## Speed control of induction motor by 7 ways

Today I will discuss very important topic … **speed control of induction motor**. The speed of a three-phase induction motor driving a given load is determined by matching the torque-speed characteristics of the motor and load, as shown in Fig.

The operating point is the intersection of the two characteristics and we can fix for a given load and motor parameters.

Until the emergence of modem solid-state drives, induction motors were not Favored for considerable speed control applications.

For design classes, A, B, and C, the normal operating slip range of a typical induction motor is restricted to less than 5%.

Even if the slip could be increased, the motor efficiency would drop significantly because of the corresponding increase in rotor-copper losses.

If we desire to change motor speed while carrying the same load, then we need a change in the torque-speed characteristic of the motor.

There are several methods of speed control of 3 phase induction motor.

We can classify into two main categories.

- Induction motor speed control through the stator.
- Induction motor speed control through the rotor.

### Speed control of induction motor (Stator):

**speed control of 3 phase induction motor** by variable frequency method (changing applied frequency):

Changing the electrical frequency applied to the stator of an induction motor causes the rate of rotation of its magnetic field *ns, *to change in direct proportion to the change in electrical frequency, and the no-load point on the torque-speed characteristic curve will change with it.

The base speed is the synchronous speed of the motor at rated conditions*.*

By using variable frequency control, it is possible to adjust the speed of the motor either above or below base speed.

A properly designed variable frequency induction-motor drive can be *very *flexible.

It can control the speed of an induction motor over a range from as little as 5% of base speed up to about twice base speed.

However, it is important to maintain certain voltage and torque limits on the motor to ensure safe operation as the frequency is varied.

###### running at speeds below the base speed

When running at speeds below the base speed of the motor, it is necessary to reduce the terminal voltage applied to the stator for proper operation.

The terminal voltage applied to the stator should be decreased linearly with decreasing stator frequency.

This is called *derating *and is needed so the iron core of the motor does not saturate and cause excessive magnetization currents to flow in the machine.

As with any transformer, the flux in the core of an induction motor can be found from Faraday’s law of sinusoidal operation as

If we reduce the electrical frequency *ω* by a factor α.

Then the flux in the core will increase by a factor 1/ α.

The magnetization current of the motor will increase.

###### In the unsaturated region of the motor’s magnetization curve,

the increase in magnetization current will also be about 1/ α. In the saturated region of the motor’s magnetization curve, however, an increase in flux 1/ α requires a much larger increase in the magnetization current.

We design induction motors to operate near the saturation point on their magnetization curves.

So the increase in flux due to a decrease in frequency will cause excessive magnetization currents to flow in the motor.

To avoid excessive magnetization currents, it is customary to decrease the applied stator voltage in direct proportion to the decrease in frequency whenever the frequency falls below the rated frequency of the motor.

When the voltage applied to an induction motor … is varied linearly with the frequency below the base speed.

The flux in the motor will remain approximately constant.

Therefore, the maximum motor torque remains fairly high. However, the maximum power rating of the motor must be decreased linearly with the decrease in frequency to protect the stator circuit from overheating.

The power supplied to a three-phase induction motor is

If the voltage *VL *is decreased, then the maximum power *P *must also be decreased.

Or else the current flowing in the motor will increase, and the motor will overheat.

###### the family of induction-motor torque-speed characteristic curves for speeds below the base speed

The following figure shows a family of induction-motor torque-speed characteristic curves for speeds below base speed, assuming that the magnitude of the stator voltage varies linearly with frequency.

When the electrical frequency applied to the motor exceeds the rated frequency of the motor, the stator voltage is held constant at the rated value.

Although saturation considerations would permit the voltage to be raised above the rated value under these conditions, it is limited to the rated voltage to protect the winding insulation of the motor.

With high electrical frequency above base speed, the resulting flux in the machine decreases and the maximum torque decreases with it.

