Why do we keep the speed of the synchronous generator constant at no-load? What happens if the speed varies?

Synchronous generators are constant speed motors. They run at the synchronous speed of the supply.

They are generally used for constant speed operation under no load conditions such as to improve the power factor¹.

When a synchronous generator is operating, something is turning the rotor and something is providing the rotor with a magnetic field.

The magnetic field is rotating through the stator conductors and generating voltage.

If nothing is connected to the stator, there is voltage at the stator terminals but no current is flowing.

The stator terminal voltage is AC voltage, but other than the fact that the voltage is AC, the stator is much like a battery on a shelf doing nothing, but ready to supply current as soon as a load is connected².

In a permanent-magnet synchronous generator, the losses at no-load are friction, aerodynamic drag (windage), reluctance torque, hystereses and eddy-current losses. A wound-field synchronous generator has additional losses associated with producing the field excitation.

Large machines may have additional losses due to the operation of cooling, lubrication, monitoring and protection systems².

If the speed varies, it will cause variations in frequency and voltage output which can be harmful to electrical equipment.