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AC power feeding systems of electric railways can be viewed as a multi-conductor chain circuit. All electrical elements along the railway, even including the short circuits and conductor breaks, can be described as series or shunt elements. According to the chain circuit topology, the mathematical model of the whole feeding system, i.e. the admittance matrix, can be assembled conveniently by appropriately modelling each element. Considering the relatively large leakage conductance of the current return rail to the ground, multi-conductor equivalent-π circuits can be adopted for each section of the feeding system. The characteristic admittance matrix, which can be calculated by the phase-modal transformation method, is introduced for the truncation treatment at terminals of a feeding system. The proposed modelling methodology has been realised using a simulation program, which can be used to investigate a wide range of problems in electric railway feeding systems, such as the conductor current distribution, the lowest train voltage at peak time, the short circuit calculation, the rail potential distribution and the harmonic propagation.