Application of Least Squares MPE technique in the reduced order modeling of electrical circuits

Reduced order models are usually derived by performing the Galerkin projection procedure, where the original equations are projected onto the space spanned by a set of approximating basis functions. For Differential Algebraic Equations this projection scheme may yield an unsolvable reduced order model. This means that a model of an electrical circuit can become ill-posed if it is reduced by the Galerkin technique. As a remedy to the problem, in this paper the reformulation of the reduced order model problem in the least squares sense is suggested. The space where the original is projected is different to the space used in the Galerkin procedure. It is shown that the resulting reduced order model will be guaranteed to be well-posed when the problem of finding a reduced order model is cast into a least squares problem. To accelerate the reduced order modeling computation, the Missing Point Estimation (MPE) technique which was successfully implemented in the PDE-models of heat transfer processes is also applied to the least-square reduced order model of the electrical circuit. The least-square based MPE model is derived by projecting a subset of the original equation onto the least-square space. The dynamics of the stiff DAE model can be approximated very closely by a reduced order model built from less than 28% of the original equations. I. ELECTRICAL CIRCUIT MODELS The dynamics of electrical circuits at time t are generally given by the Differential Algebraic Equations (DAE)