Three phase induction motors

• Three-phase induction motors are the motors most frequently encountered in industry. They are simple, low-priced, and easy to maintain

• Such machines are called induction machines because the rotor voltage (which produces the rotor current and the rotor magnetic field) is induced in the rotor windings rather than being physically connected by wires.

In this chapter we cover the basic principles of the 3-phase induction motor and develop the fundamental equations

describing its behavior

Principle components

2 main parts:

1. Stationary Stator2. Revolving Rotor “2 types”:• Cage rotor• Wound rotor

Stator

It consists of a core of stacked, insulated, iron

laminations, with windings of insulated copper wire filling the slots

in the core

Squirrel-Cage Rotor

The rotor consists of a shaft, a steel laminated rotor, and an embedded copper or aluminum squirrel cage

A wound rotor has a 3-phase winding, similar to the one on the stator. The winding is uniformly distributed in the slots and is usually connected in 3- wire wye. The terminals are connected to three slip-rings, which turn with the rotor. The revolving slip-rings and associated stationary brushes enable us to connect external resistors in series with the rotor winding.

Wound Rotor

Typical wound rotors for induction motors. Notice the slip rings and the bars connecting the rotor windings to the slip rings.

Three phase induction motors

An induction motor has 2 main parts; the Stator and Rotor. The Stator is the stationary part and the rotor is the rotating part. The Rotor sits inside the Stator. There will be a small gap between rotor and stator, known as air-gap. The value of the radial air-gap may vary from 0.5 to 2 mm.

Principle of operationExample to understand the behavior of a three phase induction motors

1. (Faraday's law): A voltage E = Blv is induced in each conductor while it is being cut by the flux

Principle of operation

2. The induced voltage immediately produces a current I, which flows down the conductor underneath the pole-face, through the end-bars, and back through the other conductors.

3. Because the current-carrying conductor lies in the magnetic field of the permanent magnet, it experiences a mechanical force (Lorentz force).

4. The force always acts in a direction to drag the conductor along with the magnetic field “Lenz law”

5. If the conducting ladder is free to move, it will accelerate toward the right.

Principle of operation

In an induction motor the ladder is closed upon itself to form a squirrel-cage and the moving magnet is replaced by a rotating field. The field is produced by the 3-phase

currents that flow in the stator windings, as we will now explain.

Rotating field

• Consider a simple stator having 6 salient poles. Each of which carries a coil, Coils that are diametrically opposite are connected in series.

• This creates three identical sets of windings AN, BN, CN, that are mechanically spaced at 120° to each other. The three sets of windings are connected in wye

• Currents flowing from line to neutral are considered to be positive.

Rotating fieldAs time goes by, we will consider the instantaneous value and direction of the current in each winding and establish the successive flux patterns

Flux pattern at instant 1

At instant 1, current is positive whereas and both have a negative value. The direction of the mmf depends upon the instantaneous current flows and, using the right-hand rule, we find that the direction of the resulting magnetic field is as shown here.

Rotating field at instant 1N

N N

S

S

S

We discover that the new field has the same shape as before, except that it has moved clockwise by an angle of 60°. In other words, the flux makes 1/6 of a turn between

instants 1 and 2.

Rotating field at instant 2

Flux pattern at instant 2

N

N

N

S

S

S

Proceeding in this way for each of the successive instants 3, 4,5,6, and 7, separated by intervals of 1/6 cycle, we find that the magnetic field makes one

complete turn during one cycle

Rotating field

The rotational speed of the field depends, therefore, upon the duration of one cycle, which in turn depends on the frequency of the source. If the frequency is 50 Hz, the resulting field makes one turn in 1/50 s, that is, 3000 revolutions per minute. Because the speed of the rotating field is necessarily synchronized with the frequency of the source, it is called synchronous speed.

