Conference Paper

NREL/CP- 550-45376

Revised July 2009

Evaluation of the Performance of 

the PVUSA Rating Methodology 

Applied to DUAL Junction PV 

Technology

Preprint

Daryl Myers

To be presented at the American Solar Energy Society Annual 

Conference

Buffalo, New York

11-16 May 2009
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ERRATA SHEET

NREL REPORT/PROJECT NUMBER: NREL/CP-550-45376 

TITLE: Evaluation of the Performance of the PVUSA Rating Methodology Applied to 

DUAL Junction PV Technology 

AUTHOR(S): Daryl Myers

ORIGINAL PUBLICATION DATE: March 2009 

DATE OF CORRECTIONS: July 17, 2009 

The following corrections were made to this report/document:

A previous version of this paper, available until July 17, 2009, mistakenly referred to a 

triple junction roof mounted USSC system, which was incorrect. The Title, Abstract, 

Introduction paragraphs 1, 3, and 4, and Conclusion paragraph 1 were changed to reflect 

the correct setup, which was a rack-mounted dual-junction PV system. 
1 

EVALUATION OF THE PERFORMANCE OF THE PVUSA RATING METHODOLOGY 

APPLIED TO DUAL JUNCTION PV TECHNOLOGY 

Daryl Myers

National Renewable Energy Laboratory

1617 Cole Boulevard

Golden, CO 80402

daryl.myers@nrel.gov

NOTE: a previous version of this paper, available until July 

17, 2009, mistakenly referred to a triple junction roof 

mounted USSC system, which was incorrect. The author is 

solely responsible for, and regrets, that error. 

ABSTRACT

The PVUSA (Photovoltaics for Utility Scale Applications) 

project in the 1990’s developed a rating methodology for 

PV performance evaluation which has become popular, and 

even incorporated into concentrating PV rating standards. 

The method is based on collecting solar, meteorological, 

and system power output data for a period of time, and 

regressing the system output against a combination of 

irradiance, wind speed, and ambient temperature. The 

selected irradiance, wind speed, and temperature rating 

conditions are Is=1000 Wm-2, Ws=1 ms-1, and Ts=20 °C, 

respectively, for a flat plate collector. Here, we apply the 

method to a rack-mounted dual-junction PV system, and 

produce a system rating. We also describe in detail the 

uncertainties associated with the method, and mathematical 

issues associated with the technique. 

1. INTRODUCTION

The PVUSA (Photovoltaics for Utility Scale Applications) 

project in the 1990’s developed a rating methodology [1, 2] 

for PV performance evaluation which has become popular, 

and even incorporated into concentrating PV rating 

standards [3]. The method is based on collecting solar, 

meteorological, and system power output data for a period 

of time, and regressing the system output, P, against a 

combination of irradiance, I, wind speed, W, and ambient 

temperature, T, variables in the form of equation 1. 

P = I * ( a + b* I + c * W + d * T) (1) 

The selected irradiance, wind speed, and temperature rating 

conditions are Is=1000 Wm-2, Ws=1 ms-1, and Ts=20 °C, 

respectively, for a flat plate collector. For concentrating 

collectors (not addressed here, but our analysis is generally 

applicable) the only difference is that the rating condition 

(direct beam) irradiance is Is=850 Wm-2). 

In this paper, we apply the method to a rack-mounted dualjunction PV system, and produce a system rating. We also 

describe in detail the uncertainties associated with the 

method, and mathematical issues associated with the 

technique. In particular, the relative contribution of each 

combination of variables is quantified, and it is argued that 

simpler regressions of PV power with respect to irradiance 

perform as well if not better. 

This analysis is based upon one United Solar System Corp. 

(USSC) system of 96 dual-junction rack-mounted modules 

at a 40 degree (NREL latitude) tilt, facing due south. The

array has a system Standard Test Condition (STC) direct 

current (DC) rating of 1800 Watts peak (Wpac) and an 

alternating current (AC) rating of 1600 Wpac. Recall that 

STC are 1000 Watt per square meter, Wm-2, irradiance, 25° 

cell temperature, and under the American Society for 

Testing and Materials (ASTM) Air Mass 1.5 hemispherical 

tilt spectrum [4]. 

