**4. Results and discussion**

446 Solar Cells – Thin-Film Technologies

In simple statistics, the data represented by the Gaussian distribution implies that 68% of the values (on either side) lie within the 1st standard deviation (1) and 95% of the values lie within the 2nd standard deviation. The confidence interval level was also analyzed when determining the mean value. The confidence interval quantifies the precision of the mean, which was vital in this analysis since the mean represents the WUF spectrum from which the devices responds best during the entire period of outdoor exposure. The increase in standard deviation means that the device spends less time on the corresponding WUF spectrum. Ideally it represents the error margin from the mean value. The percentage frequency value corresponding to the mean WUF value represents the percentage of the total time of outdoor exposure to which the device was responding best to that spectrum.

Fig. 2. Illustration of Gaussian distribution used to determine the mean WUF.

2 2

1 1

work showed a high confidence level.

*<sup>G</sup>* (which is referred to as

*sc*

*I*

*SpectralRange*

0

10

20

30

40

50

**Frequency (%)**

60

70

80

90

Depending on how the data is distributed, the Gaussian curve 'tails' differently from each side of the mean value. The increase in in this case reveals two crucial points regarding the statistical data in question. Firstly, it quantifies the total time spent at a specific spectrum as the increases during the entire period of monitoring. Secondly it reveals the entire spectral range to which PV devices respond. From figure 2, the standard deviation increases from 1 to 8 on one side of the mean WUF and from the other side varies from 1 to 3. The total range of the WUF is from 0.64 to 0.7 although it spends less time from spectral range where standard deviation is greater than a unit. A high confidence level of each Gaussian distribution indicates the accuracy of the determined mean. All results presented in this

0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 **Weighted Useful Fraction**

3 5 6 7 8

Mean WUF

PV device Spectral

3 4

Normalization of Isc was achieved by dividing the module's Isc with the total irradiance within the device spectral range (GSpectral Range). The commonly adopted correlation existing between the module's Isc and back-of-module temperature is of the form *sc* 0 1 *device S pectralRange I C CT G* (Gottschalg et al., 2004). Firstly, the relationship between

back-of-module temperature. The empirical coefficient C0 and C1 are obtained. The second

*SpectralRange* from this point onwards) is plotted against

Although the outdoor parameters might 'mimic' the STC conditions, the performance of the PV device will not perform to that expectation. By analyzing the effect of outdoor environment, the spectrum received is largely influenced by solar altitude and atmospheric composition, which in turn affect device performance.

Figure 3 illustrates the seasonal effects on the CIS module current-voltage *(I-V)*  characteristics when deployed outdoor, first on 31 January 2008 and later on 12 June 2008.

Fig. 3. Comparison of the CIS I-V characteristics for a typical summer clear sky and winter clear sky. The accompanying table lists the conditions before corrections to STC.

The January *I-V* curve was taken a few days after deployment of the modules while operating at outdoor conditions. Two aspects needed to be verified with this comparative analysis of the I-V curves for that time frame: Firstly the state of the module, i.e. whether it did not degrade within this time frame needed to be ascertained so that any effect on device Isc, FF and efficiency would be purely attributed to spectral effects. Secondly, this was done to see the effect of seasonal changes on the *I-V* characteristics. Since the outdoor conditions are almost the same when the measurements were taken, the I-V curves were normalized to STC conditions using the procedure mentioned in section 2. Since the 3 *I-V* curves had been corrected for both temperature and irradiance, therefore any

Spectral Effects on CIS Modules While Deployed Outdoors 449

**Normalized Energy Density**

0.0

0.93

Jan-08

Feb-08

Mar-08

average daily profile for the period from January to June 2008.

Apr-08

May-08

Jun-08

Evident from figure 6 is the high values of CIS WUF for the entire period which indicates that the device performs well under full spectrum. Taking the average values of the upper

Fig. 6. Evolution of daily average Weighted Useful Fraction versus timeline. Inset is an

Jul-08

Aug-08

Sep-08

Oct-08

Nov-08

Dec-08

0.94

0.95

0.96

0.97

**WUF**

0.98

0.99

1.00

0.2

0.4

0.6

0.8

1.0

1.2

Lower AM

0.935 0.940 0.945 0.950 0.955 0.960 0.965 0.970 0.975 0.980 0.985

**WUF**

**Wavelength (nm)** 200 400 600 800 1000 1200

Fig. 5. Normalized spectral distribution for January and June months.

