A KKT ‐Based Bilevel Optimization Framework for the Integrated Sizing and Operation of Renewable Generation and Hybrid Energy Storage Systems in Microgrids

Abstract

This study introduces a comprehensive optimization framework for determining the optimal sizing and operation of variable renewable energy sources (VREs) and hybrid energy storage systems to facilitate cost‐effective microgrid operations. The framework concurrently determines the optimal capacities and operational schedules for photovoltaic systems, wind generators, battery energy storage systems, and component‐level hydrogen energy storage systems, including an electrolyzer, hydrogen tank, and fuel cell. Acknowledging the interdependence between capacity sizing and operational planning, the problem is formulated as a bilevel optimization model aimed at minimizing total costs, encompassing both investment and operational expenses. By employing the Karush–Kuhn–Tucker conditions, the bilevel problem is transformed into a single‐level mixed‐integer quadratic programming (MIQP) model, which is solved efficiently using the Gurobi Optimizer. Numerical simulations conducted for a grid‐connected microgrid over a 1‐month period compared two scenarios: perfect power balance and permissible VRE curtailment. The results indicate that allowing limited curtailment reduces storage capacity requirements and decreases total system costs compared with the no‐curtailment scenario, while maintaining stable operation. The proposed approach offers a robust and computationally efficient framework for the integrated planning of renewable generation and hybrid storage in next generation microgrids. © 2026 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.