NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Overview of the PV Module Model in 

PVWatts

Bill Marion

PV Performance Modeling 

Workshop

Albuquerque, New Mexico

September 22, 2010

NREL/PR-520-49607
NATIONAL RENEWABLE ENERGY LABORATORY

Model Used in PVWatts

Model based on PVFORM Version 3.3 (1988)

– Provides estimate of maximum power, Pm

– For irradiance > 125 W/m2

where,

E = POA irradiance, W/m2

T = PV cell temperature, 0C

γ = Pm correction factor for temperature, 0C-1

Zero subscripts denote performance at SRC, the e subscript 

denotes an “effective” irradiance, which in the case of PVWatts

means corrected for AOI but not spectrum.

2

[ ( )] 0

0

1 0 P TT

E

E P m

e

m −⋅γ+⋅⋅=
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Model Used in PVWatts (cont.)

A different formula is used at low irradiances to account for 

reductions in output observed by Sandia for crystalline 

silicon PV modules. 

– For irradiance <= 125 W/m2

– PVWatts also applies an AOI correction. 

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[ ( )] 0

0

2

1 0080

0 P TT

E

E. P m

e

m −⋅γ+⋅⋅ ⋅ =
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AOI Correction

The King-Sandia 

AOI function is 

used to correct 

direct beam 

radiation for 

incident angles 

greater than 50 

degrees.

Other equivalent 

methods are shown 

in the figure.

4

0 20 40 60 80 100

Angle-of-Incidence (deg)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Angle-of-Incidence Correction Factor

Model

King et al.

Air-Glass (Sjerps-Koomen et al.), n2=1.526

Reflection and Absorption (De Soto et al.)

Martin and Ruiz, ar=0.17
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AOI Correction for Soiled PV Modules

Not used in 

PVWatts, but the 

method of Martin 

and Ruiz may allow 

for better 

predictions if the 

soiling amount is 

known. (Progress in 

PV, 2005; 13:75-84)

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0 20 40 60 80 100

Angle-of-Incidence (deg)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Angle-of-Incidence Correction Factor

Martin and Ruiz Model

ar = 0.17 (clean)

ar = 0.20 (2% soiling loss at AOI = 0)

ar = 0.27 (8% soiling loss at AOI = 0)
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No Correction for Variations in Spectrum

Analysis of data collected at NREL and FSEC indicates no 

benefit for applying spectral corrections in PVWatts for x-Si 

and m-Si PV modules.

– For a group of 5 x-Si and m-Si PV modules at NREL, use of a 

spectral model and spectral response data reduced the RMSE in 

Isc by only 0.1%, use of the Sandia AMa function increased the 

RMSE by 0.3%.

– For amorphous silicon PV modules, both methods reduced 

errors in estimating Isc, and the most favorable results were for 

the CREST air-mass function.

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AOI and Spectral Correction Results

0 400 800 1200 1600

POA Irradiance (W/m2)

0.0

1.0

2.0

3.0

4.0

5.0

Isc25 (A)

Fit Through Origin: Y = 0.0002862 * X

Number of data points used = 11562

Average X = 527.6 W/m2

Average Y = 1.503 A

RMSE = 0.048 A or 3.2% of average

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0 400 800 1200 1600

POA Irradiance, AOI Correction (W/m2)

0.0

1.0

2.0

3.0

4.0

5.0

Isc25 (A)

Fit Through Origin: Y = 0.0002883 * X

Number of data points used = 11562

Average X = 519.9 W/m2

Average Y = 1.503 A

RMSE = 0.028 A or 1.9% of average

0 400 800 1200 1600

POA Irradiance, Sandia AOI and f(AMa) Correction (W/m2)

0.0

1.0

2.0

3.0

4.0

5.0

Isc25 (A)

Fit Through Origin: Y = 0.0002888 * X

Number of data points used = 11562

Average X = 520.7 W/m2

Average Y = 1.503 A

RMSE = 0.033 A or 2.2% of average

0 400 800 1200 1600

POA Irradiance, AOI and SMARTS Correction (W/m2)

0.0

1.0

2.0

3.0

4.0

5.0

Isc25 (A)

Fit Through Origin: Y = 0.0002925 * X

Number of data points used = 11562

Average X = 513.6 W/m2

Average Y = 1.503 A

RMSE = 0.023 A or 1.6% of average
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Historical Perspective

The traditional linear expression for PV power using 

irradiance, temperature, and a power correction factor for 

temperature was published by Evans and Florschuetz in 

1977 (Solar Energy 19, 255-262).

