Department of Electrical and Computer Engineering EE20A - Electromechanical Energy Conversion Induction Machine

Department of Electrical and Department of Electrical and Computer EngineeringComputer Engineering

EE20A - Electromechanical Energy EE20A - Electromechanical Energy ConversionConversion

Induction MachineInduction Machine

Principle of Operation• The stator coils, when energised, create a

rotating magnetic field.• Rotating magnetic field cuts through the

rotor inducing a voltage in the rotor bars.• This voltage creates its own magnetic field

in the rotor.• The rotor magnetic field will attempt to line

up with the stator magnetic field.• The stator magnetic field is rotating, the

rotor magnetic field trying to line up with the stator magnetic field causes the rotor to rotate.

• The rotor magnetic field, never catches up, but follows slightly behind.

Motor AnalysisMotor Analysis

• Slip is the difference between the speed of the stator magnetic field and the speed of the rotor

• SLIP,S, = (NS - N) / NS

• When motor is stationary, it behaves like a transformer

• At a given Speed, flux cutting rate is reduced => thereby reducing output voltage by a factor of the slip.

AnalysisAnalysis

Xm

IN L

Rs jXs

V ph

I IN I1 I2

RO

a : 1IO Im

V1 V2

R rjX r

Per Phase Equivalent Circuit

AnalysisAnalysis

Xm

IN L

Rs jXs

V ph

I IN I1 I2

RO

a : 1I O I m

V1 V2

R rs

jX r


AnalysisAnalysis

Xm

IN L

Rs jXs

V ph

I IN I1

RO

IO Im R rs

jX r

Pair gap


Power per Phase Power per Phase

• Total Torque =

(3Pmech_gross- PF&W)/m

• Pag = I12Rr`/s

• Pcu = sPag

• Pmech_gross = (1-s)Pag

Xm

IN L

Rs jXs

V ph

I IN I1

RO

I O I m R rs

jX r

Pair gap



m oNL I I I

Pag = Power across the air gap

)X X j( s

R R

V I

rsr

s

ph1

s

R x I P r2

1ag


P mech_gross = (1-s) Pag per phase

r2

1cu R I P rotor,in lossesCu

m

W&Fmech_gross

ω

P - P x 3 Torque Total

s

s)-(1 R R I P rr

21ag


s

s)-(1R I RI P r

21r

21ag

Pcu_losses_in_rotor Pmech_gross

PPag ag : P: Pcu cu : P: P

mechmech = 1:s:(1-s) = 1:s:(1-s)


r2

1

r21_per_phasemech_gross

RIs

s)-(1

s

R I s)-(1 P

Slip is variable and affects only rotor circuit

Ignoring Stator values

rr

ph1

X j s

R

V I


2

r

2

r

r2

ph

m

m

2r

2

r

r2

ph

r2

1mech_gross

X s

R

R . V x

ns2

s)-(1

2 ω

ω

phaseper Power Torque

Xs

R

R . V x

s

s)-(1

s

s)-(1 R I P

n

Torque Torque Simple Algebraic manipulations yield

22

r

r

2

r

r2ph

r

2r

2

2

r

r

2r

2ph

mech_gross

s X

R

s . X

R . V

x nsX2

s)-(1

X s X

R

s . R . V x

ns2

s)-(1 T

Torque Torque

22r

2ph

2

22ph

rmech_gross

r

r

s

. s x

nX2

V . s)-(1

s

. s . V x

nsX2

s)-(1 Tget Then we

X

R let Now

2

Torque Torque

22rs

2ph

mech_gross

s

s

s

s

s x

Xn2

V T

:get n wefor ngsubstitutiBy

s)-(1n n

n

n - n s slip,But

Since the above calculations was derives as power per phase, then the total torque for all three phases would be three times the gross mechanical torque for each phase calculated above.

22

rs

2ph

22rs

2ph

s

s. .k Torque TotalThen

Xn2

3V k Let

s

s x

Xn2

V x 3 Torque Total

Torque Torque

The maximum torque is obtained when:

sor X

R s slip,

r

r

Torque CharacteristicsTorque Characteristics

Speed-Torque characteristicsSpeed-Torque characteristics

Modifications in the design of the squirrel-cage motors permit a certain amount of control of the starting current and torque characteristics. These designs have been categorised by NEMA Standards (MG1-1.16) into four main classifications:

1. Normal-torque, normal-starting current motors (Design A) 2. Normal-torque, low-starting current motors (Design B) 3. High-torque, low-starting-current, double-wound-rotor motors (Design C) 4. High-slip motors (Design D)

Design A MotorDesign A Motor

• Hp range 0.5 – 500 hp. • Starting current 6 to 10 times full-load current. • Good running efficiency (87% - 89%). • Good power factor (87% - 89%). • Low rated slip (3 –5 %). • Starting torque is about 150% of full load torque. • Maximum torque is over 200% but less than 225% of full-

load torque. • Typical applications – constant speed applications where high

starting torque is not needed and high starting torque is tolerated.

Design B MotorDesign B Motor

•Hp range – 0.5 to 500 hp •Higher reactance than the Design A motor, obtained by means of deep, narrow rotor bars. •The starting current is held to about 5 times the full-load current. •This motor allows full-voltage starting. •The starting torque, slip and efficiency are nearly the same as for the Design A motor. •Power factor and maximum torque are little lower than class A, •Design B is standard in 1 to 250 hp drip-proof motors and in totally enclosed, fan-cooled motors, up to approximately 100 hp. •Typical applications – constant speed applications where high starting torque is not needed and high starting torque is tolerated.

