An Improved Water Cycle Algorithm Using Lévy Mutation Strategy for Optimizing Power Flow in Electrical Networks

Document Type : Original Article

Authors

1 University of Science and Culture, Bahar st, Shahid Qamushi st, Ashrafi Esfahani Bulvar

2 School of Engineering, Royal Melbourne Institute of Technology (RMIT), Melbourne, Australia

3 Department of Electrical Engineering, Faculty of Engineering, University of Science and Culture, Tehran, Iran

Abstract
Optimal power flow (OPF) is a challenging nonlinear and non-convex optimization problem that requires the simultaneous satisfaction of power-flow equations and operational constraints. This study proposes an enhanced water cycle algorithm (WCA), termed Lévy WCA (LWCA), which incorporates a Lévy flight mechanism into the raining phase of the conventional WCA to improve search-space exploration and reduce the likelihood of premature convergence. Unlike the standard raining process, the proposed Lévy-based mechanism combines short local movements with occasional long-range jumps, enabling a broader exploration of promising regions of the solution space without introducing additional control parameters. The proposed method is evaluated on the IEEE 30-bus and 57-bus benchmark systems under multiple OPF operating scenarios. The obtained optimization results are compared with the conventional WCA and a range of established optimization methods. For the IEEE 30-bus system, the proposed LWCA achieves a minimum fuel cost of 798.8608 $/h in the quadratic fuel-cost case, while for the IEEE 57-bus system, it achieves a minimum fuel cost of 41,675.07 $/h. Statistical tests (e.g., the Wilcoxon signed-rank test) and optimization results further indicate improved consistency of the LWCA across independent runs. At the same time, the resulting solutions exhibit competitive fuel costs, power losses, and voltage profiles compared with the benchmark methods considered. These findings demonstrate that incorporating Lévy flights into the raining mechanism provides an effective modification of the WCA for solving constrained OPF problems.

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Articles in Press, Corrected Proof
Available Online from 26 October 2026

  • Receive Date 02 May 2026
  • Revise Date 25 September 2026
  • Accept Date 07 October 2026
  • First Publish Date 26 October 2026