13-Jan-08

2-Feb-08

22-Feb-08

13-Mar-08

2-Apr-08

22-Apr-08

WUF = 1.5%

12-May-08

1-Jun-08

21-Jun-08

January June

Higher AM

11-Jul-08

31-Jul-08

modification or changes on the Isc values is purely due to spectral effect. The difference in module's Isc is largely attributed to the outdoor spectral composition, which as have been mentioned earlier on, depends on season and time of the year amongst other factors. The CIS module was also simulated using Solar Studio Design. At each AM value, the module's *I-V* curve was obtained. Figure 4 illustrates the effects on the simulated CIS *I-V* curves as the Air Mass was varied.

Fig. 4. The effect of varying Air mass on the simulated CIS module.

The change in outdoor spectrum as characterized by the AM values affect the module's *I-V* curves, mostly the Isc. Although this module is rated at STC using the AM1.5 spectrum, the CIS module is performing less at AM1.5 as compared to AM 9.15. The *I-V* curve at AM 1.5 coincides with the *I-V* curve at AM 16.0. It should be noted that the change in AM value is an indication of the spectral content dominating. The ΔIsc = 7.5% difference between Isc at AM 1.5 and Isc at AM 9.15 is purely due to spectral changes. Returning back to figure 1, the difference in Isc between winter and summer spectrum is due to spectral changes. The typical winter and summer spectra were compared with the view of finding any variation in the profiles. All values were divided by the highest energy density in each curve so as to normalize them. Figure 5 presents the normalized spectral distribution corresponding to the two *I-V* curves in figure 3.

Clearly there is a difference in the spectral content primarily due to the difference in solar altitude and hence air mass. In the absence of the device degradation, similar irradiance and module temperatures, the reduction in module performance is attributed to the difference in spectral distribution associated with the seasonal variation. To further verify whether indeed the reduction in the module's Isc was due to spectral changes associated with seasonal changes, the device WUF for the entire year was analyzed. The monthly average WUF was considered to be sufficient to provide evidence, if any in its profile. Figure 6 shows the evolution of the monthly average WUF of the CIS module.

modification or changes on the Isc values is purely due to spectral effect. The difference in module's Isc is largely attributed to the outdoor spectral composition, which as have been mentioned earlier on, depends on season and time of the year amongst other factors. The CIS module was also simulated using Solar Studio Design. At each AM value, the module's *I-V* curve was obtained. Figure 4 illustrates the effects on the simulated CIS *I-V*

AM 0.89 AM 1.00 AM 1.51 AM 4.18 AM 9.15 AM 16.0

0 5 10 15 20 25 **Voltage (V)**

The change in outdoor spectrum as characterized by the AM values affect the module's *I-V* curves, mostly the Isc. Although this module is rated at STC using the AM1.5 spectrum, the CIS module is performing less at AM1.5 as compared to AM 9.15. The *I-V* curve at AM 1.5 coincides with the *I-V* curve at AM 16.0. It should be noted that the change in AM value is an indication of the spectral content dominating. The ΔIsc = 7.5% difference between Isc at AM 1.5 and Isc at AM 9.15 is purely due to spectral changes. Returning back to figure 1, the difference in Isc between winter and summer spectrum is due to spectral changes. The typical winter and summer spectra were compared with the view of finding any variation in the profiles. All values were divided by the highest energy density in each curve so as to normalize them. Figure 5 presents the normalized spectral distribution corresponding to the

Clearly there is a difference in the spectral content primarily due to the difference in solar altitude and hence air mass. In the absence of the device degradation, similar irradiance and module temperatures, the reduction in module performance is attributed to the difference in spectral distribution associated with the seasonal variation. To further verify whether indeed the reduction in the module's Isc was due to spectral changes associated with seasonal changes, the device WUF for the entire year was analyzed. The monthly average WUF was considered to be sufficient to provide evidence, if any in its profile. Figure 6

Fig. 4. The effect of varying Air mass on the simulated CIS module.

shows the evolution of the monthly average WUF of the CIS module.

curves as the Air Mass was varied.

0.0

two *I-V* curves in figure 3.

1.0

2.0

3.0

**Current (A)**

4.0

5.0

Fig. 5. Normalized spectral distribution for January and June months.

Fig. 6. Evolution of daily average Weighted Useful Fraction versus timeline. Inset is an average daily profile for the period from January to June 2008.

