Induction Motor Drive - University of New South Wales Section 5 - Induction... · Induction Motor...

Induction Motor Drive

ELEC4613 – Electric Drive Systems

1. Brief review of IM theory.

2. IM drive characteristics with:

• Variable input voltage

• Variable rotor resistance

• Variable rotor power

• Variable voltage and variable frequency, VVVF drive (VSI V/f inverter drive)

• Variable current and variable frequency, VCVF drive (CSII/f inverter drive)

1

Introduction Induction machines are very widely used in industry because of its ruggedness, low maintenance. and also it is cheaper than most other electric motors.

Traditionally, used as‐ constant speed drive (without an inverter) variable speed drive (with slow dynamics)

Recent developments in control techniques and power electronics has made it possible for the Induction Motor (IM) to be used in applications requiring fast dynamic response and decoupled control of torque and flux, like the brushed DC motor.

ELEC4613 – Electric Drive Systems 2

Physical Structure of the Induction Motor

3ELEC4613 – Electric Drive Systems

Stator and Rotor

3-phase Sinusoidally Distributed Stator winding

Cage rotor Wound rotor


Working Principle

Rotating Magnetic Field

rev/sec; 1 1syn

2 fp p mech rad/sec

rot 2N f / p rev/sec; 2 2rot

2 fp p mech rad/sec

1syn

fNp

3-phase balance current of a certain frequency in three-phase stator windings leads to

Speed of the rotating magnetic field is the synchronous speed,

Because of this rotating field, voltage is induced in the rotor windings (or aluminum bars). The consequent 3-phase current flow in the rotor establishes a rotor field.

Interaction between rotor and stator fields will produce the necessary torque to rotate the rotor and load with speed nrot.


IM working principle continued


Slip and slip frequencysyn rot syn1 rot

syn syn

N Ns

N

Slip,

r 1 1 2f sf f f

s = 1 when the rotor is at standstill.s = 0 when the motor runs at synchronous speed.s 0.025 – 0.07, normally. The slip frequency, sf1, is thefrequency of the voltage and current induced in the rotor.

ˆ ˆ. .2 r r r r r 1E 4 44N f 4 44N sf

Slip frequency,

Rotor induced voltage/phase:


Rotor voltages and currents are at the slip frequency sf1.

The Rotor Circuit

8

I2 sX2

sE2 R2

I2 X2

2R 1 ss

E2

R2

(b) (c)

I2 X2

2RsE2

(a)


'2X

'2R 1 s

s

'2R

'1 2 2E aE E

A

A’

' 22

IIa

' 22 2R a R ; ' 2

2 2s tan dstillX a X

'1 2 2E aE E

' 22

IIa

Rotor circuitReferred to

stator

At slip frequency At stator frequency

Mechanical load

The approximate equivalent circuits

' '

' 2 2 22

' '2

21

2 222 1

R 3sR EP = 3I =s R + s L

'

' 2 ' ' 2 22 2 2 2 2

13 3 1o

R sP P I R I s P

s

Total Rotor Power: W

Developed Output Power:

R1 X1

V1

I1

Im

Xm

Ic

Rc

'2R

'2R 1 s

s

' 22

IIa

'2X

'1 2 2E aE E

A

A’

W


Developed power and torque' 2 '

sl 2 o 2 2 2P P P sP 3I R Slip Power:

Developed torque = Developed output power/mechspeed in rad/sec:

' 2 '2 2o

devrot rot

' 2 '2 2

syn

' 2 ' ' 2 '2 2 2 2

1 1 2

3I R 1 s / sPT2 N 2 N

3I R 1 s / s2 N 1 s

I R 3 pI R3 p2 f s 2 f f

Nm

W

Nm

NmRotor Power Slip PowerSyn Speed Slip Speed


RTh XTh

VTh

I1 '2R

'2R 1 s

s

'2I '

2XA

A’

m 1

Th 221 1 m

X VVR X X

m 1 1Th Th Th

1 1 m

jX R jXZ R jX

R j X X

Note that for Xm >> (R1 and X1); RTh ≈ R1; XTh ≈ X1; andVTh ≈ V1.


