th
The 5 Student Conference on Research and Development –SCOReD 2007
11-12 December 2007, Malaysia
A Simple Overmodulation Strategy in Direct
Torque Control of Induction Machines
Auzani Jidin, Md. Zarafi Ahmad, N.R.N Idris, Senior Member, IEEE, A.H.M. Yatim, Senior Member,
IEEE
Abstract-- A fast dynamic torque and high speed operations
are so important especially in electric vehicle applications. In
principle, there are two approaches to obtain these conditions.
One is the use of mechanical gears and the other one is the use of
overmodulation strategy. Through overmodulation strategy, the
inverter voltage can be increased beyond its linear modulation
range, thus full utilization of DC-linked voltage is achieved. This
paper presents a simple overmodulation strategy that is wellsuited in a constant frequency torque controller-based of Direct
Torque Control (DTC) of induction motor drives. The simple
overmodulation strategy is constructed based on torque and flux
errors and flux position which are readily available; as required
in conventional DTC scheme. The simulation results 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.
Index Terms-- Constant switching frequency, direct torque
control, induction machine, field weakening, overmodulation.
I. INTRODUCTION
D
IRECT Torque Control (DTC) of induction motor drives
have become increasingly popular in the drives industry
due to simple control structure and it also offers high dynamic
performance of instantaneous electromagnetic torque. Since it
was introduced in the middle of 1980’s [1],[2] many
researchers have shown great interest to make several
modifications and improvements to overcome the two main
disadvantages of a conventional DTC scheme, namely the
high torque ripple and variable switching frequency of the
inverter. For examples, the problems have been solved by the
use of variable hysterisis band [3], controlled duty ratio cycle
technique [4][5] and use of space vector modulation (DTCSVM) based [10]-[13],[15]. However, all these modifications
on the conventional DTC lead to the complex DTC structure.
In [6]-[8], a simple approach to solve the problems was
introduced. In this approach, most of the main components in
the basic structure of DTC are retained except the torque
Auzani Jidin is with Department of Power Electronics and Drives, Faculty
of Electrical Engineering, Universiti Teknikal Malaysia Melaka, Locked Bag
1200, Hang Tuah Jaya, Ayer Keroh 75450 Malacca. (e-mail:
[email protected]).
Md. Zarafi Ahmad is with Department of Electrical Power Engineering,
Universiti Tun Hussien Onn Malaysia, Batu Pahat, Johor.
Nik Rumzi Nik Idris and Abdul Halim M. Yatim are with Department of
Energy Conversion, Faculty of Electrical Engineering, Universiti Teknologi
Malaysia, 81310 UTM, Johor. (email: [email protected])
hysterisis controller component. The torque hysterisis
controller is replaced with a constant frequency torque
controller. Thus, a constant switching frequency as well as
torque ripple reduction are obtained. The block diagram and
output conditions of the constant frequency torque controller
are illustrated in Fig. 1.
C p− p
Cupper
+
Te,ref +
−
−
1
+
PI
Controller
(Kp & Ki)
Tc
Te
+
q (t )
+
−1
−
C lower
C p− p
 1 for Tc ≥ Cupper

q(t ) =  0 for Clower < Tc < Cupper
− 1 for T ≤ C
c
lower

Fig. 1 Constant frequency torque controller
However, the DTC with a constant frequency torque
controller proposed in [6]-[8] is not capable to operate the
motor under overmodulation and field weakening operations.
For this reason the DC-link voltage of the inverter used in the
DTC scheme is not efficiently utilized. A full utilization of the
DC-link voltage is very important to permit high speed
operation (beyond its based speed) and fast dynamic torque
response in traction and electric vehicle implementations. In
practice, wide speed range operations (beyond the base speed)
remove the necessity of using mechanical gears. The
overmodulation strategy will efficiently utilized the available
dc-link voltage of inverter by appropriately controlling the
switching states of inverter.
In DTC, the common approach of the overmodulation
strategy is implemented in conjunction with space vector
modulation (SVM). Through SVM, linear modulation and
overmodulation ranges are clearly defined in term of
modulation index [9]. The linear control from PWM to six-
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step operations can be obtained by continuously controlling
the single reference space voltage vector. By doing so, the on
and off durations of active and zero voltage vectors perform
the desired inverter output voltage in average meaning. Since
the reference space voltage vector is unavailable in DTC, it
can be derived by the use of either dead beat control [11],[15]
and predictive stator flux control [13]. These schemes result
in satisfactory performance in overmodulation and field
weakening conditions but at the penalty of higher
computational burden. Alternatively, the Direct self control is
proposed by Depenbrock which is capable to operate in field
weakening mode [2]. However, the low order currents
harmonics are produced (since the flux locus is hexagonal)
even at below based speed and steady state operations.
