# Solar Power Prediction Modeling Based on Artificial Neural Networks under Partial Shading
## 4 Learning Parameter and Simulation  
The simulation proceeds in the following sequence: (1) the existing experimental data of the five parameters are implemented in a three-dimensional graph. (2) The five parameters are trained using an artificial neural network. (3) The consistency between the existing experimental data and the trained data is verified. (4) The trained data are generated as a Simulink block to construct a solar cell. A Simulink block generates results learned  
Figure 2: Artificial neural network structure for the simulation. through the MATLAB code for an artificial neural network [7; 10]. (5) The constructed solar cells are connected in parallel with bypass diodes to create a photovoltaic module. The five parameters and the artificial neural network are simulated using MATLAB/Simulink v.R2023a. Each of the five parameters is defined as a function of the temperature and irradiation. Therefore, the inputs of the neural network are set to the temperature and irradiation, while the outputs are set to each of the five parameters. The settings for training the neural network for each parameter are the same and are as follows: the maximum number of training epochs is 1000; the performance goal is \(1\times 10^{-9}\); and the learning rate is 0.05. The hidden layer has two layers, and each of them has three nodes. For the activation functions, the sigmoid function is used in the hidden layers, while the linear function is used in the output layer. Finally, the Levenberg-Marquardt (LM) algorithm was used as the learning algorithm. The LM iteration approach is a numerical optimization algorithm to solve nonlinear fitting problems using the method of least squares. The number of iterations is set to 1000, but the process terminates when the loss reaches the performance goal. Regression analysis is used to model the relationship between a dependent variable and one or more independent variables. In this study, regression analysis is employed to analyze the data obtained from a neural network. In regression, the dependent variable represents the variable to be predicted, while the independent variable are the variables that influence the dependent variable. In this research, when constructing the training data for regression analysis, temperature and irradiation are used as independent variables, and the five major parameters corresponding to them are used as the dependent variable. The regression model is trained using the training data, and then this model is utilized to predict the values of the five parameters based on new temperature and irradiation inputs. Regression analysis results can be interpreted using methods such as scatter plot analysis, error analysis, etc. Scatter plot analysis represents the relationship between actual values and predicted values of a graph in the form of a scatter plot. By analyzing the scatter plot, it can be determined if the data points cluster around the regression line. If the data points are concentrated around the regression line, it indicates that the model accurately predicts the relationship between the actual values and predicted values. Regression line analysis represents the relationship between the actual values and predicted values as depicted by the regression line on the graph. The slope of the regression line can be used to evaluate the predictive accuracy of the model through correlation. Generally, a slope close to 1 indicates an accurate model where actual values and predicted values match. Additionally, it is desirable for the data points around the regression line to be clustered. Error analysis allows us to examine the predicted values and actual values through the graph. If the data points are not concentrated around the regression line or show significant deviations, it may indicate that the predictive model is inaccurately predicting some of the data. The analysis of errors allows us to assess the predictive accuracy and bias of the model. The results of the regression analysis with five parameters are presented in Figure 3a-e.