Efficient simulation of DC-AC power converters using Multirate Partial Differential Equations

Abstract: Switch-mode power converters are used in various applications to convert between different voltage (or current) levels. They use transistors to switch on and off the input voltage to generate a pulsed voltage whose arithmetic average is the desired output voltage of the converter. After smoothening by filters, the converter output is used to supply devices. The simulation of these switch-mode power converters by conventional time discretization is computationally expensive since a high number of time steps is necessary to properly resolve the unknown state variables and detect switch events of the excitation. This paper proposes a multirate method based on the concept of Multirate Partial Differential Equations (MPDEs), which splits the solution into fast varying and slowly varying parts. The method is developed to work with pulse width modulated (PWM) excitation with a constant switching cycle and varying duty cycle. The important case of varying duty cycles in the MPDE framework is addressed for the first time. Switching event detection is no longer necessary and a much smaller number of time steps for a decent resolution are required, thus leading to a highly efficient method.