Development of a Predictive Model for a Photovoltaic Module’s Surface Temperature

: PV (photovoltaic) systems are receiving the spotlight in Korea due to the Renewable Energy 3020 Implementation Plan (RE3020), which has the goal of reaching 20% for the proportion of renewable energy generation by 2030. Accordingly, the actual performance evaluation of PV systems to achieve the RE3020 has become more important. PV e ﬃ ciency is mainly determined by various weather conditions (e.g., solar radiation) that a ﬀ ect the power generation of PV systems. However, the e ﬃ ciency is also a ﬀ ected by changes in module surface temperature. In particular, the e ﬃ ciency decreases when the module surface temperature rises. That is, the actual PV e ﬃ ciency falls short of the rated e ﬃ ciency. The estimation of module surface temperature is critical for evaluating the actual performance of PV systems. Many studies have been conducted to calculate the surface temperature. However, most of the previous studies focused on calculations of current surface temperatures using current environment data, which means that the previous studies have limitations related to timestep. That is, there is a lack of predictive models that calculate the future surface temperatures by using the current measured data. Therefore, this study developed a predictive model using an ANN (artiﬁcial neural network) algorithm to determine the surface temperature of PV modules for a future period of time. Then, this study evaluated the actual performance (i.e., power generation) with the predicted surface temperatures.


Introduction
Korea began implementing energy conservation design standards for buildings in 2008 to promote efficient energy management for buildings [1]. The standards were revised in 2018, and Korea was divided into four regions (Central 1, Central 2, Southern, and Jeju Island). The heat transmission coefficient standards for each region were also strengthened in the same year. Accordingly, various standards and laws are being implemented for efficient building energy management. Despite these efforts, the electricity supply and demand trend surpassed 90 million GW in Korea for the first time in 2018 [2]. As a result, renewable energy sources are receiving the spotlight for energy conservation and stable power supply in buildings.
Renewable energy sources include solar, wind, and geothermal power. Among these sources, PV (photovoltaic) systems are widely used because they are easy to use and install, unlike wind and geothermal power. In 2017, the Ministry of Trade, Industry, and Energy reported that PV systems will account for more than 57% of the total renewable energy in Korea by 2030 [3]. Accordingly, PV systems that provide small-footprint installation and distributed power generation are attracting attention

Methodology
This study developed an ANN-based predictive model using the Neural Network (NN) toolbox in MATLAB [25]. An ANN provides more accurate predictions because it is more adaptable to external changes than are mathematical control models. The developed model was trained by using the Levenberg-Marquardt algorithm (LMA) [26], and six types of measured data (ambient temperature, wind speed, solar radiation, relative humidity, cloud cover, and module surface temperature) were used as the dataset. Seventy percent of the dataset (January 2018-December 2018) was used for training, 15% for validation, and the remaining 15% for the test process. The dataset was composed of hourly data, and Table 2 shows the dataset parameters and value ranges. The measured data of the dataset were collected from a 10 kW rooftop PV installed on Building A in Daejeon (see Figure 1). Tables 3 and 4 show the system and sensor specifications. In terms of the wind speed, relative humidity, Energies 2020, 13, 4005 5 of 18 and cloud cover, this study used data measured in Daejeon (2018) from the KMA (Korea meteorological administration) open data portal [27]. The final predictive model was developed through the process of developing and optimizing the initial model.

Methodology
This study developed an ANN-based predictive model using the Neural Network (NN) toolbox in MATLAB [25]. An ANN provides more accurate predictions because it is more adaptable to external changes than are mathematical control models. The developed model was trained by using the Levenberg-Marquardt algorithm (LMA) [26], and six types of measured data (ambient temperature, wind speed, solar radiation, relative humidity, cloud cover, and module surface temperature) were used as the dataset. Seventy percent of the dataset (January 2018-December 2018) was used for training, 15% for validation, and the remaining 15% for the test process. The dataset was composed of hourly data, and Table 2 shows the dataset parameters and value ranges. The measured data of the dataset were collected from a 10 kW rooftop PV installed on Building A in Daejeon (see Figure 1). Tables 3 and 4 show the system and sensor specifications. In terms of the wind speed, relative humidity, and cloud cover, this study used data measured in Daejeon (2018) from the KMA (Korea meteorological administration) open data portal [27]. The final predictive model was developed through the process of developing and optimizing the initial model.

