SYNCHRONOUS MOTORS AND CONVERTERS
Theory and Methods of Calculation and Testing

Necessity of synchronism and stability of synchronous operation

The magnetic strength of these fields can be considered practically constant inasmuch as it also resumes the same value at every one-sixth of a period (although it may, in the intervals, undergo slight variations which are dampened by the hysteresis and the eddy currents produced in the pole-pieces of the rotor). Therefore, even though the armature (stator) may be stationary, the result is the same as if it had rervolving poles which attract or repel the poles of the field (rotor) and we can, henceforth, reason as if we were dealing with the attractions of two systems of magnets presenting the same number of poles which are alternately north and south in polarity. (Fig. 8.) The poles of unlike polarities, of the two systems, attract each other; the others repel each other. Therefore, when at rest, the poles of unlike polarity will always face each other. If the external magnets begin to rotate slowly, starting from rest, they will drag with them the stationary magnets, whose poles tend to remain opposite the poles of unlike polarity. (This result may be obtained by supplying the motor with current obtained from a generator which is started from rest and, consequently, gives polyphase currents of increasing frequency.)

Necessity of synchronism and stability of synchronous operation

The attractions can only be concordant and continuous when the two systems turn at the same speed; which explains the necessity of synchronism. Otherwise, there would only be successive attractions and repulsions which would neutralize each other.

The stability of synchronous operation is also easily demonstrated by considering the moment of the motor-couple (i.e., the torque). If the poles of the rotor remain opposite the revolving poles of the stator, the attractions produced are directed radially and consequently they produce a motor-couple or torque which is equal to zero. If, on the contrary, for any reason whatever, the rotor loses or gains speed, some tangential attractions or repulsions will appear, whose resultants tend to bring back the opposite poles of the rotor into coincidence with the poles of unlike polarity of the stator, so long as the poles of the rotor remain near these, because the attractions of unlike poles and the repulsions of like poles act in the same direction; but if the difference in phase amounts to one interpolar space, the poles of like sign of the rotor and stator will be opposite each other, the motor-couple or torque will become zero, and will then change sign if the difference in phase increases. By reason of the symmetrical construction of the motor the torque will have points of maximum and minimum value at equal distances between the points of zero-value, i.e., in the positions where the poles of the rotor are midway between the poles of the stator.

To sum up, taking as abscissae the difference of phase l of the poles of the rotor, expressed in terms of the interpolar space L, and taking as ordinates the torque C, the representative curve will take the form shown herewith (Fig. 9), the magnetic strength at the armature-poles being supposed constant, i.e., assuming the currents that produce this magnetic flux to be constant.

Stable operation for synchronous motor; lag and lead

The machine will have stable operation for the difference of phase comprised between the two maximum points B and C (the positive maximum being due to a lag, and the negative maximum being due to a lead), because every accidental advance (or lag) is corrected of itself by a contrary variation of the torque. If the rotor lags, for example, in consequence of a passive mechanical resistance, the increase in torque compensates for this resistance.

When the motor is running without load, its condition corresponds to the position O, at which there is no phase-difference. When the motor is loaded, i.e., whenever mechanical resistance is applied to the shaft, the position of the poles of the rotor changes in phase and comes to a point O', such that the couple O'm shall balance the resisting couple. If the resisting couple is greater than the maximum torque, the machine can no longer run; and even for positions of m which are a little below M, the machine will fall out of step, in consequence of unavoidable oscillations.

On the other hand, to. obtain a difference of phase ahead, between O and C, it is necessary to apply to the shaft an effort in the direction of rotation, i.e., it is necessary to apply to the shaft a certain amount of propelling power which must, evidently, be transformed into electrical energy.

The armature current has been supposed constant. In practice, it is the voltage of the supply-circuit which is constant, at its terminals; and the question is thus complicated by the spontateous variation of the current with the variation in phase-difference. This variation, itself, depends on the ratio of the induced E.M.F. of the motor to the voltage applied at its terminals.

In fact, as they displace themselves before the armature at the synchronous speed, the poles of the inducing field induce in the windings counter E.M.F.'s. which are of the same order and magnitude as the voltage at the terminals. If, mentally, we locate the E.M.F.'s. in the wires which are placed in the slots, we perceive readily that the E.M.F. in each slot varies periodically and passes through a maximum at the moment when the middle of a revolving pole comes in line with the slot. The axes of maximum values of the induced E.M.F.'s therefore coincide with the axes of the inducing poles, and revolve with them. If the currents were in phase with the E.M.F.'s, they would give rise to revolving fields whose axes would be retarded in phase by an amount equal to half the width of a pole, since each conductor forms a coil with a conductor similarly placed, but in the contrary direction, under the next pole.

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