2 2 mitchell lee_am and pwat spectral correction_pvpmc5

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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 ∙ 𝐴𝑀𝑎+ 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 + 0.050.079)

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

3 + 𝑎4 ∙ 𝐴𝑀𝑎4

Where: 𝐴𝑀𝑎 =𝑃

𝑃0∙ 𝐴𝑀

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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)

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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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Multi-Si: 2-D Cross Section

Pwat Fixed at G173Multi-Si

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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∙1000W/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

𝑀𝑃𝑤𝑎𝑡 = 0.7051 ∙ 𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 − 0. 28836

𝑅2 = 0.712

𝑀2−𝑃𝑎𝑟𝑎𝑚 = 0.7266 ∙ 𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 + 0. 258

𝑀𝐴𝑀𝑎 = 0.0360 ∙ 𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 + 0.956

𝑅2 = 0.001

𝑀2−𝑃𝑎𝑟𝑎𝑚 = 0.561 ∙ 𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 + 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;

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Golden, Colorado

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Eugene, Oregon

CdTe


Multi-Si

𝑀𝑝𝑤𝑎𝑡 = 0.536 ∙ 𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 + 0.476

𝑅2 = 0. 445


𝑅2 = 0.598

𝑀𝐴𝑀𝑎 = 1.00292 ∙ 𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 − 0.0038

𝑅2 = 0.696


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;

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Eugene, Oregon

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Cocoa, Florida

CdTe


Multi-Si

𝑀𝑃𝑤𝑎𝑡 = 0.5420 ∙ 𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 + 0.476

𝑅2 = 0. 494


𝑅2 = 0.705

𝑀𝐴𝑀𝑎 = 0.9435 ∙ 𝑀𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 + 0.0439

𝑅2 = 0.428

𝑀2−𝑃𝑎𝑟𝑎𝑚 = 0.9326 ∙ 𝑀𝑚𝑒𝑎𝑠𝑢𝑟𝑒 + 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;

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Cocoa, Florida

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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

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Measured vs Empirical Pwat

Suominet vs Empirical Formula1-2

1. C. Gueymard, “Analysis of Monthly Average Atmospheric Precipitable Water andTurbidity 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 SimplifiedSaturation Vapor Equations Using a New Reference Dataset,” Journal of AppliedMeteorology, vol. 32, pp 1294-1300, 1993.

𝑃𝑤𝑎𝑡 = 𝑓(𝑇amb, RH) = 0.1 0.4976 + 1.5265𝑇𝑎𝑚𝑏,𝐾

273.15

+ 𝑒𝑥𝑝 13.6897𝑇𝑎𝑚𝑏,𝐾273.15

− 14.9188𝑇𝑎𝑚𝑏,𝐾273.15

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× 216.7𝑅𝐻

100𝑇𝑎𝑚𝑏,𝐾𝑒𝑥𝑝 22.33 −

4,914

𝑇𝑎𝑚𝑏,𝐾

−10.922100


2

−0.39015 𝑇𝑎𝑚𝑏,𝐾

100

MAE = 0.245

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273.15

+ 𝑒𝑥𝑝 13.6897𝑇𝑎𝑚𝑏,𝐾273.15

− 14.9188𝑇𝑎𝑚𝑏,𝐾273.15

3

× 216.7𝑅𝐻


4,914


−10.922100


2

−0.39015 𝑇𝑎𝑚𝑏,𝐾

100

MAE = 0.005

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273.15

+ 𝑒𝑥𝑝 13.6897𝑇𝑎𝑚𝑏,𝐾273.15

− 14.9188𝑇𝑎𝑚𝑏,𝐾273.15

3

× 216.7𝑅𝐻


4,914


−10.922100


2

−0.39015 𝑇𝑎𝑚𝑏,𝐾

100

MAE = 0.001

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

𝐴𝑀𝑎

𝑝𝑤𝑎𝑡

2-Parameter Correlation

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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

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Regression Fit to SMARTS Output

R2 SSE

Model Equation S4-2 Mono-Si S4-2 Mono-Si

Linear 1𝑀 = 𝑏0 + 𝑏1 ∙ 𝐴𝑀𝑎

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

0.9965 0.9988 0.0112 0.0011

Linear 2𝑀 = 𝑏0 + 𝑏1 ∙ 𝐴𝑀𝑎

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

0.9988 0.9990 0.0038 0.000879

Non-Linear 1𝑀 = 𝑏0 + 𝑏1 ∙ 𝐴𝑀𝑎

+ 𝑏2 ∙ 𝑝𝑤𝑎𝑡 + 𝑏3 ∙ 𝐴𝑀𝑎

𝑏6+ 𝑏4 ∙ 𝑝𝑤𝑎𝑡

𝑏7 + 𝑏5 ∙𝐴𝑀𝑎𝑝𝑤𝑎𝑡

0.9970 0.9989 0.0060 0.0009626

Non-Linear 2𝑀 = 𝑏0 + 𝑏1 ∙ 𝐴𝑀𝑎

+ 𝑏2 ∙ 𝑝𝑤𝑎𝑡 + 𝑏3 ∙ 𝐴𝑀𝑎


𝑏7 + 𝑏5 ∙𝐴𝑀𝑎𝑝𝑤𝑎𝑡

𝑏8 0.9981 0.9995 0.0060 0.000413

Non-Linear 3 𝑀 = 𝑏0 + 𝑏1 ∙ 𝐴𝑀𝑎+ 𝑏2 ∙ 𝑝𝑤𝑎𝑡 + 𝑏3 ∙ 𝐴𝑀𝑎


𝑏8 + 𝑏5 ∙ 𝐴𝑀𝑎

𝑏9∙ 𝑝𝑤𝑎𝑡

𝑏10 0.9992 0.9996 0.0026 0.00036

Non-Linear 4 𝑀 = 𝑏0 + 𝑏1 ∙ 𝐴𝑀𝑎


𝑏5 + 𝑏3 ∙ 𝐴𝑀𝑎

𝑏6∙ 𝑝𝑤𝑎𝑡

𝑏7 0.9981 0.9976 0.0046 0.0021

2 2 mitchell lee_am and pwat spectral correction_pvpmc5

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Transcript of 2 2 mitchell lee_am and pwat spectral correction_pvpmc5