12 induction motor - direct torque control

7/31/2019 12 Induction Motor - Direct Torque Control

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Induction Motor Direct Torque ControlBy

Dr. Ungku Anisa Ungku Amirulddin

Department of Electrical Power Engineering

College of Engineering

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


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Outline Introduction

Switching Control

Space Vector Pulse Width Modulation (PWM)

Principles of Direct Torque Control (DTC)

Direct Torque Control (DTC) Rules

Direct Torque Control (DTC) Implementation

References

Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 2


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Introduction High performance Induction Motor drives consists of:

Field Orientation Control (FOC)

Direct Torque Control (DTC) Direct Torque Control is IM control achieved through

direct selection of consecutive inverter states

This requires understanding the concepts of:

Switching control (Bang-bang or Hysteresis control)

Space Vector PWM for Voltage Source Inverters(VSI)



4/42

Switching Control A subset of sliding mode control

Advantages:

Robust since knowledge of plant G(s) is not necessary Very good transient performance (maximum actuation even

for small errors)

Disadvantage: Noisy, unless switching frequency is very

high Feeding bang-bang (PWM) signal into a linear amplifier is

not advisable. But it is OK ifthe amplifier contains

switches (eg. inverters)



5/42

Switching Control

AmplifierPlant

G(s)

SwitchingController

Continuous Control

AmplifierPlant

G(s)PI

Continuous

Controller Limiter

Switching Control


6/42

PWM Voltage Source Inverter

single phase Reference current compared with actual

current

Current error is fed to a PI controller

Output of PI controller (vc) compared with

triangular waveform (vtri) to determine

duty ratio of switches

vtri

Vdc

qvc

Pulse widthmodulator

PI

Controlleriref



7/42

Same concept is extended to three-phase VSI

va*, vb* and vc* are the

outputs from closed-loop

current controllers In each leg, only 1 switch is on

at a certain time

Leads to 3 switching variables

Pulse width

modulator

Va*

Pulse width

modulator

Vb*

Pulse width

modulator

Vc*

Sinusoidal PWM Voltage

Source Inverter


Sa

Sb

Sc


8/42

+ vc -

+ vb -

+ va -

n

N

Vdc a

b

c

S1

S2

S3

S4

S5

S6

S1, S2, .S6

va*

vb*

vc

*

Pulse Width

Modulation

Sinusoidal PWM Voltage Source

Inverter


Switching signals

for the

SPWM VSI


9/42

Sinusoidal PWM Voltage Source

Inverter Three switching variables are Sa, Sb and Sc (i.e. one per phase)

One switch is on in each inverter leg at a time

If both on at same time dc supply will be shorted

If both off at same time - voltage at output is undetermined

Each inverter leg can assume two states only, eg:

Sa = 1 if S1 ON and S4 OFF

Sa = 0 if S1 OFF and S4 ON Total number of states = 8

An inverter state is denoted as [SaSbSc]2, eg:

If Sa = 1, Sb = 0 and Sc = 1, inverter is in State 5 since [101]2 = 5



10/42

Space Vector PWM Space vector representation of a three-phase quantities

xa(t), xb(t) and xc(t) with space distribution of 120o apart

is given by:

where:

a = ej2/3 = cos(2/3) +jsin(2/3)

a2 = ej4/3 = cos(4/3) +jsin(4/3)

x can be a voltage, current or flux and does notnecessarily has to be sinusoidal


)()()(3

2 2txataxtx cba x (1)


11/42


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+ vc -

+ vb -

+ va -

n

N

Vdc a

b

c

S1

S2

S3

S4

S5

S6

S1, S2, .S6

va*

vb*

vc*

We want va

, vb

and

vc to follow va*, vb*

and vc*

Space Vector PWM


These voltages

will be the voltages

applied to theterminals of the

induction motor


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Space Vector PWM From the inverter circuit diagram:

van = vaN + vNn

vbn = vbN + vNn

vcn

= vcN

+ vNn

vaN = VdcSa , vbN = VdcSb , vcN = VdcSc

where Sa, Sb, Sc = 1 or 0 and Vdc = dc link voltage

Substituting (3) (6) into (2):

cbadccnbnan SaaSSVvaavv 223

2

3

2 sv

(3)

(4)

(5)(6)

(7)



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Space Vector PWM Stator voltage space vector can also be expressed in

two-phase (dsqs frame).

Hence for each of the 8 inverter states, a space vectorrelative to the ds axis is produced.

