Overmodulation and Field Weakening in Direct
Torque Control of Induction Motor Drives
N.R.N. Idris and A.H.M. Yatim
Md Zarafi Ahmad
Department of Electrical Power Engineering
Universiti Tun Hussien Onn Malaysia
Batu Pahat, Johor MALAYSIA
Department of Energy Conversion,
Faculty of Electrical Engineering,
Universiti Teknologi Malaysia,
Johor, MALAYSIA.
Abstracts - During transient states, for instance during
acceleration and deceleration, the inverter used in an induction
motor drive normally operates in overmodulation in order to
efficiently utilize the DC-link voltage. Beyond the based-speed,
the flux is normally reduced proportionally with speed to extend
the speed range of the drive system. The capability of the
induction motor drive under overmodulation and field
weakening modes are important, especially in electric vehicle
applications, where the available power is limited and the speed
range needs to be increased to avoid the use of the mechanical
gears. This paper presents the performance of the direct torque
control (DTC) of an induction motor drive under the
overmodulation and field weakening conditions for constant
frequency torque controller-based DTC drive. The results
obtained showed that the drive system is capable of operating in
overmodulation and field weakening regions without resolving
to the common approach of space vector modulation (SVM)
based approach.
Cupper\A/
l
Te,ref
COKRLLER
T
4
Te
Clower
c
Index Terms- AC Drives, direct torque control, constant torque
controller, overmodulation, field weakening.
0
for
-1
for
Clower
<
Tc
upper
< Cupper
T < C lower
Fig. 1: Constant frequency torque controller.
INTRODUCTION
Although the constant frequency torque controller has
managed to solve the problems, the DC-link voltage of the
inverter used in DTC motor drives is not efficiently utilized.
For high speed applications, especially in traction or electric
vehicle implementation, a full utilization of the DC-link
voltage is extremely important. Therefore, the operation in
the overmodulation and field weakening (transition to sixstep) regions is required. The common approach that is used
to achieve overmodulation and field weakening condition is
based on the space vector modulation (SVM) technique [6][11]. With regard to the non-SVM-DTC approach, DirectSelf Control (DSC) presented by Depenbrock [2] is capable
to operate in field weakening mode. In DSC, the on-off states
of the three-phase VSI were directly controlled by comparing
the time integrals of line-to-line voltage with respect to the
reference flux. However, below based speed and during
steady state operation, the flux locus is hexagonal thus the
currents contained the low order harmonics.
This paper presents a new approach of overmodulation
and field weakening operation for constant frequency torque
controller-based structure DTC drives. The method only
modifies the torque and flux errors before they are being fed
Direct torque control (DTC) of induction motor drives
becomes popular and widely used in industrial applications
due to a fast and good dynamic torque response as well as
provides a simple control structure. Since it was introduced in
the middle of 1980's [1],[2] many researchers have been
working in this area and several modifications and
improvements have been made in order to overcome the two
major disadvantages of the hysteresis-based of DTC scheme,
namely the high torque ripple and variable switching
frequency of the inverter. Previous proposed techniques to
overcome these problems include the use of variable
hysteresis band, controlled duty cycle technique and use of
space vector modulation (DTC-SVM) based. All these
techniques have managed to improve the performance of
DTC, in the expense of loosing the simple structure of DTC.
In [3]-[5], a simple approach to solve the problems and at the
same time retaining the simple structure of DTC was
introduced. In this approach, a constant frequency torque
controller was used to replace the hysteresis torque controller.
The block diagram and output conditions of the constant
frequencytoqu cotole aeilsrtdnFg. 1.
1 -4244-0743-5/07/$20.OO ©2007 IEEE
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I.
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398
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Fig. 2: The structure of constant frequency torque-based of DTC with flux error status modification.
to the look-up table. Appling this strategy, the simple
structure of DTC is retained. The rest of the paper is
organized as follows. Section II present the new proposedVCO
scheme in overmodulation and field weakening operations of
DTC of IM. Section III describes the operation of DTC
under these conditions. Section IV describes the performance
of DTC under both conditions based on the simulation results4
obtained. Finally, conclusions are given in Section V.