Overall Study Process
The purpose of this study was to develop a predictive model for PV module surface temperatures to analyze the module surface temperature, efficiency, and power generation. Figure 2 shows the overall study process. The initial predictive model was developed by using a dataset that went through an optimization process. The optimized model then went through a validation process. The model was validated based on ASHRAE (American Society of Heating, Refrigerating and Air-Conditioning Engineers) Guideline 14 [29]. The ASHRAE Guideline 14 was developed to provide standardized guidelines for reliably measuring the energy, demand, and water savings achieved in conservation projects. According to ASHRAE Guideline 14, the accuracy of a predictive model using hourly data must satisfy R 2 > 0.75 and cvRMSE (coefficient of variation of the root mean squared error) < 30%. Finally, this study used the developed model to predict module surface temperatures and analyze the efficiency and power generated by the PV system accordingly.

Development Process of the ANN Model
This study developed a predictive model to calculate PV module surface temperatures for a next timestep using the current measured data. The predictive model was based on the theory of the

Development Process of the ANN Model
This study developed a predictive model to calculate PV module surface temperatures for a next timestep using the current measured data. The predictive model was based on the theory of the artificial neural networks (ANN), which simulates the way the human brain analyzes information. Artificial intelligence (AI) has been receiving more attention since it can model complex behavior that traditional engineering methods cannot model. Among the various ANN techniques, this study used the Levenberg-Marquardt algorithm (LMA), which is available in MATLAB software, to develop a predictive model using ANN [26]. The LMA was developed in the early 1960s to resolve nonlinear least squares curve-fitting problems. It is known as a hybrid technique using both the gradient descent method and the Gauss-Newton method to converge to an optimal solution.
The predictive model of this study was developed through three steps: (1) initial model development, (2) initial model optimization, and (3) optimized model validation (see Figure 3).

Results of the ANN Model
This section describes how the predictive model was developed and explains how it was structured according to the development process. Min-max normalization was used to reflect the input data for training on the same scale. However, this study normalized values between 0.1 and 0.9 to prevent returning 0 and 1 [30]. This is because 0 and 1 may have adverse effects on the prediction. The min-max normalization algorithm shown in Equation (1) was used in this study. The model was used to predict and calculate the module surface temperature, efficiency, and power generation.
where is the normalized data, is the previous data, ( ) is the minimum value of previous data, and ( ) is the maximum value of previous data [30].
In addition, the predictive model was optimized by evaluating the accuracy by using cvRMSE. Equations (2) and (3) are the RMSE and cvRMSE algorithms, respectively [28].
where is the predicted data, is the measured data, is the number of measured data points, and is the average of the measurement period [28].

Development of an Initial ANN Model
This study developed an initial predictive model using the dataset. The initial model consisted of NHN (=13) and NHL (=1), and the LR (learning rate) and MC (momentum constant) were both set to 0.3 (see Figure 4). Random variables were set by referring to the study by Moon (2015) [30]. The input data consisted of the outdoor air temperature (OA), wind speed (WS), solar radiation (SR), relative humidity (RH), and cloud cover (CC), and the output was the module surface temperature. As a result of developing the predictive model, the cvRMSE of the initial model was 22.00% and satisfied the criteria recommended in ASHRAE Guideline 14. Then, the initial model was optimized The first step was developing an initial predictive model. The initial predictive model was developed by setting a random NHN (number of hidden neurons) and NHL (number of hidden layers).
The second step was optimizing the initial predictive model. The NHN and NHL were re-determined to ensure the predictive performance of the initial model. The R 2 value and cvRMSE were analyzed, and the variables (NHN, NHL) with the highest accuracy that also satisfied the reference values required by ASHRAE Guideline 14 were used to optimize the model.

