A Mathematical Model for Stability Analysis of a DC Distribution System for Power System Integration of Plug-In Electric Vehicles

This paper proposes a systematic method for developing a model of a dc distribution system, based on the configuration of the system. The dc distribution system is assumed to host electric vehicles and photovoltaic modules, using dc-dc converters, and to integrate them with an ac power grid. The developed model is of the matrix form and, therefore, can be readily expanded to represent a dc distribution system of any desired number of dc-dc converters. The model captures both the steady-state and dynamic characteristics of the system and includes port capacitors of the converters, as well as the interconnection cables. Thus, it can be used for identifying the condition for existence of a steady state, as well as for stability analysis. This paper further proposes an alternative set of characteristic equations that are less computationally intensive than the original matrix representation, for example, for online stability assessment tasks. The adequacy of the proposed model has been demonstrated through a number of case studies conducted and compared in the PSCAD/EMTDC and MATLAB software environments.