonic subgroups) as a percentage of the IEEE 519 limits; lower ﬁgure: interharmonic level (from interharmonic subgroups) as
a percentage of the nearest even harmonic limits of IEEE 519.
200 Hz), Turbine II (middle sub-ﬁgure in Fig. 3)) emits obvious
narrowband components at 285 Hz and 385 Hz, and a broadband
spectrum up to about 400 Hz and between 2000 and 2700 Hz.
The spectrum of Turbine III (bottom sub-ﬁgure) presents two
broadband components around 280 Hz and 380 Hz, next to the narrowband components at harmonics 5 and 7.
Turbine I presents a broadband component around the fundamental frequency. The side-band components decay with
frequency. The centred 5th harmonic (250 Hz) and broadband
around 13th harmonic are apparent. The random and irregular
emission between 1 kHz and 2.5 kHz is of interest. The phenomenon
is strongly dependent on the conﬁguration of a harmonic ﬁlter
installed on the turbine side of the turbine transformer.
Turbine II is also DFIG type. The emission is mainly present
below 500 Hz (harmonic 10) and the broadband around 2.3 kHz.
The components at 285 Hz and 385 Hz (close to interharmonic
orders 5.5 and 7.5) dominate in the emission. Similarly, Turbine
III presents the same dominating emission around the two interharmonic orders. The two dominating components make a large
difference from the neighbouring orders.
3.2. Comparison with limits
Current emission from the three wind turbines has been compared with the emission limits recommended by IEEE standard 519,
which are location independent. The limit for each harmonic order
is set in this standard as a percentage of the maximum current.
The comparison with IEEE Std.519 is shown in Fig. 4. The vertical
scale for both ﬁgures is in percent of the IEEE-519 limit for each harmonic or interharmonic. A value above 100% means that the turbine
would not comply with the standard. IEEE Std.519 does not set any
limits for interharmonics; for the comparison it was assumed that
the interharmonic limits are the same as those for the nearest even
harmonic.
The harmonic level is shown as a ratio between the measured
harmonic level (harmonic subgroup as a percentage of rated current) and the current harmonic limit for voltage levels through
69 kV as in Fig. 4 (upper ﬁgure). The interharmonic level is the
ratio between the measured interharmonic level (as a percentage
of rated current) and the limits for the nearest even harmonic in
IEEE Std.519.
The ﬁgure shows that both harmonic and interharmonic levels reach high values at higher orders. It indicates a relatively high
emission at high orders at wind turbines, especially the even harmonics. Some even harmonics (order 36, 38 and 40) exceed the
limit (100%).
Compared to the harmonic level, interharmonic level shows no
obvious difference between neighbouring orders. Also some of the
lower-order interharmonics are close to the limit. Higher order
interharmonics exceed the limits. The sudden increase at order 24,
for both harmonics and interharmonics, is due to lower emission
limits for order 24 and higher.
Different from emission of other installations, even harmonics
and interharmonics from wind turbines are high compared to the
emission limits, especially for higher orders.
3.3. Primary and secondary emission
The inﬂuence of the background voltage distortion on the current distortion is often discussed informally, but no qualitative
results for wind turbines are available from the literature. The
standard IEC 61400-21 states that the measurements should be
done when the background voltage distortion is low, without further quantifying this. A study for a large off-shore wind park [19]
showed that, at the point of connection with the 150-kV grid, the
harmonic currents due to background voltage distortion may be
several orders of magnitude larger than the currents due to the
emission from the turbines.
The impact of background voltage on the current distortion is
not limited to wind-power installations. Similar phenomena have
been studied for lighting installations at frequencies of some tens
of kHz [20]. In that study a distinction was made between “primary
emission” and “secondary emission”, which proved very useful
when quantifying the interaction between devices.
The primary emission is the distortion generated within the
installation itself; while the secondary emission is the distortion
generated from somewhere else. What counts as “installation”
depends on the location of the point of evaluation. When considering one single turbine, the primary emission is the one due to
the turbine itself. The measured emission at a certain turbine is a
combination of primary and secondary emission.
308
K. Yang et al. / Electric Power Systems Research 108 (2014) 304–314
Fig. 5. Turbine I: harmonic (H 2–H 41) and interharmonic (IH 2.5–IH 41.5) subgroups as a function of active power. (For interpretation of the references to colour in the text,
the reader is referred to the web version of the article.)
For the turbines studied in this paper, the correlation coefﬁcient
has been calculated between the harmonic voltage and harmonic
current at a certain harmonic order. Results show that most harmonic orders present a low correlation coefﬁcient with a value
around 0.2. Thus the impact of secondary emission is small in this
case. Further study on the issue is needed in the future.
4. Distortion versus active power
The previous section presents the average emission levels of
the three turbines over a longer period. During the measurement period, of the order of one week, the wind speed varied
a lot in all cases. Unlike the other types of conventional generators, wind turbines show large variations in power production.
Variations in power production are associated with variations
in the rotation speed on the generator side of converters. The
emission is expected to show variations with active power production, among others because of the link between rotational
speed and active power production. The relations between the
active power production and the current emission have been
studied in more details, for the different frequency components.
4.1. Spectrogram as a function of active power
In this section a study on the emission as a function of activepower is presented. The harmonic and interharmonic subgroups of
the three wind turbines, obtained from the 200-ms windows, are
shown in Fig. 5 (Turbine I), Fig. 6 (Turbine II) and Fig. 7 (Turbine III)
as a function of the produced power. The upper ﬁgure presents the
current emission (in ampere) in logarithm (base 10) with colour.
The colour scale indicates the magnitude of the harmonic and interharmonic subgroups with red the highest and dark blue the lowest
magnitude. The horizontal axis has been obtained by sorting the
spectra by the active power, with highest production towards the
right. The sorted production values are shown in the bottom curve.
The idle states (where the wind turbine is standing still and the
converter disconnected, but where a small negative power ﬂows
through the turbine transformer due to losses and auxiliary supply) have been removed from the ﬁgure. Note that the active-power
scale is not linear.
As in Fig. 5, characteristic harmonics (H 5 and H 13) remain
apparent over the whole range of active power production. The
low order harmonics, obviously for harmonic 5, become stronger
with the increasing production. The interesting observation is that
the emission around harmonic 13 gets stronger at the higher power
production, and that the strongest emission shifts to a higher order.
The obvious changes occur above 0.5 per unit active-power production (or around data order 850). Another signiﬁcant observation
is that around 0.26 per unit active-power the emission shows a
minimum.
For Turbine II (Fig. 6) lower order harmonics increase in
magnitude and the maximum emission shifts to higher orders
(interharmonics) from around 0.25 per unit active-power production. The emission from harmonic order 10–30 remains present
until around 0.5 pu power production. Above around 0.7 pu power
blue colour regions between harmonic orders H 15–H 25 and
H 30–H 40 present low emission. Another observation is that emission at harmonic orders above H 35 increases at 0.2–0.4 pu power
production.
The type-4 turbine shows another emission pattern, as shown
in Fig. 7. The main similarity with the previous two turbines is
that low order harmonics, especially interharmonics (e.g. interharmonics 5.5 and 7.5) next to the characteristic harmonics (e.g.
harmonics 5 and 7), increase with an increasing power production.
The broadband emission from H 35 to H 40 is stronger around rated
production. The emission of these orders is relatively low from 0.2
to 0.5 pu active power.
From the above ﬁgures, it is concluded that characteristic harmonics are present for any power production; but certain lower
order emission increases with production. The increase is mainly in
the neighbouring interharmonics of characteristic harmonics. The
interharmonic magnitudes exceed those of the characteristic harmonics for certain values of active-power production. Higher order
emission presents a number of patterns, which are different for
different turbines.
K. Yang et al. / Electric Power Systems Research 108 (2014) 304–314
309
Fig. 6. Turbine II: harmonic (H 2–H 41) and interharmonic (IH 2.5–IH 41.5) subgroups as a function of active power. (For interpretation of the references to colour in the text,
the reader is referred to the web version of the article.)
Fig. 7. Turbine III: harmonic (H 2–H 41) and interharmonic (IH 2.5–IH 41.5) subgroups as a function of active power. (For interpretation of the references to colour
in the text, the reader is referred to the web version of the article.)
remains about the same. Each turbine is different; the measurements together with earlier measurements presented in [14,15]
indicate that there is no clear trend for the relation between THD
(in ampere) and active-power production. Both Turbine I and Turbine II present a narrow range (by absolute value) of the emission
for a certain active power production, if compared to that of Turbine
III.
The current total interharmonic distortions (TIDs) are shown in
Fig. 9 as a function of active-power production.
All three turbines show a clear increase of TID with active power
production. The three trends are a combination of almost linear line
with ﬂuctuations at certain active power ranges. There is a drop at
0.26 pu for Turbine I (which is also visible for the THD in Fig. 8, and
multiple lines below 0.15 pu for Turbine II and a drop from 0.15 to
0.3 pu for Turbine III.
The TID for a given value of active power production shows less
variations than for the THD. There is a strong correlation between
the emission and the active power production. The higher active
power production, the higher the TID is.
4.2. THD and TID as a function of active power
4.3. Turbine II: individual subgroups as a function of active power
The total harmonic distortions of the three turbines, as a function of active power production, are presented as in Fig. 8. The
current THDs were recorded in absolute ampere in Dranetz instrument. The paper [14] presents a constant THC (total harmonic
current in percent with the rated wind turbine current), with the
increasing active power production. Whereas the paper [15] points
out an exponentially decreasing trend (total harmonic distortion as
a percentage of fundamental current component) with respect to
active power production in a wind farm, and an unapparent trend of
that in percent of wind farm rated current. Ref. [15] however shows
results for ﬁxed-speed machines, where the mechanism behind the
emission is different than for the turbines discussed in this paper.
The total harmonic distortion (THD) versus active power is presented in Fig. 8. The horizontal axis represents the active power
in per unit. The total harmonic distortion (THD) (vertical axis) is
measured in absolute ampere.
The three wind turbines show a somewhat different relation
between emission and the active power production. Turbine I
shows an increase, Turbine II a mild decrease and Turbine III
Next to THD and TID, also the individual harmonic and interharmonic subgroups have been plotted as a function of the
active-power production. Some of the results are presented in this
and the next section. It is not possible to show all harmonic and
interharmonic subgroups, so that certain typical subgroup orders
have been chosen to be presented here.
Individual harmonic and interharmonic subgroups show different relations to the active power production. Five subgroup orders
have been chosen for Turbine II: 3rd, 5th, 6th, 32nd and 36th; and
are shown in Fig. 10. The harmonic subgroups versus active power
[pu] are presented on the left, and the interharmonic subgroups are
on the right.
The ﬁgure shows immediately that there is a wide range in
behaviour. There is no general trend for all or most subgroups. In
Turbine II, certain harmonic subgroups are not correlated with the
active power, especially the lower-order characteristic harmonics,
H 5, H 7, H 11 and H 13 (similar pattern as H 5 in the ﬁgure). The subgroups are within a wide magnitude range as a function of power,
K. Yang et al. / Electric Power Systems Research 108 (2014) 304–314
310
0.6
0.4
0.2
Current THD (A)
0
Turbine I
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.4
0.2
Turbine II
0
1
0.8
0.6
0.4
Turbine III
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Active Power [pu] (phase A)
0.7
0.8
0.9
1
Fig. 8. Total harmonic distortions (THDs) as a function of active power in phase A.
and without an obvious trend with the increasing active power.
Other harmonic orders present a narrow magnitude variation as a
function of power, e.g. H 4, H 6 and H 8 (which all show a similar pattern as H 6 in the ﬁgure). The higher-order emission decreases with
the increasing power production, e.g. H 35. Note that the emission
level for higher-order components is low compared to the emission
for lower-order components.
Interharmonic subgroups present a stronger dependence on the
active power than the harmonic subgroups. There are several patterns from the observation: a slightly low emission around 0.3 pu
active power (e.g. IH 2 and IH 3); apparent linear and increasing
trend associated with several parallel trends below 0.4 pu (interharmonics next to characteristic harmonics as IH 5, IH 7, etc.);
emission with two apparent linear trends associated with emission
between the two linear lines as a function of power (e.g. IH 4, IH 6,
etc.); and some other irregular patterns such as IH 32 and IH 36.
Although the individual subgroups present different patterns
as a function of the active-power production as well as the different emission levels in different power production, there are some
similarities between certain orders. Triplen and characteristic harmonics present a low dependence on the active power, whereas
other orders, especially interharmonics, present a strong dependence on the active power.
4.4. Individual subgroups of Turbines I and Turbine III
The individual subgroups as a function of active power production are presented for the other two wind turbines in Fig. 11. The ﬁve
chosen individual harmonic orders of each wind turbine present the
representative curves for each turbine.
Fig. 11(a) presents typical harmonic and interharmonic subgroups for Turbine I: harmonic and interharmonic orders 3, 7, 12,
16 and 19. The emission at each active power production shows less
spread for interharmonic subgroups than for harmonic subgroups.
Harmonic subgroup 7, which is similar to orders 5 and 11, shows a
large spread for a given active power production. The curve does not
show a strong relation between the emission and the active power.
There exists an emission drop at around 0.26 pu active power on
the increasing trend till 0.8 pu active power, then followed by a
decreasing emission.
The results for Turbine III are presented in Fig. 11 (b), with speciﬁed orders 3, 4, 6, 7 and 22. Same as the other two turbines, the
0.6
0.4
0.2
Current TID (A)
0
Turbine I
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
Active Power [pu] (phase A)
0.7
0.8
0.9
1
0.4
0.2
Turbine II
0
1
1
0.5
Turbine III
0
Fig. 9. Total interharmonic distortion (TID) as a function of active power.
1
K. Yang et al. / Electric Power Systems Research 108 (2014) 304–314
0.2
311
0.03
0.15
0.02
0.1
0.01
0.05
0
H3
0
0.2
0.4
0.6
0.8
1
IH3
0
0
0.2
0.4
0.6
0.8
0
0.2
0.4
0.6
0.8
1
0.3
Current Harmonic/Interharmonic subgroups (A)
0.1
0.2
0.05
0.1
IH5
H5
0
0
0.2
0.4
0.6
0.8
1
0
1
0.1
0.15
H6
IH6
0.1
0.05
0.05
0
5
−3 0.2
0
x 10
0.4
0.6
0.8
1
0
5
H32
4
3
2
2
1
1
0
0.2
0.4
0.6
0.8
1
0.04
0.6
0.8
0
1
IH32
0
0.2
0.4
0.6
0.8
1
0.04
H36
0.03
0.02
0.01
0.01
0
0.2
0.4
0.6
0.8
1
IH36
0.03
0.02
0
0.4
4
3
0
−3 0.2
0
x 10
0
0
0.2
0.4
0.6
0.8
1
Active Power in [pu] (phase A)
Fig. 10. Turbine II: individual harmonic (H) and interharmonic (IH) subgroups as a function of active power.
low order harmonic subgroups (example as harmonics 3 and 4 presented in the ﬁgure) spread in a larger range if compare to the higher
orders from the same turbine.
The three turbines present different trends of subgroups, either
for the different orders of one turbine or trends between turbines.
Individual subgroups of the two turbines present different patterns.
Some general patterns can however be observed: the emission for
characteristic harmonics is independent on active power; interharmonics (especially neighbouring interharmonics of characteristic
harmonic orders) are more dependent on the active power. The
spread from the average trend is large for harmonics but small for
interharmonics.
4.5. Quantiﬁcation study on 5th harmonic and interharmonic
The standard IEC 61400-21 recommends that the current emission is presented with the power bins: 0, 10, 20, . . ., 100% of active
power, where 0, 10, 20, . . ., 100% are the bin midpoints. Examples of
patterns for emission versus power production were shown earlier
as a scatter plot in Figs. 10 and 11.
The emission for each harmonic and interharmonic subgroup
has been quantiﬁed per active-power but by its 5th percentile value,
mean value and 95th percentile value. These values, as a function of
active power production, are shown in Fig. 12. From the total 1126
measures, there are 190, 113, 112, 109, 77, 65, 68, 41, 63, 34 and
254 measures from power bin 0% till power bin 100%.
The 5th percentile, mean and 95th percentile values of harmonic
subgroup 5 are about the same for the different power bins. The
plot also shows a large difference between the 5th and 95th percentiles. It is thus not possible to a give a representative value for
the emission within a power bin.
All three values are increasing for interharmonic subgroup 5.
Here the observation is a relatively large spread up to 30% and
a small spread for higher power. The relatively large difference
between the 5th percentile and 95th percentile below the 40%
power bin, is also visible in Fig. 10.
This study of this typical pattern shows independence between
the harmonic subgroup 5 and the active power, and the strong
dependence between the interharmonic subgroup 5 and the active
power. It also shows that the spread of the emission values within
one power bin is large for the harmonic subgroup but small for the
interharmonic subgroup.
4.6. Quantiﬁcation of variation per power bin
The level of variation in emission within the same power bin
was shown to be different for different turbines and harmonics in the previous section. It was also shown that the individual
K. Yang et al. / Electric Power Systems Research 108 (2014) 304–314
312
0.2
0.1
0.1
0.05
H3
0.2
0.5
0
1
0
0
0.5
1
H7
0.1
0.05
0.05
0
IH7
0
0.5
0
1
0
0.5
1
IH12
H12
0.2
0.05
0.1
0
0.1
0
0.5
0
1
0
0.5
1
0.05
H16
0.05
IH16
0
0
0.5
0
1
0
0.5
Current Harmonic/Interharmonic subgroups (A)
Current Harmonic/Interharmonic subgroups (A)
0
IH3
IH3
H3
0
0.5
0.5
0
0.5
1
IH4
0.2
0.1
0.1
0
0.5
0
0.5
1
0
0.2
0
0.5
H6
1
IH6
0.1
0
0
0.5
0
1
0
0.5
0
0.5
1
0.5
0.2
0.1
IH7
H7
0.03
0
0.5
1
0.02
0.05
0
0
1
H4
0
1
0
0
0.03
1
IH22
H22
H19
0
0.2
0.1
0.05
0.05
0.02
IH19
0
1
0
Active Power in [pu] (phase A)
0.5
0.01
1
0
0.5
0.01
1
0
Active Power in [pu] (phase A)
(a)
0.5
1
(b)
Fig. 11. Individual harmonic (H) and interharmonic (IH) subgroups as a function of active power in phase A. (a) Turbine I and (b) Turbine III.
subgroups show different trends for emission versus active power.
The relation between an individual subgroup and the active-power
production is thus different for different subgroups and also for
different turbines.
Within a power bin, a larger spread of the emission indicates
more independence between the emission and the active power. To
quantify the variation of an individual harmonic or interharmonic
subgroup within the power bins, the term ‘variation index’ K(h) at
harmonic order h is introduced:
11
K(h) =
(1/11)
n=1
(H95 (n) − H5 (n))
11
(1/11)
n=1
(3)
H95 (n)
where H95 (n) and H5 (n) are the 95th percentage and 5th percentage
values at power bin n; n counts from 1 to 11 and corresponds to 0,
10%, . . ., 100% centre points for the active power bins.
A variation index equal to zero occurs when the 5th and 95th
percentiles are equal to each other for all 11 power bins. The variation index is equal to unity when all 5 percentile values are equal
to zero. In that case the relative variation is very big. The lower
the variation index, the more the emission only depends on the
active-power production.
