Induction Motor – Vector Control or Field Oriented Control By M.Kaliamoorthy

Induction Motor – Vector Control or Field Oriented ControlByM.KaliamoorthyDepartment of Electrical Engineering

1

OutlineIntroductionAnalogy to DC DrivePrinciples of Field Orientation ControlRotor Flux Orientation Control

Indirect Rotor Flux Orientation (IRFO)Direct Rotor Flux Orientation (DRFO)

Stator Flux Orientation ControlDirect Stator Flux Orientation (DSFO)

References

2

IntroductionInduction Motor (IM) drives are replacing DC drives

because:Induction motor is simpler, smaller in size, less maintenanceLess costCapability of faster torque responseCapability of faster speed response (due to lower inertia)

DC motor is superior to IM with respect to ease of controlHigh performance with simple control Due to decoupling component of torque and flux

3

Introduction

4

Induction Motor Drive

Scalar Control

•Control of current/voltage/frequency magnitude based on steady-state equivalent circuit model

• ignores transient conditions

• for low performance drives•Simple implementation•Inherent coupling of torque and flux

• Both are functions of voltage and frequency

•Leads to sluggish response•Easily prone to instability

Vector Control or Field Orientation Control

• control of magnitude and phase of currents and voltages based on dynamic model

• Capable of observing steady state & transient motor behaviour

• for high performance drives•Complex implementation•Decoupling of torque and flux

• similar to the DC drive•Suitable for all applications previously covered by DC drives

Analogy to DC Drive• In the DC motor:• f controlled by controlling If

• If same direction as field f

• Ia same direction as field a

• Ia and f always perpendicular and decoupled

• Hence,

• Keeping f constant, Te controlled by controlling Ia

• Ia, If , a and f are space vectors5

f

a

Te = k f Ia

Te = k f Ia

= k’ If Ia sin 90

= k’(If x Ia)

Analogy to DC Motor• In the Induction Motor:

• s produced by stator currents

• r produced by induced rotor currents

• Both s and r rotates at synchronous speed s

• Angle between s and r varies with load, and motor speed r

• Torque and flux are coupled.6

a

b

b’c’

c

sr

Te = kr x s

Analogy to DC Motor• Induction Motor torque equation :

• Compared with DC Motor torque equation:

• Hence, if the angle betweens orr andis is made to be 90, then the IM will behave like a DC motor.

7

ss iψ22

3

PTe

sr iψ22

3

r

me L

LPT

(1)

(2)

(3) afafafe kikIIkT iψ ψ90sin'

Principles of Field Orientation Control

• Hence, if the angle betweens orr andis is made to be 90, then the IM will behave like a DC motor.

8

Achieved through orientation (alignment) of rotating dq frame on r or s

Rotor-Flux Orientation Control

Stator-Flux Orientation Control


9

Rotor-Flux Orientation Control

si

qs

ds

r dr

qr

rsdi

rsqi

)(22

3sdrqsqrd

r

me ii

LLPT

si

qs

ds

sds

qs

Ψssdi

Ψssqi

)(22

3sdsqsqsde iiPT

Stator-Flux Orientation Control


• Summary of field orientation control on a selected flux vectorf

(i.e. either r , s or m):

10

Rotor Flux Orientation Control• d- axis of dq- rotating frame

is aligned with r . Hence,

• Therefore,

11

si

qs

ds

r dr

qr

rsdi

rsqi

rrdr

0rrq

(4)

(5)

r )(22

3sqrd

r

me i

LLPT (6)

= torque producing current

= field producing currentrsdi

rsqi Similar to

ia & if in DC motor

Decoupled torque and flux control

Rotor Flux Orientation ControlFrom the dynamic model of IM, if dq- frame rotates at general

speed g (in terms of vsd, vsq, isd, isq, ird, irq) :

r rotates at synchronous speed s

Hence, drqr- frame rotates at s

Therefore, g = s

These voltage equations are in terms of isd, isq, ird, irq

Better to have equations in terms of isd, isq, rd, rq 12

rq

rd

sq

sd

rrrrgmmrg

rrgrrmrgm

mmgsssg

mgmsgss

rq

rd

sq

sd

iiii

SLRLSLLLSLRLSL

SLLSLRLLSLLSLR

vvvv

')()()(')(

(7)

(8)

Rotor Flux Orientation Control• Rotor flux linkage is given by:• From (9):

• Substituting (8) and (10) into (7) gives the IM voltage equations rotating at s in terms of vsd, vsq, isd, isq, rd, rq:

13

rdqrsdqmrdq iLiL '(9)

sdqr

m

r

rdqrdq i

LL

Li ''

(10)

ψr

ψr

ψr

ψr

ψr

ψr

ψr

ψr

''''0''0''

''''

rq

rd

sq

sd

rrslrmr

slrrrmr

rmrmsssss

rmsrmssss

rq

rd

sq

sd

ii

SLRLLRSLRLLR

LSLLLLSRLLLLLSLLSR

vvvv

(11)

Rotor Flux Orientation Control• Since , hence the equations in rotor flux

orientation are:

14

Note:Total leakage factor =

sl = slip speed (elec.)

