Abstract

The economic load dispatch (ELD) problem is a complex optimization problem in power systems. The main task for this optimization problem is to minimize the total fuel cost of generators while also meeting the conditional constraints of valve-point loading effects, prohibited operating zones, and nonsmooth cost functions. In this paper, a novel grey wolf optimization (GWO), abbreviated as NGWO, is proposed to solve the ELD problem by introducing an independent local search strategy and a noninferior solution neighborhood independent local search technique to the original GWO algorithm to achieve the best problem solution. A local search strategy is added to the standard GWO algorithm in the NGWO, which is called GWOI, to search the local neighborhood of the global optimal point in depth and to guarantee a better candidate. In addition, a noninferior solution neighborhood independent local search method is introduced into the GWOI algorithm to find a better solution in the noninferior solution neighborhood and ensure the high probability of jumping out of the local optimum. The feasibility of the proposed NGWO method is verified on five different power systems, and it is compared with other selected methods in terms of the solution quality, convergence rate, and robustness. The compared experimental results indicate that the proposed NGWO method can efficiently solve ELD problems with higher-quality solutions.

Highlights

  • Optimization problems widely exist in various fields in real-life

  • This paper proposes a noninferior solution neighborhood independent local search technique based on this analysis

  • The economic load dispatch problem (ELD) problem can be described as an optimization problem to minimize the total fuel cost of the individual dispatchable generating power while being subject to different constraints

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Summary

Introduction

Optimization problems widely exist in various fields in real-life. Some of these optimization problems are simple, while others are very complex due to nonconvex objective functions and complex model constraints. Two powerful operations parameters are designed to maintain the exploration and exploitation to avoid local optima stagnation [27] These remarkable advantages make GWO a widely studied and applied technique in practical optimization problems, such as feature selection [28], training multilayer perceptron (MLP) networks [29], optimizing support vector machines [30], clustering applications [31], design and tuning controllers [32], ELD problems [18,19,33], path planning [34], and welding production scheduling [35]. The rest of this paper is structured, as follows: Section 2 presents the proposed NGWO algorithm, Section 3 provides the formulation of the ELD problem, Section 4 addresses the methodology of NGWO for solving ELD problems, and Section 5 presents the conclusions and future work

The Proposed NGWO Algorithm
The Basic GWO Algorithm
The Compared GWOI Algorithm
The Compared GWOII Algorithm
Economic Load Dispatch Formulations
Objective Function
Constraints and Variables
Generating Capacity Limits and Variables
Ramp Rate Limits and Variables
Prohibited Operating Zones Constraints and Variables
Implementation of NGWO Method in Solving the ELD Problem
Constraints Handling in ELD Problems with NGWO Approache
ELD Problem without the Valve-Point Loading Effects
ELD Problem with Considering the Valve-Point Loading Effects
Implementation Steps of NGWO to ELD Problem
Numerical Simulation Results and Analysis
Case I
Convergence
Case III
Case IV
12. The table shows that NGWO the lowest best generation
Conclusions and Future
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