Using dedicated time-domain basis functions for the simulation of pulse-width-modulation controlled devices – Application to the steady-state regime of a buck converter

摘要

In this paper the authors present a novel approach for the time-stepping simulation of electrical devices with pulse-width- modulated (PWM) supply, based on so-called PWM basis functions which are periodic in time (at the switching frequency), piecewise polynomial and duty-cycle dependent. The state variables of the device’s lumped-parameter circuit and/or finite element model are expanded in terms of these basis functions, with slowly varying coefficients in time. This allows for a large PWM- switching-frequency-independent time step and thus significant computational savings. By way of validation, the approach is applied to a buck converter in continuous-conduction mode. For this particular application, the steady-state waveforms of the inductor current and the output (capacitor) voltage are obtained through the resolution of a system of algebraic equations. As the set of the PWM basis functions is enlarged (with increasing polynomial degree), the respective PWM ripple components are observed to converge quickly to those obtained with plain time stepping (using a very small time step).