2 2 mitchell lee_am and pwat spectral correction_pvpmc5
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Combined air mass and precipitable water spectral correction for pv modeling
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2 2 mitchell lee_am and pwat spectral correction_pvpmc5
- 1. © Copyright 2013, First Solar, Inc.
- 2. 2 ©Copyright2013,FirstSolar,Inc. Current State of Spectral Correction . Absolute Air Mass (AMa) 3-4 • Sandia Array Performance Model computes spectral shift as a function of air mass: McSi = a0 + a1·AMa + a2·(AMa)2 + a3·(AMa)3 + a4·(AMa)4 • Coefficients determined from module testing 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1 2 3 4 5 SpectralShift Absolute Air Mass Nameplate Precipitable Water (Pwat) 1-2 • First Solar spectral shift model is calculated using precipitable water: MCdTe = 1.266 – 0.091exp(1.199(Pwat + 0.5)-0.210) • Coefficients calculated empirically from 13 TMY locations across the US input into SMARTS 0.95 0.97 0.99 1.01 1.03 1.05 1.07 0 1 2 3 4 5 SpectralShift Precipitable Water (cm) Nameplate 1. L. Nelson, M. Frichtl, and A. Panchula, “Changes in cadmium telluride photovoltaic performance due to spectrum,” IEEE Journal of Photovoltaics, vol. 3, No. 1, pp. 488-493, 2013. 2. Mitchell Lee, Lauren Ngan, William Hayes, and Alex F. Panchula, “Comparison of the Effects of Spectrum on Cadmium Telluride and Monocrystalline Silicon Photovoltaic Module Performance,” 42nd IEEE Photovoltaic Specialists Conference, 2015 3. D. King, W. Boyson, and J. Kratochvill, Photovoltaic Array Performance Model, SAND2004-3535. Albuquerque, New Mexico: Sandia National Laboratories, 2004. 4. D. King, J. Kratochvill, and W. Boyson, “Measuring solar spectral and angle-of-incidence effects on photovoltaic modules and solar irradiance sensors,” in 26th IEEE Photovoltaic Specialists Conference, 1997, p. 1113 – 1116.
- 3. 3 ©Copyright2013,FirstSolar,Inc. 𝑀 = 𝑏0 + 𝑏1 ∙ 𝐴𝑀 𝑎 + 𝑏2 ∙ 𝑝 𝑤𝑎𝑡 + 𝑏3 ∙ 𝐴𝑀 𝑎 + 𝑏4 ∙ 𝑝 𝑤𝑎𝑡 + 𝑏5 ∙ 𝐴𝑀 𝑎 𝑝 𝑤𝑎𝑡 Proposed Two Variable Spectral Correction 2-Variable Correlation AMa Correlation Pwat Correlation (Series 4-2): 𝑀 ≈ 1.266 − 0.091exp(1.199 𝑃 𝑤𝑎𝑡 + 0.5 −0.210 (Series 4-1 and earlier): 𝑀 ≈ 0.632 + 0.134exp(0.976 𝑃 𝑤𝑎𝑡 + 0.05 0.079 ) 𝑓1 𝐴𝑀 𝑎 = 𝑎0 + 𝑎1 ∙ 𝐴𝑀 𝑎 + 𝑎2 ∙ 𝐴𝑀 𝑎 2 + 𝑎3 ∙ 𝐴𝑀 𝑎 3 + 𝑎4 ∙ 𝐴𝑀 𝑎 4 Where: 𝐴𝑀 𝑎 = 𝑃 𝑃0 ∙ 𝐴𝑀
- 4. © Copyright 2013, First Solar, Inc.
- 5. 5 ©Copyright2013,FirstSolar,Inc. SMARTS Overview • Simulated Spectrum with all combinations of AMa and Pwat where: — 0.1 cm ≤ Pwat ≤ 5 cm — 1.0 ≤ AMa ≤ 5 • Limit spectral range of simulation to that of CMP11 (280 nm to 2800 nm) • Kept all other parameters fixed at G173 standard — Tilt = 37° — Azimuth = 180° • Computed spectral shift factor using module specific QE curves (provided by NREL)
- 7. 7 ©Copyright2013,FirstSolar,Inc. CdTe: 2-D Cross Section AMa Fixed at G173CdTe
- 8. 9 ©Copyright2013,FirstSolar,Inc. Multi-Si: 2-D Cross Section Pwat Fixed at G173 Multi-Si
- 9. © Copyright 2013, First Solar, Inc.
