Per-Unit Modeling via Similarity Transformation

This paper presents an approach to normalize dynamical-system models into per-unit transcriptions via similarity transformation. The method applies to nonlinear control-affine and linear state-space models. In this framework, parameters of the per-unit model are not determined a priori; rather, they emerge from the similarity transformation. This is a significant upgrade to the conventional approach of identifying base values for parameters with dimensional analysis so they can be normalized. Since the approach is grounded in system theory, several frequency- and time-domain attributes of per-unit models can be formalized. Furthermore, per-unit phasor models can be derived as a special instance. Case studies demonstrate these attributes in practice for linear and nonlinear systems including $RLC$ circuits, transformers, and grid-following and grid-forming inverters. Numerical simulations incorporating these in a modified IEEE 37-bus network demonstrate accuracy and scalability.