Reduction in power loss while maintaining the acceptable voltage profile has become a challenge for distribution system operators due to expanded living standards. Properly sized shunt capacitors (SCs) allocated at suitable locations of the distribution system can enhance its performance by tackling the power quality issues and foster multiple technical and economic benefits. Most of the existing research work in this domain is accomplished at fixed loading conditions without incorporating purchasing, installation, operation and degradation costs of the SCs. In this work, an intelligent metaheuristic polar bear optimization algorithm (PBOA) is applied to solve the optimal capacitor placement and sizing problem in the radial distribution system (RDS) at various loading conditions. By formulating multiple objective functions for the annual operating cost (AOC), this work incorporates the cost of real power loss (\( P_{\text{loss}} \)) and various costs associated with SCs. The proposed technique is tested on various IEEE standard bus systems under different loading conditions. The proposed PBOA reduces AOC and \( P_{\text{loss}} \) of RDS while maintaining tolerable voltages at systems’ buses. The reductions of 51%, 35%, 26% and 53% in \( P_{\text{loss}} \) are observed for IEEE standard 15-, 33-, 34- and 85-bus systems, respectively, at 100% loading from their uncompensated cases. Similarly, reductions in AOCs for the same systems at 100% loading are 32%, 25%, 16% and 45%, respectively. These results prove superiority of proposed method over recent state-of-the-art algorithmic approaches. The results of this work can be useful for distribution system operators in achieving reliable and efficient operation of the power grid.

由于生活水平的提高，在保持可接受的电压曲线的同时降低功率损耗已成为配电系统运营商的挑战。在配电系统的适当位置分配适当尺寸的并联电容器（SC）可以通过解决电能质量问题来提高其性能，并带来多种技术和经济效益。该领域中的大多数现有研究工作都是在固定负载条件下完成的，而无需考虑SC的购买，安装，运行和降级成本。在这项工作中，智能元启发式北极熊优化算法（PBOA）用于解决在各种负载条件下径向分布系统（RDS）中的最佳电容器放置和尺寸确定问题。\（P _ {\ text {loss}} \））以及与SC相关的各种费用。所提出的技术在不同的负载条件下在各种IEEE标准总线系统上进行了测试。拟议的PBOA降低了RDS的AOC和\（P _ {\ text {loss}} \），同时保持了系统总线上的容许电压。\（P _ {\ text {loss}} \）分别减少了51％，35％，26％和53％分别针对IEEE标准15总线，33总线，34总线和85总线系统，在未补偿情况下负载为100％时观察到。同样，在100％负载下，相同系统的AOC减少量分别为32％，25％，16％和45％。这些结果证明了所提出的方法优于最新的最新算法方法。这项工作的结果对于配电系统运营商实现可靠而有效的电网运行非常有用。