- 10. 12 ©Copyright2013,FirstSolar,Inc. Field Validation: Data Source Publically Available Data From NREL • Three locations with distinct climates • IV characterization and meteorological data at 5 min (or 15 minute) resolution for 13 months • Several module types (we focused on multi-Si and CdTe) Golden, CO Eugene, OR Cocoa, FL
- 11. 13 ©Copyright2013,FirstSolar,Inc. Field Validation: Methodology 𝑀 ≈ 𝐼𝑠𝑐 𝑃𝑂𝐴 ∙ 1000 W/m2 𝐼𝑠𝑐0 : where 𝐼𝑠𝑐0 tested by Sandia ISC corrected for: • Temperature using a linear coefficient. • Angle of incidence, AOI, using the Sandia method. • Soiling losses using estimates provided by NREL. Filtered out data where: • POA ≤ 200 W/m2 • AOI losses ≥ 1 % • Kt <= .70 or Kt >= 1.0 • Full days have < 1.5 hours of data
- 12. 14 ©Copyright2013,FirstSolar,Inc. Golden, Colorado CdTe Previous Correlation New Correlation Multi-Si 𝑀 𝑃 𝑤𝑎𝑡 = 0.7051 ∙ 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 − 0. 28836 𝑅2 = 0.712 𝑀2−𝑃𝑎𝑟𝑎𝑚 = 0.7266 ∙ 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 + 0. 258 𝑀𝐴𝑀 𝑎 = 0.0360 ∙ 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 + 0.956 𝑅2 = 0.001 𝑀2−𝑃𝑎𝑟𝑎𝑚 = 0.561 ∙ 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 + 0.424 𝑅2 = 0.356 2-Var has same R2 as Pwat 2-Var improves R2 compared to AMa correlation 𝑅2 = 0.706𝑀𝐴𝐸 = 0.00827; 𝑀𝐴𝐸 = 0.0150; 𝑀𝐴𝐸 = 0.00955; 𝑀𝐴𝐸 = 0.01256;
- 14. 16 ©Copyright2013,FirstSolar,Inc. Eugene, Oregon CdTe Previous Correlation New Correlation Multi-Si 𝑀 𝑝 𝑤𝑎𝑡 = 0.536 ∙ 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 + 0.476 𝑅2 = 0. 445 𝑀2−𝑃𝑎𝑟𝑎𝑚 = 0.638 ∙ 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 + 0.373 𝑅2 = 0.598 𝑀𝐴𝑀 𝑎 = 1.00292 ∙ 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 − 0.0038 𝑅2 = 0.696 𝑀2−𝑃𝑎𝑟𝑎𝑚 = 0.767 ∙ 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 + 0.2303 𝑅2 = 0.817 2-Var improves R2 over Pwat 2-Var improves R2 over AMa 𝑀𝐴𝐸 = 0.0188; 𝑀𝐴𝐸 = 0.00406; 𝑀𝐴𝐸 = 0.00306; 𝑀𝐴𝐸 = 0.0162;
- 16. 18 ©Copyright2013,FirstSolar,Inc. Cocoa, Florida CdTe Previous Correlation New Correlation Multi-Si 𝑀 𝑃 𝑤𝑎𝑡 = 0.5420 ∙ 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 + 0.476 𝑅2 = 0. 494 𝑀2−𝑃𝑎𝑟𝑎𝑚 = 0.5805 ∙ 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 + 0.436 𝑅2 = 0.705 𝑀𝐴𝑀 𝑎 = 0.9435 ∙ 𝑀 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 + 0.0439 𝑅2 = 0.428 𝑀2−𝑃𝑎𝑟𝑎𝑚 = 0.9326 ∙ 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 + 0.0603 𝑅2 = 0. 724 2-Var improves R2 compared to Pwat correlation 2-Var improves R2 compared to AMa correlation 𝑀𝐴𝐸 = 0.0169; 𝑀𝐴𝐸 = 0.0130; 𝑀𝐴𝐸 = 0.00749; 𝑀𝐴𝐸 = 0.0157;
- 18. © Copyright 2013, First Solar, Inc.
