The purpose of this paper is to introduce methods for calculating steady‐state and transient processes in a symmetrical three‐phase matrix‐reactance frequency converter (MRFC). The MRFC in question makes it possible to obtain a load output voltage much greater than the input voltage.
MRFCs based on a matrix‐reactance chopper are used for both frequency and voltage transformation. The processes in a MRFC system are described by nonstationary differential equations. A two‐frequency complex function method is proposed for solving non‐stationary equations in steady‐state. The method is applied to a state‐space averaged mathematical model used in the analysis of the discussed MRFC. A two‐frequency matrix transform is proposed for solving non‐stationary equations. This method can be used to find both transient and steady‐state processes.
The two‐frequency complex function method permits the reduction from 12 non‐stationary differential equations to four stationary differential equations. The two‐frequency matrix transform allows the transformation of non‐stationary differential equations to stationary ones. By using these methods descriptions of steady‐state and transient properties of buck‐boost MRFCs are obtained.
A new method of solving of nonstationary differential equations is presented. The method is useful for process analyses in nonstationary power electronic converters.