(13)

0rrq

ψrψrψrψrψrrd

r

mssqsssdssdssd dt

dLLiLi

dtdLiRv

'

ψrψrψrψrψr

' rdr

mssdsssqssqssq LLiLi

dtdLiRv

ψrψrψrψr

''0 sdr

r

mrdrd

r

rrq iR

LL

dtd

LRv

ψrψrψr

'0 sqr

r

mrdslrq iR

LLv

(12)

(14)

(15)

'

2

1rs

m

LLL

Important equations for Rotor Flux Orientation Control!

Rotor Flux Orientation Control• Let • Using (16), equation (14) can be rearranged to give:

• is called the “equivalent magnetising current” or “field current”

• Hence, from (17): where • Under steady-state conditions (i.e. constant flux):

15

(16)

(18)

(19)

ψrψrψrmrd

r

rmrdsd i

dtd

RLii '

ψrψrmrdmrd iL

ψrmrdi

ψrψrmrdsd ii

ψrψrmrdrsd iSi 1

(17)

r

rr RL '

Rotor Flux Orientation Control• r rotates at synchronous speed s

• drqr- frame also rotates at s

• Hence,

• For precise control, r must be obtained at every instant in time

• Leads to two types of control:– Indirect Rotor Flux

Orientation– Direct Rotor Flux

Orientation16

si

qs

ds

r dr

qr

rsdi

rsqi

r

dt sr

(20)

dq- reference frame orientation angle

Indirect Rotor Flux Orientation (IRFO)

• Orientation angle:• Synchronous speed obtained by adding slip speed and

electrical rotor speed

• Slip speed can be obtained from equation (15):

• Under steady-state conditions ( ):

17

ψr

ψr

ψr

ψrψr

ψrmrdr

sq

rdr

sqmsq

rd

r

r

msl i

iiLiR

LL

'

(21)

(22)

dt sr

dtdt rslsr

ψr

ψr

sdr

sqsl i

i

(23)

ψrψrsdmrd ii

Indirect Rotor Flux Orientation (IRFO) - implementation

Closed-loop implementation under constant flux condition:1. Obtain isd

r* from r* using (16):

Obtain isqr* from outer speed control loop since isq

r*

Tm* based on (6):

Obtain vsdqr* from isdq

r* via inner current control loop.

18

(24)

(25)

m

rdmrdsd Lii

***

ψrψrψr

r

mt

sdt

esq L

LPkikTi

2

ψr*

*ψr*

223 where


Closed-loop implementation under constant flux condition:2. Determine the angular position r using (21) and (23):

where m is the measured mechanical speed of the motor obtained from a tachogenerator or digital encoder.

r to be used in the drqr dsqs conversion of stator voltage (i.e. vsdq

r* to vsdqs* concersion).

19

(26) dt2

dtdt ψr*

ψr**

m

sdr

sqrsls

Pii

r


20

r*

r*

2/3

isqr*

isdr*

vsqs*

vsds*

vas*

vbs*

vcs*

slip r

+

+

Rotating frame (drqr) Staionary frame (dsqs)

Eq. (24)ejr

P/2Eq. (23) m

PWMVSI

+

3/2e-jr

ias

ibs

ics

isds

isqs

PIvsd

r*

PIvsq

r*+PI

+-

isdr

isqr

--

isqr*isd

r*

r

NO field weakening

(constant flux)

2-phase (dsqs ) to 3-phase (abc)transformation

drqr dsqs transformation

IRFO Scheme


drqr dsqs transformation

dsqs drqr transformation

21

ssq

ssd

sq

sd

xx

xx

rr

rr

r

r

cossinsincos

r

r

rr

rr

sq

sdssq

ssd

xx

xx

cossinsincosvsq

s*

vsds*

vsdr*

vsqr*

ejr

e-jr

isds

isqs

isdr

isqr


• 2-phase (dsqs ) to 3-phase (abc) transformation:

