Pstatorwinding=Ms x Rs x |Is|**2 Loss of Stator Power in watts
where
|Is|=(Xms x Ns' x Ef)/[(XLs + Xms) x Rf] is stator current in Amps
Ef rotor field voltage in Volts
Rf rotor field resistance in Ohms
XLs is stator leakage reactance << Xms in Ohms
Xms is stator magnetizing reactance in Ohms
Ns' = 3 x Nr/(sqrt2 x Ms x Ns)
Ms is number of stator phases
Nr number of rotor turns
Ns number of stator turns

hey S, I think you got things mixed up.

the dc field in a syn. gen. does not "saturate", however the ac core saturates and this limits the voltage induced in the armature winding by the field.

Second, changing excitation (magnetization) levels in a synch. generator changes Var generation not Power generation.  Only the steam turbine governor can change Power output of the generator.

Now changing Vars loading will change the losses in the generator(stator core loss, armature loss, stray load loss) but these losses are small compared to the power output in any well designed generator.

It will not reduce the out put.THe change in the field excitation is only conncted to the reactive power.There by only the voltage will change if it is running in solo or the power factor will change if it is running in paralell.The active power will not get changed and it is enterly depends on the steam flow and the governertrottling if it is in parallel with grid or another gen.Or the amount of load it is impoed on.