Modelling of Three-phase Power Converters

Abstract

The port-Hamiltonian modelling and control of power converters has been the topic of a number of studies for the past couple years. However, the modelling of three-phase converters from fundamental port-Hamiltonian principles has been an unexplored direction. This study focusses on deducing a modelling procedure to model a three-phase rectifier and a three-phase inverter from a fundamental port-Hamiltonian perspective. Such a perspective involves the derivation of a model from a mathematical expression of the Dirac structure. Two procedures are formulated, where either the switches are viewed as virtual elements or as nonlinear elements. The study concludes that both techniques are equally suitable for the modelling of the rectifier and the inverter. Furthermore, incorporating non-ideal switches is easier when regarding them as nonlinear elements, but obtaining a parametrised form (parametrised by the switch state) is more straightforward when regarding them as virtual elements. Both methods require us to identify the currents and voltages in the network as efforts and flows based on the network topology. However, this turns out to be ambiguous for the conjugate variables of the interconnection ports and switches. To cope with this, two conventions are proposed.