Ah, this is why I come here. I had no idea that was the case. I feel like there was a story going around recently about how hard it is to restart some power generator if it gets knocked offline. Maybe it was about Hoover Dam now that I think about it (i.e., how bad it would be if the Colorado gets too low).
You would need supercapacitors, but you can make an inverter emulate inertia almost as well as flywheels, and more than well enough to not make a difference once you push the energy into a few kilometers of non-zero impedance grid.