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

Induction Motor – Direct Torque Control
By
Dr. Ungku Anisa Ungku Amirulddin
Department of Electrical Power Engineering
College of Engineering
Dr. Ungku Anisa, July 2008
EEEB443 - 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
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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)
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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 if the amplifier contains
switches (eg. inverters)
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Switching Control
Continuous Control
Continuous
Controller
Limiter
PI
Amplifier
Switching Control
Switching
Controller
Amplifier
Plant
G(s)
Plant
G(s)
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
Vdc
Pulse width
modulator
vtri
iref
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PI
Controller
vc
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q
6
Sinusoidal PWM Voltage
Source Inverter
 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
Va*
Pulse width
modulator
Vb*
Sa
Sb
Pulse width
modulator
Vc*
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Pulse width
modulator
Sc
7
Sinusoidal PWM Voltage Source
Inverter
S1
S3
S5
+ va -
Vdc
a
+ vb b
S4
S6
+ vc S2
c
N
va*
vb *
vc*
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Pulse Width
Modulation
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n
S1, S2, ….S6
Switching signals
for the
SPWM VSI
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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
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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:

2
2
x  xa (t )  axb (t )  a xc (t )
3

(1)
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
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Space Vector PWM
 Space vector of the three-phase stator voltage is:

2
v s  va (t )  avb (t )  a 2 vc (t )
3

(2)
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
voltage
 rotates with a speed of 2f
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These voltages
will be the voltages
applied to the
terminals of the
induction motor
Space Vector PWM
S1
S3
S5
+ va -
Vdc
a
+ vb b
S4
S6
+ vc S2
c
We want va, vb and
vc to follow va*, vb*
and vc*
N
va*
vb*
vc*
Dr. Ungku Anisa, July 2008
n
S1, S2, ….S6
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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):



2
2
2
2
v s  van  avbn  a vcn  Vdc S a  aS b  a S c
3
3
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
(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).


2
v s  Vdc S a  aS b  a 2 S c  vsds  jvsqs
3
(8)
 Hence for each of the 8 inverter states, a space vector
relative to the ds axis is produced.
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Space Vector PWM
 Example: For State 6, i.e. [110]2 (Sa = 1, Sb = 1 and Sc = 0)
qs
2
2
v s  Vdc S a  aSb  a Sc
3
vS
1
V
2
3 dc
2
 Vdc 1  a1  a 0
3
2
 Vdc 1  cos 23  j sin 23 
3
1
1
1
 Vdc  j Vdc  vsds  jvsqs
3 Vdc
3
3


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

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ds
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Space Vector PWM
 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.
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
Dr. Ungku Anisa, July 2008
[010] V3
qs
(1/3)Vdc
[110] V2
[000] V0 = 0
[111] V7 = 0
[100] V1
[011] V4
(2/3)Vdc
[001] V5
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[101] V6
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ds
Space Vector PWM
 The dsqs plane can be divided into six 60-wide sectors, i.e. S1 to
S6 as shown below( 30 from each voltage vectors)
S3
[010] V3
S4
[011] V4
S2
[110] V2
[000] V0 = 0
[111] V7 = 0
[100] V1
S1
[001] V5
Dr. Ungku Anisa, July 2008
qs
S5
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ds
[101] V6
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 2
adjacent voltage vectors and zero voltage vectors
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Space Vector PWM
In general:
Within a sampling period T, to synthesize reference voltage vs*, it is
assembled from:
qs
 vector Vx (to the right)
[010] V3
[110] V2 = vy
 vector Vy (to the left) and
vs*
Ty
 a zero vector Vz (either V0 or V7)
Vy
T
Since T is sampling
[011] V4

[100] V1 = vx ds
period of vs*:
 Vx is applied for time Tx
Vx
 Vy is applied for time Ty
Tx
T
 Vz is applied for the rest
of the time, Tz
Dr. Ungku Anisa, July 2008
[001] V5
EEEB443 - Control & Drives
Note:
[000] V0 = 0
[111] V7 = 0
[101] V6
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Space Vector PWM
In general:
(9)
 Total sampling time: T= Tx + Ty + Tz
 If  close to 0 : Tx > Ty
qs
[010] V3
 If  close to 60 : Tx < Ty
 If vs* is large: more time
spent at Vx, Vy compared
[011] V4
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
[001] V5
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[110] V2 =
vy
vs*
Vy