Fig. 13 presents the variation index for the three turbines, separately for harmonic and interharmonic subgroups.
With Turbines I and III the variation index is much lower for
interharmonics than for harmonics up to order 15 (Fig. 13). For
higher order the variation index is slightly lower for interharmonics, but the difference is small. For Turbine III the latter is
the case also for lower order, as shown in Table 2. Higher order
interharmonics for Turbine II show a high variation index, close to
unity. For Turbine I and Turbine III the variation index decreases
with increasing harmonic order. For Turbine II, large variation
0.14
0.12
Emission Trend in Power Bins [A]
0.1
0.08
0.06
0.04
0.02
0
10
20
30
40
50
60
70
H 5%
H mean
H 95% 90
80
100
0.4
0.3
0.2
IH 5%
IH mean
IH 95%
0.1
0
0
10
20
30
40
50
60
Active Power Bins in [%]
70
80
90
100
Fig. 12. Turbine II: 5% (5th percentile value), mean and 95% (95th percentile value) of harmonic (H) 5 and interharmonic (IH) 5 subgroups as a function of active power bin
according to requirement in IEC 61400-21.
K. Yang et al. / Electric Power Systems Research 108 (2014) 304–314
313
Independence factor
1
Turbine I
Turbine II
Turbine III
0.8
0.6
0.4
0.2
0
5
10
Independence factor
15
20
25
Interharmonic order
30
35
40
20
25
Harmonic order
30
35
40
Turbine I
Turbine II
Turbine III
1
0.8
0.6
0.4
0.2
0
5
10
15
Fig. 13. Interharmonic (upper) and harmonic (lower) variation index.
Table 2
Average variation index over 10 orders, for the three turbines.
TI
T II
T III
H 2–10
IH 2–10
H 11–20
IH 11–20
H 21–30
IH 21–30
H 31–41
IH 31–41
0.4439
0.4423
0.4918
0.1714
0.4417
0.2930
0.3071
0.5751
0.2839
0.2800
0.4263
0.2223
0.2352
0.5516
0.1821
0.2118
0.4155
0.1460
0.2782
0.8298
0.2622
0.2172
0.7991
0.2333
index is observed above order 15, for harmonics as well as for
interharmonics.
5. Conclusion
The three turbines show different spectra, but some general
observations can be made. The spectrum is for all three turbines a
combination of narrowband and broadband components. The consequence of this is that next to integer harmonics, the spectra have
large interharmonic contents. The levels of characteristic harmonics are relatively low, where the emission limits in IEEE Std.519
have been used as a reference. Interharmonics and even harmonics
are relatively high, especially for higher orders. The rule that emission is dominated by odd non-triplen harmonics does not hold for
wind turbines.
Contrary to earlier publications, the measurements showed different relations between THD and active-power production for
different turbines. The variation of THD with active power is relatively small. The relation between total interharmonic distortion
(TID) and active-power production is similar for the three turbines; an increase in TID with increasing active-power production.
Individual harmonic and interharmonic subgroups show different
relations between emission and active-power production. Characteristic harmonics are shown to be independent on the active
power. They show large variations even for small variations in
active power. Whereas the neighbouring interharmonics present
a strong dependency on the active power. A general observation
is that the dominant interharmonics increase with active power
production, whereas the dominant harmonics remain more constant. TID and individual harmonics have not been studied in other
publications.
The spectrogram sorted by active-power production has shown
to be a suitable graphical method for illustrating the changes in
emission spectrum with active power production. For the three turbines studied in this paper, this type of spectrogram showed that
the character of the spectrum changes with active-power production, especially where it concerns interharmonics.
The emission of a wind turbine is not only determined by the
active power production. For a given amount of active power production, there is a range in measured values of the emission. This
range is small for part of the harmonic and interharmonic subgroups and large for others. There is no obvious pattern observable
in this and the range is different for different frequency components
and for different turbines.
To know the emission from a wind turbine, it is thus not sufﬁcient to know the active-power production. This also means that
the reporting method according to IEC 61400-21 has its limits. This
method only reports the maximum emission for each power bin,
not the spread of the emission. For some applications this may be
sufﬁcient, but for research purposes, to understand the emission or
for serious planning efforts more information is needed.
Further work needed includes a study of multiple trends of
emission as a function of active-power at certain orders (e.g. interharmonic 5 together with interharmonic 7) and a study of the
shift towards higher orders for increasing active-power production.
Further work is also needed towards a method for distinguishing
between emission driven by the power electronics in the turbine
and emission driven by the background voltage distortion. An evaluation of the impact of even and interharmonics on the grid is
needed, including a possible reevaluation of limits for these frequency components.
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A14
Paper B
Aggregation and Ampliﬁcation of Wind-Turbine
Harmonic Emission in A Wind Park
K. Yang, M.H.J. Bollen and E.A. Larsson
Published in IEEE Transactions on
Power Delivery
c
2014
IEEE
B2
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
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B12
Paper C
Decompositions of Harmonic Propagation in A Wind
Power Plant
K. Yang, M.H.J. Bollen, H. Amaris and C. Alvarez
Revision to Electric Power Systems Research
The layout has been revised.
C2
1
Decompositions of Harmonic Propagation in A
Wind Power Plant
Kai Yang, Math H. J. Bollen, Hortensia Amaris, Carlos Alvarez
Abstract—This paper presents harmonic propagation in a wind
power plant. The study decomposes the propagation into two
groups based on the harmonic sources: propagation from one
individual wind turbine to other turbines and to the public
grid; and propagation from the public grid to the collection
grid and to individual wind turbines. The paper studies the
characteristics of the different harmonic propagation paths. A
case with emission from all turbines, at different production
levels, and from the public grid is presented as well. Also the
impact of a turbine ﬁlter on the propagation is studied. The
study indicates that, resonances of a wind power plant have
a signiﬁcant impact on the propagation. It is also shown that
harmonic studies should consider both emission originating from
turbines and emission originating from the public grid. It is also
shown that the ﬁlter with the turbine has a signiﬁcant impact on
the harmonic propagation.
Index Terms—Wind energy, wind farms, power quality, power
system harmonics, power system simulation, power conversion
harmonics.
I. I NTRODUCTION
T
HE environmental advantages of using wind to produce
electric power are well known and broadly documented.
Wind power does however have adverse impacts on the electric
power system. These need to be addressed to prevent that the
electric power system becomes a barrier against the introduction of wind power. One of such adverse impacts concerns
the distortion of the voltage and current waveforms. Harmonic
distortion of wind power installations, has attracted signiﬁcant
interests [1], [2], [3], [4]. Such installations emit apparent noncharacteristic and interharmonics, which are different from
conventional devices and installations [5], [6]. A new type
of distortion has been observed for wind energy conversion
system using power electronics [3], [7]. Problems caused by
harmonics, include shortened lifetime of components such as
generators, transformers, cables, and ﬁlter capacitors by overheating, extra losses of the components; mechanical vibration
of ﬁlter inductor; undesired trigging of grid and inverter; and
even shutdown of the wind power plant (WPP) [8], [9].
Harmonic distortion from wind power installations shows
signiﬁcant levels of interharmonics, and even harmonics [4],
———————————————This work has been ﬁnancial supported by Elforsk and the Swedish Energy
Administration through the Vindforsk program and by Skellefteå Kraft Elnät
AB.
K. Yang and M. H. J. Bollen are with the Electric Power Engineering
Group, Luleå University of Technology, 931 87, Skellefteå, Sweden. e-mail:
([email protected]).
H. Amaris is with Carlos III University of Madrid, 28911 Leganés, Madrid
Spain.
C. Alvarez is with Energy to Quality, 28046 Madrid, Spain.
[10]. The origin of apparent interharmonics has been addressed
in [7]. The emission of individual turbines is however low as
a percentage of the rating at the low-order odd harmonics [1],
[3], [10].
The use of underground cables in a WPP signiﬁcantly
impacts the emission of the WPP as a whole. Those cables
introduce resonances in the collection grid at relatively low
frequencies [11], [12] because of combination of the cable
capacitance and the source inductance (dominated by the grid
transformer). These resonance problems have been widely
studied [13], [14], [15]. The harmonic currents emitted by a
wind turbine are ampliﬁed by the resonance, which results in
a risk of exceeding the harmonic voltage limits set by the grid
operator.
Additionally, the harmonic distortion behaves stochastically
with certain types of probability distribution in the complex
plane [16], [17], [18], [19]. The result of the stochastic
behaviour is that the magnitude of the total emission is lower
than the sum of magnitudes of the emission from the individual
turbines; this effect is called “harmonic aggregation”.
The standard IEC 61000-3-6 recommends the use of an
aggregation model based on an “alpha exponent” for each harmonic and interharmonic order. The aggregation depends on
the distribution of the complex harmonics and interharmonics
[17], [18].
The interaction between a turbine and the grid determinate
the distortion level into and from the grid, in addition to the
interaction with other turbines [20]. The background voltage
distortion also contributes to the harmonic currents at the point
of connection and in the collection grid. This is not commonly
considered in harmonic studies. Reference [14] mentions the
importance of this and in [21] a case is shown where the contribution of the background distortion at the point of connection
if bigger than the contribution from the turbines. The spread
of the emission, either from the background distortion or from
the turbines, inside of the WPP is however not studied.
This paper considers both phenomena: the harmonic emission originating from a turbine and spreading to other locations
in a WPP or to the public grid; and the harmonic emission
driven by external sources connected elsewhere to the public
grid.
Based on the harmonic aggregation in Section II, a case
study is performed for a nine-turbine WPP in Section III.
Results of harmonic penetrations from a wind turbine and
from the external grid, emission with combined power bins
and the impact of a turbine ﬁlter are presented in Section IV.
The study is summarised in Section VI.
2
II. H ARMONIC AGGREGATION
The study is based on the traditional frequency-domain
analysis. The calculated voltage and current are valid in the
complex plane where the contributions from the different
sources add. The magnitude of the harmonic distortion at a
certain location is less than the sum of the magnitudes from
different contributions. This is because of the different phaseangles of the different vectors. Next to that the variations in
emission do not occur at the same time for the individual
turbines. Because of this the maximum of the sum of total
emission is less than the sum of the maxima of the individual
contributions.
A previous study [1] indicates that, low-order harmonics
tend to be synchronised to the fundamental voltage waveform
with small difference in phase angle, whereas the phase angles
for high frequencies vary randomly. Further studies have
shown that characteristic harmonics and non-characteristic
harmonics at low-orders behave differently. Especially interharmonics and high frequencies show uniformly distributed
phase angles [22].
The aggregation at certain harmonic order deviates between
different turbine types or WPP locations. The harmonic aggregation is chosen in this paper according to the standard
IEC 61000-3-6, which describes a “second summation law”
(applicable to both voltage and current) as:
N
α
U α
(1)
U = h
h,m
m=0
where Uh is the resulting voltage magnitude due to the
aggregation of N sources at order h, and α is the “aggregation
exponent”. The values for the aggregation exponent according
to IEC 61000-3-6, are given in Table I.
TABLE I
VALUES OF THE AGGREGATION EXPONENT IN S TANDARD IEC 61000-3-6.
Order
Value of alpha exponent
Harmonic order < 5
1
5≤ Harmonic order ≤ 10
1.4
10<Harmonic order ≤ 999
2
Interharmonic order < 999
2
III. C ASE S TUDY
A case study has been performed using the commerciallyavailable software package DIgSILENT PowerFactory. The
case study involved a WPP with nine wind turbines connected
to the public power grid.
A. Wind Power Plant Topology
Nine identical variable-speed wind turbines are connected
to two underground cable feeders, as depicted in Fig. 1; four
turbines to one feeder, ﬁve to the other. The distance between
neighbouring turbines on each feeder and the distance from
the WPP substation to the nearest turbine is 1 km.
The power produced by the nine wind turbines is sent
through the turbine transformers at the voltage level of 22 kV
Fig. 1. The topology of the studied wind power plant with nine identical
wind turbines spread over two feeders.
and further to the public grid through a single substation
transformer at 66 kV.
B. Wind Turbine Model
The wind turbine has a rated power of 3 MW and is of
Type-III (Doubly-Fed Induction Generator). Harmonic measurements, according to IEC 61400-21, were performed on
low-voltage (LV) terminal of the turbine. Current spectra
were obtained for the different active power bins (PB, e.g.,
PB 10 with 5%-15% active power; PB 20 with 15%-25% active
power). Harmonic emission at PB 100 has been used to study
the spread of emission from individual sources. The harmonic
distortion with production in different PBs is used for a study
of the total harmonic levels due to all sources.
The wind turbine is modeled as Norton equivalent circuit.
The measured current spectra within the individual wind turbine are used in the study as the harmonic current source from
the turbine. In reality the harmonic current measurement was
impacted by the background voltage distortion. As an input of
harmonic source, this is valid to assume the measurement as
the emission from a turbine.
C. Sensitivity of Skin Effect
The feeders consist of underground cables, which are
modelled as a distributed parameter. The cable resistance is
frequency-dependent. The PowerFactory uses the ratio Rf /R1
(resistance at the frequency f over resistance at the fundamental frequency fnom ) to represent the frequency dependence of
a cable series resistance:
b
f
k(f ) = (1 − a) + a ×
(2)
fnom
The choice of coefﬁcients a and b, strongly impacts the
impedance resulting from the frequency scan analysis around
resonance frequencies. A sensitivity study has been performed
with a = 1 and with b equal to 0.6, 0.8 and 1.0 respectively.
The sensitivity study has been performed at wind turbines
4 and 9; impedances seen from the terminals of these two
turbines into the grid are shown in Fig. 2.
Higher values of b present higher impedances at higher
frequencies. The differences are visible in the frequency scan
near the resonance frequency of approximately 1.5 kHz. For
frequencies beyond the resonance point, the impedances are
3
−3
1
10
3
x 10
2
0
WT4
0.6
−1
10
WT9
0.6
WT4
0.8
WT9
0.8
−2
WT4
10
1.0
Voltage harmonic [pu]
Impedance [Ω]
10
1
0
3
2 −3
x 10
4
6
8
10
12
14
16
18
2
WT9
1.0
0
500
1000
1500
2000
Frequency [Hz]
2500
3000
1
3500
0
IV. R ESULTS FROM THE C ASE S TUDY
Two separate harmonic studies have been performed: a
study has been performed for the emission originating from
an individual wind turbine spreading through the collection
grid and into the public grid. The ﬁndings of that study are
presented in Section IV-A. Similarly the harmonic penetration
from the external grid to the wind turbine terminals has been
studied and the results are presented in Section IV-B.
In real-life, the emission at a location is the combination
of harmonics propagated from multiple wind turbines and the
harmonics propagated from the external grid. The results of a
study with emission from all the wind turbines and the public
grid have been presented in Section IV-C.
A wind turbine is often equipped with a turbine low-pass
ﬁlter on the LV side of the turbine transformer. A study on
the impact of such a ﬁlter on the emission is presented in
Section IV-D.
A. Emission Penetrating from a WT
The current harmonics at the 100% PB have been used
as the harmonic source from wind turbine 9 at the end of
the second feeder. The emission, on higher voltage side of
the turbine transformer, has been modelled as a harmonic
current source. A frequency scan analysis was used to obtain
the harmonic levels at other locations. The resulting voltage
spectra at the point-of-connection (POC) to the public grid,
the terminal of wind turbine 4 (‘WT4’) and the busbar with
wind turbine 9 (‘WT9 Bar’) are shown in Fig. 3.
The voltage spectrum shows high levels at harmonic orders
11, 13 and 30. The spectrum presents a general low emission
with peak values somewhat over 0.2%. The interharmonic
voltages are relatively high compared to the harmonic voltages.
The high levels at harmonics 11 and 13 are due to the high
emission at these frequencies, whereas the high levels around
harmonic 30 are due to a resonance.
The voltage distortion at the POC is less than that at the
other three locations. The low voltage distortion at the POC
indicates a low transfer, from WT9 to the external grid.
At the terminal of WT4 the emission from WT9 results in a
low voltage distortion with an exception around harmonic 30.
22
24
26
28
30
32
(Inter)Harmonic order
34
36
38
40
These high values result from the parallel resonance of the
WPP, as depicted in Fig. 2. The characteristic harmonics 11
and 13 are also clearly visible in the spectrum. An extra study
(ﬁgures not shown in the paper) was performed to compare the
voltage spectra at the terminals of the other 8 wind turbines.
The spectra were similar to that at WT4.
The voltage distortion on higher voltage (HV) side of the
turbine transformer with WT9 (‘WT9 Bar’) shows the same
pattern as at the wind turbine terminals, it is highest around the
resonance frequency. An extra comparison (ﬁgures not shown
in the paper) was also performed for voltage distortion on
higher voltage side of the other eight turbine transformers; the
distortion was also similar for all these locations.
Current harmonics are studied on both the HV and LV
sides of the WT9 transformer (‘Trf.9’), the grid-side substation
transformer (‘Trf.grid’), and both sides of the WT4 transformer
(‘Trf.4’), as shown in the upper plot of Fig. 4.
−3
Current harmonic [pu]
not much impacted by the use of different parameters. The
study in the remainder of the paper uses the coefﬁcients a = 1
and b = 0.8 and harmonic frequencies up to 2 kHz.
20
Fig. 3. Voltage spectra at POC, ‘WT4’ and ‘WT9’ caused by injection of
the current spectrum at the full-power state of WT9.
4
x 10
Trf.9 LV
Trf.9 HV
Trf.grid HV
Trf.4 HV
Trf.4 LV
3
2
1
0
5
10
15
20
25
30
35
40
45
50
2.5
Transfer function
Fig. 2. Skin effect sensitivity study. Impedances at the terminals of turbines
4 and 9, with a = 1 and b equal to 0.6, 0.8 and 1.0 respectively.
20
POC
WT4
WT9 Bar
WT9
Trf.grid LV
Trf.grid HV
Trf.4 HV
Trf.4 LV
2
1.5
1
0.5
0
5
10
15
20
25
30
(Inter)Harmonic order
35
40
45
50
Fig. 4. Current spectra at the LV side of the WT9 transformer (‘Trf.9 LV’),
HV side (‘Trf.9 HV’), HV side of substation transformer (‘Trf.grid HV’),
both LV side (‘Trf.4 LV’) and HV side (‘Trf.4 HV’) of the WT4 transformer
caused only by injection of the current spectrum at WT9.
Both the LV and HV sides of transformers presented almost the same emission for the substation transformer and
the turbine transformers. The injected current harmonics at
WT9 resulted in less harmonic emission into the grid, and
almost zero emission at WT4. The current through the grid
transformer is higher than the emission from the turbine near
the resonance frequency at the 30th harmonic.
