Synchronous generator control

In a hydro generator this is achieved by controlling the discharge of working fluid into the Hydro turbine.

Power output= (RPM x Torque)/9550 or [2(Pi)NT] / 60

By controlling the discharge of working fluid into the turbine, you control the Torque produced by the turbine and thereby the Power output.

The minimum discharge required to keep the system at the required RPM is achieved by allowing enough discharge to overcome the system inertia so that the machine can rotate.

Synchronous generator at reactive load
the current being at ±90° phase angle (angle between voltage and current) with the voltage will create magnetic flux in the same axis as field current => No active power is needed to rotate generator except losses of the generator
Phase angle +90° (current behind the voltage) => inductive load
Phase angle -90° (current ahead the voltage) => capacitive load
Inductive current creates flux affecting opposite direction to flux created by field winding => in order to prevent voltage decreasing, field current shall be increased ( By AVR)
Capacitive current creates flux affecting same direction to flux created by field winding => in order to prevent voltage rising, field current shall be decreased( By AVR).

Synchronous generator at active load
Creates flux which affects in the axis between field poles
Caused by the effect of the crosswise flux created by the active current the rotor of the generator will turn away from it's no-load position to a new position at an angle of  (pole angle)
In order to keep the speed the shaft power produced by Prime mover shall be increased by adding or removing Fuel.

Prime Mover power controlled by the governor (Increase or decrease the fuel as the case requirement) in order to keep the frequency constant, while the AVR control the voltage level.
Accordingly, if the demand load at a particular time say X=VI1 (VA) while the counterpart input mechanical power suppose to be q1(driving power regardless to the source, fuel, steam..etc), where V is the system voltage(almost constant) and I1 is the load current at that time (variable as per the connected load) and then a new load is connected to the system say Y=VI2.
Therefore, the Total load will be X+Y and the total Input Power (say fuel, that is automatically controlled by the Governor) will be q+ power required to cover Y + losses.
Note: droop or slight drop on frequency and voltage might be observed, depends on the control system response.