• 3-phase (abc) to 2-phase (dsqs ) transform is given by:

where:

and

22

abcabcsdq xTx

sdqabcabc xTx 1

3

13

1

00

01

abcT

23

23

21211

01Tabc

2/3

vsqs*

vsds*

vas*

vbs*

vcs*

3/2

ias

ibs

ics

isds

isqs

Example – IRFO Control of IM

• An induction motor has the following parameters:

23

Parameter Symbol ValueRated power Prat 30 hp (22.4 kW)

Stator connection Delta ()

No. of poles P 6

Rated stator phase voltage (rms)

Vs,rat 230 V

Rated stator phase current (rms)

Is,rat 39.5 A

Rated frequency frat 60 Hz

Rated speed nrat 1168 rpm

Example – IRFO Control of IM ctd.

24

Parameter Symbol Value

Rated torque Te,rat 183 Nm

Stator resistance Rs 0.294

Stator self inductance

Ls 0.0424 H

Referred rotor resistance

Rr’ 0.156

Referred rotor self inductance

Lr’ 0.0417 H

Mutual inductance Lm 0.041 H

Example – IRFO Control of IM ctd.The motor above operates in the indirect rotor field orientation (IRFO)

scheme, with the flux and torque commands equal to the respective rated values, that is r* = 0.7865 Wb and Te* = 183 Nm. At the instant t = 1 s since starting the motor, the rotor has made 8 revolutions. Determine at time t = 1s:

1. the stator reference currents isd* and isq* in the dq-rotating frame2. the slip speed sl of the motor3. the orientation angle r of the dq-rotating frame4. the stator reference currents isd

s* and isqs* in the stationary dsqs

frame5. the three-phase stator reference currents ias*, ibs* and ics*

25

Example – IRFO Control of IM ctd.• Answers:

26

Indirect Rotor Flux Orientation (IRFO) – field weakening

• Closed-loop implementation under field weakening condition:– Employed for operations above base speed– DC motor: flux weakened by reducing field current if

– Compared with eq. (17) for IM:

– IM: flux weakened by reducing imrd (i.e. “equivalent magnetising current” or “field current)

27

ψrψrψrmrd

r

rmrdsd i

dtd

RLii '

ff

ff

f

f idtd

RL

iRv

imrd*

r

imrd (rated)

r (base)

Indirect Rotor Flux Orientation (IRFO) – field weakening implementation

28

r*

imrd r *

isqr*

isdr* vsq

s*

vsds*

slip r

+

+

Rotating frame (drqr) Staionary frame (dsqs)

ejr

Eq. (22) +

e-jr

isds

isqs

PIvsd

r*

PIvsq

r*+PI

+-

isdr

isqr

--

isqr*

imrdr*

r

With field weakening

+-

imrd r

rS11

r*

Same as in slide 20

PI

Indirect Rotor Flux Orientation (IRFO) – Parameter sensitivity

Mismatch between IRFO Controller and IM may occur due to parameter changes with operating conditions (eg.

increase in temperature, saturation)Mismatch causes coupling between T and producing

componentsConsequences:

r deviates from reference value (i.e. r*)

Te deviates in a non-linear relationship from command value (i.e. Te

*) Oscillations occurs in r and Te response during torque

transients (settling time of oscillations = r)

29

Direct Rotor Flux Orientation (DRFO)

• Orientation angle:

obtained from:1. Direct measurements of airgap fluxes md

s and mq

s

2. Estimated from motor’s stator voltages vsdqs

and stator currents isdqs

Note that:

30

(27)srd

srq

r

1tan

22 srq

srd rψ (28)

Direct Rotor Flux Orientation (DRFO) – Direct measurements md

s & mq

s

1. Direct measurements of airgap fluxes mds and mq

s

mds and mq

s measured using:Hall sensors – fragileflux sensing coils on the stator windings – voltages induced in

coils are integrated to obtain mds and mq

s The rotor flux r is then obtained from:

Disadvantages: sensors are inconvenient and spoil the ruggedness of IM.

