基于全纯嵌入法的电力系统高维电压稳定边界  

Analytical High-dimensional Static Voltage Stability Boundary Based on Holomorphic Embedding Method

作　　者：刘承锡 于懿兰 赖秋频 LIU Chengxi;YU Yilan;LAI Qiupin(School of Electrical Engineering and Automation,Wuhan University,Wuhan 430072,Hubei Province,China)

机构地区：[1]武汉大学电气与自动化学院,湖北省武汉市430072

出　　处：《中国电机工程学报》2024年第23期9110-9121,共12页PROCEEDINGS OF THE CHINESE SOCIETY FOR ELECTRICAL ENGINEERING

基　　金：国家自然科学基金项目(52007133)。

摘　　要：电力系统静态电压稳定边界(static voltage stability boundary,SVSB)对于判断电压稳定性、评估电压稳定裕度具有重要的指示作用,因此,快速准确地计算SVSB对于电网安全稳定运行具有重要意义。电力系统作为一个超高维多变量的复杂非线性系统,其电压稳定边界本质上是某一拓扑结构下所能维持电源和负荷功率平衡的极限电压所构成的非线性高维边界。因此,将SVSB考虑为高维场景下的电压稳定超曲面,提出计算电压稳定边界的新方法。首先,利用多维全纯嵌入法(multidimensional holomorphic embedding method,MDHEM)求得节点电压的多变量幂级数(multivariate power series,MPS)表达式;然后,基于柯西-阿达马定理,推导并证明电压稳定边界与节点电压幂级数前后项系数之间的解析关系,并通过理论证明将所提出的方法从单维推广到高维场景;接着,基于推导的SVSB解析表达式,提出高维电压稳定边界计算与电压稳定性快速评估方法;最后,在IEEE 14节点、新英格兰39节点和IEEE 118节点系统中验证所提方法的有效性。Power system static voltage stability boundary(SVSB)plays an important indication role in monitoring voltage stability and evaluating the voltage stability margin,so the rapid and accurate calculation of SVSB is of great significance for the safety and stability of power grid.As an ultra-high-dimensional multivariate nonlinear system,the SVSB of a power system is essentially a nonlinear highdimensional boundary composed of the voltages which can maintain the balance of supply and load under a certain topology.This paper considers the SVSB as a voltage stability hypersurface and proposes a new method to calculate the SVSB.First,multidimensional holomorphic embedding method(MDHEM)is used to find the multivariate power series(MPS)expressions for the bus voltages.Then,based on the Cauchy-Hadamard theorem,the analytical relationship between the SVSB and the coefficients of the voltage MPS front and back terms is derived and proved,and through theoretical proofs the proposed method is extended from single-dimensional to high-dimensional scenarios.Then,based on the derived SVSB analytical expression,the highdimensional SVSB calculation and voltage stability evaluation methods are proposed.Finally,the validity of the proposed method is verified in the IEEE 14-bus,New England 39-bus and IEEE 118-bus systems.

关 键 词：静态电压稳定边界 多维全纯嵌入 柯西-阿达马定理 多变量幂级数表达式 

分 类 号：TM712[电气工程—电力系统及自动化]