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A field-circuit coupled finite element method has been applied on one induction machines for the transient analysis in case of inverter power supply and sinusoidal voltage supply in this paper. The focus is to build the time-stepping finite element method with external circuit coupled to the electromagnetic field equations and achieve voltage supply. The problem of the motion of rotor is solved through moving boundary by interpolation in the moving coordinate system. The induction machine starting transient simulation has been completed using Finite element equations indirect coupled with mechanical equation. The influence of the electromagnetic field and performance has been analyzed compared with sinusoidal condition. This method can be used for dynamic analysis of any power supply taking into account the magnetic nonlinearity of the core material. The established machine overall structure model is closer to the actual. Compared to the traditional analysis method, we can reduce the dependency of experience design. It can also be used for analysis and optimization of the new machine