Dynamical Behavior and Singularities of a Single-machine Infinite-bus Power System  

作　　者：Jin-liangWang Sheng-weiMei QiangLu TeoKok-lay 

机构地区：[1]DepartmentofMathematics&LIMBoftheMinistryofEducation,BeijingUniversityofAeronautandAstronaut,Beijing100083,China [2]DepartmentofElectricalEngineering,TsinghuaUniversity,Beijing100084,China [3]DepartmentofAppliedMathematics,HongKongPolytechnicUniversity,HongKong

出　　处：《Acta Mathematicae Applicatae Sinica》2004年第3期457-476,共20页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Fundation of China (No.50377018);a research grant from Research Office of the Hong Kong Polytechnic University(G.63.37.T494)

摘　　要：This paper uses the geometric singular perturbation theory to investigate dynamical behaviors and singularities in a fundamental power system presented in a single-machine infinite-bus formulation. The power system can be approximated by two simplified systems S and F, which correspond respectively to slow and fast subsystems. The singularities, including Hopf bifurcation (HB), saddle-node bifurcation (SNB) and singularity induced bifurcation (SIB), are characterized. We show that SNB occurs at P Tc = 3.4382, SIB at P T0 = 2.8653 and HB at P Th = 2.802 for the singular perturbation system. It means that the power system will collapse near SIB which precedes SNB and that the power system will oscillate near HB which precedes SIB. In other words, the power system will lose its stability by means of oscillation near the HB which precedes SIB and SNB as P T is increasing to a critical value. The boundary of the stability region of the system can be described approximately by a combination of boundaries of the stability regions of the fast subsystem and slow subsystem.This paper uses the geometric singular perturbation theory to investigate dynamical behaviors and singularities in a fundamental power system presented in a single-machine infinite-bus formulation. The power system can be approximated by two simplified systems S and F, which correspond respectively to slow and fast subsystems. The singularities, including Hopf bifurcation (HB), saddle-node bifurcation (SNB) and singularity induced bifurcation (SIB), are characterized. We show that SNB occurs at P Tc = 3.4382, SIB at P T0 = 2.8653 and HB at P Th = 2.802 for the singular perturbation system. It means that the power system will collapse near SIB which precedes SNB and that the power system will oscillate near HB which precedes SIB. In other words, the power system will lose its stability by means of oscillation near the HB which precedes SIB and SNB as P T is increasing to a critical value. The boundary of the stability region of the system can be described approximately by a combination of boundaries of the stability regions of the fast subsystem and slow subsystem.

关 键 词：Singular perturbation saddle-node bifurcation Hopf bifurcation singularity induced bifurcation power system stability stability region 

分 类 号：O175.24[理学—数学]