The synchronized operation of power generators is the foundation of electric power network stability and a key to the prevention of undesired power outages and blackouts. Here, we derive the conditions that guarantee synchronization in power networks with inherent generator heterogeneity when subjected to small perturbations, and perform a parametric sensitivity analysis to understand synchronization with varied types of generators. As inverter-based resources, which are the primary interfacing technology for many renewable sources of energy, have supplanted synchronous generators in ever growing numbers, the center of attention on associated integration challenges have resided primarily on the role of declining system inertia. Our results instead highlight the critical role of generator damping in achieving a stable state of synchronization. Additionally, we report the feasibility of operating interconnected electric grids with up to 100% power contribution from inverter-based renewable generation technologies. Our study has important implications as it sets the basis for the development of advanced control architectures and grid optimization methods that ensure synchronization and further pave the path towards the decarbonization of the electric power sector.