单机无穷大系统微分代数方程模型的电压稳定性  

THE VOLTAGE STABILITY OF A DAE MODEL FOR SINGLEMACHINE INFINITE BUS SYSTEM

作　　者：廖浩辉[1] 唐云[1] 

机构地区：[1]清华大学数学科学系,北京100084

出　　处：《电力系统自动化》2000年第15期11-15,共5页Automation of Electric Power Systems

基　　金：国家重点基础研究专项经费!(G1998020307);国家自然科学基金重点资助项目!(19990510)

摘　　要：研究一个由静态负荷决定的单机无穷大系统 ,它的数学模型是一个微分代数方程 (DAE)。利用特征值分析方法 ,我们发现模型的平衡解曲线的上支是稳定的 ,下支则除了介于 1 1 .41 0 8和1 1 .41 1 5之间非常小的一段曲线外 ,都是稳定的。这与由静态负荷以及动态负荷 (Walve模型 )所决定的微分方程 (ODE)模型情况不同。为了研究系统电压失稳的模式 ,分析其奇点附近的分岔现象。利用奇点理论 ,计算出奇点为极限点。然后 ,通过把 DAE的微分方程部分投影在 (V,ω)面上 ,得到奇异微分方程。文中给出了用来判断障碍 (impasse)点的一种较简单的方法 ,并用以验证对于分岔值处奇异面上几乎所有的点都是障碍点。in this article we study a single machine infinite bus system determin ed by a static load model. The mathematicalmodel of the power system is a differential algebraic equation (DAE). By using t he eigenvalue analysis. the upper branch ofthe equilibrium curve is stable while the lower branch is stable except for a sm all section of Q, between 11. 410 8 and 11. 411 5.This is different from the results of ordinary differential equation (ODE) model determined by both static load and dynamicload (Waive model). To study the voltage collapse process of the system, we anal yse the bifurcation phenomenon near thesingular point. By using the singularity theory, the singular point of the DAE s ystem is found to be a limit point. Then byprojecting the differential equation on the (V, co) -plane. a singular ODE is ob tained. From the analysis of the phase portraitfor the singular ODE, the system is found to collapse by going through the singu lar surface. A simpler method is given toidentify the impasse point of the system and is used to prove that for the phase portrait near bifurcation value Q?. almostevery point on the singular surface is an impasse point. This method simplifies previous one by Chua et al.. and can beimplemented easily in numerical software.This project is supported by National Key Basic Research Special Fund of China ( No. G1998020307) and National NaturalScience Foundation of China (No. 19990510).

关 键 词：电力系统 电压稳定性 微分代数方程 数学模型 

分 类 号：TM71[电气工程—电力系统及自动化]