On the Compressibility of Power Grid Models

The simulation of power distribution networks is a difficult task owing to the large number of elements and ports in such circuits. In this work, the authors elaborate on the compressibility of power grid models. For this purpose, two main options are available, namely sparse or hierarchical model representations of such systems and equivalent reduced order models. A proxy for comparison is the number of nonzero entries in system representation. The problem with model order reduction methods is the large number of ports of these networks, since the number of nonzero entries of the reduced model is, in general, proportional to the square of the number of ports. In this paper, the authors propose for the first time the utilization of a specific hierarchical model representation, in which a Cholesky decomposition of the system matrix can be efficiently computed and later used in the simulation phase. Results show that for higher problem sizes the hierarchical representation is more compact than the sparse representation, while the reduced order models are of no use.