Induction Motor – Direct Torque Control By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering Dr. Ungku

Induction Motor – Direct Torque ControlByDr. Ungku Anisa Ungku AmirulddinDepartment of Electrical Power EngineeringCollege of Engineering

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

OutlineIntroductionSwitching ControlSpace Vector Pulse Width Modulation (PWM)Principles of Direct Torque Control (DTC)Direct Torque Control (DTC) RulesDirect Torque Control (DTC) ImplementationReferences

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

IntroductionHigh 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)Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 3

Switching ControlA subset of sliding mode controlAdvantages:

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

even for small errors)Disadvantage: Noisy, unless switching frequency is very

highFeeding bang-bang (PWM) signal into a linear amplifier is

not advisable. But it is OK if the amplifier contains switches (eg. inverters)


Switching Control

Amplifier Plant G(s)

Switching Controller

Continuous Control

Amplifier Plant G(s)

PI

ContinuousController Limiter

Switching Control

PWM Voltage Source Inverter – single phaseReference current compared with actual

currentCurrent error is fed to a PI controllerOutput of PI controller (vc) compared with

triangular waveform (vtri) to determine duty ratio of switches

vtri

Vdc

qvc

Pulse widthmodulator

PI Controller

iref


Same concept is extended to three-phase VSIva*, 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 variablesPulse widthmodulator

Va*


Vb*


Vc*

Sinusoidal PWM Voltage Source Inverter


Sa

Sb

Sc

+ vc -

+ vb -

+ va -

n

N

Vdc a

b

c

S1

S2

S3

S4

S5

S6

S1, S2, ….S6

va*vb*

vc*

Pulse Width Modulation


Switching signals for the

SPWM VSI

Sinusoidal PWM Voltage Source InverterThree 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 shortedIf 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 OFFSa = 0 if S1 OFF and S4 ON

Total number of states = 8An inverter state is denoted as [SaSbSc]2, eg:

If Sa = 1, Sb = 0 and Sc = 1, inverter is in State 5 since [101]2 = 5Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 9

Space Vector PWMSpace 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 not necessarily has to be sinusoidal


)()()(3

2 2 txataxtx cba x (1)

Space Vector PWMSpace vector of the three-phase stator voltage is:

where va, vb and vc are the phase voltages.If va, vb and vc are balanced 3-phase sinusoidal voltage with

frequency f, then the locus of vs :circular with radius equal to the peak amplitude of the phase

voltagerotates with a speed of 2f


(2) )()()(3

2 2 tvatavtv cba sv

+ 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*


These voltages will be the voltages

applied to the terminals of the induction motor

Space Vector PWMFrom 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 22

3

2

3

2sv

(3)

(4)

(5)

(6)

(7)


Space Vector PWMStator voltage space vector can also be expressed in

two-phase (dsqs frame).

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

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

ssq

ssdcbadc vvSaaSSV j

3

2 2 sv (8)

14

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

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

ssq

ssddcdc

dc

dc

cbadc

vvVV

V

aaV

SaaSSV

j3

1j

3

1

sinjcos13

2

0113

23

2

32

32

2

2

svvS

ds

qs

dcV31

dcV31

15

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

Voltage Vector

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

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

Space Vector PWMDefinition 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 2 adjacent voltage vectors and zero voltage vectors


In general:Within a sampling period T, to synthesize reference voltage vs*, it is

assembled 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*:

Vx is applied for time Tx

Vy is applied for time Ty

Vz is 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 yy

In general:Total sampling time: If close to 0 : Tx > Ty

If close to 60 : Tx < Ty

If vs* is large: more time

spent at Vx, Vy compared

to Vz i.e. Tx + Ty > Tz

If vs* 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 yy

Space Vector PWMIn general, if is the angle

between the reference voltage vs* and Vx (vector to it’s 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 Ty(12)

Vector Vx to the right of vs*

3

*

dcVm sv

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

T

TV x1

T

TV y2

vs*

T T

Vref is sampled

Vref is 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 is sampling period:V1 [100]2 is applied for Tx

V2 [110]2 is applied for Ty

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

T= Tx + Ty + Tz


V7 V2 V1 V0

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 switching frequency 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 Ty

S1

S2S3

S4

S5 S6

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

dsqs frame:


ssdq

ssdq

ssdq Ψiv

dt

dRs

srdq

srdq

srdq

srdq ΨΨiv rr dt

dR j0 '

srdq

ssdq

ssdq iiΨ ms LL

srdq

ssdq

srdq iiΨ '

rm LL

(13)

(14)

(15)

(16)

Direct Torque Control (DTC) – Basic Principles1. Derivative of stator flux is equal to the stator EMF.

