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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)
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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 ifthe amplifier contains
switches (eg. inverters)
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 4
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Switching Control
AmplifierPlant
G(s)
SwitchingController
Continuous Control
AmplifierPlant
G(s)PI
Continuous
Controller Limiter
Switching Control
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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
Dr. Ungku Anisa, July 2008 6EEEB443 - Control & Drives
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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
Dr. Ungku Anisa, July 2008 7EEEB443 - Control & Drives
Sa
Sb
Sc
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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
*
Pulse Width
Modulation
Sinusoidal PWM Voltage Source
Inverter
Dr. Ungku Anisa, July 2008 8EEEB443 - Control & Drives
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 9
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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:
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 10
)()()(3
2 2txataxtx cba x (1)
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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
Dr. Ungku Anisa, July 2008 12EEEB443 - Control & Drives
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)
Dr. Ungku Anisa, July 2008 13EEEB443 - Control & Drives
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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
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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
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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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 16
[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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 17
[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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 18
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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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 19
[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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 20
[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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 21
[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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 22
[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
Dr. Ungku Anisa, July 2008 23EEEB443 - Control & Drives
V7 V2 V1 V0
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Space Vector PWM
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 24
[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:
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 25
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).
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 26
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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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
srrs
rs
me
rs
rs
me
LL
LPT
LL
LPT
sin
22
3
22
3
'
'
(19)
(20)
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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)
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 28
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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]
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
Dr. 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)
rds
qs
sr
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Direct Torque Control (DTC)
Rules for Flux Control To increaseflux magnitude:
select non-zero voltage vectors
with misalignment with s(t)not
exceeding 90 To decreaseflux 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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 30
[100]V1
[110]V2[010]V3
[011]V4
[101]V6[001]V5
s(t)
r
ds
qs
sr
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Direct Torque Control (DTC)
Rules for Torque Control To increasetorque:
select non-zero voltage vectors
which acceleratess(t)
To decreasetorque:
select non-zero voltage vectors
which deceleratess(t)
To maintain torque:
select V0 or V7 (zero states) whichcauses s(t)to stop moving
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 31
[100]V1
[110]V2[010]V3
[011]V4
[101]V6[001]V5
s(t)
r
ds
qs
sr
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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 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)
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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:
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
Dr. 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 ? ?
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Direct Torque Control (DTC)
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 34
ssqssdcbadcssdq vvSaaSSV j3
2 2 v
abcsssdq iTi abc
3
1
3
1
00
0
1abcT
(21)
(22)
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Direct Torque Control (DTC)
Implementation3. Flux vector s and torque Te are calculated in the Torque
and Flux Calculatorusing the following equations:
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 35
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)
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Direct Torque Control (DTC)
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.
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 36
Note:s=s
Tm= Te
b= b
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Direct Torque Control (DTC)
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.
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 37
s
sd
s
sqss
1tan (27)
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Direct Torque Control (DTC)
ImplementationSelection of voltage vector in DTC scheme:
Counterclockwise Rotation
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 38
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
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Direct Torque Control (DTC)
ImplementationSelection of voltage vector in DTC scheme:
Clockwise Rotation
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 39
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
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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])
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 40
[100]V1
[110]V2[010]V3
[011]V4
[101]V6[001]V5
s
r
ds
qs
sr
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Direct Torque Control (DTC)
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.