Evident from figure 6 is the high values of CIS WUF for the entire period which indicates that the device performs well under full spectrum. Taking the average values of the upper

Spectral Effects on CIS Modules While Deployed Outdoors 451

by plotting the FF with WUF a functional relationship can be established. Figure 8 shows the

0.96 0.965 0.97 0.975 0.98 0.985 **WUF**

0 2 4 6 810 12 14 16 18 **Air Mass**

Fig. 8. Effect on CIS average Fill factor due to outdoor irradiance and spectral changes. Inset

0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73

**Fill Factor**

Observed from figure 6, a 6.5% increase in FF is observed within the WUF range 0.960 - 0.983 (considering the % difference between the averages of the upper and low values of the FF). It should however be noted that this percentage increase value is just an indication of the change in FF. The increase in FF as observed is attributed to the quality of the spectrum dominating which result in 'supplying' sufficient energy for the electron-hole creation, with less energy losses, which in most cases is dissipated as heat. From the inset figure, a decrease in FF as AM values increase from AM 1.5 is evident. Closely analyzing the two graphs, the spectrum dominating under the WUF range of the CIS module is a blue rich spectrum which explains a slight increase in FF. From the inset figure, the FF is higher at AM 1.5 and decrease as the spectrum becomes longer wavelength dominated. Clearly the change in outdoor spectrum has an effect on the FF of the CIS module. Often reported is the relationship between efficiency and global irradiance as measured by the pyranometer. For CIS module, the variation of aperture efficiency with WUF is visible described by a logarithmic fit into the scattered data. Both WUF and irradiance affect device performance with the same magnitude. Gottschalg et al., (Gottschalg et al., 2004) established a relationship for device aperture efficiency and Useful Fraction (UF). The efficiency is

which when interpolated to our concept of Weighted Useful Faction

*A* 

: where

(WUF) the device efficiency would be described by *WUF*

*Power P Spectral sponsiveRange UI* ( ) Re ( ) , is roughly a constant. This relationship exhibit a

slight increase in FF as the WUF varies.

0

described by *UF*

*A* 

is the variation of FF vs. Air Mass for the same device.

0.1

0.2

0.3

0.4

**Fill Factor**

0.5

0.6

0.7

0.8

(summer) and the lower for winter, a 1.5% drop in WUF is noticed (inset figure). A small change in WUF results in large change of the device's Isc. In order to verify this assumption, the change in WUF versus Air Mass was established as is presented in figure 7.

Fig. 7. Influence of the air mass on device spectral variations as characterized by WUF for CIS module.

The relationship established in figure 7 was used to calculate the change in WUF at different Air Mass values, a typical change in season. Values for low air mass (indication of a summer spectrum) and high air mass (indication of winter) were used to calculate the % change in WUF and later compared to the simulated % change in Isc at different AM values, the same values that has been used in previous calculation. Equations 12 and 13 illustrate the equations used for this calculation.

$$\text{WUF}\_{1.0} = -0.002 \times AM1.0 + 0.9856\tag{12}$$

$$\text{W}\text{LIF}\_{9.15} = -0.002 \times \text{AM9.15} + 0.9856\tag{13}$$

where: WUF1.0 is the calculated value of WUF at AM 1.0 and the WUF9.15 is the calculated value of WUF at AM 9.15.

From figure 4 the value for Isc (AM 1.0) and Isc (AM 9.15) were used to calculate the % change in Isc as the spectrum changes. The ΔWUF = WUF1.0 – WUF9.15 expressed as a %, was found to be 1.66%, while the ΔIsc = 11.88%. From this analysis, one can conclude that a small % change in ΔWUF result in large % difference of the module's Isc, which explains the 17% decrease in Isc due to a ΔWUF of 1.5%. The slight difference in the two results is due to the difference in the actual operating conditions in which case the simulated conditions are different from the actual conditions when the two I-V curves in figure 4 were measured.