Rotor current and torque

2 'Th 2

dev 2' 21 '2Th Th 2

V3 p RTsRR X X

s

' Th2 2'

2'2Th Th 2

VIRR X Xs

Nm

A


IM torque‐speed characteristic with variable voltage


V1 = 1 pu V1 = 0.7 pu

V1 = 0.5 pu

V1 = 1 pu V1 = 0.7 pu V1 = 0.5 pu

0

syn1

Torque, Nm

s = 0

s = 1

s < 0

s = 2syn1

Re-generating Fwd Motoring

Plugging s > 1Rev Motoring

, rad/sec

P T

Braking of an IM drive with plugging


Note: Operation with high slip causes high power loss; may lead to high rotor temperature as a consequence.

Two ways:

• By adjusting input frequency below shaft frequency.

• By plugging.

Tmax and slip smT for Tmax

For small slip, 2

Thdev '

1 2

V3 pT sR

For maximum torque, ' 22 '2

Th Th 2mT

R R X Xs

'2

mT 22 'Th Th 2

RsR X X

Slip for maximum torque,

2Th

max 22 '1Th Th Th 2

V3 pT2 R R X X

Maximum torque, Nm


Nm

Note that Tmax is independent of'2R

ELEC4613 – Electric Drive Systems 16

IM torque characteristic with

1

T rated T m ax

R 2 increases

T dev

Load T - characteristic

'2R

Induction Motor drives


IM drive with variable supply voltage

max1

V 1 sin 2V22

Variable AC voltage at the mains supply frequency can be obtainedfrom tap-changing transformer, from back-back phase-controlledthyristor converter or from an inverter.


T- characteristics with variable voltage

V 1 = 1 pu V1 = 0.7 p u

V1 = 0.5 p u

0

1

To rq ue , N m

L oa d T =K2

Variable voltage operation at the utility supply (base) frequencyoffers very limited speed range. Pump type loads are suitable;however, high‐slip and very lossy operation is inevitable withreduced supply voltage.


Example 1: Voltage control for a fan or compressor loads

Fan or compressor type load:

2 3o mP T K 1 s 1 s K 1 s

2o2

PP K 1 s1 s

2' 2 'sl 2 2 2P I R sP Ks 1 s

'2 '

2

KsI 1 sR

For maximum Psl : s = 0.33320ELEC4613 – Electric Drive Systems

Example 2: constant load

Constant torque type load:

1o mP T K s

2 1oPP Ks

' 2 '

sl 2 2 2P I R sP Ks '2 '

2

KsIR

Examples 1 & 2 show that, the rotor current or rotor powerloss increases less slowly with slip (or load) for a fan orcompressor type load than for a constant torque type load.


WRIM drive with variable rotor power

WoundRotor IM

AC Mains

VariableResistor

Bank

Slip Rings

3-f DiodeBridge

Rectifier

Slip RingsWound

Rotor IMVariableResistor

AC Mains

3-f DiodeBridge

Rectifier

Slip RingsWound

Rotor IM

VariableResistor

AC Mains

T

Id

Vd

Duty Cycle

D

V1

E2

E

22

T‐ω characteristic with variable rotor resistance

1

Trated Tmax

R2 increases

Tdev

Load T- characteristic

Figure 5.2.4. T‐ characteristic with variable rotor resistance.


