  This paper addresses the following fundamental research question: how does
the integration of grid-forming inverters (GFMs) replacing conventional
synchronous generators (SGs) impact the slow coherent eigen-structure and the
low-frequency oscillatory behavior of future power systems? Due to time-scale
separated dynamics, generator states inside a coherent area synchronize over a
fast time-scale due to stronger coupling, while the areas themselves
synchronize over a slower time scale. Our mathematical analysis shows that due
to the large-scale integration of GFMs, the weighted Laplacian structure of the
frequency dynamics is preserved, however, the entries of the Laplacian may be
significantly modified based on the location and penetration levels of the
GFMs. This can impact and potentially significantly alter the coherency
structure of the system. We have validated our findings with numerical results
using the IEEE 68-bus test system.
