Constant load model is widely used for an electric train to perform the static analysis of AT (Auto Transformer) feeding systems. In this model, the train will be considered as a constant load model when it drives or as a constant source model when it applies regenerative brake. However there must be some constraints imposed on the pantagraph voltage in actual operations. These constraints are established for the reason of protecting the feeding facilities from excessive rise of regenerative braking voltage or guaranteeing the minimum traction power of train. In normal operating situation, the pantagraph voltage of the train should be maintained within these limits. Keeping these facts in minds, we suggest new methods or analyzing AT feeding systems using the constant power models with the conditions of voltage constraints. The simulation results from a sample system using the proposed method illustrate both the states of system variables and the supply-demand relation of power among the trains and the systems very clearly, so it is believed that the proposed method yields more accurate results than conventional methods do. The proposed methods are believed to contribute to the assessment of TCR-TSC for compensating reactive powers too.