An improved probabilistic load flow in distribution networks based on clustering and Point estimate methods

Abstract

Clustering approaches are one of the probabilistic load flow (PLF) methods in distribution networks that can be used to obtain output random variables, with much less computation burden and time than the Monte Carlo simulation (MCS) method. However, a challenge of the clustering methods is that the statistical characteristics of the output random variables are obtained with low accuracy. This paper presents a hybrid approach based on clustering and Point estimate methods. In the proposed approach, first, the sample points are clustered based on the k-means method and the optimal agent of each cluster is determined. Then, for each member of the population of agents, the deterministic load flow calculations are performed, and the output variables are calculated. Afterward, a Point estimate-based PLF is performed and the mean and the standard deviation of the output variables are obtained. Finally, the statistical data of each output random variable are modified using the Point estimate method. The use of the proposed method makes it possible to obtain the statistical properties of output random variables such as mean, standard deviation and probabilistic functions, with high accuracy and without significantly increasing the burden of calculations. In order to confirm the consistency and efficiency of the proposed method, the 10-, 33-, 69-, 85-, and 118-bus standard distribution networks have been simulated using coding in Python® programming language. In simulation studies, the results of the proposed method have been compared with the results obtained from the clustering method as well as the MCS method, as a criterion.