Abstract
In the paper, a proposed particle swarm optimization (PPSO) is implemented for dealing with an economic load dispatch (ELD) problem considering the competitive electric market. The main task of the problem is to determine optimal power generation and optimal reserve generation of available thermal generation units so that total profit of all the units is maximized. In addition, constraints, such as generation limit and reserve limit of each unit, power demand and reserve demand, must be exactly satisfied. PPSO is an improved version of conventional particle swarm optimization (PSO) by combining pseudo gradient method, constriction factor and a newly proposed position update method. On the other hand, in order to support PPSO to reach good results for the considered problem, a new constraint handling method (NCHM) is also proposed for determining maximum reserve generation and correcting reserve generation. Three test systems with 3, 10 and 20 units are employed to evaluate the real performance of PPSO. In addition to the comparisons with previous methods, salp swarm optimization (SSA), modified differential evolution (MDE) and eight other PSO methods are also implemented for comparisons. Through the result comparisons, two main contributions of the study are as follows: (1) NCHM is very effective for PSO methods to reach a high success rate and higher solution quality, (2) PPSO is more effective than other methods. Consequently, NCHM and PPSO are the useful combination for the considered problem.
Highlights
Economic load dispatch (ELD) is one of the most important problems in power systems due to its significant contributions to economy and operation stabilization of power system
Different methods have been proposed for the problem such as Lagrange function-based evolutionary programming (LFEP) [19], Tabu search algorithm (TSA) [20], muller approach (MA) [21], memetic optimization algorithm (MOA) [22], modified artificial bee colony optimization algorithm (MABCOA) [23], ant colony optimization algorithm (ACOA) [24], multi-agent model algorithm (MAMA) [25], binary fish optimization algorithm (BFOA) [26], Lagrange function-based invasive weed optimization algorithm (LFIWOA) [27], sine function and cosine function-based algorithm (SCBA) [28], binary whale optimization algorithm (BWOA) [29], expanded Lagrange function-based Hopfield network method (ELF-HNM) [30] and five Lagrange function-based Hopfield neuron network (LF-HNN) methods [31]
The summary of the test systems and the two considered cases is as follows: Test system 1: Three units with convex fuel cost function shown in Equation (1) Test system 2: Ten units with convex fuel cost function shown in Equation (1) Test system 3: Twenty units with nonconvex fuel cost shown in Equation (2) Case 1: Total revenue and total fuel cost are obtained by using Equations (5) and (6) Case 2: Total revenue and total fuel cost are obtained by using Equations (7) and (8)
Summary
Economic load dispatch (ELD) is one of the most important problems in power systems due to its significant contributions to economy and operation stabilization of power system. The concerned problem has been solved by applying a huge number of methods such as maximum likelihood optima (MLO) [6], evolutionary particle swarm optimization algorithm (EPSO) [7], improved stochastic fractal search algorithm (ISFSA) [8], improved social spider optimization algorithm (ISSOA) [9], interior search algorithm (ISA) [10], multi-leader comprehensive learning particle swarm optimization with adaptive mutation (MLCL-PSO) [11], dragonfly algorithm (DA) [12] and ameliorated grey wolf optimization (AGWO) [13] These studies focused on demonstrating constraint handling ability and high-quality solution searching ability of original methods and improved methods rather than proposing new issues and real phenomena regarding power systems and electric components. Among the studies regarding the competitive electric market, ELF-HNM was an application of Hopfield neuron network based on expanded Lagrange
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