INTERPRETABLE AI-BASED MATHEMATICAL MODELING FOR SOLAR POWER GENERATION AND LOAD FORECASTING IN DISTRIBUTED ENERGY SYSTEMS

Abstract

With the increasing demand for decentralized and sustainable energy solutions, the requirements of precise and explainable prediction techniques in distributed energy systems are becoming ever more important. This work introduces an interpretable AI-powered framework for forecasting solar power generation and short-term load forecasting based on mathematically justified models. With the use of solar panels having capacities of 3 kWh to 6 kWh, the research utilizes mean power outputs as inputs to a series of AI models with explicit equations, such as Linear Regression, Polynomial Regression, Decision Tree Regression, and Support Vector Regression. Each model is developed using transparent mathematical expressions for easy analysis and implementation. In addition, the framework incorporates real load profiles derived from the literature to test the models' ability in demand forecasting. Performance measures like Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Coefficient of Determination (R²) are utilized to benchmark predictive performance. The findings validate that interpretable AI models not only make accurate predictions but also maximize model interpretability making them very well-posed to be used for real-time energy management in distributed power systems.