IM drive with variable rotor power (slip power control – static Scherbius system)

Id

Vd Vdi

1:nV2V1 V1


T - Id characteristic with control of DC link current

2maxd

3sEV

' 2 '' 2 '' 2 '2 22 2

sl 2 o 2 2 23I R 1 s3I RP P P 3I R sP

s s

Equating the AC and DC powers,

2max dsl 2 d d

3sE IP sP V I

2max d

23E I

P

If the slip power is small compared to the total rotor (or air-gap)power, i.e., for small slip,

2maxo 2 1 2 d

3EP T 2 n T 2 n P I

2 max 2

d d21 1

3E 3pET I I2 n 2 f

dT KI


The rectifier output DC voltage,

Speed control with slip power recovery

2 o sl retP P P P o 2P 1 s P

sl ret

2

P Ps

P

By neglecting the voltage drop across stator impedance, 12

VEa

2max 1

d3sE 3 2 sVV

aThe DC output voltage of rectifier,

2 1di

3 2V 3 2VV cos cosn

From Vd = Vdias cos ;n

Normally, n a. Why?


for > 90

Speed control with slip power recovery

d

Figure 5.2.8.


T

A C M A I N S

re f

ec

I dDC R eactor

FCCSC C C+ +__

2829 August 2017

IM drive with 3‐phase VSI VVVf inverter

29

dAn,1 d

VV m 0.354mV2 2

where m is the depth of modulation


Performance with VVVF supply

1 of f

We assume that the AC supply voltage to the motor is sinusoidal, butof arbitrarily variable amplitude (RMS value V1) and frequency f1.

0 1

for operation from zero to base speed. is higher than 1 foroperation above base speed.

Figure 5.2.1130ELEC4613 – Electric Drive Systems

R1 X1

V1

I1

Im

Xm

'2R

'2R 1 s

s

'2I

'2X

1E

VVVF (or V/f) drive with constant air gap flux

1 1 1 1 1 1 1 1 1 1 1 1 ag 1ˆV R I j L I E R I j L I K f

1 1 1 1 1R I j L IFor operation near base speed, the stator voltage drop: can be neglected, compared to V1.

1 ag 1ˆV K f 1

ag1

VˆKf

Thus, for operation near base speed, constant V/f supply implies operation with constant air‐gap flux.


T-ω characteristic with constant V/f drive

' 1 1 12 ' ' ' '

' '2 2 2 1 21 2 1 2

o1

1 ag' o2 2 2' 2 ' ' 2 '

2 1 2 2 1 2

E V sVI =R R R j2 sf L+ j L + j Ls s

Vsf ˆsf KfIR sf 2 L R sf 2 L

'2

' '2

ˆ 2ag 1

dev 221 2 1

sR K f3pT =R + s L

'1 2

' '1 2

ˆ

2 2

2ag

222

sf R K3p=R + sf L

Nm

With negligible stator impedance drop,


Thus, and Tdev values remain the same for a given sf1, regardlessof f1.

'2I

IM drive with constant V/f ratio

devT

'2I

sf1

fo

f1

f2

f4

no

n1

n2

n3

no

n1

n2

n3f2

f3

I’2

f1

fo

Slip freq, sf1 Slip freq, sf1


Starting with maximum torque, V/f drive

''22

R Xs

For maximum developed power and torque in the rotor circuit'

'2 1 12

1 2 o

R f f Xf f f

'o 2

1 1 2 '2

f Rsf f fX

Note: maximum torque occurs at the same slip frequency for all f1.' '

o 2 21 ' '

2 2

f R RfX 2 L

For maximum torque to occur at zero speed,

2ag o

max '2

ˆ3p K fT

4 X

From 5.3.26 and 5.2.27, Nm


When Tmax is developed,

IM drive with constant V/f ratio

35

fo

V1

f1

gapˆK

Rated V1


Constant max torque and power characteristics

Tdev Nm

Speed, Rad/sec

Rated V1 & fo

Tmax

Figure 5.2.14. T- characteristics under VVVF drive with f1below and above fo.