Ty
T
[100] V1 = vx ds
Vx
Tx
T
Note:
[000] V0 = 0
[111] V7 = 0
[101] V6
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Space Vector PWM
Vector Vx to the
qs right of vs*
 In general, if  is the angle
between the reference
voltage vs* and Vx (vector to
it’s right), then:

Tx  mT sin 60 
Ty  mT sin 
where m 
V
Tz = T  Tx Ty
Dr. Ungku Anisa, July 2008
[011] V4
vs*
[110] V2

[100] V1
ds
(11)
vs *
dc
 (10)
[010] V3
3
Note:
[000] V0 = 0
[111] V7 = 0

[001] V5
[101] V6
(12)
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Space Vector PWM
Example:
vs* is in sector S1
[010] V3
qs
[110] V2 = vy
• Vx = V1 is applied for time Tx
• Vy = V2 is applied for time Ty
• Vz is applied for rest
of the time, Tz
[011] V4
[001] V5
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vs*
V 2

Ty
T
[100] V1 = vx
V 1 Tx
T
ds
Note:
[000] V0 = 0
[111] V7 = 0
[101] V6
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Space Vector PWM
Example: vs* in sector S1
 Reference voltage vs* is
sampled at regular
intervals T, i.e. T is
sampling period:
Vref is sampled
 V1 [100]2 is applied for Tx
T= Tx + Ty + Tz
Tz/2 Tx Ty Tz/2
V0 V1 V2 V7
V7 V2 V1 V0
T
Vref is sampled
T
va
 V2 [110]2 is applied for Ty v
b
 Zero voltage V0 [000]2
and V7 [111]2 is applied
for the rest of the time,
i.e. Tz
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EEEB443 - Control & Drives
vc
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Space Vector PWM
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* = 240170  V.
Calculate the time Tx, Ty and Tz required.
• Since  = ______,
[010] V3
vs* is in sector _______
• Vx = ____ is applied for time Tx

Tx  mT sin 60 
S3

qs
[110] V2
S2
[011] V4
• Vy = ___ is applied for time Ty
Ty  mT sin 
• Vz is applied for time Tz
S1
S4
S5
[001] V5
[100] V1
ds
Note:
[000] V0 = 0
[111] V7 = 0
S6
[101] V6
Tz = T  Tx Ty
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Space Vector Equations of IM
 The two-phase dynamic model of IM in the stationary
dsqs frame:


d
v Ri 
Ψ ssdq
dt
d
s
' s
v rdq  0  Rr i rdq 
Ψ srdq  jr Ψ srdq
dt
s
sdq
s
s sdq


(13)
(14)
Ψssdq  Ls i ssdq  Lmi srdq
(15)
Ψsrdq  Lmi ssdq  L'r i srdq
(16)
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Direct Torque Control (DTC) –
Basic Principles
1.
Derivative of stator flux is equal to the stator EMF.
Therefore, stator flux magnitude strongly depends on stator
voltage.


d s
s
ψ sdq  e dq
 v ssdq  Rs i ssdq
dt
(17)
If voltage drop across Rs ignored, change in stator flux can be
obtained from stator voltage applied :
ψ
s
sdq
 t
 v
Stator voltage can be changed using
the space vectors of the
Voltage Source Inverter (VSI).
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
(18)
s
sdq
[010]V3
[011]V4
[001]V5
[110]V2
[100]V1
[101]V6
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Direct Torque Control (DTC) –
Basic Principles
2. Developed torque is proportional to the sine of angle
between stator and rotor flux vectors sr.
3 P Lm
ψ s  ψ r 
Te 
'
2 2 Ls Lr
3 P Lm
Te 
ψ s ψ r sin  sr
'
2 2 Ls Lr
(19)
(20)
Angle ofs is also dependant on stator voltage. Hence,
Te can also be controlled using the stator voltage
through sr.
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Direct Torque Control (DTC) –
Basic Principles
3. 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)
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Direct Torque Control (DTC) –
Basic Principles (example)
[010]V3
[110]V2
[011]V4
[100]V1
qs
[001]V5
[101]V6
s=V1(t)
s(t)
s(t+t)
sr
r
Dr. Ungku Anisa, July 2008
ds
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 voltage
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Direct Torque Control (DTC) –
Rules for Flux Control
qs
[010]V3
[011]V4
[110]V2
[100]V1
s(t)
[001]V5
[101]V6
sr
ds
r
Dr. Ungku Anisa, July 2008
 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
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Direct Torque Control (DTC) –
Rules for Torque Control
qs
[010]V3
[011]V4
[110]V2
[100]V1
s(t)
[001]V5
[101]V6
sr
ds
r
Dr. Ungku Anisa, July 2008
 To increase torque:
 select non-zero voltage vectors
which acceleratess(t)
 To decrease torque:
 select non-zero voltage vectors
which deceleratess(t)
 To maintain torque:
 select V0 or V7 (zero states) which
causes s(t) to stop moving
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Direct Torque Control (DTC) –
Rules for Flux and Torque Control
S3
[010] V3
[011] V4
qs
 The dsqs plane can be
S2
[110] V2
divided into six 60-wide
sectors (S1 to S6)
 Ifs is in sector Sk
s(t)
[100] V1
S4
 k+1 voltage vector
(Vk+1) increases s
 k+2 voltage vector
(Vk+2) decreases s
ds
S1
[001] V5
S5
Dr. Ungku Anisa, July 2008
[101] V6
S6
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 Example: heres is in
Note:
[000] V0 = 0
[111] V7 = 0
sector 2 (S2)
 V3 increases s
 V4 decreases s
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Direct Torque Control (DTC) –
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:
VK
VK+1
VK+2
VK+3
VK+4
VK+5
Vz (V0 or V7)
s






