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2006 IEEE PES Transmission and Distribution Conference and Exposition Latin America, Venezuela
Synthetic and Systemic Model for Power
Quality Evaluation
J. A. Lopera, A. E. Díez, J. A. Bohórquez, G. J. López, I. C. Díez, and S. Mesa
A. Signal nullity subject to effect’s nullity
Each indicator’s value must be zero when PQ phenomena
measured (by the indicator) is not present in the system.
B. Increment due to PQ phenomena’s severity
Each indicator’s value must increment
phenomena’s severity increment.
when
PQ
C. Defined compatibility limit for the indicator
Each indicator must have a defined compatibility limit.
When this limit is exceeded, energy supplied is inadequate for
use in sensitive equipment. This is in order to ensure for
electromagnetic compatibility.
III.
Index Terms--Flicker, Harmonics, Power Quality, Power
Systems.
I. INTRODUCTION
P
ower Quality (PQ) phenomena have been evaluated in an
independent way using indicators like PST (Defined in
Std. IEC 61000-4-15) and THDV (Defined in Std. IEEE 519).
PST indicator represents voltage fluctuation’s severity, using
lamp-eye-brain system as reference (PST = 1 pu represents a
flicker level that’s annoying to 50% of the population).
THDV indicator evaluates the percentage of energy supplied
at frequencies different from system’s nominal frequency.
This means that PQ indicators, such as the ones described
before, possesses an independent physical meaning.
Simultaneous presence of PQ phenomena in power systems
calls for an indicator that’s able to integrate simultaneous
effects using information from usually measured PQ
indicators, such as the ones described above.
However, to assure simultaneous evaluation’s adequacy,
indicators must comply with some physical and mathematic
properties.
II. INDEPENDENT PROPERTIES
Before integrating indicator’s definition the compliance
with some properties is required. The first three properties are
evaluated in an independent way.
ORTHOGONAL SPACE FOR INDICATOR’S INTEGRATION
Using linear algebra’s concepts, formal establishment of an
orthogonal space that ensembles PQ indicators is achieved.
Orthogonal space concept requires, among other things, linear
independency between indicators, which, in this case, means
that when a specific PQ phenomenon’s severity increments,
only the value of the associated indicator must increment.
Defining inCEM, as a vectorial space in n called
Electromagnetic Incompatibility, with internal product and
norm (inCEM,<>,|| ||).
If X and Y are a couple of vectors that belong to inCEM, X
and Y are orthogonal if their intern product is zero (<X, Y> =
0). This property extends to any couple of unitary vectors Ci y
Cj. In this case, every unitary vector points out toward a
specific PQ phenomena direction. Normalization is achieved
by dividing each indicator by its compatibility limit, as
defined in (1):
PQ
(1)
PQinC
UmbPQ
Where,
PQ: PQ indicator (PST, THDV, …).
PQinC: Normalized value of PQ indicator.
UmbPQ: Compatibility Limit for PQ indicator.
This procedure also guaranties dimensional unification in
compatibility levels, and allows the definition of the
orthogonal space called Total Degradation (DT).
IV. VERIFICATION OF THDV AND PST PROPERTIES
A. Signal nullity subject to effect’s nullity
PST and THDV indicators yield zero, when they’re
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B. Increment due to PQ phenomena’s severity
The following figures show how PST and THDV comply
with this property.
Instantaneous Flicker [pu]
4000
3500
0.30pu (PST=5.0617)
0.20pu (PST=3.5730)
3000
0.15pu (PST=2.7541)
0.8
THD 0%
0.6
THD 10%
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
2500
-1
0
2000
1500
2
4
6
8
10
12
Time [miliseconds]
14
16
18
Fig. 4. Increment in THDV value due to an increment in distortion.
1000
500
0
49.5
C. Defined limit for the indicator
50.0
50.5
51.0
Time [seconds]
51.5
52.0
Fig. 1. Increment in PST value due to an increment in voltage change, 'V.
