The Assessment of Solar PV Module Using RSM Approach

Figure 16a,b show the contour plots of solar PV plants under uncertain conditions. For instance, as depicted in Figure 16a, in case the wind speed is above 2 m per second, and the outdoor temperature is between 30 and 38 ◦C, the PV yield is 28 MWh. Similarly, Figure 16b shows the contour plots of the PV energy yield, when the wind speed is between 3 and 5.5 m per second and the radiation is above 820 W/m2. Figure 16c,d shows the three-dimensional graph called response surface plot of solar PV energy generation versus wind speed, outdoor temperature, and radiation.

The difference of response is not the same at all levels of the factors in some problems. There is an interaction between the factors. Hence, the parallel lines in Figure 17, indicate, approximately, the factors' lack of interaction. Therefore, when Figure 17 is examined, the lines seem not to be parallel. This indicates interaction between the factors. In general, optimal solar PV generation is attained at average module surface temperature, high radiation, wind direction and wind speed level. Changing from low to high module surface temperature and outdoor temperature reduce the PV yield. Changing from intermediate to high degree module surface temperature, and outdoor temperature essentially reduces the PV generation. Figure 18 shows the individual effect of factors on the PV system. Hence, optimal PV generation levels of characteristics were determined and presented in Figure 18. Generating maximum PV of 42.27 MW is possible when the radiation level is 896.3 W/m2, the module surface temperature is 50 ◦C, the outdoor temperature is 40.3 ◦C, the wind direction is 305.6 and the wind speed is 6.7 m/s.

**Figure 13.** The ratio of PV systems meeting the hourly electricity need of the hospital (**a**) 25 MW of PV capacity, (**b**) 35 MW of PV capacity, (**c**) 45 MW of PV capacity.


**Table 1.** Self-sufficiency ratios of PV systems.

**Figure 14.** The annual distribution of electricity generation of PV systems for an average day.

**Figure 15.** Total annual electricity generation of PV systems of different capacities.

**Figure 16.** The contour plot of solar PV generation versus wind speed and outdoor temperature (**a**) and wind speed and radiation (**b**). The three-dimensional graph of solar PV energy generation versus wind speed, outdoor temperature (**c**), and wind speed radiation (**d**).

**Figure 17.** The plots of independent parameter interaction for solar PV generation.

**Figure 18.** The individual effect of factors on solar PV generation system.

Figure 18 clearly shows that the intermediate module surface temperature, and outdoor temperature essentially increase the solar PV generation with high radiation, and wind speed. Hence, the optimal solar PV generation characteristics are determined and presented in Figure 18. When the operation conditions of solar PV are simulated under certain conditions, it was determined that the optimal solar PV of 33.96 MW is obtained if the radiation is 896.3, module surface temperature is 43.4 ◦C, outdoor temperature is 40.3 ◦C, wind direction is 305.9 and the wind speed is 6.7 m/s.

The effect analysis of the main factors *x*1, *x*2, *x*3, *x*<sup>4</sup> and *x*<sup>5</sup> and the interactions *x*1*x*2, *x*1*x*3, *x*1*x*<sup>4</sup> and etc are presented in the regression model. The effects of interactions and main factors showed that four factors positively affect the solar PV generation, only wind direction negatively affected it. Our investigation showed that the coefficients of *x*1*x*2, *x*1, *x*1*x*2, *x*<sup>1</sup> <sup>2</sup> and *x*<sup>1</sup> <sup>2</sup> are very small, hence these interactions can be bounded. The effects of interactions and the main parameters are plotted in Figures 17 and 18, respectively. Four effects are positive in this equation, only wind direction has a negative effect. Hence all main effects are only considered to determine the optimal level and maximize the solar PV level.

#### *4.2. The Assessment of Performance of Developed Models Using ANFIS Approach*

For inferencing and obtaining the outcomes, fuzzy reasoning is used. As appears in Figure 19, fuzzy 'If-Then' rules are used for reasoning procedure, a nine rules ANFIS model was developed for the PV energy generation system. As appears in Figure 16, when the radiation is 249 W/m2, the module surface temperature is 28 ◦C, the outdoor temperature is 31.2 ◦C, the wind direction is 180 and the wind speed is 2.92 m/s, then according to ANFIS approach, the PV module can generate 14.90 MW power.

**Figure 19.** Fuzzy reasoning for PV energy generation system.

For testing the developed RSM and ANFIS models, the randomly selected input data were used to test the methods and to determine how perfectly they can generate and predict the consequences of the parameters. This step covers testing the performance of RSM and ANFIS approaches for the validation of the models. As appears in Table 2, a large amount of data set was utilized to identify the input–output interactions of the model. The findings of the RSM and ANFIS models for certain input factors are presented in Table 2.


**Table 2.** Actual and predicted solar PV generated for certain parameters.

The results and findings showed that the average prediction error of the RSM model was found to be 1.743%. Similarly, the ANFIS models were evaluated with three different numbers of fuzzy rules: five, nine, and eleven rules. It was determined that the ANFIS model with five rules generated 1.96%, the one with nine rules had 0.75%, and the model with eleven rules had 1.16% error level on average. Figure 20 shows the actual solar PV versus predicted solar PV levels for real life data of certain parameters for the RSM and the ANFIS model with nine rules. The results and findings clearly depicted that these ANFIS models can be successfully employed for the performance prediction of solar PV modules. For instance, when the radiation is 573.58 W/m2, the module surface temperature is 48.56 ◦C, the outdoor temperature is 38.70 ◦C, the wind direction is 278.39 and the wind speed is 4.42 m/s, the ANFIS model predicts the PV panels' performance to be 24.96 MW. Similarly, it is also predicted by the ANFIS approach that the PV module can generate 41.19 MW power when the radiation is 750 W/m2, the module surface temperature is 25 ◦C, the outdoor temperature is 20 ◦C, the wind direction is 250 and the wind speed is 12.43 m/s.

**Figure 20.** The comparison of actual and predicted solar PV generation model outcomes.
