Optimal FACTS Placement in Power Systems with Load Uncertainty Using a Lévy Flight and Chaotic Search-Based Whale Optimization Algorithm

The Balanced Whale Optimization Algorithm (BWOA) is proposed to address the optimal power flow (OPF) problem in grids incorporating flexible AC transmission systems (FACTS) and renewable energy sources. The standard Whale Optimization Algorithm (WOA) is enhanced through the integration of Lévy Flight (LF) dynamics for global exploration and Chaotic Local Search (CLS) for refined exploitation, producing a balanced search that mitigates premature convergence and local-optima stagnation typical of metaheuristic OPF solvers. The BWOA is benchmarked on the modified IEEE 30-bus system under both fixed and dynamic loading conditions and against five state-of-the-art metaheuristics (ALCPSO, CLPSO, MFO, SaDE, and the standard WOA) across eight study cases. Across the full set of cases, the BWOA delivers, on average, lower gross cost (mean reduction of approximately 1.3–6.8% relative to the comparators), lower active power loss (mean reduction of 6–22%), and lower expected gross cost under load and renewable uncertainty (mean reduction of 0.5–4.9%). The BWOA additionally attains the leading or co-leading position in the Friedman rank test (FRT) in the majority of cases, while incurring only a marginal runtime overhead (≤1% over the next-fastest comparator). The algorithm shows slightly higher voltage deviations in some scenarios, which is discussed as a controllable trade-off. The results indicate that the BWOA is a robust and cost-effective solver for OPF in grids with FACTS devices and stochastic renewable generation.