This document summarizes a research paper on direct torque and flux control (DTFC) strategy for an induction motor. It presents the DTFC control scheme which estimates stator flux and uses voltage space vectors to achieve low torque ripple and constant switching frequency. The paper describes the induction motor model, DTFC theory, implementation using voltage space vectors, and advantages over field oriented control. Simulation results validating the DTFC model and control strategy are presented for a 10hp induction motor.

1. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –
INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING
6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME
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ISSN 0976 – 6553(Online)
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SIMULATION OF DIRECT TORQUE AND FLUX CONTROL
STRATEGY FOR AN INDUCTION MOTOR USING
MATLAB/SIMULINK SOFTWARE PACKAGE
Deepak Kumar Goyal
M.Tech from IIT Roorkee
Assistant Professor, Department of Electrical Engineering, Govt Engg. College, Bharatpur,
Rajasthan., India
ABSTRACT
This paper describes a control scheme for direct torque and flux control of in
induction motor based on stator flux estimation, which has many of the desirable features of
conventional constant v/f ratio. The use of simple equation to obtain the control algorithm
makes it easier to understand and implement. Switching instant and low torque ripple are
obtained using voltage space vector.
Keywords : control strategy, direct torque and Flux control, induction motor, space vector.
I. INTRODUCTION
In recent year many studies have been developed to find out different solution for
induction motor control having the feature of precise and quick torque response, Flux control
and reduction of the complexity of field oriented algorithms. The Direct Torque and Flux
Control (DTFC) technique has been recognized as viable solution to achieve these
requirements.
In principle the DTFC selects one of the six voltage vector and two zero voltage
vectors generated by a VSI in order to keep stator flux and torque within limits of two
hysteresis bands. The right application of this principle allows a decoupled control of flux
and torque without need of speed or position sensor, coordinate transformation, PWM pulse
generation and current regulator. However, the presence of hysteresis leads to a variable
switching frequency operation.
In [3]-[4] different method has been presented which allow constant switching
frequency operation. In general, they require control schemes which are more complex with
respect to the basic DTFC scheme.
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II. INDUCTION MOTOR MODEL
The d-q axis dynamics equation for squirrel case induction motor with the reference
frame which rotating with ω speed are given by[7]
vqs = Rs iqs + ωλ ds + pλqs − − − (1)
vds = Rsids − ωλ qs + pλds − − − (2)
vqr = Rr iqr + (ω −ω r )λ dr + pλqr − − − (3)
vdr = Rr idr − (ω −ω r )λ qr + pλdr − − − (4)
λqs = Lls iqs + Lm (i qs +iqr ) − − − (5)
λds = Lls ids + Lm (i ds +idr ) − − − (6)
λqr = Llr iqr + Lm (i ds +idr ) − − − (7)
λdr = Llr idr + Lm (i ds +idr ) − − − (8)
Because machine parameter is taken in per unit so it is convenient to express the
voltage and flux linkage in terms of reactance rather than induction. And now flux linkage
become flux linkage per second.
 ωb  
ψ qs =   vqs −  ω ψ ds +  Rs ( mq −ψ qs ) − − − (9)
  
 p  ω   X ψ
 
   b  ls  
 ωb      
ψ ds =   v ds −  ω ψ qs +  R s (ψ md − ψ ds ) − − − (10)
 p   ω  X  
   b  ls  
 ωb  
ψ qr =   vqr −  ω − ω r

  R 
ψ dr +  s ( mq − ψ qr ) − − − (11)
 p     X ψ 
   ωb   lr  
 ωb  
ψ dr =   v dr −  ω − ω r

  R
ψ qr +  s

(ψ md − ψ dr ) − − − (12 )
 p   ω  X  
   b   lr  
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6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME
and electromagnetic torque is given as
 3  P  1 
( ds i qs − ψ qs i ds ) − − − (13)
Te =      ψ
 2  2  ω b
 
