These plants are normally self-powered for normal operations and use offsite power sources for backup.
If you lose both then you have a very serious situation.
OTFoolish
Gravity works well in ours. }};-D
Anymouse
http://nuclearsafety.gc.ca/eng/reactors/power-plants/nuclear…
Shutdown systems
All nuclear power reactors in Canada have two independent, fast-acting and equally effective shutdown systems.
The first shutdown system is made up of rods that drop automatically and stop the chain reaction if something irregular is detected.
The second system injects a liquid, or poison, inside the reactor to immediately stop the chain reaction.
Both systems work without power or operator intervention. However, they can also be manually activated.
These systems are regularly and safely tested.