microsoft word - 4_ induction machines.pdf

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Topic 4: Three-phase Induction (Asynchronous) Machines

Electromechanical Energy Conversion

Various devices can convert energy to mechanical energy and vice versa. The structure of these

devices may be different depending on functions they perform. Some devices are used for continuous

energy conversion and these are known as motor and generators. Even though there various devices used

in the conversion of energy, but they all operate on similar principles. In this topic, we extensively discuss

on electric machines only.

Electric Machines

Some applications such as light bulbs and heaters require energy in electrical form while others, such

as fans and rolling mills, require energy in mechanical form. One form of energy can be obtained from the

other form with the help of converters. Converter that is used to translate electrical input to mechanical

output or vice versa are called electric machines.

The process of translation is known as electromechanical energy conversion. In these machines, the

conversion is reversible. If the conversion is from mechanical to electrical, the machine is said to act as a

generator. If the conversion is from electrical to mechanical, the machine is said to act as a motor.

Same electric machine can be made to operate as a generator as well as a motor. Machines are called

ac machines if the electrical system is ac and dc machines if the electrical system is dc.

Figure 1. Electromechanical Energy Conversion

In electric machines, conversion of energy from electrical to mechanical forms or vice versa results

from the following two electromagnetic phenomena:

1. When a conductor moves in a magnetic field, voltage is induced in the conductor.

2. When a current-carrying conductor is placed in a magnetic field, the conductor experiences a

mechanical force.

These two effects occur simultaneously whenever energy conversion takes place from electrical to

mechanical or vice versa.

Basic Structure of Electric Machines

An electric machines has two major components, stator and rotor that separated by the air gap. Fig. 2

shows the structure of electric machines. Generally, the structure of electric machine can be divided into

two parts; stator and rotor. The Stator is referred to the static part of the machine (the outer frame) while

the rotor is the moving part (inner frame) of the machine.

Electrical machines Electrical system Mechanical system

Energy flow Motor

Generator

(a)

Figure 2. Structure of electric machine.

Both stator and rotor are made of ferromagnetic materials. In most

inner periphery of the stator and outer periphery of the rotor str

slots. Theses conductors (in the slots of stator or rotor) are interconnected to form windings.

The winding in which voltage is induced is called the armature winding. The winding through which a

current is passed to produce the primary source of flux is called the field winding. Permanent magnets are

used in some machines to provide the major

The three basic electric machines are dc machines, induction machines and synchronous machines.

Three-Phase Induction Machines

It is the most widely used machine in industry. In the induction machines both stator and rotor

winding carry alternating currents (ac). The ac is supplied to the stator winding directly and to the rotor

winding by induction.

Induction machine can operate both as motor and as generator. But, this machine is extensively use

as a motor in many applications.

Construction

An induction machines consist of two main parts; stator and rotor. There are two types of roto

squirrel-cage rotor and wound rotor.

The squirrel-cage winding consists of aluminum or copper bars embedded in the rotor slots and

shorted at both ends by aluminum or copper end rings. This type of rotor is the most commonly used rotor.

The wound-rotor winding has a complete set of three

Usually, it is Y-connected and the rotor coils are tied to the slop rings.

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(b)

Structure of electric machine. (a) cylindrical machine (uniform air gap). (b) salient pole

machine (non-uniform air gap)

Both stator and rotor are made of ferromagnetic materials. In most machines, slots are cut on the

inner periphery of the stator and outer periphery of the rotor structure. Conductors are placed in these



produce the primary source of flux is called the field winding. Permanent magnets are

used in some machines to provide the major source of flux in the machine.




Induction machine can operate both as motor and as generator. But, this machine is extensively use

consist of two main parts; stator and rotor. There are two types of roto

cage winding consists of aluminum or copper bars embedded in the rotor slots and


rotor winding has a complete set of three-phase windings similar to stator winding.

connected and the rotor coils are tied to the slop rings.

(a) cylindrical machine (uniform air gap). (b) salient pole

, slots are cut on the

e. Conductors are placed in these



produce the primary source of flux is called the field winding. Permanent magnets are




Induction machine can operate both as motor and as generator. But, this machine is extensively used

consist of two main parts; stator and rotor. There are two types of rotor;

cage winding consists of aluminum or copper bars embedded in the rotor slots and


phase windings similar to stator winding.

Figure 3. Cutaway diagram of a typical (a) small (b) large squirrel

Figure 4. Cutaway diagram of a wound

Three Modes of Operation

The induction machine can be operated in three modes: motoring, generating and plunging. These

three modes of operation can be represented by a t

can determine several conditions such as

a) How does the torque of an induction motor change as the load changes?

b) How much can an induction motor supply at starting conditions?

c) How much does the speed of an induction motor drop as its shaf

Fig. 5 and 6 provides some important information about the operation of induction motors. The

information is summarized below:

a) The induced torque of the motor is zero at synchronous speed

b) There is a maximum torque that cannot be exceeded.

c) The starting torque on the motor is slightly la

the motor to start. It also known as initial torque.