2. PV SYSTEM DATA COLLECTION

The PV system parameters listed in table 1 were measured 

with a Campbell Scientific CR 21X Data logger, with signal 

conditioning of the array electrical parameters including 

monitors for voltage, current, and module temperature. The 

data were sampled every 3 seconds and integrated over 1 

minute. Fifteen minute averages of the data were reported. 

In this subsection, we address the uncertainty associated 

with the measurement of performance parameters and input 

variables for the model. The combined CR21X data logger 

and sensor uncertainties are summarized and applied to the 

range of parameters applicable to this system.
2 

Table 2 reports the measurement uncertainty in each 

parameter and combined overall measurement uncertainty 

for the NREL Photovoltaic Energy Rating Testbed (PERT) 

as reported in NREL technical report NREL/TP-520-26909 

“Validation of a Photovoltaic Module Energy Ratings 

Procedure at NREL” [5]. 

TABLE 1: USSC 1.6 kW SYSTEM MEASUREMENTS.

Field Parameter

SYS_ID System Identification

YEAR Year

DAY Day of the year (1 to 365)

TIME Mountain Standard Time HHMM

POA_IRR Plane of Array solar irradiance Wm-2

DC_POWER

Array Direct Current power output Watts 

(W)

AC_POWER

Array Alternating Current power output 

(W)

POS_VOLTS Array Positive leg voltage, Volts (V)

POS_AMPS Array Positive leg current, Amperes (I)

NEG_VOLTS Array negative leg voltage, (V)

NEG_AMPS Array negative leg current, (I)

AC_VOLTS Array Alternating current volts (V) 

AC_AMPS Array Alternating current (I)

T_AMB Ambient Temperature °C

T_MOD1 Module 1 Temperature °C

T_MOD2 Module 2 Temperature °C (not measured)

T_MOD3 Module 3 Temperature °C(not measured)

T_INV Inverter Temperature °C

T_DAS

Data Acquisition System (DAS) 

Temperature °C

DAS_BATV DAS battery Voltage (V)

2.1 System Monitoring Transducer Accuracy

The accuracy of the CR21X data logger with respect to the 

several electrical parameters measured (as derived from 

Campbell Scientific and Ohio Semitronics Incorporated 

(OSI) specifications) is summarized here.

CR21X current and voltage accuracy: 

DC & AC Voltage: (range: 0 to 233 V DC, 0 -126 AC V)

Ohio Semitronics Inc (OSI) VT8-005B RMS Voltage 

Transducer, 0-150 V ac and/or dc input, 0-1 mA output,

Temperature Coefficient. Tc = ± 1.0% of reading (-10oC to 

+60oC). 

Accuracy = ± 0.25% F.S. (Full Scale)

Note 0.25% of system voltage of 150 V = 0.38 V Ac

DC & AC Current: (0- 3.8 DC amp, 0-12 AC amp)

OSI CTA-214 RMS Current Sensor Signal Conditioner

0-1 mA output proportional to RMS value of ac and/or dc 

input, Linearity: ± 0.1% F.S. 

Tc = ± 0.005%/oC (0o to +70oC), 

with OSI CTL-50 Hall-Effect Current Sensor 

50 Ampere (A) rms input

30 mV output typical, 

Tc = -0.15%/oC (-40oC to +65oC). 

0.1% of 50 Arms = 0.05 Amp out of 12 A ac = 0.42%

AC Power: (0-1900 Watts)

OSI PC8-003-01B Variable-Frequency Watt Transducer

0-150 V and 0-100 A input; ±1 mA output

Tc = ±1.0% of reading, ±0.1% F.S. output (0oC to +40oC). 

