  Synchronized operation of generators in a power network is paramount to the
stability and reliability of energy delivery. In this paper, we address the
synchronization problem in a heterogeneous power grid, consisting of both
synchronous generators and inverter-based generators, and derive the necessary
and sufficient condition guaranteeing the existence of a unique locally stable
synchronized mode. Further, our results have implications for utilizing
grid-following inverters versus grid-forming inverters in order to enhance
network stability. This work is of particular importance as power grids around
the world are undergoing a transition from being predominantly composed of
synchronous generators towards a grid consisting of a preponderance of inverter
based generators.
