含相关性随机变量的概率最优潮流问题的蒙特卡罗模拟方法

A Monte Carlo simulation method for probabilistic optimal power flow with correlated stochastic variables

采用三阶多项式变换技术构建了一个可以处理非正态相关的多变量随机因素的概率最优潮流蒙特卡罗模拟模型。并使用该模型讨论了风力发电和负荷随机性对最优潮流解的影响,具体分析了随机变量的相关性以及波动幅度对系统运行成本、发电机组出力、边际电价以及节点电压、节点相角和线路潮流的影响。基于IEEE-118节点的算例分析表明,给出的三阶多项式变换技术所生成的相关系数和边际概率分布的随机数与指定值具有良好的拟合精度,而随机因素的相关性对概率最优潮流的影响显著,不可忽略。该方法提供了一个具有理论基础的的讨论工具。

A Monte Carlo simulation model based on third-order polynomial normal transformation （TPNT） is proposed to deal with probabilistic optimal power flow problems with non-normal dependent random variables. The model is employed to discuss the influence on the solutions of optimal power flow which is caused by wind generation and load stochastic variation. The influence of the relevance and fluctuation magnitude of stochastic variables on system operation costs, power output of generating units, marginal price, bus voltage, bus phase angle, and line flow is analyzed in depth. A case study on a slightly modified IEEE-118 system shows that the TPNT method is capable of generating stochastic samples with fixed marginal distributions and correlation matrixes. Besides, the influence of the correlation between stochastic variables is so significant that it could not be neglected. The presented method is a good tool to deal with the case.