VIII. Characteristic Curves of Synchronous Motor 17. In Fig. 66 are shown, at constant impressed e.m.f. E, the nominal counter-generated e.m.f. EQ and thus the field excitation FQ required, 1. At no phase displacement, 6 = 0, or for the condition of minimum input; 144 ELEMENTS OF ELECTRICAL ENGINEERING 2. For 0 = + 60, or 60 deg. lag: p = 0.5, q = + 0.866, and 3. For 0 = - 60, or 60 deg. lead: p = 0.5, q = - 0.866, with the current I as abscissas, the constants being r = 0.1, z0 = 5, and E = 1000. These curves are called the compounding curves of the syn- chronous motors. In Fig. 67 are shown, with the power output PI = i (Ep — ir) — (iron loss and friction) as abscissas, and the same constants 1= E = =0.1, 000 XQ= 1100 20 40 60 80 100 120 140 160 180 200 FIG. 66. — Synchronous motor compounding curves. r = 0.1, XQ = 5, E = 1000, and constant field excitation F0' that is, constant nominal counter-generated e.m.f. EQ = 1109 (corresponding to p = 1, # = 0 at 7 = 100), the values of current I and power-factor p. As iron loss is assumed 3000 watts, as friction 2000 watts. Such curves are called load characteristics of the synchronous motor. 18. In Fig. 68 are shown, with constant power output = PO, SYNCHRONOUS MACHINES 145 i (Ep — ir), and the same constants, r = 0.1, XQ = 5, E = 1000, and with the nominal counter-generated voltage E0, that is, field excitation FQ, as abscissas, the values of current / for the four conditions, PO = 5 kw., or PI = 0, or no load, Po = 50 kw., or Pi = 45 kw., or half load, Po = 95 kw., or Pi = 90 kw., or full load, Po = 140 kw., or PI = 135 kw., or 150 per cent, of load. 10 20 30 40 50 60 70 80 90 100 110 120 130 140 FIG. 67. — Synchronous motor load characteristics. Such curves are called phase characteristics of the synchronous motor. We have Po = iEp - i*r. Hence, Po + iV P = EQ = - p (Eq - ix0)2. Similar phase characteristics exist also for the synchronous generator, but are of less interest. It is seen that on each of the four-phase characteristics a certain field excitation gives 146 ELEMENTS OF ELECTRICAL ENGINEERING minimum current, a lesser excitation gives lagging current, a greater excitation leading current. The higher the synchronous reactance XQ, and thus the armature reaction of the synchronous motor, the flatter are the phase characteristics; that is, the less sensitive is the synchronous motor for a change of field excitation or of impressed e.m.f. Thus a relatively high armature reaction is desirable in a synchronous motor to secure stability, that is, independence of minor fluctuations of impressed voltage or of field excitation. 19. The theoretical maximum output of the synchronous motor, or the load at which it drops out of step, at constant impressed voltage and frequency is, even with very high armature reaction, usually far beyond the heating limits of the machine. 200 100 600 800 1000 1200 UOO 1600 1800 2000 FIG. 66. — Synchronous motor phase characteristics. The actual maximum output depends on the drop of terminal voltage due to the increase of current, and on the steadiness or uniformity of the impressed frequency, thus upon the individual conditions of operation, but is as a rule far above full load. Hence, by varying the field excitation of the synchronous motor the current can be made leading or lagging at will, and the syn- chronous motor thus offers the simplest means of producing out of phase or wattless currents for controlling the voltage in trans- mission lines, compensating for wattless currents of induction motors, etc. Synchronous machines used merely for supplying wattless currents, that is, synchronous motors or generators running light, with over-excited or under-excited field, are called synchronous condensers. They are used as exciters for induc- tion generators, as compensators for the reactive lagging currents SYNCHRONOUS MACHINES 147 of induction motors, for voltage control of transmission lines, etc. Sometimes they are called "rotary condensers" or "dynamic condensers" when used only for producing lead- ing currents.