To obtain the fastest dynamic torque response, the
overmodulation stategy with only one active voltage vector is
selected during torque transient as proposed in [15]. However
the scheme results in expense of losing the simple structure of
DTC.
This paper presents a simple approach of overmodulation
which is capable to operate under field weakening operation
and to give the fastest dynamic torque response. The proposed
overmodulation strategy uses a constant frequency torque
controller-based structure DTC drive as proposed in [6]-[8].
The rest of the paper is organized as follows. Section II
presents the simple overmodulation strategy in DTC structure
of IM. Section III describes the operation of the simple
overmodulation strategy. Section IV describes the
performance of DTC under overmodulation and field
weakening modes based on simulation results obtained.
Finally, conclusions are given in Section V.
error status q(t ) and ‘modified flux error status’ ψ − . The
flux hysterisis comparator as in [6]-[8] is used to control the
flux error to be within the hysterisis band and to generate flux
error status ψ + . The flux error status ψ + is then modified by
the ‘MODIFIED FLUX ERROR STATUS’ block before it is
being fed to the voltage vectors selection table. The
‘MODIFIED FLUX ERROR STATUS’ block is responsible
in performing the operation in dynamic overmodulation and
transition from PWM to six-step waveform in field weakening
mode.
Te*
∆Te
+
Constant
Torque
Controller
Flux
Hysterisis
Comparator
+
ψ *s
-
Unlike in FOC, the DTC scheme offer simple control
structure wherein the torque and flux can be separately
controlled using hysterisis comparators. However, the
hysterisis-based of DTC scheme has two main disadvantages
namely the high torque ripple and variable switching
frequency of the inverter. Since the switching frequency is
strongly affected by the hysterisis torque controller, it is
possible to solve the problems by replacing the hysterisis
torque controller with a constant frequency torque controller
as illustrated in Fig. 1. As reported in [6]-[8], this simple
modification has greatly achieved in obtaining constant
switching frequency as well as torque ripple reduction. Fig. 2
shows the block diagram of the proposed overmodulation
strategy of DTC with most all the main components are
retained as employed in [1] and [6]-[8] including the voltage
vectors selection table, which is tabulated in Table 1. The
table is constructed based on the stator flux space vector plane
and switching voltage space vectors as depicted in Fig. 3. The
appropriate voltage should be chosen in a particular sector,
either to increase stator flux or to decrease stator flux and
either to increase torque or to reduce torque; based on torque
ψ−
Voltage
Vector
Selection
Table
Sa
Sb
Sc
Voltage
Source
Inverter
IM
θs
ψˆ e
+ Vdc Stator Flux and
Torque Estimator
T̂e
Fig. 2. The structure of constant frequency torque-based of DTC with flux
error status modification.
TABLE 1
VOLTAGE VECTORS LOOKUP TABLE
Counter clockwise
Inc
Flux
Dec
Flux
Inc Torque
Dec Torque
Inc Torque
Dec Torque
Clockwise
II. STRUCTURE OF DTC WITH A SIMPLE OVERMODULATION
STRATEGY
ψ+
Modified
Flux Error
Status
q(t)
Inc
Flux
Dec
Flux
Inc Torque
Dec Torque
Inc Torque
Dec Torque
Sec I
Sec II
Sec III
Sec IV
Sec V
Sec VI
100
000
110
111
110
111
010
000
010
000
011
111
011
111
001
000
001
000
101
111
101
111
100
000
Sec I
Sec II
Sec III
Sec IV
Sec V
Sec VI
001
000
011
111
101
111
001
000
100
000
101
111
110
111
100
000
010
000
110
111
011
111
010
000
V4
V3
V2
V5
V6
V1
Fig. 3. Six sectors of stator flux plane and switching voltage space vectors
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The next section will discuss the operations of dynamic
overmodulation and field weakening using proposed
overmodulation strategy with a constant frequency torque
controller-based of DTC.
III. THE PROPOSED OVERMODULATION STRATEGY
In a 3-phase 2-level inverter, there exists only 8 voltage
space vectors, made up of 6-active and 2-zero switching states
as depicted in Fig. 4(a). The 6-active switching state vectors
are evenly distributed at π / 3 intervals in complex plane.