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Cutaway diagram of a typical (a) small (b) large squirrel-cage induction motor.

Cutaway diagram of a wound-rotor induction motor.


represented by a torque-speed characteristic curve. From the curve, we

can determine several conditions such as

How does the torque of an induction motor change as the load changes?

How much can an induction motor supply at starting conditions?

How much does the speed of an induction motor drop as its shaft load increases?

provides some important information about the operation of induction motors. The

The induced torque of the motor is zero at synchronous speed 0. There is a maximum torque that cannot be exceeded.

The starting torque on the motor is slightly larger than its full-load torque. This torque is required by

the motor to start. It also known as initial torque.

cage induction motor.


From the curve, we

provides some important information about the operation of induction motors. The

load torque. This torque is required by

d) During 0 , induction machine operatdirection of the rotating magnetic field

induction machine.

e) During , induction machine operates in generating mode. Tproduce a generating torque that is acting

the rotating magnetic field). This mode is utilizes to provide regenerative breaking in some drive

application. To stop the drive system, the

frequency. In this process, the rotor speed is higher than synchronous speed because of the inertia of

the drove system. As a result, the generating action of the induction machine will cause the power

flow to reverse and the kinetic energy of the drive system will be fed back to the supply (

mechanical power to electric power

f) During 0, induction machine operates in plugging mode. Trotating magnetic field but will oppose the motion of the rotor. This torque is a braking torque.

mode is utilized in drive application where the drive system is required to stop very quickly. It

happens when the terminal ph

rotate opposite to the rotation of the rotor. The motor will come to zero speed rapidly and will

accelerate in the opposite direction, unless the supply is disconnected at zero speed.

Figure 5.

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induction machine operates in motoring mode. The rotor

direction of the rotating magnetic field. This is the natural (or motoring) mode of operation of the

induction machine operates in generating mode. The induction machi

produce a generating torque that is acting opposite to the rotation of the rotor (or acting opposite

This mode is utilizes to provide regenerative breaking in some drive

To stop the drive system, the synchronous speed will be reduced by reducing the supply



ow to reverse and the kinetic energy of the drive system will be fed back to the supply (

mechanical power to electric power). The process is known as regenerative breaking.

induction machine operates in plugging mode. The torque will be in the direc

rotating magnetic field but will oppose the motion of the rotor. This torque is a braking torque.


ase sequence is changed suddenly, the rotating magnetic field will



A typical torque-speed characteristic curve

rotor will rotate in the

. This is the natural (or motoring) mode of operation of the

he induction machine will

(or acting opposite

This mode is utilizes to provide regenerative breaking in some drive

by reducing the supply



ow to reverse and the kinetic energy of the drive system will be fed back to the supply (converting

). The process is known as regenerative breaking.

ill be in the direction of

rotating magnetic field but will oppose the motion of the rotor. This torque is a braking torque. This


ase sequence is changed suddenly, the rotating magnetic field will



Figure 6. A torque-speed characteristic curve showing the extended operating ranges

Principles of Operation

If the stator windings are connected to a three

voltages in the rotor windings produce rotor currents that interact with the air gap field to produce torque.

The rotor, if free to do so, will then start rotating.

According to Lenzs law, the rotor rotates in the direction of the rotating field

speed between the rotating field and the rotor winding decrease. The rotor will eventually reach a steady

state speed that is less than the synchronous speed gap. The revolution per minutes (rpm) of the

where the supply frequency in Hz number of pole

It is obvious that at there will be no induced voltage and current in the rotor circuit and hence no torque. During this state, there will be no cutting of flux and rotor current equals zero. Therefore, it is

not possible for the rotor to rotate at synchronous speed.

The different between the rotor speed and the synchronous speed of the rotating field is called the

slip speed or slip rpm and is defined as

The slip is defined as the relative speed expressed on a perrepresented by

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speed characteristic curve showing the extended operating ranges

If the stator windings are connected to a three-phase supply and the rotor circuit is closed, the induced

oduce rotor currents that interact with the air gap field to produce torque.

The rotor, if free to do so, will then start rotating.

