Mapping of Dynamics between Mechanical and Electrical Ports in SG-IBR Composite Grids

Power grids are traditionally dominated by synchronous generators (SGs) but are currently undergoing a major transformation due to the increasing integration of inverter-based resources (IBRs). The state space method with transparent apparatus models can be readily used. However, models of IBRs are usually not disclosed by manufacturers. Alternatively, the port-based approach represents dynamics by input-output transfer functions without exposing internal states. These transfer functions at various ports are normally configured with a particular focus: an SG-dominated grid is traditionally analyzed in a \textit{mechanical-centric} view which ignores fast electrical dynamics and focuses on the torque-speed dynamics, whereas the emergent IBR-dominated grid usually takes an electrical-centric view which focuses on the voltage-current interaction. In this article, a new perspective called the port-mapping method is proposed to combine these two views. Specifically, the mechanical dynamics are mapped to the electrical impedance seen at the electrical port; and the electrical dynamics are also mapped to the torque coefficient seen at the mechanical port. The bidirectional mapping gives additional flexibility and insights to analyze the sub-system interactions in whole-system dynamics and guide the tuning of parameters. Application of the proposed method is illustrated in three cases with increasing scales.