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Systematic equation formulation for simulation of power electronic circuits using explicit methods

Mahesh B. Patil

TL;DR

This work addresses the instability and inefficiency of explicit time integration in power-electronic circuit simulation when using ideal switch models. It strengthens the ELEX framework by augmenting ES/CTD formulations and introducing robust procedures for switches, inductors, and transformers, including the Switch Loop (SL) algorithm, Shorting and Path tests, and systematic CTD rules. The paper provides extensive examples to illustrate how to assemble solvable equation sets across switch loops, isolated sections, and transformer interactions, enabling accurate and fast explicit simulations. The methods are implemented in the open-source GSEIM tool, highlighting practical impact for researchers and engineers seeking efficient circuit simulation without resorting to traditional SPICE-based approaches.

Abstract

Use of explicit integration methods for power electronic circuits with ideal switch models significantly improves simulation speed. The PLECS package [1] has effectively used this idea; however, the implementation details involved in PLECS are not available in the public domain. Recently, a basic framework, called the ``ELEX" scheme, for implementing explicit methods has been described [2]. A few modifications of the ELEX scheme for efficient handling of inductors and switches have been presented in [3]. In this paper, the approach presented in [3] is further augmented with robust schemes that enable systematic equation formulation for circuits involving switches, inductors, and transformers. Several examples are presented to illustrate the proposed schemes.

Systematic equation formulation for simulation of power electronic circuits using explicit methods

TL;DR

This work addresses the instability and inefficiency of explicit time integration in power-electronic circuit simulation when using ideal switch models. It strengthens the ELEX framework by augmenting ES/CTD formulations and introducing robust procedures for switches, inductors, and transformers, including the Switch Loop (SL) algorithm, Shorting and Path tests, and systematic CTD rules. The paper provides extensive examples to illustrate how to assemble solvable equation sets across switch loops, isolated sections, and transformer interactions, enabling accurate and fast explicit simulations. The methods are implemented in the open-source GSEIM tool, highlighting practical impact for researchers and engineers seeking efficient circuit simulation without resorting to traditional SPICE-based approaches.

Abstract

Use of explicit integration methods for power electronic circuits with ideal switch models significantly improves simulation speed. The PLECS package [1] has effectively used this idea; however, the implementation details involved in PLECS are not available in the public domain. Recently, a basic framework, called the ``ELEX" scheme, for implementing explicit methods has been described [2]. A few modifications of the ELEX scheme for efficient handling of inductors and switches have been presented in [3]. In this paper, the approach presented in [3] is further augmented with robust schemes that enable systematic equation formulation for circuits involving switches, inductors, and transformers. Several examples are presented to illustrate the proposed schemes.
Paper Structure (28 sections, 162 equations, 35 figures, 2 algorithms)

This paper contains 28 sections, 162 equations, 35 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Switch circuits
  3. Switch loops
  4. Switch circuits: example 1
  5. Switch circuits: example 2
  6. Switch circuits: example 3
  7. Switch circuits: example 4
  8. Isolated circuit sections
  9. Switch circuits: example 5
  10. Switch circuits: example 6
  11. Inductor circuits
  12. Inductors in series
  13. Inductor circuits: example 1
  14. Inductor circuits: example 2
  15. Conduction path for inductors
  16. ...and 13 more sections

Figures (35)

  • Figure 1: Switch circuit example 1.
  • Figure 2: Circuit of Fig. \ref{['fig_sw_1']} with all switches on.
  • Figure 3: Switch tree for identifying switch loops in the circuit of Fig. \ref{['fig_sw_1a']}, starting with node B.
  • Figure 4: Circuit of Fig. \ref{['fig_sw_1a']} with loop switches with $R_{\mathrm{on}}$.
  • Figure 5: Circuit of Fig. \ref{['fig_sw_1']} with $S_3$ off and all other switches on.
  • ...and 30 more figures