Cross-Scale Performance Analysis of Metaheuristic Algorithms for Simultaneous DG and DSTATCOM Placement in Radial Distribution Networks

Jul 16, 2026

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Simultaneous placement of distributed generators and DSTATCOMs in radial distribution networks is formulated as a combinatorial mixed-integer optimization problem with limited understanding of scalability as decision dimensionality increases. A cross-scale study evaluates seven metaheuristics—GWO, SCA, PSO, WOA, GA, HHO, and SMA—on IEEE 33-, 69-, and 136-bus systems at d = 4, 8, 12 using 30 independent runs and Wilcoxon/Friedman tests. Catastrophic Failure Rate (CFR) extends mean-based metrics, showing dimensional scaling as a behavior discriminator: Friedman χ2 peaks at 143.79 for 136-bus at d = 12, with algorithm clustering into high and low performance.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages5

Reading Time13 min

Introduction

Literature Review

DG Siting in Distribution Networks

DSTATCOM Placement on Distribution Networks

Simultaneous DG and DSTATCOM Placement

Cross-Scale Performance Analysis of Metaheuristic Algorithms for Simultaneous DG and DSTATCOM Placement in Radial Distribution Networks 1st Md. Tanvirul Islam Department of Electrical and Electronic Engineering Bangladesh University of Engineering and Technology Dhaka, Bangladesh Email: [2006095@eee.buet.ac.bd](2006095@eee.buet.ac.bd) arXiv :2607 .04954v1 [ ee ss . SY] 6 Jul 2026 Abstract—The problem of simultaneous placement of distributed generators and DSTATCOMs in radial distribution networks (RDNs) is a combinatorial mixedinteger optimization problem whose scalability with growing decision dimensionality has been insufficiently explored. A cross-scale analysis of seven metaheuristic algorithms, GWO, SCA, PSO, WOA, GA, HHO and SMA, is conducted on the IEEE 33-bus, 69-bus, and 136-bus systems at three problem dimensions d = 4 , 8 , 12, with 30 independent runs per configuration being validated through Wilcoxon and Friedman tests. Mean-performance statistics are extended with a Catastrophic Failure Rate (CFR) metric. The main result will be that dimensional scaling serves as a behavioral discriminator. The Friedman χ2 rises with the dimensionality, reaching its maximum value of χ2 = 143 .79 in the 136-bus at d = 12 that corresponds to the progressive phase separation of the algorithms into two clusters of high and low performance. GA is the best performer in terms of the lowest rank in all the configurations. SCA has low variance but convergence to increasingly sub-optimal solutions. HHO exhibits catastrophic instability at all scales. Perhaps most strikingly, GA and PSO obtain a 3.3% CFR on the 136-bus at d = 12 while the 33-bus at identical dimensionality has a 73% − 83% CFR, showing that topology influences the reliability in a manner that isnot captured by single-system measures. Index Terms—Distributed Generation, DSTATCOM, Radial Distribution Network, Metaheuristic Optimization, Cross-Scale Comparative Analysis, Catastrophic Failure Rate I. Introduction Active power losses continue to be a major operational issue in radial distribution systems. For example, in the IEEE 33-bus benchmark network, base-case active power losses are approximately 210 kW, corresponding to about 5.7% of the total load [1] . Distributed generators (DGs) reduce upstream I2 R losses by 40-70% in benchmark studies [2], while DSTATCOMs provide reactive power support that improves voltage profiles within the ±5% limits of IEEE Std. 1547 [3] . However, the effectiveness of both mentioned technologies strongly depends on their placement and sizing. Suboptimal siting may reduce expected benefits, but it may introduce new constraint violations [4] . The simultane- ous optimization of multiple DGs and DSTATCOMs is a mixed-integer nonlinear programming problem, where location variables are discrete and device sizes are continuous within operational limits. For the IEEE 136-bus system, the location space alone yields approximately 6.33 × 1012 possible configurations for three DGs and three DSTATCOMs, making comprehensive search computationally intractable. Several metaheuristic optimization techniques have been applied to this problem individually. A key question is whether algorithm ranking remains stable as dimensionality increases or changes when multiple devices are optimized simultaneously. This is particularly important in distribution planning, since an algorithm performing well for single-device cases may not scale effectively to multidevice scenarios. Therefore, the proper understanding of these scalability characteristics is essential for reliable practical scenarios. This paper addresses this gap by systematically evaluating seven metaheuristic algorithms across multiple problem dimensions and IEEE radial distribution systems. The main contributions are summarized as follows: • A scalable optimization framework for simultaneous placement and sizing of NDG distributed generators and NDST DSTATCOMs, enabling consiste

FAQs

What optimization problem does the study address?

The study addresses simultaneous placement of distributed generators and DSTATCOMs in radial distribution networks, modeled as a combinatorial mixed-integer optimization problem.

Which metaheuristic algorithms are compared and how is scalability tested?

Seven metaheuristics (GWO, SCA, PSO, WOA, GA, HHO, SMA) are evaluated across IEEE 33-, 69-, and 136-bus systems while varying the problem dimension d = 4, 8, 12.

Why is the Catastrophic Failure Rate (CFR) introduced?

CFR captures convergence failures that can be hidden by mean-based performance measures, providing a fitness metric focused on reliability.

Jul 16, 2026

Upload by Violet