A condensed form for nonlinear differential-algebraic equations in circuit theory

Abstract

We consider nonlinear differential-algebraic equations arising in modelling of electrical circuits using modified nodal analysis and modified loop analysis. A condensed form for such equations under the action of a constant block diagonal transformation will be derived. This form gives rise to an extraction of over- and underdetermined parts and an index analysis by means of the circuit topology. Furthermore, for linear circuits, we construct index-reduced models which preserve the structure of the circuit equations.