II.
TABLE I
VOLTAGE VECTORS LOOKUP TABLE
SPo
CounterlllEhUll!
cil
lckwise Sec
Inc
STRATEGY
SllE SLECIT
Flux
IncToque
FDec Toque
100
000
110
111
010
000
011
111
Dec
IncToque
110
010
011
001
0
Sec
li
0
Secil
0
SecI
1
000
111
000
111
IDec Toque 111
CIo4uis111I
Flux
IX n ou
FluO ADecUToque
DTC STRUCTURE WITH PROPOSED OVERMODULATION
U
000
111
000
SccS
001
000
101
1 11
SecETI
101
111
100
000
Sec
S11ecVI
1
1
000
111
Basically, the working principle of the proposed DTC
Dec
IncToque
011
001
101
100
110
010
that capable to operate under overmodulation condition is
111 |000 |111 |000|
|Flux |Dec Toque |111 |000
almost similar to the constant torque controller-based [3]-[5].
Fig. 2 shows the block diagram of the proposed
overmodulation strategy of DTC with all the main
components are retained as employed in [1] and [3] -[5]
V4
V13
including the voltage vectors selection table, which is
(110)
/Sector IV Sector l \(010)
tabulated in Table I. The table is constructed based on the \/
/
\
/\5
,\/ _ /
stator flux space vector plane and switching voltage space
vectors controller,
as depicted
in Fig.
3. By employing
thetheconstant
Sector\
Sectorl
(011) '
\ '(10OC)
it gives
a constant
/V w
torque
frequency of
torque
DT
\ /
|
\ /011O
error status q(t). This output signal is fed to the voltage
vectors lookup table to determine the appropriate voltage
SectorVI SectorI (0)
(1)
vectors either to increase or decrease the torque and flux.
During transition from sinusoidal to six-step operation, the
Fi.3Storfuplnadswchgvlaesaevcos
magnitude of the reference flux is changed inversely with the
rotor speed. The flux hysteresis comparator as in [1]-[3] is
used to control the flux error to be within the hysteresis band
and to generate flux error status yr.The flux error status is
III. THE OPERATION OF DTC UNDER OVERMODULATION
then modified by the 'MODIFIED FLUX ERROR STATUS"
AND FIELD WEAKENING MODES
block before it is being fed to the voltage vector selection
Voltage source inverters (VSI) are widely use in AC
table. This block is responsible in performing the operation in
dynamic overmodulation and transition from PWM to sixmotor drive as means for DC to AC electric energy
step waveform in field weakening modes The operations of conversion. In most of the applications, the voltage supplied
DTC in overmodulation and field weakening will be
to the controlled object is corresponds to the limit of dc
discussed in the next section.
bus voltage of the inverter. The maximumpossible output
399
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line in Fig. 5. In the proposed approach, each of six sectors
are further sub-divide into two equal smaller regions, shown
in Fig. 5 named as subsector 1 and subsector 2 for Sector I.
The operation of the proposed method can be divided into
two parts as follows.
voltage of the inverter can be produced when it is operated in
six-step mode. At this particular moment, there is no pulse
dropping on the voltage waveform. Thus, in order to fully
utilize the dc-link voltage, the appropriate control algorithm
under overmodulation and goes to field weakening regions of
drive system is required.
However, the DTC scheme that has been described in
[2]-[4] does not consider the operations in overmodulation
and field weakening modes. Thus, to achieve these
conditions, the inverter output voltage needs to constitute a
cyclic and symmetric sequence of six active voltage vectors.
This in turn will cause the stator flux to move along a
hexagonal path as depicted in Fig. 4.
,
V5 (011)
,'
\
\ /
\/
/ '\
'\
\\
V2 (100)
B. Field weakening and the transition from PWM to six step.
,/ \
In order to control the transition from PWM to six-step
waveform, the locus of the stator flux is control such that it
will gradually change from circular to hexagonal shapes and
this is achieved by controlling the angle oh as shown in Fig. 6.
