Because the accuracy of the traditional minimum voltage drop method used to commutation failure is not high enough, a new commutation failure criterion was proposed. In order to clarify the effect of the fault impedance on the commutation failure, the mathematical relationship between the fault impedance and the commutation voltage was analyzed in detail by two methods of the sensitivity analysis and node impedance matrix. According to the two commutation voltage analysis methods, the critical fault and critical coupling impedance solving methods of local and simultaneous commutation failures were given, respectively. The simulation results showed that the accuracy of the new commutation failure criterion is very high, and two kinds of commutation voltage expressions deduced by the two analysis methods of commutation voltage have also a certain accuracy. At last, the effects of AC fault, load characteristics and system parameters on the commutation voltage were analyzed, and some useful and instrumental conclusions were obtained.