Multi-Operator Differential Evolution for Coordinated Active and Reactive Battery Scheduling in Active Distribution Networks

Battery energy storage systems can reduce the operating cost of active distribution networks while supporting voltage control through their power electronic converters. This paper develops an application-specific multi-operator Differential Evolution (DE) framework for the coordinated active and reactive power scheduling of distributed battery energy storage systems in radial distribution networks with photovoltaic generation. The optimization model minimizes the daily operating cost associated with conventional energy supply, photovoltaic and storage operation and maintenance, and battery degradation. Candidate schedules encode hourly active and reactive power references for three storage converters, producing a 144 dimensional decision vector for a 24 h horizon. Each candidate is repaired to satisfy active power, state of charge, terminal energy, and converter apparent power limits before being evaluated through an alternating current power flow based on matrix successive approximations. The search framework generates three competing trial schedules per target individual by combining established best-guided, random, and current-to-random DE mutation families with a discrete parameter pool, a common feasibility-repair operator, and greedy selection after AC network evaluation. The method is tested on modified 33-node and 69-node active distribution networks and compared with AJAYA, genetic algorithm, multiverse optimizer, and particle swarm optimization. In the deterministic 33-node case, Differential Evolution obtains the lowest best cost, USD 6846.206, and the largest best cost reduction, 2.1838 percent. The scenario study performs separate deterministic optimizations for pre-generated operating realizations and is therefore interpreted as a scenario-conditioned sensitivity assessment rather than as stochastic or robust optimization of one here-and-now schedule. In this assessment, DE achieves the largest average savings: 2.3487 percent in the 33-node network and 2.9314 percent in the 69-node network. Voltage magnitudes, branch loading, converter ratings, and cyclic state of charge constraints are satisfied in all evaluated cases. The results identify the proposed framework as a competitive day-ahead solver within the evaluated cases, while no claim of global optimality or universal superiority over alternative optimizers is made.