Download - Ch 3 - Induction Motors

BEE 4123Electrical Machines & Drives

Chapter 3Chapter 3

Induction MotorsInduction Motors

Module Outlines

Induction Motor Construction Basic Induction Motor Concepts The Equivalent Circuit of an Induction Motor Power and Torque in an Induction Motor Induction Motor Torque-Speed Characteristics Starting Induction Motors Speed Control of Induction Motors Determining Circuit Model Parameters Induction Motor Ratings

Induction Motor Construction

The single-phase induction motor is the most frequently used motor in the world.

Most appliances, such as washing machines and refrigerators, use a single-phase induction machine

Highly reliable and economical

Power Supply

Rotor

Stator

Shaft


Using amortisseur windings, no DC field circuit. Called “induction machines” because the rotor

voltage is induced in the rotor windings instead of physically connected by wires.

Mostly used as motor, rarely as generator. 2 types of rotor – squirrel cage & wound rotors. Most motors use the squirrel-cage rotor because

of the robust and maintenance-free construction.


Squirrel-cage rotor


Squirrel cage rotor This rotor has a laminated iron core with slots, and is mounted

on a shaft. Aluminum bars are molded in the slots and the bars are short

circuited with two end rings. The bars are slanted on a small rotor to reduce audible noise. Fins are placed on the ring that shorts the bars. These fins work

as a fan and improve cooling.

Rotor bars (slightly skewed)

End ring


Wound rotor Large or older motors use a

wound rotor with three phase windings placed in the rotor slots.

The windings are connected in a three-wire wye.

The ends of the windings are connected to three slip rings.

Resistors or power supplies are connected to the slip rings through brushes for reduction of starting current and speed control.

Basic Induction Motor Concepts

IRBS

BR

Bnet

R

ER

Net voltageMaximum induced voltage

Maximum induced current

Apply 3-phase voltage

to stator, 3-phase currentflowing in stator

produces BS.

Apply 3-phase voltage

to stator, 3-phase currentflowing in stator

produces BS.

P

fn esync

120 IBveind )(

BR and BS rotate at nsync, but rotor turns at a slower speed.

BR and BS rotate at nsync, but rotor turns at a slower speed.

The Development of Induced Torque

SRind BkB

Basic Induction Motor ConceptsThe Concept of Rotor Slip

The voltage induced in rotor bar depends on the speed of the rotor relative to the magnetic fields.

2 terms to define the relative motion: Slip speed -- difference between synchronous speed

and rotor speed:

Slip -- relative speed expressed on p.u. basis:

msyncslip nnn

sync

slip

n

ns

sync

msyncs

syncm nsn )1(

Basic Induction Motor Concepts

The Electrical Frequency on the Rotor

Induction motor also called as rotating transformer due to its induced voltage and current.

Primary (stator) & Secondary (rotor). Unlike transformer, frequency not necessarily same at

secondary and primary. If rotor is locked, fr = fs or fe.

If rotor at nsync, fr = 0.

If rotor rotate in between the above speeds,

er sff )(120 msyncr nnP

f

The Equivalent Circuit An induction motor has two magnetically coupled circuits:

the stator and the rotor. The latter is short-circuited. This is similar to a transformer, that the secondary side is

rotating and short-circuited. The motor has balanced three-phase circuits;

consequently, the single-phase representation is sufficient. Both the stator and rotor have windings, which have

resistance and leakage inductance. The stator and rotor winding are represented by a

resistance and leakage reactance connected in series.

The Equivalent Circuit A transformer represents the magnetic coupling between

the two circuits. The stator produces a rotating magnetic field that induces

voltage in both windings. A magnetizing reactance (XM) and a resistance

connected in parallel represent the magnetic field generation.

The resistance (RC) represents the eddy current and hysteresis losses in the iron core.

The induced voltage is depend on the slip and the turn ratio.

The Equivalent Circuit

The Transformer Model of an Induction Motor

Stator Rotor

jXR

RR

IR

ER

R1I2

E1VP

I1

jXMRC

IM

aeffjX1


Magnetization curve (Wb)

(A-turns)

Induction motor

Transformer

The curve is more shallower because of the air gap in an induction motor that increases the reluctance of the flux path. More magnetizing current is needed!

The curve is more shallower because of the air gap in an induction motor that increases the reluctance of the flux path. More magnetizing current is needed!


The Rotor Circuit Model

The magnitude of induced rotor voltage is directly proportional to slip (s) of the rotor; largest during locked-rotor and smallest during synchronous speed with stator magnetic field.

RR is constant but XR is dependent of slip.

