In my book Solar Storm, I touched on what would happen to a nuclear power plant in the event of a complete grid and transport shutdown. At the time, within the story, I assumed that problems at the McGuire Nuclear Power Plant to the north-west of Charlotte would produce some unique problems for the city. It wasn't until I did my research for the third book Solar Dawn that I discovered that there were two nuclear power plants on the Catawba River, and that Charlotte's problems wouldn't be unique at all. The threat of nuclear meltdown and fallout would affect both of the Carolina States.
With this in mind I went looking for nuclear power plants on the Mississippi River, which is where my next novel, Into Darkness, will be based. I found not one, not two, but three nuclear plants on the river between New Orleans and Vicksburg. That's a 200 mile stretch of the busiest and most important waterway in the US under threat.
In the whole of the US, there are 90 nuclear reactors, mostly scattered from mid to eastern USA. If you live in the midwest, you're less likely to be affected waves of radiation swamping your town when things go pear shaped. The same can't be said for anywhere else.
So why would a solar EMP cause problems for nuclear reactors in particular? The first thing to understand is that nuclear reactors are very difficult to shut down. The reactor core, usually a series of metal rods, is where fission takes place. This fission creates a lot of energy, but it also creates a lot of heat. Like, a lot of heat. If you were to immerse the rods into a municipal swimming pool, it would probably boil dry in 24 hours. Reactor cores need a lot of cooling, so water has to be continually pumped around them. Switching a reactor off, however, does not instantly stop the fission. It takes time. Several days, actually. And it's necessary to maintain the cooling, otherwise the core will literally melt down and cause an explosion. And water pumps require electricity to work. Do you see where I'm going with this?
Let's take a specific real-world example: Fukushima.
In 2011, an earthquake off the coast of Japan caused a giant tidal wave, a tsunami, that swamped coastal areas. The Fukushima nuclear plant, situated on the coast, was affected. Nuclear plants seem always to be situated near water. I assume it's because they need access to water for cooling, but I'm not sure. Anyway, Fukushima got more water than it bargained for. The plant was flooded and the power distribution system destroyed. The backup pumps were also destroyed. In the emergency, the reactor temperatures started to climb.
Okay, this was Japan. The plant was modern, unlike that of Chernobyl. The Japanese are excellent engineers and incredibly hard working and efficient. After the tsunami, assistance could be called for. The electricity grid in the rest of the country remained intact and functioning. Communication systems remained intact. It was theoretically possible for every skilled engineer in the country to be driven or flown to the site. The army, navy and air force were available to help. Replacement generators and pumps could be shipped in from the mainland, or even from abroad, in just a few hours. Japan is a wealthy nation, and some way could have been found to keep the cooling water pumping in the reactors.
As it turned out, however, it wasn't that simple, and in spite of the best efforts of many skilled people, the reactors overheated and blew up. It was the second worst nuclear disaster in history.
So a reactor blew up in spite of all the theoretically available assistance, in a country that maintained a working infrastructure.
Again, I think you can see where I'm going with this. Imagine a devastating Carrington Event-sized (or bigger!) solar storm blowing the grid and wreaking havoc with the entire infrastructure of the continental United States. Imagine that engineers at the 90 or so reactors in the country only had some local help, because they couldn't call for assistance and nobody could bring any even if they knew it was necessary. I think you can guess the likely outcome.
If you're prepping for the end of the world, you don't want to be within 50 miles of a reactor. In fact, to be sure, make that 250 miles. Doesn't matter how many cans of food you have stored, nor how deep your home-made bunker is. The land around you will be poisoned. And you don't want to be down-river of a reactor either, no matter how far away, because the water will be poisoned too.
We put a lot of effort into making sure that nuclear power is safe. Currently it's the safest of all power production. Nature, however, never sleeps and is more than capable of rendering our best efforts futile.
Which is why writers like me continue to write post-apocalypse stories. Because one never knows.