具有励磁控制的电力系统的稳定性和分岔分析  

ANALYSIS OF STABILITY AND BIFURCATION FOR GENERATOR POWER SYSTEMS WITH EXCITED CONTROL

作　　者：蒋永新[1] 王进良 

机构地区：[1]南京大学数学系,南京210093 [2]北京航空航天大学应用数学系,北京100083

出　　处：《应用数学学报》2005年第1期44-54,共11页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10371037)中国科学院研究基金(KZCX2-SW-118)资助项目.

摘　　要：本文根据[1]所提供的带有励磁控制的发电机电力系统,对该系统的平衡点的局部稳定性和分岔进行了定性分析,当0<Pm≤Vs2(Xd-X'd)/2XdΣ'XdΣ或Pm>Vs2(Xd-X'd)/2XdΣ'XdΣ且控制量uf>Efdsc+ufc-Efds时,系统存在两类平衡点,其中一类是不稳定的平衡点,而另一类总是稳定的平衡点.Efds+uf=Efdsc+ufc是鞍结点分岔值,相应于电力系统崩溃.当Efds+uf<Efdsc+ufc时,系统不存在任何平衡点.利用数值模拟和计算过鞍点的一维稳定流形的局部二次近似表达式,得到整个系统的稳定域及近似稳定边界的解析表达式.In this paper, we study the complex nonlinear phenomena in a fundamental power system provided by paper, We analyze local stability and bifurcation of equilibriumin the dynamics systems. When 0 < Pm ≤ Vs2(Xd-X'd)/2XdΣ'XdΣ, or Pm > Vs2(Xd-X'd)/2XdΣ'XdΣ and withcontrol uf > Efdsc + ufc - Efds , there are two fixed points, one is stable, the other is always unstable. Efds + uf = Efdsc + ufc is saddle-node bifurcation value corresponding to collapse of the power system. As Efds + uf < Efdsc + ufc, there is not any fixed point. We obtain the stability region and the analytical expression of the approximate stability boundary of the operation point of the full system by numerical simulation and computating the local quadratic approximate of one-dimensional stable manifold at saddle point.

关 键 词：平衡点 近似表达式 鞍点 分岔分析 一维 稳定流形 解析表达式 系统 结点 控制量 

分 类 号：O175[理学—数学] TP183[理学—基础数学]