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Field-Oriented Control of

Induction Machine

Dr. Nik Rumzi Nik Idris

Department of Energy Conversion,

Faculty of Electrical Engineering,

Universiti Teknologi Malaysia

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IM is superior to DC machine with respect tosize, weight, inertia, cost, speed

Why FOC ?

DC motor is superior to IM with respect to easeof control High performance with simple control due de-coupling

component of torque and flux

FOC transforms the dynamics of IM to becomesimilar to the DC motors decoupling thetorque and flux components

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Basic Principles DC machine

Current in

Current out

a

f

By keeping flux constant,torque can be controlled

by controlling armature

current

Te = k IfIa

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Basic Principles of IM

a

b

bc

c

Stator current produce statorflux

s r

Interaction between stator

and rotor fluxes produces

torque

Space angle between stator

and rotor fluxes varies with

load, and speed

Stator flux induces rotor

current produces rotor

flux

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FOC of IM drive

Torque equation :

sse i

2

p

2

3T

sr

r

me i

L

L

2

p

2

3T

In d-q axis :

)ii(L

L

2

p

2

3T sdrqsqrd

r

me

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FOC of IM drive

In d-q axis :

)ii(L

L

2

p

2

3T sdrqsqrd

r

me

Choose a frame such that:

rrdr

0rrq

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FOC of IM drive

Choose a frame such that:

rrdr

0rrq

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FOC of IM drive

)ii(L

L

2

p

2

3T sdrqsqrd

r

me

Choose a frame such that:

rrdr

0rrq

qs

ds

si

r

sqi

rq

sdi rd

As seen by stator reference frame:

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FOC of IM drive

r

sqr

r

me iL

L

2

p

2

3

T

si

Choose a frame such that:

rrdr

0rrq

qs

ds

r

dr

qr

rsdi

r

sqi

)ii(L

L

2

p

2

3

T sdrqsqrdr

m

e

Rotating reference frame:

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FOC of IM drive

To implement rotor flux FOC need to know rotor flux position:

(i) Indirect FOC

grrg

grg

s

r

rmgr

r

r )(jdt

di

L

RL

L

R0

rsliprrsqrsdr

rmr

r

r )(jdt

djii

L

RL

L

R0

Synchronous speed obtain by adding slip speed and rotor speed

Rotor voltage equation:

g

rrg

g

rg

rr )(jdt

diR0

gsm

grr

gr iLiL

Rotor flux equation:

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FOC of IM drive - indirect

dt

di

L

RL

L

R0 rrsd

r

rmr

r

r

d component

rslipr

sq

r

rm )(i

L

RL0

q component

rsliprrsqrsdr

rmr

r

r )(jdt

djii

L

RL

L

R0

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FOC of IM drive - indirect

dt

di

L

RL

L

R0 rrsd

r

rmr

r

r

d component

rslipr

sq

r

rm )(i

L

RL0

q component

rsliprrsqrsdr

rmr

r

r )(jdt

djii

L

RL

L

R0

m

*

rsd

L*i r

r

sq

r*r

rmslip i

L

RL)(

m

r

r

*e

sqL

L

p3

T4*i r

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FOC of IM drive - indirect

T*

*

2/3

1/s

irsq*

irsd*

isq*

isd*

ia*

ib*

ic*

CC

VSI

slip r

+ +

Rotating frame Stationary frame

m

*

rsd

L*i r

m

r

r

*e

sqL

L

p3

T4*i r

r

sq

r

*

r

rmslip i

L

RL)(

ej

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FOC of IM drive

g

rrr

s

r

rmr

r

r jdt

di

L

RL

L

R0

(ii) Direct FOC

Rotor flux can be estimated by:

Rotor flux estimated from motors terminal variables

sr

r

me i

L

L

2

p

2

3T

Express in stationary frame

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FOC of IM drive

grr

rs

r

rmr

r

r jdt

di

L

RL

L

R0

(ii) Direct FOC

)j(jdt

)j(di)jii(

L

RL)j(

L

R0 rqrdr

rqrd

sqsd

r

rmrqrd

r

r

dtiLRLLR rqrsdrrm

rd

r

rrd dtiLRLLR rdrsqr

rmrq

r

rrq

d q

rd

rq

2rq

2

rdr

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FOC of IM drive - direct

T*

r*2/3

isq*

isd*

ia*

ib*

ic*

CC

VSI

TC

FC

irsq*

irsd*ej

Te

r

sr

r

me i

L

L

2

p

2

3T

grr

rs

r

rmr

r

r jdt

di

L

RL

L

R0

Rotating frame Stationary frame