A 10 point moving average was applied so that a clear correlation can be seen. By fitting a 3rd order polynomial fit, a functional relationship between FF and WUF is observed. The FF of the device is an indication of the series and junction quality of the device cells; therefore

(summer) and the lower for winter, a 1.5% drop in WUF is noticed (inset figure). A small change in WUF results in large change of the device's Isc. In order to verify this assumption,

> 0 2 4 6 8 10 12 14 16 18 **Air Mass**

Fig. 7. Influence of the air mass on device spectral variations as characterized by WUF for

The relationship established in figure 7 was used to calculate the change in WUF at different Air Mass values, a typical change in season. Values for low air mass (indication of a summer spectrum) and high air mass (indication of winter) were used to calculate the % change in WUF and later compared to the simulated % change in Isc at different AM values, the same values that has been used in previous calculation. Equations 12 and 13 illustrate the

where: WUF1.0 is the calculated value of WUF at AM 1.0 and the WUF9.15 is the calculated

From figure 4 the value for Isc (AM 1.0) and Isc (AM 9.15) were used to calculate the % change in Isc as the spectrum changes. The ΔWUF = WUF1.0 – WUF9.15 expressed as a %, was found to be 1.66%, while the ΔIsc = 11.88%. From this analysis, one can conclude that a small % change in ΔWUF result in large % difference of the module's Isc, which explains the 17% decrease in Isc due to a ΔWUF of 1.5%. The slight difference in the two results is due to the difference in the actual operating conditions in which case the simulated conditions are different from the actual conditions when the two I-V curves in figure 4 were measured. A 10 point moving average was applied so that a clear correlation can be seen. By fitting a 3rd order polynomial fit, a functional relationship between FF and WUF is observed. The FF of the device is an indication of the series and junction quality of the device cells; therefore

1.0 *WUF* 0.002 1.0 0.9856 *AM* (12)

9.15 *WUF* 0.002 9.15 0.9856 *AM* (13)

y = -0.002x + 0.9856 R2 = 0.6571

the change in WUF versus Air Mass was established as is presented in figure 7.

0.0

equations used for this calculation.

value of WUF at AM 9.15.

CIS module.

0.2

0.4

0.6

**WUF**

0.8

1.0

1.2

by plotting the FF with WUF a functional relationship can be established. Figure 8 shows the slight increase in FF as the WUF varies.

Fig. 8. Effect on CIS average Fill factor due to outdoor irradiance and spectral changes. Inset is the variation of FF vs. Air Mass for the same device.

Observed from figure 6, a 6.5% increase in FF is observed within the WUF range 0.960 - 0.983 (considering the % difference between the averages of the upper and low values of the FF). It should however be noted that this percentage increase value is just an indication of the change in FF. The increase in FF as observed is attributed to the quality of the spectrum dominating which result in 'supplying' sufficient energy for the electron-hole creation, with less energy losses, which in most cases is dissipated as heat. From the inset figure, a decrease in FF as AM values increase from AM 1.5 is evident. Closely analyzing the two graphs, the spectrum dominating under the WUF range of the CIS module is a blue rich spectrum which explains a slight increase in FF. From the inset figure, the FF is higher at AM 1.5 and decrease as the spectrum becomes longer wavelength dominated. Clearly the change in outdoor spectrum has an effect on the FF of the CIS module. Often reported is the relationship between efficiency and global irradiance as measured by the pyranometer. For CIS module, the variation of aperture efficiency with WUF is visible described by a logarithmic fit into the scattered data. Both WUF and irradiance affect device performance with the same magnitude. Gottschalg et al., (Gottschalg et al., 2004) established a relationship for device aperture efficiency and Useful Fraction (UF). The efficiency is described by *UF A* which when interpolated to our concept of Weighted Useful Faction (WUF) the device efficiency would be described by *WUF A* : where

Spectral Effects on CIS Modules While Deployed Outdoors 453

January June

0.88 0.90 0.92 0.94 0.96 0.98 1.00 **WUF**

Fig. 10. Average outdoor aperture efficiency as a function of WUF of CIS module for both

Trend 2 for G > 1kW/m2

y = -0.001x + 0.9997 R2 = 0.7602

Trend 1 for G < 0.8 kW/m2

10 15 20 25 30 35 40 45 50 55 60 **Tmod (o C)**

Fig. 11. Relationship between the outdoor WUF and back of module temperature of the CIS

Observing the results in figure 11, two temperature coefficients for WUF are obtained during the winter period. This trend in behavior could have been attributed to the different outdoor weather patterns observed for winter period. Some days even during winter, the outdoor climatic conditions would resemble a typical clear sky summer season, indicated by

0

y = -4E-05x + 0.9729 R2 = 0.7132

WUF

20

40

60

**Frequency (%)**

80

100

120

0

winter and summer period.

0.940

module during winter period.