ψ ψ 
ψ mq = X aq  qs + qr  − − − (14)
X 
 ls X lr 
−1
ψ ψ   1 1 1 
ψ md = X aq  ds + dr  − − − (15) Where X aq =
X + X + X  
X 
 ls X lr   ls lr m 
1
i qs = (ψ qs −ψ mq ) − −(16)
X ls
1
i ds = (ψ ds −ψ md ) − − − (17 )
X ls
1
iqr = (ψ qr −ψ mq ) − − − (18)
X lr
1
i dr = (ψ dr −ψ md ) − − − (19)
X lr
As we require machine model in stator reference frame so put ω=0 and for squirrel
cage induction motor vqr = 0 and vdr = 0
Rs and Rr are the stator and rotor resistance.
Ls,Lr and Lm are the self and mutual induction.
ωr is the rotor angular speed in electrical radian.
III. THEORY OF DTFC[5]
From eq. (1-2)
λqs = ∫ (vqs − iqs Rs )dt − − − (20)
λds = ∫ (vds − ids Rs )dt − − − (21)
The stator flux is given by
λs = (λ2 + λ2 )∠θ e − − − (22)
qs ds
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These v qs and v ds can be estimated as below
vqs = vas − − − (23)
 1 
vds =   (vcs − vbs ) − − − (24)
 3
And electromagnetic torque can be calculated as
 3P 
Te =   (λds iqs − λqs ids ) − − − (25)
 4 
Fig 1 shows the block diagram of DTFC of an induction motor. As shown in Fig. 1, the
inverter switching states are selected according to the error of the torque and flux, which are
indicated by, ∆Te and ∆λs , respectively.
∆Te = Te* − Te − − − (26)
∆λs = λs* − λs − − − (27)
+ Vdc -
∆Te 1 HTe I
Sa
Te* + 0
VI
II
- -1 Sb VSI
V
Te III Sc
IV
∆λs 1 Hλs
*
λ
s - -1
λs
Ia,Ib
Torque and flux
estimation
Va,Vb
Induction
motor
Fig. 1:Block diagram of DTFC of Induction motor
induction motor
Where Te* and λs* are reference torque and stator flux.The table II shows the
associated inverter switching states which are determined by the error of torque and flux, and
position of stator flux, which calculated as
 λqs 
θ e = tan −1   − − − (28)
 λds 
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θe S(k) (sector)
п/3 <θe≤ 2п/3 S(1)
0 <θe ≤ п/3 S(2)
-п/3 <θe ≤ 0 S(3)
-2п/3 <θe ≤ -п/3 S(4)
-п <θe ≤ -2п/3 S(5)
2п/3 < θe ≤ п S(6)
Table I: Position (Sector ) of flux
HTe Hλs S (1) S (2) S (3) S (4) S (5) S (6)
1 1 VI I II III IV V
(1,1,0) (1,0,0) (1,0,1) (0,0,1) (0,1,1) (0,1,0)
1 0 VIII VII VIII VII VIII VII
(1,1,1) (0,0,0) (1,1,1) (0,0,0) (1,1,1) (0,0,0)
1 -1 II III IV V VI I
(1,0,1) (0,0,1) (0,1,1) (0,1,0) (1,1,0) (1,0,0)
0 1 V VI I II III IV
(0,1,0) (1,1,0) (1,0,0) (1,0,1) (0,0,1) (0,1,1)
0 0 VII VIII VII VIII VII VIII
(0,0,0) (1,1,1) (0,0,0) (1,1,1) (0,0,0) (1,1,1)
0 -1 III IV V VI I II
(0,0,1) (0,1,1) (0,1,0) (1,1,0) (1,0,0) (1,0,1)
Table II: Switching states for possible HTe, Hλs and S(k)
Noting that an adjustable speed drives can obtain by adding a speed controller to generate
torque command. The phase voltage can be determined as
V 
vas =  dc  (2 S a − Sb − S c )
 3 
V 
vbs =  dc  (2 Sb − S c − S a ) − − − (29)
 3 
V 
vcs =  dc  (2 S c − S a − Sb )
 3 
Where vas , vbs , vcs are phase voltages
Sa , Sb , Sc denote as inverter switching state, in which Si =1 (i=a,b,c), if the upper leg switch is
on and
Si =0 (i=a,b,c) if the upper leg switch is off.
Vdc is the dc link voltage.
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q-axis
VI
VVI VII
S(1)
S(6) S(1)
π/3 π/3 d-axis
Reference
S(5) π/3 S(3)
