Mathematical models for energy production forecasting in photovoltaic power plants

Abstract

This article presents an adaptive mathematical model designed for accurate energy production forecasting in photovoltaic power plants. The research object includes climatic parameters such as solar radiation (300–800 W/m²), temperature, humidity, and wind speed. The primary issue addressed is enhancing forecasting accuracy under variable weather conditions and ensuring the adaptability of the model. As a result, a hybrid neural network model based on LSTM and iTransformer was developed. The model improved forecasting accuracy up to 93.1%, achieving MAE = 1.75 and MSE = 3.25. When applying the transfer learning method, the MAE was reduced by up to 30% (e.g., in the “dry” scenario – from 3.1 to 2.2). Computation time was reduced from 12.5 seconds to 4.3 seconds (–65.6%) using a GPU (RTX 3060). The main advantage of the model lies in its ability to accurately account for complex seasonal and temporal dependencies, showing higher accuracy than traditional methods (70–90%). This solution can be effectively applied in real-time forecasting systems, grid load management, and solar energy storage strategies.