The three-phase isolated transformer is the key primary equipment of the mobile substation. A reduced order model of the transformer is established based on the Arnoldi algorithm to fast simulate the input and output characteristics of the transformer in the laboratory environment. The high-precision electromagnetic equivalent circuit of the three-phase isolated transformer is built according to the electromagnetic induction and Ampere laws, and the quantitative relationship between the input voltage, current and the change rate of magnetic flux is obtained. The transformer core is made equivalent to a multi-set of ring loops using the block approximation method, and the equivalent magnetic circuit model of the core is obtained. Based on this model, the functional relations among the magnetic resistance, magnetic inductance, magnetic flux and the change rate of magnetic flux can be obtained, and then the state equation of the transformer can be obtained. The Arnoldi algorithm is applied to reduce the order of the state equation, and the reduced order model of the three-phase isolated transformer is obtained. Corresponding simulation and experiment are carried out to verify the correctness and accuracy of the reduced order model of the transformer. This work is supported by National Natural Science Foundation of China (No. 51677036 and No. 51777042) and China Postdoctoral Fund (No. 2017T100241).