Performance and mathematical model of three-phase three-winding transformer used in 2×25 kV electric railway

A three-phase three-winding transformer, the so-called cross-connected transformer, has been used in a 2×25 kV electric railway in China. Based on the magnetomotive force balance equations, winding connection equations, output-port equations and voltage transfer equations, the performance and mathematical model of the cross-connected transformer are analysed. The input current and output voltage equations and nodal admittance matrix of the transformer are obtained, which can be used in future analyses. The problem of omitting substation autotransformers is addressed by virtue of two equivalent circuits put forward. The applicability of the proposed formulas and mathematical model is validated by comparison of measured and calculated busbar voltages and short-circuit simulations. Finally, the reasons that led to the low catenary voltage of one section of the Datong-Qinghuangdao railway, supplied by a cross-connected transformer, are investigated.