In this paper, a new technique of optimization known as Moth-Flam Optimizer (MFO)
IntroductionOptimal power flow (OPF) is a well studied optimization problem in power systems. In 1962, such an issue was first introduced by Carpentier [2]. The problem of the OPF can be defined as a nonlinear programming problem [1]. The main objective of the OPF problem is to optimize chosen objective functions such as piecewise quadratic cost function, fuel cost with valve point effects and voltage profile improvement, by optimal adjusting the power system control variables and satisfying various system operating such as power flow equations and inequality constraints, simultaneously [3][4][5][6].To solve this problem, the researchers proposed a number of optimization algorithms over the years. Therefore optimization is known as one of the most current problem facing research, a good optimization leads to an optimal solution for an efficient system. The first solution method for the OPF problem was proposed by Dommel and Tinney [7] A new method known as the Moth-Flame Optimization MFO algorithm this method has been proposed by Seyedali Mirjalili [25] in 2015 is a nature-inspired method from navigating mechanism of moths in nature called transverse orientation, which has not received yet much attention in the power system. Hence, the first objective of this paper is to apply a new method that is the MFO in order to solve the OPF problem. In what follows, we will briefly give the mathematical model on the proposed algorithm of spiral flying path of moths around artificial lights (flames) [25].In this paper, an approach based on MFO is proposed to solve the OPF problem. This problem has been formulated as a nonlinear optimization problem with equality and inequality constraints. Indeed, different objectives are considered in this work to minimize the cost of fuel, emission, and improve the voltage profile. Moreover, this method is simulated and tested on the Algerian power system network. In addition, the results are compared with other methods reported in any relevant literature dealing with the subject.