Implementation of Modified Effective Butterfly Optimizer in Solving Multi-Objective Pareto Optimal Power Flow Problem with Renewable Uncertainties

The power flow problem is one of the most challenging tasks in power systems, affecting both generation cost and energy quality. Optimal power flow (OPF) further complicates this task by requiring the optimal adjustment of system variables and parameters. This paper adapts the Modified Effective Butterfly Optimizer (MEBO) to solve multi-objective optimal power flow (MOOPF) problems with the contribution of optimized weighting using multiple Pareto archives. MEBO is an advanced optimization algorithm that utilizes population reduction and parameter learning to guide subsequent searches for unconstrained problems. The proposed technique has been tested on IEEE 30 and 57 bus test systems, and the results have been compared with existing methods reported in the literature. In the paper, four single-objective functions, namely generator cost, active power loss, fuel emission, and voltage deviation, are used to construct four multi-objective (MO) problems: cost–loss, cost–voltage, cost-emission, and emission–loss. For the cost-emission case, the proposed MEBO achieved compromised solutions of 791.1951 $/h fuel cost with 0.10873 ton/h emission and 801.8172 $/h fuel cost with 0.10044 ton/h emission under different Pareto-based optimization metrics. In the emission–loss case, the algorithm obtained 0.20539 ton/h emission with 3.1403 MW/h power loss, demonstrating the effectiveness of the proposed approach in balancing conflicting objectives. The Pareto curves of MEBO in achieving MO problems are presented, along with the suggested compromised solutions acquired from the literature. In the literature, this is the first application of MEBO for solving MOOPF problems. The results demonstrate that MEBO performs better than most other alternatives; this shows potential for further improvements with respect to the MOOPF problem.