Accuracy = ±1.0% F.S. (includes combined effects of 

voltage, current, load, & power factor), 

We compute the total uncertainty in the AC power by root 

sum square of 

 (12

+ 12 + 0.12)

1/2 = 1.45% of 1900 Wp = ±27.5 Watts AC

For power computed from AC Amps and AC Volts:

(0.422 + 0.252

)

 1/2 = 0.5% of 1900 Wp = ± 9.5 Watts. 

TABLE 2: PERT UNCERTAINTY SUMMARY 

PARAMETER %Uncertainty 

Voltage 0.1% 

Current 0.1% 

Irradiance 4.0% 

ModuleTemp 0.5% 

Module Power N/A 

RSS 4.0% 

Excluding the irradiance component in table 2 (discussed 

below), the root-sum-square of the current, voltage, and 

power uncertainty measurements from table 2 is 0.22%.

3. PVUSA TEST CONDITION MODEL

3.1 PVUSA Model Structure

The PVUSA TC method is based on the regression of AC 

power output (P) in W (or kW) against a function of three 

variables: Plane of Array Irradiance (I) in Wm-2 (or kW m-2), 

Wind speed (W) in meters per second (ms-1), and ambient 

temperature (T) in °C. Recall the form of the PVUSA TC 

model, as in equation 1, is: 
3 

P = I * ( a + b* I + c * W + d * T) 

Note the model includes four irradiance terms (one of which 

is squared) and only one each of temperature and wind 

speed related terms. This fact leads to some interesting 

conclusions regarding the accuracy of the model. Only 

conditions where the irradiance data is greater than 500 

Wm-2 (sometimes 700 Wm-2 is recommended) are used to 

determine the regression coefficients a, b, c, and d. We note 

the following:

- Uncertainty in the irradiance carries significantly 

more weight than uncertainty in the other variables.

- Ambient temperature is highly positively correlated 

with solar irradiance 

- Rating condition is established for a wind speed of 1 

ms-1; a relatively infrequent condition

The selected values for irradiance, wind speed, and 

temperature to produce a rating for a flat plate collector are 

Is=1000 Wm-2, Ws=1 ms-1, and Ts=20 °C, respectively. 

3.2 Meteorological Data

 

In addition to the irradiance independent variable in eq. 1, 

wind speed and temperature are also required. Ambient 

temperature is monitored at the system, but for the wind 

speed, we utilized wind speed data from the Reference 

Meteorological and Irradiance System (RMIS) deployed at 

the OTF along the north side of the OTF test field boundary. 

RMIS data is collected and archived at 1 minute intervals. 

We downloaded the archived 2006 1 minute RMIS data, and 

averaged the wind speed data over 15 minute intervals to 

provide average wind speed data for the regression analysis.

3.3 Model Sensitivity Coefficients

Considering eq. 1, the uncertainty in the ‘rating’ at test 

conditions, Ps, is dependent upon the uncertainty in each of 

the independent variables. The uncertainty in each variable 

is propagated through sensitivity coefficients, which are the 

partial derivatives of the right hand side of eq. 1 with 

respect to each ‘independent’ variable [6, 7]: 

∂P/∂I = a + 2* I *b + c*W + d*T (2)

∂P/∂W = c*I (3)

∂P/∂T = d*I (4)

Given measurement errors, or uncertainties, e, in each of the 

independent variables, eI, eT, and eW, the error in P, eP is 

computed from:

eP

2 = (∂P/∂I * eI)

2 + (∂P/∂W * eW ) 2 + (∂P/∂T * eT )2 (5) 

ep = [ (∂P/∂I * eI)

2 + (∂P/∂W * eW ) 2 + (∂P/∂T * eT )2 ] 1⁄2

 

Note that ep is dependent upon the absolute magnitude of 

the irradiance, wind speed, and ambient temperature, as well 

as the measurement errors or uncertainties or eI, eW, and eT, 

through equations 2, 3, and 4.

4. USSC PTSC REGRESSION FITS

AC power output for the USSC system was first filtered for: 

- Daylight only data

- Removal of any record with missing data for any 

parameter

- Removal of any record with Irradiance < 500 Wm-2

- Removal of any record where the AC power was less 

than 1.2 x Irradiance (indicating the array was 

shadowed, covered with snow, shut down for 

maintenance, or otherwise not in a standard 

operational mode).

