一种基于蒙特卡洛方法的配电网概率可靠性快速计算方法

A fast calculation method for probabilistic reliability of distribution network based on Monte Carlo method

配电网的概率可靠性能够弥补传统可靠性指标的期望值仅从均值角度衡量系统可靠性的不足,但随着配电网规模扩大以及数据量的剧增,能够同时兼顾计算准确性与计算速度的概率可靠性计算方法是亟待研究的。为此,提出一种基于蒙特卡洛方法的配电网概率可靠性快速计算方法,利用改进三点估计法以及三阶多项式正态变换,在保留输入变量相关性的同时有效缩减输入样本点规模,并采用级数展开得到概率可靠性。首先采用改进三点估计法,在独立标准正态空间内选取样本点,再通过三阶多项式正态变换将其转换为原始变量空间的样本点;接着采用序贯蒙特卡洛方法,在考虑孤岛划分的情况下对样本点进行可靠性计算;最后通过Edgeworth级数展开,得到可靠性指标的概率分布。对改进的IEEE-RBTS Bus6的F4馈线进行算例分析,结果表明:该文所提方法与传统蒙特卡洛方法的配电网系统可靠性计算结果之间仅存在2.195%的最大偏差,而该文所提方法计算时间仅为传统蒙特卡洛方法的1.05%,证明该文所提方法在保证较高精度的同时可以显著提升计算速度。

Probabilistic reliability can overcome the shortage of traditional reliability index expectation which only measures system reliability from the mean perspective.However,with the expansion of distribution network scale and the surge of data volume,a probabilistic reliability calculation method that can balance calculation accuracy and calculation speed is urgently needed.Therefore,a fast calculation method for probabilistic reliability of distribution network based on Monte Carlo method is proposed.The improved three-point estimation method and the third-order polynomial normal transformation are used to effectively reduce the size of input sample points while retaining the correlation of input variables,and the probabilistic reliability is obtained by series expansion.Firstly,the improved three-point estimation method is used to select sample points in the independent standard normal space,which are then transformed into sample points in the original variable space through the third-order polynomial normal transformation.Then,the sequential Monte Carlo method is used to calculate the reliability of the sample points considering the island division.Finally,the probability distribution of reliability index is obtained through Edgeworth series expansion.The example analysis of the improved IEEE-RBTS Bus6 F4 feeder shows that there is only a maximum deviation of 2.195%between the reliability calculation results of the proposed method and the traditional Monte Carlo method,while the calculation time of the proposed method is only 1.05%of the traditional Monte Carlo method.It proves that the proposed method can significantly improve the calculation speed while ensuring high accuracy.