How to effectively monitor a PV system - accuracy of Solar
Analytics performance modelling algorithms
Stefan Jarnason1, Jessie Copper2, Avantika Basu3, Alistair Sproul2
1
Suntech R&D Australia, Sydney, NSW, 2060 Australia
2
School of Photovoltaic and Renewable Energy Engineering,
University NSW, Sydney, NSW, 2052 Australia
3
Solar Analytics, Sydney, NSW, 2060 Australia
Contact author: Stefan Jarnason - [email protected]
Keywords: Monitoring, diagnostic, yield, simulation, modelling, performance.
Abstract
Less than 1% of the 1.2 million PV systems in Australia have effective monitoring.
To determine how well a PV system is performing, a comparison between actual
energy generation and the theoretical energy generation under the same weather
conditions is required. The reliability of such monitoring tools is dependent on the
accuracy of the algorithms used to model the theoretical performance of the PV
system and the inputs for the models. This paper firstly presents a summary and
validation of the prediction algorithm, then provides a real world comparison between
the modelling results from the Stage 2 Solar Analytics algorithms and the measured
performance of seventeen PV systems across Sydney.
Introduction
Solar Analytics is a program developed from a set of algorithms used to predict the
AC electrical output of Photovoltaic (PV) systems. To test the efficacy of any
modelling a real world comparison between the expected AC energy generation and
the predicted AC energy generation is required.
Acronyms/Nomenclature
Acronym
BOM
Symbol
kt
CSA
DHI
DKASC
DNI
DP
GHI
MBE
MOS
NMBE/NRMSE
NREL
RMSE
Rsqd
dt
Ih,d
Ih,b
Ih
R2
Description
Bureau of Meteorology
Clearness Index
Clear sky adjusted model – DP currently uses ASHRAE
method
Diffuse fraction
Direct horizontal irradiance in W/m2
Desert Knowledge Australia Solar Centre
Direct normal irradiance in W/m2
Development Platform – the solar analytics algotithms
Global horizontal irradiance in W/m2
Mean bias error
Satellite derived irradiance in W/m2 by 3Tier
Normalised MBE or RMSE
National Renewable Energy Laboratory
Root mean squared error
Coefficient of determination
Solar2014: The 52nd Annual Conference of the Australian Solar Council
Proceedings of the 52nd Annual Conference, Australian Solar Energy Society (Australian
Solar Council) Melbourne May 2014 ISBN: 948-0-646-92219-5
Algorithm Modelling – Irradiance
A number of algorithms are required in order to calculate the theoretical PV system
performance based on the PV system specifications and hourly weather data [1-5].
The first is estimating direct normal and diffuse horizontal irradiance when global
horizontal irradiance is known and measured. This estimation is required since the
direct and diffuse are usually not
known or able to be sourced. For this
analysis the ground based hourly
measured data from the BOM is used
as the GHI field. As shown in Figure
1 for five sites across Australia, the
standard Maxwell separation model
still contains a considerable level of
uncertainty at estimating both direct
normal and diffuse horizontal
irradiance, accounting for over 30%
of the total uncertainty [6].
Figure 1: Hourly DHI BOM versus DHI DP
(modelled) in W/m2.day.
The second algorithm required is to determine the level of diffuse irradiance
falling on a tilted plane. Usually reflections are only a small component of the
total level of irradiance falling on a surface, however they still need to be
incorporated into the model. At the hourly level, results showed that the
transposition model in isolation has a level of modelling uncertainty of 12%.
Figure 2: Scatterplot of hourly and daily measured irradiance on 34° tilted plane vs. DP
with sequential inputs of DP Daily GHI (modelled using daily insolation from BOM), DP
with GHI (hourly measured GHI from BOM) and DP with GHI, DHI (hourly measured GHI
and DHI from BOM).
Algorithm Modelling – DC Power
A number of well documented models have been in use to model the DC power of
the PV array [7, 8]. This output is derated due to losses in cables and due to
mismatch and soiling. Figure 3 shows the hourly results for modelling derated
DC power versus measured DC data for a specific site. The results highlight that
the DC algorithm achieves a good correlation to the measured parameters, at
both the hourly and daily level, particularly when in plane irradiance is known
Solar2014: The 52nd Annual Conference of the Australian Solar Council
Proceedings of the 52nd Annual Conference, Australian Solar Energy Society (Australian
Solar Council) Melbourne May 2014 ISBN: 948-0-646-92219-5
and measured. The figures also demonstrate the increased level of uncertainty of
the results when only daily GHI is used as input.