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

ssqssdcbadc vvSaaSSV j3

2 2 sv (8)

14


15/42

Space Vector PWM Example: For State 6, i.e. [110]2 (Sa = 1, Sb = 1 and Sc = 0)

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

s

sq

s

sddcdc

dc

dc

cbadc

vvVV

V

aaV

SaaSSV

j3

1j

3

1

sinjcos1

3

2

0113

23

2

32

32

2

2

sv

vS

ds

qs

dcV31

dcV31

15


16/42

Therefore, the voltage vectors for all the 8 inverter states can be

obtained.

Note for states [000] and [111], voltage vector is equal to zero.

Space Vector PWM


[100] V1

[110] V2[010] V3

[011] V4

[001] V5[101] V6

(2/3)Vdc

(1/ 3)Vdc

[000] V0 = 0

[111] V7 = 0

ds

qs

VoltageVector Inverter state[SaSbSc]2

V0 State 0 = [000]2

V1 State 4 = [100] 2

V2 State 6 = [110] 2

V3 State 2 = [010] 2

V4 State 3 = [011] 2

V5 State 1 = [001] 2

V6 State 5 = [101] 2

V7 State 7 = [111] 2


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The dsqs plane can be divided into six 60-wide sectors, i.e. S1 to

S6 as shown below( 30 from each voltage vectors)Space Vector PWM


[100] V1

[110] V2[010] V3

[011] V4

[001] V5 [101] V6

[000] V0 = 0

[111] V7 = 0

ds

qs

S1

S2S3

S4

S5 S6


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Space Vector PWM Definition of Space Vector Pulse Width Modulation

(PWM):

modulation technique which exploits space vectors to

synthesize the command or reference voltage vs* within

a sampling period

Reference voltage vs* is synthesized by selecting 2adjacent voltage vectors and zero voltage vectors



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In general:

Within a sampling period T, to synthesize reference voltage vs*, it isassembled from:

vector Vx (to the right)

vector Vy (to the left) and

a zero vector Vz(either V0 or V7)

Since T is sampling

period of vs*:

Vxis applied for time Tx

Vyis applied for time Ty Vzis applied for the rest

of the time, Tz

Space Vector PWM


[100] V1

[110] V2[010] V3

[011] V4

[001] V5 [101] V6

Note:

[000] V0 = 0

[111] V7 = 0

ds

qs

vs*

= vx

= vy

T

TV xx

T

TV

y

y


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In general:

Total sampling time:

If close to 0: Tx > Ty

If close to 60: Tx < Ty Ifvs* is large: more time

spent at Vx, Vy compared

to Vz i.e. Tx + Ty > Tz

Ifvs* is small: more time

spent at Vz compared

to Vx, Vy , i.e. . Tx + Ty < Tz

Space Vector PWM


[100] V1

[110] V2[010] V3

[011] V4

[001] V5 [101] V6

Note:

[000] V0 = 0

[111] V7 = 0

ds

qs

vs*

= vx

= vy

T= Tx + Ty + Tz (9)

T

TV xx

T

TV

y

y


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Space Vector PWM In general, if is the angle

between the reference

voltage vs* and Vx(vector to

its right), then:

where


[100] V1

[110] V2[010] V3

[011] V4

[001] V5 [101] V6

Note:

[000] V0 = 0

[111] V7 = 0

ds

vs*

60sinmTTx

sinmTTy

(10)

qs

(11)

Tz

= T Tx T

y (12)

Vector Vxto the

right ofvs*

3*

dcVm

sv


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Space Vector PWM


[100] V1

[110] V2[010] V3

[011] V4

[001] V5 [101] V6

Note:

[000] V0 = 0

[111] V7 = 0

ds

qsExample:

vs* is in sector S1

Vx = V1 is applied for time Tx Vy = V2 is applied for time Ty

Vz is applied for rest

of the time, Tz= vx

= vy

TT

V

x

1

T

TV

y2

vs*


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T T

Vrefis sampled

Vrefis sampled

V1

Tx

V2

TyTz/2

V0

Tz/2

V7

va

vb

vc

Space Vector PWMExample: vs* in sector S1 Reference voltage vs* is

sampled at regular

intervals T, i.e. T issampling period:

V1 [100]2 is applied for Tx

V2 [110]2 is applied for Ty

Zero voltage V0 [000]2and V7 [111]2 is appliedfor the rest of the time,i.e. Tz

T= Tx + Ty + Tz


V7 V2 V1 V0


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Space Vector PWM


[100] V1

[110] V2[010] V3

[011] V4

[001] V5 [101] V6

Note:

[000] V0 = 0

[111] V7 = 0

ds

qs

Example:

A Space Vector PWM VSI, having a DC supply of 430 V and a switchingfrequency of 2kHz, is required to synthesize voltage vs* = 240170 V.