The transfer function is the ratio between the harmonic
current resulted at a certain location and the emission at source
location. The current transfer functions from WT9 to the grid
and to HV and LV sides of the turbine transformer with WT4
4
TABLE II
I NJECTED BACKGROUND VOLTAGE DISTORTION WITH THE INDICATIVE PLANNING LEVELS FOR HARMONIC VOLTAGES ( IN PERCENT OF THE
FUNDAMENTAL VOLTAGE ) IN HIGH VOLTAGE POWER SYSTEMS FROM STANDARD IEC 61000-3-6, AND SPECIFIED VERY LOW LEVELS FOR
INTERHARMONICS
Odd harmonics
Non-multiples of 3
Multiples of 3
Order
Voltage
Order
Voltage
h
harmonic %
h
harmonic %
5
2
3
2
7
2
9
1
11
1.5
15
0.3
13
1.5
21
0.2
17 ≤ h ≤ 49
1.2 17
21 < h ≤ 45
0.2
h
Even harmonics
Order
h
2
4
6
8
10 ≤ h ≤ 50
Order
h
Voltage
harmonic %
1.5 ≤ h ≤ 50.5
0.2
1.4
Transfer admittance [S]
are shown in the lower plot of Fig. 4. The transfer function
presents the resonance (peak) at harmonic 30 for both the
transfer to the grid and the transfer to WT4. The emission to
the grid is ampliﬁed by approximately 1.8 times at harmonic
30, whereas for the transfer to WT4 the resulting harmonic
current is about 20% of the emission at WT9.
The current propagations have been determined for to other
8 wind turbines, together with the transfer function from WT9
to these turbines, as shown in Fig. 5.
Interharmonics
Voltage
harmonic %
1.4
0.8
0.4
0.4
10
0.19 h + 0.16
T9 − Grid
T9 − T4
1.2
1
0.8
0.6
0.4
0.2
0
0
5
10
15
20
25
30
(Inter)Harmonic order
35
40
45
50
Fig. 6. Transfer admittance from the harmonic source WT9 to the grid POC
and wind turbine 4.
Current harmonic [pu]
8
Transfer function
−5
0.2
x 10
6
4
2
0
5
10
15
20
25
30
35
40
45
50
40
T8
T7
T6
T5
T4
T3
T2
45 T1
50
0.15
0.1
0.05
0
5
10
15
20
25
30
(Inter)Harmonic order
35
Fig. 5. Current harmonics propagated to the terminals of individual wind
turbines caused by the emission of WT9.
All the transfer functions present a resonance around harmonic 30, which is the ﬁrst parallel resonance of this WPP. The
harmonic current propagates to the closer wind turbine (from
WT9) slightly more than to the more remote wind turbines up
to harmonic order 15. The propagation is almost the same for
all turbines at higher orders. The highest value of the transfer
functions, at the resonance frequency, is about 0.2. This means
that the current ﬂowing into each of the other turbines is about
20% of the current emitted by WT9.
The harmonic propagation has been also evaluated in terms
of the transfer admittance. The transfer admittance is deﬁned
as the ratio between the resulting harmonic current at the grid
POC or at WT4 and the harmonic voltage presented at the
source location WT9. The result is shown in Fig. 6.
The transfer admittance from WT9 to WT4 is lower than
that from WT9 to the public grid, whereas the transfer admittance is high near the resonance frequency, with a maximum
at harmonic 32. The high transfer admittance indicates the
ampliﬁcation of harmonic currents at the resonance frequency.
The low transfer admittance from WT9 to WT4 indicates that
harmonic propagation from WT9 to WT4 is more difﬁcult,
which corresponds to the nearly zero emission in Fig. 4.
The emission propagation from one turbine to another is
similar to that from WT9 to WT4. The impedance or admittance between the two locations is of particular importance.
The ﬁnal propagated emission is the consequence of the
impedance (or admittance) and the harmonic source. This is
also applicable for the propagation from any turbine to the
external grid. Thus the harmonic propagation originating from
one turbine can be decomposed into propagations to other
turbines, and into the external grid.
B. Emission Penetrating from the Grid
This section studies the harmonic emission originating from
the external grid, when no other harmonic sources are present.
The emission from the external grid is considered as a
voltage harmonic source (Thevenin equivalent) located at POC
at 66 kV. The indicated planning levels of voltage harmonics from the standard IEC 61000-3-6 are used for harmonic
frequencies, and the level of 0.2% is used for interharmonic
frequencies. The levels used are summarized in Table II.
The voltage spectra at the POC and the 22 kV busbar
(‘22 kV Bus’) of the WPP and WT9 resulting from the
background voltage are shown in Fig. 7.
The background voltage distortion is highest at harmonic 3
and at the characteristic harmonics (5, 7, 11, 13 etc.). The
voltage distortion is similar at the main 22 kV busbar and
at the turbine terminals. Both harmonics and interharmonics
are ampliﬁed around harmonic 30 (1.5 kHz): this is where the
voltage distortion at the turbine terminals is much higher than
that at the POC.
The voltage distortion at the main 22 kV busbar is similar
to the voltage distortion at close to the wind turbines; the
spectrum at WT9 presents a similar pattern to that of the other
eight wind turbine terminals. Ampliﬁed voltage harmonics
5
0.12
Transfer admittance [S]
Voltage harmonic [pu]
1
POC
22kV Bus
WT9
0.1
0.08
0.06
0.04
0
0.6
0.4
0.2
0
0.02
5
10
15
20
25
(Inter)Harmonic order
30
35
Grid − T4
Grid − T9
0.8
5
10
15
20
25
30
(Inter)Harmonic order
35
40
45
50
40
Fig. 9. Transfer admittance from the grid harmonic source to WT4 and WT9.
Fig. 7. Voltage spectra at POC and 22 kV busbar and WT9 terminal caused
by the background voltage harmonics.
(around the resonance) are present throughout the whole WPP
but at levels much higher than the levels at the POC. For the
other frequencies, the distortion levels in the WPP are slightly
lower than the background distortion. Additionally the voltage
distortion at the terminals of the wind turbines is slightly less
than on higher voltage side of the turbine transformer.
Certain harmonic voltages present a higher level in the
collection grid than the background distortion (as a harmonic
source) around the resonance frequency. The high emission
levels are resulted from the resonance of the collection grid.
Current harmonics from the grid also propagate to the HV
and LV sides of the substation transformer and to WT4 and
WT9 transformers. These current and the transfer function
from the grid to WT4 and WT9, are shown in Fig. 8.
Current harmonic [pu]
0.06
Trf.grid HV
Trf.grid LV
Trf.9 HV
Trf.9 LV
Trf.4 HV
Trf.4 LV
0.04
0.02
0
5
10
15
20
25
30
35
40
45
50
Transfer function
40
Trf.9 HV
Trf.9 LV
Trf.4 HV
Trf.4 LV
30
20
10
0
5
10
15
20
25
30
(Inter)Harmonic order
35
40
45
50
Fig. 8. Current spectra at both HV and LV sides of the substation transformer
(‘Trf.grid HV’ and ‘Trf.grid LV’), WT4 transformer (‘Trf.4 HV’ and ‘Trf.4
LV’) and WT9 transformer (‘Trf.9 HV’ and ‘Trf.9 LV’) caused by injection
of the voltage spectrum at the grid.
The background voltage harmonics results in high levels
current harmonics around harmonic 30 because of the resonance. The levels at low-order harmonics at both WT4 and
WT9 are much lower. In contrast, the transfer function did not
show a high transfer at the resonant harmonic order; rather,
high transfer has been observed at order 9.
The other wind turbines also present a high transfer function
at order 9, with similar current harmonics present at the
turbines.
The transfer admittances from the grid to WT4 and WT9 are
similar. There is a peak at around harmonic order 30 because
of the ampliﬁcation effect. The transfer admittance decreases
above the resonance harmonic order, which damps the higherfrequency harmonic current from the grid into the WPP.
The only emission considered in this section originates from
the external grid. The harmonic propagations take place from
the grid into the collection grid and towards each wind turbine.
The voltage and current distortion are heavily impacted by
resonances. A different pattern of current transfer function and
transfer admittance is present than in the previous subsection.
C. Emission with Combined Power Bins
Next the total harmonic currents, combination of different
power bins, has been calculated for number of cases. The
background emission (voltage distortion) from the grid side
is as presented previously. It is further assumed that different
turbines have different productions and therewith different
emission spectra. Three cases, with different levels of power
productions, are deﬁned in the case study:
• Group 1, WT1 with PB10 (power bin 10), WT2 with
PB20, WT3 with PB30, WT4 with PB10, WT5 with
PB20, WT6 with PB30, and so on;
• Group 2, WT1 with PB40, WT2 with PB50, WT3 with
PB60, and so on;
• Group 3, WT1 with PB70, WT2 with PB80, WT3 with
PB90, . . . .
The zero power bin and the 100% power bin are excluded
from the case study.
Voltage spectra at both POC and the 22 kV busbar do not
present much different, when perform respectively with the
three cases. An additional study was performed with all power
bins (except the zero power bin and the 100% power bin) in
the WPP, and the voltage distortion did not present a visible
difference from the study with the three cases.
As well the current distortion was studied with the above
approach; and a similar conclusion is obtained: with different
power bins injected, the current distortion didn’t change much
at both the wind-power-plant side and the grid side.
D. Impact of A Turbine Filter
A case study has been performed where a ﬁlter is installed
on the turbine-side of the turbine transformer. The ﬁlter branch
(with R, L and C) is connected in parallel with the transformer
between the transformer and the converter reactance. This ﬁlter
branch, together with the inductance of the transformer and the
converter reactance, attenuates the emission of the remnants
of the switching frequency into the collection grid. It fulﬁls
a very similar role as the EMC ﬁlter in smaller equipment.
The harmonic emission from WT9 to the grid and to WT4
is studied with a ﬁlter (the previous sections are without a
6
ﬁlter). The transfer functions are obtained and are shown as
in Fig. 10.
0
Impedance [Ω]
Transfer function
Current harmonic [pu]
10
−2
10
Impedance seen from WT9 to the grid
−3
x 10 5
10
15
20
5
0
35
40
45
50
Trf.9 LV
Trf.grid HV
Trf.4 LV
5
10
15
20
25
30
35
(Inter)HarmonicTrf.grid
order HV
Trf.4 LV
40
45
50
5
10
15
20
25
30
(Inter)Harmonic order
40
45
50
0.5
0
25
30
Frequency [Hz]
35
Fig. 10. Impedance seen from WT9 to the grid (upper ﬁgure); current spectra
at the LV side of the WT9 transformer, HV side of POC and LV side of the
WT4 transformer (middle ﬁgure); transfer functions from WT9 to POC and
WT4 (lower ﬁgure).
The ﬁlter shifts the resonance frequencies to lower orders.
There are two parallel resonances present in the frequency
range up to harmonic 50. However, the ﬁrst resonance presents
around harmonic 11, which results in a high emission at
harmonic 11 and 13 for both the grid side and WT4. Because
of the resonance, the transfer functions present apparent ampliﬁcations around harmonic 12 and harmonic 41. The current
harmonics into the grid and WT4 are similar, in contrast to
the reduced emission at WT4 without a turbine ﬁlter. The use
of a turbine ﬁlter causes the harmonics to be propagated more
to the turbine than to the external grid.
It should be noted that, the study has been performed for a
particular case. In practical use, the design of a WPP will avoid
resonances, especially around high emission frequencies.
V. D ISCUSSION OF R ESULTS
The study in this paper is based on a speciﬁc case study,
so that the results strictly speaking only hold for this speciﬁc
WPP. Despite this a number of general conclusions can be
extracted, based on similarities between WPPs.
The decomposition between primary and secondary emission is valid for all wind power installations. Resonance
frequency (see below), background voltage distortion and
emission per turbine are of the same order of magnitude
for a large part of the installations. Although there will
be differences between installations, the general pattern that
primary as well as secondary emission need to be considered
is expected to hold generally for all WPPs. It is recommended
to study primary and secondary emission for each installation.
Resonances have been observed commonly for wind-power
collection grids. The conﬁguration of a WPP is rather standard: a medium-voltage underground collection grid, with a
transmission transformer and a turbine transformer to each
turbine. The main resonance occurs, as an approximation, due
to the capacitance of the cable network and the inductance
of the transmission transformer. With an increasing number of
turbines (of the same size), the total cable length (and thus the
capacitance) increases linearly with the number of turbines.
At the same time the size of the transmission transformer
increases linearly with reduction in inductance as a result. The
resonance frequency will remain about the same. Simulations
performed by our group (but not yet published) show that
the ﬁrst resonance frequency for a 10-turbine WPP is very
similar to the one for a 100-turbine plant. When a larger
plant consists of larger turbines instead of more turbines also
both total cable length and transformer size will increase. The
increase of distance between turbines is however less than the
increase in rated power of the turbines, so that the resonance
frequency will become somewhat less with the increase in size
of the installation. In short: although each WPP will have its
own resonance frequency, the variation in resonance frequency
between WPPs is expected to be signiﬁcantly less than the
variation in WPP size.
It is shown in this paper that a non-negligible fraction of
the current from a turbine ﬂows to other turbines at frequency
around the main resonance frequency. It was shown that this
depends strongly on the properties of the ﬁlter with the turbine.
Therefore, this conclusion may not hold generally and could
differ a lot between installations.
The amplitude of the secondary emission at the point of
connection is determined by the level of background voltage
distortion and the input admittance of the wind park. The
primary emission at this location is determined by the primary
emission of the turbines and the transfer functions. Each of
these contributing factors will be park and location dependent.
But the variations will still be relatively small (the values
will be of the same order or magnitude) for the majority of
cases. Therefore secondary emission dominating over primary
emission, for certain frequency ranges, is expected with many
WPPs.
The study in this paper is based on a WPP that is directly
connected to the public grid. Any resonance effects in the
public grid are neglected and the public grid is modeled simply
as the series connection of a resistance and an inductance.
Some WPPs are connected to the grid through long ac cables.
The resonance of that cable capacitance could occur at a lower
frequency than the resonance due to the cables in the collection
grid. The harmonic propagation with such WPPs could be
different in such cases and the conclusions presented in this
paper might not be valid for such WPPs. However the presence
of secondary emission is also likely to be of importance in such
WPPs and it is recommended to include secondary emission
in the study of such WPPs as well.
VI. C ONCLUSION
The paper shows a study on harmonic propagations in a
wind power plant (WPP). In the study the propagation is
decomposed into two different ones corresponding to two
fundamentally different harmonic sources. The characteristics
of the propagation paths are studied.
For a speciﬁc WPP conﬁguration, a sensitivity study of
the impedance seen from individual wind turbines has been
performed. A resonance occurs and the impedance as a
function of frequency has been calculated with different skineffect exponents, which results in different peak values of the
impedances.
7
The study decomposes the harmonic propagation into two
groups depending on the harmonic source that drives the
propagation: propagation from an individual wind turbine to
other turbines and to the public grid; and propagation from
the public grid to the individual turbines. The characteristics
of these propagation have been analyzed. An important conclusion from the studies is that both emission from the turbines
and emission from the public grid should be considered
in harmonic studies for WPPs. In this case the emission
originating from the public grid by far dominates the current at
the point of connection. A similar conclusion has been drawn
in an earlier study [21] and following the reasoning in the
previous section it is concluded that this will be the case for
many WPPs. The current measured at the point of connection
between the WPP and the public grid does not by itself give
any information on the emission from the individual turbines.
A study is performed for the impact of the turbine ﬁlter on
the propagation. It is shown that more harmonics propagate
into a turbine than into the public grid when a ﬁlter is present.
A ﬁlter has a signiﬁcant impact on the harmonic propagation,
which needs to be considered during harmonic studies of a
wind power plant.
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C8
Paper D
Interharmonic Currents from A Type-IV Wind Energy
Conversion System
K. Yang and M.H.J. Bollen
Submitted to Electric Power Systems Research
The layout has been revised.
D2
1
Interharmonic Currents from A Type-IV Wind
Energy Conversion System
Kai Yang and Math H.J. Bollen
Abstract—This paper presents a simpliﬁed model for the
origin of interharmonic emission of a Type-IV wind turbine and
the veriﬁcation of that model using long-term measurements.
Interharmonic variations in magnitude and in frequency are due
to the difference between the turbine-side and grid-side frequency
of the full-power converter. The model veriﬁcation consists of
three parts: correlation between frequencies; relation between
magnitude of interharmonics and active-power production, and
relation between magnitudes of different interharmonics. The
measurements are in agreement with the model predictions.
Next to having conﬁrmed the proposed model, the paper also
introduces a graphical correlation method to extract information
on interharmonics from long-term measurement series.
Index Terms—Wind power generation, Power quality, Power
conversion harmonics, Harmonic analysis.
I. I NTRODUCTION
T
HE presence of harmonic emission from wind turbines
is well documented in various papers and books. A
ﬁeld measurement of harmonic voltage and current from a
wind park with ﬁve variable-speed on-shore wind turbines is
presented in [1], [2]. Characteristics of harmonics and interharmonics from a number of modern on-shore wind turbines
are presented in [3], [4].
The presence of interharmonics due to the employment
of power electronics in wind turbines is documented in a
lesser number of sources [5], [6], [7]. Papers [5], [6] present
theoretical sources of interharmonics, and paper [7] presents
ﬁeld measurements from a wind turbine. It is shown in [8]
that certain interharmonic currents have the general tendency
to increase with the active-power production, whereas most
others present a varying and complicated tendency.
General explanations for the emission of interharmonic
currents from wind turbines with power-electronic converters
are given in [5], [7], [9]. But none of these publications
goes into sufﬁcient details. Interharmonics are observed in a
number of loads, which include static frequency converters,
cycloconverters, subsynchronous converter cascades and loads
non-pulsating synchronously with the fundamental frequency
[5], [10], [11]. It is stated in [7] that the interharmonics from
a Type-III wind turbine are due to the slot harmonics from
the induction machine. However no further detail is given (for
example about how these slot harmonics propagate through
the converters) and the simulations presented in [7] also do
———————————————This work has been ﬁnancial supported by the Vindforsk program and by
Skellefteå Kraft Elnät AB.
K. Yang and M. H. J. Bollen are with the Electric Power Engineering
Group, Luleå University of Technology, 931 87, Skellefteå, Sweden. e-mail:
([email protected]).
not include the slot harmonics so that the statement cannot
be veriﬁed. For the same reasons it is not possible to verify
if slot harmonics can be the explanation for harmonics from
Type-IV wind turbines.
Reference [5] only mentions the presence of interharmonics
in wind turbines, but without giving more details. A model
of a power conversion system including a six-pulse windturbine power converter is presented in [9]. Interharmonics
are generated according to this model, because the generator
speed is not synchronized with the power-system frequency.
As the generator speed varies, the interharmonic frequencies
will vary. That model has however not been veriﬁed using
measurements.
Harmonic distortion from a Type III wind turbine presents
a time-varying characteristic; the difference between the average, 90, 95 and 99-percentile levels indicates large variations in time at certain frequency bands [12]. Phenomena
also indicate varying emission in frequency. When looking
at individual spectra, obtained for example over a 200-ms
window, most of them show high emission at narrowband
interharmonic frequencies, whereas the emission has shifted
to another frequency a few minutes later. When taken over a
longer duration, days of weeks, the average or high-percentile
spectrum presents a broadband characteristic for interharmonics together with narrowbands for harmonics [8].
In this paper an improved model from [9] for the emission
of interharmonics from a Type-IV wind turbine is proposed
and veriﬁed by measurements.
The model explaining the origin of interharmonics from a
Type-IV wind-turbine is introduced in Section II. This section
also gives an overview of the veriﬁcation methods used. The
emission frequencies and their correlations, predicted from the
model are presented in Section III, together with a description
of the measurements used to verify the model. The predicted
correlation between the emission at different frequencies is
presented in Section IV. Further veriﬁcation is presented in
the next two sections. The relation between emission and
active-power has been studied in Section V. The relationship
of amplitudes between emission at different frequencies has
been studied in Section VI. The conclusions of the work are
presented in Section VII.
