The structure differences of the double-fed induction generator (DFIG) and permanent magnet synchronous machine (PMSG) are introduced. From the research of two mathematical models, the AC-DC-AC converters adopts the same control strategy, machine side converter uses decoupling control, and grid side converter applies constant power factor control. The simulation models with the same wind speed power curve of the two are constructed respectively in EMTPWorks. The differences of transient characteristics of the two under three-phase short circuit and single-phase short circuit fault of power system are analyzed. It is concluded that the reactive power variation amplitude of the PMSG during the fault is bigger than that of DFIG, but the bus voltage drop, active power output, system frequency fluctuation and inverter DC capacitor change of voltage amplitude are much smaller than that of DFIG, which has important significance to the wind turbine type selection.