Results of the ANN Model
This section describes how the predictive model was developed and explains how it was structured according to the development process. Min-max normalization was used to reflect the input data for training on the same scale. However, this study normalized values between 0.1 and 0.9 to prevent returning 0 and 1 [30]. This is because 0 and 1 may have adverse effects on the prediction. The min-max normalization algorithm shown in Equation (1) was used in this study. The model was used to predict and calculate the module surface temperature, efficiency, and power generation.
where X new is the normalized data, X is the previous data, min(x) is the minimum value of previous data, and max(x) is the maximum value of previous data [30].
In addition, the predictive model was optimized by evaluating the accuracy by using cvRMSE. Equations (2) and (3) are the RMSE and cvRMSE algorithms, respectively [28].
Energies 2020, 13, 4005 where S is the predicted data, M is the measured data, N interval is the number of measured data points, and A period is the average of the measurement period [28].

Development of an Initial ANN Model
This study developed an initial predictive model using the dataset. The initial model consisted of NHN (=13) and NHL (=1), and the LR (learning rate) and MC (momentum constant) were both set to 0.3 (see Figure 4). Random variables were set by referring to the study by Moon (2015) [30]. The input data consisted of the outdoor air temperature (OA), wind speed (WS), solar radiation (SR), relative humidity (RH), and cloud cover (CC), and the output was the module surface temperature. As a result of developing the predictive model, the cvRMSE of the initial model was 22.00% and satisfied the criteria recommended in ASHRAE Guideline 14. Then, the initial model was optimized to more accurately evaluate predictive performance.

Optimization of the Initial ANN Model
The initial model went through an optimization process. The cvRMSE was evaluated by changing the NHN and NHL. The optimization process was performed by changing the NHN from 8 to 18 and the NHL from 1 to 5. Table 5 shows the optimization results. After the optimization process, the model showed the highest accuracy (cvRMSE = 19.81%) when NHN =16 and NHL =5, and it satisfied the criteria specified in ASHRAE Guideline 14. The optimized model's accuracy improved by about 2.19% compared to that of the initial model. Figure 5 shows a diagram of the optimized predictive model.

Optimization of the Initial ANN Model
The initial model went through an optimization process. The cvRMSE was evaluated by changing the NHN and NHL. The optimization process was performed by changing the NHN from 8 to 18 and the NHL from 1 to 5. Table 5 shows the optimization results. After the optimization process, the model showed the highest accuracy (cvRMSE = 19.81%) when NHN = 16 and NHL = 5, and it satisfied the criteria specified in ASHRAE Guideline 14. The optimized model's accuracy improved by about 2.19% compared to that of the initial model. Figure 5 shows a diagram of the optimized predictive model.

Validation of the Optimized ANN Model
The validation step was performed to confirm the applicability of the optimized predictive model. The output and errors of the training, validation, and test datasets were checked to confirm validation. Figure 6 shows the error (MSE; mean squared error). The MSE of the X-axis is the error and the epochs of the Y-axis are the points at which iterative training stops. Figure 7 shows the result of the regression analysis on the optimized predictive model. The target of the X-axis is the measured data and the output of the Y-axis is the output of the predictive model.
As a result of error analysis, iterative training stopped after 16 iterations. The predictive performance showed the best validation performance in the 10th iteration. The error characteristics of the training, validation, and test datasets also showed similar patterns. This shows that the optimized predictive model will provide high accuracy.
In terms of the regression analysis results, the R 2 value was 0.97 for training, 0.97 for validation, 0.96 for test, and 0.97 overall. This shows that the optimized predictive model will predict the measured data with high accuracy.

Validation of the Optimized ANN Model
The validation step was performed to confirm the applicability of the optimized predictive model. The output and errors of the training, validation, and test datasets were checked to confirm validation. Figure 6 shows the error (MSE; mean squared error). The MSE of the X-axis is the error and the epochs of the Y-axis are the points at which iterative training stops. Figure 7 shows the result of the regression analysis on the optimized predictive model. The target of the X-axis is the measured data and the output of the Y-axis is the output of the predictive model.

