AC motor Drives are used in many industrial and domestic ... · application, such as in conveyer, lift, mixer, escalator etc. INDUCTION MOTOR DRIVES Three-phase induction motor are

AC DRIVES

The AC motor have a number of advantages :

• Lightweight (20% to 40% lighter than equivalent DC motor)

• Inexpensive

• Low maintenance

The Disadvantages AC motor :

* The power control relatively complex and more expensive

There are two type of AC motor Drives :

1. Induction Motor Drives

2. Synchronous Motor Drives

AC motor Drives are used in many industrial and domestic application, such as in conveyer, lift, mixer, escalator etc.

INDUCTION MOTOR DRIVES

Three-phase induction motor are commonly used in adjustable-speed

drives (ASD).

Basic part of three-phase induction motor :

• Stator

• Rotor

• Air gap Stator

Three-phase

windings

RotorAir gap

T

Rotor windings

Three-

phase

supply

ms

The stator winding are supplied with balanced three-phase AC voltage,

which produce induced voltage in the rotor windings. It is possible to

arrange the distribution of stator winding so that there is an effect of

multiple poles, producing several cycle of magnetomotive force (mmf) or

field around the air gap.

The speed of rotation of field is called the synchronous speed s , which

is defined by :

ps

2

ωs is syncronous speed [rad/sec] Ns is syncronous speed [rpm]

p is numbers of poles

ω is the supply frequency [rad/sec]

f is the supply frequency [Hz]

Nm is motor speed

Stator

Three-phase

windings

RotorAir gap

T

Rotor windings

Three-

phase

supply

ms

p

fNs

120

or

Stator

Three-phase

windings

RotorAir gap

T

Rotor windings

Three-

phase

supply

ms

The rotor speed or motor speed is : )1( Ssm

Where S is slip, as defined as : S

mSS

Or

S

mS

N

NNS

The motor speed

Equivalent Circuit Of Induction Motor

Stator

Three-phase

windings

RotorAir gap

T

Rotor windings

Three-

phase

supply

ms

Stator Air gap motor

Vs

Is

Im Ir’

Xs Xr’Rs

RmXm

Rr’/s

Where :

Rs is resistance per-phase of stator winding

Rr is resistance per-phase of rotor winding

Xs is leakage reactance per-phase of the

winding stator

Xs is leakage reactance per-phase of the

winding rotor

Xm is magnetizing reactance

Rm Resistane responsible for Core losses

Performance Characteristic of Induction Motor

Stator copper loss :


Vs

Is

Im Ir’

Xs Xr’Rs

RmXm

Rr’/s

sscus RIP2

3

'2')(3 rrcur RIP Rotor copper loss :

m

s

m

mc

R

V

R

VP

22

33 Core losses :

S

RIP r

rg

'

2')(3

)1()(3'

2'S

S

RIPPP r

rcurgd

)1( SPP gd

- Power developed on air gap (Power fropm stator to

rotor through air gap) :


- Power developed by motor :

or

- Torque of motor :

m

dd

PT

s

g

S

g P

S

SP

)1(

)1(or

m

dd

N

PT

2

60or

mssi IVP cos3

gcusc PPP

Input power of motor :


loadnodo PPP

gcusc

loadnod

i

o

PPP

PP

P

P

Output power of motor :

Efficiency :

)( cuscg PPP

loadnod PP

SP

SP

P

P

g

g

g

d

1)1(

If

and

so, the efficiency can calculated as :


)(222

ssm XRX

Generally, value of reactance magnetization Xm >> value Rm (core

losses) and also

So, the magnetizing voltage same with the input voltage : sm VV

Therefore, the equivalent circuit is ;


Vs

Is

Im Ir’

Xs Xr’Rs

RmXm

Rr’/s

Stator Air gap rotor

Vs

Ii

Im Ir’

Xs Xr’Rs

Rr’/s

PiPo

Is=Ir’

Xm


)(

)()(

''

''

rsmr

s

rsmrsm

i

XXXjS

RR

S

RRjXXXX

Z

Total Impedance of this circuit is :



Vs

Ii

Im Ir’

Xs Xr’Rs

Rr’/s

PiPo

Is=Ir’

Xm

The rotor current is :

