电力系统奇异摄动模型霍普夫分岔分析  

HOPF BIFURCATION ANALYSIS OF POWER SYSTEM SINGULARLY PERTURBED ORDINARY DIFFERENTIAL MODEL

作　　者：王庆红[1] 周双喜[1] 

机构地区：[1]清华大学电机工程与应用电子技术系,北京100084

出　　处：《中国电机工程学报》2003年第8期1-6,共6页Proceedings of the CSEE

基　　金：国家重点基础研究专项经费资助项目(G1998020306)。~~

摘　　要：该文讨论了多时标电力系统模型中的奇异诱导分岔(SIB)和奇异霍普夫分岔(SHB)的特点及其相互关系;拓展了SHB理论的应用范围,使之适用于一类和其本身慢性流型维数无关的电力系统奇异摄动常微分方程 (ODE) 模型;阐述了电力系统微分代数方程(DAE)模型发生SIB分岔和ODE模型发生SHB分岔存在一一对应的特点。最后,以一个三机系统为例,通过时标变换求解带阻尼项电力系统ODE模型平衡点的方法,巧妙地回避了DAE模型在奇异诱导分岔点处无法求解的困难,展示了带阻尼项的电力系统DAE模型会发生双奇异诱导分岔这一特点,并验证了它和带阻尼项的ODE模型发生霍普夫分岔存在对应关系,为多时标电力系统 模型分岔分析提供了新的思路和分析方法。The singularity induced bifurcation and singular Hopf bifurcation theorems and the degeneracies that arises when Newtons laws are coupled to Kirchhoffs laws are explored. Such models are used in the electrical engineering literature to describe electrical power systems and they can take the form of either an index-1 differential algebraic equation (DAE) model or a singularly perturbed ordinary differential equation (ODE) model which are called multi time scale power system model, The characteristics and relationships of above mentioned bifurcations between DAE and ODE are analyzed, a discussion is included of the consequences of the power engineers load flow singularity for both ODE and DAE with a three bus system, some new methods and ideas analyzing multi time scale model of power system are proposed.

关 键 词：电力系统 稳定性 奇异摄动模型 霍普夫分岔分析 SHB理论 微分代数方程 

分 类 号：TM712[电气工程—电力系统及自动化]