电力系统摇摆方程的近似解析解及分析  

Approximate Analytical Solution and Analysis of Power System Swing Equation

作　　者：李京 甘德强[1] 李振垚 刘新元 程雪婷 LI Jing;GAN Deqiang;LI Zhenyao;LIU Xinyuan;CHENG Xueting(School of Electrical Engineering,Zhejiang University,Hangzhou Zhejiang 310027,Zhejiang Province,China;Shanxi Electric Power Research Institute,State Grid Company of China,Taiyuan 030000,Shanxi Province,China)

机构地区：[1]浙江大学电气工程学院,浙江省杭州市310007 [2]国网山西省电力公司电力科学研究院,山西省太原市030000

出　　处：《中国电机工程学报》2024年第12期4589-4600,I0001,共13页Proceedings of the CSEE

基　　金：国家电网有限公司科技项目(52053022001C)。

摘　　要：该文开展大扰动背景下电力系统摇摆方程的近似解研究。首先,在摇摆方程自身正弦耦合特征的基础上,利用泰勒展开公式,给出其摄动形式的一般化多项式型矩阵描述;其次,考虑电力系统稳定过程中的多阶段特性,分别采用线性系统理论和正则摄动技术给出摇摆方程在故障中、故障切除后的近似解析解;然后,分析近似解的结构,揭示电网稳定运动形态特征的数学基础,并论证受扰系统功角摆幅的单调性规律;最后,IEEE 3机9节点系统、IEEE 10机39节点系统的算例验证所提方法及分析的有效性。This paper studies the approximate analytical solution of the power system swing equation under large disturbance.Firstly,based on the inherent sinusoidal coupling characteristics of the swing equation itself,a generalized polynomial matrix description of its perturbation form is provided using the Taylor expansion formula.Secondly,considering the different stage of power system when suffered disturbance,the approximate analytical solutions of the swing equation in fault and after fault are obtained by using linear system theory and regular perturbation technique respectively.Then,the structure of the approximate solution is analyzed,revealing the mathematical foundation of the characteristic of the stable motion of the power grid,and the monotonicity of the amplitude of rotor angle is demonstrated.Finally,numerical examples of IEEE 3-machine 9-bus system and IEEE 10-machine 39-bus system verify the effectiveness of the results in this paper.

关 键 词：摇摆方程 近似解析解 正则摄动 暂态稳定 

分 类 号：TM71[电气工程—电力系统及自动化]