2

1

2'

2'

'

rsr

s

sr

XXS

RR

VI

2'

2'

2'3

rsr

ss

srd

XXS

RRS

VRT


Vs

Ii

Im Ir’

Xs Xr’Rs

Rr’/s

PiPo

Is=Ir’

Tmax

Smax

Tst

Td

S=0s

Ns

S=1

TL

S=Sm

m

NmNm =0

Tm=TL

Operating point

Torque – speed Characteristic

Tmax

Smax

Tst

S=0

s

Ns

S=1

S=Sm

Nm =0

ss =0s

-Tmax

-Smax

S=-1S=2

Forward

regenerationForward

motoring

Reverse

plugging

s m s m

s m

Torque

Three region operation :

1. Motoring :

2. Regenerating :

3. Plugging :

10 S

0S

21 S

Starting speed of motor is m = 0 or S = 1,


Starting torque of motor is :

2'

2'

2'3

rsr

ss

srst

XXS

RR

VRT

Slip for the maximum torque Smax can be found by setting : 0dS

Td d

So, the slip on maximum torque is :

21

2'2

'

max

rss

r

XXR

RS

2'2

2

max

2

3

rssss

s

XXRR

VT


Torque maximum is :

And the maximum regenerative torque can be found as :

2'2

2

max

2

3

rssss

s

XXRR

VT

Where the slip of motor s = - Sm

2'

2'

2'3

rsr

ss

srd

XXS

RRS

VRT

Speed-Torque Characteristic :

2

'2'

S

RRXX r

srs

2'

2'3

rss

srd

XXS

VRT

2'

2'3

rss

srst

XX

VRT

For the high Slip S. (starting)

So, the torque of motor is :

And starting torque (slip S=1) is :

sr

rs RS

RXX

'2'

rs

sd

R

SVT

'

3 2

For low slip S region, the motor speed near unity or synchronous

speed, in this region the impedance motor is :

So, the motor torque is :

21

2'2

'

max

rss

r

XXR

RS

And the slip at maximum torque is :

The maximum motor torque is :

2'

2'

2'3

rsr

ss

srd

XXS

RRS

VRT

Stator Voltage Control

Controlling Induction Motor Speed by

Adjusting The Stator Voltage

2'

2'

2'3

rsr

ss

srd

XXS

RRS

VRT

Td

IM

AC

Variable

Voltage

Sources

Vs

Statorair

gaprotor

Ii

Im Ir’

Xs Xr’Rs

Rr’/s

PiPo

Is=Ir’

Vs

Tmax

S=0s

Ns

S=1

TL

Nm =0

Td

Vs1Vs Vs2> >

12

Tst

Tst1

Tst2

AC Voltage controller for 3

phase Induction Motor

Frequency Voltage Control

Controlling Induction Motor Speed by

Adjusting the Frequency of Stator

Voltage Td

IM

AC

Variable

Voltage

Sources

Vs

f

StatorAir

gaprotor

Ii

Im Ir’

Xs Xr’Rs

Rr’/s

PiPo

Is=Ir’

Vsf

Tmax

S=0S=1

TL

m =0

Td

< <

1 2

Tst

Tst1

Tst2

s

fsS=0

fs1fs2

S=0

fs2 fsfs1

2'

2'

2'3

rsr

ss

srd

XXS

RRS

VRT

Block diagram of Variable frequency

speed control

Voltage source inverter fed Induction

motor drive

Current Source Inverter fed Induction motor

drive

Comparison of CSI and VSI drives

Cycloconverter fed Induction motor

drive

CONTROLLING INDUCTION MOTOR SPEED USING

ROTOR RESISTANCE (Rotor Voltage Control)

Wound rotor induction motor applications

cranes

CONTROLLING INDUCTION MOTOR SPEED USING

ROTOR RESISTANCE (Conventional Rotor Resistance Control)

Equation of Speed-Torque :

2'

2'

2'3

rsr

ss

srd

XXS

RRS

VRT

rs

sd

R

SVT

'

3 2

In a wound rotor induction motor, an external

three-phase resistor may be connected to its

slip rings,

Three-phase

supply

Rotor

Stator

RX

RX

RX

Approximate Torque produced in three phase IM is

2 '' 2 2

' 2 2 2

2 2

d

KsE RT

R s X

2

2 2

2 2 2

2 2

d

KsE RT

R s X

External resistance is added in each phase of rotor through slip rings as shown in the fig. Corresponding torque,

The starting torque at s=1 for and can be written as and

2R '

2R

2

2 2

2 2

2 2

st

KE RT

R X

2 '' 2 2

' 2 2

2 2

st

KE RT

R X

The maximum torque condition i.e. We get

2 2/ Xs R

2

2max

22

KET

X

Maximum torque is independent of rotor resistance, whatever may be the rotor resistance.

