抄録
In longitudinal power systems, there is a possibility that a low-frequency oscillation mode gets unstable because of autoparametric resonance. The resonance occurs through interaction between two oscillation modes. In this paper, we calculate the stable region for the resonance by considering the interaction of the modes. First, we calculate steady-state solutions by the harmonic balance method. The steady-state solutions are stable or unstable. If we decrease the amplitude of one mode at an unstable solution, the modes decay. Conversely, if we increase the amplitude, then the modes diverge. Namely, the unstable solution is located on the boundary of the stable region. The amplitudes of the modes are rarely the same as those of the steady-state solution. However, the amplitudes approach to a steady-state after some transients. If the state is in the stable region, the system is stable. If in the unstable region, it diverges. Lastly, we estimate the amount of damping torques necessary to stabilize the system with the newly calculated stable region. Similar results as those by the Mathieu diagram are obtained, for example, certain amount of damping torques can stabilize the system irrespective of its size, AVRs can substantially reduce the amount of damping torques, etc.
