Study of electro mechanical coupling system by codimension-3 dynamical bifurcation
机电耦联系统余维3动态分岔研究

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.