An Orthogonal Learning Bird Swarm Algorithm for Optimal Power Flow Problems

A dominant statistical method, in which the best combination of factors’ levels are predicted by analyzing a few representative combinations of factors’ levels, named as orthogonal experimental design (OED). The OED is an effective approach for analyzing the effect of multi-levels factors simultaneously and it works on orthogonal learning (OL) strategy. An evolutionary programming based heuristic method has two contradictory features–exploration and exploitation, balancing in these features have significant impact on its optimization performance. We have applied an OED based auxiliary search strategy for enhancing performance of the bird swarm algorithm (BSA) by improving its exploitation search ability. It is a challenging task to keep balance among two contradictory features–exploration and exploitation of a heuristic approach, while addressing optimal power flow (OPF) problems in power systems. In this research study, we have proposed improved BSA (IBSA) for solving the OPF problems in thermal power systems. We have conducted a study of the OPF problems with objective functions-reducing electricity generation cost, emission pollution, and active power loss to measure the efficiency of proposed IBSA. In this work, we have utilized five benchmark functions and solved OPF problems using three IEEE test systems including IEEE-30 bus system, IEEE-57 bus system, and IEEE-118 bus system to verify stability, effectiveness, and performance of proposed IBSA. The statistical and simulation results have indicated that the proposed IBSA has better convergence, efficiency, and robustness features than the original BSA as well as other heuristic approaches. It is observed that lowest electricity generation cost 800.3975 $\$ $ /h on IEEE-30 bus system, 41663.5500 $\$ $ /h on IEEE-57 bus system, and 134941.0367 $\$ $ /h on IEEE-118 bus system have been achieved using proposed IBSA to address the OPF problems. Furthermore, in transmission lines of the power system network minimum active power loss 16.2869MW has been observed by conducting a case study on the IEEE 118-bus system based on the proposed IBSA approach.