0.945

0.950

0.955

0.960

**WUF**

0.965

0.970

0.975

0.980

2

4

6

**Efficiency (%)**

8

10

12

linear trend of efficiency with WUF in our case. The other key performance indicator in PV analysis is the device aperture efficiency. The efficiency of CIS module was also analyzed using the same procedure for FF analysis. Figure 9 indicate the efficiency versus WUF of the CIS device.

Fig. 9. Correlation between aperture efficiency versus outdoor WUF of the CIS module.

The efficiency increases logarithmically with an increase in Weighted Useful fraction (WUF > 0.960), which do not agree with the theoretical relationship illustrated in the previous section ( *WUF A* ). One can attribute this discrepancy of the measured data and theory as follows: The α in the equation above is assumed to be a constant, but in actual fact it is strongly dependant on the irradiance available within the denominator function (UI). The irradiance within the Responsive Spectral Range (UI) is assumed to be a constant, a single value to be precise. In reality the irradiance does fluctuates within this range, rendering the α not to be a constant parameter. However the device efficiency exhibits a logarithmic increase as a function of WUF, due to the irradiance variations, resulting in α not to be a constant. The effect of season on device efficiency was also investigated; the results are shown in figure 10. It is observed from figure 10 that the device efficiency is stable for both summer and winter.

The PV module's performance parameters e.g. Isc, Voc, FF and η are characterized by what is referred to as temperature coefficients. Temperature coefficient is described as the rate of change (derivative) of the parameter with respect to the temperature of the PV device performance parameters (King et al., 1997). For PV system sizing and design, knowing the device temperature coefficient plays a very critical role. Quantifying the spectral effects on its own has proved to be a challenge; as a result no temperature coefficient with respect to outdoor spectrum has been documented. In figures 11 and 12, the relationship between outdoor spectral effects (WUF) and the average back - of module temperature is presented. Using a linear fit to the data, a spectral temperature coefficient is obtained. Figure 11 illustrates the relationship between WUF and temperature for a winter period.

linear trend of efficiency with WUF in our case. The other key performance indicator in PV analysis is the device aperture efficiency. The efficiency of CIS module was also analyzed using the same procedure for FF analysis. Figure 9 indicate the efficiency versus WUF of the

> 0.96 0.965 0.97 0.975 0.98 0.985 **WUF**

The efficiency increases logarithmically with an increase in Weighted Useful fraction (WUF > 0.960), which do not agree with the theoretical relationship illustrated in the previous

follows: The α in the equation above is assumed to be a constant, but in actual fact it is strongly dependant on the irradiance available within the denominator function (UI). The irradiance within the Responsive Spectral Range (UI) is assumed to be a constant, a single value to be precise. In reality the irradiance does fluctuates within this range, rendering the α not to be a constant parameter. However the device efficiency exhibits a logarithmic increase as a function of WUF, due to the irradiance variations, resulting in α not to be a constant. The effect of season on device efficiency was also investigated; the results are

It is observed from figure 10 that the device efficiency is stable for both summer and winter. The PV module's performance parameters e.g. Isc, Voc, FF and η are characterized by what is referred to as temperature coefficients. Temperature coefficient is described as the rate of change (derivative) of the parameter with respect to the temperature of the PV device performance parameters (King et al., 1997). For PV system sizing and design, knowing the device temperature coefficient plays a very critical role. Quantifying the spectral effects on its own has proved to be a challenge; as a result no temperature coefficient with respect to outdoor spectrum has been documented. In figures 11 and 12, the relationship between outdoor spectral effects (WUF) and the average back - of module temperature is presented. Using a linear fit to the data, a spectral temperature coefficient is obtained. Figure 11

illustrates the relationship between WUF and temperature for a winter period.

). One can attribute this discrepancy of the measured data and theory as

Fig. 9. Correlation between aperture efficiency versus outdoor WUF of the CIS module.

CIS device.

0

section ( *WUF A* 

shown in figure 10.

2

4

6

**Efficiency (%)**

8

10

Fig. 10. Average outdoor aperture efficiency as a function of WUF of CIS module for both winter and summer period.

Fig. 11. Relationship between the outdoor WUF and back of module temperature of the CIS module during winter period.

