  Power grids are traditionally dominated by synchronous generators (SGs) but
are currently undergoing a major transformation through the increasing
integration of inverter-based resources (IBRs). The SG-dominated grid is
traditionally analyzed in a mechanical-centric view which ignores fast
electrical dynamics and focuses on the torque-speed dynamics. By contrast,
analysis of the emergent IBR-dominated grid usually takes the
electrical-centric view which focuses on the voltage-current interaction. In
this article, a port-mapping method is proposed to fill the gap between these
approaches and combine them in a unified model. 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 parameter. Application of the proposed method is
illustrated in three cases with increasing scales, namely a
single-SG-infinite-bus system, a single-IBR-weak-grid system, and a modified
IEEE 14-bus SG-IBR composite system.
