I need to know the heat flow equation produced at the level of the alternator of a gas cycle power plant to calculate the power required Qcold produced by a cooling system to control its temperature.
I have modeled and tested countless combined cycle power plants, but don't know what you mean by the "alternator". Are you referring to the generator? I have lots of generator curves I could redact and send you. Large generators of this type are most often hydrogen cooled. While controlling the temperature of the generator is important, it is a trivial contribution to the overall heat transfer in such a system. Operators rarely give this a thought until an alarm goes off. They are far more concerned with lube oil temperature and bearing vibration. Still, the generator is rarely the source of a forced outage. Perhaps do you mean the relationship between generator output and heat input from the fuel into the gas turbine? I can send you that too.
Hydrogen is used for cooling in this case because it has low electrical conductivity and the highest specific heat of any common fluid. Some old generators were water-cooled, but that leads to problems (don't mix electricity and water).
Kinetic energy is usually associated with moving objects. The torque applied to the shaft by the steam turbine drives the generator, which produces the electrical output. Rotational power is most often reported in brake horsepower or Newton-meters/second to distinguish it from electrical power in kW. I know of several very expensive oops! mistakes when kWe (electric) have been confused with kWm (mechanical), which is why it's best to never refer to rotational power in kW. Here are two sets of redacted generator curves: one showing efficiency and the other showing losses eff=net/gross=(gross-loss)/gross=net/(net+loss). I have lots more information if you're looking for something specific.