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Well lets see here it goes. There are several different types of power plants available and each will respond differently to a no human presence. I will start with the most basic unit which would be a simple cycle gas trubine. These unit are used mostly for peaking and are seldom base loaded. The age on these unit can vary from brand new to about 40 years old. Gas turbines only really came into use in the 1960's. A gas turbine will continue to run almost indefinitely as long as it has a good supply of gas. That is a key point. The units are designed to trip if they see to low a pressure on the gas. The trip would happen automatically without human intervention. The other problem I can see with a gas turbine is the generator. Most of the older generators and many of the larger generators are filled with hydrogen gas for cooling. The stator cores and generator fields have gas passages where the hydrogen flows. Hydrogen is used because it is light, cheap and a good conductor of heat. The problem with it is that it is inflammable and gets used up. A certain amount of it escapes through the oil seal and through the walls of the piping. The generators have to constantly have a source of fresh hydrogen. Typically only one or two bottles are connected at a time and depending on the generator a new one will need to be connected every day to maybe a week at most. Once the hydrogen pressure starts to drop in the generator it does not conduct enough heat out of the generator and the unit may very well alarm and trip. This process would take down all electrical generators that use hydrogen cooling, this includes all coal and nuclear units. I never worked hydro and I don't believe they use hydrogen so they might still run. The other problem with the hydrogen gas is that it requires seal oil to be maintained. Typically the seal oil system is connected as a scavenger system to the main lube oil system on a turbine. When the turbine is running it uses a shaft driven oil pump so plently of seal oil is available. During a shut dwon the auxilliary electric pumps keep the seal oil system functioning. Most installations have two AC pumps and one DC pump feed by it's own set of station batteries. In a complete shutdown only the dc pump would operate and that will quit within tfour to eight hours. Seal oil would be lost and the hydrogen gas would then escape the generator and possible catch fire.

Combined cycle(Gas turbine with the exhaust being fed to a boiler to generate steam which is then used in another turbine), Coal and Nuclear all share the same problems. Balance of plant which includes everything not related to the Boiler/reactor and turbine generator equipment is not automated very well. From what I have seen this is the most common area requiring operator intervention in the day to day operation of a power plant. This can be everything from water treatment plants , Evaporative coolers, fuel handling(Several people mentioned that coal plants are fairly operator intensive and they are right about that) and other systems. Any and all of these can have problems or need human intervention to operate correctly on a day to day basis.

Nuclear presents it's own special problems. Like all units they are designed to react automatically to dangerous situation where the response time needs to be in seconds or fractions of a second. The problme comes later the units will require some sort of operator intervention to complete safe shut down. Motors need to be started and valves operated, that sort of thing.

Trying to restart units that have been improperly shut down could be very difficult in most cases. First off station batteries would have to be recharged. Power plants use 125V DC power to run their internal relays, meters, control systems and switch gear. Without that power nothing works. If a turbine rotor is stopped in one position while it is still hot you can get a situation called rotor bow. The residual heat in the turbine collects in the top of the casing and the rotor will grow towards this heat. This causes the rotor to become unbalanced. It takes a good long while to spin out a rotor bow. A host of other issues could plauge any startup attempt. Contaminated boiler water. Plugged injectors in boilers. Tube breaks in boilers due to water slugging. I could go on and on.

One other issue exists and that is the varying system load throughout the day. Generators are all run in synch with each other. System load is balanced by dispatchers calling up the plants and asking them to raise or lower power and voltage( Really Var) output. This system is not automated to the best of my knowledge. Unbalanced systems will cause the frequency of the system to speed up or slow down. All generators have a protective relay called Volts per Hertz. Essentially this realy looks at the voltage output of the genertor and divides that by the frequency. This matters because electrical insultion has the ability to work better at higher frequency than lower frequency. For instance GE sells generators rated at 13.8kv and 60 Hz. They sell the same generator over seas and it is rated at 12.5kV and 50 Hz. Any system underfrequency will start tripping out units at about 58.5 Hz. That is a little less than 3% variance from the current load point of the system. Likewise the all generators are equipped with overspeed devices. Usually anywhere between 108 to 111 percent of rated frequncy will cause them to trip. Feel free to emial me if you have any other questions.