-
Te
?


?



 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 Te
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Direct Torque Control (DTC) –
Implementation
1. DC voltage Vdc and three phase stator currents iabcs are
measured
2. vsdqs and current isdqs are determined in Voltage and Current
Vector Synthesizer by the following equations:
v
s
sdq


2
 Vdc S a  aS b  a 2 S c  vsds  jvsqs
3
i ssdq  Tabc i abcs
where Sa, Sb ,Sc = switching variables of VSI and Tabc
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EEEB443 - Control & Drives
(21)
(22)
1 0 0 
 1 1 
0 3  3 
34
Direct Torque Control (DTC) –
Implementation
3. Flux vector s and torque Te are calculated in the Torque
and Flux Calculator using the following equations:

  v

 dt
ψ ssd   v ssd  Rs i ssd dt
ψ ssq
s
sq
ψs  ψ

 Rs i ssq
s 2
sd
ψ
EEEB443 - Control & Drives
(24)
s 2
sq
3P s s
Te 
isq ψ sd  isds ψ ssq
22
Dr. Ungku Anisa, July 2008
(23)
(25)

(26)
35
Direct Torque Control (DTC) –
Implementation
4. 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
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EEEB443 - Control & Drives
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Direct Torque Control (DTC) –
Implementation
7. Selection of voltage vector (i.e. inverter state) is based on:
 values of b and bT (i.e. output of the flux and torque bangbang controllers )
 angle of flux vector s
s


ψ
1
sq
 s  ψ s  tan 
s 

ψ
sd 

(27)
 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.
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Direct Torque Control (DTC) –
Implementation
[010]V3
Selection of voltage vector in DTC scheme:
 Counterclockwise Rotation
b
1
[011]V4
[100]V1
[001]V5
[101]V6
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
Dr. Ungku Anisa, July 2008
[110]V2
EEEB443 - Control & Drives
To minimize
number of
switching:
• V0 always
follows V1, V3
and V5
• V7 always
follows V2, V4
and V6
38
Direct Torque Control (DTC) –
Implementation
[010]V3
Selection of voltage vector in DTC scheme:
 Clockwise Rotation
b
1
[011]V4
[100]V1
[001]V5
[101]V6
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
Dr. Ungku Anisa, July 2008
[110]V2
EEEB443 - Control & Drives
To minimize
number of
switching:
• V0 always
follows V1, V3
and V5
• V7 always
follows V2, V4
and V6
39
Direct Torque Control (DTC) –
Implementation
(Example)
q
s
[010]V3
 s is in sector S2 (assuming
[110]V2
counterclockwise rotation)
[011]V4
[100]V1
s
 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])
[101]V6
[001]V5
sr
ds
r
b
1
0
bT
1
0
-1
1
0
-1
S2
V3
V0
V1
V4
V7
V6
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
40
Direct Torque Control (DTC) –
Implementation
Based on
Table in
Slides 37 or 38
Flux
control
loop
Eq. (21) &(22)
vs= vsdqs
iis= isdqs
Eq. (25)
ds=sds
qs= sqs
Eq. (27)
Torque
control
loop
Note:
s=s
Tm= Te
b= b
a = Sa
b = Sb
c = Sc
vi = Vdc
Eq. (23) , (24)
&(26)
EEEB443 - Control & Drives
41
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.
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
42