31

(29)s

sdqlrs

mdqm

rsrdq iL

LL '

'

Direct Rotor Flux Orientation (DRFO) – Direct measurements md

s & mq

s

32

r*

r*

2/3

tan-1

isqr*

isdr*

vsqs*

vsds*

vas*

vbs*

vcs*

r

+

Rotating frame (drqr) Stationary frame (dsqs)

Eq. (24)ejr

P/2

Eq. (29)m

PWMVSI

3/2e-jr

ias

ibs

ics

isds

isqs

PIvsd

r*

PIvsq

r*+PI

+-

isdr

isqr

--md

s

mqs

rd

s

rq

s

r

r

NO field weakening

(constant flux)

DRFO Scheme

Flux sensing coils arranged in quadrature

Direct Rotor Flux Orientation (DRFO) – Estimated from vsdq

s & isdq

s

2. Estimated from motor’s stator voltages and currentssd

s and sq

s obtained from stator voltage equations:

The rotor flux r is then obtained from:

Disadvantages: dc-drift due to noise in electronic circuits employed, incorrect initial values of flux vector components sdq(0)

33

(30) 0s

sdqs

sdqss

sdqs

sdq iRv

ssdqss

sdqm

rsrdq iL

LL

'

(31)


s & isdq

s

2. Estimated from motor’s stator voltages and currentsThis scheme is part of sensorless drive scheme

using machine parameters, voltages and currents to estimate flux and speed

sdqs calculations (eq. 30) depends on Rs

Poor field orientation at low speeds ( < 2 Hz), above 2 Hz, DRFO scheme as good as IRFO

Solution: add boost voltage to vsdqs at low speeds

Disadvantages: Parameter sensitive, dc-drift due to noise in electronic circuits employed, incorrect initial values of flux vector components sdq(0)

34


s & isdq

s

35

r*

r*

2/3

tan-1

isqr*

isdr*

vsqs*

vsds*

vas*

vbs*

vcs*

r

+


Eq. (24)ejr

P/2

Eq. (31)m

PWMVSI

3/2e-jr

ias

ibs

ics

isds

isqs

PIvsd

r*

PIvsq

r*+PI

+-

isdr

isqr

--sd

s

sqs

rd

s

rq

s

r

r

Eq. (30)vsdq

s

isdqs

NO field weakening

(constant flux)

DRFO Scheme

Direct Rotor Flux Orientation (DRFO) – field weakening implementation

36

r*

imrd r *

isqr*

isdr* vsq

s*

vsds*

r

+


ejr

e-jr

isds

isqs

PIvsd

r*

PIvsq

r*+PI

+-

isdr

isqr

--

With field weakening

+-

imrd r

rS11

r*

Same as in

slide 26 or 29

tan-1

rds

rq

s

r

r

PI

Stator Flux Orientation Control• d- axis of dq- rotating frame

is aligned with s. Hence,

• Therefore,

37

sψsd ψψ s

0ψ sψsq

(32)

(33)

)(22

3sqsde iPT (34)

= torque producing current

= field producing currentΨssdi

Ψssqi

Similar to ia & if in DC motor

Decoupled torque and flux control

si

qs

ds

sds

qs

Ψssdi

Ψssqi

Stator Flux Orientation ControlFrom the dynamic model of IM, if dq- frame rotates at general

speed g (in terms of vsd, vsq, isd, isq, ird, irq):

s rotates at synchronous speed s

Hence, dsqs- frame rotates at s

Therefore, g = s

These voltage equations are in terms of isd, isq, ird, irq

Better to have equations in terms of isd, isq, sd, sq 38

rq

rd

sq

sd

rrrrgmmrg

rrgrrmrgm

mmgsssg

mgmsgss

rq

rd

sq

sd

iiii

SLRLSLLLSLRLSL

SLLSLRLLSLLSLR

vvvv

')()()(')(

(7)

(8)

Stator Flux Orientation Control• Stator flux linkage is given by:• From (9):

• Substituting (8) and (36) into (7) gives the IM voltage equations rotating at s in terms of vsd, vsq, isd, isq, sd, sq:

39

rdqmsdqs iLiL sdqΨ (35)

sdqm

s

mrdq i

LL

Li sdqΨ

(36)

ψs

ψs

ψs

ψs

ψs

ψs

ψs

ψs

1111

00

sq

sd

sq

sd

rrslrssrsl

rslrsrslrs

ss

ss

rq

rd

sq

sd

ii

SSLLSLSL

SRSR

vvvv

(37)

Stator Flux Orientation Control• Since , hence the equations in stator flux

orientation are:

40

(39)

0ψ sψsq

ψsψsψssdsdssd dt

diRv

ψsψsψssdssqssq iRv

ψsψsψsψsψsψs 0 sqsrslsdrsdssdrsdrd iLidtdiL

dtdv

(38)

(40)

(41) ψsψsψsψsψs 0 sdssdrslsqrsqsrq iLidtdiLv

Important equations for Stator Flux Orientation Control!