The ‘floor’ value of P > 1.2 * Irradiance was chosen based 

on the nominal 1.6 kW rating of the system at 1.0 kWm-2 

Standard Reporting Condition irradiance. 

Figure 1 shows the data set as received, and figure 2 shows 

the filtered data set, from which the regression coefficients 

for the model were derived. 

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400

POA Irradiance Wm2

System Power Watts

Fig 1. All raw USSC Array data versus plane of array 

irradiance for 2006

y = 1.5284x - 46.48

R2

 = 0.9749

y = -3.344E-04x2 + 2.081E+00x - 2.637E+02

R2

 = 9.762E-01

0

500

1000

1500

2000

400 600 800 1000 1200 1400

POA Irradiance Wm-2

System Power Watts

Fig 2. USSC Array data after filtering for non-standard 

operating conditions and for POA> 500 Wm-2 

The derived regression coefficients for this filtered data set 

were:
4 

a= 1.4187, b= 5.0583 •10-5, c= 2.2908•10-3, 

d = 3.61332 •10-4 

It is instructive to examine the relative magnitude of the 

coefficients, since all are coefficients of I three times over , 

as well as the b coefficient of I2

. Using Watts as the units of 

power, at a rating condition of I = 1000 Wm-2, the relative 

contribution of each term in the PVUSA model to the rating 

value is approximately (in the absence of any measurement 

error at all):

a: 96.4%, b: 2.9%, c: 0.4%, and d: 0.4%. (sums to 100.1% 

due to rounding). 

Note that a and b (irradiance and irradiance square terms

only) contribute 99.3% of the eventual rating value. This 

will be discussed further below. A linear fit (1.5284*I – 

46.48, r2 = 0.975, standard deviation of regression = 45.2 

Wm-2) of the array power to the irradiance (only) is shown 

by the line in fig 2. The quadratic fit is also shown.

5. PVUSA TC (PTC) RATING

Using the regression coefficients, a, b, c, and d, and the 

rating standard condition of Is=1000 Wm-2, Ws=1 ms-1, and 

Ts=20 °C, in equation (1) we compute:

Ps = Is * ( a + b* Is + c * Ws + d * Ts)= 1480.6 W.

Table 3 shows the measured and modeled power data for the 

POA irradiance within ±0.5 Wm-2 of the 1000 Wm-2

PVUSA TC point. 

TABLE 3: MEASURED AND MODELED P 

(I=1 kW ± 0.5 W)

AC Power

W 

POA 

Irradiance

Wm-2

Wind 

Speed

m/s

Temp °C PTC 

Model 

AC W

1506.4 999.9 7.4 9.0 1489.28

1467.4 999.8 2.8 19.5 1482.39

1506.8 1000.0 2.3 16.6 1480.50

1504.0 999.6 2.3 16.2 1479.74

1454.4 1000.1 2.0 26.6 1483.58

1468.4 999.7 2.2 25.1 1482.08

1481.9 999.9 2.8 26.6 1485.11

1528.8 999.9 2.0 16.4 1479.49

1558.7 999.9 2.2 17.9 1480.59

1545.3 1000.4 1.7 1.1 1474.13

1565.1 1000.2 3.8 16.9 1484.35

1513.3 1000.0 0.5 11.4 1474.50

1493.0 1000.4 1.4 4.0 1474.50

1516.7 1000.1 1.3 0.4 1472.51

PTCRATE 1000.0 1.0 25.0 1480.56

Note this one watt per meter square window is somewhat 

unrealistic, since typical pyranometer calibration error for a 

well characterized pyranometer is ±0.5% at 1000 Wm-2, or

± 5 Wm-2, ten times our specified window here.

