Abstract

In this paper, an improved hybridization of an evolutionary algorithm, named permutated oppositional differential evolution sine cosine algorithm (PODESCA) and also a sensitivity-based decision-making technique (SBDMT) are proposed to tackle the optimal planning of shunt capacitors (OPSC) problem in different-scale radial distribution systems (RDSs). The evolved PODESCA uniquely utilizes the mechanisms of differential evolution (DE) and an enhanced sine–cosine algorithm (SCA) to constitute the algorithm’s main structure. In addition, quasi-oppositional technique (QOT) is applied at the initialization stage to generate the initial population, and also inside the main loop. PODESCA is implemented to solve the OPSC problem, where the objective is to minimize the system’s total cost with the presence of capacitors subject to different operational constraints. Moreover, SBDMT is developed by using a multi-criteria decision-making (MCDM) approach; namely the technique for the order of preference by similarity to ideal solution (TOPSIS). By applying this approach, four sensitivity-based indices (SBIs) are set as inputs of TOPSIS, whereas the output is the highest potential buses for SC placement. Consequently, the OPSC problem’s search space is extensively and effectively reduced. Hence, based on the reduced search space, PODESCA is reimplemented on the OPSC problem, and the obtained results with and without reducing the search space by the proposed SBDMT are then compared. For further validation of the proposed methods, three RDSs are used, and then the results are compared with different methods from the literature. The performed comparisons demonstrate that the proposed methods overcome several previous methods and they are recommended as effective and robust techniques for solving the OPSC problem.

Highlights

  • The numerous technical and operational problems that might occur in the vital radial distribution systems (RDSs) have forced the operators to make more efforts towards solving theseAppl

  • It is clear that the selected locations by permutated oppositional differential evolution sine cosine algorithm (PODESCA) in the first case are included in the search space

  • PODESCA is reapplied on the OPSC problem with a reduced search space by the sensitivity-based decision-making technique (SBDMT), where it is limited to only 25 buses

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Summary

Introduction

The numerous technical and operational problems that might occur in the vital radial distribution systems (RDSs) have forced the operators to make more efforts towards solving these. Various formulas of this OF were studied utilizing many EA methods, as in [19], where minimizing the SC costs was a main part of the formulated bi-objective The cost of both total installed capacitors and power loss was the considered OF in [20], where a fuzzy-based technique was used for solving the OPSC problem. Few previous works consider a comprehensive cost OF that includes all required costs especially for large-scale RDSs. Some EA approaches do not guarantee obtaining the optimal solutions especially for large-scale RDSs. Most of the methods utilize only one or two SBIs for reducing the search space of the OPSC problem. The evolved PODESCA uniquely utilizes three effective search techniques in order to present a new and robust method, where the mechanisms of differential evolution (DE) and enhanced sine cosine algorithm (SCA) constitute the algorithm’s main loop.

Mathematical Formulation of OPSC Problem
Research Steps and Methodology
Structure of PODESCA
Structure of SBDMT
Sensitivity-Based Indices
TOPSIS
Performance Analysis of PODESCA
Results and Discussions
Results without Reducing the Search Space
Method
Results with Reducing the Search Space by SBDMT
Convergence
Convergence characteristics of of PODESCA
Conclusions
Full Text
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