Port-Hamiltonian Systems’ Modelling in Electrical Engineering

The port-Hamiltonian (pH) modelling framework allows for models that preserve essential physical properties such as energy conservation or dissipative inequalities. If all subsystems are modelled as pH systems and the inputs are related to the output in a linear manner, the overall system can be modelled as a pH system, 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 framework of pH systems is especially suitable for modelling multiphysical systems. In this paper, we show that pH systems are a natural generalization of Hamiltonian systems, define coupled pH systems as ordinary and differential-algebraic equations. To highlight the suitability for electrical engineering applications, we derive pH models for MNA network equations, electromagnetic devices and coupled systems thereof.