Within any sector, if the flux angle is less than 0h, only one
voltage vector is selected continuously and the selection is
similar to the overmodulation mode as described above. On
the other hand, if the angle is larger than oh but less than (60°
- oh), the flux is regulated within its hysteresis band; stator
voltage is in the PWM mode. This means that the shape of the
flux is fully hexagonal if oh= 2/6 and the transition from
PWM to six-step is accomplished by gradually controlling the
angle from 0 to 21/6.
V1 (1 01)
v6 (001)
Fig. 4: The inverter switching state vectors and
maximum output voltage boundaries
In the drive system, the circular locus of the stator flux
corresponds to sinusoidal wave of the flux and current which
is shown by the outer line of Fig. 5. The sinusoidal stator
current is obtained through the PWM waveform of the
voltage which is generated through the voltage vector
Sector IV
Sector III
_
X
X\
Dynamic overmodulation
In order to obtain a fast dynamic torque response only
one voltage vector is selected during torque transient. This
means that instead of regulating the flux by selecting two
active vectors alternately, the flux path will follow the
hexagonal shape. For this purpose, the flux selection is made
such in subsector 1, a voltage vector to increase the flux is
selected continuously. On the other hand in subsector 2, a
voltage vector to reduce the flux is selected continuously. By
doing so, the flux will follow the hexagonal shape as
indicated by dashed arrow line in Fig. 5. The selected voltage
vectors produce the largest stator flux tangential components
hence will ensure a fast torque response.
V3 (110)
V4 (010)
,'
A.
4
V5 mA
3
4
3
ff~~~~~~~~~~~~~~~~~~~~~~~~~~ul -
2~~~~~~~~~~~~~~~~eco 11 \V6
V
vI
II~~~~~~~~~~~~~ScorI
Sector
0h
/
Sectir VI
//
/
1
I
; - 1
Subsector
Sector
SectorI
Sector VI
Subsector 2
Fig. 6: Sector I of stator flux plane
Fig. 5: Six sectors of stator flux plane
IV.
selections based on the torque and flux errors and the stator
flux position (either to increase stator flux or to reduce stator
flux and either to increase torque or to reduce torque). The
operation is in fully six-step mode when the flux locus
follows the hexagonal shape as indicated by the dashed arrow
PERFORMANCE OF DTC
The simulation of the DTC induction motor drive with
the proposed overmodulation and field weakening strategies
was performed using MATLAB/SIMULINK simulation
400
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package. The parameters of induction machine as tabulated in
Table II were used in the simulation.
TABLE II
INDUCTION MACHINE PARAMETERS
Stator resistance
5.5 Q,°
Rotor reistance
4.51 Q
Stator self inductance
306.5 mH
Rotor self inductance
306.5 mH
Mutual inductance
291.9 mH
Moment of inertia
0.01 kgm2
Number of poles Number of poles 4
Rated speed
1410 rpm
Vdc
654 V
1 Nm
Load torque
/
15
-0o5 0 05
(Wb)
~~~~~~~~~~~~~~~~~~~~~fsd
b) Hexagon flux locus in field weakening mode
-1.
Fig. 7:
In order to establish a constant switching the frequency
of upper and lower triangular waveforms employed forE
constant torque controller is set at 20 kHz with a peak-topeak of 100 units. For PI torque controller, the gain value of
Kp and Ki are restricted to ensure the absolute slope of the
output signal, T, does not exceed the absolute slope of
triangular carrier [4]. Thus, the corresponding gain
parameters for this setting were 57 and 3630 respectively [5].
The magnitude of stator flux reference is set at its rated value
which is 1.2 Wb and the stator flux is restricted within its
hysteresis band of 0.05 Wb.