There is measurement uncertainty associated with the array 

power, as well. An estimate of this measurement uncertainty 

is ±1%, or 15 Watts. Note the standard deviation, sigma, of 

the measured AC power in table 3 is ±36 Watts, (2.4% of 

the 1480 W rating) and 2-sigma would be ±72 Watts. 

The mean measured AC power for the table 3 data points is 

1507.8 ± 36.6 Wm-2; the mean PTC modeled AC power is 

1480.3 ± 4.8 Wm-2 (a 1.8% difference). Mean Wind speed 

and temperatures are 2.4 ± 1.6 ms-1 and 14.5 ± 8.7 °C, 

respectively. This difference is about the measurement 

uncertainty in the power from V and A transducer 

measurement (1.2%, 2 sigma) derived in section 2.1. 

Figure 3 shows the residuals (measured – modeled) between 

measured and modeled array power (for prevailing 

temperature and wind speeds) over a twenty watt irradiance 

‘window’ centered on the PVUSA TC rating point of 1000 

Wm-2. With the exception of one residual of -307 Wm-2

(where T = 0.6 °C and W = 1.7 ms-1; possible frost or snow 

on the array) the range of residuals is -124 Wm-2 to + 100 

Wm-2 in this irradiance regime. This range represents – 

0.8% to +0.7% of the rating at PVUSA TC. Thus, an 

uncertainty component due to the model fit can be assumed 

as ~ ± 1.0%. This same scatter is apparent in figure 2, about 

the linear fit line in that plot. 

-400

-300

-200

-100

0

100

200

300

990 995 1000 1005 1010

POA Irradiance

AC Power PTC Model Residual 

Watts

Fig. 3. Residuals (measured – modeled) of measured data 

from the PVUSA TC model line for irradiance levels from 

990 Wm-2 to 1000 Wm-2. Note this includes temperature 

range from -32.5 °C to 36 °C and wind speeds from 0.4 to 

9.1 ms-1. 

6. CORRELATIONS OF POWER WITH MODEL 

VARIABLES

Since the PVUSA TC model is based on an assumed 

correlation of array power with the three independent 

variables, expressed as four terms in the model equation 1, it 
5 

is interesting to look at the correlation of the array power 

with each model term, as in figure 5. Here we plot the array 

power versus the corresponding term of the model, e.g. a 

times Irradiance, a * I, b times Irradiance squared, b*I2

, c 

times Irradiance times wind speed, c*I*W, and d * I * T.

The strong correlation of the array power with the irradiance 

terms is immediately obvious. There is a great deal of noise 

and virtually zero correlation between array power and the 

wind and temperature terms, except for the extremely cold 

days (Feb 16, 2006, March 27, 28 2006 where the reported 

temperature was less than -5 °C).

Fig. 5. Correlations of array power with each independent 

term of the PVUSA TC model. Top left to bottom right: 

array power versus a*I, b*I2

, c*I*w, d*I*T. The values of a, 

b, c, and d developed from the model are used. Note the lack 

of strong correlation between wind speed and temperature 

components of the model and the array output, except for 

very cold (T<-5 °C) day [135 data points] in the bottom 

right graph.

7. UNCERTAINTY IN THE PTC RATING

The uncertainty in the PTC rating value depends on the 

magnitude of the measurement errors in the independent 

variables, the magnitudes of the fixed reporting conditions, 

and the sensitivity coefficients, equation 5.

7.1 NREL USSC 1.6 kW System Rating Uncertainty

An Excel spreadsheet was constructed which permits one to 

compute the absolute uncertainty in P at various 

combinations of I, W, and T, with assumed values of eI, eW, 

and eT, of course incorporating equation 6. 

Table 4 displays a typical result, with error terms (assumed 

for measurements) of eI=25 Wm-2, eW = 1 ms-1, and eT= 1° C 

for the USSC 1.6 kW system at NREL at each of the 

indicated plane of a array (POA) irradiance levels in 

column 1. The Ps ‘error’ result is computed from eq. 5 and 

the values in the columns to the left.

