An Improved Approach to Enhance Training Performance of ANN and the Prediction of PV Power for Any Time-Span without the Presence of Real-Time Weather Data

: In this work, an improved approach to enhance the training performance of an Artiﬁcial Neural Network (ANN) for prediction of the output of renewable energy systems is proposed. Using the proposed approach, a signiﬁcant reduction of the Mean Squared Error (MSE) in training performance is achieved, speciﬁcally from 4.45 × 10 − 7 to 3.19 × 10 − 10 . Moreover, a simpliﬁed application of the already trained ANN is introduced through which photovoltaic (PV) output can be predicted without the availability of real-time current weather data. Moreover, unlike the existing prediction models, which ask the user to apply multiple inputs in order to forecast power, the proposed model requires only the set of dates specifying forecasting period as the input for prediction purposes. Moreover, in the presence of the historical weather data this model is able to predict PV power for different time spans rather than only for a ﬁxed period. The prediction accuracy of the proposed model has been validated by comparing the predicted power values with the actual ones under different weather conditions. To calculate actual power, the data were obtained from the National Renewable Energy Laboratory (NREL), USA and from the Universiti Teknologi Malaysia (UTM), Malaysia. It is envisaged that the proposed model can be easily handled by a non-technical user to assess the feasibility of the photovoltaic solar energy system before its installation.


Introduction
Solar photovoltaic (PV) modules of various sizes have been commercialized due to their potential long term economic and environmental benefits [1][2][3][4]. The prospects of PV are enhanced by continuous price reduction in the modules and inverter. However, like most sustainable energy sources, its availability is intermittent due to varying weather conditions [2,[5][6][7][8][9][10][11][12][13]. It is established that PV power depends on various complex weather conditions like temperature, radiation, wind speed, dust and humidity. To handle these kinds of complexities and to provide accurate predictions, development of authentic as well as practical prediction models is extremely significant [14]. Moreover, in order to standard FFBP neural network to be the best choice for the PV prediction model, which is not true according to the most recent research [40][41][42].
In view of these shortcomings, a bayesian regulation backpropagation neural network with multiple hidden layers is proposed in this paper to overcome the highlighted problems. The proposed work needs no normalization and denormalization steps before or after training of the ANN, which simplifies the model. Moreover, unlike the previous work where five years data were considered for training purposes [23], one year's data is used here for both training and testing of the ANN, while achieving better training performance in terms of reduced MSE. Using these data, PV power is calculated with the help of the single diode model and Newton Raphson Method. For better training performance, the ANN is provided with two sets of inputs. The first set of inputs consists of the weather parameters in their original fluctuating form. The second set of inputs comprises the smooth values (obtained by applying a moving average) of the most fluctuating parameters. Application of the moving average removes short-term variation from the data [43,44], and thus helps the ANN to be trained accurately.
It is worth mentioning that almost all existing prediction models require the same number of inputs at the time of prediction as were applied while training the ANN. Consequently, the user is unable to predict PV power without having current real-time weather data. To overcome this shortcoming, the proposed model can be simply used for PV power prediction (for various time spans) by applying a set of dates as the only input by the user. This model is configured in such a way that the remaining inputs required by the already-trained network are automatically extracted from the existing database (having historical weather parameters) instead of real-time current weather parameters, as per the user-applied dates. Thus, the contributions of this work are summarized as:

•
Improving the training performance of the ANN • Prediction of PV power without real-time current weather data • Model needs only the set of dates for prediction from the user • Proposed model can predict PV power for various time spans The rest of the paper is organized as follows: In the second section, a PV single diode model to calculate the module's output power is presented. The third section explains the overall methodology. In the fourth section, the results and discussion are presented. Lastly, conclusions and possibilities for future work are provided.