II. T URBINE M ODEL AND V ERIFICATION
A. Model of Type-IV Turbine
A Type-IV wind turbine (with a full-power converter) is
studied, for the purpose of this work, as an AC-DC-AC
converter connecting the turbine to the grid, as shown in Fig. 1.
2
•
Fig. 1.
Type-IV wind turbine with a full-power converter.
The frequency of the voltage on the generator-side of the
converter, f1 , is typically different from the power system
frequency on the grid-side of the converter, f0 . The former
varies with wind speed and thus with active-power production,
whereas the latter is independent of wind speed and activepower production. The power-system frequency varies in a
small range, and throughout this work the power-system
frequency will be considered as constant.
The AC-DC part of the converter on the generator side is a
six-pulse rectiﬁer resulting in a DC-bus voltage, which consists
of a DC component and a voltage ripple of frequency 6f1 .
The DC-AC part is a voltage-source converter (VSC) using
pulse-width modulation (PWM) to create a close-to-sinusoidal
voltage behind impedance. The slight distortion of the voltage
source is partly due to imperfections in the converter and
its control algorithm, and partly due to the DC-bus voltage
not being a perfect DC voltage. In this work the latter
contribution will be considered. The PWM pattern will also
result in waveform distortion, starting at frequencies close to
the switching frequency used. This distortion takes place at
higher frequencies than the ones discussed here and they will
not be considered in this paper.
The voltage generated by the VSC drives a current through
the impedance connecting the VSC with the grid, including the
source impedance of the grid at the point of connection. It is
this current that is referred to as the “emission from the wind
turbine”. That impedance consists of the converter reactor, the
turbine transformer and in many cases a harmonic ﬁlter. In this
work, it is assumed that this impedance is purely inductive for
the frequencies of interest.
B. Model Veriﬁcation
The model for interharmonic emission that described in a
number of formulas can be veriﬁed using measurements. A
series of measurements used for this purpose are presented
in Section III-B, Section IV-B, Section V-B and Section VI-B.
The number of veriﬁcations and their limitations are listed:
• The dominant time-varying broadband interharmonics
in the average, 90-, 95- and 99-percentile spectra are
within the expected frequency ranges. The frequencies
are calculated in Section III-A and the average spectrum is
studied in Section III-B. However the frequency-varying
emission cannot be tracked and visualized in the above
statistical spectra.
• A very important part of the veriﬁcation concerns the
correlation between interharmonic frequencies. Those
correlations are predicted in Section IV-A and veriﬁed by
means of a graphical correlation diagram in Section IV-B.
The varying frequency pairs, due to the frequency change
•
of the generator-side, are visualized and the relations
between interharmonics are present. The track of the
varying frequency is well present even in 5 Hz resolution.
The model used predicts that the magnitude of the
interharmonics is strongly correlated with the activepower production. The predicted relation is derived in
Section V-A and the measurement results are shown in
Section V-B. The main trend is shown, however the
measurement results are impacted by certain noise and
spectral leakage.
The model used also predicts a constant ratio between the
emissions at related interharmonic frequencies. The ratio
is derived in Section VI-A and the measurement results
are shown in Section VI-B. In this case, there is less
impact of noise and spectral leakage since the emission
of studied frequency pairs are related to each other and
simultaneously impacted.
III. I NTERHARMONIC O RIGIN AND F REQUENCIES
A. Model of Frequency Conversion
The frequency on the generator side of the converter is equal
to f1 . For a six-pulse rectiﬁer this results in a voltage ripple
on the DC bus with frequency 6f1 . The DC voltage is with the
ripples at frequency 6kf1 . The DC-bus voltage will contain,
next to the DC component, components with frequencies 6f1 ,
12f1 , 18f1 , etc. The ﬁrst frequency component is the dominant
one.
The DC component is inverted into the power system
frequency through the grid-side inverter, by modulation with a
PWM switching pattern [13], [14]. The resulting waveform on
the grid side is regenerated mathematically by multiplication
with cos(ω0 t) where ω0 = 2πf0 and f0 the power system
frequency.
At the AC output of a converter, the current is the ratio
of output voltage of the VSC and the grid-side impedance,
assuming there is no background voltage distortion. In addition
to the conversion, where a sinusoidal grid frequency has been
assumed, interactions with harmonics in the grid voltage will
also impact the interharmonic emission. The characteristic
harmonics cos((6n ± 1)ω0 t), which are dominant in the grid
voltage, will produce the frequencies ω+ = 6kω1 +(6n±1)ω0
and ω− = 6kω1 − (6n ± 1)ω0 . Consequently the generated
frequency components due to both power-system frequency
and its characteristic harmonics are written as:
iAC (t) = I0 cos(ω0 t) +
∞
I0 cos((6n ± 1)ω0 t)
n=1
+
+
∞
∞ V6k
cos(6kω1 + (6n ± 1)ω0 )t + φ6k )
2Zω+
n=0
k=1
∞ ∞
V6k
cos(6kω1 − (6n ± 1)ω0 )t + φ6k )
2Z
ω−
k=1 n=0
(1)
here I0 is the current at the power-system frequency; Zω± the
impedance at radian frequency ω± at the grid-side.
The group of leading-frequency components is written as:
3
k,n
fleading
= 6kf1 + (6n ± 1)f0
(2)
The group of lagging-frequency (in Hz) component is:
k,n
= 6kf1 − (6n ± 1)f0
flagging
(3)
These resulted frequencies have been pointed out in papers
[5], [6]. Whereas no references with real measurements and
analytical methods are found to prove the existence of these
frequencies, as well as the variation of these frequencies.
B. Measurement and Time-Varying Spectrum
Measurements have been performed on a Type-IV turbine
in a wind park. The measurements have been done on the
medium voltage side of the turbine transformer. Details of the
measurements are presented in [8].
Harmonic current [A]
1
285Hz
80Hz
0.6
15Hz
0.4
0.2
0
0
50
0.1
Harmonic current [A]
385Hz
0.8
100
150
200
250
300
350
720Hz
620Hz
400
450
Average
90 percentile
95 percentile
99 percentile
0.08
0.06
0.04
0.02
0
500
600
700
800
900
Frequency [Hz]
1000
1100
1200
Fig. 2. Current average spectrum, 90-, 95- and 99-percentile values of a
Type-IV wind turbine. Note the different vertical scales of the 0 - 450 Hz and
450 - 1200 Hz frequency ranges.
TABLE I
F REQUENCY COMPONENTS WITH FIRST THREE ORDERS FOR
f1 = 55.8333 Hz AND f0 = 50 Hz.
Order k
leading component
lagging component
1
385 Hz
285 Hz
2
720 Hz
620 Hz
3
1055 Hz
955 Hz
harmonic (6n ± 1) = 5, it generates 6f1 − 5f0 = 85 Hz; and
the seventh harmonic gives 6f1 − 7f0 = −15 Hz, which will
appear as 15 Hz in a spectrum.
The broadband around 80 Hz is different from the approximated calculation at 85 Hz. The approximation is attempt to
calculate related to the 5 Hz frequency components as in the
spectrum. The difference of the series approximated frequencies may be due to the measurement frequency resolution to
be 5 Hz. The broadband character of the spectrum is caused by
the variation in frequency of the interharmonic components.
The frequency components, at 15 Hz, 80 Hz, 285 Hz and
385 Hz, indicate a most frequent operational state of the wind
turbine. The variation of the frequency components (both
frequencies and magnitudes) are presented in [8].
One spectrum is not enough to show the time varying
emission. The variations in the different frequency bands are
shown here by using different statistical spectra. The larger
the variation, the larger the difference between the statistical
spectra. Paper [8] presents the variation of the emission in
time through a spectrogram and the variation as a function of
active power through scatter plots. The variation in frequency
is however not visualized through either of these methods.
IV. C ORRELATION BETWEEN F REQUENCY C OMPONENTS
A. Expected Correlations
The measurement includes waveforms which each has a
200 ms window every 10-minute interval during 13 days.
The measurement involves 1864 spectra within the duration,
which covers all operational states (as Turbine III in [8]).
Four types of statistical current spectrum, average spectrum,
90-, 95- and 99-percentile values, have been obtained from
the measurement, as shown in Fig. 2. The main differences
between the four spectra are at the clearly-visible broadband
components around 15 Hz, 80 Hz, 285 Hz, 385 Hz, 620 Hz and
720 Hz. Within the frequency ranges, the variation of emission
makes the difference between the four statistical spectra. The
larger difference, the more the frequency component varies.
The differences of emission indicate the obvious time-varying
emission at these broadband.
Inversely calculated according to formula (2) and (3), the
approximated turbine-side frequency f1 = 55.8333 Hz can
result in these grid-side frequency components as listed in
Table I. These frequencies are observed as the centered frequencies of the time-varying broadband components.
With a consideration of characteristic harmonics in the gridside voltage, and with the generator-side frequency f1 =
55.8333 Hz, the ﬁfth and seventh harmonics will result in
frequency components with the lagging component 6kf1 −
(6n ± 1)f0 when k = 1, n = 1. For the ﬁfth characteristic
The model presented in Section II and Section III-A shows
that emission is expected at frequencies varying with the
turbine-side frequency f1 .
A certain generator-side frequency results in a number of
frequency components in the grid-side current. The abovementioned model also predicts that different frequency components will show strong correlations in magnitude. Such
correlations are expected among others, between the following
frequencies:
• A: 6f1 − f0 and 6f1 + f0 ;
• B: 12f1 − f0 and 12f1 + f0 ;
• C: 6f1 ± f0 and 12f1 ± f0 ;
• D: 6f1 ± f0 and 6f1 − 5f0 ;
• E: 6f1 ± f0 and 6f1 − 7f0 ;
• F: 6f1 − 5f0 and 6f1 − 7f0 ;
• G: 12f1 ± f0 and 6f1 − 5f0 ;
• H: 12f1 ± f0 and 6f1 − 7f0 ;
Depending on a combination of integers k and n of (2) and
(3), more correlations are found.
B. Observed Correlations
During the 13-day period of measurements about 1800
spectra (with 5-Hz resolution) have been obtained. To verify
4
Fig. 3. The correlation coefﬁcient between different frequencies. The coefﬁcient ranges from -1 to 1, with the lowest correlation blue and highest red color.
the proposed model, the correlation in magnitude between
different frequencies has been obtained from the number
of spectra. The correlation coefﬁcients have been calculated
between each two frequency components (up to 800 Hz), as
shown in Fig. 3.
The correlation coefﬁcient ranges from -1 to 1. Unity
correlation (represented in dark red) indicates an exact linear
increase between two data series; while negative unity (dark
blue) indicates the decrease of one series with the increase of
the other series.
The eight types of correlation lines (A through H) predicted
from the model in the previous section are all clearly visible
and marked in the ﬁgure. Note that the color plot is symmetrical.
• A: 6f1 − f0 and 6f1 + f0 , two lines in parallel with the
diagonal around 250 and 350 Hz;
• B: 12f1 − f0 and 12f1 + f0 , the same lines around 600
and 700 Hz;
• C: 6f1 ± f0 and 12f1 ± f0 , lines with double or half
the slope of the diagonal, slightly below the middle on
the right-hand side of the diagram and slightly left of the
middle on the upper side of the diagram;
D: 6f1 ± f0 and 6f1 − 5f0 , two lines in parallel with the
diagonal slight left of the middle near the bottom of the
diagram and slightly below the middle near the left side
of the diagram;
• E: 6f1 ± f0 and 6f1 − 7f0 , this one is vaguely visible as
lines in opposite direction as the diagonal near the previous lines; the opposite direction is due to the expressions
resulting in negative frequencies which obviously show
up as positive frequencies in the spectrum obtained from
the measurements;
• F: 6f1 − 5f0 and 6f1 − 7f0 , the anti-diagonal line in the
bottom-left corner of the diagram;
• G: 12f1 ± f0 and 6f1 − 5f0 , lines with double or half the
diagonal slope at the bottom right of the diagram;
• H: 12f1 ± f0 and 6f1 − 7f0 , lines with double or half the
diagonal slope, but in opposite direction, at the bottom
right of the diagram.
Note that the correlation diagram shows the presence of
interharmonic components at frequencies that are not visible
or just barely visible in the four statistical spectra. Despite
•
5
V. D EPENDENCY ON ACTIVE -P OWER P RODUCTION
A. Model
In case of symmetrical voltage waveform on the generatorside of the converter being sinusoidal at the frequency f1 , the
DC-bus voltage contains a voltage ripple with frequency 6f1 .
The ripples are smoothed by a capacitor C. The capacitor
will be charged when the voltage is lower than the rectiﬁed
AC-side voltage with a charging time t1 ; then the capacitor
will be discharged exponentially when the rectiﬁed AC-side
voltage drops below the capacitor voltage with a discharging
time t2 .
The charging time t1 is much shorter than the discharging
time t2 ; the discharging time is considered equal to T /6 =
1/6f1 , where T the period of the fundamental frequency
on generator-side of the converter. The relation between the
voltage and the current for a capacitor is:
dv
(4)
dt
The current discharging the capacitor is a function of the
active power P :
P
(5)
i=
VDC
Thus the voltage drop during the discharging period is:
i=C×
ΔV =
i
P
Δt =
C
VDC · C · 6f1
(6)
This voltage drop is the peak-to-peak amplitude of the
voltage ripple.
The VSC uses pulse-width modulation (PWM) to invert the
DC component into a power-system frequency AC component,
with a resulting current emission as in (1). The amplitude of
the interharmonic current is proportional to the amplitude of
the fundamental-frequency component (at frequency 6f1 ) of
the ripple voltage V6k .
The coefﬁcient α6kf1 ±(6n±1)f0 is used for the relation
between the amplitude of the voltage component at the ripple
frequency and the peak-to-peak amplitude of the ripple voltage. This results in the following expression for the amplitude
of the interharmonic current:
P
I6kf1 ±(6n±1)f0 = α6kf1 ±(6n±1)f0 ×
(7)
6f1 CVDC
This reasoning indicates that the amplitude of the interharmonic current is proportional to the active power P .
B. Measurement
The measured interharmonic magnitudes as a function of
active-power are shown in Fig. 4.
0.4
15 Hz
0.2
80 Hz
0.2
0.1
Harmonic/interharmonic curent [A]
the rather low frequency resolution of 5 Hz, the presence of
interharmonics is clearly visible in the diagram.
The frequency pairs of strongest correlation are shown to be
shifting in frequency, which is according to the change of the
generator side frequency. The color plot, in a novel approach,
reveals the varying emission in frequency. The change of
generator side frequency, shown indirectly with the strongest
correlation, is possible to be tracked in the color plot. Thus
the range of the generator side frequency is indicated with the
two ends of one red line (strong correlation). The change of
the generator side frequency is visible in the color plot, which
cannot be presented with one spectrum or scatter plots of one
frequency component.
Since the measurements are with 5 Hz resolution, variations
(of correlated frequency pairs) due to deviation of the power
system frequency f0 are not visible in the correlation plot in
Fig. 2. The impact of the generator side frequency is much
more than the variation in grid side frequency.
Additionally the low (negative) correlation-coefﬁcients between the frequencies around 250 Hz, 350 Hz and other frequencies are probably due to a harmonic reduction schema
from the converter, which is designed for shifting the 5th and
7th harmonic phase-angles to cancel the corresponding voltage
harmonics in the background distortion.
0
1
0
0.2
0.4
0.6
0.8
1
285 Hz
0
0
0.2
0.5
0.4
0.6
0.8
1
0.6
0.8
1
0.6
0.8
1
385 Hz
0.6
0.4
0.2
0
0.1
0
0.2
0.4
0.6
0.8
620 Hz
0
0
0.2
0.1
0.05
0
1
0.4
720 Hz
0.05
0
0.2
0.4
0.6
0.8
0
1
0
0.2
Active power [pu]
0.4
Fig. 4. Interharmonics produced by the wind turbine conversion system as
a function of the active-power [pu], for a Type-IV turbine.
All six frequencies 15 Hz, 80 Hz, 285 Hz, 385 Hz, 620 Hz
and 720 Hz show higher amplitudes for higher active power.
The values that are close to zero correspond with periods
when the generator is not operating close to 55.8333 Hz. The
fact that not all points are close to a straight line of linear
amplitude versus power can be explained from the limited
frequency resolution (5 Hz) resulting in spectral leakage when
the interharmonic component is not an integer multiple of
5 Hz. It is therefore not possible to obtain a clear trend. However, the relation shown in the plot is what one would expect
from the model together with the measurement inaccuracy.
Measurements in [8] show a full range of operational states
of the turbine and a higher power increase up to 1 pu. The
number of dots in the power range does not make a signiﬁcant
difference from the lower power range.
The scatter plots for the components at 285 Hz and 385 Hz
are very similar. The same holds for the pair 620 Hz and
720 Hz. These frequency pairs are generated with the same
order k in (2) and (3), where one is the leading component
and the other the lagging component.
Spectral leakage, and quantization noise, limits the information that can be extracted from the scatter plots. This makes
6
that no clear trend of interharmonics as a function of active
power is visible.
VI. R ATIO BETWEEN I NTERHARMONIC C URRENTS
A. Model
As presented in Section III-A, the wind power conversion
system generates two groups of frequency components: the
leading component group 6kf1 + f0 as in (2) and the lagging
component group 6kf1 − f0 as in (3). For simpliﬁcation the
effect of characteristic harmonics in the grid voltage is ignored:
n = 0 in the two equations.
The harmonic voltages at the VSC terminals for the leading
and lagging components are equal: V6kf1 +f0 = V6kf1 −f0 as
in (1). The current injected into the grid is determined by this
voltage and the impedance between the VSC terminals and
the grid.
The impedance at frequency 6kf1 ± f0 , assuming it to be
purely inductive, is written as:
Z6kf1 ±f0 = 2π(6kf1 ± f0 )L
(8)
The ratio of the current magnitudes for the lagging and
leading frequency components is inversely proportional to the
ratio of the frequencies:
Rlagging,leading =
I6kf1 −f0
6k1 f1 + f0
=
I6k2 f1 +f0
6k2 f1 − f0
(9)
For instance, the ratio between a 285 Hz and a 385 Hz
components will be
RI,285,385 =
I285
= 385/285 = 1.35
I385
(10)
B. Measurement
The six pairs of interharmonic currents, between 285 Hz,
385 Hz, 620 Hz and 720 Hz, have been plotted in Fig. 5.
1
0.1
385 vs. 285
Interharmonic curent [A]
0.5
0
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
620 vs. 385
0.05
0.05
0
0.2
0.4
0.6
0.8
1
720 vs. 385
0.1
0
0.1
0.05
0
0
0.1
720 vs. 285
0.1
0
620 vs. 285
0.05
0
0.2
0.4
0.6
0.8
720 vs. 620
0.05
0
Fig. 5.
0.2
0.4
0
0.6
0
0.02
Interharmonic current [A]
0.04
0.06
0.08
line. The slope of the line equals the ratio of the frequencies
according to the model presented in the previous section.
The other pairs show more spread. They still indicate a
linear relation, but the correlation is weaker compared to the
one for the pair 285 and 385 Hz. It might be due to the very
low emission at the frequencies 620 Hz and 720 Hz, due to the
dots being concentrated around zero, or it might be due to the
ripple waveform not always being the same. It is the waveform
that gives the ratio between the 6f1 and 12f1 components in
the DC-bus voltage.
