Complexity of power system energy flow is mainly reflected in the features of dynamic behavior such as real-time, nonlinear, uncertainty, etc. The analysis of dynamics on network is a critical means. The potential energy function models of system and branches are established, which are based on power system dynamic equilibrium equation to extract the system energy information after the fault duration. And the complexity of the system energy flow evolution is analyzed by using the multi-scale entropy method. The analysis results show that the system complexity under steady operation is much low. In addition, the complexity of the fault system increases with the increase of fault duration. Moreover, the system complexity under unstable operation shows a strong uncertainty in a small time scale and obvious regularity in a large time scale. And the most important is that the system complexities of the critical stable state and the critical unstable state are clearly distinct in different time scales. Such a difference can be used as a positive reference to the identification of the critical point in the dynamic state. Research results reveal the evolution of power energy flow in physical dynamic process. This can provide new ideas and methods for analyzing the dynamics behavior of power system.