2000
100ms (PST=3.5730)
1800
Instantaneous Flicker [pu]
1
Instantaneous Voltage [pu]
measured over the standard waveform (Senoidal wave at
system’s nominal frequency and with an amplitude of
nominal voltage times 2 ).
1600
20ms (PST=1.9937)
TABLE I
10ms (PST=1.0691)
THDV LIMITS
1400
Nominal Voltage
UmbTHDV (%)
V < 69 kV
5.0
69 kV V < 161 kV
2.5
V 161 kV
1.5
Those values have been defined taking in account the
sensitivity of end user’s equipment.
1200
1000
800
600
400
200
0
49.5
A limit for PST is found in Std. IEC 61000-3-7. This
standard recommends PST = 1pu (UmbPST) as a limit in low
and medium voltage systems. A limit for THDV, for each
nominal voltage, is found in Std. IEEE-519 [1992]. This
standard recommends the following limits, in function of
nominal voltage.
50.0
50.5
51.0
Time [seconds]
51.5
52.0
Fig. 2. Increment in PST value due to an increment in duration of voltage
fluctuations.
3500
D. Orthogonallity
The requirements found Std. IEEE-519 for a THDV
instrument response (especially dynamic response and
bandwidth) and the requirements found Std. IEC 61000-4-15
for a PST instrument (especially the weighting filters defined
in block 3) , guaranties orthogonallity between PST and
THDV.
Instantaneous Flicker [pu]
2 (PST=5.7449)
3000
V. INTEGRATION OF VARIABILITY AN NON LINEALITY
EFECTS
1 (PST=3.5730)
2500
2000
1500
1000
500
0
49.5
50.0
50.5
51.0
Time [seconds]
51.5
52.0
Fig. 3. Increment in PST value due to an increment in the number of voltage
fluctuations.
When the independent properties and orthogonallity of
some PQ indicators (PST and THDV in this case) is guarantied
a Total Degradation space can be defined. In this case (1)
yields:
PST
THDV
inC
(2)
PST
, THDVinC
UmbPST
UmbTHDV
Equation (3) shows Total Distortion Vector (DTPQ) in its
polar form:
2
2
§ PST ·
§ THDV ·
¨¨
¸¸ ¨
¸ T (3)
UmbP
UmbTHDV
©
¹
ST ¹
©
Where Ԧ is the angle between PST’s component y and
THDV’s component, as shown in Fig. 5.
DTPQ
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Fig. 6. DTPQp vector
VII. CONCLUSIONS
Fig. 5. DTPQ vector
VI. DTPQ VECTOR’S MAGNITUDE
Taking in account the properties defined for DTPQ’s
components (and verified for PST y THDV in this case) is
possible to demonstrate that DTPQ vector’s magnitude has a
direct relation with the quantity of energy that even though it
has been delivered, it can’t be adequately used, and on the
contrary it affects end user equipment. This energy is called
bad supplied energy.
If DTPQ vector’s magnitude is greater than 1, there are PQ
problems regarding voltage fluctuations and harmonic
distortion. If angle Ԧ tends to 90 degrees, impact of harmonic
distortion (due to non-lineal loads) is greater than impact of
voltage fluctuations (due to fluctuating loads). This issue it’s
needed in order to determinate the problem and to take
corrective actions.
In polyphase systems a third component (compliant with
defined properties) which measures voltage unbalance can be
added. This indicator, called Vumb, measures polyphase
system’s unbalance in magnitude and angle by measuring the
relative size of negative and positive sequence components.
Vumb indicator is calculated as shown in (4):
V
(4)
Vumb
100%
V
Where,
V-: Negative sequence voltage at fundamental frequency.
V+: Positive sequence voltage at fundamental frequency.
A limit for Vumb is usually 2% (UmbVumb). In this case
(1) yields:
Vumb
(5)
VumbinC
UmbVumb
Fig. 6 shows DTPQ vector in polyphase systems – DTPQp:
The model proposed in this paper allows synthetic (because
it homologues and superpose various phenomena) and
systemic (oriented to system’s performance) evaluation of PQ
using voltage information processed using measuring devices
currently available at the utilities, like flicker and harmonic
meters.
