Dynamic iteration schemes and port-Hamiltonian formulation in coupled DAE circuit simulation

TL;DR

This paper develops a port-Hamiltonian framework for coupled DAE circuit models, introducing new classes of port-Hamiltonian differential-algebraic equations and analyzing dynamic iteration schemes within this structure.

Contribution

It introduces novel port-Hamiltonian DAE models for coupled circuits and dynamic iteration schemes that preserve the port-Hamiltonian structure, including nonlinear dissipation.

Findings

Jacobi and Gauss-Seidel iteration schemes preserve port-Hamiltonian structure.

Structural analysis confirms the suitability of the new models.

Dynamic iteration schemes are effectively integrated into the port-Hamiltonian framework.

Abstract

Electric circuits are usually described by charge- and flux-oriented modified nodal analysis. In this paper, we derive models as port-Hamiltonian systems on several levels: overall systems, multiply coupled systems and systems within dynamic iteration procedures. To this end, we introduce new classes of port-Hamiltonian differential-algebraic equations. Thereby, we additionally allow for nonlinear dissipation on a subspace of the state space. Both, each subsystem and the overall system, possess a port-Hamiltonian structure. A structural analysis is performed for the new setups. Dynamic iteration schemes are investigated and we show that the Jacobi approach as well as an adapted Gauss-Seidel approach lead to port-Hamiltonian differential-algebraic equations.