Validation of the Optimized ANN Model
The validation step was performed to confirm the applicability of the optimized predictive model. The output and errors of the training, validation, and test datasets were checked to confirm validation. Figure 6 shows the error (MSE; mean squared error). The MSE of the X-axis is the error and the epochs of the Y-axis are the points at which iterative training stops. Figure 7 shows the result of the regression analysis on the optimized predictive model. The target of the X-axis is the measured data and the output of the Y-axis is the output of the predictive model.
As a result of error analysis, iterative training stopped after 16 iterations. The predictive performance showed the best validation performance in the 10th iteration. The error characteristics of the training, validation, and test datasets also showed similar patterns. This shows that the optimized predictive model will provide high accuracy.
In terms of the regression analysis results, the R 2 value was 0.97 for training, 0.97 for validation, 0.96 for test, and 0.97 overall. This shows that the optimized predictive model will predict the measured data with high accuracy.

Results Analysis and Discussion
This section discusses the analysis of the module surface temperatures predicted by the optimized model and the efficiency and power generation calculated using the predicted module surface temperatures. The calculated power generation was analyzed by comparing it with the actual power generation data.

Module Surface Temperature
The accuracy of the predicted module surface temperatures was evaluated by comparing them with the measured module surface temperatures. The module surface temperature analysis was performed in the daytime with solar radiation and also in the nighttime without solar radiation. Figure 8 shows the distribution of module surface temperatures and cvRMSE by each month. In the figure, the Min, 25%, Mid, 75%, and Max refer to the minimum, 25% (first quartile value), median, 75% (third quartile value), and maximum values, respectively. As a result of error analysis, iterative training stopped after 16 iterations. The predictive performance showed the best validation performance in the 10th iteration. The error characteristics of the training, validation, and test datasets also showed similar patterns. This shows that the optimized predictive model will provide high accuracy.
In terms of the regression analysis results, the R 2 value was 0.97 for training, 0.97 for validation, 0.96 for test, and 0.97 overall. This shows that the optimized predictive model will predict the measured data with high accuracy.

Results Analysis and Discussion
This section discusses the analysis of the module surface temperatures predicted by the optimized model and the efficiency and power generation calculated using the predicted module surface temperatures. The calculated power generation was analyzed by comparing it with the actual power generation data.

Module Surface Temperature
The accuracy of the predicted module surface temperatures was evaluated by comparing them with the measured module surface temperatures. The module surface temperature analysis was performed in the daytime with solar radiation and also in the nighttime without solar radiation. Figure 8 shows the distribution of module surface temperatures and cvRMSE by each month. In the figure, the Min, 25%, Mid, 75%, and Max refer to the minimum, 25% (first quartile value), median, 75% (third quartile value), and maximum values, respectively.
In terms of the distribution of predicted module surface temperatures for the daytime, the cvRMSE was about 18% and satisfied ASHRAE Guideline 14. The 25~75% values of the annual module surface temperature showed a distribution of about 15 • C~38 • C. The accuracy of module surface temperature for winter (January, February, and December) was relatively low. On the other hand, the cvRMSE was about 12~26% for the rest of the year (March-November) and satisfied the criteria specified in ASHRAE Guideline 14.  In terms of the distribution of predicted module surface temperatures for the daytime, the cvRMSE was about 18% and satisfied ASHRAE Guideline 14. The 25~75% values of the annual module surface temperature showed a distribution of about 15 °C~38 °C. The accuracy of module surface temperature for winter (January, February, and December) was relatively low. On the other hand, the cvRMSE was about 12~26% for the rest of the year (March-November) and satisfied the criteria specified in ASHRAE Guideline 14.
In terms of the distribution of the predicted module surface temperatures for the nighttime, the cvRMSE was about 12% and satisfied ASHRAE Guideline 14. The 25~75% values of the annual In terms of the distribution of the predicted module surface temperatures for the nighttime, the cvRMSE was about 12% and satisfied ASHRAE Guideline 14. The 25~75% values of the annual module surface temperature showed a distribution of about 0 • C~19 • C. Unlike the daytime value, the cvRMSE ranged from 4% to 26% and satisfied ASHRAE Guideline 14 during all periods except the months of February and December. The predictive performance of the annual module surface temperature for the nighttime was about 6% higher than that of the daytime and about 8% higher than that of the entire period.
Therefore, the developed model was able to predict the module surface temperatures for the entire period, daytime, and nighttime, among which the predictive performance for nighttime was considered the best.
As mentioned above, the accuracy of predicting the module surface temperatures for winter was relatively low. However, the trend of predicted module surface temperature needs to be examined because the results derived from cvRMSE evaluation are numerical indicators. Figure 9 shows graphs comparing the predicted module surface temperatures with the measured data. entire period, daytime, and nighttime, among which the predictive performance for nighttime was considered the best.
As mentioned above, the accuracy of predicting the module surface temperatures for winter was relatively low. However, the trend of predicted module surface temperature needs to be examined because the results derived from cvRMSE evaluation are numerical indicators. Figure 9 shows graphs comparing the predicted module surface temperatures with the measured data. Figure 9a compares the hourly module surface temperatures for winter (January). The cvRMSE results show that the predictive performance for January was low but relatively similar to the measured data. Figure 9b compares the hourly module surface temperatures for summer (August). The predicted module temperatures were also similar to the measured data. Figure 9c shows a graph comparing the hourly module surface temperature for the year 2018. The predicted data were similar to the measured data. The predictive model's R 2 was 0.9536 and predicted the measured data with high accuracy. The results show that the model has excellent performance in predicting module surface temperature.

