This article investigates a clustering‐based approach to simultaneously seek the optimal allocation of wind farm (WF) and shunt capacitor (SC) in distribution systems. The stochastic nature of wind turbines leads the allocation problem to become more intricate nowadays. Hence, the application of probabilistic methods for this stochastic analysis is a vital requirement. This study implements a K‐means clustering method to bunch the wind turbines output power into appropriate clusters. Then, the data, clustered by K‐means, are directly used in the Monte Carlo calculations. This results in computational burden reduction. The optimization process is performed by particle swarm optimization (PSO) methodology. The decision variables of PSO are the location and capacity of WF and SCs. The energy loss cost and investment costs of WF and SCs are selected as the objective functions for the proposed optimization problem. The proposed optimal allocation methodology is implemented on several benchmark IEEE case studies to illustrate its effectiveness and thereby to draw the relevant conclusions.

中文翻译：

---

径向配电系统中基于风场和并联电容器分配的基于聚类的技术经济分析

本文研究了一种基于聚类的方法，以同时寻求配电系统中风电场（WF）和并联电容器（SC）的最佳分配。如今，风力涡轮机的随机性导致分配问题变得更加复杂。因此，概率方法在这种随机分析中的应用是至关重要的。本研究采用K均值聚类方法将风力涡轮机的输出功率聚集成适当的聚类。然后，由K聚类的数据均值，直接在蒙特卡洛计算中使用。这导致计算负担减少。优化过程是通过粒子群优化（PSO）方法执行的。PSO的决策变量是WF和SC的位置和容量。选择WF和SC的能量损失成本和投资成本作为所提出的优化问题的目标函数。在几个基准IEEE案例研究中实施了建议的最佳分配方法，以说明其有效性并得出相关结论。