Simultaneous Integration of Photovoltaic Systems and Capacitor Banks in Radial Distribution Networks via the Grey Wolf Optimizer for Steady-State Voltage Regulation and Active Power Loss Minimization

This paper presents a structured planning framework for the coordinated integration of photovoltaic (PV) systems and capacitor banks (CBs) in radial distribution networks to improve steady-state voltage regulation and reduce active-power losses. The proposed methodology combines deterministic power-flow assessment, index-based candidate screening, and constrained joint placement and sizing using the Grey Wolf Optimizer (GWO) with an embedded CAPEX proxy. Compared with PV-only integration, the coordinated PV–CB strategy provides a more effective improvement in steady-state electrical performance, particularly in terms of slack-bus power factor and voltage regulation. In addition, relative to fixed coordinated PV–CB scenarios, the GWO-based formulation yields more balanced technical–economic solutions by improving power factor and voltage conditions while avoiding unnecessary overdimensioning of installed capacity. On the IEEE 15-bus system, the optimized configuration achieves a 45.9% reduction in active-power losses, improves the slack-bus power factor to 0.947, and reduces the average voltage deviation to 2.57%, with convergence reached in approximately 16 iterations. On the IEEE 34-bus system, the optimized solution yields a 49.8% loss reduction, increases the slack-bus power factor to 0.955, and reduces the average voltage deviation to 2.39%, with convergence reached in approximately 133 iterations. Using an energy price of 8.14 ctUSD/kWh, the corresponding annual loss–cost savings are approximately 19,975 USD and 78,475 USD for the IEEE 15- and 34-bus systems, respectively. The results demonstrate that the proposed GWO-based coordinated planning approach can achieve electrically effective and economically feasible solutions through the combined provision of local active-power injection and reactive-power compensation in radial distribution networks under steady-state operating conditions.