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Ramping up a Generator while RPM is Constant.
How exactly does the power output of a generator increase, by increasing the fuel input and keeping RPM constant.

I'm having a bit of trouble getting my head around this so I ask for help.

Recently, as our plant was starting up, I saw the following:
GT running at full speed (3000 rpm) so as to produce a 50Hz frequency to Sync with the grid. Once it was at this speed it synchronized with the grid but was producing only 40MW at the time (Max Capacity of 120MW). Gradually the load was increased and the output was ramped up to 120MW.

Now I understand this increase in load is due to injecting more fuel. What I don't understand is how does it produce more power by running at the same speed? What exactly is the relation between fuel and power output if the RPM is kept constant? And how much of a role does the excitation play during this ramping up? I feel I'm probably overlooking something very basic here but I just can't seem to understand it.

The answer lies in the basic AC frequency formula:

F=(P*N)/120

And, synchronization. It's a VERY powerful word--and if it wasn't so important to synchronize a machine when connecting it to a grid (of any size) with other generators and their prime movers, then why would it be so critical that it be done so correctly, with very damaging consequences and effects if it's not done correctly?

The answer lies in the fact that no matter how many AC synchronous generators (more correctly called alternators) are synchronized together, or even a single synchronous generator, they (or it) must run at a constant speed to maintain a constant frequency (see the formula above). And, any number of synchronous generators (one, two, twenty-three or 3,167) all have to run at the same frequency because they are synchronized together and in effect are operating as a single generator supplying what appears to be a single load (no matter the number of motors and lights and televisions and computers and computer monitors and tea kettles are energized and powered by the transmission and distribution system (the "grid")).

And the excitation which produces the rotating magnetic field which is locked into synchronism with the "apparently" rotating stator magnetic field (here's where YouTube can be your friend!) is necessary for keeping the rotor locked into synchronism with the stator.

How large is the grid you are connected to? Do you think your 120 MW machine can have any appreciable effect on grid frequency? Can it really make all the other generators and their prime movers go faster (or slower)? It might have an impact of ten-thousandths of a Hertz if it was loaded very quickly and the grid operators weren't paying any attention, or if it tripped of the grid very suddenly it might have the same ten-thousandths of a Hertz effect if the grid operators weren't paying attention.

You are correct--the load on the generator is increased by increasing the fuel flow-rate into the prime mover (in the case the gas turbine). BUT, any fuel in excess of that required to maintain synchronous speed is converted by the generator into amperes (because it CAN'T go any faster because it's synchronized to the grid with other generators and their prime movers). If the generator were NOT synchronized to the grid with other generators and their prime movers any fuel in excess of that required to maintain excess speed would, indeed, be translated into more speed. But, the generator converts that excess torque into amperes.

Ask yourself this question: Why is it that people never have a problem with the fact that motors convert amperes into torque, but they ALWAYS have a problem when told that generators convert torque into amperes? Don't generators drive motors? So, what's the problem then with making the leap that if motors can convert amperes into torque, and that if generators drive motors (via amperes), that generators then have to convert torque into amperes? That's what generators do. And prime movers provide the torque, and then that torque is in excess of what's required to maintain synchronous speed and the generator is synchronized to the grid the generator--because it CAN'T run faster than synchronous speed (as you have told)--the generator converts that torque to amperes. And, then at the other end of the wire the motor converts the amperes to torque.

It's a simple as that. (Televisions don't do useful work, and neither do lights or tea kettles or computers and their monitors, but they are still driven by amperes and the amperes come from generators, that converted torque into amperes.)