The risk of nuclear power plant meltdown in the case of a power failure

Description of how nuclear power plants work.

In the Fukushima Daiichi nuclear disaster, a power failure and disruption of the backup generators lead to meltdown.

In a scenario of widespread grid collapse, all powered-down nuclear plants would be forced to run their backup cooling systems, which need to be continually supplied with diesel fuel.

Could nuclear plants still power their own cooling systems?

But wait: Why would nuclear plants not continue to provide their own electricity. Even if the grid was disrupted and electricity couldn’t be properly moved around, wouldn’t the plant still be able to power its own cooling system?

ref: Arnie Gundersen and Mat Stein - Solar storms, EMP and grid vulnerability