Module Efficiency according to the Module Surface Temperature
The results in Section 5.1 show that the developed model has excellent predictive performance. Based on this, the predictive model is expected to show high performance in calculating power generation. As noted in the introduction, the module surface temperature affects the efficiency and  Figure 9a compares the hourly module surface temperatures for winter (January). The cvRMSE results show that the predictive performance for January was low but relatively similar to the measured data. Figure 9b compares the hourly module surface temperatures for summer (August). The predicted module temperatures were also similar to the measured data. Figure 9c shows a graph comparing the hourly module surface temperature for the year 2018. The predicted data were similar to the measured data. The predictive model's R 2 was 0.9536 and predicted the measured data with high accuracy. The results show that the model has excellent performance in predicting module surface temperature.

Module Efficiency According to the Module Surface Temperature
The results in Section 5.1 show that the developed model has excellent predictive performance. Based on this, the predictive model is expected to show high performance in calculating power generation. As noted in the introduction, the module surface temperature affects the efficiency and power generation of PV systems. In particular, the efficiency of PV systems decreases as the module surface temperature increases. Therefore, this section calculates and evaluates power generation efficiency by reflecting the predicted module surface temperature. The power generation efficiency of PV modules is calculated as shown in Equation (4) [4].
where η m is the actual module efficiency (%), η re f is the rated efficiency (%), β is the temperature coefficient ( • C −1 ), T m is the module surface temperature ( • C), and T re f is the reference temperature of the rated efficiency ( • C). This study used 0.0045 • C −1 for β and 25 • C for T re f , which are typical general electrical characteristics at STC (standard test conditions) [4]. Figure 10 shows a graph of the PV system power generation efficiency according to the module surface temperature. The bar graphs with the data label indicate solar radiation in W/m 2 . The analysis was based on the days when the module surface temperature was highest during winter and summer (February 26 and August 1), where the rated efficiency of the PV system is 15.89% (see Table 2).

Module Efficiency according to the Module Surface Temperature
The results in Section 5.1 show that the developed model has excellent predictive performance. Based on this, the predictive model is expected to show high performance in calculating power generation. As noted in the introduction, the module surface temperature affects the efficiency and power generation of PV systems. In particular, the efficiency of PV systems decreases as the module surface temperature increases. Therefore, this section calculates and evaluates power generation efficiency by reflecting the predicted module surface temperature. The power generation efficiency of PV modules is calculated as shown in Equation (4) where is the actual module efficiency (%), is the rated efficiency (%), is the temperature coefficient (°C 1 ), is the module surface temperature (°C), and is the reference temperature of the rated efficiency (°C). This study used 0.0045 °C −1 for and 25 °C for , which are typical general electrical characteristics at STC (standard test conditions) [4]. Figure 10 shows a graph of the PV system power generation efficiency according to the module surface temperature. The bar graphs with the data label indicate solar radiation in W/m 2 . The analysis was based on the days when the module surface temperature was highest during winter and summer (February 26 and August 1), where the rated efficiency of the PV system is 15.89% (see Table 2).  In winter, the actual efficiency was between 14.7% and 18.2%. The actual efficiency decreased as the module surface temperature increased. It also changed in inverse proportion to the module surface temperature. In particular, the actual efficiency was lower than the rated efficiency from 12:00 to 16:00 when solar radiation is concentrated. When the module surface temperature rose to 41.7°C, the actual efficiency was about 14.7%, 1.2% lower than the rated efficiency. When there was no or low solar radiation in winter, the actual efficiency was about 2.4% higher than the rated efficiency. In summer, the actual efficiency was between 13.1% and 15.9%. Similar to winter, the actual efficiency decreased as the module surface temperature increased. When the module surface temperature rose to 64.4°C, the actual efficiency was about 13.1%, 2.7% lower than the rated efficiency. These results show that the efficiency decreases as the module surface temperature increases.