PV Diode Model for Power Prediction
The most commonly used model to calculate power production by PV cell is the single diode equivalent circuit [1,45,46]. Due to its non-ideal structure in nature, there are some losses which occur in real PV cells. These losses are expressed by series (R s ) and parallel (R sh ) resistances in equivalent circuits, as shown in Figure 1 [47][48][49][50].
the ANN, while normally it is not feasible to get data for such a long period; and considers a standard FFBP neural network to be the best choice for the PV predic model, which is not true according to the most recent research [40][41][42].
In view of these shortcomings, a bayesian regulation backpropagation neural work with multiple hidden layers is proposed in this paper to overcome the highlig problems. The proposed work needs no normalization and denormalization steps be or after training of the ANN, which simplifies the model. Moreover, unlike the prev work where five years data were considered for training purposes [23], one year's da used here for both training and testing of the ANN, while achieving better training formance in terms of reduced MSE. Using these data, PV power is calculated with the of the single diode model and Newton Raphson Method. For better training performa the ANN is provided with two sets of inputs. The first set of inputs consists of the wea parameters in their original fluctuating form. The second set of inputs comprises smooth values (obtained by applying a moving average) of the most fluctuating para ters. Application of the moving average removes short-term variation from the [43,44], and thus helps the ANN to be trained accurately.
It is worth mentioning that almost all existing prediction models require the s number of inputs at the time of prediction as were applied while training the ANN. sequently, the user is unable to predict PV power without having current realweather data. To overcome this shortcoming, the proposed model can be simply use PV power prediction (for various time spans) by applying a set of dates as the only i by the user. This model is configured in such a way that the remaining inputs require the already-trained network are automatically extracted from the existing database ( ing historical weather parameters) instead of real-time current weather parameters, a the user-applied dates. Thus, the contributions of this work are summarized as: • Improving the training performance of the ANN • Prediction of PV power without real-time current weather data • Model needs only the set of dates for prediction from the user • Proposed model can predict PV power for various time spans The rest of the paper is organized as follows: In the second section, a PV single d model to calculate the module's output power is presented. The third section explain overall methodology. In the fourth section, the results and discussion are presen Lastly, conclusions and possibilities for future work are provided.

PV Diode Model for Power Prediction
The most commonly used model to calculate power production by PV cell is the gle diode equivalent circuit [1,45,46]. Due to its non-ideal structure in nature, there some losses which occur in real PV cells. These losses are expressed by series (Rs) parallel (Rsh) resistances in equivalent circuits, as shown in Figure 1 [47][48][49][50]. By applying Kirchhoff's law, the output current I will be obtained by Equatio [49]: By applying Kirchhoff's law, the output current I will be obtained by Equation (1) [49]: where I L is photo current, i.e., current generated by the incidence of light, I D is diode current and I sh is leakage current in shunt resistor. Photo current can be obtained by Equation (2) where I sc, re f is the short circuit reference current (in Ampere) at STC, G is the surface irradiance of the cell, G re f is irradiance at STC (1000 W/m 2 ), µ I sc,re f is short circuit current coefficient provided by manufacturer, T c is temperature of environment in Kelvin, and T ref is temperature at STC (298 • K). The diode current can be obtained by Equation (3) [49]: where I 0 is saturation or leakage current of the diode, q is electron charge (1.602 × 10 −19 C), V is voltage imposed on the diode, and n is ideality factor. The value of the ideality factor is typically 1 ≥ n ≤ 2 [51]; n is taken as 1 in this work, as suggested in [1], k is Boltzmann constant defined as 1.381 × 10 −23 J/K and T is actual cell temperature, which is normally equal to environmental temperature. For multiple solar cells connected in series and parallel, the value of output current of PV module can be found by Equation (4) [1,[52][53][54]: where N P and N S is number of solar cells connected in parallel and in series, respectively. The value of R S can be obtained analytically; however, R Sh is assumed to be infinity [51]. The output voltage can be calculated by Equation (5) [22,51]: where V oc,ref is the reference voltage at STC given by the manufacturer and µ V oc,re f is the temperature coefficient of voltage, also normally given by the manufacturer. The module's reverse saturation current can be found by Equation (6) [53].
The saturation or leakage current of diode can be found by Equation (7) [52,53,55,56]: where E g is the energy gap or band gap for silicon, equal to 1.1 eV for silicon and 1.39 for gallium arsenide [49,57] The value of PV power (considering maximum power point tracking, i.e., MPPT) is then calculated using Equation (8) [57][58][59].
The PV power calculation is discussed in detail under the following subsection on methodology.

