Periodic Flows Analysis of a Nonlinear Power System Based on Discrete Implicit Mapping

This study focuses on the periodic solutions of single-machine-infinite-bus system under a periodic load disturbance. The qualitative behavior of this system is described by the well-known 'swing equation', which is a nonlinear second-order differential equation. Periodic solutions of the system are analytically predicted through discrete implicit mapping. The discrete implicit maps are obtained from the swing equation. From mapping structures, bifurcation trees of periodic solutions of the simple connection power system are predicted analytically, and the corresponding stability and bifurcation analysis of periodic solutions are carried out through eigenvalue analysis. Finally, from the analytical prediction, numerical results of periodic solutions are performed by numerical method of the differential equation to show good agreements.