IV. Induction Generator 1. INTRODUCTION 163. In the range of slip from s = 0 to s = 1, that is, from synchronism to standstill, torque, power output, and power input of the induction machine are positive, and the machine thus acts as a motor, as discussed before. Substituting, however, in the equations in paragraph 1 for s values > 1, corresponding to backward rotation of the ma- chine, the power input remains positive, the torque also remains positive, that is, in the same direction as for s < 1 ; but since the speed (I — s) becomes negative or in opposite direction, the power output is negative, that is, the torque in opposite direc- tion to the speed. In this case the machine consumes electrical energy in its primary and mechanical energy by a torque oppos- ing the rotation, thus acting as brake. The total power, electrical as well as mechanical, is con- sumed by internal losses of the motor. Since, however, with large slip in a low-resistance motor the torque and power are small, the braking power of the induction machine at backward INDUCTION MACHINES 341 rotation is, as a rule, not considerable, excepting when using high resistance in the armature circuit. Z0« Zj- 0.1+ 0.3 j Y - 0.01 - 0.1 J 110 VOLTS CONSTANT FREQUENCY -1000 -2000 -3000 -4000 -5000 -6000 -7000 -8000 -9000 FIG. 185. — Induction generator load curves. TORQUE POWER 8000 _0 loo; -4000 -6000 113 1.2 1U 1009 0,8 0:7 o!e 0 5 0!4 Oi3 ol2 0. ACTI A ^ SLIP FACTION OF SYNCHROS SM CONSTANT FREQUENCY CONSTANT TERMINAL VOLTAGE OF 110 Z0- Y - 0.01 - 0.4 05 060 160 140 100. FIG. 186. — Induction machine speed curves. Substituting for s negative values, corresponding to a speed above synchronism, torque and power output and power input 342 ELEMENTS OF ELECTRICAL ENGINEERING become negative, and a load curve can be plotted for the induc- tion generator which is very similar, but the negative counter- part of the induction motor load curve. It is for the machine shown as motor in Fig. 176 given as Fig. 185, while Fig. 186 gives the complete speed curve of this machine from s = 1.5 to * = -1. The generator part of the curve, for s < 0, is of the same char- acter as the motor part, s > 0, but the maximum torque and maximum output of the machine as generator are greater than as motor. Thus an induction motor when speeded up above synchronism acts as a powerful brake by returning energy into the lines, and the maximum braking effort and also the maximum electric power returned by the machine will be greater than the maxi- mum motor torque or output. 2. CONSTANT-SPEED INDUCTION OR ASYNCHRONOUS GENERATOR 154. The curves in Fig. 185 are calculated at constant fre- quency /, and thus to vary the output of the machine as gen- erator the speed has to be increased. This condition may be realized in case of induction generators running in parallel with synchronous generators under conditions where it is desirable that the former should take as much load as its driving power permits; as, for instance, if the induction generator is driven by a water power while the synchronous generator is driven by a steam engine. In this case the control of speed would be effected on the synchronous generator, and the induction gen- erator be without speed-controlling devices, running up beyond synchronous speed as much as required to consume the power supplied to it. Conversely, however, if an induction machine is driven at constant speed and connected to a suitable circuit as load, the frequency given by the machine will not be synchronous with the speed, or constant at all loads, but decreases with increasing load from practically synchronism at no load, and thus for the induction generator at constant speed a load curve can be con- structed as shown in Fig. 187, giving the decrease of frequency with increasing load in the same manner as the speed of the induction motor at constant frequency decreases with the load. In the calculation of these induction generator curves for con- INDUCTION MACHINES 343 slant speed the change of frequency with the load has obviously to be considered, that is, in the equations the reactance x0 has to be replaced by the reactance XQ (1 — s), otherwise the equa- tions remain the same. FIG. 187. — Induction generator load curves. 3. POWER-FACTOR OF INDUCTION GENERATOR 155. The induction generator differs 'essentially from a syn- chronous alternator (that is, a machine in which an armature revolves relatively through a constant or continuous magnetic field) by having a power-factor requiring leading current ; that is, in the synchronous alternator the phase relation between current and terminal voltage depends entirely upon the external circuit, and according to the nature of the circuit connected to the synchronous alternator the current can lag or lead the ter- minal voltage or be in phase therewith. In the induction or asynchronous generator, however, the current must lead the ter- minal voltage by the angle corresponding to the load and voltage of the machine, or, in other words, the phase relation between current and voltage in the external circuit must be such as required by the induction generator at that particular load. Induction generators can operate only on circuits with lead- ing current or circuits of negative effective reactance. 