Port-Hamiltonian Systems Modelling in Electrical Engineering

TL;DR

This paper discusses the port-Hamiltonian systems framework, emphasizing its ability to model multi-physical systems in electrical engineering while preserving physical properties like energy conservation.

Contribution

It introduces coupled port-Hamiltonian systems as ODEs and DAEs, and derives PHS models for MNA network equations and electromagnetic devices.

Findings

PHS models preserve energy and dissipative properties.

Coupled PHS can be derived without increasing complexity.

Application to electrical network equations demonstrates practical relevance.

Abstract

The port-Hamiltonian modelling framework allows for models that preserve essential physical properties such as energy conservation or dissipative inequalities. If all subsystems are modelled as port-Hamiltonian systems and the inputs are related to the output in a linear manner, the overall system can be modelled as a port-Hamiltonian system (PHS), too, which preserves the properties of the underlying subsystems. If the coupling is given by a skew-symmetric matrix, as usual in many applications, the overall system can be easily derived from the subsystems without the need of introducing dummy variables and therefore artificially increasing the complexity of the system. Hence the PHS framework is especially suitable for modelling multi-physical systems. In this paper, we show that port-Hamiltonian systems are a natural generalization of Hamiltonian systems, define coupled port-Hamiltonian systems as ordinary and differential-algebraic equations. To highlight the suitability for electrical engineering applications, we derive PHS models for MNA network equations, electromagnetic devices and coupled systems thereof.