Optimal power flow problem considering the cost, loss, and emission by multi-objective electromagnetism-like algorithm

Realistic optimal power flow is a non-convex and complicated optimization problem which tries to economically dispatch the load between different generation units and some other objective functions, while the operational limitations of each unit are satisfied. In this paper three non-commensurable and contradictory objectives namely total fuel cost, total emission, and total real power loss are considered which conclude to a multi-objective (MO) optimization problem. Also, this paper proposes a multi-objective electromagnetism-like algorithm (MOEMA) based on the Pareto dominance concept and external archive strategy to solve the formulated MO problem. The feasibility and effectiveness of the proposed method is tested on the IEEE 30-bus test system and obtained numerical results are compared with the results of other heuristic methods reported in recent literature. The single and MO optimization results prove the effectiveness of the proposed optimization algorithms over other methods.