LRR sEE During locked-rotor

RrRrR LfLX 2


The Rotor Circuit Model

By fr=sfe,

Rotor current,

LRR sXX

jXR=jsXLR

ER=sELR RR

IR

+

-

LRR

LR

RR

RR jXsR

E

jXR

EI

/ LRReqR jXsRZ /,


Final Equivalent Circuit (Per phase circuit)

Referred rotor circuit to stator side (similar to transformer – secondary referred to primary).

SS

SSP

SSP

ZaZ

a

III

aVVV

2'

'

'

LRR

eff

eff

R

LReffR

jXs

RaZ

a

II

EaEE

22

2

'1

TransformerTransformer Induction motorInduction motor


Per-phase Equivalent circuit of induction motor

I1

V

jX1 R1

E1

jX2

R2/s RcjXM

IM

I2

LReff

Reff

XaX

RaR

22

22

Power and Torque

Transformer has electric power output from secondary, but induction motor has no electric power output from rotor as it is shorted out.

Only mechanical power output from rotor.

Pout=loadm

Pstray (Pmisc.)

Pfriction and windage losses

Pcore (Core losses)

PSCL (Stator copper loss)

Pin=3VTILcos

PRCL (Rotor copper loss)

Air-gap powerindm

PAG Pconv

I2R

Mechanical power

RC

Power and Torque

I1

V

jX1 R1

E1

jX2

R2/s RcjXM

IM

I2

22

11

1

11

jXsRjBG

jXRZ

Z

VI

MC

eq

eq

Power and Torque

The stator copper losses

The core losses

The air-gap power

The rotor copper losses

1213 RIPSCL

Ccore GEP 213

s

RIPPPP coreSCLinAG

2223

222

2 33 RIRIP RRRCL

AGRCL sPP

Power and Torque

The electrical power is then converted to mechanical power, called Pconv or developed mechanical power.

The output power,

s

sRI

PPP RCLAGconv

13 2

22

AG

AGAG

RCLAGconv

Ps

sPP

PPP

)1(

miscWFconvout PPPP &

Power and Torque

The induced torque or developed torque,

sync

AG

sync

AG

m

convind

P

s

Ps

P

)1(

)1(

Power and Torque

I1

V

jX1 R1

E1

jX2

R2(1-s)/s Rc jXM

IM

I2

(SCL)

(Core loss)

R2

(Pconv)

(RCL)

s

sRR

s

RRconv

122

2

Torque-Speed CharacteristicsI1

V

jX1 R1

E1

jX2

R2/s jXM

I2

V

jX1 R1

VTHjXM+-

jX1 R1

jXM)(

)(

11

11

M

MTH XXjR

jXRjXZ

VXXR

XV

M

MTH 2

121 )(

Thevenin Equivalent Voltage Thevenin Equivalent Impedance

Torque-Speed Characteristics

Since XM>>X1, XM>>R1 and XM+X1>>R1,

jXTH RTH

E1

jX2

R2/s VTH+-

I2

VXX

XV

M

MTH

1

2

11

M

MTH XX

XRR

1XXTH


From the circuit,

The magnitude of I2,

The air-gap power,

2222 jXjXsRR

V

ZZ

VI

THTH

TH

TH

TH

222

2

2XXsRR

VI

THTH

TH

22

22

22

222

33

XXsRR

sRV

s

RIP

THTH

THAG


The rotor-induced torque,

][

32

22

2

22

XXsRR

sRVP

THTHsync

TH

sync

AGind

Torque-Speed CharacteristicsTypical induction motor torque-speed characteristic curve

in

d (%

of

full

lo

ad)

100

200

300

400

500Pullout torque

Full-load torque

Starting torque

nsync

Mechanical Speed

Torque-Speed CharacteristicsTorque-speed characteristic curve (extended operating ranges)

in

d (%

of

full

lo

ad)

nm2nsyncnsync Mechanical Speed

Generator region

Motor regionBraking region

max

-800

400


Torque and power converted versus motor speed

100

200

300

400

500

600

700

800

250 20001000

15

30

45

60

75

90

105

120

Ind

uce

d t

orq

ue

(N-m

)

Po

wer

(kW

)

Mechanical speed (r/min)


Maximum (Pullout) Torque

Maximum torque occurs when the air-gap power is maximum and it is equal to the power consumed in load resistor, R2/s.

Maximum power transfers to R2/s when the magnitude is equal to the magnitude of the source impedance, Zsource.

2jXjXRZ THTHsource

22

22 )( XXRs

RTHTH


The slip at pullout torque,

The pullout torque,

22

2

2max

)( XXR

Rs

THTH

])([2

32

22

2

maxXXRR

V

THTHTHsync

TH

Starting Induction Motor

Simply start the induction motors by connecting them to the power line may cause voltage dip in the power system.

