When a utility company uses the term "installed capacity" does it mean energy or power?
Megawatts is a unit of power not energy.  What the utility is telling you is that they have enough electric generators on hand to generate up to 36,800 megawatts of power at one time. You need to multiply time by power to get energy.  However since this maximum capacity will almost never be used at one time, it is somewhat meaningless to use this number for energy calculations.