Improved Pied Kingfisher Optimization Algorithm for optimal scheduling of microgrids with hybrid energy storage.

With the increasing penetration of renewable energy sources, microgrids have become an effective platform for integrating distributed generation and energy storage. However, renewable intermittency and the integration of hybrid energy storage systems lead to a highly nonlinear and nonconvex scheduling problem, for which conventional deterministic solvers can be computationally demanding and may struggle with nonconvexity and coupled constraints. To address this challenge, this paper proposes an Improved Pied Kingfisher Optimization algorithm (IPKO) for microgrid optimal scheduling. The proposed IPKO integrates four complementary enhancement strategies, including Chebyshev-chaotic initialization, multi-source guidance with adaptive perturbation, differential-spiral development, and periodic dynamic adjustment, to improve population diversity, search adaptability, and convergence stability. A grid-connected microgrid scheduling model with a hybrid energy storage system comprising battery storage and hydrogen storage is further developed, with demand response modeled as time-of-use price-driven load shifting. Simulation results demonstrate that the IPKO-based scheduling framework consistently reduces both economic and environmental costs. Compared with representative metaheuristic algorithms over multiple independent runs, IPKO achieves about 4-10% lower mean daily operating cost with significantly reduced solution dispersion, confirming its superior solution quality and robustness for complex microgrid scheduling problems.