Methodology
The proposed work was carried out using Matlab (R2021a) software. The illustration of the overall prediction system in a graphical manner is shown in Figure 2. For accurate training of the ANN and in order to use the data at the time of prediction without having current real-time weather data, a main database must be maintained consisting of the historical metrological parameters. Data were taken from two sources with different weather conditions. The first source was the National Renewable Energy Laboratory (NREL), USA. The hourly NREL data were obtained from the official website, http://www.nrel.gov/, accessed on 27 August 2021. This database consists of ten years of data from 1st July 2003 to 30th June 2013. The one-year data were selected as a case study for training and testing purposes while the remaining data were used for prediction purposes in the absence of current weather data. The second source of data was the PV-based EV charging station at the Universiti Teknologi Malaysia (UTM), Malaysia. The Centre of Electrical Energy Systems, UTM has established a 15kW grid-connected PV setup with a fully equipped data logging system, as shown in Figure 3. For accurate training of the ANN and in order to use the data at the time of prediction without having current real-time weather data, a main database must be maintained consisting of the historical metrological parameters. Data were taken from two sources with different weather conditions. The first source was the National Renewable Energy Laboratory (NREL), USA. The hourly NREL data were obtained from the official website, http://www.nrel.gov/, accessed on 27 August 2021. This database consists of ten years of data from 1st July 2003 to 30th June 2013. The one-year data were selected as a case study for training and testing purposes while the remaining data were used for prediction purposes in the absence of current weather data. The second source of data was the PVbased EV charging station at the Universiti Teknologi Malaysia (UTM), Malaysia. The Centre of Electrical Energy Systems, UTM has established a 15kW grid-connected PV setup with a fully equipped data logging system, as shown in Figure 3. For accurate training of the ANN and in order to use the data at the time of prediction without having current real-time weather data, a main database must be maintained consisting of the historical metrological parameters. Data were taken from two sources with different weather conditions. The first source was the National Renewable Energy Laboratory (NREL), USA. The hourly NREL data were obtained from the official website, http://www.nrel.gov/, accessed on 27 August 2021. This database consists of ten years of data from 1st July 2003 to 30th June 2013. The one-year data were selected as a case study for training and testing purposes while the remaining data were used for prediction purposes in the absence of current weather data. The second source of data was the PV-based EV charging station at the Universiti Teknologi Malaysia (UTM), Malaysia. The Centre of Electrical Energy Systems, UTM has established a 15kW grid-connected PV setup with a fully equipped data logging system, as shown in Figure 3. The data logger has ability to track and store weather parameters and electrical variables for every minute, thirty minutes and one hour of the day. These weather parameters are directly used to calculate the output power of the PV array.

PV Power Calculations
For output power calculation, the parameters of the PV module of Kyocera company were taken as the case study. These parameters are given in Table 1. The reverse saturation current is calculated using Equation (6). Similarly, the saturation or leakage current and photo current are calculated using Equatizons (7) and (2), respectively. The series resistance of the single diode model is calculated using the simple relation RS = (Voc − Vmp)/Imp and the parameters from Table 1. Rsh is taken as 10 kΩ, because Rsh is very high [51]. Based on the parameters given in the PV datasheet, the maximum power (Pmp) is calculated using values given in Table 1 as Pmp = Vmp × Imp. Since Equation (4) is transcendental in nature, the method of Newton-Raphson (NR) iteration was applied to find photovoltaic current, as shown in Figure 4 [1,49,57]. NR algorithm has the advantage of very quick quadratic convergence for initial values near the root; thus, a good solution can be achieved within a few iterative steps [1].

Parameter
Value The data logger has ability to track and store weather parameters and electrical variables for every minute, thirty minutes and one hour of the day. These weather parameters are directly used to calculate the output power of the PV array.

PV Power Calculations
For output power calculation, the parameters of the PV module of Kyocera company were taken as the case study. These parameters are given in Table 1. The reverse saturation current is calculated using Equation (6). Similarly, the saturation or leakage current and photo current are calculated using Equatizons (7) and (2), respectively. The series resistance of the single diode model is calculated using the simple relation R S = (V oc − V mp )/I mp and the parameters from Table 1. R sh is taken as 10 kΩ, because R sh is very high [51]. Based on the parameters given in the PV datasheet, the maximum power (P mp ) is calculated using values given in Table 1 as P mp = V mp × I mp . Since Equation (4) is transcendental in nature, the method of Newton-Raphson (NR) iteration was applied to find photovoltaic current, as shown in Figure 4 [1,49,57]. NR algorithm has the advantage of very quick quadratic convergence for initial values near the root; thus, a good solution can be achieved within a few iterative steps [1].
The PV power using Equation (8) is calculated and maximum power (P maxc ) extracted by taking maximum power point tracking into account. To calculate the accurate value of current and power, a small iteration termination threshold for error was taken equal to 0.0001; the error was calculated as (P maxc − P mp ) [1]. Table 1. Module specifications at STC, KD325GX-LFB Model.

