Estimating the Performance Loss Rate of Photovoltaic Systems Using Time Series Change Point Analysis
Abstract
:1. Introduction
2. Materials and Methods
2.1. Experimental Setup and Data Acquisition
2.2. Data Processing and Creation of PV Datasets
2.3. PLR Estimation Using Statistical Methods
- (1)
- Each change point corresponds to two data segments (e.g., one segment from the start month of the reporting period to the corresponding month of the change point, and the other from the change point month to the end month of the time series) with supposedly different means. In case of more than one change point, the number of segments is equal to the number of change points plus one (number of segments = number of change points + 1).
- (2)
- For each change point, we subtract the data of its second segment from the data of its first segment (i.e., the data difference, xd) and ensure that the months of the subtracted data correspond. If the detected change point is not statistically significant, then the mean of xd should be statistically zero. Otherwise, if the mean of xd is not statistically zero, then the detected change point is statistically significant.
- (3)
- We test the following hypothesis (assuming that the differences xd,i are random from normal distribution such as the E (xd,i) = 0):
- Null hypothesis H0: E (xd,i) = 0
- Alternative hypothesis Hα: Ε(xd,i) 0
2.4. Validation through Indoor Testing and Synthetic Dataset
3. Results and Discussion
3.1. Linear PLR Estimates Using the LOESS Technique
3.2. Nonlinear PLR Estimates Using CP Algorithms
3.3. Indoor Testing Results and Validation
3.4. Summary and Future Directions
- The LOESS trend can be used for an initial screening to detect obvious change points within the PV performance time series.
- The application of change point algorithms proved to be an efficient statistical technique for detecting nonlinear power loss in PV systems.
- The identified change points may be attributed to failures/defects, maintenance events and/or actual degradation mechanisms. Suggestions for future research include the development of a detailed methodology for attributing the reason (e.g., maintenance events, fault, and degradation modes) behind the detected change points.
- Different numbers and locations of change points were detected based on the applied algorithm. This reveals the method dependency of the PLR estimation.
- The indoor testing validation revealed invisible defects that may be the root cause of PV’s low performance and the existence of change points.
- The validation of the FBP model on the created PV performance time series with data anomalies showed its capability for capturing trend changes, even in the presence of anomalous conditions. Though, further investigation and validation on data with different types of outliers, such as global (i.e., point anomalies), contextual (i.e., conditional anomalies), and collective outliers, is needed to verify the above statement.
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
a-Si | Amorphous silicon |
ARIMA | Autoregressive integrated moving average |
Beast | Bayesian estimation of abrupt change, seasonality, and trend |
Bkp | Breakpoints |
CdTe | Cadmium telluride |
CP | Change point |
CSD | Classical seasonal decomposition |
CIGS | Copper indium gallium diselenide |
EL | Electroluminescence |
FBP | Facebook prophet |
HW | Holt–Winters |
IR | Infrared |
IEC | International Electrotechnical Commission |
LCOE | Levelized cost of energy |
LOESS | Locally weighted scatterplot smoothing |
mono-c Si | Mono-crystalline silicon |
multi-c Si | Multi-crystalline silicon |
OLS | Ordinary least squares |
OTF | Outdoor test facility |
PLR | Performance loss rate |
PR | Performance ratio |
PV | Photovoltaic |
PCA | Principal component analysis |
PELT | Pruned exact linear time |
STC | Standard test conditions |
UCY | University of Cyprus |
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System ID | Manufacturer | Technology | Series Modules | Parallel Module | Rated Power (kWp) |
---|---|---|---|---|---|