The following figure shows a family of induction-motor torque-speed characteristic curves for speeds above base speed, assuming that we hold the stator voltage constant.

If the stator voltage is varied linearly with the frequency below base speed and is held constant at the rated value above base speed, then the resulting family of torque-speed characteristics is as shown in Fig.

**The principal disadvantage** of electrical-frequency control as a method of speed changing was that it requires a dedicated generator or mechanical frequency changer.

The development of modem solid-state variable-frequency motor drives has overcome this limitation, and it is now the method of choice for induction-motor speed control.

Note that we can use this method with *an *induction motor, unlike the pole changing technique, which requires a motor with special stator windings.

### speed control of induction motor by stator voltage method

*Line- Voltage Control *The torque developed varies with the square of the applied voltage.

As shown in Fig. 6.23, the speed can be varied simply by changing the voltage applied to the stator. This method is common for squirrel- cage motors.

## Speed control of induction motor using v/f

Improved performance of adjustable-speed drives is associated with a variable frequency stator supply.

The air-gap flux is directly proportional to the stator applied voltage and inversely proportional to the frequency.

A reduction in the supply frequency to achieve speed control below rated synchronous speed will be associated with an increase in the air-gap flux if the applied voltage is maintained at rated value.

To avoid saturation due to the increased flux, variable-frequency drives employ a variable voltage as well, with the object of maintaining an acceptable air-gap flux level.

This concept is generally referred to as constant *(v/f)* control and is used in drives employing squirrel-cage induction motors of all classifications.

We discuss the theory of variable-frequency operation of the induction motor.

*Speed Control of induction motor by Pole Changing*:

There are three major approaches to changing the number of poles in an induction motor

(a) The method of consequent poles

(b) Multiple stator windings

(c) Pole-amplitude modulation (PAM)

The method of consequent poles is one of the earliest speed-control methods. It allows us to change *n, *in discrete steps.

A two-pole stator set of windings is changed to a four-pole configuration by a simple switching operation, as shown in Fig

Of course, we can do this for any number of poles for a ratio of 2: 1. This mechanism is simple to implement in squirrel-cage rotor motors, but for the wound-rotor type, we must also rearrange the rotor windings.

This mechanism is simple to implement in squirrel-cage rotor motors, but for the wound-rotor type, we must also rearrange the rotor windings.

A traditional approach to overcome the limitations of the consequent pole method employs multiple stator windings with different numbers of poles and to energize only one set at a time.

This method increases the cost and weight of the motor and is, therefore, we use only when absolutely necessary.

Combining the method of consequent poles with multiple stator windings, allows us to build a four-speed induction motor.

For example, with separate four- and six-pole windings, we can produce

a 60-Hz motor that has synchronous speeds of 600, 900, 1200, and 1800 rpm.

**The PAM method**

The PAM method achieves multiple sets of poles in a single stator winding, where the resulting number of poles can be in ratios other than 2 : 1.

Switching the number of poles in a winding is achieved by changing the connections at six terminals, in the same manner as in the method of consequent poles.

To create an induction motor with two close speeds, PAM windings are preferred over multiple-stator windings because they cost about 75% of two completely separate windings.

In PAM, the spatial distribution of the magneto motive-force waves in the machine stator is multiplied together.

With the resulting output consisting of components with frequencies equal to the sum and the difference of two original frequencies.

If the winding of a machine normally having *P *poles is modulated by making *N *switches in the connections on the phase groups in a given phase, then two magneto motive-force waves will be produced in the stator winding, one of them having *P *+ *N *poles and the other having *P *– *N *poles.

If one of these waveforms can be selected over the other, then the motor will have that number of poles on its stator.

and the same number of poles will, of course, be induced in the squirrel cage rotor.

