This paper aims to present a new equivalent scheme of multi-windings traction transformers, based on multiport purely inductive circuit. The mathematical background of this equivalent scheme is described. The determination of the different scheme elements is made through a finite-elements calculation of both main and leakage inductances, for the case of a four-winding transformer. A procedure is defined, which allows to estimate the values of these elements from some measurements on the transformer at no-load and short-circuit operations. A specific strategy of short-circuit tests is described, allowing to determine all parameters in a rather simple way.
This paper presents a concept of an NxM Matrix Converter (MC) modeling under periodic control strategy patented in Poland. This strategy allows to change an Nphase input system of voltages and current with the frequency fi to the M-phase output system with the frequency fo, maintaining both systems symmetrical and providing small distortions of voltage and current waveforms at rather high frequencies. In this paper the control strategy is extended for dynamic states when one of the frequencies is changed. Matrix converter equations have been derived using the constrain matrix, which is determined by the switch states. The equations have the hybrid form of a multi-port circuit. To simplify these equations the symmetrical components of input and output voltages and currents have been applied. As a result, rather simple equations have been found. They can be interpreted to an equivalent scheme. All considerations are illustrated using an exemplary 6H3 matrix converter.