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The auto-compensation and harmonic shielding converter transformer, namely the new converter transformer, adopts the prolonged delta wiring in the secondary winding, and there is a tap between the common winding and the prolonged winding, which is connected with the inductive filters. Compared with the traditional converter transformer, the electrical connection in the new converter transformer is more complex. Based on the principle of phase-coordinate method and the actual design parameter of the new converter transformer, the mathematical models with various short-circuit faults are presented in this paper combined with the directed graph of the coupled circuit. Finally, the simulation results demonstrate that the short-circuit faults calculated by the phase-coordinate method is accurate and effective. The model can be selected flexibly in practical project and has universal significance in solving various actual engineering problems correlated with multi-transformers.