An Energy-based, always Index $\le1$ and Structurally Amenable Electrical Circuit Model

TL;DR

This paper introduces a new, energy-based port-Hamiltonian model for electrical circuits that is simple, symmetric, always has index at most 1, and demonstrates good numerical properties, with implementation and results provided.

Contribution

It develops a novel compact port-Hamiltonian circuit model combining energy and structural analysis, ensuring index at most 1 and improved numerical stability.

Findings

Model has index at most 1

Implementation in Matlab demonstrates effectiveness

Numerical results confirm theoretical properties

Abstract

Combining three themes: port-Hamiltonian energy-based modelling, structural analysis as used in the circuit world, and structural analysis of general differential-algebraic equations, we form a new model for electrical circuits, the compact port-Hamiltonian equations. They have remarkable simplicity and symmetry, and always have index at most 1 and other good numerical properties. The method has been implemented in Matlab. We give proofs and numerical results.