T‐ characteristics with VSI V/f drive

37

, rad /sec

T , N mT m axT ra ted

S equence: a-b -c

S equence: a-c-b

B ase speed w ith ra ted V 1

and base f1

Q 1Q 2

Q 3 Q 4


V/f drive at low speed1 1 1 1 1 1 1 1 1 1 1 1 ag 1

ˆV R I j L I E R I j L I K f

At low speed, the stator impedance drop: 1 1 1 1 1R I j L Imay not remain negligible compared to V1 or E1. It implies reduction of the air-gap flux , , and consequent reduction of Tdev

ˆ 22 ag 1

dev 221 2 1 2

sR K f3pT =R + s L

38

ag


V/f drive at low speed

Tdev Nm

Speed, Rad/sec

1 increases with negligible stator impedance with stator impedance

Base Speed

Figure 5.3.1. Drooping T- characteristic at low speed with VVVF drive


V/f drive with low frequency voltage boost

fo

Rated V1

low-frequency voltage boost

f1

Vbo

bo 1 1ratedV R I The zero-frequency boost is

Figure 5.3.2. Voltage boost of VVVF drive at low speed


VSI V/f drive controller – open loop

sT11

fSpeed

reference

f1 Reference

V1 Reference

Open‐loop V/f controller


Speed control with an inner slip loop

ag 1' 1 1

2 ' ' 22 '' '2 22 1 21 2 1 2

ˆsK fE VI =R R R sf 2 L+ j L + j Ls s

‐+

*sl

+

V1

f1

Fig 5.3.5. Closed‐loop speed controller with inner slip control42ELEC4613 – Electric Drive Systems

CSI drive structure for IM

AB

CMotorVdc

PWM

PWM

PWM

*ai

*bi

*ci


IM drive with variable I-f supply

I1

Im

jXm

'2R

s

'2I '

2j X

1E

I1A

A’

Figure 5.4.1. Per-phase equivalent circuit with current source input


IM drive with variable I-f supply' 2 '2 2

dev1

3pI RT2 f s

Torque is inversely proportional to slip frequency


IM drive with variable I-f supplyMaximum rotor power and hence developed torque occurs when

'

'2m 2

R X Xs

'2

mT 'm 2

RsX X

'

'2 1 1m 2

1 2 o

R f f X Xf f f

'o 2

1 1 2 'm 2

f Rsf f fX X

For maximum torque to occur at start ' '

o 2 21 ' '

m 2 m 2

f R RfX X 2 L L

'2

'm 2

RX X


Normally, Xm >> X’2 . SmT for CSI drive is much smaller than for VSI.

When Tmax is developed

For starting from standstill with Tmax

IM drive with variable I-f supply contd.

2 2m 1

max 'm 2 o

3p X IT4 X X f

' 2 '2 2

dev1 2

3pI RT2 f f

For a given I1, the rotor current is given by (using current division)'2I

' m 12 '

'2m 2

j X II

R j X Xs

Using the slip condition for maximum torque, '2

mT 'm 2

RsX X

Nm


I-f drive with constant air-gap flux

''22

m 1 ''2

m 2

R j Xs

I IR j X Xs

2' 2 '2 1 2

m 1 2' 2 '2 1 m 2

R 2 sf LI I

R 2 sf L L


I1 for constant air‐gap flux operation

Q4

Q2

+sf1 -sf1

I1

No load I1

0

Q1

Q3

I1 in reverse sequence


I1 at no-load

1 m m ag 1ˆE X I K f 1rated1

ag1 o

VEˆKf f

1ratedm m m m1ag

1 1 o o

VX I X IEˆKf f f f

1ratedm 1,no load

m

VI I

X


Speed-control system block diagram

MI1

f1

ref

+

sl

+

+

I N V

I-RefGen

Figure 5.4.5. Variable current, variable frequency inverter drive scheme.


CSI I/f drive for large IM machines

T1

T1

T3 T5

T4 T6 T2

M

T

ec1 ec2 ec3

C C

C

C C

C

L Inverter Rectifier

AC Mains

FCCI T6

Id

FCCR*

dI


Quasi-square phase current waveforms

T 1

T 3

T 2

T 5

T 4

T 3

T 4

T 2

T 6

T 1

T 6

T 5

T 6

T 1 ia

ib

i c

- I d

+ I d

Figure 5.4.7. Motor current waveforms and thyristor switching states for a current source drive.


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