According to Lenzs law, the rotor rotates in the direction of the rotating field such that

speed between the rotating field and the rotor winding decrease. The rotor will eventually reach a steady

that is less than the synchronous speed at which the stator rotating field rotates in the air revolution per minutes (rpm) of the synchronous speed of this rotating magnetic flux is

frequency in Hz

there will be no induced voltage and current in the rotor circuit and hence

there will be no cutting of flux and rotor current equals zero. Therefore, it is

at synchronous speed.


and is defined as

the relative speed expressed on a per-unit or sometimes as percentage basis.

speed characteristic curve showing the extended operating ranges

phase supply and the rotor circuit is closed, the induced

oduce rotor currents that interact with the air gap field to produce torque.

such that the relative

speed between the rotating field and the rotor winding decrease. The rotor will eventually reach a steady-

at which the stator rotating field rotates in the air

of this rotating magnetic flux is

(4.1)

there will be no induced voltage and current in the rotor circuit and hence

there will be no cutting of flux and rotor current equals zero. Therefore, it is


(4.2)

unit or sometimes as percentage basis. It

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(4.3)

From Eq. (4.3), the rotor speed can be derived as

1 (4.4)

The radian per second (rad/s) of rotor speed is

1 (4.5)

where synchronous speed in rad/s The frequency of the induced voltage and current in the rotor circuit will correspond to this slip rpm, because this is the relative speed between the rotating field and the rotor winding. The rotor frequency can

be expressed as

(4.6)

Example 1

A three-phase 460 V, 100 hp, 60 Hz, four-pole induction machine delivers rated output power at a slip of

0.05. Determine

a) Synchronous speed and motor speed.

b) Frequency of the rotor current.

c) Slip rpm.

Equivalent Circuit

The per-phase equivalent circuit of a three-phase induction motor is similar to a single-phase

equivalent circuit of a transformer. The only difference is that the secondary winding of an induction motor

is short-circuited.

stator circuit rotor circuit

Figure 7. The per phase circuit of induction motor

The value of variable resistance of rotor / can be replaced by two resistors in series. From Eq. (4.7), the equivalent circuit of three-phase induction motor can be drawn as Fig. 6.

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" + $ % (4.7)

Figure 8. The complete circuit of induction motor per-phase with rotor having two resistors in series

The equivalent circuit per phase referred to stator of induction motor is illustrated in Fig. 9. This circuit

is similar to equivalent circuit per phase of transformer referred to the primary side.

Figure 9. The equivalent circuit per-phase referred to stator of induction motor

The circuit of Fig. 9 can be simplified to an approximate equivalent circuit to allow a simple calculation

to be performed to calculate the currents in the circuit as shown in Fig. 9.

Figure 10. Approximate per-phase equivalent circuit of induction motor referred to stator

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Power Flow Diagram or Losses in Induction Motor

An induction motor can be described as a rotating transformer. Its input is from the three-phase

supply. The secondary (rotor) winding of an induction motor is shorted, so no electrical output exists.

Instead, the output will be mechanical. The flow of power from the input to the output is shown below.

Figure 11. The overall power in induction motor

Power flow diagram is normally represented as a fish bone, where it illustrates the power flow in the

machine from the input part into the output part. The branches indicate the losses that present in the

machine.

Figure 12. Power flow diagram of induction motor

The losses of Fig. 12 is corresponding with the approximate circuit as shown in Fig. 10.

+

Es

-

I1 I2 RsjXs

RrjXr

IIc Im

Rc jXm Rr (1-s)/s

Figure 13. All losses obtained from approximate circuit

Motor input (Pin)

Stator copper and core loss (PSCL &

Pc)

Air gap power (PAG) or rotor

input power (RIP)

Rotor copper loss (PRCL)

Mechanical power (Pm) or power

converted (Pconv)

Windage, friction, stray losses and etc

(P)

Motor output (Pout)

Pin Pout

PSCL PRCL Pc P

PAG/RIP Pm/Pconv

PSCL PRCL

Pc

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From the above circuit, the following power equations can be derived.

& 3|)||+| cos 3|01||+1| cos 2 (4.8)

&3 4565 7"8 (4.9)

&9:1 3|+; | (4.10)

+& 3|+; | $"< % (4.11)

&":1 3|+; | ; (4.12)

&3=> 3|+; | ; $ % (4.13)

&=?@ &3=> & (4.15)

From Eq. (4.11), (4.12) and (4.13), we can obtain this relationship.

+& A8BCD AEFG (4.16)

Example 2

A three-phase induction 100 hp, 400 V, 50 Hz 6-pole Y-connected squirrel cage induction motor has the

following parameters refer to the stator.

Rs = 0.125 Rr = 0.095 X = 0.45 Xm = 10

If the rotational losses are 550 W, using approximate equivalent circuit, find the following at 5% slip;

a) The line current and power factor

b) The output horsepower

c) The efficiency

Example 3

A 480 V, 50 hp Y-connected induction motor has line current 60 A at 0.85 power factor lagging. This motor

has these following power losses

PSCL = 2 kW PRCL = 700 W P = 600 W Pc = 1800 W

Find

a) the air gap power

b) the power converted

c) the output power

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d) the efficiency

e) of the motor

Torque Equation for Induction Motor

The output power of an induction motor is in the form of mechanical power. This mechanical power is

proportional to torque and rotational speed/angular velocity (). There are four different torques that we

are interested to analyzed in induction motor, i.e. starting torque, Ts, maximum torque, Tmax, mechanical

torque, Tm and output torque, To. Torque equation can be derived from basic power equation.