These active switching state vectors represent 6-active voltage
vectors which are limited by the magnitude of 2/3Vdc. By
definition of space vector, the locus of desired voltage vector
becomes circular under sinusoidal PWM operation. The limit
of sinusoidal PWM is defined, as the circular locus of desired
voltage vector is the largest inscribed in the hexagon. Beyond
the limit, the overmodulation operations are occurred. In the
proposed overmodulation strategy, the stator flux is weaken at
this range as the voltage vector is required to be increased in
order to extend the motor speed beyond its based speed. The
maximum possible output 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. Note that, the stator voltage and stator flux locus
follow the hexagonal shape (during six-step operation) outer
and inner to their respective circular locus (during sinusoidal
PWM operation) as shown in Fig. 4.
In order to fully utilize the dc-link voltage, the appropriate
control algorithm under overmodulation and field weakening
operations of drive system is required. In the proposed
overmodulation-DTC scheme, the sinusoidal PWM operation
is considered through the PWM waveform of the voltage
which is generated through the voltage vector 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). On the other hand,
under overmodulation and field weakening operations, the
flux error status is adjusted before it is being fed to the voltage
vector selection table. By doing so, the simple strategy to
operate under overmodulation can be obtained without
resolving to the common approach of SVM-based. For the
convenience of discussion, two operations that are generally
occurred under overmodulation mode are presented to
describe the operation of the proposed overmodulation
strategy for constant frequency torque controller-based DTC.
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. 4(b). The
selected voltage vectors produce the largest stator flux
tangential components hence will ensure a fast torque
response.
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 controlled such that it
will gradually change from circular to hexagonal shapes and
this is achieved by controlling the holding angle θ h as shown
in Fig. 5. Within any sector, if the flux angle is less than θ h ,
only one voltage vector is selected continuously and the
selection is similar to the overmodulation mode as described
above. On other hand, if the angle is larger than θ h but less
(
)
than 60 0 − θ h , the flux is regulated within its hysterisis
band; stator voltage is in the PWM mode. This means that the
shape of the flux is completely hexagonal if θ h = π / 6 and
the transition from PWM to six-step is accomplished by
gradually controlling the angle from 0 to π / 6 .
*
vs
V5 (011)
ψs
θh
Fig. 4. Six sectors of (a) stator voltage plane (b) stator flux plane
V4
V5
60 0
V2
V6
θh
A. Dynamic Overmodulation
In order to obtain a fast dynamic torque response only one
active 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 (in Fig. 4(b)), a voltage vector to increase
V3
Fig. 5. Sector I of stator flux plane
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V1
IV. SIMULATION RESULTS
The simulation of the DTC induction motor drive with the
proposed overmodulation strategy was performed using
MATLAB/SIMULINK simulation 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 Ω
Rotor resistance
4.51 Ω
Stator self inductance
306.5 mH
Rotor self inductance
306.5 mH
Mutual inductance
291.9 mH
Momen of inertia
0.01 kg.m2
Number of poles
4
Rated speed
1410 rpm
DC-link voltage
654 V
Load torque
1 Nm
In order to establish a constant switching frequency, the
frequency of upper and lower triangular waveforms employed
for 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, Tc does not exceed the absolute slope of
triangular carrier [7]. Thus, the corresponding gain parameters
for this setting were 57 and 3630 respectively [8]. The
magnitude of stator flux is set at its rated value which is 1.2
Wb and the stator flux is restricted within its hysterisis band of
0.05 Wb.
From Fig. 6, it can be observed that, the motor speed is able
to operate beyond its rated speed using the proposed
overmodulation method. In this case, the speed control is
utilized in which a step reference speed occurred at t=0.25 s.
Before a step reference speed is applied, the speed is operated
at rated speed (steady state), thus the stator flux locus of the
machine is almost circular as depicted in Fig. 7(a). At this
moment, the voltage vectors are switched between two active
and zero vectors to regulate the torque and flux as in [6]-[8].
In the field weakening region, the magnitude of stator flux
is weakened proportionally to the rotor speed as depicted in
Fig. 6.
To verify the effectiveness of the proposed
overmodulation method, let us examine the stator flux locus
plotted in Fig. 7(b). The stator flux locus is plotted during
transition from PWM to six-step operations particularly at
time interval ∆t12 (as indicated in Fig. 6). From Fig. 7(b), it
can be observed that, the stator flux trajectory tends to become
hexagon as the holding angle, θh increases. The complete
hexagonal stator flux locus is depicted in Fig. 7(c). The
voltage waveform and the corresponding holding angle during
transition from PWM to six-step operations are shown in Fig.
8. Clearly, Fig. 8 indicates the number of pulse dropping is
gradually decreased as the holding angle, θh increases during
the transition.
∆t12
Fig. 6. Simulation results of speed, stator flux magnitude and stator flux
angle.
t = t2
ωe t = t
1
(a)
(b)
(c)
Fig. 7. Stator flux locus (a) at base speed (steady state) (b) during time
interval ∆t12 in field weakening region (c) hexagon flux locus in field
weakening mode.