These resistors Rx are used to control motor starting and stopping

anywhere from reduced voltage motors of low horsepower up to

large motor applications such as materials handling, mine hoists,

cranes etc.

The most common applications are:

AC Wound Rotor Induction Motors – where the resistor is wired into the

motor secondary slip rings and provides a soft start as resistance is

removed in steps.

AC Squirrel Cage Motors – where the resistor is used as a ballast for soft

starting also known as reduced voltage starting.

The developed torque may be varying the resistance Rx

The torque-speed characteristic for variations in rotor resistance

This method increase the starting torque while limiting the starting current.

The wound rotor induction motor are widely used in applications requiring

frequent starting and braking with large motor torque (crane, hoists, etc)

Advantages:

• Reduce the starting current

• Increase the starting torque

• Power factor of the line is improved

• There is no harmonics in the line current

• Speed control is smooth and of wide range

Disadvantages:

• Efficiency is reduced due to wastage of slip energy in the rotor

circuit

• If rotor resistances are not equal, unbalance in currents and

voltages

The three-phase resistor may be replaced by a three-phase diode rectifier

and a DC chopper. The inductor Ld acts as a current source Id and the DC

chopper varies the effective resistance:

)1( kRRe Where k is duty cycle of DC chopper

The speed can controlled by varying the duty cycle k, (slip power)

Three-phase

supply

Rotor

StatorD1

D2

D3

D6D4

D5

GTOR Vdc

Id

Ld

Vd

Static Rotor Resistance Control

Slip-Recovery Drives for Wound-Field Induction Motors

The power in the air gap portion which is not

converted into mechanical power is called

slip power.

In a wound-field induction motor the slip rings

allow easy recovery of the slip power which

can be electronically controlled to control the

speed of the motor.

Slip-Recovery Drives for Wound-Field Induction Motors (cont’d)

The oldest and simplest technique to invoke this slip-

power recovery induction motor speed control is to

mechanically vary the rotor resistance.

Slip-power recovery drives are used in the

following applications:

Large-capacity pumps and fan drives

Variable-speed wind energy systems

Shipboard VSCF (variable-speed/constant

frequency) systems

Variable speed hydro-pumps/generators

Utility system flywheel energy storage systems

The slip power in the rotor circuit may be returned to the supply by

replacing the DC converter and resistance R with a three-phase full

converter (inverter)

Three-phase

supply

Rotor

StatorD1

D2

D3

D6D4

D5

Id

Ld

Vd

T2

T5

T4

T3T1

T6

Vdc

Transformer Na:Nb

Diode rectifierControlled rectifier/

inverter

Slip Power

Example:

A three-phase induction motor, 460, 60Hz, six-pole, Y connected, wound rotor

that speed is controlled by slip power such as shown in Figure below. The

motor parameters are Rs=0.041 , Rr’=0.044 , Xs=0.29 , Xr’=0.44 and

Xm=6.1 . The turn ratio of the rotor to stator winding is nm=Nr/Ns=0.9. The

inductance Ld is very large and its current Id has negligible ripple.

The value of Rs, Rr’, Xs and Xr’ for equivalent circuit can be considered

negligible compared with the effective impedance of Ld. The no-load of motor is

negligible. The losses of rectifier and Dc chopper are also negligible.

The load torque, which is proportional to speed square is 750 Nm at 1175 rpm.

(a) If the motor has to operate with a minimum speed of 800 rpm, determine

the resistance R, if the desired speed is 1050 rpm,

(b) Calculate the inductor current Id.

(c) The duty cycle k of the DC chopper.

