A probabilistic framework for effective battery energy storage sizing in microgrids with demand response

Microgrids (MGs) are increasingly integrating Battery Energy Storage Systems (BESSs) to improve operational flexibility and minimize overall costs. However, probabilistic BESS sizing remains computationally demanding due to uncertainties associated with renewable energy generation, load demand, and market price volatility. This paper presents a hybrid probabilistic sizing framework that integrates the 2m + 1 Point Estimation Method (PEM) with the Equilibrium Optimizer (EO), referred to as the EO–PEM approach. Unlike conventional Monte Carlo simulation–based formulations, the presented method embeds EO within the PEM uncertainty evaluation loop, enabling accurate results with substantially reduced computational effort. Additionally, an incentive-based Demand Response (IDR) model is integrated into the Energy Management (EM) framework. The main objective of the EM is to minimize operational costs and maximize the MG operator’s benefits while ensuring customer satisfaction. Simulation results from the test MG system confirm the superiority of the EO over other applied optimization techniques in solving the deterministic EM problem without BESS. Under uncertainties, the EO–PEM method identifies an optimal BESS capacity of 1 kWh, achieving a reduction in the expected operational cost while maintaining high computational efficiency and robustness. Overall, the results demonstrate the effectiveness of the EO–PEM framework for probabilistic BESS sizing under multi-source uncertainties.