Superposition feature of the switching functions for the dynamic phasor model of the converters under commutation failure

Switching function is very important for the dynamic phasor model of converters. It is used to represent the relationship between the AC side voltage/current and the DC side voltage/current in the dynamic phasor models of converters. The existing switching functions consider no effect of the commutation failure (CF), which restricts the development of the dynamic phasor model of converters. A method to obtain the switching functions considering the effects of the CF is proposed in this study. First, following a detailed analysis, the two phenomenon are found that: (1) if there is only a single CF, then the corresponding switching functions can be calculated through the normal three phase switching functions; and (2) if there is an occurrence of continuous CFs, the switching functions in the dynamic phasor model can be obtained through the normal switching functions and the corresponding single CFs, which consists of the continuous CFs. Second, the details of the method to obtain the switching functions considering various operation conditions are presented. Finally, numerical tests show that the proposed method and the modified switching functions are valid and effective.