- 19. 22 ©Copyright2013,FirstSolar,Inc. Precipitable Water Data United States Always available • TMY3 • MERRA • Empirical derivation • Meteonorm Sometimes Available • Aeronet • Suominet World Always Available • MERRA • Empirical derivation • Meteonorm Sometimes Available • Aeronet
- 20. 23 ©Copyright2013,FirstSolar,Inc. Measured vs Empirical Pwat Suominet vs Empirical Formula1-2 1. C. Gueymard, “Analysis of Monthly Average Atmospheric Precipitable Water and Turbidity in Canada and Northern United States,” Solar Energy, vol. 53, No.1, pp. 57- 71, 1994. 2. C. Gueymard, “Assessment of the Accuracy and Computing speed of Simplified Saturation Vapor Equations Using a New Reference Dataset,” Journal of Applied Meteorology, vol. 32, pp 1294-1300, 1993. 𝑃 𝑤𝑎𝑡 = 𝑓(𝑇amb, RH) = 0.1 0.4976 + 1.5265 𝑇 𝑎𝑚𝑏,𝐾 273.15 + 𝑒𝑥𝑝 13.6897 𝑇𝑎𝑚𝑏,𝐾 273.15 − 14.9188 𝑇𝑎𝑚𝑏,𝐾 273.15 3 × 216.7𝑅𝐻 100𝑇𝑎𝑚𝑏,𝐾 𝑒𝑥𝑝 22.33 − 4,914 𝑇𝑎𝑚𝑏,𝐾 −10.922 100 𝑇𝑎𝑚𝑏,𝐾 2 − 0.39015 𝑇𝑎𝑚𝑏,𝐾 100 MAE = 0.245
- 21. 24 ©Copyright2013,FirstSolar,Inc. Measured vs Empirical Pwat Suominet vs Empirical Formula1-2 1. C. Gueymard, “Analysis of Monthly Average Atmospheric Precipitable Water and Turbidity in Canada and Northern United States,” Solar Energy, vol. 53, No.1, pp. 57- 71, 1994. 2. C. Gueymard, “Assessment of the Accuracy and Computing speed of Simplified Saturation Vapor Equations Using a New Reference Dataset,” Journal of Applied Meteorology, vol. 32, pp 1294-1300, 1993. 𝑃 𝑤𝑎𝑡 = 𝑓(𝑇amb, RH) = 0.1 0.4976 + 1.5265 𝑇 𝑎𝑚𝑏,𝐾 273.15 + 𝑒𝑥𝑝 13.6897 𝑇𝑎𝑚𝑏,𝐾 273.15 − 14.9188 𝑇𝑎𝑚𝑏,𝐾 273.15 3 × 216.7𝑅𝐻 100𝑇𝑎𝑚𝑏,𝐾 𝑒𝑥𝑝 22.33 − 4,914 𝑇𝑎𝑚𝑏,𝐾 −10.922 100 𝑇𝑎𝑚𝑏,𝐾 2 − 0.39015 𝑇𝑎𝑚𝑏,𝐾 100 MAE = 0.005
- 22. 25 ©Copyright2013,FirstSolar,Inc. Measured vs Empirical Pwat Suominet vs Empirical Formula1-2 1. C. Gueymard, “Analysis of Monthly Average Atmospheric Precipitable Water and Turbidity in Canada and Northern United States,” Solar Energy, vol. 53, No.1, pp. 57- 71, 1994. 