(a) | Atersa | mono-c Si | 6 | 1 | 1.020 |
(b) | BP Solar | mono-c Si | 6 | 1 | 1.110 |
(c) | Sanyo | mono-c Si | 5 | 1 | 1.025 |
(d) | Suntechnics | mono-c Si | 5 | 1 | 1.000 |
(e) | Schott Solar | multi-c Si (edge defined film-fed growth—EFG) | 6 | 1 | 1.000 |
(f) | Schott Solar | multi-c Si (multi-crystalline advanced industrial cells—MAIN) | 4 | 1 | 1.020 |
(g) | SolarWorld | multi-c Si | 6 | 1 | 0.990 |
(h) | Solon | multi-c Si | 7 | 1 | 1.540 |
(i) | Würth Solar | thin film (CIGS) | 6 | 2 | 0.900 |
(j) | First Solar | thin film (CdTe) | 3 | 6 | 1.080 |
(k) | Mitsubishi Heavy Industries (MHI) | thin film (a-Si) | 2 | 5 | 1.000 |
Parameter | Manufacturer Model | Accuracy |
---|---|---|
Ambient temperature | Rotronic HC2A-S3 | ±0.1 °C at 23 °C |
In-plane irradiance | Kipp Zonen CMP11 | ±2% expected daily accuracy, ±20 W/m2 for 1000 W/m2 |
DC voltage | Muller Ziegler Ugt | ±0.5% |
DC current | Muller Ziegler Igt | ±0.5% |
AC energy | Muller Ziegler EZW | ±1% |
System ID | Annual PLR (%/Year) ± Standard Error |
---|---|
(a) | −0.78 ± 0.00 |
(b) | −0.60 ± 0.01 |
(c) | −0.74 ± 0.00 |
(d) | −0.75 ± 0.00 |
(e) | −0.84 ± 0.00 |
(f) | −0.68 ± 0.00 |
(g) | −1.09 ± 0.00 |
(h) | −1.09 ± 0.00 |
(i) | −2.52 ± 0.03 |
(j) | −2.04 ± 0.00 |
(k) | −1.46 ± 0.00 |
System ID | Number of CPs | Location of CPs |
---|---|---|
(a) | 2 | 04/2011, 10/2013 |
(b) | 3 | 03/2008, 12/2009, 04/2012 |
(c) | 1 | 04/2008 |
(d) | 1 | 04/2008 |
(e) | 1 | 02/2011 |
(f) | 2 | 05/2012, 09/2012 |
(g) | 1 | 03/2009 |
(h) | 1 | 02/2009 |
(i) | 2 | 04/2008, 03/2012 |
(j) | 2 | 04/2008, 04/2011 |
(k) | 2 | 11/2008, 12/2011 |
System ID | Number of CPs | Location of CPs |
---|---|---|
(a) | 1 | 04/2011 |
(b) | 2 | 03/2008, 08/2009 |
(c) | 1 | 04/2008 |
(d) | 1 | 04/2008 |
(e) | 1 | 02/2011 |
(f) | 1 | 03/2012 |
(g) | 1 | 03/2009 |
(h) | 1 | 02/2009 |
(i) | 3 | 04/2008, 04/2010, 04/2012 |
(j) | 3 | 03/2008, 02/2010, 01/2012 |
(k) | 3 | 10/2007, 12/2008, 12/2011 |
System ID | Number of CPs | Location of CPs |
---|---|---|
(a) | 2 | 09/2011, 10/2013 |
(b) | 2 | 09/2008, 03/2010 |
(c) | 1 | 09/2010 |
(d) | 1 | 08/2009 |
(e) | 0 | - |
(f) | 2 | 01/2009, 02/2012 |
(g) | 0 | - |
(h) | 2 | 02/2009, 02/2012 |
(i) | 1 | 07/2012 |
(j) | 1 | 06/2012 |
(k) | 3 | 09/2008, 11/2009, 12/2011 |
System ID | Number of CPs | Location of CPs |
---|---|---|
(a) | 0 | - |
(b) | 2 | 12/2008, 05/2011 |
(c) | 1 | 07/2009 |
(d) | 1 | 04/2009 |
(e) | 0 | - |
(f) | 0 | - |
(g) | 0 | - |
(h) | 1 | 05/2011 |
(i) | 1 | 06/2011 |
(j) | 1 | 08/2009 |
(k) | 1 | 04/2010 |
System ID | Linear FPB | FPB PLR1 | FPB PLR2 | FPB PLR3 |
---|---|---|---|---|
(a) | −0.83 ± 0.01 | - | - | - |
(b) | - | −4.27 ± 0.01 | −2.49 ± 0.01 | −1.42 ± 0.01 |
(c) | - | −1.35 ± 0.01 | −0.45 ± 0.01 | - |
(d) | - | −1.07 ± 0.00 | −0.61 ± 0.00 | - |
(e) | −0.96 ± 0.00 | - | - | - |
(f) | −0.80 ± 0.00 | - | - | - |
(g) | −1.23 ± 0.00 | - | - | - |
(h) | - | −1.21 ± 0.01 | −0.90 ± 0.01 | - |
(i) | - | −2.52 ± 0.00 | −2.66 ± 0.01 | - |
(j) | - | −2.80 ± 0.00 | −1.99 ± 0.04 | - |
(k) | - | −1.78 ± 0.01 | −1.48 ± 0.00 | - |
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Livera, A.; Tziolis, G.; Theristis, M.; Stein, J.S.; Georghiou, G.E. Estimating the Performance Loss Rate of Photovoltaic Systems Using Time Series Change Point Analysis. Energies 2023, 16, 3724. https://doi.org/10.3390/en16093724
Livera A, Tziolis G, Theristis M, Stein JS, Georghiou GE. Estimating the Performance Loss Rate of Photovoltaic Systems Using Time Series Change Point Analysis. Energies. 2023; 16(9):3724. https://doi.org/10.3390/en16093724
Chicago/Turabian StyleLivera, Andreas, Georgios Tziolis, Marios Theristis, Joshua S. Stein, and George E. Georghiou. 2023. "Estimating the Performance Loss Rate of Photovoltaic Systems Using Time Series Change Point Analysis" Energies 16, no. 9: 3724. https://doi.org/10.3390/en16093724
APA StyleLivera, A., Tziolis, G., Theristis, M., Stein, J. S., & Georghiou, G. E. (2023). Estimating the Performance Loss Rate of Photovoltaic Systems Using Time Series Change Point Analysis. Energies, 16(9), 3724. https://doi.org/10.3390/en16093724