Normal form analysis of auto-parametric resonance in longitudinal power system

In longitudinal power systems, the transient stability could be restricted by not an unstable equilibrium point but an unstable limit cycle due to auto-parametric resonance. In such a case, it is important to find the unstable limit cycle. However, there has been no systematic method to find it as far as the authors know. This paper presents a systematic method to find the unstable limit cycle that anchors the transient boundary using normal form analysis. The approximated amplitude of the limit cycle can be obtained by the proposed method. The method can consider the auto-parametric resonance. The numerical results of a longitudinal power system confirm the effectiveness of the proposed method.