rapidly and then slower, and becomes fairly constant afterwards, as seen in Fig. 8. In the particular motor under discussion, the whole variation of current is practically comprised within the range from 8= + 4 to 8 = - .3, that is, the current at standstill is very large and remains practically constant until about of synchronous speed is reached. Thus such a motor with low armature resistance will require a very large current, not only in starting, but also at intermediate speeds.

=

Restricting our attention to that part of the torque curve below synchronism, we see that the torque curve consists of two branches, the upper branch from maximum torque to synchronism, and the lower branch from maximum torque to standstill. The same torque is reached on either branch; for instance, the torque of 4,800 synchronous watts at 8.05, and at 8 = .6. The currents corresponding to the two values of speed at the same torque are very different, however, 52.5 amperes on the upper, 171 amperes on the lower branch. On the upper branch the motor is stable, that is, with constant load runs at constant speed. On the lower branch, however, the motor is unstable and cannot maintain its speed, but must either slow down and come to standstill, or accelerate and reach the upper or stable branch, if loaded by constant torque.

In the same way above synchronism the machine as brake is stable between synchronism and maximum torque, and unstable beyond maximum torque.

As seen from the preceding, the motor number 1, while very satisfactory at speed, requires excessive current and gives little torque at low speed and in starting, and is thus unsatisfactory therein.

In the discussion of load curves in the preceding, we have seen that high resistance motors have a large drop of speed and thus reach a maximum torque point at lower speeds, that is, are in starting nearer to the maximum torque point, or in other words, have a greater starting torque.

From the equations of the induction motor it is obvious that this greater torque at low speeds is not due to the primary resistance, but exclusively to the secondary or armature resistance. The armature resistance, enters only in the equation of secondary current:

and in the further equations only indirectly in so far as r is contained in a, and a2.

Increasing the armature resistance n-fold, to n r, we get at an n-fold increased slip n 8:

that is the same value, and thus the same values for e, I。, T, P。, &, while the power is decreased from P= (1-8)r to P = (1 — ns) T, and the efficiency and apparent efficiency are correspondingly reduced. The power factor is not changed. Hence:

An increase of armature resistance r, produces a proportional increase of slip n, and thereby corresponding decrease of power, efficiency and apparent efficiency, but does not change the torque, current and power factor.

Thus the insertion of resistance in the armature or secondary of the induction motor offers a means to reduce the speed corresponding to a given torque, and thereby any desired torque can be produced at any speed below that corresponding to armature short circuit, without changing torque or current.

Hence, given the speed-torque curve of a short-circuited motor, the torque curve with resistance inserted in the armature can be derived therefrom directly by increasing the slip in proportion to the increased resistance.

This is done in Fig. 10, in which are shown the speed curves of the motor number 1 between standstill and synchronism, for: Short-circuited armature: r1 = .1.

.15 ohms resistance inserted in armature: r1 = .25.

.5 ohms additional resistance inserted in the armature: r1 = .6. 1.5 ohms additional resistance inserted in the armature: 71 = 1.6.

The corresponding current curves are shown on the same sheet. As seen, with short-circuited armature the maximum torque of 8,250 synchronous watts is reached at 16.5% slip. The starting torque is 2,950 synchronous watts, and the starting current 176

amperes.

With armature resistance r1 = .25, the same maximum torque is reached at 40% slip, the starting torque is increased to 6,050 synchronous watts, and the starting current decreased to 160

amperes.

With armature resistance r1 = .6, the maximum torque of 8,250 synchronous watts takes place in starting, and the starting current is decreased to 124 amperes.

AMPERES

180

TORQUE WATTS AT SYNCHRONISM

6000

5000

4000

3000

2000

1000

0

FIG. 10.-Induction Motor. +1j. Z= .1 - .3 j. Arm.

Torque and Current.
.1, .25, .6, 1.6.

Y = .01

r1

With armature resistance = 1.6, the starting torque is below the maximum, 5,620 synchronous watts, and the starting current is only 64 amperes.

In the two latter cases the lower branch of the torque curve has altogether disappeared and the motor speed is stable over the whole range, that is, the motor starts with the maximum torque which it can reach, and with increasing speed torque and current decrease, that is, the motor has the characteristic of the continous current series motor, except that it cannot race, but its maximum speed is limited by synchronism.

On the same diagram, Fig. 10, are shown the currents corresponding to the different values of secondary resistance.

The apparent torque efficiencies of the motor under the four conditions of armature resistance are given in Fig. 11. They show that, although a considerable starting torque can be reached by a moderate armature resistance, of r = .25, the apparent torque efficiency or torque per ampere input is still very low under this condition, that is, the motor starts very inefficiently, and, as seen in the preceding discussion of high resistance motors, is rather inefficient at speed. The same diagram also shows the torque efficiencies. It follows herefrom that permanent resistance in the armature of an induction motor can be used to secure good starting torque at the sacrifice of current in starting, and of efficiency and speed regulation when running, but cannot be used to limit the starting current, the latter requiring so large an armature resistance as to make the motor entirely unfit when running.

This brings us to the investigation of the action of the induction motor in starting.

The condition in starting is 8 = 1.

Substituting & = 1 in the induction motor equations gives starting torque, current, power factor, etc.

1。 = I1 + I‰o = e [(a1 + g) + j (a2 + b)] [(a1 + g) + j (α2 + b) ] = e (b1 +j b2)