Fig. 8. Stator phase voltage and holding angle θh during transition from PWM
to six-step.
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The torque response with dynamic overmodulation during
torque transient has improved as shown in Fig. 9. From the
figure, it can be seen that the torque response is faster than the
one without the dynamic overmodulation mode. This is
because only one active voltage vector is applied rather than
two active voltage vectors as for the case without the dynamic
overmodulation as shown in Fig 10.
response and smooth transitions from PWM to six-step mode
were achieved.
VI. REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
Fig. 9. Dynamic torque response with and without dynamic overmodulation.
[8]
[9]
[10]
[11]
[12]
[13]
[14]
Fig. 10. Switching of phase A (Sa), Switching of phase B (Sb), Switching of
phase C (Sc) during dynamic torque response (a) without dynamic
overmodulation (b) with dynamic overmodulation.
V. CONCLUSION
[15]
I. Takahashi and T. Noguchi, "A new quick-response and highefficiency control strategy of an induction motor",IEEE Trans. Ind.
Appl. Vol. IA-22, No. 5, pp. 820-827.
M. Depenbrock, "Direct Self Control of inverter-fed of induction
machine , IEEE Trans. Power Electron., vol3,pp. 420-429, 1988.
J.K. Kang, D.W. Chung, S.K. Sul, “Direct torque control of induction
machine with variable amplitude control of flux and torque hysterisis
bands,” in Proc. Int. Conf. Electrical Machines and Drives, 1999, pp.
640-642.
Mir. S, Elbuluk. M.E, “Precision torque control in inverter-fed induction
machines using fuzzy logic,” in Conf. Rec. IEEE-IAS Annual Meeting,
pp. 396-401.
J. K. Kang, S. K. Sul, “New direct torque control of induction motor for
minimum torque ripple and constant switching frequency,” IEEE Trans.
Ind. Application. Vol. 35, pp. 1076-1082, Sept/Oct. 1999.
N.R.N.Idris, A.H.M. Yatim; N.A Azli,, "Direct torque of induction
machines with constant switching frequency and improved stator flux
estimation".; 27th Annual Conference of the IEEE ,Industrial Electronics
Society, 2001. IECON '01. Vol. 2 , pp.1285 - 1291 Dec. 2001.
N.R.N. Idris, A. H. M. Yatim, N. D. Muhamad and T. C.Ling, "Constant
frequency torque and flux controllers for direct torque control of
induction machines", Accepted for the 34th IEEE Power Electronics
Specialist Conference PESCO3, Acapulco, Mexico June 2003.
N.R.N.Idris, C.L. Toh, and M.E. Elbuluk, "A New Torque and Flux
Controller for Direct Torque Control of Induction Motor Drives" IEEE
Transaction on Industry Application, Vol. 42, No. 6, pp. 1358-1365
Nov. 2006.
J. Holtz, "Pulsewidth modulation- a survey", IEEE Transaction on
Industrial Electronics, Vol. 38, No. 5,pp. 410-420, 1992.
Wang Cong; Lu Qiwei, "Analysis of naturally sampled space vector
modulation PWM in overmodulation region", IEEE Power Electronics
an Motion Control Conference, 2004 IPEMC, Vol. 2, pp. 694-698, Aug
2004.
G. Giovani, Thomas G. and Habetler, "Performance evaluation of a
direct torque controlled drive in the continuos PWM-square wave
transition region".IEEE Transaction on Power Electronics, vol. 10, no.4,
July 1995.
Bon-Ho Bae; Seung-Ki Sul "A novel dynamic overmodulation strategy
for fast torque control of high-saliency-ratio AC motor", IEEE
Transactions on Industry Applications,Vol. 41, No. 4, pp. 1013-lOl9
July-Aug 2005.
A. M. Kambadkone and J. Holtz, "Compensated synchronous pi current
controller in overmodulation range and six-step operation of spacevector-modulation based vector-controlled drives", IEEE Transactions
on Industrial Electronics, vol. 49, no. 3, pp. 574-580, June 2003.
Bon-Ho Bae, Sang-Hoon Kim, and Seung-Ki Sul, "A new
overmodulation strategy for traction drive", AppliedPower Electronics
Conference and Exposition, IEEE APEC'99 14th Annual, vol.1, p.p 437442, March 1999.
A. Tripathi, A. M. Khambadkone, and S. K. Panda, “Space-vector based,
constant frequency, direct torque control and dead beat stator flux
control of ac machines,” in Proc. IEEE Int. Conf. Ind. Electron., Contr.,
Instrum. Autom. (IECON’01), Nov. 2001, vol. 2, pp. 1219–1224.
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 stator 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
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