This paper presents a new power flow method to analyze the AC electric railway system effectively in both cases of traction and regenerative braking of the trains. The algorithm to easily solve the power flow of the AC electric railway system with the trains of regenerative braking from the system without a train of regenerative braking is derived. Using this new power flow method, the voltage characteristics of a typical AC electric railway system is easily analyzed in both cases of traction and regenerative braking of the trains. We show that the presented method can be applied effectively in order to analyze the AT-fed AC electric railway system in both cases of traction and regenerative braking of the trains. A STATCOM(Static Synchronous Compensator) is applied to the system in order to improve the voltage drop problem and this case is also analyzed to show the effect of STATCOM.