Parameter
Value Unit The PV power using Equation (8) is calculated and maximum power (Pmaxc) extracted by taking maximum power point tracking into account. To calculate the accurate value o current and power, a small iteration termination threshold for error was taken equal to 0.0001; the error was calculated as (Pmaxc − Pmp) [1]. The calculated PV power is stored in the already maintained database to use as target during the training phase of ANN and for comparison purposes. Nevertheless, be fore applying the fluctuating parameters to the network for its training, the moving aver age was applied on these parameters.

Application of Moving Average
As per the help document of MATLAB R2021a, Arima enables a user to create varia tions of the autoregressive integrated moving average (ARIMA) model, including an au toregressive (AR(p)), moving average (MA(q)), or ARMA(p,q) model. As discussed ear lier, weather conditions are always fluctuating and thus influencing the generation of PV power directly [5,6]. To remove these short-term variations/fluctuations for better training of the network, the moving average (MA) of these variables was obtained before applying them to the ANN in this work. For this purpose, the abruptly fluctuating parameters wer divided into more than one value by taking their moving average for one day, two day and so forth. The increased number of variables with less variation helped the ANN to b trained in a more generalized way. This is because the moving average smoothens th The calculated PV power is stored in the already maintained database to use as a target during the training phase of ANN and for comparison purposes. Nevertheless, before applying the fluctuating parameters to the network for its training, the moving average was applied on these parameters.

Application of Moving Average
As per the help document of MATLAB R2021a, Arima enables a user to create variations of the autoregressive integrated moving average (ARIMA) model, including an autoregressive (AR(p)), moving average (MA(q)), or ARMA(p,q) model. As discussed earlier, weather conditions are always fluctuating and thus influencing the generation of PV power directly [5,6]. To remove these short-term variations/fluctuations for better training of the network, the moving average (MA) of these variables was obtained before applying them to the ANN in this work. For this purpose, the abruptly fluctuating parameters were divided into more than one value by taking their moving average for one day, two days and so forth. The increased number of variables with less variation helped the ANN to be trained in a more generalized way. This is because the moving average smoothens the data, which then provide a clear visual picture of the variable to the neural network for better training [43,44]. The simple moving average (MA) concept can be explained by the Equation (9) [44].
A t+1 is the average value, A t and A t−i are historical values, and D is the number of days for which the moving average is to be calculated. The most important and directly affecting parameter on PV power generation is solar irradiance, of which the actual and moving average-based patterns for eleven days (i.e., D = 11) are shown in Figure 5. In this figure, the blue lines show the actual values of solar irradiance and the orange lines represent their moving average.  [43,44]. The simple moving average (MA) concept can be explained by th Equation (9) [44].
is the average value, are historical values, and D is the number o days for which the moving average is to be calculated. The most important and directl affecting parameter on PV power generation is solar irradiance, of which the actual an moving average-based patterns for eleven days (i.e., D = 11) are shown in Figure 5. In th figure, the blue lines show the actual values of solar irradiance and the orange lines rep resent their moving average. The moving average of irradiance shows the same pattern as the original one, how ever with considerably reduced and smooth variations. Therefore, the inclusion of MA based parameters during the training phase of the ANN has enhanced training perfo mance by reducing the MSE by a significant amount, as shown in the results section. Th is the main contribution of this work, which is proved in the next section. It is to be men tioned here that MSE to measure the training performance of feedforward neural ne works is used by various researchers [50,60].