Figure 3: Scatterplot of hourly DC Array data for Nyngan vs. DP derated DC output with
measured in plane irradiance as input (left) and daily GHI as input (right).
Algorithm Modelling – AC Power
The derated DC power is multiplied by the inverter efficiency to obtain the final
AC output of the system. Figure 4 present the results, on both the hourly and
daily level, of the AC power algorithm [7]. The results indicate that the AC
algorithm achieves a very close correlation to the measured AC power data set at
both the hourly and daily level with normalised levels of uncertainty around 5%.
Figure 4: Scatterplots of hourly (left) and daily (right) AC array data for Nyngan vs. DP AC
predicted power with measure DC Array data as input.
Algorithm Modelling – Summary
The overall model uncertainties are shown in Figure 5. This graph shows that the
irradiance modelling contains the greatest level of uncertainty.
Solar2014: The 52nd Annual Conference of the Australian Solar Council
Proceedings of the 52nd Annual Conference, Australian Solar Energy Society (Australian
Solar Council) Melbourne May 2014 ISBN: 948-0-646-92219-5
50%
NMBE
40%
Daily NRMSE
Hourly NRMSE
30%
20%
10%
0%
DC Power
Irradiance on Plane
Hourly GHI, DNI, DHI
Hourly GHI
Daily GHI
-10%
Figure 5: Normalised levels of bias and RMSE for AC predicted power versus array data,
plotted for each step of the modelling process.
Initial Algorithm Validation
An initial real world validation analysis was undertaken using data from the
Desert Knowledge Australia Solar Centre (DKASC) to test the improvement in
modelling accuracy when hourly GHI was available. Four systems were
investigated. The systems included a roof mounted poly system and rack
mounted a-Si, Mono and Poly systems. On site measurements for GHI, DHI and
temperature as well as the AC output of the arrays were available for these
systems.
Figure 6 presents the statistical results for AC predicted power versus measured
array data using either daily GHI (the DP results) or hourly measured GHI as
input into the modelling process. These results are on par with the 65%
improvement in modelling uncertainty at the daily level observed for the Nyngan
location. For the DKASC site, the normalised levels of uncertainty were 25% at
the hourly level. Large errors were observed for a-Si systems due to the DC
modelling algorithm which has since been significantly improved.
60%
NMBE
50%
NRMSE Daily
40%
NRMSE Hourly
30%
20%
10%
0%
-10%
Daily GHI Hourly GHI Daily GHI Hourly GHI Daily GHI Hourly GHI Daily GHI Hourly GHI Daily GHI
GHI
Rooftop BPS
Sunpower Mono
BPS Poly
Kaneka A-Si
Figure 6: Normalised levels of bias and RMSE for AC predicted power versus array data
using either daily GHI (DP results) or hourly measured GHI as input.
Solar2014: The 52nd Annual Conference of the Australian Solar Council
Proceedings of the 52nd Annual Conference, Australian Solar Energy Society (Australian
Solar Council) Melbourne May 2014 ISBN: 948-0-646-92219-5
Real World Validation Methodology
The performance analysis presented in this paper was undertaken on an hourly dataset
from 17 PV Systems across Sydney (see Figure 7). On site AC power measurements
were recorded at each of 17 locations, with and plane of array (POA) irradiance also
recorded at some of the locations. Meteorological data of temperature, wind speed,
daily solar exposure and gridded hourly solar irradiance were sourced from the
Australian Bureau of Meteorology (BOM) for each of these locations.
Figure 7: Location of test sites.
Processing of the raw data was undertaken to exclude missing or erroneous values.
The data cleaning process attached flags to the hourly data points under the following
conditions:
•
Predicted power –if the hourly Predicted value was zero or missing
•
Array data –if the hourly Array value was zero or missing
•
Altitude flag – if Array data > 0 but Altitude <= 0
•
Temperature flag – if ambient Temperature was <-10°C or greater than +50°C
With the exception of the temperature flag, the flagged data points were excluded
from the analysis. For the flagged erroneous temperature data points, the hourly
ambient temperature was extrapolated from the adjacent hourly temperatures.
