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22 mitchell lee_am_and_pwat_spectral_correction
1.
© Copyright 2015,
First Solar, Inc.
2.
2 ©Copyright2015,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 ©Copyright2015,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 2015,
First Solar, Inc.
5.
6 ©Copyright2015,FirstSolar,Inc. SMARTS Overview • Simulated
Spectrum with all combinations of AMa and Pwat where: — 0.5 cm ≤ Pwat ≤ 5 cm — 0.8 ≤ AMa ≤ 4.75 (Pressure of 800 mbar and 1.01 ≤ AM ≤ 6) • Limit spectral range of simulation to that of CMP11 (280 nm to 2800 nm) • Kept all other parameters fixed at G173 standard • Computed spectral shift factor using module specific QE curves (provided by NREL)
6.
7 ©Copyright2015,FirstSolar,Inc. SMARTS Output CdTe Multi-Si
7.
9 ©Copyright2015,FirstSolar,Inc. CdTe: 2-D Cross
Section AMa Fixed at G173CdTe
8.
10 ©Copyright2015,FirstSolar,Inc. CdTe: 2-D Cross
Section Pwat Fixed at G173CdTe
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12 ©Copyright2015,FirstSolar,Inc. Multi-Si: 2-D Cross
Section Pwat Fixed at G173Multi-Si
10.
13 ©Copyright2015,FirstSolar,Inc. Multi-Si: 2-D Cross
Section AMa Fixed at G173Multi-Si
11.
© Copyright 2015,
First Solar, Inc.
12.
15 ©Copyright2015,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
13.
16 ©Copyright2015,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
14.
18 ©Copyright2015,FirstSolar,Inc. Golden, Colorado CdTe Previous Correlation
New Correlation Multi-Si 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 1.010 ∙ 𝑀 𝑃𝑤𝑎𝑡 − 0.00492 𝑅2 = 0.712 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.901 ∙ 𝑀2−𝑃𝑎𝑟𝑎𝑚 + 0.108 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.0396 ∙ 𝑀 𝑃𝑤𝑎𝑡 + 0.954 𝑅2 = 0.001 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.570 ∙ 𝑀2−𝑃𝑎𝑟𝑎𝑚 + 0.431 𝑅2 = 0.316 2-Var has same R2 as Pwat 2-Var improves R2 compared to AMa correlation 𝑅2 = 0.722𝑀𝐴𝐸 = 0.00827; 𝑀𝐴𝐸 = 0.01253; 𝑀𝐴𝐸 = 0.00955; 𝑀𝐴𝐸 = 0.00903;
15.
19 ©Copyright2015,FirstSolar,Inc. Golden, Colorado
16.
20 ©Copyright2015,FirstSolar,Inc. Eugene, Oregon CdTe Previous Correlation
New Correlation Multi-Si 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.832 ∙ 𝑀 𝑃𝑤𝑎𝑡 + 0.150 𝑅2 = 0. 445 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.775 ∙ 𝑀2−𝑃𝑎𝑟𝑎𝑚 + 0.207 𝑅2 = 0.540 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.694 ∙ 𝑀 𝑃𝑤𝑎𝑡 + 0.305 𝑅2 = 0.696 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 1.033 ∙ 𝑀2−𝑃𝑎𝑟𝑎𝑚 − 0.0360 𝑅2 = 0.832 2-Var improves R2 over Pwat 2-Var improves R2 over AMa 𝑀𝐴𝐸 = 0.01881; 𝑀𝐴𝐸 = 0.00406; 𝑀𝐴𝐸 = 0.00401; 𝑀𝐴𝐸 = 0.01781;
17.
21 ©Copyright2015,FirstSolar,Inc. Eugene, Oregon
18.
22 ©Copyright2015,FirstSolar,Inc. Cocoa, Florida CdTe Previous Correlation
New Correlation Multi-Si 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.911 ∙ 𝑀 𝑃𝑤𝑎𝑡 + 0.074 𝑅2 = 0. 494 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 1.191 ∙ 𝑀2−𝑃𝑎𝑟𝑎𝑚 − 0.211 𝑅2 = 0.636 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.454 ∙ 𝑀 𝑃𝑤𝑎𝑡 + 0.556 𝑅2 = 0.428 𝑀 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.726 ∙ 𝑀2−𝑃𝑎𝑟𝑎𝑚 + 0.277 𝑅2 = 0. 720 2-Var improves R2 compared to Pwat correlation 2-Var improves R2 compared to AMa correlation 𝑀𝐴𝐸 = 0.01686; 𝑀𝐴𝐸 = 0.01305; 𝑀𝐴𝐸 = 0.00302; 𝑀𝐴𝐸 = 0.01690;
19.
23 ©Copyright2015,FirstSolar,Inc. Cocoa, Florida: Spectral
Timeseries
20.
24 ©Copyright2015,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. Our spectral correction has been submitted to PVLib. 𝑀 = 𝑏0 + 𝑏1 ∙ 𝐴𝑀 𝑎 + 𝑏2 ∙ 𝑝 𝑤𝑎𝑡 + 𝑏3 ∙ 𝐴𝑀 𝑎 + 𝑏4 ∙ 𝑝 𝑤𝑎𝑡 + 𝑏5 ∙ 𝐴𝑀 𝑎 𝑝 𝑤𝑎𝑡 2-Parameter Correlation
21.
25 ©Copyright2015,FirstSolar,Inc. Acknowledgements Special Thanks To: •
Bill Marion and NREL for making such a great data set of PV module field performance, and providing us with anonymized QE curves. • Lauren Ngan for all of the work she did to understand spectral effects on CdTe Modules, and for helping me to understand her work. • Chris Gueymard; without SMARTS, this work would have been impossible.
22.
26 ©Copyright2015,FirstSolar,Inc. Questions?
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