Rotating field direction

When the positive crests of the currents follow each other in the order A-B-C, this phase sequence produces a field that rotates clockwise. If we interchange any two of the lines connected to the stator, we find that the field now revolves at synchronous speed in the opposite, or counterclockwise direction.

Interchanging any two lines of a 3-phase motor will, therefore, reverse its direction of rotation.

Number of poles- synchronous speed

2 pole stator 4 pole stator

How to construct a 4-pole stator??

The four identical coils of phase A now span spaced 90° instead of 180 ° The 4 coils are connected to each others in such a way that when a current flows in the stator winding of phase A, it creates four alternate N-S poles.

N

S

N

S

Rotating field

In comparing the two figures, it is clear that the entire magnetic field has shifted by an angle of 45°-and this gives us the clue to finding the speed of rotation. The flux moves 45° in one half cycle and so it takes 8 half-cycles (= 4 cycles) to make a complete turn. On a 50 Hz system the time to make one turn is therefore 4 x 1/50 = 0.08 s. Consequently, the flux turns at the rate of 12.5 r/s or 750 r/min.

Rotating field

The speed of a rotating field depends therefore upon the frequency of the source and the

number of poles on the stator.

= synchronous speed [r/min]f= frequency of the source [Hz]p= number of poles

Starting characteristics of a squirrel-cage motor ”rotor locked”

1. A 3-phase voltage is applied to the stator of an induction motor.

2. This 3 phase voltage creates a three phase current which creates a revolving magnetic field

3. The revolving field induces a voltage in the rotor bars.

4. The induced voltage creates large circulating currents which flow in the rotor bars and end-rings.

5. The current-carrying rotor bars are immersed in the magnetic field created by the stator; they are therefore subjected to a strong mechanical force. ”Lorentz force”

6. The sum of the mechanical forces on all the rotor bars produces a torque which tends to drag the rotor along in the same direction as the revolving field. “LENZ Law”

Acceleration of the rotor-slip

As soon as the rotor is released, it rapidly accelerates in the direction of the rotating field. “Lenz law”

The speed will continue to increase, but it will never catch up with the revolving field, In effect, if the rotor did turn at the same speed as the field (synchronous speed), the flux would no longer cut the rotor bars and the induced voltage and current would fall to zero. Under these conditions the force acting on the rotor bars would also become zero and the friction and windage would immediately cause the rotor to slow down.

The rotor speed is always slightly less than the synchronous speed

Slip

The slip s of an induction motor is the difference between the synchronous speed and the rotor speed, expressed as a percent (or per-unit) of synchronous speed. The per-unit slip is given by the equation

=slip (%)= synchronous speed [r/min] = rotor speed [r/min]

The slip is less than 0.1%at no-load and is equal to 1 (or 100%) when the rotor is locked.

Frequency of the voltage induced in the rotor

The frequency induced in the rotor depend upon the slip. It is given by the following equation:

Where =Frequency of the voltage and current in the rotor [Hz]f = frequency of the source connected to the stator [Hz]s =slip

Equivalent Circuit of a squirrel cage Induction Motor at standstill

At standstill, it acts exactly like a conventional transformer and so its equivalent circuit is the same as

that of a transformer.

On standstill

This equivalent circuit of an induction motor is so similar to that of a transformer that it is not

surprising that the induction motor is sometimes called a rotary transformer.

Equivalent Circuit of the Induction Motor

Can we remove the magnetizing branch composed of j and under load for simplifying?

In the case of a conventional 3-phase transformer, we would be justified in removing

the magnetizing branch composed of j and because the exciting current is negligible

compared to the load current. However, in a motor this is no longer true: may be as high as

40 percent of because of the air gap.

!

Simplifying the equivalent circuit

However for motors exceeding 2 hp, we can shift the magnetizing branch to the input terminals. This greatly simplifies the equations that describe the behavior of

the motor, without compromising accuracy

Equivalent Circuit of the Induction Motor when the motor starts turning at slip s

• the frequency in the secondary winding will become the secondary leakage reactance will change from to .

