Metaheuristic-Based PV–BESS Planning for Radial Distribution Networks with Inverter-Based Voltage Support

High photovoltaic (PV) penetration can reduce grid-energy imports but may worsen voltage performance in radial distribution feeders. This paper develops a unified mixed-discrete PV–BESS planning framework that jointly optimizes siting, sizing, hourly storage operation, and a common inverter voltage-support gain subject to inverter capability limits. Five metaheuristic algorithms are compared over 30 independent runs on the 33-bus system using an explicitly converged under-relaxed fixed-point iteration. Adaptive Differential Evolution achieves the lowest best and median fitness values. Its best solution reduces active-loss energy by 38.0%, grid-energy import by 14.9%, peak grid power by 12.5%, voltage deviation by 53.7%, voltage-violation duration by 100%, and annual cost by 8.4% relative to the no-PV/no-BESS case. A separately optimized comparison shows substantial additional voltage and loss improvements from inverter reactive-power support. Objective-weight, voltage-penalty, BESS energy-CAPEX, and representative-day analyses clarify key planning trade-offs. On the 69-bus feeder, the 30-run ADE validation reduces active-loss energy by 51.2%, grid-energy import by 19.5%, peak grid power by 10.5%, voltage deviation by 39.5%, voltage-violation duration by 98.8%, and annual cost by 12.2%. A supplementary analysis with a higher PV upper bound further clarifies the influence of the adopted planning limit.