2. C. Gueymard, “Assessment of the Accuracy and Computing speed of Simplified Saturation Vapor Equations Using a New Reference Dataset,” Journal of Applied Meteorology, vol. 32, pp 1294-1300, 1993. 𝑃 𝑤𝑎𝑡 = 𝑓(𝑇amb, RH) = 0.1 0.4976 + 1.5265 𝑇 𝑎𝑚𝑏,𝐾 273.15 + 𝑒𝑥𝑝 13.6897 𝑇𝑎𝑚𝑏,𝐾 273.15 − 14.9188 𝑇𝑎𝑚𝑏,𝐾 273.15 3 × 216.7𝑅𝐻 100𝑇𝑎𝑚𝑏,𝐾 𝑒𝑥𝑝 22.33 − 4,914 𝑇𝑎𝑚𝑏,𝐾 −10.922 100 𝑇𝑎𝑚𝑏,𝐾 2 − 0.39015 𝑇𝑎𝑚𝑏,𝐾 100 MAE = 0.001
- 23. 26 ©Copyright2013,FirstSolar,Inc. Conclusion • The proposed two parameter spectral correction was as good, or better than, existing simple corrections in all cases. • It enables the use of a simple functional form which works for both c-Si and CdTe. • We recommend that all PV prediction software include this two variable correlation. A preliminary version of our spectral correction is in PVLib. • High Pwat climates, prediction software is under predicting energy • Empirically based Pwat is sufficient for spectral correction of PV models 𝑀 = 𝑏0 + 𝑏1 ∙ 𝐴𝑀 𝑎 + 𝑏2 ∙ 𝑝 𝑤𝑎𝑡 + 𝑏3 ∙ 𝐴𝑀 𝑎 + 𝑏4 ∙ 𝑝 𝑤𝑎𝑡 + 𝑏5 ∙ 𝐴𝑀 𝑎 𝑝 𝑤𝑎𝑡 2-Parameter Correlation
- 24. 27 ©Copyright2013,FirstSolar,Inc. Acknowledgements • Sandia — Cliff Hansen for provide insight into how to improve our spectral model • NREL — Bill Marion and others who made field data set possible
- 26. 29 ©Copyright2013,FirstSolar,Inc. Regression Fit to SMARTS Output R2 SSE Model Equation S4-2 Mono-Si S4-2 Mono-Si Linear 1 𝑀 = 𝑏0 + 𝑏1 ∙ 𝐴𝑀 𝑎 + 𝑏2 ∙ 𝑝 𝑤𝑎𝑡 + 𝑏3 ∙ 𝐴𝑀 𝑎 + 𝑏4 ∙ 𝑝 𝑤𝑎𝑡 + 𝑏5 ∙ 𝐴𝑀 𝑎 𝑝 𝑤𝑎𝑡 0.9965 0.9988 0.0112 0.0011 Linear 2 𝑀 = 𝑏0 + 𝑏1 ∙ 𝐴𝑀 𝑎 + 𝑏2 ∙ 𝑝 𝑤𝑎𝑡 + 𝑏3 ∙ 𝐴𝑀 𝑎 + 𝑏4 ∙ 𝑝 𝑤𝑎𝑡 + 𝑏5 ∙ 𝐴𝑀 𝑎 𝑝 𝑤𝑎𝑡 0.9988 0.9990 0.0038 0.000879 Non-Linear 1 𝑀 = 𝑏0 + 𝑏1 ∙ 𝐴𝑀 𝑎 + 𝑏2 ∙ 𝑝 𝑤𝑎𝑡 + 𝑏3 ∙ 𝐴𝑀 𝑎 𝑏6 + 𝑏4 ∙ 𝑝 𝑤𝑎𝑡 𝑏7 + 𝑏5 ∙ 𝐴𝑀 𝑎 𝑝 𝑤𝑎𝑡 0.9970 0.9989 0.0060 0.0009626 Non-Linear 2 𝑀 = 𝑏0 + 𝑏1 ∙ 𝐴𝑀 𝑎 + 𝑏2 ∙ 𝑝 𝑤𝑎𝑡 + 𝑏3 ∙ 𝐴𝑀 𝑎 𝑏6 + 𝑏4 ∙ 𝑝 𝑤𝑎𝑡 𝑏7 + 𝑏5 ∙ 𝐴𝑀 𝑎 𝑝 𝑤𝑎𝑡 𝑏8 0.9981 0.9995 0.0060 0.000413 Non-Linear 3 𝑀 = 𝑏0 + 𝑏1 ∙ 𝐴𝑀 𝑎 + 𝑏2 ∙ 𝑝 𝑤𝑎𝑡 + 𝑏3 ∙ 𝐴𝑀 𝑎 𝑏7 + 𝑏4 ∙ 𝑝 𝑤𝑎𝑡 𝑏8 + 𝑏5 ∙ 𝐴𝑀 𝑎 𝑏9 ∙ 𝑝 𝑤𝑎𝑡 𝑏10 0.9992 0.9996 0.0026 0.00036 Non-Linear 4 𝑀 = 𝑏0 + 𝑏1 ∙ 𝐴𝑀 𝑎 𝑏4 + 𝑏2 ∙ 𝑝 𝑤𝑎𝑡 𝑏5 + 𝑏3 ∙ 𝐴𝑀 𝑎 𝑏6 ∙ 𝑝 𝑤𝑎𝑡 𝑏7 0.9981 0.9976 0.0046 0.0021