This paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.

The uncontrolled power flow in the AC power system caused by renewable energy sources (restless sources, distributed energy sources), dynamic loads, etc., is one of many causes of voltage perturbation, along with others, such as switching effects, faults, and adverse weather conditions. This paper presents a three-phase voltage and power flow controller, based on direct PWM AC/AC converters. The proposed solution is intended to protect sensitive loads against voltage fluctuation and problems with power flow control in an AC power system. In comparison to other solutions, such as DVR, UPFC, the presented solution is based on bipolar matrix choppers and operates without a DC energy storage unit or DC link. The proposed solution is able to compensate 50% voltage sags, in the case of three-phase symmetrical voltage perturbation, and single phase voltage interruptions. Additionally, by means of a voltage phase control with a range of ±60◦ in each phase, it is possible to control the power flow in an AC power system. The paper presents an operational description, a theoretical analysis based on the averaged state space method and four terminal descriptions, and the experimental test results from a 1 kVA laboratory model operating under active load.