Modelling of transient phenomena of complex electrical circuits under periodic non-harmonic converter supply

Abstract

Paper deals with chosen mathematical methods for modelling and analysis of electrical converter circuits as dynamical systems with periodic non-harmonic exciting function. These functions are represented by output voltages with strongly non-harmonic waveforms. The voltage waveforms can be pure impulse one—in case of voltage source inverters—or disturbed harmonic waveforms—in case of network supplied phase-controlled converter (AC/DC, AC/AC ones). Suitable methods for the investigation of transient phenomena of such circuits are described: Z-transform, Laplace–Carson transform, simple numerical successive approximation method and also new direct numeric method for instantaneous state determination of electrical circuit as dynamical system. Inverse transformation of Z and Laplace–Carson methods using Cauchy theorem of residua makes it possible to predict the behavior of the system based on the evaluation of denominator of transfer functions and pole assignment in complex Gauss plain. As examples of complex electrical circuits were investigated the one-leg matrix converter and resonant inverter with fourth-order filter. Theoretically derived waveforms are verified by Matlab/Simulink simulation results and are compared to the analytically worked-out results.