Hybrid PSO–WOA Algorithm for Optimal Siting and Sizing of Capacitor Banks and Photovoltaic Generators in Distribution Networks

The increasing growth in electricity demand leads to higher voltage drops and power losses in distribution networks. The integration of capacitor banks (CBs) and photovoltaic generators (PVGs) helps improve network performance; however, their effectiveness depends on their optimal sizing and placement within the electrical network. This study proposes a hybrid metaheuristic algorithm to determine the optimal locations and sizes of CBs and PVGs in distribution networks under hourly AC power flow, hourly dynamic switching of capacitor banks, and an economic model with tariffs differentiated by consumer type. The proposed PSO–WOA algorithm combines the fast convergence capability of Particle Swarm Optimization (PSO) with the local refinement capability of the Whale Optimization Algorithm (WOA). In addition, to guide the initialization of the population, loss sensitivity indices based on the derivatives of active power losses with respect to voltage and reactive power are employed. The hybrid algorithm begins with the PSO phase to intensively exploit the search space and subsequently transfers the population without reinitialization to the WOA phase to refine promising solutions and improve the final convergence. The application of the proposed PSO–WOA algorithm to the IEEE 33-bus distribution system achieved a 51.92% reduction in active power losses, increased the minimum voltage from 0.9163 p.u. to 0.9500 p.u., and reduced the total annual cost by 50.05% (from 2.573 to 1.285 MUSD/year). A comparison with similar optimization algorithms, namely PSO, WOA, the reverse hybrid WOA–PSO, and the Genetic Algorithm (GA), showed that the proposed PSO–WOA achieved the best overall performance in terms of feasibility and statistical stability, with a mean solution quality comparable to that of PSO but with lower dispersion and a better worst case across independent runs. GA and WOA showed the greatest difficulty in satisfying the operational constraints, achieving only 60% and 79% feasible solutions, respectively, whereas the proposed algorithm achieved a 100% feasibility rate.