The limitation of the measurement veriﬁcation is also from
a possible spectral leakage and noise. Unlike the scatter plots
as a function of power, the current pairs are less impacted due
to both frequencies of the pair are impacted simultaneously.
VII. C ONCLUSION
The paper shows how a Type-IV wind power conversion
system results in interharmonics being emitted into the grid.
The origin of the interharmonics is due to the difference
between the generator-side and the grid-side frequencies of the
full-power converter. It is also shown that the interharmonic
frequencies and their amplitudes are related to the voltage
ripple on the DC bus. This in turn is about linear with the
produced power.
The AC-DC-AC converter results in a series of interharmonic frequencies in the grid-side current, which appear at
interharmonic pairs with 100 Hz difference. As the generator
side frequency is not constant, the interharmonic frequencies
vary as well.
The model has been veriﬁed in a number of ways using a
set of current waveforms obtained every ten minutes over a
two-week period.
The correlation coefﬁcient plot shows the existence of the
frequency pairs that follow from the model and their predicted
correlations. The observed increase of interharmonic emission
with increasing power production can be explained from the
model as well. Finally, the ratio in magnitude between the
currents in an interharmonic pair corresponds with the value
obtained from the model.
The correlation plot can be used to extract information even
in case of limited measurement accuracy and resolution, to
allow the study of varying interharmonics in a much better
way than using the spectrum only.
The turbine studied in this paper uses a six-pulse diode
rectiﬁer, but different rectiﬁer conﬁgurations are in use. More
measurements are needed on other Type-III and Type-IV
turbines to study the origin of interharmonic components as
found in this paper. A preliminary conclusion from the study
presented in this paper is that different Type-IV wind turbines
may have rather different emission spectra.
0.1
Interharmonic current pairs.
The current pair 285 Hz versus 385 Hz is strongly correlated,
which results in the scatter points laying close to a straight
ACKNOWLEDGMENT
The authors would like thank especially to Mats Wahlberg,
Skellefteå Kraft Elnät AB, for the measurements and the
technical information of the measured wind turbine.
7
R EFERENCES
[1] S. T. Tentzerakis and S. A. Papathanassiou, “An investigation of the
harmonic emissions of wind turbines,” IEEE Transactions on Energy
Conversion, vol. 22, no. 1, pp. 150–158, March 2007.
[2] S. Tentzerakis, N. Paraskevopoulou, S. Papathanassiou, and P. Papadopoulos, “Measurement of wind farm harmonic emissions,” in IEEE
Power Electronics Specialists Conference (PESC), June 2008, pp. 1769–
1775.
[3] M. Bollen, L. Yao, S. Rönnberg, and M. Wahlberg, “Harmonic and
interharmonic distortion due to a windpark,” in Proceedings of 2010
IEEE Power and Energy Society General Meeting, July 2010, pp. 1–6.
[4] K. Yang, M. Bollen, and M. Wahlberg, “Characteristic and noncharacteristic harmonics from windparks,” in Proceedings of the 21st
International Conference and Exhibition on Electricity Distribution,
Frankfurt, Germany, June 2011.
[5] A. Testa, M. Akram, R. Burch, G. Carpinelli, G. Chang, V. Dinavahi,
C. Hatziadoniu, W. Grady, E. Gunther, M. Halpin, P. Lehn, Y. Liu,
R. Langella, M. Lowenstein, A. Medina, T. Ortmeyer, S. Ranade,
P. Ribeiro, N. Watson, J. Wikston, and W. Xu, “Interharmonics: Theory
and modeling,” IEEE Transactions on Power Delivery, vol. 22, no. 4,
pp. 2335–2348, 2007.
[6] F. De Rosa, R. Langella, A. Sollazzo, and A. Testa, “On the interharmonic components generated by adjustable speed drives,” IEEE Transactions
on Power Delivery, vol. 20, no. 4, pp. 2535 – 2543, Oct 2005.
[7] C. Larose, R. Gagnon, P. Prud’Homme, M. Fecteau, and M. Asmine,
“Type-III wind power plant harmonic emissions: Field measurements
and aggregation guidelines for adequate representation of harmonics,”
IEEE Transactions on Sustainable Energy, vol. 4, no. 3, pp. 797–804,
July 2013.
[8] K. Yang, M. H. Bollen, E. Larsson, and M. Wahlberg, “Measurements
of harmonic emission versus active power from wind turbines,” Electric
Power Systems Research, vol. 108, no. 0, pp. 304 – 314, 2014.
[9] K. Yang, “Wind-turbine harmonic emissions and propagation through a
wind farm,” Licentiate Thesis, Luleå University of Technology, Skellefteå, Sweden, 2012.
[10] R. Yacamini, “Power system harmonics. IV. interharmonics,” Power
Engineering Journal, vol. 10, no. 4, pp. 185–193, Aug 1996.
[11] M. Bollen and I. Gu, Signal Processing of Power Quality Disturbances,
ser. IEEE Press Series on Power Engineering. New York: Wiley, 2006.
[12] K. Yang, M. Bollen, E. Larsson, and M. Wahlberg, “A statistic study
of harmonics and interharmonics at a modern wind-turbine,” in 16th
International Conference on Harmonics and Quality of Power (ICHQP),
May 2014, pp. 1–8.
[13] N. Mohan, T. Undeland, and W. Robbins, Power electronics: converters,
applications, and design, ser. Power Electronics: Converters, Applications, and Design. New York: John Wiley & Sons, 2003, no. Vol.1.
[14] B. Wu, Y. Lang, N. Zargari, and S. Kouro, Power Conversion and
Control of Wind Energy Systems, ser. IEEE Power Engineering Series.
Hoboken, NJ: Wiley, 2011.
Kai Yang (S’10) received the M.Sc. degree from Blekinge Institute of
Technology, Sweden in 2009 and the Licentiate of Engineering degree from
Luleå University of Technology in 2012. Currently he is a PhD student at the
Department of Engineering Sciences and Mathematics at Luleå University of
Technology, Skellefteå, Sweden. The main research interest is in the ﬁeld of
wind power quality, harmonics and distortion.
Math H.J. Bollen (M’93-SM’96-F’05) received the M.Sc. and Ph.D. degrees
from Eindhoven University of Technology, Eindhoven, The Netherlands, in
1985 and 1989, respectively. Currently, he is professor in electric power
engineering at Luleå University of Technology, Skellefteå, Sweden. He has
among others been a lecturer at the University of Manchester Institute of
Science and Technology (UMIST), Manchester, U.K., professor in electric
power systems at Chalmers University of Technology, Gothenburg, Sweden,
technical expert at the Energy Markets Inspectorate, Eskilstuna, Sweden, and
R&D Manager Electric Power Systems at STRI AB, Gothenburg, Sweden. He
has published a few hundred papers including a number of fundamental papers
on voltage dip analysis, two textbooks on power quality, “understanding power
quality problems” and “signal processing of power quality disturbances”,
and two textbooks on the future power system: “integration of distributed
generation in the power system” and “the smart grid - adapting the power
system to new challenges”.
D8
Paper E
A Systematic Approach for Studying the Propagation of
Harmonics in Wind Power Plants
K. Yang and M.H.J. Bollen
Submitted to IEEE Transactions on
Power Delivery
The layout has been revised.
E2
1
A Systematic Approach for Wind Power Harmonics
with Decomposed Primary and Secondary Emission
Kai Yang and Math H.J. Bollen
Abstract—The paper presents a systematic approach to study
the harmonic emission and propagation of harmonics with wind
power plants. The voltage or current transfer function, transfer
impedance and transfer admittance are introduced as they can
be used without detailed knowledge of the harmonic sources.
The harmonic transfers are classiﬁed into different types, where
an important distinction is the one between “primary emission”
and “secondary emission”. The systematic approach provides
methods evaluating a total harmonic emission at any node, as well
as evaluating harmonic contributions from certain sources. A case
study has been performed, with showing a dominating secondary
emission from the public grid. The systematic approach can be
used for a harmonic evaluation in another network beyond a
wind power plant.
Index Terms—Wind energy, wind farms, wind power generation, power quality, power system harmonics, power system
simulation, harmonic analysis, propagation.
I. I NTRODUCTION
T
HE amount of wind-power is growing worldwide, at
transmission and distribution levels [1]. The increasing
amount of wind power impacts the grid in different ways,
where increased levels of harmonics is a potential issue [2].
Harmonic distortion originating from wind power installations
has been reported by several authors [3], [4], [5], [6]. This
emission will impact the harmonic voltage level at the point
of connection (PoC) and at nearby locations [7]. Case-speciﬁc
studies are needed to evaluate the impact of the installation
on the harmonic distortion with integration of any new wind
power plant.
Harmonic voltages or currents exceeding certain limits at
the PoC are not accepted either by the regulator (regulator
limits) or by a network operator (planning levels). Harmonic
studies are therefore often a compulsory part of the connection
agreement. High harmonic voltages or currents in the collection grid may also cause interference like protection maloperation or even damage to equipment. This is of interest
to a wind-power plant (WPP) owner and another reason for
performing harmonic studies. These studies are however not
regularly done.
Harmonic distortion at the PoC and inside of the WPP is
due to two fundamentally different sources: emission from
the individual turbines or from other equipment in the WPP,
background voltage distortion in the public grid [8], [9]. Both
sources need to be included to get a complete picture of the
harmonic distortion. The background voltage distortion at the
terminals of a few individual wind turbines (in different WPPs)
was observed during a few weeks [10]. The scatter plots of
voltage vs. current subgroups at around order 13 present to
be identiﬁed by idle and operational states [11]. Interactions
between a current source inverter and a voltage source grid
have been modeled in [12], [13], [14]; the result shows that
the impedances of both inverter and on the grid side play
an important role in the harmonic distortion. A few papers
study the harmonic distortion either excluding the grid side
background distortion [9], [15], or excluding the emission
from the wind turbine [16].
Studies in association with connection of WPPs typically
model all sources in detail and do not consider the individual
sources one by one. That makes it harder to understand the
different contributions and to understand where additional
modeling efforts will have their biggest impact. The same is
true when deciding about mitigation methods. This approach
is also not useful when deciding about further research and
development efforts or for educational purposes. A systematic
approach to the study of harmonic distortion, is more specifically considering the different contributions to the harmonic
distortion.
Harmonic sources of wind turbines are uncertain depending
on a number of issues. The harmonic emission from a wind
turbine is time-varying both in magnitude [11] and in phaseangle [17], [18]. This is partly due to variations in wind speed,
partly due to variations in emission even for the same wind
speed. Next to that the emission of the turbines is often not
known when the harmonic studies are done and estimation has
to be made. Also the background voltage distortion is often
not accurately known at that time. The harmonic voltage and
current levels are however strongly dependent on both emission from the turbines and background voltage distortion. A
study method is needed that gives information about harmonic
levels without detailed knowledge of the sources. The transfer
functions (current transfer, voltage transfer, transfer impedance
and transfer admittance), as used in electric circuit theory, are
suitable tools to base such a study on. These functions are
independent of the levels of emission or background distortion
but quantify the impact of the collection grid on the distortion
levels.
A systematic approach for harmonic studies, based on the
above-mentioned transfer functions, is proposed in Section II,
with the transfer functions being introduced in Section II-A
and the different harmonic transfers associated with a WPP in
Section II-C. The proposed systematic approach is applied to
a simpliﬁed model of a hypothetical but realistic WPP. The
details of that case study and the model used are presented in
Section III. Details of the studies and results for applying the
proposed approach are presented in Section IV. The overall
emission at the terminals of a wind turbine and at the PoC of
2
the WPP is presented in Section V. The paper is concluded in
Section VI.
II. S YSTEMATIC A PPROACH
The systematic approach proposed in this paper includes
multiple harmonic transfers from different harmonic sources
and results in the resulting harmonic voltage and current
distortion due to all sources. The description of the method
in this paper is directed to the PoC and at the medium-voltage
terminals of the turbine transformers. However, the approach
can be applied to any location in the network.
B. Overall Transfer Functions
Suppose there are N identical wind turbines in a WPP.
The term “overall transfer function” (for either voltage or
current) is deﬁned as the transfer function from all turbines
together to the node of interest, e.g. PoC. That is where
an aggregation comes in. There are two extreme aggregation
cases: with identical phase-angle for all emitting sources and
with uniformly-distributed phase-angles.
The overall voltage or current transfer function (written
in magnitude) assuming identical phase-angle is obtained by
summarizing all the magnitudes of transfer functions:
Hf,identical =
A. Harmonic Transfers
N
|H f,i |
(5)
i=1
As aforementioned, the study of harmonic transfer properties in a network is a merit by means of transfer function (TF),
transfer impedance (TI) and transfer admittance (TA).
Suppose a harmonic current source is located at node A
(the input). The resulting emission at node A and at node B
(output) are of interest. The complex voltage and current at
A
A
node A at frequency f are U f and I f ; at node B they are
B
B
U f and I f .
The transfer function is deﬁned as the (dimensionless) ratio
of the output and the input, either voltage or current. The
voltage transfer function is written as:
B
U
H f,A,B =
Uf
A
(1)
=
i=1
Similar deﬁnitions are used for “overall transfer impedance”
and “overall transfer admittance”. For the overall transfer
impedance:
N
Zf,identical =
|Z f,i |
(7)
i=1
Uf
The current transfer function is:
I
H f,A,B
where H f,i is the transfer function from the i-th turbine to the
studied node.
The overall voltage or current transfer function assuming
uniformly-distributed phase-angles is obtained from the square
root rule:
N
Hf,unif orm = |H f,i |2
(6)
Zf,unif orm
B
If
A
If
(2)
A
2
(8)
The overall transfer admittance:
Yf,identical =
(3)
The current harmonics are studied in this paper. Thus the
current transfer function is used with implicitly assuming harmonic current sources for the wind turbines; and the transfer
admittance is used with the background voltage distortion from
the public grid.
As long as the harmonic current source is known at node
A (e.g. at the terminal of a turbine), the contribution of the
harmonic current at node B is obtained from (2). Similarly
known background harmonic voltage at the PoC with the
public grid will give the harmonic current at another location
using (4).
|Y f,i |
Yf,overall
N
=
|Y
If
The transfer admittance is deﬁned as the ratio of output
current and input voltage with a unit of (Mho) or S
(Siemens):
B
If
Y f,A,B = A
(4)
Uf
N
(9)
i=1
B
Z f,A,B =
f,i |
i=1
The transfer impedance is deﬁned as the ratio of output
voltage and input current with a unit of Ω (Ohm):
Uf
N
=
|Z
f,i |
2
(10)
i=1
In Section III, both extremes will be used to give a range
of expected emission. In Section IV, where the emission from
the individual turbines is included, a Monte-Carlo Simulation
has been used to model the aggregation based on real measurements as proposed in [18]. Among others, currents with
uniformly-distributed phase-angle are in accordance with (6).
C. Harmonic Classiﬁcations
To be able to study the harmonic transfers in a systematic
way, they have been classiﬁed into two groups: the primary
emission (P) and the secondary emission (S). The primary
emission is the emission from the object that is studied, e.g.
the emission originated from one individual wind turbine
or from the studied WPP. The secondary emission is the
emission from anywhere else. In a WPP the harmonic voltages
and currents are of interest at different locations, that makes
the subdivision into primary and secondary insufﬁcient and
3
actually not completely precise. A more detailed classiﬁcation
is therefore proposed, which is the base of the systematic study
method. The following harmonic ﬂows are distinguished in a
WPP:
• P1: the primary emission from one wind turbine at the
PoC of the collection grid to the public grid;
• P2: the primary emission from one wind turbine to
another wind turbine in the collection grid;
• P3: the total primary emission of a WPP; it is the
sum of contributions of all wind turbines to the primary
emission of a whole WPP; aggregations are presented in
Section II-D;
• S1: the secondary emission from the public grid to a
studied wind turbine;
• S2: the secondary emission from another turbine to a
studied wind turbine; this is the same transfer as P2 but
seen from the viewpoint of the turbine at the output node;
• S3: the secondary emission from the public grid to a
WPP;
• S4: the overall secondary emission from all other turbines
to a studied wind turbine; this is the sum of all secondary
emission S2 to the studied turbine.
D. Harmonic Aggregation
Different from the aggregation rule in IEC 61000-3-6 (four
aggregation exponents are proposed for low-, medium-, highorders and interharmonics), [18] uses an “aggregation factor”
to quantify the harmonic and interharmonic aggregation from
all turbines in a WPP. The aggregation factor is deﬁned as the
ratio between the resulting average spectrum summarized at
the PoC and ten times (ten turbines in the WPP) the average
spectrum of a turbine. Measurements show that, the aggregation factor is different for characteristic harmonics, noncharacteristic harmonics and interharmonics [18]. Differences
are also observed from order to order and from turbine to
turbine.
Excluding the aggregation from turbines, the aggregation
of all primary and secondary emission is studied at one node
in this study. In the complex plane, the total emission at a
location L is the sum of all primary and secondary emission,
and thus the sum of the N contributions from the turbines and
the public grid:
grid
I f,L = Y f,grid,L × U f
+
N
H f,i,L × I f,i
(11)
i=1
grid
where U f is the background voltage distortion at the public
grid, Y f,grid,L the transfer admittance from the public grid to
L, I f,i the current harmonics at the i-th turbine, and H f,i,L
the current transfer function from i-th turbine to L.
If L is at certain turbine, the contribution of transferred
harmonics is the emission by itself (the transfer function is
thus unity). In this case it is the primary emission, while
others are the secondary emission. If L is at the PoC, harmonic
contributions are from the public grid to the WPP, and from
all turbines to the PoC.
III. C ASE S TUDY
To illustrate the systematic approach, the harmonic emission
of a WPP with 5 wind turbines is studied. The topology of
the WPP is shown in Fig. 1.
Fig. 1.
A wind power plant with 5 wind turbines.
The 30 kV collection grid is connected to the public grid
(110 kV, 800 MVA, assumed pure inductive) through the substation transformer (30 MVA, 10%, X/R = 12). The wind
turbines are connected by underground cables (1 km distance
between neighboring turbines), which have a resistance of
0.13 Ω/km at 50 Hz, a capacitance of 0.25 μF/km and an
inductance of 0.356 mH/km.
Each cable section is modeled as a lumped Π model with
the following parameters: a left shunt capacitance C L , a series
inductance L, a series frequency-dependent resistance R with
f αc
) , the
a damping exponent αc = 0.6 (R(f ) = R50 × ( 50
resistance R at frequency f is obtained from the resistance
R50 at 50 Hz), and a right shunt capacitance C R . The transformer is modeled as a series inductance Ltrf and a series
frequency-dependent resistance Rtrf with a damping exponent
αtrf = 1.0. The impedance on turbine-side of the turbine
transformer is modeled as a series impedance representing the
turbine-transformer (2.5 MVA, 6% leakage impedance) and a
series impedance representing the converter reactor (4 MVA,
10%). The losses of the turbine transformer and the converter
reactor are neglected in this study. Only the turbine at the
output node is modelled as impedance. For the other turbines
the impedance is assumed to be inﬁnite. Also the harmonic
ﬁlter that is typically present on turbine-side of the turbine
transformer is not included here. The equivalent circuit is
based on the approximation that neglects the impedances of the
ﬁve turbines, for the study considering the WPP as a while.
