Solving multi‐objective optimal power flow problem via forced initialised differential evolution algorithm

This study proposes a multi‐objective differential evolution algorithm (MO‐DEA) based on forced initialisation to solve the optimal power flow (OPF) problem. The OPF problem is formulated as a non‐linear MO optimisation problem. The considered objective functions are fuel cost minimisation, power losses minimisation, voltage profile improvement, and voltage stability enhancement. For solving the MO‐OPF, the proposed approach combines a new variant of DE (DE/best/1) with the ɛ ‐constraint approach. This combination guarantees high convergence speed and good diversity of Pareto solutions without computational burden of Pareto ranking and updating or additional efforts to preserve the diversity of the non‐dominated solutions. The proposed approach has the ability to generate Pareto‐optimal solutions in a single simulation run through adaptive variation of the ɛ ‐value. In addition, the best compromise solution is extracted based on fuzzy set theory. The effectiveness of the proposed MO‐DEA is tested on the IEEE 30‐bus and IEEE 57‐bus standard systems. The numerical results obtained by the proposed MO‐DEA are compared with other evolutionary methods reported in this literature to prove the potential and capability of the proposed MO‐DEA for solving the MO‐OPF at acceptable economical and technical levels.