Observing the results in figure 11, two temperature coefficients for WUF are obtained during the winter period. This trend in behavior could have been attributed to the different outdoor weather patterns observed for winter period. Some days even during winter, the outdoor climatic conditions would resemble a typical clear sky summer season, indicated by

Spectral Effects on CIS Modules While Deployed Outdoors 455

The outdoor spectral effects using the Weighted Useful Fraction (WUF) of CIS module was analyzed. Observed was a 17% decrease in the device short - circuit (Isc) current attributed due to a change in season. The change in season (summer/winter) result in the outdoor spectrum to vary by ΔWUF = 1.5%, result in the decrease in the device Isc. From the analysis done, it was concluded that a small percentage change in ΔWUF resulted in large % difference of the module's Isc as the outdoor spectrum changed during the course of the day, which confirmed that the 17% decrease in Isc was due to a ΔWUF of 1.5 %. A strong correlation between FF and the WUF exists for CIS module. It is observed that the FF increases by 6.5% as WUF increases. The temperature coefficient of a device is one of the important concepts for characterizing device performance parameter. A close correlation between WUF and temperature was established. Temperature coefficients for spectral induced effect (WUF) were found to be -0.001/oC for winter period and -4×10-5/oC for summer seasons. This difference in WUFβ for summer and winter indicated that the temperature coefficients obtained in controlled environment (indoor procedure) can not be truly dependable for modeling purposes or system sizing since the outdoor conditions has an effect also. It should also be noted that the temperature coefficient for spectral effect is

Christian NJ, Gottschalg TR, Infield DG, Lane K (2002). Influence of spectral effects on the

Gottschalg TR, Infield DG, Lane K, Kearney MJ (2003) Experimenatal study of variations of

Minemoto T, Toda M, Nagae S, Gotoh M, Nakajima A, Yamamoto K, Takakura H,

M Simon and E.L Meyer (2008). Spectral distribution on photovoltaic module performance

Meyer, E.L, (2002). On the Reliability, Degradation and Failure of Photovoltaic Modules.

King, D.L, Kratochvil JA (1997). Measuring solar spectral and angle-of-incident effects on

Riordan C, Hulstrom R (1990). What is an Air Mass 1.5 spectrum. *20th IEEE Phovoltaic* 

Gottschalg R, Betts TR and Infield DG (2004). On the importance of considering the

Poissant Y, Lorraine C, Lisa DB (2006) (http://www.cete-vareness.nrcan.gc.ca).

modules., *Solar Energy Materials and Solar Cells*, Vol.91, pp. 120-122

performance of multijunction amorphous silicon cells. *Photovoltaic Conference and* 

solar spectrum of relevance to thin film solar cells. *Solar Energy materials and solar* 

Hamakawa Y (2007). Effect of spectral irradiance distribution on the outdoor performance of amorphous Si//thin-film crystalline Si stacked photovoltaic

in South Africa. evaluation for c-Si modules", *33rd IEEE Phovoltaic Specialist* 

photovoltaic modules and solar irradiance sensors. *26th IEEE Phovoltaic Specialist* 

Incident Spectrum when measuring the outdoor performance of amorphous

**5. Conclusion** 

**6. References** 

indeed an important parameter to consider.

*cells*, vol 79, pg 527 – 537.

*Conference,Anaheim,CA,USA*

*Conference*, *San Diego,* California, USA.

*University of Port Elizabeth, PhD-Thesis*, 74-77, 34-38.

*Specialist Conference*, *New York,* pg 1085 – 1088.

*Exhibition*, Rome

very high temperature (indicated by trend 2), while the rest of the days would be for typical winter season, normally characterized by mostly low temperature. In both cases, a negative WUF temperature coefficient is observed, with trend 1 being -0.001/oC and for trend 2 being -0.4×10-5/oC.

The same procedure was also used to find the effect of temperature on WUF for summer months of CIS module. Figure 12 shows the WUF versus temperature relationship.

Interesting to note from figure 12 is that the spectral effect temperature coefficient for summer period is the same as the one obtained during winter, clear sky (trend 2) although for summer the highest temperature reached was above 60oC while for trend 2 (figure 11), the highest was less than 60oC. From the two figures, it has been shown that temperature coefficient due to spectral effect (WUFβ) can be obtained once the outdoor spectrum data for a device is correctly calculated using the Weighted Useful Fraction (WUF) concept. Like other performance parameters, whose temperature coefficients are equally important in PV characterization and system design, the WUF should be also be considered as this might help to minimize some of the system sizing errors, which in most instances lead to under performance, unreliable and financial repercussions.

Fig. 12. Relationship between the outdoor WUF and back of module temperature of the CIS module during summer period.
