VI. Phase Converter 158. It may be seen from the preceding that the induction machine can operate equally well as motor, below synchronism, and as generator, above synchronism. In the single-phase induction machine the motor or generator action occurs in one primary circuit only, but in the direction in quadrature to the primary circuit there is a mere magnetizing current either in the secondary, in the single-phase motor proper, or in an auxiliary field-circuit, in the monocyclic motor. The motor and generator action can occur, however, simul- taneously in the same machine, some of the primary circuits acting as motor, others as generator circuits. Thus, if one of the two circuits of a quarter-phase induction machine is con- nected to a single-phase system, in the second circuit an e.m.f. is generated in quadrature with and equal to the generated e.m.f. in the first circuit; and this e.m.f. can thus be utilized to produce currents which, with currents taken from the primary single- phase mains, give a quarter-phase system. Or, in a three-phase motor connected with two of its terminals to a single-phase sys- 352 ELEMENTS OF ELECTRICAL ENGINEERING tern, from the third terminal an e.m.f. can be derived which, with the single-phase system feeding the induction machine, com- bines to a three-phase system. The induction machine in this application represents a phase converter. The phase converter obviously combines the features of a single-phase induction motor with those of a double transformer, transformation occurring from the primary or motor circuit to the secondary or armature, and from the secondary to the ter- tiary or generator circuit. Thus, in a quarter-phase motor connected to single-phase mains with one of its circuits, if Y = g — jb = primary polyphase exciting admittance, ZQ = TQ -f- JXQ = self -inductive impedance per primary or ter- tiary circuit, Zi = ri + jxi = resultant single-phase self-inductive impe- dance of secondary circuits. Let e = e.m.f. generated by the mutual flux and Z = r + jx = impedance of the external circuit supplied by the phase converter as generator of second phase. We then have /> I = 71? — current of second phase produced by phase Zr T Z»o converter, E — IZ = „ . „ = - — ;=- = terminal voltage at genera- & -\- LQ 1 L o ~~z tor circuit of phase converter. The current in the secondary of the phase converter is then /! = / + /'+ I", where ^ I = load current = ~ „ I' = eY = exciting current of quadrature magnetic flux, €S I' = - ; — : — = current required to revolve the machi ri+jsxi and the primary current is ?•'-&> !', where /' = eY = exciting current of main magnetic flux. INDUCTION MACHINES 353 From these currents the e.m.fs. are derived in a similar manner as in the induction motor or generator. Due to the internal losses in the phase converter, the e.m.fs. of the two circuits, the motor and generator circuits, are prac- tically in quadrature with each other and equal only at no load, but shift out of phase and become more unequal with increase of load, the unbalancing depending upon the constants of the phase converter. An interesting application of the phase converter is made in single-phase induction motor railroading. In this, the phase converter is connected in series to the induction motor which drives the car. This avoids the increase of unbalanc- ing of the phases with increase of load, and makes it possi- ble by properly connected series transformers to maintain perfect phase and voltage balance on the driving motor. Usually, a quarter-phase phase converter and quarter-phase induction motor is used, and the motor phase of the phase converter is connected in series to one of the phases of the motor into the single-phase supply circuit, while the genera- tor phase of the phase converter feeds the other phase of the driving motor. It is obvious that the induction machine is used as phase con- verter only to change single-phase to polyphase, since a change from one polyphase system to another polyphase system can be effected by stationary transformers. A change from single- phase to polyphase, however, requires a storage of energy, since the power arrives as single-phase pulsating, and leaves as steady polyphase flow, and the momentum of the revolving phase con- verter secondary stores and returns the energy. With increasing load on the generator circuit of the phase converter its slip increases, but less than with the same load as mechanical output from the machine as induction motor. An application of the phase converter is made in single-phase motors by closing the tertiary or generator circuit by a condenser of suitable capacity, thereby generating the exciting current of the motor in the tertiary circuit. The primary circuit is thereby relieved of the exciting current of the motor, the efficiency essentially increased, and the power- factor of the single-phase motor with condenser in tertiary cir- cuit becomes practically unity over the whole range of load. At the same time, since the condenser current is derived by double 354 ELEMENTS OF ELECTRICAL ENGINEERING transformation in the multitooth structure of the induction machine, which has a practically uniform magnetic field, irre- spective of the shape of the primary impressed e.m.f. wave, the application of the condenser becomes feasible irrespective of the wave shape of the generator. Usually the tertiary circuit in this case is arranged on an angle of 60 deg. with the primary circuit, and in starting a powerful torque is thereby developed, with a torque efficiency superior to any other single-phase motor starting device, and when com- bined with inductive reactance in a second tertiary circuit, the apparent starting torque efficiency can be made even to exceed that of the polyphase induction motor (see page 336). For further discussion hereof, see A. I. E. E. Transactions, 1900, page 37.