(d) The voltage Vd.

(e) The efficiency.

(f) The power factor of input line of the motor.

voltVs 58.2653

460

6p

sradx /377602

sradxs /66.1256/3772

The equivalent circuit :

The dc voltage at the rectifier output is :

)1( kRIRIV dedd

ms

s

rsr nVS

N

NVSE

and

For a three-phase rectifier, relates Er and Vd as :

rrd EExV 3394.2265.1

Using : ms

s

rsr nVS

N

NVSE

msd nVSV 3394.2

If Pr is the slip power, air gap power is : S

PP r

g

Developed power is : S

SPS

S

PPPP rr

rgd

)1(3)(3)(3

Because the total slip power is 3Pr = Vd Id and mLd TP

So, )1(

)1(STT

S

IVSP mLmL

ddd

Substituting Vd from msd nVSV 3394.2 In equation Pd above, so

: Solving for Id gives :

ms

sLd

nV

TI

3394.2

Which indicates that the inductor current is independent of the speed.

From equation : )1( kRIRIV dedd and equation : msd nVSV 3394.2

So, msd nVSkRI 3394.2)1(

Which gives :

ms

d

nVS

kRIS

3394.2

)1(

The speed can be found from equation :

ms

d

nVS

kRIS

3394.2

)1( as :

ms

dssm

nV

kRIS

3394.2

)1(1)1(

2)3394.2(

)1(1

ms

sLsm

nV

kRT

Which shows that for a fixed duty cycle, the speed decrease with load

torque. By varying k from 0 to 1, the speed can be varied from minimum

value to s

sradm /77.8330/180

From torque equation : 2

mvL KT

Nmx 67.3471175

800750

2

From equation :

ms

sLd

nV

TI

3394.2

The corresponding inductor current is :

Axx

xId 13.78

9.058.2653394.2

66.12567.347

The speed is minimum when the duty-cycle k is zero and equation :

ms

dssm

nV

kRIS

3394.2

)1(1)1(

)9.058.2653394.2

13.781(66.12577.83

xx

R

And : 3856.2R

Speed Control by Rotor Rheostat

Recall that the torque-slip equation for an

induction motor is given by:

From this equation it is clear that the torque-slip

curves are dependent on the rotor resistance

Rr. The curves for different rotor resistances are

shown on the next slide for four different rotor

resistances (R1-R4) with R4>R3>R2>R1.

2

2 2 23 .

2 / ( )

sre

e s r e ls lr

VRPT

s R R s L L

Speed Control by Rotor Rheostat (cont’d)

An electronic chopper implementation is also

possible as shown below but is equally

inefficient.

Slip power recovery schemes

Instead of wasting the slip power in the rotor

circuit resistance, a better approach is to convert

it to ac line power and return it back to the line.

Two types of converter provide this approach:

1) Static Kramer Drive - only allows

operation at sub-synchronous speed.

2) Static Scherbius Drive - allows

operation above and below

synchronous speed.

Static Kramer Drive (cont’d) A schematic of the static Kramer drive is shown

below:

Static Kramer Drive (cont’d)

The machine air gap flux is created by the stator

supply and is essentially constant. The rotor current

is ideally a 6-step wave in phase with the rotor

voltage.


The motor fundamental phasor diagram referred to

the stator is as shown below:

Vs = stator phase voltage, Is=stator current, Irf’ = fundamental rotor current referred to the stator, g = air gap flux, Im=magnetizing current, and =PF angle.


The voltage Vd is proportional to slip, s and the

current Id is proportional to torque. At a

particular speed, the inverter’s firing angle can

be decreased to decrease the voltage VI. This

will increase Id and thus the torque. A

simplified torque-speed expression for this

implementation is developed next.

Expression for torque and speed

Voltage Vd (neglecting stator and rotor voltage

drops) is given by:

where s=per unit slip, VL= stator line voltage and

n1=stator-to-rotor turns ratio. The inverter dc

voltage VI is given by:

1

1.35 Ld

sVV

n

Expression for torque and speed

The inverter dc voltage VI is given by:

where n2=transformer turns ratio (line side to inverter

side) and =inverter firing angle.

