In this study, optimal economic load dispatch problem (OELD) is resolved by a novel improved algorithm. The proposed modified moth swarm algorithm (MMSA), is developed by proposing two modifications on the classical moth swarm algorithm...
moreIn this study, optimal economic load dispatch problem (OELD) is resolved by a novel improved algorithm. The proposed modified moth swarm algorithm (MMSA), is developed by proposing two modifications on the classical moth swarm algorithm (MSA). The first modification applies an effective formula to replace an ineffective formula of the mutation technique. The second modification is to cancel the crossover technique. For proving the efficient improvements of the proposed method, different systems with discontinuous objective functions as well as complicated constraints are used. Experiment results on the investigated cases show that the proposed method can get less cost and achieve stable search ability than MSA. As compared to other previous methods, MMSA can archive equal or better results. From this view, it can give a conclusion that MMSA method can be valued as a useful method for OELD problem. Keywords: Discontinuous objective function Modified moth swarm algorithm Optimal economic load dispatch This is an open access article under the CC BY-SA license. Nomenclature Btn, B0t, B00 Coefficients of B-matrix for transmission power loss Cp The number of randomly selected control variables among Dim variables Ds Total system demand Dim The number of control variables of each solution 12 , , r1, r2, r3 Random numbers distributed uniformly within the interval [0,1] j The jth variable of the pth new solutions Lp1, Lp2 Two Lévy flight distributions mt, nt, ot Fuel cost function coefficients of the tth thermal generator mtS, ntS, otS Fuel cost function coefficients for the S fuel type of the tth thermal generator n1, n2, n3 The number of solutions in group 1, group 2 and group 3 tS tS PP ,min ,max , The minimum and maximum power output of the tth thermal generator corresponding to the fuel cost source S Pt Power output of the tth thermal generator TELKOMNIKA Telecommun Comput El Control Modified moth swarm algorithm for optimal economic load dispatch problem (Thang Trung Nguyen) 2141 tt PP ,min ,max , The minimum and maximum power output of the tth thermal generator tj tj l u PP 1 , The lower and upper limits of the jth prohibited operating zone of the tth generation unit t, T The current iteration and the maximum iteration Vr1, Vr2, Vr3, Vr4, Vr5, VrA Randomly selected solutions from solutions best Gbest V V , The best solution in group 1, group 2 and all groups 1. INTRODUCTION In a power system, electric energy is produced by thermal plants, hydropower plants and renewable power plants. The fuel cost of renewable power plants such as solar thermal plants, photovoltaic power plants and wind turbines is approximately equal to zero; however, the sources are unstable and changeable during a small interval. On the contrary, the fuel cost for power generation of thermal plants is very expensive owing to fossil fuel. In the future, the fossil fuel including gas coal, and oil becomes exhausted. So, the fuel cost of thermal plants is the main objective during the operation of the power systems. So far, a solution for dealing with the fuel cost of thermal plants can be implemented by an optimal economic load dispatch problem (OELD). The work in OELD problem is to determine the best effective strategy for allocating the power output of all available thermal plants so that total fuel cost of plants can be decreased at least level [1]. In this paper, we concentrate to study three systems that are employed to test the powerful ability of optimization tools. The first system with 6 units considers single fuel, prohibited zones and power loss. The second system with 10 units considers multiple fuels. The last system with 20 units considers power losses in the line transmission. For the first system, a huge number of methods consisting of modified particle swarm optimization (MPSO) [1], hybrid bacterial foraging algorithm and Nelder Mead algorithm (HBFNM) [2], differential evolution (DE) algorithm [3], multiple tabu search algorithm (MTS) [4], self-organizing hierarchical particle swarm optimization (SOH_PSO) [5], new adaptive particle swarm optimization (NAPSO) [6], krill herd algorithm (KHA) [7], chaotic bat method (CBM) [8], exchange market method (EMM) [9], adaptive charged system search method (ACSS) [10], opposition based krill herd method (OKHM) [11], and improved social spider optimization algorithm (ISSO) [12] have been satisfactorily applied. In this method group, MPSO [1] is a version of particle swarm optimization developed in 2007 while ISSO [12] is a variant of social spider optimization algorithm (SSO) proposed in 2019. ISSO was improved based on the classical SSO by proposing three improvements. As a result, optimal solutions found by ISSO were better than MPSO and other methods. For 10-unit system, many methods as DE [3], antlion optimization algorithm (ALO) [13], artificial immune system (AIS) method [14], enhanced augmented Lagrange Hopfield network (EALHN) [15], enhanced lagrangian artificial neural network (ELANN) [16], improved quantum-behaved particle swarm optimization (IQPSO) [17], modified firefly algorithm (MFA) [18] and modified stochastic fractal search algorithm (MSFS) [19] have been successfully employed with the impressive results. Among these methods, MSFS is the latest tool that has been formed by proposing three modifications based on the structure of stochastic fractal search (SFS). By applying these modifications, the search ability of MSFS has been significantly improved when compared to SFS in term of solution quality, convergence speed and stabilization. For the last system, several methods are used for OELD problem. They include MFA [18], MSFS [19], Hopfield model (HM) [20], biogeography-based optimization (BBO) algorithm [21], general algebraic modeling system (GAMS) [22], improved group search optimizer (IGSO) [23], backtracking search algorithm (BSA) [24] and improved cuckoo search algorithm (ICSA) [25]. The contribution of the above algorithms is worthy of recognition in dealing with such OELD problem because these algorithms supply different solutions in aim to the most economical and stable power system operation. Moth Swarm Algorithm (MSA) was a population-based method that proposed in 2017 [26]. Although MSA has used three phases including reconnaissance phase, transverse orientation phase and celestial navigation phase for producing new solution, it only has produced a number of new solutions equaling to population. The disadvantage of MSA is low solution quality, many calculation processes and variation searches by owning many formulas. In this study, a modified moth swarm algorithm (MMSA) is proposed pursuant to the traditional MSA by canceling ineffective formulas and using effective one to deal with drawbacks of MSA. Via three test systems, the results found by the proposed method are compared to other ones for solving OELD problem. Consequently, the key work considered as contributions in the study can be presented as follows:-Point out disadvantages of MSA-Suggest highly effective improvements on MSA-MMSA has a faster simulation time and reaches a high performance and enhances stable search ability