Research on the Effect of the Activation Functions in the Hidden Layer and Features in NARX Models to Improve the Photovoltaic Power Generation Forecasting

Photovoltaic power forecasting is important because solar generation varies with weather conditions. Accurate forecasts help improve grid operation, reduce costs, enhance system stability, and support battery management. This paper presents a hybrid methodology that combines statistical analysis and machine learning to forecast photovoltaic power generation. First, the data are cleaned and preprocessed. Then, the input vector is selected using two criteria: collinearity analysis to remove redundant variables, and Granger causality to identify variables with predictive value in a nonlinear autoregressive with exogenous inputs artificial neural network (NARX-ANN) framework. Next, an experimental design is used to evaluate two training algorithms and activation functions for the hidden layer available in Matlab® version 26.1.0.3276743 (R2026a Update 3, MathWorks Inc., Natick, MA, USA). The methodology is validated by comparing hundreds of input-variable combinations generated through binomial coefficients. A case study using data from Sonora, Mexico, shows that the best model is the Collinearity–Causality (CC)-NARX-4 model, which uses four input variables, a radial basis function in the hidden layer, and Bayesian regularization backpropagation. This model achieves a root-mean-square error (RMSE) of approximately 132 watts (W) for the forecasting stage/forecasting horizon. The results are also compared with a nonlinear autoregressive (NAR) model to assess the predictive benefit of including exogenous inputs. The final outcome is a robust methodology for improving multivariable neural networks through (i) optimized input-vector selection using collinearity and causality tests, validated by an exhaustive combinatorial algorithm; and (ii) a systematic procedure for configuring the hidden-layer transfer function and the neural network training function.