The results from the simulation show that at the steady
state condition and operated below its rated speed, the stator
flux locus trajectories of the machine is circular as depicted in
Fig. 7(a). At this moment the voltage vectors are switched
between two active and zero vectors. The machine capable to
operate beyond the base speed when the DTC is operated in
the field weakening mode where only two active voltage
vectors are switched in each sector of the stator flux. At this
particular moment, the flux locus trajectories are in hexagonal |
shape as shown in Fig. 7(b). In the field weakening region,
the magnitude of flux reference is weakened proportionally to
the rotor speed. The transition of stator flux magnitude
waveforms from sinusoidal (PWM) to field weakening region
(six-step) and the stator flux weakening during transition
region are demonstrated in Fig. 8 and Fig. 9 respectively.
i
o-
-1.5
-1
-0.5
-0.5
0.5
1
'
B O
x
0
|
/
-
,, _
|
/
\)
/
X
021
Time (s)
/l
\\
\\ /
/
\
0624
22
01-2
Flux locus trajectory
r
|
U
0628
|
6 32
03
Fig. 8: Transition of stator flux (yd and yVq) magnitude from
sinusoidal (PWM) to hexagonal (six-step) region.
Stator flux
1.5
x
u
1
..
..
----------
0.5 -
...........
0 16
0.18
0.2
0.22
Time (s)
0.24
....-
0.26
0.28
Fig. 9: Stator flux weakening during transition region.
The transition of the voltage from PWM to six-step
operation is shown in Fig. 10 and clearly indicates the gradual
pulse dropping in the voltage waveform during the transition.
Fig. 11 shows the magnitude of the current within transition
region. The torque response with dynamic overmodulation
during torque transient has improved as shown in Fig. 12.
From the figure, it can be seen that the torque response is
faster
1
-1
than
the
one
without
the
dynamic
overmodulation
osLmode. This is because only one active voltage vector is
applied rather than two active voltage vectors as for the case
without the dynamic overmodulation.
1.5
fsd (Wb)
a) Circular flux locus
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REFERENCES
Soo
3
200 ]l
|
aOk
> 200
^
l
t
t
[1] I. Takahashi and T. Noguchi, "A new quick-response and
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~~~~~~~~~~~~~~~~~Sept.
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t | t t Al
100
l
>
-300 |
|
-400 *
_,
-500
0.1
0.12 0.14
11
0.16
11
|
|
0.18
0(2
0.22
l l 11 1l
=, " u H t
0.24 0.26 0.28
Fig. 10: Voltage transition from PWM to six-step
10
8
~~~~~~~~~\
~~~~2001
^ 2 0 | / /~ /N\|
g | Tj
[4] N.R.N. Idris, A. H. M. Yatim, N. D. Muhamad and T. C.
\
\ /
Ling, "Constant frequency torque and flux controllers for
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°-4F
\ I
u
J
g
\ J/
for the 34th IEEE Power Electronics Specialist
-8 0
v
l
-16
Conference PESCO3, Acapulco, Mexico June 2003.
0 26
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0 2
0 2E
0_22
0_24
Time (s)
[5] N.R.N.Idris, C.L. Toh, and M.E. Elbuluk, "A New
Torque and Flux Controller for Direct Torque Control of
Fig. 11: Current transition from sinusoidal operation to field
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z
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0ZDF°
_10k
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ft,,f{,/
-15 F
{?
Without
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0.1
0.1005
0.101
0.1015
20.099
0.0~915
Time (s)
Fig. 12: Dynamic torque response with and without dynamic
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-20
V.
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vrouainsrtg
ple
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CONCLUSIONS
In this paper, the potential and performance of constant
frequency torque controller DTC drive under overmodulation
and field weakening modes has been presented. With simple
modifications on the flux error status, the drive can be
operated in dynamic overmodulation and field weakening
regions. With the proposed strategies, the use of SVM is
avoided thus retaining the simple control structure of DTC.
The simulation results showed that good dynamic torque
response and smooth transitions from PWM to six-step mode
weeahivd
were
achieved.
402
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