The performance of the Stage 2 Solar Analytics algorithms were analysed via the use
of graphical interpolation and the statistics of mean bias error (MBE), root mean
squared error (RMSE) and the coefficient of determination (R2).
Solar2014: The 52nd Annual Conference of the Australian Solar Council
Proceedings of the 52nd Annual Conference, Australian Solar Energy Society (Australian
Solar Council) Melbourne May 2014 ISBN: 948-0-646-92219-5
Daily Results
A scatterplot analysis of the Predicted
power versus the Array data (Figure 8)
indicates that the platform achieves a
reasonable correlation to the measured
array data with a similar level of scatter,
at the daily level. The statistics
indicate that a significant level of bias
of -7.1% is apparent between the
predicted power and the array data.
NMBE
NRMSE
Rsqd
DP to Array
-7.1%
22.1%
0.94
Figure 8: Scatterplot of predicted power versus Array Data with daily data.
In particular it was found that on average Solar Analytics slightly underestimates
the amount of Predicted power, and this was more evident for the larger
systems.
Hourly Results
In comparison to the results on the daily level,
the hourly level results show a greater spread
in the data (Figure 9). The bias error NMBE is
reduced to below 5%, however the hourly
RMSE error is almost doubled due to the larger
influence of the hourly irradiation modelling.
NMBE
NRMSE
Rsqd
Daily
-7.1%
22.1%
0.94
Hourly
-4.7%
41.2%
0.86
Figure 9: Scatterplot of predicted power versus Array Data with hourly data.
Improvement in algorithms
Based on the analysis of the performance of the algorithms, the following
improvements were subsequently implemented on the algorithms.
•
The calculation of altitude/sun position was refined through the use of the
NREL output of altitude/sun position [9]. Differences of up to 1.5 degrees
occurred between the initial and improved algorithm results.
•
Use of PV panel specific DC modelling parameters rather than generic PV
panel type parameters.
•
Correction of an error that randomly flipped between the correct inverter size
and an incorrect size.
•
Improvement of the lookup function used to calculate the inverter efficiencies,
particularly during the middle of the day.
•
Using a detailed extrapolation of the inverters efficiency curve for each
specific inverter rather than five fixed inverter efficiency points.
Solar2014: The 52nd Annual Conference of the Australian Solar Council
Proceedings of the 52nd Annual Conference, Australian Solar Energy Society (Australian
Solar Council) Melbourne May 2014 ISBN: 948-0-646-92219-5
•
Improved DC modelling of a-Si systems.
Discussion and Conclusion
The performance analyses of the individual algorithms that make up Solar Analytics
indicated that the primary driver of uncertainty was due to modelling hourly GHI,
with 30% uncertainties due to insolation separation, 12% due to transposition, and 5%
due to AC and DC power modelling.
There was a significant level of uncertainty at both the daily and hourly level for the
DNI and DHI parameters. The average levels of normalised uncertainties for DNI
were 23.3% at the daily level, and 42.7% at the hourly level. The main driver for the
difference would be caused by the methodology used to estimate the hourly values of
solar irradiance, as this modelling process does not factor in changes at the hourly
level that would occur due to cloud coverage.
These uncertainty levels were validated using four sites and three cell technologies
from DKASC, and tested with the 17 monitored sites in Sydney. The results showed
that the Stage 2 Solar Analytics algorithms at the daily level predict the electrical
output of the 17 systems with an average level of normalised uncertainty and bias of
22.1% and -7.1% respectively.
These results show that while a reasonable estimate of the daily energy generation of
a PV system can be achieved, significant further refinement of the algorithms is
required to achieve the level of accuracy necessary reliably predict when a PV system
is underperforming. This refinement is being undertaken.
Acknowledgements
Solar Analytics is a unique monitoring system
Australia and Envais Solar with the support of the
Australian NGO dedicated to reducing green
environment. To learn more about CRC
www.lowcarbonlivingcrc.com.au.
co-developed by Suntech R&D
CRC for Low Carbon Living, an
house emissions in the built
Low Carbon Living visit:
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Proceedings of the 52nd Annual Conference, Australian Solar Energy Society (Australian
Solar Council) Melbourne May 2014 ISBN: 948-0-646-92219-5
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Solar2014: The 52nd Annual Conference of the Australian Solar Council
Proceedings of the 52nd Annual Conference, Australian Solar Energy Society (Australian
Solar Council) Melbourne May 2014 ISBN: 948-0-646-92219-5