344 ELEMENTS OF ELECTRICAL ENGINEERING In Fig. 188 are given for the constant-speed induction gen- erator in Fig. 230 as function of the impedance of the external circuit z = -?• as abscissas (where eQ = terminal voltage, iQ = 2o current in external circuit), the leading power-factor p = cos 6 required in the load, the inductance factor q = sin 6, and the frequency. Hence, when connected to a circuit of impedance z this induc- tion generator can operate only if the power-factor of its circuit is p', and if this is the case the voltage is indefinite, that is, the circuit unstable, even neglecting the impossibility of securing exact equality of the power-factor of the external circuit with that of the induction generator. FIG. 188. — Three-phase induction generator power factor and inductance factor of external circuit. Two possibilities thus exist with such an induction generator circuit. 1st. The power-factor of the external circuit is constant and independent of the voltage, as when the external circuit consists of resistances, inductances, and capacities. In this case if the power-factor of the external circuit is higher than that of the induction generator, that is, the leading current less, the induction generator fails to excite and generate. If the power-factor of the external circuit is lower than that of the induction generator, the latter excites and its voltage rises until by saturation of its magnetic circuit and the consequent increase of exciting admittance, that is, decrease of internal power-factor, its power-factor has fallen to equality with that of the external circuit. INDUCTION MACHINES 345 In this respect the induction generator acts like the direct- current shunt generator, and gives load characteristics very similar to those of the direct-current shunt generator as dis- cussed in B; that is, it becomes stable only at saturation, but .Z^O.I + O.Sjl ATFULL V«0.01— O.lj I FREQUENCY FIG. 189. — Induction generator and synchronous motor load curves. loses its excitation and thus drops its load as soon as the voltage falls below saturation. Since, however, the field of the induction generator is alter- nating, it is usually not feasible to run at saturation, due to ex- cessive hysteresis losses, except for very low frequencies. 346 ELEMENTS OF ELECTRICAL ENGINEERING 2d. The power-factor of the external circuit depends upon the voltage impressed upon it. This, for instance, is the case if the circuit consists of a syn- chronous motor or contains synchronous motors or synchronous converters. In the synchronous motor the current is in phase with the impressed e.m.f. if the impressed e.m.f. equals the counter e.m.f. of the motor plus the internal loss of voltage. It is leading if the impressed e.m.f. is less, and lagging if the impressed e.m.f. is more. Thus when connecting an induction generator with a synchronous motor, at constant field excitation of the latter the 01 02 0,3 04 05 06 017 0.8 019 IjO 11. 12 13 14 lf.5 FIG. 190. — Induction generator and synchronous converter, phase control, no line impedance. voltage of the induction generator rises until it is as much below the counter e.m.f. of the synchronous motor as required to give the leading current corresponding to the power-factor of the generator. Thus a system consisting of a constant-speed induc- tion generator and a synchronous motor at constant field excita- tion is absolutely stable. At constant field excitation of the synchronous motor", at no load the synchronous motor runs practically at synchronism with the induction generator, with a terminal voltage slightly below the counter e.m.f. of the syn- chronous motor. With increase of load the frequency and thus the speed of the synchronous motor drops, due to the slip of frequency in the induction generator, and the voltage drops, INDUCTION MACHINES 347 due to the increase of leading current required and the decrease of counter e.m.f. caused by the decrease of frequency. By increasing the field excitation of the synchronous motor with increase of load, obviously the voltage of the generator can be maintained constant, or even increased with the load. When running from an induction generator, a synchronous motor gives a load curve very similar to the load curve of an induction motor running from a synchronous generator; that is, a magnetizing current at no load and a speed gradually decreas- ing with the increase of load up to a maximum output point, at which the speed curve bends sharply down, the current curve upward, and the motor drops out of step. The current, however, in the case of the synchronous motor operated from an induction generator is leading, while it is lag- ging in an induction motor operated from a synchronous genera- tor. In either case it demagnetizes the synchronous machine and magnetizes the induction machine, that is, the synchronous machine supplies magnetization to the induction machine. In Fig. 189 is shown the load curve of a synchronous motor operated from the induction generator in Fig. 187. In Fig. 190 is shown the load curve of an over-compounded synchronous converter operated from an induction generator, the over-compounding being such as to give approximately constant terminal voltage e. 156. Obviously when operating a self-exciting synchronous converter from an induction generator