A Port-Hamiltonian, Index \(\le 1\) , Structurally Amenable Electrical Circuit Formulation

We present a recently developed electrical circuit formulation that has port-Hamiltonian (pH) structure and results in a structurally amenable differential-algebraic equation (DAE) system of index \(\le 1\) . Being pH assures energy stability—the total energy of the system cannot increase. It also provides compositionality—larger pH models can be assembled from smaller ones in a standard way that facilitates building pH models in software. Structurally amenable and index \(\le 1\) eliminate the phases of DAE index analysis and reduction, which are commonly used in circuit simulation software. Thus, standard numerical solvers can be applied directly to integrate the DAE. In addition, it has a known a priori block-triangular form that can be exploited for efficient numerical solution. A prototype Matlab code shows high potential for development of this “compact port-Hamiltonian” (CpH) methodology.