I'm working on a story where an energy wave from space just hits the earth and all the electrics burn out. This is a question which has been on my mind for a little while. If there were no computers, no automated handling of such a big power, what could that cause?
Nuclear Reactors are engineered for a host of eventuallities and likely have several critical infrastructures hardened against EMP waves as they were a known issue in a Nuclear War (during the cold war, it was thought that the first Soviet Nuke to go off would be in the Upper Atmosphere over the U.S., which would create a EMP that would destroy the lower 48 states electrical equipment instantly). Since most commercial reactors were made at this time, it's likely they would been given some EMP shielding.
Additionally, most Nuclear Plants will "switch off" in the event of a disturbance if they are running by having a power cut by automatically drop the control rods into the fissile core (a power source is required to keep the control rods out to allow the reaction, so no power, no reaction), which will stop further reaction. From there the heat of the current reaction needs to dissapate but core would not detonate (actually, no explosion related to fissile material would occur at a Nuclear plant... but booms happen for other reasons.).
In this scenario we're not out of the woods and the Fukashima-Diachii power plant disaster is a good idea of what to expect as the heat sink is likely the fail point. Nuclear reactors generate electricity by converting water to steam to turn turbines that produce electricity. This also has a dual purpose of cooling the reactor core, as evaporating water removes heat (this is why humans sweat) and is quite good at it. But it requires pumps to pump the water in once the water is cooled and liquid again. With no pumps, the water covering the reactor core will quickly boil away from the still lingering heat and the core can be exposed to oxygen which doesn't cool the core. The effects of this can be seen in Fukashima and to a lesser extent Three Mile Island (the explosion seen at the Fukashima plant was due to a build up of Hydrogen and Oxygen igniting and blowing the containment building open... not the react blowing up.
In an absolute worst case scenario, where neither the control rods nor the water pumps function, a disaster known as a "China Syndrome" will occure. In this scenario, with no way to shut down the reaction or remove heat, the reaction runs out of control and becomes hot enough to melt the core. The molten slage will melt through the containment structures into the very earth itself, boring a hole downward to the core of the planet... except it won't get there... Nuclear plants have a high water demand and this means their built by large replenishable natural bodies of water, usually rivers or oceans. This means that the core will likely strike an aquifer, which will have a cooling effect and produce a lot of radioactive steam... steam which has no place to escape to the atmoshere... so it will erupt from the ground much like a geyser... and can cause radioactive geysers to form for miles around the nuclear power plant.
Almost all reactors will melt down. Some very new or experimental ones will turn off safety
As has been pointed out, many reactors are EMP shielded - but you didn't say it was EMP. If that wave behaves as advertised (eg it is something unknown in physics), then, yeah, we're royally screwed.
Nuclear power plants have backup generators on site whose purpose is to circle coolant for a few days after they switch off, as there is residual energy that's enough to cause a meltdown. Your wave breaks the generators, and the pumps. Almost all reactors world-wide will melt down without coolant circulation.
There's no generators to transport in. There's no pumps to transport in. And there's no power to the factories to make more in the limited timeframe.
There is a failsafe reactor design which can survive at total loss of everything without melting down. If your design has passive coolant circulation, then it may be ok. (Most of the examples on that Wikipedia link would still melt down, as they require the pumps to be turned on within 3 days) The ones that have truly passive safety systems are at the end of the list, and are scale models and demonstration models at university and company labs.
As above, many older reactors will overload without active controls regulating the reaction.
3rd & 4th generation reactors, & the new small reactor designs, may be designed to automatically drop control rods into the core, shutting down the fission process mechanically by default.
MSRs, especially the Thorium catalyst flavor, have reaction processes which must be actively fired & fed. If the plant shuts down, whether by big red panic button, or EMP, or tsunami, or bomb, the reaction just stops and cools naturally, safely. No Chernobyl event is possible.
Fusion plants need massive amounts of power to fire the lasers or throw particles, etc, to fuse the core elements. Remove the power supply via EMP? Yes the magnetic containment will fail but so will the lasers or etc. Might be a localized boom as steam cannot escape, as described above, but not likely a big mushroom cloud type boom.
So when exactly your story is set effects the chain of events. Near past, present, near future, and far future, will each have these different standard reactors.