ANN Training Phase
Only one year of data out of the main ten-year database was used for ANN trainin (80%) and testing (20%) purposes; the remaining data were used for validation and pr diction of PV power. The purpose of using only one year of data for training was to mak the proposed model comparable with existing work, as most researchers use one year da for training of the ANN [15,[27][28][29][30]. The specifications of selected networks in this wor are as follows: Algorithm: Bayesian regulation backpropagation The trainbr (Bayesian regularization) training function was used in this work. This because the trainbr algorithm generally works best when the network falls approximatel in both the positive and negative range of inputs [42]. Though it takes a longer trainin time than other training functions, this is good choice in the case of complex problem because it produces better generalization capability [42]. It updates the weight and bia values according to Levenberg-Marquardt optimization and then determines the corre combination to produce a well-generalized network [61]. The moving average of irradiance shows the same pattern as the original one, however with considerably reduced and smooth variations. Therefore, the inclusion of MA-based parameters during the training phase of the ANN has enhanced training performance by reducing the MSE by a significant amount, as shown in the results section. This is the main contribution of this work, which is proved in the next section. It is to be mentioned here that MSE to measure the training performance of feedforward neural networks is used by various researchers [50,60].

ANN Training Phase
Only one year of data out of the main ten-year database was used for ANN training (80%) and testing (20%) purposes; the remaining data were used for validation and prediction of PV power. The purpose of using only one year of data for training was to make the proposed model comparable with existing work, as most researchers use one year data for training of the ANN [15,[27][28][29][30]. The specifications of selected networks in this work are as follows: Algorithm: Bayesian regulation backpropagation The trainbr (Bayesian regularization) training function was used in this work. This is because the trainbr algorithm generally works best when the network falls approximately in both the positive and negative range of inputs [42]. Though it takes a longer training time than other training functions, this is good choice in the case of complex problems because it produces better generalization capability [42]. It updates the weight and bias values according to Levenberg-Marquardt optimization and then determines the correct combination to produce a well-generalized network [61].
It is worth mentioning that, in order to train the network accurately, the average of weather parameters was also added as an input besides their actual values. The weather parameters used for training the ANN were quite fluctuating, and their quantity has thus been increased by adding their average values. This makes the system more complex; thus, in order to enhance the training performance of the network and to have more generalized prediction capabilities, the number of hidden layers was increased. To get the finalized structure as shown in Figure 6, different combinations of hidden layers and number of neurons were checked until getting the smallest MSE in training performance on a trial basis, as adopted in existing research works [62][63][64][65]. Matlab has the capability to generate the graph of MSE against each iteration (epoch) during the training phase of the network, as shown in Figure 7. This MSE actually represents the training performance of the network. Transfer function: Tan-sigmoid for each hidden and linear transfer function for output layer was selected. This was because the tan-sigmoid covers both positive and negative values, which suits the nature of the applied input variables in this work. For ease of reading, the parameters of the proposed ANN structure are given in Table 2.
Input data: The inputs applied to the neural network are given in Table 3  The details of input parameters with their names are given in next subsection. The first four inputs in Table 2 were used (in the form of dates) during the training and prediction phases in order to extract the remaining parameters from the already-maintained historical database.
The next five inputs, humidity, wind speed, air pressure, irradiance and temperature, were the main inputs used for training the network. The remaining average inputs (obtained by means of RA) were used mainly for reduction of training and prediction errors.
Target: PV Power Target is the variable that is the mandatory input of the ANN at the time of training. This is the input which is to be predicted by using the already trained network; that is, PV power in this work. The structure of the proposed multilayer neural network is shown in Figure 6. Figure 6a shows the detailed structure of the proposed ANN showing each hidden layer, their neurons and the transfer functions within entire network.
Matlab has the capability to generate the graph of MSE against each iteration (epoch) during the training phase of the network, as shown in Figure 7. This MSE actually represents the training performance of the network.
It is clear from Figure 7 that the obtained error (i.e., MSE) with the proposed structure of network was 3.19 × 10 −10 , which is much lower than the least obtained error in the existing literature (i.e., 4.45 × 10 −7 [23]). It is worth mentioning that the data of a five year period was used in [23] for training and testing purposes, while in our proposed work the data of only one year's span was used for the same purpose. Even then, the obtained error in the case of the proposed model was smaller, which shows the remarkable improvement in the training performance of the ANN.
The Matlab generated regression plots, as shown in Figure 8, clearly depict the accuracy of the training as well as the testing phases of the proposed network. It is clear from Figure 7 that the obtained error (i.e., MSE) with the propose of network was 3.19 × 10 −10 , which is much lower than the least obtained error i ing literature (i.e., 4.45 × 10 −7 [23]). It is worth mentioning that the data of a five y was used in [23] for training and testing purposes, while in our proposed wo of only one year's span was used for the same purpose. Even then, the obtain the case of the proposed model was smaller, which shows the remarkable im in the training performance of the ANN.
The Matlab generated regression plots, as shown in Figure 8, clearly depi racy of the training as well as the testing phases of the proposed network.   It is clear from Figure 7 that the obtained error (i.e., MSE) with the proposed structur of network was 3.19 × 10 −10 , which is much lower than the least obtained error in the exis ing literature (i.e., 4.45 × 10 −7 [23]). It is worth mentioning that the data of a five year perio was used in [23] for training and testing purposes, while in our proposed work the dat of only one year's span was used for the same purpose. Even then, the obtained error i the case of the proposed model was smaller, which shows the remarkable improvemen in the training performance of the ANN.
The Matlab generated regression plots, as shown in Figure 8, clearly depict the accu racy of the training as well as the testing phases of the proposed network. Once the network was trained, it could be used for predicting PV power by applyin the required input parameters.

