Originally posted by: PowerEngineer
CycloWizard and Mark R are correct (as usual)

I'll add a few comments...
The DC field for synchronous generators is produced by running current through a winding (made up of copper bars) in the rotor. The current is produced by the so-called excitation system, which draws its power from the output of the generator (or where ever else the other power plant loads are fed from). The amount of current produced by the excitation system is controlled by a voltage regulator. As the name implies, the voltage regulator tries to adjust excitation to maintain acceptable voltage at the terminals of the generator or at some nearby substation bus.
This brings me around to what might be a misconception on the part of the OP. The electrical power output of the generator is not produced by establishing the DC field; it is produced by moving that field across the windings in the generator's stator (the windings surrounding the rotor). Any movement is opposed by currents induced in the stator winding. The "prime mover" provides the energy required to spin the rotor against the opposing forces of induced current in the stator.
Consider the simple demonstration of Faraday's Law using a permanent magnet and a loop of wire. The magnet does not provide the energy needed to produce the current in the loop, it's you pulling it back and forth that does.
Because the stator coils have inductance, there is some voltage drop as current increases that does slightly change the amount of current needed in the rotor winding. Generator power output, however, is a direct result of the so called phase angle between the rotor excitation and the stator's voltage from the induced currents. The harder you spin the shaft, the bigger the angle, the more power is produced.
Many generators do use what amount to smaller generators on the same shaft to produce the excitation current. Newer units often use DC rectifiers off the plant's AC power supply to do it; these have the advantage of responding faster to voltage fluctuations (but are also more vulnerable to these fluctuations).