As far as I know, military bases don’t have their own nuclear reactors or coal plants.
EDIT: Apparently the DoD requires diesel backup with enough fuel to last… “one to two weeks.” Meh… if I’m an EMP-empowered nation who hates the US, the grid looks tempting… sure, they can counterattack, but if you make investigating difficult and spread enough pandemonium… all you need to do is keep the government haphazardly distracted and confused for two weeks and you win…