& H where IJ rad/s (4.17)

Therefore, general equation for torque is define as

H A

JAI (4.18)

where T = torque in Nm

N = speed in rpm

a) Mechanical Torque

Also known as induced torque;

HK A8BCD (4.19)

b) Output Torque

Also known as shaft or load torque;

H=?@ ABLM (4.20)

c) Starting Torque

At starting, 0. Therefore, 1. Thus, equation for starting torque is

H@ N "

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KWX "

Figure 14. Variable-frequency speed control in induction motor.

characteristic curve for speeds (a) below base speed, (b) above base speed (c) for all frequencies.

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(a)

(b)

(c)

frequency speed control in induction motor. The family of torque


family of torque-speed


2. Speed control by pole changing.

In the day before modern solid-state control circuits were commons, the stator windings of induction

motors were often constructed so that the number of poles in the stator windings could be changed. But

now, this technique is largely outdated.

3. Speed control by changing the line voltage.

The torque developed by an induction motor is proportional to the square of the applied voltage. This

method is sometimes used on small motors driving fans.

4. Speed control by changing the rotor resistance.

In wound-rotor induction motors, it is possible to change the shape of the torque

inserting extra resistances into the rotor circuit of the machine. However, inserting extra resistances into

the rotor circuit seriously reduces the efficiency of the machine. Such method is normally used only for

short periods because of this efficiency problem.

Figure 15.

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Speed control by pole changing.

state control circuits were commons, the stator windings of induction


ue is largely outdated.

Speed control by changing the line voltage.


method is sometimes used on small motors driving fans.

e rotor resistance.

rotor induction motors, it is possible to change the shape of the torque


educes the efficiency of the machine. Such method is normally used only for

short periods because of this efficiency problem.

Variable-line-voltage speed control

state control circuits were commons, the stator windings of induction



rotor induction motors, it is possible to change the shape of the torque-speed curve by


educes the efficiency of the machine. Such method is normally used only for

Figure 16.

Starting of an Induction Motor

Squirrel-cage induction motors are frequently started by connecting them directly across the supply

line (self-start). A large starting current of the order of 500 to 800 percent of full

the line. This initial excessive current wil

the same line. Also, if a large current flows for a long time it may overheat the motor and damage the

insulation. In such a case, reduced-voltage starting must be used.

1. Using primary resistors

The purpose is to apply a reduced voltage across the motor terminals so that the initial current is

reduced. This method is useful for smooth starting small machine.

S

S

S

Three-phase Supply

Figure 17. Starting of induction motor using primary resistor

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Speed control by varying the rotor resistance

cage induction motors are frequently started by connecting them directly across the supply

start). A large starting current of the order of 500 to 800 percent of full-load current may flow in

the line. This initial excessive current will effect the operation of other electrical equipment connected to


voltage starting must be used.


reduced. This method is useful for smooth starting small machine.

IM

R

R: running contactsS: starting contactsStart: S closed , R openRun: S open , R closedR

R

Starting of induction motor using primary resistors

cage induction motors are frequently started by connecting them directly across the supply

load current may flow in

l effect the operation of other electrical equipment connected to



running contactsstarting contacts

R openR closed

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2. Using star-delta starter

This method is used for delta-connected motors. It consists of two-way connects the motor in star for

starting and delta for normal running.

At starting, when star-connected, the voltage is reduced by 1/3. Hence, the developed torque is reduced by 1/3. This method is cheap and effective provided the starting torque required does not exceed 1.5 full-load torque. This method is used for machine tools, pumps and motor-generators.

Figure 18. Starting of induction motor using star-delta starter

3. Using auto transformer

This method can be both for star and delta connected motors. At starting, a reduce voltage is applied

across the motor terminals. When the speed is about 80%, the autotransformer is cut-off and full supply

voltage is supplied.

S S

R

S S

R

S S

R

IM

R: running contacts

S: starting contacts

Start: S closed, R open

Run: S open, R closed

Three-phase

Supply

Figure 19. Starting of induction motor using auto transformer

4. Using solid-state voltage controller for starting

A solid-state voltage controller can also be used as a reduces-voltage starter. The controller can

provide smooth starting. This arrangement can also be used to control the speed of the induction motor.

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IMThree-phase

Supply

Figure 20. Starting of induction motor using solid-state voltage controller

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