Induction Motor – Vector Control or Field Oriented Control By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering

Induction Motor – Vector Control or Field Oriented ControlByDr. Ungku Anisa Ungku AmirulddinDepartment of Electrical Power EngineeringCollege of Engineering

Dr. Ungku Anisa, July 2008 1EEEB443 - Control & Drives

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

Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 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


Introduction


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 DriveIn 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 vectorsDr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 5

f

a

Te = k f Ia

Te = k f Ia

= k’ If Ia sin 90

= k’(If x Ia)

Analogy to DC MotorIn the Induction Motor:

s produced by stator currentsr produced by induced rotor

currentsBoth 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.

a

b

b’c’

c

sr


Te = kr x s

Analogy to DC MotorInduction 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.

ss iψ22

3

PTe

sr iψ22

3

r

me L

LPT


(1)

(2)

(3) afafafe kikIIkT iψ ψ90sin'

Principles of Field Orientation ControlHence, if the angle betweens orr andis is made to be

90, then the IM will behave like a DC motor.


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

Rotor-Flux Orientation Control

Stator-Flux Orientation Control

Principles of Field Orientation Control


Rotor-Flux Orientation Control

si

qs

ds

r dr

qr

rsdi

rsqi

)(22

3sdrqsqrd

r

me ii

L

LPT

si

qs

ds

sds

qs

Ψssdi

Ψssqi

)(22

3sdsqsqsde ii

PT

Stator-Flux Orientation Control

Principles of Field Orientation ControlSummary of field orientation control on a selected flux vectorf

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


Rotor Flux Orientation Controld- axis of dq- rotating frame is

aligned with r . Hence,

Therefore,

Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

si

qs

ds

r dr

qr

rsdi

rsqi

rrdr

0r

rq

(4)

(5)

r )(22

3sqrd

r

me i

L

LPT (6)

= torque producing current

= field producing currentrsdi

rsqi

Similar to ia & if in DC motor

Decoupled torque and flux control

11

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 Dr. Ungku Anisa, July 2008 12EEEB443 - Control & Drives

rq

rd

sq

sd

rrrrgmmrg

rrgrrmrgm

mmgsssg

mgmsgss

rq

rd

sq

sd

i

i

i

i

SLRLSLL

LSLRLSL

SLLSLRL

LSLLSLR

v

v

v

v

')()(

)(')(

(7)

(8)

Rotor Flux Orientation ControlRotor 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:


rdqrsdqmrdq iLiL ' (9)

sdqr

m

r

rdqrdq i

L

L

Li

''

(10)

ψr

ψr

ψr

ψr

ψr

ψr

ψr

ψr

''''0

''0''

''

''

rq

rd

sq

sd

rrslrmr

slrrrmr

rmrmsssss

rmsrmssss

rq

rd

sq

sd

i

i

SLRLLR

SLRLLR

LSLLLLSRL

LLLLSLLSR

v

v

v

v

(11)

Since , hence the equations in rotor flux orientation are:

Note:Total leakage factor =

sl = slip speed (elec.)

Rotor Flux Orientation Control


(13)

0r

rq

ψrψrψrψrψrrd

r

mssqsssdssdssd dt

d

L

LiLi

dt

dLiRv

'

ψrψrψrψrψr

' rdr

mssdsssqssqssq L

LiLi

dt

dLiRv

ψrψrψrψr

''0 sdr

r

mrdrd

r

rrq iR

L

L

dt

d

L

Rv

ψrψrψr

'0 sqr

r

mrdslrq iR

L

Lv

(12)

(14)

(15)

'

2

1rs

m

LL

L

Important equations for 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):

Rotor Flux Orientation Control


(16)

(18)

(19)

ψrψrψrmrd

r

rmrdsd i

dt

d

R

Lii

'

ψrψrmrdmrd iL

ψrmrdi

ψrψrmrdsd ii

ψrψrmrdrsd iSi 1

(17)

r

rr R

L '

Rotor Flux Orientation Controlr 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 OrientationDirect Rotor Flux Orientation


si

qs

ds

r dr

qr

rsdi

rsqi

r

dt sr (20)

16

dq- reference frame orientation angle

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 ( ):

Indirect Rotor Flux Orientation (IRFO)


ψr

ψr

ψr

ψrψr

ψrmrdr

sq

rdr

sqmsq

rd

r

r

msl i

iiLi

R

L

L

'

(21)

(22)

dt sr

dtdt rslsr

ψr

ψr

sdr

sqsl i

i

(23)

ψrψrsdmrd ii

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.

Indirect Rotor Flux Orientation (IRFO) - implementation


(24)

(25)

m

rdmrdsd Lii

***

ψrψrψr

r

mt

sdt

esq L

LPk

ik

Ti

2

ψr*

*ψr*

22

3 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).



(26) dt2

dtdtψr*

ψr**

m

sdr

sqrsls

P

i

ir


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*

PI

vsqr*

+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

Indirect Rotor Flux Orientation (IRFO) - implementationdrqr dsqs transformation

dsqs drqr transformation


ssq

ssd

sq

sd

x

x

x

x

rr

rr

r

r

cossin

sincos

r

r

rr

rr

sq

sdssq

ssd

x

x

x

x

cossin

sincosvsq

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



abcabcsdq xTx

sdqabcabc xTx 1

3

13

1

00

0

1abcT

23

23

21

211

01

Tabc

2/3

vsqs*

vsds*

vas*

vbs*

vcs*

3/2

ias

ibs

ics

isds

isqs

Example – IRFO Control of IMAn induction motor has the following parameters:


Parameter Symbol Value

Rated 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.


