The main impact of solar flare on nuclear power plant would be in the form of electric grid collapse cutting power to the power plant. But this is certainly not the first or only time when many nuclear power stations faced the need to shutdown quickly and simulate doubly due to power grid collapse. In 2003 14 nuclear power plants in the northeastern US had to shut down in a few minutes due to electric grid collapse. During 2011 japan earth quake. I believe all of Japan’s 50 odd nuclear powerplants shut down in a few minutes.
In all these cases, backup internal power immediately kicked in to restore required internal plant services required to safe the reactors, except the Fukushima plant, where the backup internal power also failed because the tsunami overtopped the sea wall around the plant and drowned the backup diesel generators.
In the unrelated case of Chernobyl, the operators actually took the extraordinary step of shutting off the backup diesel generator during a simulated black out, more or less to see what will happen, while also simultaneously running the reactor well outside of its designed range of safe operating levels. So they spiked the power of the reactor while there was no cooling water circulating in the reactor.
In all these cases, backup internal power immediately kicked in to restore required internal plant services required to safe the reactors, except the Fukushima plant, where the backup internal power also failed because the tsunami overtopped the sea wall around the plant and drowned the backup diesel generators.
In the unrelated case of Chernobyl, the operators actually took the extraordinary step of shutting off the backup diesel generator during a simulated black out, more or less to see what will happen, while also simultaneously running the reactor well outside of its designed range of safe operating levels. So they spiked the power of the reactor while there was no cooling water circulating in the reactor.