Solving Nonlinear Circuits With Pulsed Excitation by Multirate Partial Differential Equations

Abstract

In this paper the concept of Multirate Partial Differential Equations (MPDEs) is applied to obtain an efficient solution for nonlinear low-frequency electrical circuits with pulsed excitation. The MPDEs are solved by a Galerkin approach and a conventional time discretization. Nonlinearities are efficiently accounted for by neglecting the high-frequency components (ripples) of the state variables and using only their envelope for the evaluation. It is shown that the impact of this approximation on the solution becomes increasingly negligible for rising frequency and leads to significant performance gains.

Multirate PWM balance method for the efficient field-circuit coupled simulation of power converters

“…Furthermore the PWM basis functions and thus also the PWM eigenfunctions might not be able to represent the solution of problems with nonlinear elements [4]. If the amplitude of the ripples is small compared to the amplitude of the envelope, the particular efficient approach described in [3] can be applied. It uses only the slowly varying envelope to evaluate the nonlinearities.…”

“…For example the induced currents in the conducting materials of an inductor usually cause eddy current losses, which can easily be accounted for in a field model but not in a circuit model. In this paper the multirate method from [3,4] is applied to a linear buck converter circuit (see Fig. 1) in which the inductor is represented by a 2D finite element model.…”

Simulation and Automated Modeling of Microwave Circuits: State-of-the-Art and Emerging Trends

“…This method was applied in system-level steady-state including a propagation link [82], and also in different applications, e.g. [83]. It was extended for handling autonomous circuits in [84], [85].…”

Efficient simulation of DC‐AC power converters using multirate partial differential equations

“…Since the solution is periodic with respect to t 2 in the interval [0, T s ), the boundary term vanishes. Inserting (6) and substituting t 2 with τ leads to…”

“…The resulting method is a (high-order) multirate approach, which is based on a concept called Multirate Partial Differential Equations (MPDEs) [4,5]. For DC-DC power converters the method has already been proposed in earlier papers by Pels et al [6,7]. We extend the concept to DC-AC power converters (also called inverters), in the following.…”