AP1000s run with a negative reactor coefficient. Translation, if they lose power they shut down, not melt down.
Not that I'm a fan, but they are still built on old (but proven) technology. The US was well on its way to a much better design in the Integral Fast Reactor, but killed it in 1994, mostly based on reasons the IFR designed to fix, like nuclear waste. The IFR was a fast reactor, meaning fast neutrons are used to breed fertile Uranium (U-238, aka nuclear waste) into fissile Plutonium-239 and then burning it in the reaction. With onsite reprocessing, (which is a proliferation risk, but let's be frank, all nuclear power is in some way) the remaining waste will decay to background in 100 years. Incidentally, that is about the same as fusion due to deuterium and tritium created by fusion.