1. School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China;2. NARI Group Corporation(State Grid Electric Power Research Institute), Nanjing 211106, China;3. State Key Laboratory of Smart Grid Protection and Control, Nanjing 211106, China;4. National Electric Power Dispatching and Control Center, State Grid Corporation of China, Beijing 100031, China

This paper reveals the similarities and differences between the view of the complementary-cluster inter-group energy and the sinusoidal amplitude of characteristic frequency in power system oscillation behavior analysis. It is strictly proved that they are consistent in the Hamilton one-machine infinite-bus(H-OMIB)system. However, the nonlinear factors may cause large errors to the linear analysis. Besides, the time-varying factors and inherently nonlinear factors such as saturation may make the equilibrium point eigenvalue method completely invalid. In order to overcome these difficulties, this paper describes the oscillation characteristic of the complex disturbed system from the view of complementary-cluster inter-group energy. For the multi-machine system, the trajectories can be mapped into a series of time-varying image system trajectory through complementary-clusters center-of-inertial relative-motion(CCCOI-RM)transform. Then, the oscillation behavior of the original multi-machine system is reflected by the oscillation energy of the image systems including the time-varying nonlinear oscillation with multi-frequency.