Therefore, stator flux magnitude strongly depends on stator voltage.

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

Stator voltage can be changed using the space vectors of the Voltage Source Inverter (VSI).


ssdqs

ssdq

sdq

ssdq R

dt

diveψ

tssdq

ssdq vψ

[100]V1

[110]V2[010]V3

[011]V4

[101]V6[001]V5

(17)

(18)

Direct Torque Control (DTC) – 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

srrsrs

me

rsrs

me

LL

LPT

LL

LPT

sin22

3

22

3

'

'

ψψ

ψψ

(19)

(20)

Direct Torque Control (DTC) – 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)


Direct Torque Control (DTC) – 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] stator voltage 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 voltageDr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 29

[100]V1

[110]V2[010]V3

[011]V4

[101]V6[001]V5

s=V1(t)

s(t)s(t+t)

r

ds

qs

sr

sr

Direct Torque Control (DTC) – Rules for Flux Control

To increase flux magnitude:select non-zero voltage vectors

with misalignment with s(t) not exceeding 90

To decrease flux magnitude:select non-zero voltage vectors

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

Direct Torque Control (DTC) – Rules for Torque Control

To increase torque:select non-zero voltage vectors

which acceleratess(t)

To decrease torque:select non-zero voltage vectors

which deceleratess(t)

To maintain torque:select V0 or V7 (zero states) which

causes s(t) to stop moving


[100]V1

[110]V2[010]V3

[011]V4

[101]V6[001]V5

s(t)

r

ds

qs

sr

Direct Torque Control (DTC) – Rules for Flux and Torque Control

The dsqs plane can be divided into six 60-wide sectors (S1 to S6)

Ifs is in sector Skk+1 voltage vector

(Vk+1) increases s

k+2 voltage vector (Vk+2) decreases s

Example: heres is in sector 2 (S2)V3 increases s

V4 decreases s Dr. 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)

Direct Torque Control (DTC) – Rules for Flux and Torque ControlStator 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) doesn’t affect s but reduces TeDr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 33

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

s -

Te ? ?

Direct Torque Control (DTC) – Implementation1. DC voltage Vdc and three phase stator currents iabcs are

measured2. vsdq

s and current isdqs are determined in Voltage and Current

Vector Synthesizer by the following equations:

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


ssq

ssdcbadc

ssdq vvSaaSSV j

3

2 2 v

abcsssdq iTi abc

3

13

1

00

0

1abcT

(21)

(22)

Direct Torque Control (DTC) – Implementation3. Flux vector s and torque Te are calculated in the Torque

and Flux Calculator using the following equations:


dt ssds

ssd

ssd R ivψ

dt ssqs

ssq

ssq R ivψ

ssq

ssd

ssd

ssqe ii

PT ψψ

22

3

22 ssq

ssds ψψψ

(23)

(24)

(25)

(26)

Direct Torque Control (DTC) – Implementation4. Magnitude of s 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

Direct Torque Control (DTC) – Implementation7. Selection of voltage vector (i.e. inverter state) is based on:

values of b 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.Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 37

ssd

ssq

ss ψψ

ψ 1tan (27)

Direct Torque Control (DTC) – 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 V1

S4 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, V3 and V5 • V7 always follows V2, V4 and V6

Direct Torque Control (DTC) – 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 V1

S4 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, V3 and V5 • V7 always follows V2, V4 and V6

b 1 0

bT 1 0 -1 1 0 -1

S2 V3 V0 V1 V4 V7 V6

Direct Torque Control (DTC) – 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

Direct Torque Control (DTC) – Implementation

EEEB443 - Control & Drives 41

Flux controlloop

Torque controlloop

Eq. (21) &(22)

Eq. (23) , (24) &(26)

Eq. (25)

Eq. (27)

Note:s=s

Tm= Te

b= b

a = Sa

b = Sb

c = Sc vi = Vdc

vs= vsdqs

iis= isdqs

ds=sds

qs= sqs

Based on Table in Slides 37 or 38

ReferencesTrzynadlowski, 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.


Documents

Induction Motor – Direct Torque Control By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering Dr. Ungku