Prediction Phase
In this work, the utilization of the already trained neural network was made quit simple compared to the already-proposed networks in the existing literature. The existin models need current real-time weather parameters as an input (exactly equal in numbe Once the network was trained, it could be used for predicting PV power by applying the required input parameters.

Prediction Phase
In this work, the utilization of the already trained neural network was made quite simple compared to the already-proposed networks in the existing literature. The existing models need current real-time weather parameters as an input (exactly equal in number to those applied during the training phase) in order to predict PV power. However, in our proposed work, the operator needs to apply only a set of dates (to specify prediction period) as an input in order to forecast the power. The remaining input parameters are extracted from a historical database which already contains the time, day and weather parameters. A simple data extraction algorithm (the pseudocode is given in the next section) was developed to automatically extract the remaining input parameters from this database by matching the days with the user's applied date. Firstly, the user's applied date is converted to day of week, month and year using the built-in functions of Matlab. As the database contains the value of each parameter for ten years against that specific date, the algorithm takes the mean of each variable for every hour to obtain a single value of each parameter. This average gives a very close value of each parameter to the real one. Thus, the extracted parameters are applied to the already trained NN for PV power prediction without having current real-time data. Therefore, the proposed work not only improves the training performance of the ANN but also makes use of this trained network for prediction of PV power without the presence of the real-time weather parameters. Thus, the proposed work makes the prediction process completely independent of any kind of external data except a set of dates.
A flowchart describing the overall functionality of the final prediction algorithm is shown in Figure 9.
to those applied during the training phase) in order to predict PV power. However, in our proposed work, the operator needs to apply only a set of dates (to specify prediction period) as an input in order to forecast the power. The remaining input parameters are extracted from a historical database which already contains the time, day and weather parameters. A simple data extraction algorithm (the pseudocode is given in the next section) was developed to automatically extract the remaining input parameters from this database by matching the days with the user's applied date. Firstly, the user's applied date is converted to day of week, month and year using the built-in functions of Matlab. As the database contains the value of each parameter for ten years against that specific date, the algorithm takes the mean of each variable for every hour to obtain a single value of each parameter. This average gives a very close value of each parameter to the real one. Thus, the extracted parameters are applied to the already trained NN for PV power prediction without having current real-time data. Therefore, the proposed work not only improves the training performance of the ANN but also makes use of this trained network for prediction of PV power without the presence of the real-time weather parameters. Thus, the proposed work makes the prediction process completely independent of any kind of external data except a set of dates.
A flowchart describing the overall functionality of the final prediction algorithm is shown in Figure 9. For ease of reading, the above flowchart provides self-explanatory details of the overall methodology of the proposed work. It is important to note that the proposed prediction model is capable of forecasting power for different time spans depending upon the applied dates used to extract the data. This is another contribution of this work, as the exiting models can make predictions for a fixed time span.

Pseudocode of Data Extraction Algorithm
The pseudocode of the simple algorithm used for extraction of required input data from the main ten-year historical database according to the dates entered by the user is presented in this section. The extracted inputs were automatically applied to the already-trained network in order to predict the PV power for every hour of the mentioned time span.
Data The data extraction algorithm facilitates a user (without requiring any knowledge of AI) to predict PV power for any time span in the absence of real-time weather parameters by merely entering a set of dates.