Stator Flux Orientation Control• Equation (40) can be rearranged to give:

• should be independent of torque producing current• From (42), is proportional to and .• Coupling exists between and .

41

sψsqi sψ

sdψVarying to control torque causes change in

(42) ψsψsψs 11 sqsrslsdsrsdr iLiLSS

sψsdψ sψ

sdi sψsqi

sψsdψ sψ

sqi

sψsqiTorque will not react immediately to

sψsdψ sψ

sqi

Stator Flux Orientation Control – Dynamic Decoupling

• De-coupler is required to – overcome the coupling between and (so that has

no effect on ) – Provide the reference value for

• Rearranging eq. (42) gives:

• can be obtained from outer speed control loop• However, eq. (43) requires

42

(43)

ψssdψ ψs

sqi

r

sqsls

sd

rsd

S

iL

Si

1

1 ψs**ψs*

ψs*

ψs*sdi

ψs*sqi

*sl

ψssqiψs

sdψ


• can be obtained from (41):

• in (43) and (44) is the reference stator flux vector

• Hence, equations (43) and (44) provide dynamic decoupling of the flux-producing and torque-producing currents.

43

(44)ψs*

ψs*ψs*

*

1

sq

sds

sd

rsl i

iL

S

*sl

ψs*sdψ *

sψ

ψssqiψs*

sdi


• Dynamic decoupling system implementation:

44

x

s*

isqs*

isds*+

+sL1

r

S1

r

S

1

r

S

11

x sl*

ψs**sψ

1

sds

iL

isqs*

from speed controller

Stator Flux Orientation Controldsqs- frame also rotates at s

For precise control, s must be obtained at every instant in time

Leads to two types of control:Indirect Stator Flux OrientationDirect Stator Flux Orientation

s easily estimated from motor’s stator voltages vsdq

s and stator currents isdqs

Hence, Indirect Stator Flux Orientation scheme unessential.

45

s

dq- reference frame orientation

angle

si

qs

ds

sds

qs

Ψssdi

Ψssqi

Direct Stator Flux Orientation (DSFO) - implementation

Closed-loop implementation:

1. Obtain isds* from s control loop and dynamic

decoupling system shown in slide 38.

Obtain isqs* from outer speed control loop since isq

r* Te

* based on (34):

Obtain vsdqs* from isdq

s* via inner current control loop.

46

(45)223 where*ψs

*ψs* Pk

ikTi tsdt

esq



2. Determine the angular position s using:

sds and sq

s obtained from stator voltage equations:

Note that:

Eq. (48) will be used as feedback for the s control loop

47

(46)s

sd

ssq

1ψ tan

s

22

sψ ssq

ssd

(47) 0s

sdqs

sdqss

sdqs

sdq iRv (48)



3. s to be used in the dsqs dsqs conversion of stator voltage (i.e. vsdq

s* to vsdqs* concersion).

s estimated from pure integration of motor’s stator voltages equations eq. (47) which has disadvantages of:

dc-drift due to noise in electronic circuits employed incorrect initial values of flux vector components sdq

s(0)

Solution: A low-pass filter can be used to replace the pure integrator and avoid the problems above.

48


49

r*

s*2/3

tan-1

isqs*

isds*

vsqs*

vsds*

vas*

vbs*

vcs*

r

+

Rotating frame (dsqs ) Stationary frame (dsqs )

Decoupling system

ejs

P/2 m

PWMVSI

3/2e-js

ias

ibs

ics

isqs

isds

PIvsq

s*

PIvsd

s*

+

PI+

-

isqs

isds

-

-

sds sq

s

s

s

Eq. (47)vsdq

s

isdqs

+

-PI

Eq. (48)

sds

sqs

+

+

|s|r

S

11

References• Trzynadlowski, A. M., Control of Induction Motors, Academic

Press, San Diego, 2001.• Krishnan, R., Electric Motor Drives: Modeling, Analysis and

Control, Prentice-Hall, New Jersey, 2001.• Bose, B. K., Modern Power Electronics and AC drives, Prentice-

Hall, New Jersey, 2002.• Asher, G.M, Vector Control of Induction Motor Course Notes,

University of Nottingham, UK, 2002.

50

Induction Motor – Vector Control or Field Oriented Control By M.Kaliamoorthy

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Transcript of Induction Motor – Vector Control or Field Oriented Control By M.Kaliamoorthy