The results of these computations need to be combined with 

the measurement uncertainty in the array power, the 

dependent variable of the model, to achieve an overall 

uncertainty for the entire method. If instrumentation similar 

to that described in table 2 above (used in the PV Energy 

Rating Testbed experiments) then the combined current, 

voltage, and power measurement uncertainty is 0.22%.

Note the magnitude of the uncertainty in Ps (gray cell), 42 

Watts, or about 2.8% of the rating. Compare this with the 

fact that 0.7% of the rating value, or 10.3 W, is contributed 

by the combined wind speed and temperature terms in the 

model equation. These latter two elements contribute to the 

rating value an amount that is 4 times smaller than the 

uncertainty contributed by the irradiance uncertainty. The

25 Wm-2 irradiance uncertainty is 2.5% of the rating 

irradiance value of 1000 Wm-2. Such accuracy is 

representative of an exceptionally well

TABLE 4: UNCERTAINTY IN P AS FUNCTION OF 

UNCERTIANTY IN VARIABLES (USSC 1.6 kW)

POA

kWm-2

Note: 

eI=25 Wm-2, eW = 1 ms-1, and eT= 1° C.

PTC Rating = 1480 W. Ps RSS 

ERROR

% 

error 

wrt 

(ei*∂/∂i) 1480 2 (ew*∂/∂w) 2 (∂/∂t) 2

0.5 781.39 1.3 0.033 28.0 1.9%

0.6 942.90 1.9 0.047 30.7 2.1%

0.7 1119.57 2.6 0.064 33.5 2.3%

0.8 1311.41 3.4 0.084 36.3 2.5%

0.9 1518.40 4.3 0.106 39.0 2.6%

1.0 1740.56 5.2 0.131 41.8 2.8%

1.1 1977.87 6.3 0.158 44.5 3.0%

Mean residual when 990 Wm-2<POA<1010 Wm-2 is 2.5 W

calibrated and maintained pyranometer. This irradiance 

uncertainty in table 1 is typical. Combining the 2.8% 

combined uncertainty contributions from the independent 

variables with the 0.22% uncertainty in measured power, the 

overall uncertainty in the PVUSA TC approach for the 

USSC system tested is 2.8%.

7.2 Uncertainty in PVUSA Ratings for Other Systems 

From PVUSA TC model coefficients for several large (~ 

200 kW or larger) PV systems in a 1993 PVUSA project 

progress report [8]. IPC US-1, at Davis, CA and SSI-US-2 

at Kerman systems were selected (page 3-9). We replicated 

the above calculations for these systems. The systems in 

tables 5 and 6 are much larger than the NREL, rated at ~ 

190 kW and 500 kW, respectively. The units of power for 

the systems and the input irradiance in these cases are kW 

and kWm-2. 

Results in tables 4, 5 and 6, for assumed measurement 

uncertainty in irradiance, temperature, and wind speed of 

±25 Wm-2, ±1 °C and ±1 ms-1, respectively, show that the 
6 

derived uncertainty in the PVUSA TC results is between 2% 

and 3% at the rating condition. This uncertainty is primarily 

driven by the uncertainty in irradiance measurement 

(25 Wm-2 at 1000 Wm-2 = 2.0%). Factors of 10 increases in 

the measurement errors for the temperature and wind speed

hardly influence the resultant uncertainty at all. In these two 

cases, PVUSA quoted an uncertainty in their rating at

TABLE 5: UNCERTAINTY IN P AS FUNCTION OF 

UNCERTAINTY IN VARIABLES IPC US-1 DAVIS 

POA

kWm-2

Note: eI=25 Wm-2, eW = 1 ms-1, and eT= 1° C 

PVUSA* rating 192.25 kW ± 3 kW =1.6%.

a=282.14 b=-70.152 c=1.5824 d=-0.8998

RSS 

Power

Uncert 

(kW)

% 

error 

wrt 

(ei*∂/∂i) 190 kW 2 (ew*∂/∂w) 2 (∂/∂t) 2

0.5 28.17 0.6 0.198 5.4 2.7%

0.6 24.59 0.8 0.285 5.1 2.6%

0.7 21.26 1.1 0.388 4.8 2.4%

0.8 18.17 1.4 0.506 4.5 2.3%

0.9 15.32 1.8 0.641 4.2 2.2%

1.0 12.71 2.3 0.792 4.0 2.0%

1.1 10.35 2.7 0.958 3.7 1.9%

*Quoted uncertainty by PVUSA; no documentation of derivation. 

