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Focuses on steady state modelling of basic unipolar non‐isolated PWM AC line matrix‐reactance choppers (MRC). Their single‐phase topologies are similar to well‐known basic DC/DC converter ones. The MRC are built up through the adaptation of DC/DC converter topologies, which are based on the substitution of self‐commutated unidirectional switches by bi‐directional ones.

Presents an approach to modelling of the MRC with averaging operator different to the one used in averaged modelling of the DC/DC converters. There is running averaging of each switching period in the proposed approach. Following this, there is a demonstration of the solutions convergence of the state space and averaged state space equations for infinitive switching frequency.

The running averaging of each switching period should be used if averaged state space method is applied to the analysis of presented choppers. A circuit averaged model build‐up procedure of the presented choppers is the same as for the DC/DC ones.

Presents a quantitative assessment of accuracy for the averaged models of the presented MRC for finite switching frequency.

Aims to focus on steady state and transient state analysis of basic properties of new solution for a single‐phase serial AC voltage controller. Furthermore, simulation and experimental test results of 3 kVA models are provided to confirm and verify the theoretical approach.

Presents a converter with auxiliary transformer and bipolar PWM AC matrix‐reactance chopper (MRC), based on Ćuk B2 topology. The MRC has the possibility of bipolar AC voltage conversion with magnitude of voltage transformation function greater than 1. The peak voltage detection method in the control circuit is applied to fast control of the load voltage changes. The steady state and transient state theoretical analysis based on averaged models of the presented controller is used. There is a four‐terminal description of the basic properties in the presented approach.

In the proposed solution only half the number of switches compared with the case of full bridge matrix chopper solution is used. The nominal load voltage can be obtained even for 50 per cent step‐down of the supply voltage.

Presents new topology and properties of single‐phase serial AC voltage controller.

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.