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*


Example – IRFO Control of IM ctd.Answers:


Closed-loop implementation under field weakening condition:Employed for operations above base speedDC 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)

Indirect Rotor Flux Orientation (IRFO) – field weakening


ψrψrψrmrd

r

rmrdsd i

dt

d

R

Lii

'

ff

ff

f

f idt

d

R

Li

R

v

imrd*

r

imrd (rated)

r (base)

Indirect Rotor Flux Orientation (IRFO) – field weakening implementation

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*

PI

vsqr*

+PI+

-

isdr

isqr

--

isqr*

imrdr*


r

With field weakening

+

-imrd

r

28

rS1

1

r*

Same as in slide 20

PI

Indirect Rotor Flux Orientation (IRFO) – Parameter sensitivityMismatch 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 components

Consequences: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)


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:

Direct Rotor Flux Orientation (DRFO)


(27)s

rd

s

rq

r

1tan

22 srq

srd rψ (28)

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.

Direct Rotor Flux Orientation (DRFO) – Direct measurements md

s & mq

s


(29)s

sdqlr

s

mdqm

rs

rdq iLL

L ''

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*

PI

vsqr*

+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

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)

Direct Rotor Flux Orientation (DRFO) – Estimated from vsdq

s & isdq

s


(30) 0s

sdq

s

sdqs

s

sdq

s

sdq iRv

ssdqs

s

sdqm

rs

rdq iLL

L '

(31)

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)


s & isdq

s



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*

PI

vsqr*

+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

r*

imrd r *

isqr*

isdr* vsq

s*

vsds*

r

+


ejr

e-jr

isds

isqs

PIvsd

r*

PI

vsqr*

+PI+

-

isdr

isqr

--


With field weakening

+

-imrd

r

36

rS1

1

r*

Same as in

slide 26 or 29

tan-1

rds

rq

s

r

r

PI

Stator Flux Orientation Controld- axis of dq- rotating frame is

aligned with s. Hence,

Therefore,


sψsd ψψ s

0ψ sψsq

(32)

(33)

)(22

3sqsde i

PT (34)

= torque producing current

= field producing currentΨssdi

Ψssqi

Similar to ia & if in DC motor

Decoupled torque and flux control

37

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 Dr. Ungku Anisa, July 2008 38EEEB443 - Control & Drives

rq

rd

sq

sd

rrrrgmmrg

rrgrrmrgm

mmgsssg

mgmsgss

rq

rd

sq

sd

i

i

i

i

SLRLSLL

LSLRLSL

SLLSLRL

LSLLSLR

v

v

v

v

')()(

)(')(

(7)

(8)

Stator Flux Orientation ControlStator 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:


rdqmsdqs iLiL sdqΨ (35)

sdqm

s

mrdq i

L

L

Li sdqΨ

(36)

ψs

ψs

ψs

ψs

ψs

ψs

ψs

ψs

11

11

0

0

sq

sd

sq

sd

rrslrssrsl

rslrsrslrs

ss

ss

rq

rd

sq

sd

i

i

SSLL

SLSL

SR

SR

v

v

v

v

(37)

Since , hence the equations in stator flux orientation are:

Stator Flux Orientation Control


(39)

0ψ sψsq

ψsψsψssdsdssd dt

diRv

ψsψsψssdssqssq iRv

ψsψsψsψsψsψs 0 sqsrslsdrsdssdrsdrd iLidt

diL

dt

dv

(38)

(40)

(41) ψsψsψsψsψs 0 sdssdrslsqrsqsrq iLidt

diLv

Important equations for Stator Flux Orientation Control!

Equation (40) can be rearranged to give:

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

sψsqi

sψsdψVarying to control torque causes change in

Stator Flux Orientation Control


(42) ψsψsψs 11 sqsrslsdsrsdr iLiLSS

sψsdψ sψ

sdi sψsqi

sψsdψ sψ

sqi

sψsqiTorque will not react immediately to

sψsdψ sψ

sqi

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 loopHowever, eq. (43) requires

Stator Flux Orientation Control – Dynamic Decoupling


(43)

ψssdψ ψs

sqi

r

sqsls

sd

rsd

S

iL

S

i

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.



(44)ψs*

ψs*ψs*

*

1

sq

sds

sd

rsl i

iL

S

*sl

ψs*sdψ

*sψ

ψssqi

ψs*sdi

Dynamic decoupling system implementation:



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 isdq

s

Hence, Indirect Stator Flux Orientation scheme unessential.


s

45

dq- reference frame orientation

angle

si

qs

ds

sds

qs

Ψssdi

Ψssqi

Closed-loop implementation:1. Obtain isd

s* 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.

Direct Stator Flux Orientation (DSFO) - implementation


(45)22

3 where

*ψs

*ψs* P

kik

Ti t

sdt

esq

Closed-loop implementation: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



(46)s

sd

ssq

1ψ tan

s

22

sψ ssq

ssd

(47) 0s

sdq

s

sdqs

s

sdq

s

sdq iRv (48)

Closed-loop implementation:3. s to be used in the dsqs dsqs conversion of

stator voltage (i.e. vsdqs* to vsdq

s* 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

sdqs(0)

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




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/2m

PWMVSI

3/2e-js

ias

ibs

ics

isqs

isds

PIvsq

s*

PI

vsds*

+

PI+

-

isqs

isds

-

-

sds


sqs

s

s

Eq. (47)vsdq

s

isdqs

+

-PI

Eq. (48)

sds

sqs

+

+

|s|r

S

11

ReferencesTrzynadlowski, 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.


Documents

Induction Motor – Vector Control or Field Oriented Control By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering