Dirac Structures and Implicit Lagrangian Systems in Electric Networks

Abstract

In this paper, we apply Dirac structures and the associated theory of implicit Lagrangian systems to electric networks. We show how a Dirac structure on the flux linkage phase can be induced from a KCL (Kirchhoff Current Law) constraint distribution on a configuration charge space in analogy with mechanics. In this context, a notion of implicit port-controlled Lagrangian systems is developed. As a specific illustrative example, it is demonstrated that a one-dimensional L-C transmission line can be formulated in the context of implicit port-controlled Lagrangian systems, where the transmission line may be regarded as an interconnected system of a chain of constituent primitive modules, each of which is given by an L-C circuit with external ports.