Study of electro mechanical coupling system by codimension-3 dynamical bifurcation

The destabilizing oscillations, which are foundin the single-machine infinite-bus power system with series compensatecapacitors, are studied with bifurcating parameters r_sl, r_f, x_c,using the theory of Dynamical Bifurcation. Under certainbifurcating parameters, three pairs of pure imaginary eigenvalues emergesimultaneously in the above system. For the multi-parameter high-codimensionbifurcation, Center Manifold Theory is applied to simplify the equations ofthe original system. For the simplified nonlinear system, its Normal Form isobtained by means of 7, the analytical solutions are obtained by usingthe Multiple Parameter Stability Theory, Harmonic Balance Method andUnification Technique. From an analysis of solutions, some complicatedphenomena in the system are revealed: Hopf bifurcations, 2-D Toribifurcations, 3-D Tori bifurcations, 4-D Tori bifurcations and even higherdimension bifurcations. The stability of solutions is discussed indetail, the stable conditions and regions are computed for each solution. Inaddition, a detailed numerical analysis is carried out to verify thetheoretical results. The numerical results are in good agreement with thetheoretical results. The study of this paper provides some theoretical guides forthe parameter design for the stability of power system and the accidentprevention of generators.