Based on the research of complex network, branch potential energy was proposed as edge weight to be included in the complex network modeling of power system. Element information and network parameters were also analyzed. Simulation results illustrated that, like topology distribution features, some transition variables ware proved to have typical complex network characteristics, such as scale and small-world. The static branch energy distribution was found to be exponential and power-law distribution. The phenomenon indicated that there are some elements that play much more important role than others in the status transition. It presented a new idea for studying the state evolution of power system from the perspective of static energy distribution.