S(4)
VV VIII
VIV
Fig 2: Voltage Space Vector and Flux Sector
IV. ADVANTAGE OF DTFC BASED DRIVES
The field oriented control approach invokes the concept of transforming the stationary
quantities into synchronous ones and orienting the referred flux along the d-axis of the
synchronous frame while in contrast the DTFC does not invoke any such works.
V. IMPLEMENTATION RESULT
The figures (3 to 7) present simulation results based on model of a 10h.p. induction
motor. Its main parameters are shown below. Rated power: 10 hp; rated voltage: 220V(line to
line); rated frequency: 60 Hz; stator resistance Rs=.0453 p.u.; rotor resistance Rr =.0222 p.u.
stator reactance Xls =.0775 p.u. rotor reactance Xlr = .0322 p.u.; mutual reactance Xm = 2.042
p.u. and inertia H= .5 sec.
VI. CONCLUSION
In this paper, a direct torque and flux control scheme is presented. It based on the
induction motor model and space vector theory. As a result, both flux and torque can be
controlled separately without any transforming the stationary quantities into synchronous
one.
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VII. SIMULATION RESULTS
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VIII. REFERENCES
[1] Y.A.Chapuis, D.Roya, J.Davoine, “Principles and implementation of Direct Torque
Control by stator flux orientation of an Induction Motor”, IEEE Applied Power Electronic
conference and Exposition-Industry –Dallas, March 1995.
[2] T.G.Habetler, “ Control Strategy for Direct Torque Control of Using Discrete pulse space
Modulation”, IEEE Trans. Ind. App. , vol. 27, no. 5, pp.893-901, sept./oct. 1991
[3] Yen-Shin Lai and Jian-Ho Chen, “ A New Approach to Direct torque control of induction
motor for constant Inverter Switching Frequency and Torque Ripple Reduction”, IEEE
Transaction on energy conversion, vol. 16, NO. 3, Sept. 2001
[4] T.G.Habetler, “ Direct Torque Control of Using space Vector Modulation”, IEEE
Trans. Ind. App. , vol. 28, no. 5, pp.1045-1053, sept./oct. 1992
[5] R. Krishnan, “ Electric motor drives, modeling, analysis and control”, Prentice- Hall of
india private limited, New Delhi-110001,2003
[6] B.K. Bose, ”Modern Power electronics and AC Drives”, Published by Pearson Education
(Singapore) pte, Ltd. Indian Branch, 2003
[7] P. C. Krause, “Analysis of electric machinery”, McGraw-Hill, 2001.
[8] P. Tiitinen, “The next generation motor control method, DTC direct torque control,” in
Proceedingss of the IEEE Intl. Conf. on Power Electronics,Drives, and Energy Systems
for Industrial Growth, 1996, pp.
[9] Domenico Casadei, Giovanni Serra and Angelo Tani, “Improvement of Direct Torque
Control Performance by using a Discrete SVM technique”, IEEE Trans. Ind. App. ,1998.
[10] Vaibhav B. Magdum, Ravindra M. Malkar and Darshan N. Karnawat, “Study &
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[12] Vishal Rathore and Dr. Manisha Dubey, “Speed Control of Asynchronous Motor Using
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[13] Bhagirath Ahirwal and Prof. Tarun Kumar Chatterjee, “Effect of starting torque on the
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