Self-excited induction generator (SEIG) has received a lot of attentions for its increasing application in distributed generation systems with the essential feature of low cost. To analysis, the dynamic and transient performance of SEIG, several modifications of the mathematical models have been developed for improving the regulation of voltage and frequency. But these models are still complicated to be used in practice. Based on the transient equivalent circuit, a reduced-order model of SEIG with complex transformation in the two-phase stationary reference frame is realized for the transient analysis of voltage build-up. In this simplified model, the coefficients of the characteristic polynomial with multi-timescale time constants are proposed. Moreover, the physical interpretation of system transient behavior with the reconstructed time constants is established and visualized. Particularly, the upper and lower limits of the capacitance and speed for the SEIG with different parameters variation are simulated and analyzed respectively. The validation and the accuracy of the SEIG model are verified for the transient analysis of the voltage build-up. It is proved that the reduced-order model can be effectively used to insight the dynamic stability of SEIG voltage build-up with the multi-timescale. INDEX TERMS Autonomous system, characteristic polynomial equations, complex coefficients, multi-timescale, self-excited induction generator, voltage build-up analysis.