Calculate the time Tx, Ty and Tz required.

Vx = ____ is applied for time Tx

Vy = ___ is applied for time Ty

Vz is applied for time Tz

Since = ______,vs* is in sector _______

60sinmTTx

sinmTTy

Tz

= T Tx T

y

S1

S2S3

S4

S5 S6


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Space Vector Equations of IM The two-phase dynamic model of IM in the stationary

dsqs frame:


s

sdq

s

sdq

s

sdq iv dt

d

Rs

srdqsrdqsrdqsrdq iv rrdt

dR j0 '

srdq

ssdq

ssdq ii ms LL

s

rdq

s

sdq

s

rdq ii'

rm LL

(13)

(14)

(15)

(16)


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Direct Torque Control (DTC)

Basic Principles1. Derivative of stator flux is equal to the stator EMF.

Therefore, stator fluxmagnitude strongly depends on statorvoltage.

If voltage drop across Rs ignored, change in stator flux can beobtained from stator voltage applied :

Stator voltage can be changed using

the space vectors of the

Voltage Source Inverter (VSI).


s

sdqs

s

sdq

s

dq

s

sdq Rdt

d

ive

ts

sdq

s

sdq

v

[100]V1

[110]V2[010]V3

[011]V4

[101]V6[001]V5

(17)

(18)


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Basic Principles2. Developed torque is proportional to the sine of angle

between stator and rotor flux vectors sr.

Angle ofs is also dependant on stator voltage. Hence,

Te can also be controlled using the stator voltage

through sr.Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 27

srrs

rs

me

rs

rs

me

LL

LPT

LL

LPT

sin

22

3

22

3

'

'

(19)

(20)


28/42


Basic Principles3. Reactions of rotor flux to changes in stator voltage is

slower than that of stator flux.

Assume r remains constant within short time t

that stator voltage is changed.

Summary DTC Basic Principles:

Magnitude of stator flux and torque directly controlled

by proper selection of stator voltage space vector (i.e.through selection of consecutive VSI states)



29/42


Basic Principles (example)Assuming at time t,

Initial stator and rotor flux are denoted as

s(t) and r

the VSI switches to state [100]

statorvoltage vector V1 generated

After short time interval t,

New stator flux vector s(t+ t) differs

from s(t) in terms of :

Magnitude (increased by s=V1(t)) Position (reduced by sr)

Assumption:Negligible change in rotor

flux vector r within t

Stator flux and torque changed by voltage


[100]V1

[110]V2[010]V3

[011]V4

[101]V6[001]V5

s=V1(t)

s(t)

s(t+t)

rds

qs

sr


30/42


Rules for Flux Control To increaseflux magnitude:

select non-zero voltage vectors

with misalignment with s(t)not

exceeding 90 To decreaseflux magnitude:


with misalignment with s(t)that

exceeds 90 V0 and V7 (zero states) do not

affect s(t), i.e. stator flux stops

moving


[100]V1

[110]V2[010]V3

[011]V4

[101]V6[001]V5

s(t)

r

ds

qs

sr


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Rules for Torque Control To increasetorque:


which acceleratess(t)

To decreasetorque:


which deceleratess(t)

To maintain torque:

select V0 or V7 (zero states) whichcauses s(t)to stop moving


[100]V1

[110]V2[010]V3

[011]V4

[101]V6[001]V5

s(t)

r

ds

qs

sr


32/42


Rules for Flux and Torque Control The dsqs plane can be

divided into six 60-wide

sectors (S1 to S6)

Ifs is in sector Sk

k+1 voltage vector

(Vk+1) increases s

k+2 voltage vector

(Vk+2) decreases s

Example: heres is insector 2 (S2)

V3 increases s

V4 decreases sDr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 32

[100] V1

[110] V2[010] V3

[011] V4

[001] V5 [101] V6

Note:

[000] V0 = 0

[111] V7 = 0

ds

qs

S1

S2S3

S4

S5 S6

s(t)


33/42


Rules for Flux and Torque Control Stator flux vector s is associated with a voltage vector VK

when it passes through sector K (SK)

Impact of all individual voltage vectors on s and Te is

summarized in table below:

Impact of VK and VK+3 on Te is ambiguous, it depends on

whether s leading or lagging the voltage vector

Zero vector Vz (i.e. V0 or V7) doesnt affect s but reduces Te


VK VK+1 VK+2 VK+3 VK+4 VK+5 Vz (V0 or V7)

s -

Te ? ?