The assumptions are made for the case study in this paper,
which aims at illustrating the systematic approach. An accurate
model is needed for a real study.
IV. S IMULATION R ESULTS
The transfer function for a primary emission is called primary TF. The transfer function and the transfer admittance for
a secondary emission are called secondary TF and secondary
TA.
A. Primary TF from Turbines to Grid (P1)
The equivalent circuit used for studying this harmonic ﬂow
is shown in Fig. 2. The cable section between the studied wind
turbine and the PoC is labeled with subscript 1 (segment 1),
the rest of the cable is with subscript 2 (segment 2); and the
other feeder is with subscript 3 (segment 3).
4
Fig. 2. Equivalent circuit used to calculate the primary transfer function
from a turbine to the public grid. Emission classiﬁcation: P1.
A number of combined impedances are introduced to simplify the expression for the transfer function, as shown in
the ﬁgure. Note that ZS represents the impedances of the
transformer and the grid; and Zn represents the series part of
segment n (the same for the following). Based on the principle
that a current is inversely proportional to the impedance at a
branch, the current transfer function from the turbine to the
public grid according to deﬁnition (2) is obtained:
HT,grid (ω) =
Z13
Z12
×
Z13 + ZS
Z12 + Z1 +
(12)
Z13 ×ZS
Z13 +ZS
and frequency. The damping exponents αc = 0.4, αtrf = 0.8
give the magnitude of the ﬁrst resonance 30.53, and the second
0.25. Using αc = 0.2, αtrf = 0.6 gives 56.86 and 0.7.
The resonance frequencies are not impacted by the damping
exponents. An accurate study of the harmonic emission of a
WPP needs detailed parameters of cables and transformers.
This is not in the scope of this case study, which merely aims
at illustrating the proposed systematic approach.
B. Primary TF from Turbine to Turbine (P2)
In a WPP with N turbines there are N × (N − 1) possible
transfer functions from one turbine to another, each of which
may be different. Here only the primary emission from turbine
T1 is considered, for which there are four different TFs. The
equivalent circuit used to calculate the TF from T1 to T2 and
T3 is shown in Fig. 4. Segment 1 represents the cable from T1
to T2 or T3; segment 2 the cable between T1 and the PoC;
and the other feeder is segment 3. Note that for the transfer
from T1 to T2, the cable between T2 and T3 is segment 4 as
marked with red.
The resulting current transfer functions from the ﬁve turbines to the public grid are shown in Fig. 3. The transfer
functions are shown up to 40 kHz. Above this frequency the
transfer is close to zero. The upper ﬁgure shows up to 3 kHz;
the lower ﬁgure up to 40 kHz.
15
Transfer Function |HT,grid|
10
5
0
0
0.5
1
1.5
2
2.5
3
0.1
T1 − Grid
T2 − Grid
T3 − Grid
T4 − Grid
T5 − Grid
0.08
0.06
0.04
The resulting current transfer function is written as:
0.02
0
Fig. 4. Equivalent circuit to calculate the transfer functions from turbine T1
to T2 and T3. Note that, Segment 4 (marked red) only exists for the transfer
from T1 to T2. Emission classiﬁcation: P2.
HT 1,T 2/3 (ω) =
5
10
15
20
25
Frequency [kHz]
30
35
40
Fig. 3. Primary current transfer functions from the ﬁve wind turbines (T1
to T5) to the public grid. Emission classiﬁcation: P1.
All ﬁve wind turbines present the ﬁrst resonances at
1.235 kHz with 16. This means that, at this frequency, the
contribution of one turbine to the emission of the WPP at
the PoC is 16 times the primary emission at the terminals of
the turbines. A second resonance appears around 9 kHz, and a
third 15 kHz. Whereas the higher resonance frequencies with a
larger difference between the turbines. For frequencies above
5 kHz the contribution of one turbine to the emission of the
WPP is less than 10% of the original emission of the turbine.
For most frequencies the contribution is much less than 10%.
Note that the magnitude (especially the resonances) of a
transfer function depends on the cable and transformer damping exponents, which deﬁne the relation between resistance
Z14
Z12
×
Z14 + ZT
Z12 + Z1 +
Z14 ×ZT
Z14 +ZT
(13)
The TF from T1 to T4 and T5 is calculated using a different
circuit. In this case segment 1 is the cable between T1 and the
PoC; the rest of the feeder is represented by segment 2; from
the PoC to T4 or T5 is segment 3. Segment 4 is the cable from
T4 to T5 if the transfer is from T1 to T4. The equivalent circuit
used to calculate the transfer function is shown in Fig. 5.
Fig. 5. Equivalent circuit to calculate the transfer functions from turbine T1
to T4 and T5. Note that, Segment 4 with red mark only exists for transfer
from T1 to T4. Emission classiﬁcation: P2.
5
With the replacement of the impedance to the right of R1
with Z134T , the transfer function is obtained in a similar way:
80
Z34
Z13
HT 1,T 4/5 (ω) =
×
ZT
Z34 + ZT
Z13 + Z3 + ZZ3434+Z
T
(14)
Z12
×
Z12 + Z1 + Z134T
The four transfer functions from T1 to T2, T3, T4 and T5
are shown in Fig. 6.
40
Overall Transfer Function
60
20
0
1
|
T1,T2/3/4/5
Transfer Function |H
1
1.5
2
2.5
3
Identical
Uniform
0.1
5
10
15
20
25
Frequency [kHz]
30
35
40
Fig. 7. Primary current overall transfer functions from the WPP to the public
grid, with an identical phase-angle and with uniformly-distributed phase-angle.
Emission classiﬁcation: P3.
0.5
0
0.5
0.2
0
1.5
0
0.3
0
0.5
1
1.5
2
2.5
3
0.01
turbine is referred to as segment 1, the rest of the cable as
segment 2 and the other cable as segment 3 (the segment does
not exist if it is turbine T3 or T5). The equivalent circuit used
to calculate the TA is shown in Fig. 8.
T1 − T2
T1 − T3
T1 − T4
T1 − T5
0.008
0.006
0.004
0.002
0
5
10
15
20
25
Frequency [kHz]
30
35
40
Fig. 6. Primary current transfer functions from T1 to the other four wind
turbines (T2 to T5). Emission classiﬁcation: P2.
The ﬁrst resonance frequencies of all the four TFs are at
1.29 kHz with the magnitude of 1.5. The second and third
resonances are around 10 and 15 kHz, with different magnitudes. The transfer functions decay to zero above 40 kHz.
The primary transfer function from a turbine to another (P2),
around the ﬁrst resonance frequency, is around one tenth of
the primary transfer function from a turbine to the public grid
(P1). It indicates an easier harmonic propagation to the public
grid rather than to another turbine.
C. Primary TF from WPP to grid (P3)
As presented in Section II-A, the overall transfer function is
in between the two extreme cases: identical phase-angle and
uniformly-distributed phase-angle. The magnitudes of the two
resulting overall transfer functions are plotted up to 40 kHz in
Fig. 7.
Both overall transfer functions present the ﬁrst resonance at
1.235 kHz. The one assuming an identical phase-angle shows
the maximum TF of about 80, which is 5 times the value of 16
that was obtained for the individual TF. While the maximum of
the TF assuming uniformly-distributed
phase-angle
is 35.55,
√
√
approximately 80 divided by 5. The factor 5 follows from
the square-root rule. There are two more resonances around 10
and 15 kHz with a TF less than unity. For a higher frequency
the TF decays to zero.
D. Secondary TA from Grid to Turbine (S1)
The transfer admittance quantiﬁes the transfer of voltage
from the public grid to be the resulting current at a wind
turbine terminal. Suppose the part from the PoC to the studied
Fig. 8. Equivalent circuit used to calculate the transfer admittance from the
public grid to a turbine. Emission classiﬁcation: S1.
I1 is the resulting current at the PoC; I2 is the current
through the series part of segment 1. The resulting current
IT at the studied turbine is written as:
IT = I2 ×
Z12
Z12 + ZT
(15)
The current I2 is obtained from I1 using the expression for
the current divider:
Z13
I2 = I1 ×
(16)
ZT
Z13 + Z1 + ZZ1212+Z
T
I1 is due to the total input impedance ZgT of the WPP:
I1 =
Ugrid
ZgT
(17)
The above three equations give the following expression for
the transfer admittance Ygrid,T :
Ygrid,T =
Z13
Z12
×
ZgT × (Z12 + ZT ) Z13 + Z1 +
Z12 ZT
Z12 +ZT
(18)
The magnitudes (base 10 logarithmic scale) of the transfer
admittances from the public grid to the ﬁve turbines are shown
in Fig. 9.
The ﬁve transfer admittances are similar up to 5 kHz, with
a clearly-visible peak at 1.29 kHz with value 0.0139. At the
peak a relatively high current passes through the circuit. The
transfer admittances show a number of maxima and minima
6
0
10
Grid − T1
Grid − T2
Grid − T3
Grid − T4
Grid − T5
TA |Ygrid,T1/2/3/4/5| [Siemens]
−2
10
−4
10
−6
10
Fig. 11. Equivalent circuit used to calculate the transfer admittance from the
public grid to the WPP. Emission classiﬁcation: S3.
−8
10
−10
10
0
0
5
10
15
20
25
Frequency [kHz]
30
35
10
40
Grid − WP
Fig. 9. Secondary transfer admittances from the public grid to the ﬁve
turbines. Emission classiﬁcation: S1.
between 5 kHz and 35 kHz. Above 35 kHz the admittance decays smoothly (not shown in the ﬁgure). The low values of the
transfer admittance at high frequencies limit the propagations
of any high frequency harmonics from the public grid to the
individual turbines.
TA |Ygrid,WP| [Siemens]
−1
10
−2
10
−3
10
−4
10
−5
10
0
5
10
15
20
25
Frequency [kHz]
30
35
40
Fig. 12. Secondary transfer admittance from the public grid to the WPP.
Emission classiﬁcation: S3.
E. Secondary TF from Turbine to Turbine (S2)
The secondary current TFs from other turbines to one
turbine are similar as the primary TF from one turbine to
another. Consider the secondary current TFs from turbines T1,
T2, T3 and T4 to turbine T5. Using the earlier expression, the
resulting current TFs are shown in Fig. 10.
1.5
Transfer Function |HT1/2/3/4,T5|
1
0.5
0
0
0.5
1
1.5
2
2.5
3
0.025
T1 − T5
T2 − T5
T3 − T5
T4 − T5
0.02
0.015
0.01
0.005
0
5
10
15
20
25
Frequency [kHz]
30
35
40
Fig. 10. Secondary current transfer functions from T1, T2, T3 and T4 to
T5. Emission classiﬁcation: S2.
The four TFs have a similar ﬁrst resonance at 1.29 kHz with
a magnitude of 1.5 and multiple resonances.
F. Secondary TA from Grid to WPP (S3)
The current transferring into the WPP, IW P , goes through
the two feeders which are marked with segment 1 and segment
2, in Fig. 11.
The overall transfer admittance equals the reciprocal of the
P
, which is shown
whole circuit impedance Ygrid,W P = UIW
grid
in Fig. 12. The high admittance is at 1.235 kHz; and then the
transfer admittance decreases rapidly.
V. T OTAL E MISSION
There are a number of contributions to the harmonic voltage
or current at certain location in the collection or public grid,
where the subdivision in primary and secondary emission is
the most basic one. The different contributions are presented
in Section II-C. By using the transfer functions as presented
in Section IV, the different contributions can be quantiﬁed
when the harmonic sources are known or can be estimated
with sufﬁcient accuracy. The total harmonic current at two
locations has been calculated using the transfer functions and
admittances calculated in the earlier part of this paper. The primary emission from the individual turbines has been obtained
from measurements; the aggregation between the contributions
from individual turbines has been modeled using the approach
presented in [18]; the background voltage distortion has been
estimated from the indicative planning levels in IEC 61000-36.
The transfer function from the individual turbines to the
public grid are similar up to 3 kHz, as presented in Section IV-B. When the primary emission at the individual turbines is similar as well, the contributions from the ﬁve turbines
to the primary emission at the PoC is similar.
The secondary emission and the overall emission at a
turbine are presented in Section V-A. The primary emission,
the secondary emission and the overall emission at the PoC
are presented in Section V-B.
A. Emission at Turbine
The harmonic current at the medium-voltage side of the
turbine transformer, consists of three contributions (as shown
in Section II-D): primary emission from the turbine; secondary
emission from the other turbines; and secondary emission from
the grid. The background voltage harmonic levels are set equal
7
3
Grid − T1, S1
Grid − T2, S1
Grid − T3, S1
Grid − T4, S1
Grid − T5, S1
2
1
0
0.1
500
1000
1500
2000
Current [A]
0.05
3
500
1000
1500
2000
2500
T1/2/3/4/5 − Grid, P3
1
0.5
0
500
1000
1500
15
2000
2500
Grid − WP, S3
10
5
0
500
1000
1500
15
2000
2500
Total Emission at PCC
10
5
0
500
1000
1500
Frequency [Hz]
2000
2500
Fig. 14. Primary emission from all turbines to the public grid (upper ﬁgure,
emission classiﬁcation: P3); secondary emission from the public grid to the
WPP (medium ﬁgure, emission classiﬁcation: S3); and total emission at the
PoC. The vertical scale of the upper ﬁgure is one tenth of those for the middle
and lower ﬁgures.
Total Emission at T5
2
1
0
1.5
2500
T1/2/3/4 − T5, S2
0
summation of these two contributions, as shown in Fig. 14.
Current [A]
to one third of the MV planning level in IEC 61000-3-6; one
third of the planning levels for interharmonics that set at 0.2%
of the fundamental voltage, according to IEC 61000-2-2. The
phase angles are assumed to be zero. The turbine current
harmonic source is assumed to be the number of measurements
as in [18].
The harmonic current has been calculated for all ﬁve turbines and is shown in Fig. 13. The secondary emission from
the grid to a turbine (S1), from other turbines to turbine T5
(S2) and the overall emission at T5 are obtained with the
approaches in Section IV-D, Section IV-E and Section II-D.
500
1000
1500
Frequency [Hz]
2000
2500
Fig. 13. Secondary emission from the public grid to the turbines (upper
ﬁgure, emission classiﬁcation: S1), from other turbines to T5 (medium ﬁgure,
emission classiﬁcation: S2) and the total emission at T5 (lower ﬁgure).
The secondary emission is obtained using Monte-Carlo
Simulation: the spectra are average spectra from ten-thousand
scenarios, with random samples from 1087 spectra which were
measured during few weeks and covering the whole range of
output power, in the same way as in [18].
The upper ﬁgure (S1) clearly shows the impact of the
resonance around 1.25 kHz, where the spectrum consists of a
broadband component and several narrow band components.
The highest emission takes place however at the lower frequencies. The emission from other turbines to the turbine, as
in the middle ﬁgure (S2), also shows broad and narrow band
emission around the resonance frequency although the magnitude is less than that from the grid to a turbine. Harmonics
below 500 Hz are also clearly visible for the S2 emission. The
highest emission for this contribution to the harmonic current
occurs for a narrow band component around the resonance
frequency. In general the emission from the other turbines is
about one order of magnitude less than the emission from the
grid to a turbine. The emission from the public grid is the
dominant emission among the secondary emission.
The spectra shown in Fig. 14 are obtained as the average
from a Monte-Carlos Simulation with ten thousand scenarios
in a similar way as in Section V-A.
The primary emission is dominating for frequencies below
500 Hz. But around the resonance frequency of 1.25 kHz, the
primary emission is less than one tenth of the secondary
emission.
The overall spectrum at the PoC shows that the narrow
bands are mainly due to emission from the turbines, whereas
the broadband and narrow band around the resonance frequency are driven by the background voltage distortion of the
public grid.
VI. C ONCLUSION
This paper proposes a systematic approach to evaluate the
harmonic emission associated with a wind-power plant (WPP),
at the point-of-connection (PoC) with the public grid and at
locations inside of the collection grid. A case study has been
performed for a 5-turbine WPP using a simpliﬁed model of the
collection grid to illustrate the proposed systematic approach.
The proposed systematic approach consists of three main
parts:
•
B. Emission at WP
The primary and secondary harmonic emission, as well as
the overall emission, are also calculated at the PoC of the
WPP. At this location there are only two contributions: primary
emission coming from the turbines and secondary emission
coming from the public grid. The overall emission is the
•
A number of transfer functions: voltage transfer, current
transfer, transfer impedance and transfer admittance. The
type of harmonic source (voltage or current), and the
type of output distortion of interest (voltage or current),
determines which transfer function to use. The transfer
functions can be used to get information on the harmonic
levels without detailed knowledge of the sources.
The classiﬁcation of harmonic transfers: the harmonic
transfers are classiﬁed into two basic groups: primary
emission (harmonic emission originated from a studied
object that propagates to anywhere else) and secondary
emission (harmonic emission transferred from anywhere
8
else); seven different transfers are being identiﬁed in a
WPP.
• Harmonic summation: the total voltage or current distortion at a certain location is obtained by summation of
the transfer from all sources. This includes all relevant
primary emission and secondary emission.
The proposed systematic approach provides methods to
estimate harmonic contributions from certain group of sources,
e.g. the primary emission of a WPP at the PoC, the secondary
emission from the public grid into individual turbines at the
medium-voltage side of the turbine transformer. The approach
helps in estimating of harmonic emission for a WPP, without
having detailed data available on emission from individual
turbines or on the background voltage distortion. The different
transfer functions, together with only rough information on
the emission and background voltage distortion, allow for
an estimation of where high levels of voltage and/or current
distortion can be expected. That in turn can provide feedback
on where mitigation methods, like harmonics ﬁlters, might be
necessary.
The case study illustrates that the systematic approach is
feasible and gives results that can be interpreted. For the
WPP that was subject of the case study it was found that, for
frequencies around the main resonance point, the background
distortion from the public grid is dominating at the PoC. It
was also shown that at the terminals of the wind turbines,
around the same resonance frequency, the emission from other
turbines and driven by the background voltage distortion at
the PoC is a signiﬁcant part of the harmonic current at this
location. For frequencies well above the ﬁrst resonance point,
the primary emission at the PoC is small. All these conclusions
hold, strictly speaking, only for this case study. However, the
differences between WPPs are rather small where it concerns
harmonic emission and propagation, so that these conclusions
are expected to hold for many other WPPs as well. The
conclusions from the case study in this paper also conﬁrm
the studies from other study, where more detailed models of
the WPP and the winds turbines were used [19].
In this paper a simpliﬁed model of the WPP was used;
this model has been used only to illustrate the proposed
systematic approach. A detailed model of the wind power
installation and of the public grid is needed for an accurate
harmonic estimation in a real situation. It is however strongly
recommended to apply the systematic approach as proposed
in the paper, or other similar approaches, when performing
studies of harmonics in association with WPPs.
Further work related to this study would among others
involve the application of the systematic approach to different
WPPs, of different size, to verify the expectations that the
conclusions from the case study have more general validity.
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[5] K. Yang, M. H. Bollen, E. A. Larsson, and M. Wahlberg, “Measurements
of harmonic emission versus active power from wind turbines,” Electric
Power Systems Research, vol. 108, no. 0, pp. 304 – 314, 2014.