For wound-rotor induction motor, the insertion of extra resistance increases the starting torque and reduces the starting current.

For squirrel-cage induction motor, the starting current is depends on the rated power (Sstart in kVA) and the rated voltage (VT in V),

) )( ( factorlettercoderhoursepoweratedSstart

T

startL

V

SI

3


The code letter factor (in kVA/hp) is given on the nameplate. The example of code letters,

Nominal code letter

Locked rotor, kVA/hp

A 0-3.15

B 3.15-3.55

C 3.55-4.00

D 4.00-4.50


Starting circuit is use to reduce the starting current, but it also reduce the starting torque.

Common approach is to reduce the motor’s terminal voltage during starting by using autotransformers.

1 1 12 22

3 3

Line terminals

Motor terminals

Th

ree-

ph

ase

auto

tran

sfo

rmer

Speed Control of Induction Motors

2 techniques to control the speed of induction motor:

i. Vary the nsync (changing fe and pole)

ii. Vary the slip (changing VT and rotor resistance)

Changing Pole Old technique, greatly obsolete nowadays!


Changing Line Frequency From the below equation,

To decrease the magnetization current, voltage applied to the stator need to be decreased. Thus maximum power rating of the motor must be decreased to avoid motor overheat.

tN

Vt

P

M

cos fe , Excessive magnetization current flow in the motor!

cos3 LLIVP


Changing the Line Voltage The motor torque is proportional to (Vapp)2. The changing of torque will vary the motor speed and

it can be analyzed from the torque-speed characteristic curve.

Sometimes used on small motors driving fan.

Changing Rotor Resistance It is applicable for wound-rotor induction motors only

by inserting extra resistances. The extra resistances seriously reduces the efficiency

of the motor. Used only for short periods.

Determining Circuit Model Parameters

Why important? To determine the torque-speed curve of the real induction motor.

What parameters? R1, R2, X1, X2, and XM.

What tests? DC Test – to find stator resistance, R1.

No-load test – to find Znl = X1+XM.

Locked-rotor test – to find RLR=R1+R2 and XLR=X1+X2.


DC voltage is applied to stator windings. Since it is DC, thus, no eind and I2, and jX=0.

I1 is adjusted to I1,rated and voltage between terminals is measured. The total resistance, 2R1,

A

VVDC (variable)

Current limiting resistorI1=I1,rated

R1

R1

R1

DC

DC

I

VR 12

DC Test

R1 R2

R2(1-s)/sjXM

jX1 jX2

RC

I2=0

IM

I1

V

+

-

R1

RF&W= R2(1-s)/s

jXM

jX1

RC

I1

V

+

-

R1

RF, W, & core >> XM

jXM

jX1

V

+

-

Determining Circuit Model ParametersNo-load Test

Initial equivalent circuit

Initial equivalent circuit

Since R2(1-s)/s >> R2 and R2(1-s)/s >> X2.

Since R2(1-s)/s >> R2 and R2(1-s)/s >> X2.

Combining RF&W and RC

Combining RF&W and RC

P1 AV

Variable voltage, variable frequency, three-phase power source P2 A

A

IA

IB

IC

No load 3

CBAL

IIII

Mnl

eq XXI

VZ 1

,1

miscWFcorerot PPPP &

rotSCLin PPP 1213 RIPSCL

Determining Circuit Model ParametersLocked-rotor Test

PAV

Adjustable voltage, adjustable frequency, three-phase power source PA

A

IA

IB

IC

Locked rotor

a

b

c

R1

R2/s=R2jXM

jX1 jX2

RC

I2I1

V

+

-

tester fff

ratedLCBA

L IIII

I ,3

MC

C

M

XR

jXRR

jXRX

and neglect So22

22


One problem with this test: During normal operating conditions, s of the motor is only 2-4%, and resulting the frotor is in the range of 1-3 Hz.

The fe,rated (50/60 Hz) does not represent the normal operating conditions of the rotor.

A typical compromise is to use a frequency (ftest) 25% or less of fe,rated, examples: 12.5 Hz and 15 Hz.

Locked-rotor Test


The input power to the motor,

The magnitude of total impedance in motor circuit,

The total equivalent reactance at normal operating frequency,

Locked-rotor Test

cos3 LTin IVP

L

TLR

I

V

I

VZ

31

sincos'

LRLRLRLRLR ZjZjXRZ

21 RRRLR '2

'1

' XXX LR and

21' XXX

f

fX LR

test

ratedLR

Induction Motor Ratings Typical ratings on the nameplate of induction motor:

Output power Voltage Current Power factor Speed Nominal efficiency NEMA (National Electrical Manufacturers

Association) design class (Class A, B, C, and D). Starting code

Download - Ch 3 - Induction Motors

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