Aren't the large Tesla battery farms in Australia being used for that purpose? [1] Basically they use batteries and control systems to correct instead of a rotating mass. I'm not sure about the ability to push several hundreds of MW into the system but at least it gets something done.
The rotor in a synchronous machine is coupled magnetically to the grid (basically a spring-mass system where the spring is a rotary field); there is virtually no reaction time in this mechanism.
(It should be noted that other motors, including asynchronous machines, contribute as well)
AIUI the HPR has reaction times on the order of a few seconds.
[1] http://www.bbc.com/news/world-australia-42190358