Presumably model standard error

TABLE 6: UNCERTAINTY IN P AS FUNCTION OF 

UNCERTAINTY IN VARIABLES KERMAN

POA

kWm-2

Note: eI=25 Wm-2, eW = 1 ms-1, and eT= 1° C 

PVUSA* Rating: 498.4 ± 6 kW =1.2%.

a=701.1 b=-142.2 c=6.412 D=-3.384 Power

RSS 

Uncert

% 

error 

wrt 

(ei*∂/∂i) 498 kw 2 (ew*∂/∂w) 2 (∂/∂t) 2

0.5 196.35 10.2 2.89 14.5 2.9%

0.6 177.16 14.7 4.16 14.0 2.8%

0.7 158.95 20.1 5.66 13.6 2.7%

0.8 141.73 26.2 7.39 13.2 2.7%

0.9 125.50 33.2 9.36 13.0 2.6%

1.0 110.25 41.0 11.56 12.8 2.6%

1.1 95.99 49.6 13.98 12.6 2.5%

*Quoted uncertainty by PVUSA; no documentation of derivation. 

Presumably model standard error

about 1⁄2 that of the analysis here; however there is no report

of how the uncertainty was calculated. 

7.3 Residual Analysis for the USSC PVUSA Model.

The residuals for the PVUSA TC (eq. 1) fit, and a linear and 

quadratic fit of the AC power as a function of irradiance 

alone (see figure 2) for the NREL USSC 1.6 kW system are 

shown in figure 6.

Note that the PVUSA TC model produces the widest range 

of residuals (Squares), due mainly to the additional wide 

dispersion of the correlation of the AC power with respect 

to the wind and temperature components of the model 

shown in figure 5. The range of residuals for the linear (+) 

and quadratic (circles) fits are somewhat smaller. The mean 

residual for the PVUSA model is -0.56 W, however the 

mean residuals for the linear and quadratic fits are 10 orders 

of magnitude smaller and near very near zero (1.6• 10-12 W 

and 6.2 •10-12 W, respectively). 

Fig. 6. Residuals between measured and modeled PTC (gray

squares), and quadratic (open circle) and linear (+) fits of 

AC power versus irradiance alone for the USSC system.

This suggests that the addition of the wind speed and 

temperature terms in the PVUSA model results in 

additional noise being introduces into the model, and not 

improvement in the model performance. 

Multicollinearity [9] between the ambient temperature and 

the irradiance, and the ‘weighting’ of the wind and 

temperature data by the irradiance term increases the 

multiple correlation coefficient of the PVUSA TC model, 

but increases the residuals to the fit, and results in a lower 

performance model than a simple linear or quadratic for of 

AC power versus irradiance.

The uncertainty in the irradiance measurements is the 

largest contributor to the uncertainty in the model results. 

To achieve a rating uncertainty of 1.0%, the uncertainty in 

the irradiance must be reduced to this level (better than ± 

1% accuracy). The only way to achieve this level or 

uncertainty is to apply incidence angle modifiers to the 

pyranometer data used to collect the irradiance data.

