© Copyright 2015, First Solar, Inc.

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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

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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

Spe

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l Sh

ift

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.

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𝑀 = 𝑏0 + 𝑏1∙ 𝐴𝑀

𝑎+ 𝑏2 ∙ 𝑝𝑤𝑎𝑡 + 𝑏3 ∙ 𝐴𝑀𝑎 + 𝑏4 ∙ 𝑝𝑤𝑎𝑡 + 𝑏5 ∙

𝐴𝑀𝑎

𝑝𝑤𝑎𝑡

Proposed Two Variable Spectral Correction

2-Variable Correlation

AMa Correlation

Pwat Correlation

(Series 4-2): 𝑀 ≈ 1.266 − 0.091exp(1.199 𝑃𝑤𝑎𝑡 + 0.5 −0.210

(Series 4-1 and earlier): 𝑀 ≈ 0.632 + 0.134exp(0.976 𝑃𝑤𝑎𝑡 + 0.05 0.079)

𝑓1 𝐴𝑀𝑎 = 𝑎0 + 𝑎1 ∙ 𝐴𝑀𝑎 + 𝑎2 ∙ 𝐴𝑀𝑎2 + 𝑎3 ∙ 𝐴𝑀𝑎

3 + 𝑎4 ∙ 𝐴𝑀𝑎4

Where: 𝐴𝑀𝑎 =𝑃

𝑃0∙ 𝐴𝑀

© Copyright 2015, First Solar, Inc.

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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)

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SMARTS Output

CdTe Multi-Si

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CdTe: 2-D Cross Section

AMa Fixed at G173 CdTe

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CdTe: 2-D Cross Section

Pwat Fixed at G173CdTe

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Multi-Si: 2-D Cross Section

Pwat Fixed at G173Multi-Si

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Multi-Si: 2-D Cross Section

AMa Fixed at G173Multi-Si

© Copyright 2015, First Solar, Inc.

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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

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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

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Golden, Colorado

CdTe

Previous Correlation New Correlation

Multi-Si

𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 1.010 ∙ 𝑀𝑃𝑤𝑎𝑡 − 0.00492

𝑅2 = 0.712𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.901 ∙ 𝑀2−𝑃𝑎𝑟𝑎𝑚 + 0.108

𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.0396 ∙ 𝑀𝑃𝑤𝑎𝑡 + 0.954

𝑅2 = 0.001

𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 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;

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Golden, Colorado

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Eugene, Oregon

CdTe

Previous Correlation New Correlation

Multi-Si

𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.832 ∙ 𝑀𝑃𝑤𝑎𝑡 + 0.150

𝑅2 = 0. 445

𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.775 ∙ 𝑀2−𝑃𝑎𝑟𝑎𝑚 + 0.207

𝑅2 = 0.540

𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.694 ∙ 𝑀𝑃𝑤𝑎𝑡 + 0.305𝑅2 = 0.696

𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 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;

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Eugene, Oregon

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Cocoa, Florida

CdTe

Previous Correlation New Correlation

Multi-Si

𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.911 ∙ 𝑀𝑃𝑤𝑎𝑡 + 0.074𝑅2 = 0. 494

𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 1.191 ∙ 𝑀2−𝑃𝑎𝑟𝑎𝑚 − 0.211

𝑅2 = 0.636

𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 0.454 ∙ 𝑀𝑃𝑤𝑎𝑡 + 0.556

𝑅2 = 0.428

𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 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;

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Cocoa, Florida: Spectral Timeseries

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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 ∙ 𝑝𝑤𝑎𝑡 + 𝑏3 ∙ 𝐴𝑀𝑎 + 𝑏4 ∙ 𝑝𝑤𝑎𝑡 + 𝑏5 ∙

𝐴𝑀𝑎

𝑝𝑤𝑎𝑡

2-Parameter Correlation

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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.

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Questions?