II. Electromotive Forces 6. In a synchronous machine we have to distinguish between terminal voltage E, real generated e.m.f. #1, virtual generated e.m.f. EZ, and nominal generated e.m.f. EQ. The real generated e.m.f. EI is the e.m.f. generated in the alter- nator armature turns by the resultant magnetic flux, or mag- netic flux interlinked with them, that is, by the magnetic flux passing through the armature core. It is equal to the terminal voltage plus the e.m.f. consumed by the resistance of the arma- ture, these two e.m.fs. being taken in their proper phase relation; thus Ei = E + Ir, where / = current in armature, r = effective resistance. The virtual generated e.m.f. E2 is the e.m.f. which would be generated by the flux produced by the field poles, or flux corre- sponding to the resultant m.m.f., that is, the resultant of the SYNCHRONOUS MACHINES 129 m.m.fs. of field excitation and of armature reaction. Since the magnetic flux produced by the armature, or flux of armature self-inductance, combines with the field flux to the resultant flux, the flux produced by the field poles does not pass through the armature completely, and the virtual e.m.f. and the real gener- ated e.m.f. differ from each other by the e.m.f. of armature self- inductance; but the virtual generated e.m.f., as well as the e.m.f. generated in the armature by self-inductance, have no real and independent existence, but are merely fictitious components of the real or resultant generated e.m.f. EI. The virtual generated e.m.f. is Ei = Et + jlx, where x is the self -inductive armature reactance, and the e.m.f consumed by self-inductance Ix is to be combined with the real generated e.m.f. EI in the proper phase relation. 7. The nominal generated e.m.f. EQ is the e.m.f. which would be generated by the field excitation if there were neither self- inductance nor armature reaction, and the saturation were the same as corresponds to the real generated e.m.f. It thus does not correspond to any magnetic flux, and has no existence at all, but is merely a fictitious quantity, which, however, is very useful for the investigation of alternators by allowing the combination of armature reaction and self-inductance into a single effect by a (fictitious) self-inductance or synchronous reactance XQ. The nominal generated e.m.f. would be the terminal voltage with open circuit and load excitation if the saturation curve were a straight line. The synchronous reactance XQ is thus a quantity combining armature reaction and self-inductance of the alternator. It is the only quantity which can easily be determined by experiment by running the alternator on short circuit with excited field. If in this case IQ = current, PQ = loss of power in the armature coils, EQ = e.m.f. corresponding to the field excitation at open w p circuit, 7— = ZQ is the synchronous impedance, y^ = r0 is the -to J-o effective resistance (ohmic resistance plus load losses), and XQ = A/202 — ro2 the synchronous reactance. In this feature lies the importance of the term " nominal generated e.m.f." EQ, E0 = Ei + J!XQ, = E + (r + jx) I 130 ELEMENTS OF ELECTRICAL ENGINEERING the terms being combined in their proper phase relation. In a polyphase machine, these considerations apply to each of the machine circuits individually.