The Signature Method for DAEs arising in the modeling of electrical circuits

We consider the Signature Method (Σ-method) for the structural analysis of differential-algebraic equations (DAEs) that arise in the modeling and simulation of electrical circuits. Different formulations of the set of model equations are considered. We show that for some formulations the structural approach may fail for certain circuit topologies, while other formulations are better suited for a structural analysis. In particular, we show that for the branch-oriented model equations the Signature Method always succeeds with a structural index that corresponds to the differentiation index of the system. The results are illustrated by a number of examples.