I am trying to understand how the grid works. Lets say we have some gas turbines, where we have a combination of air and fuel being used to turn turbine blades which in turn drives a generator to generate lets say three phase power. This 3-phase power is essentially 3 sinusoidal voltages out of phase with each other by 120 degrees. Now lets say that the load demand on the grid were to increase, then we need more power, so probably more air and fuel are used to make the turbines spin faster. What is the effect of this on the three phase power being generated. My understanding is that the three phase power will be 3 voltage waveforms each at 120V RMS and out of phase by 120 degrees with a frequency of 60 or 50 Hz, depending on where you live and it this three phase power should remain constant. So how is more power being generated at the turbine/generated affecting this output voltage. I don't understand the relationship between the power generated and voltage.
For one thing, turbine plants use much higher voltages than 120. 4140V or 12kV are more typical for a large turbine, with that voltage stepped up further for long lines distribution.
For another, a turbine like you describe would be only for a backup generator. Large turbines for a municipal-size grid use steam heated by the fuel, be it natural gas, coal or nuclear fission.
Anyway, what happens with any generator linked to the grid is that they vary the torque to match the load, while keeping RPM constant. This is because the generator's waveforms not only need to be the same frequency, but the same phase.
For example, windmills in groups run at the same RPM together, varying their power output by feathering the props and thus varying their torque, but all in lockstep with the grid frequency and phase.
Think of it like what happens when your car climbs a hill at a constant speed: the engine RPM doesn't change, but to maintain speed you have to give it more accelerator to increase the torque, and thus, the power (power being basically torque x RPM.)