•Unsuitable for applications where there is a high load peak

Design C MotorDesign C Motor

•Hp range – 3 to 200 hp •This type of motor has a "double-layer" or double squirrel-cage winding. •It combines high starting torque with low starting current. •Two windings are applied to the rotor, an outer winding having high resistance and low reactance and an inner winding having low resistance and high reactance. •Operation is such that the reactance of both windings decrease as rotor frequency decreases and speed increases. •On starting a much larger induced currents flow in the outer winding than in the inner winding, because at low rotor speeds the inner-winding reactance is quite high.

Design C MotorDesign C Motor

•As the rotor speed increases, the reactance of the inner winding drops and combined with the low inner-winding resistance, permits the major portion of the rotor current to appear in the inner winding. •Starting current about 5 times full load current. •The starting torque is rather high (200% - 250%). •Full-load torque is the same as that for both A and B designs. •The maximum torque is lower than the starting torque, maximum torque (180-225%).

•Typical applications – constant speed loads requiring fairly high starting torque and lower starting currents.

Design D MotorDesign D Motor •Produces a very high starting torque-approximately 275% of full-load torque.

•It has low starting current,

•High slip (7-16%),

•Low efficiency.

•Torque changes with load

•Typical applications- used for high inertia loads

The above classification is for squirrel cage induction motor

Wound RotorWound Rotor

•Hp 0.5 to 5000hp •Starting torque up to 300% •Maximum torque 225 to 275% of full load torque •Starting current may be as low as 1.5 times starting current •Slip (3 - 50%) •Power factor high •Typical applications – for high starting torque loads where very low starting current is required or where torque must be applied very gradually and where speed control is needed.

Current Effects on the MotorCurrent Effects on the Motor

•Induction motor current consists of reactive (magnetizing) and real (torque) components. •The current component that produces torque (does useful work) is almost in phase with voltage, and has a high power factor close to 100%•The magnetizing current would be purely inductive, except that the winding has some small resistance, and it lags the voltage by nearly 90°. •The magnetizing current has a very low power factor, close to zero.•The magnetic field is nearly constant from no load to full load and beyond, so the magnetizing portion of the total current is approximately the same for all loads.

•The torque current increases as the load increases

•At full load, the torque current is higher than the magnetizing current. •For a typical motor, the power factor of the resulting current is between 85% and 90%. •As the load is reduced, the torque current decreases, but the magnetizing current remains about the same so the resulting current has a lower power factor. •The smaller the load, the lower the load current and the lower the power factor. Low power factor at low loading occurs because the magnetizing remains approximately the same at no load as at full load

Current Effects on the MotorCurrent Effects on the Motor

Methods to vary speed of theMethods to vary speed of the Induction Motor Induction Motor

An induction motor is a constant-speed device. Its speed depends on the number of poles in the stator, assuming that the voltage and frequency of the supply to the motor remain constant.

•One method is to change the number of poles in the stator, for example, reconnecting a 4-pole winding so that it becomes a 2-pole winding will double the speed. This method can give specific alternate speeds but not gradual speed changes.

•Another method is to vary the line voltage this method is not the best since torque is proportional to the square of the voltage, so reducing the line voltage rapidly reduces the available torque causing the motor to stall

Methods to vary speed of theMethods to vary speed of the Induction Motor Induction Motor

•Sometimes it is desirable to have a high starting torque or to have a constant horsepower output over a given speed range. These and other modifications can be obtained by varying the ratio of voltage to frequency as required. Some controllers are designed to provide constant torque up to 60 Hz and constant hp above 60 Hz to provide higher speeds without overloading the motor.

•An excellent way to vary the speed of a squirrel-cage induction motor is to vary the frequency of the applied voltage. To maintain a constant torque, the ratio of voltage to frequency must be kept constant, so the voltage must be varied simultaneously with the frequency. Modern adjustable frequency controls perform this function. At constant torque, the horsepower output increases directly as the speed increases.

NO LOAD TESTNO LOAD TEST

Watt

meter

AC

I

V

C urren tC o il

Volta

geCo

il

Xm

IN L

Rs jXs

V ph

I IN I1

RO

I O I m R rs

jX r

Pair gap



n - ns = 0 ‘No load Speed Synchronous Speed’

i.e. no power transfer which implies that Torque = 0

I1 = 0 & T = 0

Power Consumed = Core Losses + Friction & Windage

Measure Vph , IIN and Wph

( Infinite Impedance ) since I1 = 0

E

sr

R

• INL = I0 – jIm

= INL ( cos NL - jsin NL )

• cos NL = Wph

Vph INL

• Ro = Vph Xm = Vph

I0 Im


Lock Rotor TestLock Rotor Test

Wattm

eter

AC

I

V

C urren tC o il

Volta

ge Coil

Xm

IN L

Rs jXs

V ph

I IN I1

RO

I O I m R r

jX r

Pair gap

s


• In the Lock Rotor test, No Load Speed, n = 0

Slip, s = ns – 0 = 1, s = 1

ns

• Then Rr Rr

s

•Apply Voltage to Variac, VLR = (10% - 25% ) Vph

• Since INL<< I1 Then INL 0

• Measure values VLR , ILR and WLR

Lock Rotor TestLock Rotor Test•Zeq = VLR / ILR

•cos LR= WLR

VLR ILR

• Zeq = Zeq {cos LR - jsin LR}

= Zeq cos LR - Zeq jsin LR

Rs+ Rr Xs + Xr

•At Standstill Under d.c. conditions = 0

X= L

X = 0

•R1 & R2 can be measured using an ohmmeter over two stator windings, which gives a value of Rs

• Rr = Zeq cos LR - Rs


Rs jXs

Ohmmeter

R 1

R 2

STATOR ROTOR

Documents

Department of Electrical and Computer Engineering EE20A - Electromechanical Energy Conversion Induction Machine