2

1.35 cosL

I

VV

n

Expression for torque and speed(cont’d)

For inverter operation, /2<<. In steady state

Vd=VI (neglecting losses in inductor)

The rotor speed r is given by:

if n1=n2

1

2

cosn

sn

1

2

(1 ) (1 cos ) (1 cos )r e e e

ns

n


Thus rotor speed can be controlled by controlling

inverter firing angle, .

At =, r=0 and at =/2 , r=e.


Neglecting losses, the power equations can

be written as

Where =air gap power, =mechanical

output power, P= number of poles

2(1 s)P (1 s)

g I d

m g e m e e

sP V I

P T TP

gP mP

Expression for torque and speed (cont’d)

We know that the torque

The torque may be expressed as:

1

1.35

2L

e d

e

VPT I

n

2

g

e

e

PPT

The below figure shows the torque-speed curves at

different inverter angles.


At zero speed (s=1) the motor acts as a

transformer and all the real power is transferred

back to the line (neglecting losses). The motor

and inverter only consume reactive power.

At synchronous speed (s=0) the power factor is

the lowest and increases as slip increases. The

PF can be improved close to synchronous

speed by using a step-down transformer. The

inverter line current is reduced by the

transformer turns ratio -> reduced PF.


A further advantage of the step-down transformer

is that since it reduces the inverter voltage by the

turns ratio, the device power ratings for the

switching devices in the inverter may also be

reduced.

AC Equivalent Circuit of Static Kramer Drive(cont’d)

The per-phase equivalent circuit derived from

these equations (referred to the rotor) is shown

below:

Torque Expression

The average torque developed by the motor =

total fundamental air gap power

synchronous speed of motor

where Pgf’ = fundamental frequency per-phase

air gap power.

' 2

3 32 2

gf rf A

e

e

P I RP PT

s

Torque Expression (cont’d)

The torque equation in term of circuit

parameters

'2

22

' '

32

s Ae

Ae s ls lr

sV RPT

RsR sX sX

s

Static Scherbius Drive

The static Scherbius drive overcomes the

forward motoring only limitation of the static

Kramer drive.

Regenerative mode operation requires the slip

power in the rotor to flow in the reverse

direction. This can be achieved by replacing the

diode bridge rectifier with a thyristor bridge. This

is the basic topology change for the static

Scherbius drive from the static Kramer drive.

Static Scherbius Drive (cont’d)

Modes of Operation

Four modes of operation of a Scherbius drive

Mode 1: Subsynchronous motoring

Mode 2: Supersynchronous motoring

Mode 3: Subsynchronous regeneration

Mode 4: Supersynchronous regeneration

Mode-1:Subsynchronous motoring

Identical to Static Kramer system

Stator I/P or air gap power(Pg)

is +ve

Slip power (sPg) is +ve and

Return back to line

Line supplies Pm=(1-s)Pg consumed

by the shaft

Slip frequency current creates RMF in the same

direction as in the stator

Mode 3: Subsynchronous regeneration

The shaft is driven by load

mechanical energy converted into electrical

energy and pumped out of stator

With –ve torque, mech. Power i/p Pm increases

with speed

Slip is +ve and Pg is –ve

-ve slip power is fed to the rotor

Mode 2:Supersynchronous motoring

Speed increases beyond synchronous speed

Slip is –ve

Slip power absorbed by the rotor

The phase sequence of slip frequency is reversed

so RMF is opposite to that of stator

Mode 4: Supersynchronous regeneration

Pg remains constant but additional mech power i/p is

reflected as slip power o/p

Cycloconverter phase sequence is now reversed so

that the rotor field rotates in opposite direction


One of the limitations of the previous topology is

that line commutation of the machine-side

converter becomes difficult near synchronous

speed because of excessive commutation angle

overlap. A line commutated cycloconverter can

overcome this limitation but adds substantial

cost and complexity to the drive.

(a) Subsynchronous motoring (b) Subsynchronous regeneration

(c) Supersynchronous motoring (d) Supersynchronous regeneration


Another approach is to use a double-sided PWM

voltage-fed converter system as shown below:

AC motor Drives are used in many industrial and domestic ... · application, such as in conveyer, lift, mixer, escalator etc. INDUCTION MOTOR DRIVES Three-phase induction motor are

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