基于自适应稀疏伪谱逼近新方法的随机潮流计算  

Stochastic Power Flow Using a New Adaptive Sparse Pseudospectral Approximation Method

作　　者：林济铿[1] 申丹枫 刘阳升[1] LIN Jikeng;SHEN Danfeng;LIU Yangsheng(College of Electronics and Information Engineering, Tongji University, Yangpu District, Shanghai 200092, China)

机构地区：[1]同济大学电子与信息工程学院,上海市杨浦区200092

出　　处：《中国电机工程学报》2019年第10期2875-2884,共10页Proceedings of the CSEE

摘　　要：提出基于自适应稀疏伪谱逼近新方法(newadaptive sparse pseudospectral approximation method,NA-SPAM)的随机潮流计算新方法。该方法的基本过程如下:首先提出基于Nataf-Margin变换的相关随机变量独立化处理方法,并以命题及推论的形式证明了该变换是有效的并且能够最大程度地保持NA-SPAM的计算效率;然后通过在NA-SPAM中用Kronrod-Patterson嵌套积分序列代替传统的高斯积分序列提出了嵌套NA-SPAM,以减少NA-SPAM所需的积分点和计算量;最后将Nataf-Margin变换和嵌套NA-SPAM结合为综合NA-SPAM,实现了随机潮流快速且准确的计算,得到系统状态量的期望、方差以及概率密度。用基于IEEE-9、IEEE-118节点系统的算例验证了综合NA-SPAM的有效性,以及其相比于经典伪谱SCM、LHS和MCM的计算效率优势。A new method for power flow calculation using a new adaptive sparse pseudospectral approximation method was proposed. The basic procedures of the proposed method were as follows. First, the Nataf-Margin transformation for transforming the correlated random variables to independent ones was proposed and proved to be effective and most efficiency-maintaining for NA-SPAM bya proposition and a corollary. Next, the nested NA-SPAM was proposed by replacing traditional Gaussian quadrature rules with nested Kronrod-Patterson quadrature rules in NA-SPAM, which reduced the number of integral points and corresponding computational effort of NA-SPAM. Finally, the integrated NA-SPAM that combined the Nataf-Margin transformation and the nested NA-SPAM was proposed and applied in stochastic power flow calculation, by which the expectations, variances and probability density functions of state variables can be calculated quickly and accurately. The effectiveness of NA-SPAM and its advantage over classic pseudospectral SCM, LHS and MCM were validated by several cases on IEEE-9 system and IEEE-118 system.

关 键 词：自适应稀疏伪谱逼近新方法 随机潮流计算 Nataf-Margin变换 Kronrod-Patterson嵌套积分序列 

分 类 号：TM72[电气工程—电力系统及自动化]