MATHEMATICAL AND COMPUTATIONAL APPROACHES TO MODELING RENEWABLE ENERGY INTEGRATION IN POWER GRIDS

Abstract

 The rapid global transition toward renewable energy sources has introduced new challenges in maintaining the stability, reliability, and efficiency of modern power grids. The intermittency of solar, wind, and other renewables disrupts traditional deterministic grid models, demanding advanced mathematical and computational frameworks to predict, optimize, and stabilize system performance. This study presents a hybrid modelling approach that integrates mathematical optimization techniques such as linear programming, stochastic modelling, and differential equation systems with computational algorithms, including machine learning and numerical simulations, to enhance grid adaptability. The proposed framework evaluates renewable energy integration through multi-objective optimization, focusing on minimizing power imbalance, forecasting demand-supply variations, and improving real-time decision-making. Using simulation data, the results reveal a significant improvement in system stability (by 18%) and reduction in energy curtailment (by 12%) compared to conventional deterministic models. These findings underscore the potential of mathematically driven computational tools in achieving sustainable energy transitions. The paper contributes a robust model for policy makers and energy engineers to design intelligent, data-driven power networks that efficiently integrate renewable sources while ensuring reliability, cost-effectiveness, and environmental sustainability.