APPLICATION OF BIFURCATION-THEORY TO SUBSYNCHRONOUS RESONANCE IN POWER-SYSTEMS

A bifurcation analysis is used to investigate the complex dynamics of a heavily loaded single-machine-in finite-busbar power system modeling the characteristics of the BOARDMAN generator with respect to the res t of the North-Western American Power System. The system has five mech anical and two electrical modes. The results show that, as the compens ation level increases, the operating condition loses stability with a complex conjugate pair of eigenvalues of the Jacobian matrix crossing transversely from the left- to the right-half of the complex plane, si gnifying a Hopf bifurcation. As a result, the power system oscillates subsynchronously with a small limit-cycle attractor. As the compensati on level increases, the limit cycle grows and then loses stability in a secondary Hopf bifurcation, resulting in the creation of a two-perio d quasiperiodic subsynchronous oscillation, a two-torus attractor. On further increases of the compensation level, the quasiperiodic attract or collides with its basin boundary, resulting in the destruction of t he attractor and its basin boundary in a bluesky catastrophe. Conseque ntly, there are no bounded motions. The results show that adding dampe r windings may induce subsynchronous resonance.