Energy Production and Performance of Polycrystalline Silicon Technology Photovoltaic Modules in the Field: Preprint Page: 4 of 4
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nearly identically to that of the insolation. Added variations
of EOUT occur at similar values of insolation due primarily to
temperature and spectral effects, amounting to ~10% ( 5%).
This added 10% scatter is better examined by removing
variations in light intensity from the data and analyzing
nEFF, which exhibit strong dependence with module
temperature (TM). Fig. 2 portrays nIEFF plotted against TM-
daily averages computed weekly over both modules of each
three types. The nIEFF of module types Y and Z vary between
8.5% and 10.1%, while those of type X fluctuate between
9.4% and 11%, as the mean TM change, respectively, from
400C down to 120C. This temperature dependence may be
quantified by least-squares fitting of the nIEFF data against
TM. Although the specifics vary between the three module
types, the slopes resulting from this analysis yield similar
temperature coefficients varying between -0.046 and -0.049
absolute-% per 0C. The squares of the linear correlation
coefficients of the regression reveal that 77% to 79% of the
variations in nEFF are correlated with variations in TM.
11.0 t x xS10.5
10.0
i9.5
_9.0
S8.5
8.010 14 18 22 26 30 34 38 42
Average Daily Module Temperature (0)
Fig. 2. Average poly-c-Si lEFF against module temperature
Fig. 3 depicts the average PRs (TIEFF/TSRC) for the three
module types along the left-hand abscissa plotted against
time along the ordinate. Also plotted and read along the
right-hand abscissa are the concurrent average daytime air
temperatures. The vertical gridlines and tick-marks along
the ordinate axis correspond to the first days of each month.
The PRs achieve their highest values in winter and vice
versa-exposing largely seasonal temperature effects-
fluctuating between 78% and 93% for module types Y and
Z, and ranging 82%-96% for module type X. Seasonal
variations in performance range between 11% and 15%.
7 xX
95% x--- -cy
93% ----__a Z
-1 x O ---Air Tern.
9?87% 0 V~; & 3% -
-87% 25.9
a.85% x 2
6/00 8/00 1 0/00 1 2/00 2/01 4/01 6/01 8/01
Time (month/year)
Fig. 3. Average poly-c-Si PRs and air temperatures vs. timeThe output for each module type may be expressed by
the product of insolation times a linear expression in TM, as
per Eq. 1: where E is the insolation in kW-hrs/m2; EOUT
units are in W-hrs; and the coefficients Eo and Ei represent,
respectively, the intercept and linear temperature-dependent
terms. A synopsis of the coefficients for EOUT for each
module type is summarized in Table I. These coefficients
are derived from the product of the regression of rIEFF versus
TM data shown in Fig. 2, times respective module areas. For
example, module type X at average TM = 00C and for every
1 kW-hr/m2 of insolation: one obtains -36.4 W-hrs output
energy, regardless of whether that insolation accumulates
during the course of a day or in several hours; and for every
100C temperature rise above 00C, this output declines by 1.6
W-hrs. Both the example output and temperature derating
are proportional to the actual insolation incident on module
surface, regardless of the specific angle of tilt chosen for
deployment. The values tabulated under the columns labeled
"Error" represent one standard deviation in their respective
derived coefficients.
EQUT {W -hrs}= (c0 +1-e- TM> -E {kW -hrs/m2}1
Table I. Coefficients and standard errors relating module
EOUT to incident insolation and average module temperature
Module Eo (W-hr per kW-hr/m2) 81 (W-hr/'C per kW-hr/m2)
Type Coeficient Error Coeicient Error
X 36.4 0.31 f6l0
V41 .1-.000
Z 37.0 36 -0. 0 .1
4. Analysis and Conclusions
The energy production capacities of six poly-c-Si PV
modules from three manufacturers were measured under
actual ambient conditions over the course of a year. Energy
production was formulated by the product of the incident
insolation times an expression characterized by a constant
plus a linear temperature-dependent term. Values for the
coefficients were derived and tabulated for all three module
types. Using our locale as example, in the course of a year,
at fixed latitude tilt, we get 5.3 kW-hr/m2/day insolation,
and all three module types obtain 26.50 0.50C average
temperature. The yearly EOUT anticipated from types X, Y,
and Z is, respectively, 62.4, 75.3, and 63.7 kW-hrs apiece-
standard variance of 2% for all three types. Expressing the
output energy as per Eq. 1 has reduced the variance from
about 5% to 2% by accounting for temperature effects.
Spectral effects may account for the remaining variance.
5. Acknowledgements
This work was funded by U.S. Dept. of Energy,
contract no. DE-AC36-99G010337.
REFERENCES
[1] B. Marion, B. Kroposki, K. Emery, J. del Cueto, D.
Myers, C. Osterwald, NREL/TP520-26909, 1999.
[2] J.A. del Cueto, Prog. Photovolt., Res. & Appl. 1998; 6
(6): 443-446.A x :
o x F
~Aj
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del Cueto, J. A. Energy Production and Performance of Polycrystalline Silicon Technology Photovoltaic Modules in the Field: Preprint, article, October 1, 2001; Golden, Colorado. (https://digital.library.unt.edu/ark:/67531/metadc1400020/m1/4/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.