# Thermal Effects on Photovoltaic Array Performance: Experimentation, Modeling, and Simulation
## 5 Results
### Experimental Results
Furthermore, looking at the energy balance shown in Equation (2), the rate at which heat is lost to the environment is directly proportional to the temperature difference between the array temperature and ambient temperature. As wind velocity increases, the temperature difference decreases, somewhat linearly. It also illustrates the importance of air flow in producing a change in temperature difference, which will significantly affect array efficiency. In addition to wind speed, wind direction has been shown in previous work [13, 14, 24] as an important variable of interest in PV cooling. We compiled experimental data and plotted array and ambient temperature difference with wind direction in Figure 8. It shows that for this case, wind direction does not significantly affect heat transfer and does not affect the overall performance of the array. Thus, it is a fair assumption to neglect wind direction in determining the thermal loss factor/heat transfer coefficient. It is well known that ambient temperature has a significant effect on PV performance, and this is shown in Figure 9. As ambient temperature becomes warmer, the efficiency declines. Figure 6: Efficiency vs. array temperature at different wind speeds. The red line is the theoretical efficiency line provided by the manufacturer using Equation (1). Figure 8: Wind speed vs. temperature difference between ambient and array. Figure 7: Wind speed vs. temperature difference between ambient and array. Figure 9: Relationship between PV array efficiency and ambient temperature. Figure 10 shows the relationship between electrical efficiency and ambient temperatures at wind speeds of 0, 3, 4, and 5 m/s. These speeds were chosen due to completeness of data, and these plots illustrate the variation in efficiency at ambient temperatures between 6 and 35 \({}^{\circ}\)C. We can clearly observe the dependence of PV efficiency with ambient temperature in all wind speeds, with increasing ambient temperature, leading to decreasing PV efficiency. At 0 m/s, the mean efficiency is between 13.2% and 14.1% in the range of 15 and 28 \({}^{\circ}\)C, or \(-0.09\%/^{\circ}\)C. At 3 m/s, the mean efficiency lies between 12.7% and 14.3% in the range of 13 and 35 \({}^{\circ}\)C, or \(-0.07\%/^{\circ}\)C. At 4 m/s, the mean efficiency lies between 13.5% and 14.7% in the range of 7 and 33 \({}^{\circ}\)C, or \(-0.046\%/^{\circ}\)C. At 5 m/s, the mean efficiency lies between 13.4% and 14% in the range of 18 and 30 \({}^{\circ}\)C, or \(-0.05\%/^{\circ}\)C. This means that, as wind speed increases, we observe that the average slope of efficiency and ambient temperature decreases. Additionally, when wind speed increases, the thermal loss factor/heat transfer coefficient increases, and the temperature difference between array and ambient decreases. The PV efficiency data were also compiled and plotted against wind speed, shown in Figure 11 as a box plot. As velocity increases from <1.5 to 5.5 m/s, we see the mean efficiency increase from 13.2% to 13.8%, or approximately a 5% increase in relative efficiency. Thus, wind effects should be part of the design consideration. Based on these observations, it is important to note that interactions between building structures and  
Figure 10: Efficiency vs. temperature at different wind speeds. wind can significantly affect the air flow. Thus, PV engineers should take these effects into account when selecting the location of PV array, similar to that of a small wind turbine site assessment. Onsite wind resource measurements should be conducted for a minimum of one year using anemometers, wind vanes, and temperature sensors that are mounted as close to the location where PV arrays will be placed [25; 26].