Example pole ratios available with the PAM technique and the resulting synchronous speed ratios for 60-Hz operation are as follows:

Pole ratio1 = 4/6 -+ 1800/1200

PR2= 6/8 -+ 1200/900

PR 3= 8/10 -+ 900/720

###### From a mathematical point of view:

we express the magnetomotive force produced by a conventional P-pole winding in terms of time and position as

If *Q *is the desired final number of poles on the machine, then *P *– *Q *is the *difference *between the original number of poles and the desired number of poles. Now, modulate the original spatial waveform by switching connections at *P-Q *uniformly spaced points in each phase. The resulting magneto motive-force waveform is

Now, use the trigonometric identity

so the magneto motive-force expression reduces to

###### We Can Express this magnetomotive force as

Note that there are two different spatial distributions of poles present in the resulting magnetomotive force.

If *Q *is the desired number of poles in the motor, then we need to reject the other distribution.

we can accomplish it by a proper choice of the distribution and chording of the stator windings.

This analysis is approximate because we assume the modulating spatial wave is sinusoidal when it is a square wave.

Square-wave modulation introduces more spatial harmonics into the magnetomotive force distribution; which we can reduce it by the proper choice of winding chording.

In practice, the choice of spatial modulating frequency; winding chording; winding distribution, and other factors we required to achieve a given speed ratio is an art based on the experience of the designer.

## Speed control of induction motor through the Rotor:

*Rotor-Resistance Control*

**EFFECTS OF ROTOR IMPEDANCE**

This is suitable for the wound-rotor type … The resulting torque-speed characteristics in Fig.

We can achieve speed control of induction motors of the wound-rotor type by inserting additional rotor resistance *(Ra ). *In addition to this, we can achieve torque control at a given speed using this method. Let

where the subscript 1 refers to operating conditions without additional rotor resistance and the subscript 2 refers to conditions with the additional rotor resistance.

Neglect stator resistance in the present analysis and we have

Introducing a resistance in the rotor winding will change *a. *Let the original torque be TI Thus

Let the new torque with additional resistance be *T**2 *Thus

By the definition of the torque ratio, α we get

Equation provides us with the means to derive the value of additional resistance, Ra, required to obtain the same torque *(T**1 *= *T**2)* at two different values of slip (or rotor speed). To do this we set α= 1, to obtain

###### Rotor-Slip Energy Recovery

The input power to the rotor is

The rotor power output is

As a result, the theoretical rotor efficiency is

*ɳ**r *= 1 – *s*

It is thus clear that speed control by increasing *(s)* results in an increase in rotor losses, which results in decreased efficiency.

There exist many methods for recovering this energy from the rotor (at rotor frequency *(fr *= sfs), converting it to supply frequency, and subsequently returning it to the source.

The devices used to achieve this are solid-state power devices.

#### Speed control of induction motor through cascading operation:

In this method, we use two motors and both are installed on a common shaft as shown in fig.

From the previous Diagram:

The motor number 1 feeds from a three-phase power source.

The other motor feeds through induced e.m.f via slip rings.

Assume that motor 1 is main and motor 2 is auxiliary.

while:

Ns1: synchronous speed of the motor no. 1.

P1: No. of stator poles of the motor no.1.

Ns2: synchronous speed of the motor no. 2.

P2: No. of stator poles of the motor no. 2.

N: Set speed of both motor 1 & 2.

F: supply frequency.

For motor no. 1 (main motor):

S1= (Ns1-N)/Ns1

So,

F1= S1* f

For motor no. 2 (aux. motor):

Ns2= (120*f1) / P2 = (120 * S1 * f) / P2

So,

Ns2= (120 * f * (Ns2-N)) / (P2 * Ns1)

We can conclude that:

So,

N= (120 * f) / (P1+P2)

In this equation we conclude 4 cases where we can obtain different speeds:

- If the motor 1 is working only

So, Ns1= (120 * f) / P1

- If the motor 2 is working only

So, Ns2= (120 * f) / P2

- If both motors work (cumulative cascading)

So, N= (120 * f) / (P1+P2)

- If both motors works (differential cascading)

So, N= (120 * f) / (P1-P2)

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