Work

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

Year: 2026

Type: article

Abstract: 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.

Source: Energies

DOI: 10.3390/en19122879

Authors: Eduardo Rangel-Heras, Beatriz A. Rivera-Aguilar, Itzel Aranguren, Erasmo Correa-Gómez, Oscar D. Sanchez, Víctor E. Moreno

Institutions: Universidad Aeronáutica en Querétaro, Universidad de Guadalajara, Universidad Nacional Autónoma de México, Universidad Autónoma de Guadalajara

Language: English

Topic: Solar Radiation and Photovoltaics

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

SDGs: Affordable and clean energy, Climate action

Open Access status: gold

Estimated APC paid: $3,137