Ever studied nuclear power plants? Do you know anything about their safety protocols?
What is a "control rod?"
There are procedures in place in EVERY nuclear power plant that covers a grid down contingency. What do you think happens if a tornado wipes out the distribution near any given Nuclear Facility? That aspect is covered.
What is not covered is if the distribution network is destroyed continent wide. The power plants will simply shut down. No problem with them. The citizens, however, will have to deal with having no power, just like Puerto Rico right now . . . only for 1 – 10 years. That is the projected amount of time it would take to get all of those huge transformers back online.
Many folks can deal with a week without power. Maybe two weeks. Could they handle 50 weeks?
From where will their fresh water come? Most places, especially cities, have it pumped. That requires electricity.

Rule of three's applies:
3 weeks without food
3 days without water <--
3 minutes without air