•

Equivalent Circuit of the Wound Induction Motor

In practice, to construct a final simplified equivalent diagram, we divide the secondary

mesh equation by s, which shows an inductance equivalent leakage at frequency f. The

frequencies of the primary and secondary then being identical with this manipulation, the

elements are than shifted to the transformer primary.

Equivalent Circuit of the Wound Induction Motor

In this diagram, the circuit elements are fixed, except for the resistance. Its value depends upon the slip and hence upon the speed of the motor. Thus, the value of will vary from to infinity as the motor goes from start-up (s= 1) to synchronous speed (s=0).

Active power flow

Active power flow

• active power flows from the line into the 3-phase stator.

• is dissipated as heat in the windings. • is dissipated as heat in the stator core• The remaining active power is carried across

the air gap and transferred to the rotor by electromagnetic induction.

• is dissipated as heat in the rotor windings• The remainder is finally available in the form

of mechanical power

Active power flow

The power flow diagram enables us to identify and to calculate three important properties of the induction motor:

(1) its efficiency (2) its power(3) its torque

Efficiency of an induction motor

By definition:

the efficiency of a motor is the ratio of the output power to the input power:

Efficiency (η) = /

losses in the rotor

1. Active power absorbed by the motor is . 2. Reactive power absorbed by the motor is (x=3. Apparent power absorbed by the motor is 4. Power factor of the motor is

5. Line current is 6. Active power supplied to the rotor is

7. Power dissipated as losses in the rotor circuit is

losses in the rotor

=

Equation above shows that as the slip increases, the rotor losses consume a larger and larger

proportion of the power transmitted across the air gap to the rotor. A rotor turning at half

synchronous speed (s= 0.5) dissipates in the form of heat 50 percent of the active power it receives.

When the rotor is locked (s = 1), all the power transmitted to the rotor is dissipated as heat.

Mechanical power

Mechanical power developed by the motor is

Example

Show that the efficiency can be written:

Motor torque

The torque Tm developed by the motor at n speed is given by

Therefore, =9.55 / Where = torque developed by the motor at any speed [N. m] = power transmitted to the rotor [W] = synchronous speed [r/min]

Torque versus speed curve

• T• Nominal full-load

torque is T.• The starting torque is

1.5 T• The maximum torque

(called breakdown torque) is 2.5 T.

• Pull-up torque is the minimum torque developed by the motor while it is accelerating from rest to the breakdown torque.

Torque versus speed curve• The induced torque of the motor is zero at synchronous speed. This fact hasbeen discussed previously.

• The torque- speed curve is nearly linear between no load and full load. In this range, the rotor resistance is much larger than the rotor reactance, so the rotor current , the rotor magnetic field, and the induced torque increase linearly with increasing slip.

• There is a maximum possible torque that cannot be exceeded. This torque, called the pullout torque or breakdown torque, is 2 to 3 times the rated full load torque of the motor.

• The starting torque on the motor is slightly larger than its full -load torque, so this motor will start carrying any load that it can supply at full power.

• Notice that the torque on the motor for a given slip varies as the square of the applied voltage. This fact is useful in one form of induction motor speed control that will be described later.

Torque versus speed curve

At full-load the motor runs at a speed n. If the mechanical load increases slightly, the speed will drop until the motor torque is again equal to the load torque. As soon as the two torques are in balance. The motor will turn at a constant but slightly lower speed. However, if the load torque exceeds 2.5 T (the breakdown torque), the motor will quickly stop.

Motor under load

The motor and the mechanical load will reach a state of equilibrium when the motor torque is exactly equal to the load torque. When this state is reached, the speed will cease to drop and the motor will turn at a constant rate. It is very important to understand that a motor only turns at constant speed when its torque is exactly equal to the torque exerted by the mechanical load. The moment this state of equilibrium is upset, the motor speed will start to change.