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Implementation1. DC voltage Vdc and three phase stator currents iabcs are

measured

2. vsdqs and current isdq

s are determined in Voltage and Current

Vector Synthesizer by the following equations:

where Sa, Sb ,Sc = switching variables of VSI and


ssqssdcbadcssdq vvSaaSSV j3

2 2 v

abcsssdq iTi abc

3

1

3

1

00

0

1abcT

(21)

(22)


35/42


Implementation3. Flux vector s and torque Te are calculated in the Torque

and Flux Calculatorusing the following equations:


dts

sds

s

sd

s

sd R iv

dtssqsssqssq R iv

ssqssdssdssqe iiP

T 22

3

22 s

sq

s

sds

(23)

(24)

(25)

(26)


36/42


Implementation4. Magnitude ofs is compared with s* in the flux control

loop.

5. Te is compared with Te* in the torque control loop.

6. The flux and torque errors, s and Te are fed to

respective bang-bang controllers, with characteristics shown

below.


Note:s=s

Tm= Te

b= b


37/42


Implementation7. Selection of voltage vector (i.e. inverter state) is based on:

values ofb and bT(i.e. output of the flux and torque bang-

bang controllers )

angle of flux vector s

direction of motor rotation (clockwise or counter clockwise)

Specifics of voltage vector selection are provided based on

Tables in Slide 37 (counterclockwise rotation) and Slide 38

(clockwise rotation) and applied in the State Selector block.


s

sd

s

sqss

1tan (27)


38/42


ImplementationSelection of voltage vector in DTC scheme:

Counterclockwise Rotation


b 1 0

bT 1 0 -1 1 0 -1

S1 V2 V7 V6 V3 V0 V5

S2 V3 V0 V1 V4 V7 V6

S3 V4 V7 V2 V5 V0 V1S4 V5 V0 V3 V6 V7 V2

S5 V6 V7 V4 V1 V0 V3

S6 V1 V0 V5 V2 V7 V4

[100]V1

[110]V2[010]V3

[011]V4

[101]V6[001]V5

To minimize

number of

switching:

V0 always

follows V1, V3and V5

V7 always

follows V2, V4

and V6


39/42


ImplementationSelection of voltage vector in DTC scheme:

Clockwise Rotation


b 1 0

bT 1 0 -1 1 0 -1

S1 V6 V7 V2 V5 V0 V3

S2 V5 V0 V1 V4 V7 V2

S3 V4 V7 V6 V3 V0 V1S4 V3 V0 V5 V2 V7 V6

S5 V2 V7 V4 Vv1 V0 V5

S6 V1 V0 V3 V6 V7 V4

[100]V1

[110]V2[010]V3

[011]V4

[101]V6[001]V5

To minimize

number of

switching:

V0 always

follows V1, V3and V5

V7 always

follows V2, V4

and V6


40/42

b 1 0

bT 1 0 -1 1 0 -1

S2 V3 V0 V1 V4 V7 V6


Implementation (Example) s is in sector S2 (assuming

counterclockwise rotation)

Both flux and torque to be

increased (b = 1 and bT = 1)

apply V3 (State = [010])

Flux decreased and torque

increased (b = 0 and bT = 1)

apply V4 (State = [011])


[100]V1

[110]V2[010]V3

[011]V4

[101]V6[001]V5

s

r

ds

qs

sr


41/42


Implementation

EEEB443 - Control & Drives 41

Flux

control

loop

Torque

control

loop

Eq. (21) &(22)

Eq. (23) , (24)

&(26)

Eq. (25)

Eq. (27)

Note:

s=s

Tm= Te

b= b

a = Sab = Sbc = Sc

vi = Vdcvs= vsdq

s

iis= isdqsds=sd

s

qs= sqs

Based on

Table in

Slides 37 or 38


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

Press, San Diego, 2001.

Asher, G.M, Vector Control of Induction Motor Course Notes,

University of Nottingham, UK, 2002.

12 induction motor - direct torque control

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