– Is it appropriate for today’s PV modules?

– How do it’s predictions compare with later models when using 

the same inputs of irradiance and temperature?

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Comparison with Sandia Model

For the three modules and data sets for this workshop 

study, PVWatts module power estimates were compared 

with those using the Sandia model. 

For PVWatts:

– Pm0 determined using the Sandia model for SRC.

– Pm correction factor for temperature determined using the Sandia 

model for SRC and for 1000 W/m2 and 55 C

– This ensured agreement at 1000 W/m2 and allowed differences 

at other irradiances to be more readily observed.

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PVWatts versus Sandia for the Mobil Module

Differences at low irradiances from PVWatts using a 

different algorithm below 125 W/m2.

10

0 100 200 300 400

Sandia Model (W)

0

100

200

300

400

PVWatts Model (W)

1:1 slope

PVWatts Average = 99.7% of Sandia Average
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PVWatts versus Sandia for SunPower

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0 50 100 150 200 250

Sandia Model (W)

0

50

100

150

200

250

PVWatts Model (W)

1:1 slope

PVWatts Average = 99.9% of Sandia Average
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PVWatts versus Sandia for Shell

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0 20 40 60 80 100

Sandia Model (W)

0

20

40

60

80

100

PVWatts Model (W)

1:1 slope

PVWatts Average = 103.0% of Sandia Average
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Correction for Irradiance Nonlinearity

Previous work (Marion, 2008 PVSC) presented a method 

for correcting for irradiance nonlinearity.

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0 20 40 60

Measured Power (W)

0

20

40

60

Modeled Power (W)

Slope equals 1

Power Temperature Coefficient Model

0 200 400 600 800 1000 1200

Irradiance (W/m2)

-20

0

20

40

60

80

Modeled Power % Error

Power Temperature Coefficient Model

Scatter plot and percent error graph showing nonlinearity with respect to

Irradiance for a multi-crystalline PV module. 
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Correction for Irradiance Nonlinearity

Error function applies a nonlinear correction below 200 

W/m2 and a linear correction 

above 200 W/m2

– k is determined using a 

power measurement at 200 

W/m2 (now required by IEC 

61215 and 61646)

– Results in a model using 3 

parameters: Pm0, γ, and P200

– k=0.011 for Mobil, 0.009 for 

SunPower, 0.030 for Shell

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0 200 400 600 800 1000 1200

Irradiance (W/m2)

-0.10

-0.05

0.00

0.05

0.10

(Modeled P

m - Measured P

m) / P

m0

k

Error = k [(Eo-Ee)/(Ee-200)]

Error = k [1-(1-Ee/200)4]

Error in watts normalized by Pm0

0

0 200 2.0

m

m

P

PP

k −⋅ =
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3-Parameter versus Sandia for Mobil Module

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0 100 200 300 400

Sandia Model (W)

0

100

200

300

400

3-Parameter Model (W)

1:1 slope

3-Parameter Average = 100.0% of Sandia Average
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3-Parameter versus Sandia for SunPower

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0 50 100 150 200 250

Sandia Model (W)

0

50

100

150

200

250

3-Parameter Model (W)

1:1 slope

3-Parameter Average = 100.1% of Sandia Average
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3-Parameter versus Sandia for Shell

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0 20 40 60 80 100

Sandia Model (W)

0

20

40

60

80

100

3-Parameter Model (W)

1:1 slope

3-Parameter Average = 100.7% of Sandia Average
NATIONAL RENEWABLE ENERGY LABORATORY

Summary

The historical PV model in PVWatts is acceptable for 

estimating the energy production of PV systems.

– Even larger nonlinearities with respect to irradiance only impact 

estimates on the order of 3%, which may be inconsequential 

considering other sources of error: resource data, 

manufacturer’s ratings, long-term degradation, shading, 

availability, etc.

– The addition of a 3rd parameter to the model could reduce errors 

associated with nonlinearity if the additional data proved reliable.

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