Electr Eng DOI 10.1007/s00202-017-0518-2 ORIGINAL PAPER Solution of multi-objective optimal power flow using efficient meta-heuristic algorithm S. Surender Reddy 1 Received: 7 October 2016 / Accepted: 27 February 2017 © Springer-Verlag Berlin Heidelberg 2017 Abstract An efficient meta-heuristic algorithm-based multi- objective optimization (MOO) technique for solving the multi-objective optimal power flow (MO-OPF) problem using incremental power flow model based on sensitivities and some heuristics is proposed in this paper. This paper is aimed to overcome the drawback of traditional MOO approach, i.e., the computational burden. By using the pro- posed efficient approach, the number of power flows to be performed is reduced substantially, resulting the solution speed up. In this paper, the generation cost minimization and transmission loss minimization are considered as the objec- tive functions. The effectiveness of the proposed approach is examined on IEEE 30 and 300 bus test systems. All the simulation studies indicate that the proposed efficient MOO approach is approximately 10 times faster than the evolutionary-based MOO algorithms. In this paper, some of the case studies are also performed considering the practi- cal voltage-dependent load modeling. The simulation results obtained using the proposed efficient approach are also com- pared with the evolutionary-based Non-dominated Sorting Genetic Algorithm-2 (NSGA-II) and the classical weighted summation approach. Keywords Evolutionary algorithms · Generation cost · Multi-objective optimal power flow · Pareto optimal solutions · Sensitivity · Transmission loss B S. Surender Reddy salkuti.surenderreddy@gmail.com 1 Department of Railroad and Electrical Engineering, Woosong University, Daejeon, Republic of Korea 1 Introduction The role of optimal power flow (OPF) is more significant in modern power system operation and control. Engineers continue to find new uses for OPF programs. Thus, OPF may become more popular and easy to use as conventional power flows. The OPF problem can be solved for minimum generation cost which satisfies the power balance equations and system operating constraints. Normally, the classical optimization methods uses sensitivity analysis and gradient- based techniques. But, the OPF is a highly nonlinear, discrete and multi-modal optimization problem. Therefore, these con- ventional techniques are not suitable for solving this problem. The real-world problems naturally involve multiple and con- flicting objectives to be optimized simultaneously. Defining multiple objectives often gives better idea of the problem. Majority of the classical multi-objective optimization (MOO) algorithms convert the true multi-objective prob- lem into a single-objective optimization problem by using some user defined functions. The challenges of multi- objective optimal power flow (MO-OPF) are generation of best solutions, generation of uniformly distributed Pareto set, maximizing the diversity of the developed Pareto set, computational efficiency, etc. In this paper, an attempt has been made to improve the computational efficiency of MO- OPF. Several MOO approaches have been developed in the literature. For example, classical weighted summation approach [1], penalty function approach [2], non-dominated sorting genetic algorithm (NSGA)-based approach [3], ε- constrained approach [4], etc. The main challenge in a multi-objective environment is to minimize the distance of the generated solutions to the Pareto set and maximize diver- sity of the developed Pareto set. A good Pareto set may be obtained by appropriate guiding of search process through careful design of reproduction operators and fitness assign- 123