Electricity Power Generation
According to the analysis results in Section 5.2, the module efficiency changes according to the module surface temperature. In particular, the module efficiency decreased as the module surface temperature increased. This is consistent with the results of previous studies [4][5][6][7]. Therefore, this study evaluated the effect of the changed efficiency on power generation. Equation (5) shows how to calculate the power generation [10].
where is the actual module power generation (W), is the module surface area (m 2 ), is the solar radiation (W/m 2 ), and is the actual module efficiency (%) [10]. Figure 11 shows the amount of power generated by the PV system. Figure 11a,b shows the power generated during the periods analyzed in Section 5.2, and Figure 11c shows the annual cumulative power generation. In terms of power generation, this study compared the measured data (actual), the data without considering module surface temperature (i.e., W/O Tm), and the data considering module surface temperature (i.e., W/Tm). In winter, the actual efficiency was between 14.7% and 18.2%. The actual efficiency decreased as the module surface temperature increased. It also changed in inverse proportion to the module surface temperature. In particular, the actual efficiency was lower than the rated efficiency from 12:00 to 16:00 when solar radiation is concentrated. When the module surface temperature rose to 41.7 • C, the actual efficiency was about 14.7%, 1.2% lower than the rated efficiency. When there was no or low solar radiation in winter, the actual efficiency was about 2.4% higher than the rated efficiency. In summer, the actual efficiency was between 13.1% and 15.9%. Similar to winter, the actual efficiency decreased as the module surface temperature increased. When the module surface temperature rose to 64.4 • C, the actual efficiency was about 13.1%, 2.7% lower than the rated efficiency. These results show that the efficiency decreases as the module surface temperature increases.

Electricity Power Generation
According to the analysis results in Section 5.2, the module efficiency changes according to the module surface temperature. In particular, the module efficiency decreased as the module surface temperature increased. This is consistent with the results of previous studies [4][5][6][7]. Therefore, this study evaluated the effect of the changed efficiency on power generation. Equation (5) shows how to calculate the power generation [10].
where P m is the actual module power generation (W), A m is the module surface area (m 2 ), G T is the solar radiation (W/m 2 ), and η m is the actual module efficiency (%) [10]. Figure 11 shows the amount of power generated by the PV system. Figure 11a,b shows the power generated during the periods analyzed in Section 5.2, and Figure 11c shows the annual cumulative power generation. In terms of power generation, this study compared the measured data (actual), the data without considering module surface temperature (i.e., W/O T m ), and the data considering module surface temperature (i.e., W/T m ).
As a result of analyzing the power generation in winter, the maximum power generated per hour of W/O T m and W/T m were 9.1 kW and 8.4 kW, respectively. W/T m was similar to the actual amount of power generated. In addition, W/ T m was similar to the actual power generation between 13:00 and 16:00 when there was high solar radiation. On the other hand, W/T m was higher than W/O T m between 10:00-11:00 and 17:00-18:00. This is due to the results (increased efficiency) of Figure 10a.
In terms of the daily cumulative power generation, actual (45 kW) was about 18% lower than W/O T m (53 kW) and 4% lower than W/T m (51 kW). As a result of analyzing the power generation in winter, the maximum power generated per hour of W/O Tm and W/Tm were 9.1 kW and 8.4 kW, respectively. W/Tm was similar to the actual amount of power generated. In addition, W/ Tm was similar to the actual power generation between   Figure 11. Electricity power generation according to improvement of the module efficiency.
As a result of analyzing the power generation in summer, the maximum power generated per hour of W/O T m and W/T m were 9.3 kW and 7.7 kW, respectively. The power generation of W/T m was similar to the actual amount of power generated. In contrast to winter, W/T m was always lower than W/O T m in terms of the power generated in summer. In the case of the daily cumulative power generation, actual (48 kW) was about 44% lower than W/O T m (69 kW) and W/T m (60 kW) was about 15% lower than W/O T m .
The annual cumulative power generation was 10,984 kW for actual, 11,691 kW for W/O T m , and 11,341 kW for W/ T m . In terms of power generation, actual was about 707 kW lower than W/O T m and W/T m was about 350 kW lower than W/O T m . In terms of relative error, the power generation of W/T m considering module surface temperature was about 50.5% lower than that of W/O T m without considering module surface temperature. These results show that considering the module surface temperature is advantageous for calculating the power generation more accurately. These results will help calculate system capacity and prevent overdesign in the future.

