I have a DC motor with independent excitation, power by a ward-leonard system. The nominal voltage applied to the motor is 250 V. I have to calculate what regulation(%) to apply to the generator so that the motor rotates at 500 rpm. I calculated that for the motor to have that speed it needs a voltage of 121.44 V applied at the terminals and that for the generator to supply that voltage it needs EMF of 138.6 V. In my notes, I have that to calculate the regulation I need to following formula, where U0 is the generator's EMF, Un the nominal voltage at the terminals and U the voltage at the terminals:
According to this formula I get a regulation of 6.9%. But I don't really get this formula. Why do I divide the voltage difference by Un and not U0?