The orthogonallity property assures that DTPQ vector’s
magnitude correctly reflects system’s incompatibility level.
A general methodology for new indicator’s validation and
inclusion was developed. Therefore, other components can be
added in order to measure the integrated effect of more types
of PQ phenomena, such as impulsive transients.
Adequate measuring methodology, like the one described
above, is the first step toward efficient assignation of PQ
responsibilities.
VIII. REFERENCES
[1]
[2]
[3]
J. A. Blandón, Procesamiento de medidas de resistividad. Medellín:
IEB, 1989, 123p.
M. Bollen, Understanding Power Quality Problems: Voltage Sags and
interruptions. New York: IEEE Press, 2.000, 200 p.
IEEE Recommended Practices and Requirements for Harmonic Control
in Electrical Power Systems, IEEE Standard 519-1992, Apr. 1992.
IX. BIOGRAPHIES
Jairo A. Lopera was born in Colombia in 1.965. He graduated form
Electrical Engineering at Universidad Pontificia Bolivariana in 1.987. He
graduated form T&D’s Specialization at Universidad Pontificia Bolivariana in
1.995. He obtained his MSc title in 2.005. From 1.987 to 1.988 he worked for
P&R Ltd as Resident engineer. From 1.988 to 1.996 he worked for UPB as
teacher. He has been dean since 1.996. He’s member of T&D Research Group
at UPB. [email protected]
Andrés. E. Díez was born in Colombia in 1.979. . He graduated form
Electrical Engineering at Universidad Pontificia Bolivariana in 2.001. He
graduated form T&D’s Specialization at Universidad Pontificia Bolivariana in
2.005. He obtained his MSc title in 2.005. He has been teacher at UPB and
engineer at “Maquinas Industriales” since 2.001. He’s member of T&D
Research Group at UPB. [email protected]
José. A. Bohórquez was born in Colombia in 1.965. He graduated form
Electrical Engineering at Universidad Pontificia Bolivariana in 1.989. He
graduated form T&D’s Specialization at Universidad Pontificia Bolivariana in
1.996. He obtained his MSc title in 2.004. From 1.989 to 1.990 he worked for
“Textiles Panamericanos Ltda” as Electrical department chief. In 1.990 he
worked for Fabricato. Since 1.990 he’s teacher at UPB. Since 1.992 he’s
teacher at EAFIT University too. He has been Electrical Engineering Lab’s
chief since 1.999. He’s member of T&D Research Group at UPB.
[email protected]
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Gabriel J. López was born in Colombia in 1.980. He graduated form
Electrical Engineering at Universidad Pontificia Bolivariana in 2.001. He
graduated form T&D’s Specialization at Universidad Pontificia Bolivariana in
2.005. He’s member of T&D Research Group at UPB. [email protected]
Iván C. Díez was born in Colombia in 1.982. He graduated form Electrical
Engineering in Universidad Pontificia Bolivariana in 2.004. In 2.004 he was
awarded by Colombia’s national government for his good results in the
undergraduate quality exams – ECAES-. From 2004 to 2005, he advised
“Comisión de Regulación de Energía y Gas” – CREG – in Reactive Power,
transmission and LPG issues. Currently he’s studying T&D’s specialization at
UPB and teaching at UPB. [email protected]
Santiago Mesa was born in Colombia in 1.980. From 2.001 to 2.003, he
worked as Matlab Monitor/Teacher at Universidad Pontificia Bolivariana. In
the second semester of 2.003 he worked at Interconexión Eléctrica SA (ISA)
as practice student. He graduated form Electrical Engineering in Universidad
Pontificia Bolivariana in 2.003. In 2.004 he was awarded by Colombia’s
national government for getting the first place in the undergraduate quality
exams – ECAES-. From 2004 to 2005, he advised “Comisión de Regulación
de Energía y Gas” – CREG – in PQ and power market issues. Nowadays he’s
working at CIDET and he’s member of T&D Research Group at UPB. He’s
currently studying T&D’s specialization at UPB. [email protected].