the system is unstable also; if both machines are below magnetic saturation, since in this case in both machines the generated e.m,f. is proportional to the field excitation and the field excitation proportional to the voltage; that is, with an unsaturated induction generator the synchronous converter operated therefrom must have its mag- netic field excited to a density above the bend of the saturation curve. Since the induction generator requires for its operation a circuit with leading current varying with the load in the manner de- termined by the internal constants of the motor, to make an induction or asynchronous generator suitable for operation on a general alternating-current circuit, it is necessary to have a syn- chronous machine as exciter in the circuit consuming leading current, that is, supplying the required lagging or magnetizing current to the induction generator; and in this case the voltage 348 ELEMENTS OF ELECTRICAL ENGINEERING of the system is controlled by the field excitation of the syn- chronous machine, that is, its counter e.m.f. Either a synchro- nous motor of suitable size running light can be used herefor as exciter of the induction generator, or the exciting current of the induction generator may be derived from synchronous motors or converters in the same system, or from synchronous alternating- current generators operated in parallel with the induction gen- erator, in which latter case, however, these currents can be said to come from the synchronous alternator as lagging currents. Electrostatic condensers, as an underground cable system, may also be used for excitation, but in this case besides the condensers a synchronous machine or other means is required to secure stability. The induction machine may thus be considered as consuming a lagging reactive magnetizing current at all speeds, and con- suming a power current below synchronism, as motor, supplying a power current (that is, consuming a negative power current) above synchronism, as generator. Therefore, induction generators are best suited for circuits which normally carry leading currents, as synchronous motor and synchronous converter circuits, but less suitable for circuits with lagging currents, since in the latter case an additional syn- chronous machine is required, giving all the lagging currents of the system plus the induction generator exciting current. Obviously, when running induction generators in parallel with a synchronous alternator no synchronizing is required, but the induction generator takes a load corresponding to the excess of its speed over synchronism, or conversely, if the driving power behind the induction generator is limited, no speed regulation is required, but the induction generator runs at a speed exceeding synchronism by the amount required to consume the driving power. The foregoing consideration obviously applies to the polyphase induction generator as well as to the single-phase induction generator, the latter, however, requiring a larger exciter in con- sequence of its lower power-factor. Therefore, even in a single- phase induction generator, preferably polyphase excitation is used, that is, the induction machine and its synchronous exciter wound as polyphase machines, but the load connected to one phase only of the induction machine. The curves shown in the preceding apply to the machine as polyphase generator. The effect of resistance in the secondary is essentially the INDUCTION MACHINES 349 same in the induction generator as in the induction motor. An increase of resistance increases the slip, that is, requires an in- crease of speed at the same torque, current, and output, and thus correspondingly lowers the efficiency. Induction generators have been proposed and used to some extent for high-speed prime movers, as steam turbines, since their squirrel-cage rotor appears mechanically better suited for very high speeds than the revolving field of the synchronous generator. The foremost use of induction generators will probably be for collecting small water powers in one large system, due to the far greater simplicity, reliability, and cheapness of a small induction generator station feeding into a big system compared with a small synchronous generator station. The induction generator station requires only the hydraulic turbine, the induction ma- chine, and the step-up transformer, but does not even require a turbine governor, and so needs practically no attention, as the control of voltage, speed, and frequency takes place by a syn- chronous generator or motor main station, which collects the power while the individual induction generator stations feed into the system as much power as the available water happens to supply. The synchronous induction motor, comprising a single-phase or polyphase primary and a single-phase secondary, tends to drop into synchronism and then operates essentially as reaction machine. A number of types of synchronous induction genera- tors have been devised, either with commutator for excitation or without commutator and with excitation by low-frequency synchronous or commutating machine, in the armature, or by high-frequency excitation. For particulars regarding these very interesting machines, see " Theory and Calculation of Alternat- ing-current Phenomena."