Summary and Conclusions
In general, PV efficiency is determined by weather conditions and affects the amount of power generated. PV efficiency changes according to not only solar radiation but also to module surface temperature. In particular, the efficiency decreases as the module surface temperature rises. Therefore, analyzing the module surface temperature is an essential process in the evaluation of the performance of PV systems.
Therefore, this study developed a predictive model for module surface temperatures to analyze the efficiency and power generation according to module surface temperatures. Unlike conventional methods, the developed model predicts the module surface temperature of the next hour using data from the previous hour. This model uses ANN. Based on the analysis of the results, the findings of this study are as follows.

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The initial predictive model consisted of NHN = 13, NHL = 1, LR 0.3, and MC 0.3. The model's cvRMSE was 22.00%. However, the predictive model's accuracy was improved through an optimization process. The optimized predictive model showed the highest accuracy when NHN = 16, NHL = 5, LR 0.3, and MC 0.3. Under this configuration, the cvRMSE was 19.81%, an improvement of 2.19% over the initial predictive model. This model satisfied the recommendations specified in ASHRAE Guideline 14. In terms of the regression analysis results, the R 2 value of the optimized predictive model was 0.97 for training, 0.97 for validation, 0.96 for test, and 0.97 overall. This shows that the optimized predictive model has high accuracy.

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The accuracy of module surface temperatures was higher during the nighttime than the daytime and higher in the summer than in winter. As a result of evaluating the annual cvRMSE, the daytime cvRMSE was about 18% and the nighttime cvRMSE was 12%. These results also satisfied the criteria specified in ASHRAE Guideline 14. In addition, the R 2 value of the predicted annual module surface temperature was 0.95 when compared to the measured data. The model predicted the actual data with high accuracy. This shows that the developed model has high predictive performance.

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As a result of analyzing efficiency according to module surface temperature changes, the efficiency decreased as the module surface temperature increased. When the module surface temperature rose during winter, the actual efficiency was about 14.7%, 1.2% lower than the rated efficiency. When the module surface temperature rose to 64.4 • C in the summer, the actual efficiency was about 13% and 2.7% lower than the rated efficiency. These results show that the module surface temperature may have adverse effects on the actual PV efficiency.

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In terms of annual power generation, W/T m considering module surface temperature was closer to the measured power generation than W/O T m without considering module surface temperature.
In the case of relative error, W/T m was about 50.5% lower than W/O T m . That is, W/Tm was closer to the actual amount of power generated. These results will help calculate system capacity and prevent overdesign in the future.
This study can help to estimate the module surface temperature, efficiency, and power generation. The predictive model developed in this study has the potential to improve the performance of PV systems. However, this model limited the number of input variables to five. This study assumed and considered that these five variables would have the greatest effect on module surface temperature, but other variables may affect the performance of PV systems. Therefore, further research should consider additional input variables that may affect the performance of PV systems. If various other input variables are further considered, this model will predict the performance of PV systems with higher accuracy.