Effect of rotor resistance

the starting torque doubles locked-rotor current dcreases

breakdown torque remain unchanged

The motor develops its breakdown torque at a speed of 500 r/min. compared to the original breakdown speed of 800 r/min.

Effect of rotor resistance

If we again double the rotor resistance so that it becomes 5 R, the locked-rotor torque attains a maximum value of 250 for a corresponding current of 70 A

In summary:

• a high rotor resistance is desirable because it produces a high starting torque and a relatively low starting current. Unfortunately, it also produces a rapid fall-off in speed with increasing load. Furthermore, because the slip at rated torque is high, the motor losses are high. The efficiency is therefore low and the motor tends to overheat.

• Under running conditions it is preferable to have a low rotor resistance. The speed decreases much less with increasing load, and the slip at rated torque is small. Consequently, the efficiency is high and the motor tends to run cool.

Effect of rotor resistance

Wound-rotor vs squirrel rotor

Although a wound-rotor motor costs more than a squirrel-cage motor, it offers the following advantages:

1. The locked-rotor current can be drastically reduced by inserting three external resistors in series with the rotor. Nevertheless, the locked-rotor torque will still be as high as that of a squirrel-cage motor. 2. The speed can be varied by varying the external rotor resistors. 3. The motor is ideally suited to accelerate high-inertia loads, which require a long time to bring up to speed.

Circuit used to start a wound-rotor motor

ExampleThe stator of an induction motor is connected in wye during startup, and then in delta for normal operation.1- Show that the line current consumed in wye connection is three times smaller that in delta connection.2- It is assumed that the engine output torque is proportional to the square of the voltage.Show that the output torque is divided by three during the starting phase.3- What is the advantage of starting “wye - delta"?What is it’s disadvantage?

Speed control of induction motors

It can accomplished by :

1. Changing the number of poles on the machine2. Changing the applied electrical frequency3. Changing the applied terminal voltage “torque

proportional to the square of the applied voltage”

4. Changing the rotor resistant in the case of a wound-rotor induction motor

Induction motor operating as a generator

We can make an asynchronous generator by connecting an ordinary squirrel-cage motor to a 3- phase line and coupling it to a gasoline engine. As soon as the engine speed exceeds the synchronous speed, the motor becomes a generator, delivering active power P to the electrical system to which it is connected. However, to create its magnetic field, the motor has to absorb reactive power Q. This power can only come from the ac line. With the result that the reactive power Q flows in the opposite direction to the active power P

Complete torque-speed characteristic of an induction machine

Induction motor operating as a generator

Induction generators are usually rather small machines and are used principally with

alternative energy sources, such as windmills, or with energy recovery systems.

Almost all the really large generators in use are synchronous generators

Tests to determine the equivalent circuit

No load s<<< >>>> is negligible compared to No-load test

Tests to determine the equivalent circuit

a. Measure the stator resistance between any two terminals. Assuming a wye connection, the value of is

b. Run the motor at no-load using rated line-to line voltage . Measure the no load current and the total 3-phase active power .

No-load test

The following calculations of total apparent power and total reactive power are then made:

• = windage, friction, and iron losses= • The resistance representing, is ) • The magnetizing reactance is:

No-load test

Tests to determine the equivalent circuit

Under rated line voltage, when the rotor of an induction motor is locked, the stator current is almost six times its rated value.

Furthermore, the slip s is equal to one. This means that is equal to where is the resistance of the rotor reflected into the stator.

Becauseis much greater than the exciting current , we can neglect the magnetizing branch

Locked rotor test

Locked rotor equivalent circuit

Tests to determine the equivalent circuit

a. Apply reduced 3-phase voltage to the stator so that the stator current is about equal to its rated value

b. Take readings of (line-to-line) and the

total 3-phase power

Locked rotor test

The following calculations are then made:•

Hence,

Locked rotor test