8. CONCLUSION

We applied the PVUSA rating system to a thin film dual 

junction 1.6 kW (nominal) PV system at NREL. Our 

analysis of the uncertainties associated with the 
7 

measurement instrumentation, and propagation of errors 

through sensitivity coefficients for the variables in the 

model equation demonstrated an uncertainty in the rating 

using the PVUSA PTC model of about 2.8 % for a rating of 

1.480 kW, or ±41 watts. Analogous results were obtained 

for two other larger PV systems reported by PVUSA. We 

have shown a lack of strong correlation between system 

output and two variables (wind speed, ambient temperature) 

in the PTC rating model. The lack of true independence in 

the ‘independent’ variable terms, or multicollinearity, 

engendered by multiplying these variables by irradiance, 

artificially inflates the correlation coefficient for the model, 

and may be adding noise to the model. Simple linear and 

quadratic regressions of AC power versus plane of array 

irradiance produce within 3% of the PVUSA TC results; 

with essentially same uncertainties (3%), the error bars

about the simple and PVUSA TC results would overlap, and 

the results would be considered comparable. Residuals from 

the three fits essentially overlay one another, however the 

spread in the residuals from the PTC model have a 

somewhat larger spread. Measured AC power with POA 

irradiance within ±0.5 watts of 1 kWm-2, over several days 

produced a rating within 1.8% of the PTC rating, or within 

the PTC uncertainty. 

From these results, we conclude that the PTC, simple linear 

and quadratic regression of AC power versus POA 

irradiance, and measured AC power near STC irradiance 

conditions all produce results (‘ratings’) within about 3% of 

each other, with similar uncertainties. The results from all 

four techniques are comparable, and have uncertainties on 

the order of 3%, mainly due to measurement system 

(particularly radiometer) uncertainties. 

9. ACKNOWLEDGMENTS

NREL Outdoor Test Facility measurement data for the 

USSC system was kindly provided by Bill Marion and Peter 

McNutt. This work was supported by the U.S. Department 

of Energy under Contract No. DE-AC36-99GO10337 with 

the National Renewable Energy Laboratory.

10. REFERENCES

1. Whitaker, C.M., Townsend, T.U., Wenger, H.J., et al., 

“Effects of Irradiance and Other Factors on PV 

Temperature Coefficients” Proceedings”, 22nd IEEE 

Photovoltaic Specialists Conference, October 1991. 

2. Whitaker, C.; Newmiller, J. . Photovoltaic Module 

Energy Rating Procedure: Final Subcontract Report, 

NREL/SR-520-23942, Golden, CO: National 

Renewable Energy Laboratory, 1998.

3. ASTM, ASTM E2527-09, “Standard Test Method for

Rating Electrical Performance of Concentrator 

Terrestrial Photovoltaic Modules and Systems Under 

Natural Sunlight”, American Society for Testing and 

Materials, West Conshohocken, PA. 2009.

4. ASTM, ASTM E1036 - 08 “Standard Test Methods for 

Electrical Performance of Nonconcentrator Terrestrial 

Photovoltaic Modules and Arrays Using Reference 

Cells” American Society for Testing and Materials, 

West Conshohocken, PA. 2008.

5. Marion, B.; Kroposki, B.; Emery, K.; del Cueto, J.; 

Myers, D.; Osterwald, C. “Validation of a Photovoltaic 

Module Energy Ratings Procedure at NREL” 

NREL/TP-520-26909. National Renewable Energy 

Laboratory. 1999.

6. BIPM, “Guide to the Expression of Uncertainty in 

Measurement.” Published by ISOTAG 4, 1995. 

International Bureau of Weights and Measures (BIPM) 

Sevres, France. 1995. 

7. Taylor, B. N., C E Kuyatt, “Guidelines for Evaluation 

and Expressing the Uncertainty of NIST Measurement 

Results.” NIST Technical Note 1297. National Institute 

of Standards and Technology. 1993.

8. PVUSA Project Team, 1993 PVUSA Project Report. 

PVUSA, 1993.

9. Myers, Raymond H. Classical and Modern Regression 

with Applications. Duxbury Press, Boston MA. 1986.
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Evaluation of the Performance of the PVUSA Rating Methodology 

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The PVUSA (Photovoltaics for Utility Scale Applications) project in the 1990's developed a rating methodology for PV 

performance evaluation which has become popular, and even incorporated into concentrating PV rating standards 

This report apply that method to rack-mounted dual-junction PV system, and produces a system rating. 

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PFUSA; performance; concentrating solar; CSP, dual junction

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