Exploiting structure in large-scale electrical circuit and power system problems

The rapid increase in complexity of systems such as electrical circuits and power systems calls for the development of efficient numerical methods. In many cases, direct application of standardized methods for numerical problems is computationally not feasible or inefficient. However, the performance of such methods can be improved considerably by taking into account the structure of the underlying problem. In this paper, we describe when and how this – mathematical and/or physical – structure can be exploited to arrive at efficient algorithms that also suffer less from other numerical issues such as round-off errors. Eigenvalue and stability problems are considered in particular, but applications to other problems are shown as well.