[6] C. Larose, R. Gagnon, P. Prud’Homme, M. Fecteau, and M. Asmine,
“Type-III wind power plant harmonic emissions: Field measurements
and aggregation guidelines for adequate representation of harmonics,”
IEEE Transactions on Sustainable Energy, vol. 4, no. 3, pp. 797–804,
July 2013.
[7] M. Bradt, B. Badrzadeh, E. Camm, D. Mueller, J. Schoene, T. Siebert,
T. Smith, M. Starke, and R. Walling, “Harmonics and resonance issues
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for Offshore Wind Farms, Lisbon, Portugal, Nov. 2012, pp. 555–562,
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[10] K. Yang, M. Bollen, and M. Wahlberg, “A comparison study of harmonic
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[11] ——, “Comparison of harmonic emissions at two nodes in a windpark,”
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[12] J. Sun, “Impedance-based stability criterion for grid-connected inverters,” IEEE Transactions on Power Electronics, vol. 26, no. 11, pp. 3075–
3078, Nov 2011.
[13] J. Sun and M. Chen, “Analysis and mitigation of interactions between
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pp. 99–104 Vol.1.
[14] X. Chen and J. Sun, “A study of renewable energy system harmonic
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Annual IEEE Applied Power Electronics Conference and Exposition
(APEC), March 2011, pp. 995–1002.
[15] Ł. H. Kocewiak, J. Hjerrild, and C. L. Bak, “Statistical analysis
and comparison of harmonics measured in offshore wind farms,” in
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[16] B. Andresen, P. Brogan, and N. Goldenbaum, “Decomposition and
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[17] S. T. Tentzerakis and S. A. Papathanassiou, “An investigation of the
harmonic emissions of wind turbines,” IEEE Transactions on Energy
Conversion, vol. 22, no. 1, pp. 150–158, March 2007.
[18] K. Yang, M. H. Bollen, E. A. Larsson, and M. Wahlberg, “Aggregation
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Paper F
A Statistic Study of Harmonics and Interharmonics at A
Modern Wind-Turbine
K. Yang, M.H. Bollen, E. A. Larsson and M. Wahlberg
Published in Proceedings of ICHQP2014
c
2014
IEEE
F2
A Statistic Study of Harmonics and Interharmonics
at A Modern Wind-Turbine
Kai Yang, Math H. J. Bollen and E.O. Anders Larsson
Mats Wahlberg
Electric Power Engineering Group
Luleå University of Technology
931 87, Skellefteå, Sweden
Email: [email protected]
Skellefteå Kraft AB
931 80 Skellefteå, Sweden
Email: [email protected]
Abstract—The work presents measurements of harmonics and
interharmonics from a modern wind turbine over a period of
several days, using a conventional power quality monitor. A
statistical study has been performed to present the characteristics
of the emission during the measurement. A variation of emission
has been observed, especially for interharmonics within certain
low-frequency bands and for the switching frequency. Multiple
relations between voltage and current components have been presented, as well as multiple relations between the emission and the
active-power production. Generally, harmonics are independent
of the active-power, whereas interharmonics are dependent on it.
Index Terms—Wind power generation, Power quality, Power
conversion harmonics, Harmonic analysis.
I. I NTRODUCTION
M
ODERN wind turbines equipped with power electronics emit new type of waveform distortions. Wind-power
harmonic emission has been studied by a number of papers
[1], [2], [3], [4], [5]. The studied wind power harmonics have
been observed to be different from the low-voltage domestic
devices [6], [7], [8], by the observation of even harmonics
and interharmonics [5], [9], [10]. For a Type-III turbine, the
sources of the harmonics have been pointed to the induction
generator, the rotor-side converter and grid-side converter [11],
[12], [13].
Beyond the speciﬁc characteristics of even harmonics and
interharmonics from a wind turbine, a variation of emission is
a concern for the wind turbine. The variation of emission is
partly linked with the varying input wind power by the wind
energy conversion system. Among various factors, the harmonics have been recommended to be evaluated within power
bins in IEC 61400-21 [14]. The harmonic and interharmonic
subgroups versus the output active-power have been studied
for three modern wind turbines [15], showing several patterns
of emission versus active-power.
Emission of a wind turbine varies with time, according to
varying operation states. A standard method for measuring
harmonics will rarely show new types of disturbances. A
measurement will record the variation of disturbances when
turbines are in various operation states. This paper studies the
behavior of a wind turbine emission. The voltage and current
c
978-1-4673-6487-4/14/$31.00 2014
IEEE
waveforms (200-ms) are recorded and analyzed every 10minutes during around one week. The variation of the waveform distortion has been studied and the results are presented
in this paper. The wind turbine emission will be presented in
different ways, obtained from the statistical analysis. Voltage
and current spectra will be studied to reveal the emission
characteristics. Individual characteristics of harmonics and
interharmonics will be presented.
Section II presents the harmonic measurement set-up. Section III present the statistical analysis of the measurements of
voltage and current emission. The paper is summarized in
Section IV.
II. H ARMONIC M EASUREMENT
The measurement has been performed at a Type-III DFIG
wind turbine, with a rated power 2 MW. The turbine contains
a four-pole doubly-fed asynchronous generator with wound
rotor, and a partial rated converter. The output voltage is 690 V,
and connected to the collection grid through a low to medium
voltage transformer (installed inside the nacelle).
The harmonic measurement of the wind turbine has been
performed at the medium voltage side of the turbine transformer (with a rated voltage 32 kV and rated current 36 A).
The three voltage and current waveforms were recorded by
the monitor through the conventional voltage and current
transformers at medium voltage, with a sufﬁcient accuracy for
the frequency range up to few kHz [6], [16].
Both voltage and current waveforms (200-ms windows)
have been captured with a sampling frequency of 256 times
the power-system frequency (approximately 12.8 kHz) using a
standard power quality monitor Dranetz-BMI Power Xplorer
PX5. The Discrete Fourier Transform has been applied using
a rectangular window of 10 cycles, which results in a 5 Hz
frequency resolution spectrum. Such a 200-ms window has
been recorded every 10 minutes during 8 days.
III. VOLTAGE AND C URRENT S PECTRA
During the measurement period, a number of spectra in all
operation cases (from idle to the rated power production) have
been obtained.
Both voltage and current average spectra (at phase-A) have
been derived to present the wind turbine emission as well as
the 90-percentile, 95-percentile and 99-percentile spectra, as
shown in Fig. 1 and Fig. 2.
Harmonic voltage [V]
100
Average
90 percentile
95 percentile
99 percentile
80
60
40
20
0
0
50
100
150
Harmonic current [A]
0.4
200
250
300
350
400
450
500
Average
90 percentile
95 percentile
99 percentile
0.3
0.1
0
50
100
150
200
250
300
Frequency [Hz]
350
400
450
500
Harmonic voltage [V]
Fig. 1. Average, 90-percentile, 95-percentile and 99-percentile spectra (up
to 500 Hz) of voltage and current from a number of waveforms on phase-A.
The vertical scale is about 1% of rated voltage or current.
Average
90 percentile
95 percentile
99 percentile
150
100
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
1400 1600 1800
Frequency [Hz]
2000
2200
2400
2600
Harmonic current [A]
0.2
Average
90 percentile
95 percentile
99 percentile
0.15
0.1
0.05
0
600
800
1000
The current spectrum presents apparent emissions at loworder harmonics below 500 Hz and at the switching frequencies. The harmonics 2, 3, 4 5 and 7 are the apparent ones.
Specially components at 285 Hz and 385 Hz dominate in the
spectrum.
The current components around 285 Hz and 385 Hz are
more than a narrow band in the spectrum. They are derived
from the variations of a number of spectra, the neighboring
components are varying with the different operation states
[15]. These components are originate from the power electronics, according to [17], and are probably from the so-called
space harmonics according to [11].
C. Correlation of Voltage and Current Spectra
50
0
The voltage spectrum presents signiﬁcant harmonic components at the characteristic harmonics 5 and 7, and also
at harmonic frequencies 1150 Hz, 1250 Hz and 1750 Hz and
as well as around 2300 Hz (probably due to the switching
frequency of the converter).
The voltage spectrum does not contain signiﬁcant harmonic
distortion at orders 2, 3, 4, whereas these components are
clearly visible in the current spectrum. The components at
285 Hz and 385 Hz are visible in the voltage spectrum, but
not as obvious as in the current spectrum. The components
at 1150 Hz, 1250 Hz and 1750 Hz are not as apparent in the
current spectra as in the voltage spectra.
B. Current Spectra
0.2
0
A. Voltage Spectra
1200
Fig. 2. Average, 90-percentile, 95-percentile and 99-percentile spectra (up
to 2700 Hz) of voltage and current from a number of waveforms on phase-A.
The vertical scale is about 1% of rated voltage or current.
The average, 90-percentile and 95-percentile spectra show a
similar pattern of the turbine emission. While the 99-percentile
spectrum show a different representation of emission in certain
frequency ranges. It leads at the broadband from 1.7 to 2.5 kHz
for both voltage and current spectra. And it leads at the lowfrequency broadband around the interharmonic 5 and 7 of
the current spectrum. A large difference between 99% and
the others (average, 90-percentile and 95-percentile) would
indicate that the distortion comes in short-duration peaks or at
least is present only a short part of the time (between 1 and
5% to be more accurate).
Both voltage and current distortion are presented in Fig. 1
and Fig. 2. Certain frequency components occur only in one
of the two, others occur in both. When both are present this
could indicate that the voltage distortion causes the current
distortion, but also the other way around. The origin of
harmonics is of interest to reveal the schema of distortions. The
study starts with the relation of voltage and current harmonics
at the wind turbine.
The measured voltage and current spectra are with 5-Hz
resolution; and a number of these spectra can be analyzed
statistically for the voltage and current components at each
frequency. The correlation coefﬁcient between the voltage
and the current magnitude series (within the same measuring
period and order) has been chosen to study the relation of
voltage and current spectra, as shown in Fig. 3.
Unity correlation coefﬁcient means that there is a linear
relation between voltage and current, as in Ohm’s law. A
correlation of minus one also means that there is a linear
relation, but with a negative sign. Zero correlation coefﬁcient
means that voltage and current are statistically independent.
Fig. 3 shows the correlation coefﬁcient between the voltage
and current components at each frequency (5-Hz resolution)
up to 3200 Hz.
Fig. 3 shows apparent strong correlation (high correlation
coefﬁcient) between the harmonic voltage and current components at 50 Hz, 85 Hz, 100 Hz, 285 Hz, 385 Hz, 620 Hz,
720 Hz, 850 Hz, 950 Hz, and at several frequencies above
285Hz
0.8
385Hz
100
100
50
50
720Hz
620Hz
0.6
0.4
0
Correlation Coefficient
0.2
0
−0.2
−0.4
0
100
200
300
400
500
600
700
800
900
1000
0.1
0.15
0.2
60
40
20
20
Voltage component [V]
850 Hz
0
0.005
0.01
0.015
0.02
200
0.2
0
1200
1400
1600
1800
2000 2200 2400
Frequency [Hz]
2600
2800
3000
3200
0
0
1150 Hz
0
0.01
0.02
0.03
0.04
0.05
0.1
0.15
950 Hz
0
0.002 0.004 0.006 0.008 0.01 0.012
1250 Hz
1550 Hz
50
0
20
10
10
0
0.005
0
0.01
0
0.02
0.04
0.06
30
20
0
0.05
100
30
Fig. 3. Correlation coefﬁcient of voltage and current harmonics in a 5-Hz
resolution up to 3200 Hz.
0
150
100
0.4
0
40
0
0.6
1000
0.05
60
1
0.8
250 Hz
0
350 Hz
1650 Hz
0
2
4
6
8
−3
x 10
1750 Hz
100
D. Individual Components
Studies on the correlation of voltage and current show
an apparent correlation at certain frequencies. The apparent
correlation is classiﬁed into two situations: one with a linear
relation of voltage and current components; the other with a
distribution of voltage and current at a limited scale.
1) Linear Correlation: Up to 2500 Hz, the frequencies with
high correlation are at 850 Hz, 950 Hz, 1150 Hz, 1250 Hz,
1550 Hz, 1650 Hz and 1750 Hz. Additionally 250 Hz, 350 Hz
and 1850 Hz do not present a strong correlation, but with a
linear relation of voltage and current. The plots of voltage
versus current for these frequencies are presented in Fig. 4.
A strong correlation corresponds with a linear line of the
voltage versus current. The voltage versus current ﬁgures of
other frequency components (not shown here) are distributed
more or less randomly in the plot.
The slops of the linear line (for the frequencies with a high
correlation) indicates an impedance value. From Ohm’s law,
the impedance at certain frequency f can be estimated by the
slope of the best ﬁt of the linear line with least-square method.
The Ohm’s law can be easily applied for the frequency
1150 Hz and 1750 Hz, with the apparent one linear line. However the phenomena of frequencies 250 Hz, 350 Hz, 1250 Hz
and 1550 Hz are with multiple lines in ﬁgure. The multiple
slops of the multiple lines are due to the different impedances
20
50
0
10
0
0.01
0.02
0.03
0
0.04
0
0.002
Curent component [A]
1850 Hz
0.004
0.006
0.008
0.01
Fig. 4.
Scatter plot of voltage versus current distortion at ten selected
frequencies.
when the operation states change. It might be caused by the
idle states of other turbines in the collection grid.
2) Other Correlation: Other relatively strong positive correlation happens at 285 Hz, 385 Hz, 620 Hz and 720 Hz as
shown in Fig. 5 and negative correlation at 400 Hz, 450 Hz
500 Hz and 550 Hz as shown in Fig. 6.
25
Voltage [V]
1000 Hz. There is a broadband with a strong correlation around
the frequencies 285 Hz, 385 Hz, 620 Hz and 720 Hz. According to [11] these are “space harmonics” from the induction
generator, which details are presented in [12], [13]. Most
correlation coefﬁcients are around zero or positive. Negative
correlation coefﬁcients are observed at frequencies 400 Hz,
450 Hz, 500 Hz and at some frequencies around 1500 Hz. A
negative correlation coefﬁcient means that the voltage distortion decreases when the current distortion increases.
30
50
100 Hz
20
40
15
30
10
20
5
10
0
0
10
0.1
0.2
0.3
0
385 Hz
0
0.1
0.2
12
620 Hz
0.3
720 Hz
10
8
8
6
6
4
4
2
0
2
0
0.01
0.02
0
0.03
0
Current [A]
0.01
0.02
0.03
Fig. 5.
Individual voltage versus current component pairs of positive
correlation.
The type of strong correlation, e.g. 100 Hz, presents a
concentrated distribution of voltage versus current pairs. The
kind of distribution can be extended to the weaker correlation
25
15
400 Hz
450 Hz
20
10
15
10
5
Voltage [V]
5
0
0
0.01
0.02
0.03
8
0
0.04
500 Hz
6
30
4
20
2
10
0
0
0.005
0.01
0.015
0
0.005
0.01
0.015
0.02
40
0.025
550 Hz
IV. C ONCLUSION
0
0.02
0
Current [A]
0.01
0.02
0.03
0.04
Fig. 6.
Individual voltage versus current component pairs of negative
correlation.
at 200 Hz and 300 Hz. The second type of strong correlation
happens at the broadband components, e.g. 285 Hz, 385 Hz,
620 Hz, 720 Hz. A large number of the voltage and current
pairs distribute in a line, whereas others are much varying.
The negative correlation has been shown for 400 Hz, 450 Hz,
500 Hz and 550 Hz for instance. The current is with inversely
proportional to the voltage. Note that all the shown frequencies
are with a linear slope at a low current.
E. Individual Current as A Function of Power
Due to the variation of wind turbine emission, the study has
been performed for emission as a function of active power for
certain frequencies selected from the above studies: 85 Hz,
100 Hz, 285 Hz, 500 Hz, 620 Hz and 720 Hz, as shown in
Fig. 7.
0.2
0.4
85 Hz
Harmonic/interharmonic curent [A]
0.1
0
0.4
0.2
0.4
0.6
0.8
1
100 Hz
0.2
0
0
0.04
0
0.2
0.4
0.6
0.8
1
0.6
0.8
1
620 Hz
0.02
0
0.2
0.4
0.6
0.8
1
500 Hz
0.02
0
0.04
0
0.2
0.4
720 Hz
0
0.2
Fig. 7.
0.4
0.6
0.8
0
1
0
0.2
Active power [pu]
0.4
The paper studies harmonics and interharmonics from a
number of measurements during one week. The statistic representation has been employed to characterize the wind turbine
emission.
Statistical methods have been used to present the voltage
and current emission of the wind turbine. The different methods indicate a large varying emission at certain low frequencies
and the switching frequency range. The varying emission
in the wind turbine is present at interharmonics rather than
harmonics, and within a frequency band.
The voltage emission and current emission have been compared. Characteristic harmonics are present in the voltage
emission; while they are not apparent in the current emission.
Instead low-order harmonics and certain interharmonics within
a band are apparent. This impacts the voltage emission.
The correlation of voltage and current at each frequency
(5-Hz resolution) has been studied. The apparent correlation
points to three cases: a linear relation of voltage and current;
a strong correlation but with varying voltage and current;
negative correlation between voltage and current. The linear
relation happens at certain harmonics. The other strong correlation occurs at broadband components.
Also the individual emission as a function of active-power
has been studied. Harmonics are in general independent with
the active power; whereas interharmonics are in general dependent on the active power. The study indicates a varying
dependence of emission with the power production. However
the active power is not the only factor determing the emission.
Further study should be done for multiple dependence.
The measurements present a varying emission, especially
for interharmonics at certain bands. The varying emission and
the complicated behavior presented in the wind turbine need
a further study.
ACKNOWLEDGMENT
0.02
0.01
0
285 Hz
0.2
0
of the other harmonic frequencies. While the interharmonics
present a different trend with the active power. The studied
interharmonics show an increase with the active-power as the
main trend. Next to that there is low emission till half per-unit
active power for all the presented frequencies.
The study of the emission as a function of active power
leads to the conclusion that: harmonic emission is generally
independent of active power; while interharmonic emission
depend strongly on the active power. A similar study based
on the harmonic and interharmonic subgroups pointed to the
same conclusion, as presented in [15].
0.6
0.8
1
Individual harmonics/interharmonics versus active-power.
Some of the studied harmonics, e.g. 100 Hz and 500 Hz are
almost constant with the active power. This also holds for most
The authors would like to thank their colleagues in Electric
Power Engineering group at Luleå University of Technology,
S. K. Rönnberg and C.M. Lundmark, for their useful discussions within writing this paper.
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Kai Yang (S’10) received the M.Sc. degree from Blekinge Institute of
Technology, Sweden in 2009 and the Licentiate of Engineering degree from
Luleå University of Technology in 2012. Currently he is a PhD student at the
Department of Engineering Sciences and Mathematics at Luleå University of
Technology, Skellefteå, Sweden. The main research interest is in the ﬁeld of
wind power quality, harmonics and distortion.
Math H.J. Bollen (M’93-SM’96-F’05) received the M.Sc. and Ph.D. degrees
from Eindhoven University of Technology, Eindhoven, The Netherlands, in
1985 and 1989, respectively. Currently, he is professor in electric power
engineering at Luleå University of Technology, Skellefteå, Sweden and R&D
Manager Electric Power Systems at STRI AB, Gothenburg, Sweden. He has
among others been a lecturer at the University of Manchester Institute of
Science and Technology (UMIST), Manchester, U.K., professor in electric
power systems at Chalmers University of Technology, Gothenburg, Sweden,
and technical expert at the Energy Markets Inspectorate, Eskilstuna, Sweden.