Results and Discussion
It is important to note that in the existing literature, researchers have validated their work through comparisons of predicted data with actual data from a single source [5,30,[66][67][68]. However, in this work, the data from two different countries (Malaysia and United States) having entirely different weather conditions are used for validation purposes. Due to its existence on the equator, the weather of Malaysia is quite unstable compared to that of the USA. Figure 10a The previous results in Figure 10 validate the accuracy of the prediction by means of comparison between actual and predicted power. Figure 11 shows the capability of the proposed model to use the already-trained neural network to predict power for any span of time without the presence of real-time weather data by utilizing historical data only. Figure 11a-d show the predicted power for one day, one week, one month and three years using the proposed algorithm. This shows that the proposed model is quite flexible in predicting power for various time periods.
The comparison of errors for training performance (mean squared error, i.e., MSE) and prediction performance (mean absolute percentage error, i.e., MAPE) obtained with the proposed and the already published models is given in Table 4. The results in the table clearly show the significant reductions in MSE and MAPE in the case of the proposed work.
Since the application of the already-trained network is made simple in this work, the proposed solution also provides a guide to the installers of the PV system to estimate its yield (by predicting PV power) prior to its installation in the presence of the historical weather data only. The comparison of errors for training performance (mean squared error, i.e., MSE) and prediction performance (mean absolute percentage error, i.e., MAPE) obtained with the proposed and the already published models is given in Table 4. The results in the table clearly show the significant reductions in MSE and MAPE in the case of the proposed work. Since the application of the already-trained network is made simple in this work, the proposed solution also provides a guide to the installers of the PV system to estimate its yield (by predicting PV power) prior to its installation in the presence of the historical weather data only.

Conclusions and Future Work
PV power prediction through ANN is a real life application of artificial intelligence in the field of renewable energy systems. This work has improved the training performance of a neural network by applying the moving average of the most sensitive and fluctuating weather parameters and increasing the hidden layers of the ANN. The results evidently show that the training performance error has been considerably reduced (from 4.45 × 10 −7 to 3.19 × 10 −10 ) compared to the errors obtained in existing ANN-based models. Moreover, prediction of PV power without real-time current weather data is made possible by exploiting historical weather data. It is worth mentioning that the proposed model asks the user to apply externally only the set of dates for prediction purpose, instead of multiple weather parameters. Unlike the existing prediction models, the proposed model has the capability to predict PV power for various time spans. Though the proposed approach is simple, it is quite novel and very useful for prediction of PV power without real-  Note: Bold to highlight the superiority of proposed approach over existing approaches.

Conclusions and Future Work
PV power prediction through ANN is a real life application of artificial intelligence in the field of renewable energy systems. This work has improved the training performance of a neural network by applying the moving average of the most sensitive and fluctuating weather parameters and increasing the hidden layers of the ANN. The results evidently show that the training performance error has been considerably reduced (from 4.45 × 10 −7 to 3.19 × 10 −10 ) compared to the errors obtained in existing ANN-based models. Moreover, prediction of PV power without real-time current weather data is made possible by exploiting historical weather data. It is worth mentioning that the proposed model asks the user to apply externally only the set of dates for prediction purpose, instead of multiple weather parameters. Unlike the existing prediction models, the proposed model has the capability to predict PV power for various time spans. Though the proposed approach is simple, it is quite novel and very useful for prediction of PV power without real-time current weather data. As a future work, the accuracy of the proposed work can be further enhanced by training the network with larger historical weather data (more than one year) and by using the two-diode model of solar cell instead of the single diode model. Funding: This research was funded by the Ministry of Education of Saudi Arabia, grant number IFP-2020-01 and the APC was funded through IFP-2020-01.

Institutional Review Board Statement:
Since this study is not involving humans or animals, no need of Institutional Review Board Statement and its approval number.

Informed Consent Statement:
Since this study is not involving humans or animals, no need of Consent Statement.
Data Availability Statement: The major portion of data were taken from National Renewable Energy Laboratory (NREL), USA through its official website, http://www.nrel.gov/ (accessed on 27 August 2021).