机电耦联系统余维3动态分岔研究  

STUDY OF ELECTRO MECHANICAL COUPLING SYSTEM BY CODIMENSION-3 DYNAMICAL BIFURCATION

作　　者：邱勇[1] 邱宇[2] 邱家俊[2] 

机构地区：[1]天津大学管理学院,天津300072 [2]天津大学机械学院力学系,天津300072

出　　处：《力学学报》2006年第3期421-428,共8页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(10202017).

摘　　要：以rsl,rf以及xc为分岔参数,对具有串补电容的单机无穷大电力系统的失稳振荡问题,运用动态分岔理论进行了研究．对系统同时出现有3对纯虚根特征值的一类多参数高余维分岔情况,运用中心流行方法降维后得到约化方程,对此强非线性约化方程的求解难点,运用多参数稳定性理论、谐波平衡法、归一化技术和 Normal Form方法,得到了系统的解析解．由分析得知,系统会出现3种Hopf分岔情况、二维环面情况,以及三维环面分岔解,甚至会出现四维环面,或者更高维的环面分岔．详细讨论了系统各种分岔解的稳定性条件和稳定区域,并作了详细的数值分析加以验证．The destabilizing oscillations, which are found in the single-machine infinite-bus power system with series compensate capacitors, are studied with bifurcating parameters rsl, rf, xc, using the theory of Dynamical Bifurcation. Under certain bifurcating parameters, three pairs of pure imaginary eigenvalues emerge simultaneously in the above system. For the multi-parameter high-codimension bifurcation, Center Manifold Theory is applied to simplify the equations of the original system. For the simplified nonlinear system, its Normal Form is obtained by means of [7], the analytical solutions are obtained by using the Multiple Parameter Stability Theory, Harmonic Balance Method and Unification Technique. From an analysis of solutions, some complicated phenomena in the system are revealed： Hopf bifurcations, 2-D Tori bifurcations, 3-D Tori bifurcations, 4-D Tori bifurcations and even higher dimension bifurcations. The stability of solutions is discussed in detail, the stable conditions and regions are computed for each solution. In addition, a detailed numerical analysis is carried out to verify the theoretical results. The numerical results are in good agreement with the theoretical results. The study of this paper provides some theoretical guides for the parameter design for the stability of power system and the accident prevention of generators.

关 键 词：电力系统 发电机 串补电容 稳定性 动态分岔 次同步振荡 

分 类 号：O322[理学—一般力学与力学基础]