He has published a few hundred papers including a number of fundamental
papers on voltage dip analysis, two textbooks on power quality, “understanding power quality problems” and “signal processing of power quality
disturbances”, and two textbooks on the future power system: “integration of
distributed generation in the power system” and “the smart grid - adapting
the power system to new challenges”.
Anders Larsson received the Licentiate and Ph.D. degrees from Luleå
University of Technology, Skellefteå, Sweden in 2006 and 2011, respectively.
Currently he is a Postdoctoral researcher at the same university. During his
employment at Luleå University of Technology, since 2000, the main focus
has been on research on power quality and EMC issues. During this time he
has made signiﬁcant contributions to the knowledge on waveform distortion
in the frequency range 2 to 150 kHz. At the moment his research is focused
towards lighting installations and power quality issues. Anders is an active
member of two IEC working groups with the task to bring forward a new
set of standards regarding the frequency range between 2 and 150 kHz. At
the moment he is also involved in teaching and managing a B.Sc. program in
electric power engineering.
Mats Wahlberg is currently working at Skellefteå Kraft Elnät, Skellefteå,
Sweden. He has been with the company for about 30 years. He has a long and
broad experience obtained from involvement in a wide range of tasks. Some
examples are calculations of constructions, losses and protection relays. In the
last 15 years the main focus of his work has been with power quality issues
and different kinds of communications. He is also senior research engineer at
Luleå University of Technology, Skellefteå, Sweden.
F6
Paper G
Wind Power Harmonic Aggregation of Multiple Turbines
in Power Bins
K. Yang, M.H.J. Bollen and E.A. Larsson
Published in Proceedings of ICHQP2014
c
2014
IEEE
G2
1
Wind Power Harmonic Aggregation of Multiple
Turbines in Power Bins
Kai Yang, Math H. J. Bollen and E.O. Anders Larsson
Electric Power Engineering Group
Luleå University of Technology
931 87, Skellefteå, Sweden
Email: [email protected]
Abstract—The paper presents current harmonic and interharmonic measurement of a Type-IV wind turbine. Characterizations and classiﬁcations have been performed with the
representation of harmonics and interharmonics in a complex
plane. The study of aggregations due to the summation of
complex currents has been performed based on Monte-Carlo
Simulation for harmonics and interharmonics. Aggregations occur less for low-order harmonics, more for high-order harmonics
and most for interharmonics. Aggregations are shown to be
largely independent of the produced power.
Index Terms—Wind power generation, Power quality, Power
conversion harmonics, Harmonic analysis.
I. I NTRODUCTION
T
HE employment of power electronics in modern wind
turbines results in the emission of waveform distortions.
The characteristics of the wind power emission have been
studied by a number of papers [1], [2], [3], [4], [5], [6].
Many studies have been done for the magnitude of the
harmonics, while few papers have been done in terms of
phase angle [7], [8]. The measured phase-angles of windpower harmonics have been presented in [1], [9]. They are
concluded to possess a narrow normal-type distribution at
low frequencies, and at high frequencies the phase-angles are
uniform distributed.
There is no simple description of the distributions of phase
angle of harmonic current from wind turbines; measurements
and a analysis of complex harmonics have been described in
papers [1], [10].
The papers presenting phase-angle studies have not involved
components of frequencies other than integer harmonics. This
paper has performed a characterization of complex current
harmonics (magnitude and phase angle), as well as interharmonics. The aggregation effect, or the extent of harmonic
summation, due to the characteristics of the complex currents
has been studied by Monto-Carlo Simulation.
The harmonics and interharmonics of wind power have
been presented to be varying with active power [11]. The
distribution of the complex currents will be impacted by the
magnitudes and phase angles at different power bins. The
study of the aggregation factor as a function of the active
power has therefore been performed.
Section II presents the measurement on a wind turbine, with
the characterization of complex current. Section III presents
c
978-1-4673-6487-4/14/$31.00 2014
IEEE
the aggregation by the Monte-Carlo Simulation, including
the aggregation as a function of active power. The paper is
summarized in Section IV.
II. H ARMONIC C URRENT M EASUREMENT
A. Measurement Set-up
The measurement has been performed on a Type-IV wind
turbine, with a full-power converter. The rated power is 2 MW.
The turbine is equipped with a synchronous generator based
on a gearless drive. The inverters are self commutating and
pulse the installed IGBTs with variable switching frequency.
The current waveforms have been measured during 13
days with a standard power quality monitor Dranetz-BMI
PX5 at the medium voltage side of the turbine transformer.
The existing instrument transformers have been used for the
measurements with a sufﬁcient accuracy for the frequency
range up to few kHz [12], [8].
The 10-cycle current waveforms (about 200 ms) have been
acquired every 10 minutes with a sampling frequency of 256
times the power system frequency (50 Hz). The current spectra
are derived with Discrete Fourier Transform from the 10-cycle
current waveforms, with a 5-Hz resolution. The upward zerocrossing of phase A voltage has been used to be the reference
for the complex harmonic phase angles.
B. Complex Harmonic Current
Scatter plots of complex currents at certain orders (harmonics or interharmonics at centered orders, e.g. 100 Hz
for harmonic H 2, 150 Hz for H 3, 125 Hz for interharmonic
IH 2, 175 Hz for IH 3, the same throughout the whole paper)
have been presented in the complex plane. The scattered
dots represent the complex (inter)harmonic components at the
corresponding order.
Complex harmonics and interharmonics at several orders
and frequencies have been chosen for the representation. The
chosen orders represent the three typical scatter distributions
for all other (inter)harmonic components:
1) Characteristic harmonics (plus H 3): Scatter plots of
characteristic harmonics (plus H 3) are distributed centered
on a point of the complex plane. The scatter points of the
harmonic orders 3, 5, 7, 11, 13 and 17 in Fig. 1 distribute either
along a line (H 3 and H 5) or a curve (H 13), which are offset
from the coordinate origin. The characteristic of the similar
2
60
distributions also holds for other characteristic harmonics (not
presented here).
600
−40
400
−60
0
Imaginary part of complex (inter)harmonic current [mA]
−200
−300
H3
−100
0
100
200
300
H7
200
−200
−400
150
H5
−800 −600 −400 −200
0
200
H 11
−300
−50
−200
0
200
−100
−200 −150 −100
20
50
−50
0
50
−50
20
20
0
50
100
H9
10
0
0
−10
−20
H8
0
30
50
H 10
20
−30
−40
−20
0
20
20
10
10
0
0
H 17
−10
−10
10
−20
−20
0
0
0
30
−60
−50
0
−200
−50
−40
50
0
−100
−100
40
−20
100
100
−50
H4
−80
200
−100
0
−20
Imaginary part of complex (inter)harmonic current [mA]
0
50
20
0
800
100
H6
40
−30
−40
−10
−50
−20
−30
0
20
−20
−10
0
10
Real part of complex (inter)harmonic current [mA]
H 12
20
30
−20
−100
H 13
−100
−50
−30
0
50
100
−30 −20 −10
Real part of complex (inter)harmonic current [mA]
0
10
20
Fig. 1. Complex characteristic harmonic (plus H 3) currents at centered
harmonic orders H 3 (150 Hz), H 5 (250 Hz), H 7 (350 Hz), H 11 (550 Hz),
H 13 (650 Hz), and H 17 (850 Hz) at phase A.
2) Non-characteristic harmonics (except H 3): The scatter
plots of non-characteristic harmonics are centered on a point
which is with an offset that is different for each harmonic
from the coordinate origin. An example is shown as H 4, H 6,
H 8, H 9, H 10 and H 12 in Fig. 2. Note that, a small number
of points around the coordinate origin represent the emission
when the wind turbine is not producing any active power. The
other non-characteristic harmonics present a similar distribution as H 4. Additionally clusters of higher order harmonics
(greater than order 20) present a center with less offset from
the coordinate origin.
3) Interharmonics: Interharmonics IH 4, IH 5, IH 6 and
IH 7, as well as 280 Hz and 380 Hz components have been
shown as in Fig. 3. The scatter plots are centered around
the coordinate origin of the complex plane. The points in
these scatter plots are randomly distributed in the complex
plane, which indicates a randomly distributed phase-angle. It
is different from the previous two types. The phase-angles of
the interharmonics are close to a uniform distribution.
III. H ARMONIC AGGREGATION
Complex harmonics and interharmonics can be represented
by vectors (as shown in Fig. 1, Fig. 2 and Fig. 3), with two
variables: the magnitude and the phase-angle. For a group of
wind turbines in a wind park, the (inter)harmonics of the group
or park are obtained as the summation of all (inter)harmonics
Fig. 2. Complex non-characteristic harmonic (except H 3) currents at centered
harmonic orders H 4 (200 Hz), H 6 (300 Hz), H 8 (400 Hz), H 9 (450 Hz), H 10
(500 Hz) and H 12 (600 Hz), at phase A.
from the individual turbines. The summation of two or more
vectors depends on both magnitudes and phase-angles of the
individual vectors.
Take multiple wind turbines in a wind park as an example,
the summation of the overall harmonics and interharmonics at
the point of connection will be impacted by the characteristics
of each wind turbine. The capacitance and inductance of the
components in the collection grid will cause resonances that
impact the transfer of the harmonics and interharmonics, as is
studied in [13]. In this work we will not consider the impact of
the collection grid. The total harmonic current from the group
or park is assumed to be equal to the sum of the currents from
the individual turbines.
A. Monte-Carlo Simulation
As an input to the stochastic model, the series of measured
complex currents has been used as the emission for all the
turbines in a wind park consisting of 10 turbines. Assume that
all the ten wind turbines present the same emission distribution
in the complex plane; and assume that the emission from
different turbines is statistically independent.
The overall emission of the ten wind turbines, at the point of
connection of the wind park, is obtained by the summation of
the emission from the ten wind turbines. At each scenario, the
emission of each wind turbine has been presented randomly
with one spectrum from all the measurements. Thus the
spectrum of the wind park is derived from the summation
of all the complex spectra of the ten turbines. The process
3
50
500
IH 4
Imaginary part of complex (inter)harmonic current [mA]
0
IH 5
0
−50
−50
0
50
50
−500
−500
0
500
40
H6
IH 7
20
0
0
−20
−50
−50
0
50
500
−40
−40
−20
0
20
500
280 Hz
40
The blue line represents the average spectrum of the individual turbine; and the blue line represents the average spectrum
of the wind park. The upper ﬁgure is with the scale of the
wind park spectrum 10 times the individual turbine. Note that,
the summation of the ten turbines is less than ten times the
individual spectrum. It remains the similar phenomenon for
the lower ﬁgure that summation of the ten turbines is less
than ten times the individual spectrum.
The ratio of the average current spectrum in the wind park
to ten times the individual average spectrum is deﬁned as the
aggregation factor. The value of the aggregation factor is unity
when there is no aggregation between the turbines; while the
aggregation factor is low when there is much aggregation in
the wind park.
Studies have been performed to derive the aggregation factor
for all the measurement spectra, as shown in Fig.5.
380 Hz
1
0
0.8
0
−500
−500
−500
0
500
−500
0
Real part of complex (inter)harmonic current [mA]
500
Fig. 3. Complex interharmonic currents at centered interharmonic orders IH 4
(225 Hz), IH 5 (275 Hz), H 6 (325 Hz), H 7 (375 Hz), as well as components
280 Hz and 380 Hz at phase A.
Aggregation factor
0.6
0.4
0.2
200
400
600
800
1000
1200
1400
1
0.8
0.6
has been repeated with 100,000 scenarios, which results in
100,000 spectra. The average of the 100,000 complex currents
has been used to represent both emission from the individual
turbine and the emission at the connection of the wind park.
With the above-mentioned Monte-Carlo Simulation, the
average spectrum of the harmonic current from one individual
turbine (input of one turbine) and the average current spectrum
of the wind park (output of ten turbines) have been presented
in Fig. 4.
280Hz
380Hz
0
0
100
Input Harmonics [A]
0.06
200
300
400
500
600
700
800
900
Input of one turbine
Output of ten turbines
5
Output Harmonics [A]
Input Harmonics [A]
Input of one turbine
Output of ten turbines
0
1000
0.15
0.04
0.1
0.02
0.05
0
1000
1200
1400
1600
1800 2000 2200
Frequency [Hz]
2400
2600
2800
Output Harmonics [A]
0.5
0
3000
Fig. 4. Average current spectra of input at an individual turbine and the
output of the multiple turbines after aggregation.
0.4
0.2
Fig. 5.
1600
1800
2000
2200
2400
2600
Frequency [Hz]
2800
3000
3200
Aggregation factors at full range of power.
The aggregation factor is high at harmonics, while low at
interharmonics. The aggregation factor at low-order harmonics
is greater than that of the high-orders. In other words, harmonics aggregate less than interharmonics; low-order harmonics
aggregate less than high-order harmonics.
The (inter)harmonic aggregation depends on both magnitudes and phase-angles of vectors, which are the signiﬁcant
parameters of the complex current distribution. The phaseangle has a signiﬁcant impact on the aggregation. The offset
of the cluster shifts the phase angle into a certain quadrant
of the complex plane. It results in less cancellation of vectors
compared to the random distribution of phase angles. Thus
harmonics aggregate less than interharmonics. Furthermore,
clusters of high-order harmonics have a smaller offset from the
coordinate origin than the low-order harmonics. Consequently
the high-order harmonics aggregate more than the low-order
harmonics.
Interharmonics aggregate to a large extent. It is caused by
the random phase-angle, which is distributed uniformly.
The
√
resulted aggregation factor is around 0.3162 or 1/ 10, with
the square-root of the number of turbines.
There is no frequency component for which the aggregation
factor is close to unity, which indicates that all components
4
are aggregated to some extent.
B. Aggregation in Power bins
It is recommended in the standard IEC 61400-21 that, wind
power harmonics are measured according to the active power
in power bins. The power bin 0, 10, 20, . . . , 100 refer to the
active power in percent of the rated power in the corresponding
ranges 0% - 5%, 5% - 15%, 15% - 25%, . . . , 95% - 100%. It
was shows in earlier studies [11] that harmonics and especially
interharmonics vary with active-power production. Thus the
spectrum is different for different power bins. A study was
made to ﬁnd out if also the aggregation would be different
for different power bins. Due to lack of data points it was not
possible to use the same bins as in IEC 61400-21. Instead, the
three ranges of power bins 10 - 30, 40 - 60 and 70 - 90 have
been chosen to study the aggregation for the wind park. The
aggregation factors for these three power bins are shown in
Fig. 6.
1
Power Bin 10−30
0.5
Aggregation factor
0
500
1000
1500
2000
2500
3000
1
Power Bin 40−60
0.5
0
ACKNOWLEDGMENT
500
1000
1500
2000
2500
3000
1
Power Bin 70−90
0.5
0
of harmonics from multiple wind turbines at different levels
of power production.
The characteristics of harmonics and interharmonics of a
wind turbine have been classiﬁed. Three types are distinguished: characteristic harmonics (with H 3) present a complex
current distribution with a non-round cluster with an offset
from the coordinate origin; non-characteristic harmonics with
a round cluster with an offset from the coordinate origin;
interharmonics are round cluster, centered at the origin and
with random phase-angle.
Due to the different characteristics of complex currents,
the aggregations of (inter)harmonics present the phenomenon
that: high frequency harmonics aggregate more than the low
frequency harmonics; interharmonics aggregate much more
than harmonics. The aggregation is determined by distribution
of magnitudes and especially phase-angles.
Aggregation has been studied for different ranges of active power bins. With increasing power production certain
harmonics aggregate more, while others aggregate less. The
aggregation of interharmonics is however not impacted by the
power production.
Further work is needed to study the characteristics of certain
harmonics with different power productions, the behavior of
magnitudes and phase angles. Further work is also needed to
verify the assumption made for calculating the aggregation
factor.
500
1000
1500
2000
Frequency [Hz]
2500
The authors would like to thank their colleagues in Electric
Power Engineering group at Luleå University of Technology,
S. K. Rönnberg and C.M. Lundmark, for their useful discussions within writing this paper. Many thanks especially to Mats
Wahlberg, Skellefteå Kraft Elnät AB, for the measurements.
3000
Fig. 6. Aggregation factors at three ranges of power bins 10 - 30, 40 - 60
and 70 - 90.
The Monte-Carlo Simulation has been performed with only
10,000 scenarios because of the lower number of samples a
power bin.
In general, the aggregation follows the rule that, harmonics
at high frequencies aggregate more than those at lower frequencies; and interharmonics aggregate more than harmonics.
The fundamental frequency (50 Hz) component approaches
unity especially in power bins 40 - 60 and 70 - 90.
Fig. 6 presents some differences between the three power
bin ranges. With the increasing active-power the components
at 100 Hz, 350 Hz, 850 Hz and 1450 Hz aggregate less. While
the components at 400 Hz, 450 Hz, 650 Hz aggregate more
with a larger active-power. The aggregation has been impacted
by the distribution of complex currents with the different active
power bins.
IV. C ONCLUSION
The paper presents the complex harmonics and interharmonics of a full-power-converter wind turbine, and the aggregation
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Kai Yang (S’10) received the M.Sc. degree from Blekinge Institute of
Technology, Sweden in 2009 and the Licentiate of Engineering degree from
Luleå University of Technology in 2012. Currently he is a PhD student at the
Department of Engineering Sciences and Mathematics at Luleå University of
Technology, Skellefteå, Sweden. The main research interest is in the ﬁeld of
wind power quality, harmonics and distortion.
Math H.J. Bollen (M’93-SM’96-F’05) received the M.Sc. and Ph.D. degrees
from Eindhoven University of Technology, Eindhoven, The Netherlands, in
1985 and 1989, respectively. Currently, he is professor in electric power
engineering at Luleå University of Technology, Skellefteå, Sweden and R&D
Manager Electric Power Systems at STRI AB, Gothenburg, Sweden. He has
among others been a lecturer at the University of Manchester Institute of
Science and Technology (UMIST), Manchester, U.K., professor in electric
power systems at Chalmers University of Technology, Gothenburg, Sweden,
and technical experts at the Energy Markets Inspectorate, Eskilstuna, Sweden.
He has published a few hundred papers including a number of fundamental
papers on voltage dip analysis, two textbooks on power quality, “understanding power quality problems” and “signal processing of power quality
disturbances”, and two textbooks on the future power system: “integration of
distributed generation in the power system” and “the smart grid - adapting
the power system to new challenges”.
Anders Larsson received the Licentiate and Ph.D. degrees from Luleå
University of Technology, Skellefteå, Sweden in 2006 and 2011, respectively.
Currently he is a Postdoctoral researcher at the same university. During his
employment at Luleå University of Technology, since 2000, the main focus
has been on research on power quality and EMC issues. During this time he
has made signiﬁcant contributions to the knowledge on waveform distortion
in the frequency range 2 to 150 kHz. At the moment his research is focused
towards lighting installations and power quality issues. Anders is an active
member of two IEC working groups with the task to bring forward a new
set of standards regarding the frequency range between 2 and 150 kHz. At
the moment he is also involved in teaching and managing a B.Sc. program in
electric power engineering.