The unpredictable load variations and raising presence of wind farms have caused modern‐day distribution system operation and planning extremely complex. This paper puts an earliest effort toward the optimal allocation of the shunt capacitors in radial distribution system (RDS) under uncertain load and wind power generation. The authors aim to minimize the annual operating cost (AOC) for RDS by deciding the optimum placements of shunt capacitors. Here, three‐point estimate method is applied to estimate the uncertainties in the load demand and power output from the wind generator. The stochastic behavior of wind generators and load demands are modeled by using Weibull and normal distribution functions, respectively. An opposition‐based competitive swarm optimizer (OCSO) algorithm is applied to minimize the AOC, and the optimization problem is solved for both probabilistic and deterministic approach. The Cornish‐Fisher expansion is used in this work to provide more accurate probability distribution functions of AOC. Furthermore, the impact of VAr injection on AOC values and power losses are also studied in this work. Moreover, the results obtained from the OCSO algorithm are compared with the original competitive swarm optimizer results. The proposed problem is tested on 69 bus RDS with different loading conditions, and results are analyzed for each scenario.

中文翻译：

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估算不确定性对风集成径向配电系统中最佳电容器放置的影响

不可预测的负荷变化和风电场的兴起使现代配电系统的运行和计划变得极为复杂。本文致力于在不确定负载和风力发电情况下，在径向配电系统（RDS）中优化并联电容器的分配。作者的目的是通过确定并联电容器的最佳位置来使RDS的年度运行成本（AOC）最小化。在此，采用三点估计方法来估计风力发电机的负荷需求和功率输出中的不确定性。分别使用Weibull和正态分布函数对风力发电机的随机行为和负荷需求进行建模。应用了基于对手的竞争群优化器（OCSO）算法，以最小化AOC，通过概率和确定性方法解决了优化问题。在这项工作中使用了Cornish-Fisher扩展来提供AOC的更准确的概率分布函数。此外，在这项工作中还研究了VAr注入对AOC值和功率损耗的影响。此外，将从OCSO算法获得的结果与原始竞争群优化器结果进行了比较。所提出的问题在具有不同加载条件的69总线RDS上进行了测试，并针对每种情况分析了结果。将从OCSO算法获得的结果与原始竞争群优化器结果进行比较。所提出的问题在具有不同加载条件的69总线RDS上进行了测试，并针对每种情况分析了结果。将从OCSO算法获得的结果与原始竞争群优化器结果进行比较。所提出的问题在具有不同加载条件的69总线RDS上进行了测试，并针对每种情况分析了结果。