DTC

Direct Torque Control of Induction Motor

Department of Electrical Engineering, College of Engineering, Trivandrum 1

SIMULATION OF

DIRECT TORQUE CONTROL OF

INDUCTION MOTOR

Project work done by

Melvin Koshy

[email protected]

mailto:[email protected]



1.0 INTRODUCTION

Industrial loads require operation at wide range of speeds. Such loads are generally termed as

variable speed drives. These drives demand precise adjustment of speed in a stepless manner

over the complete speed range required. The loads may be constant torque or a function of

speed. These loads are driven by hydraulic, pneumatic or electric motors. An industrial drive

has some special features when driven by electric motors. Induction machines have provided

the most common form of electromechanical drive for industrial, commercial and domestic

applications that can operate at essentially constant speed. Induction machines have simpler

and more rugged structure, higher maintainability and economy than dc motors. They are also

robust and immune to heavy loading.

The possible forms of drive motors are dc drives, ac drives. DC motors are versatile for the

purpose of speed control but they suffer from the disadvantage imposed by the commutator.

On the other hand ac drives are viable competitors with the advent of thyristor power converter

technology. The main features of ac drives

Small size

Robust

Simple

Light and compact

Low maintenance

Low cost

The evolution of ac variable speed drive technology has been partly driven by the desire to

emulate the performance of dc drive such as fast torque response and speed accuracy, while

utilizing the advantage offered by standard ac motor. The Field Oriented Control (FOC) and the

Direct Torque Control (DTC). Vector controlled induction motors are employed in high

performance drives having precise speed control and good static as well as dynamic response.

Modern control methods use state space techniques. The method of stabilising the drives and

improvement in their transient responses have been realised by modern power electronic

devices.



1.1 OBJECTIVES

i) Simulation of classical direct torque control scheme of induction motor

ii) Effect of flux and torque hysteresis band

iii) Feasibility study for improvement in performance

iv) Modified DTC scheme

2.0 DIRECT TORQUE CONTROL

Direct Torque Control (DTC) has become an alternative to field oriented control or vector

control of induction machine. It was introduced in Japan by Takahashi(1984) and

Depenbrock(1985). DTC of induction machine has increasingly become the best alternative to

Field-Oriented Control methods [1,2].

The block diagram of DTC system for an induction motor is as shown in Fig. 1. The DTC

scheme comprises torque and flux estimator, hysteresis comparators for flux and torque and a

switching table.

Fig. 1 Block diagram of classical DTC scheme



The configuration is much simpler than the vector control system due to the absence of

coordinate transforms between stationary frame and synchronous frame and PI regulators. It

also doesn’t need a PWM and position encoder, which introduces delay and requires

mechanical transducers respectively [2,3]. DTC based drives are controlled in the manner of a

closed loop system without using the current regulation loop. DTC scheme uses a stationary

d-q reference frame (fixed to the stator) having its d-axis aligned with the stator q-axis. Torque

and flux are controlled by the stator voltage space vector defined in this reference frame.

The basic concept of DTC is to control directly the stator flux linkage (or rotor flux linkage or

magnetising flux linkage) and electromagnetic torque of machine simultaneously by the

selection of optimum inverter switching modes [2, 3]. The use of a switching table for voltage

vector selection provides fast response, low inverter switching frequency and low harmonic

losses without the complex field orientation by restricting the flux and torque errors within

respective flux and torque hysteresis bands with the optimum selection being made.

The DTC controller comprises hysteresis controllers for flux and torque to select the switching

voltage vector in order to maintain flux and torque between upper and lower limit [4,6]

The main advantages offered by DTC are

Decoupled control of torque and stator flux

Excellent torque dynamics with minimal response time.

Inherent motion-sensorless control method since the motor speed is not required to

achieve the torque control.

Absence of coordinate transform (required in FOC)

Absence of voltage modulator as well as other controllers

Robust for rotor parameter variation. Only the stator resistance is needed for torque and

flux estimation.

Stator flux is a time integral of stator EMF

s

s s s

dV i R

dt

(1)

Selection of appropriate voltage vector in the inverter is based on stator equation in stator-coordinates

0

0

LT

s s s s s s s iV i R dt V i T (2)

Electromagnetic torque can be expressed as

3

2 2e s s

PT I

(3)



s qs dsj (4)

s qs dsI i ji (5)

m

s r s s

r

LL I

L (6)

3

2 2

m

e r s

r s

LPT X

L L

(7)

Fig. 2 shows the phasor for Eqn. (5) indicating that the vectors , s r sand I for positive

developed torque. If the rotor flux remains constant and the stator flux is changed incrementally

by the stator voltage Vs as shown, the corresponding change of angle is and the

incremental torque eT is given as

3

sin2 2

r s s

e r s s

PT

(8)

Fig. 2 Stator and rotor flux space vectors

2.1 DTC Development

The command stator flux and torque magnitudes are compared with the respective estimated

values and the errors are processed through hysteresis band controller [4,6].

The torque control of the inverter fed machine is carried out by hysteresis control of magnitude

of stator flux and torque that selects one of the six active and two zero inverter voltage vectors

as shown in Fig. 3. The selection is made in order to maintain the torque and flux error inside

the hysteresis band in which the errors are indicated by eT and s respectively.



*

e e eT T T (9)

*

s s s (10)

The six different directions of sV are denoted as 0,1, 2 6iV i . Considering , and a b cS S S as

the combination of switches, the status of the inverter are given by (11)

2 4

3 32

3

j js

i a b c

VV S e S e S

(11)

The flux loop controller has two levels of digital output according to the following relations

1

-1

H for E HB

H for E HB

(12)

The total hysteresis band width of the flux loop controller is 2H . The actual stator flux is

constrained within this band and it tracks the command flux in zigzag path as shown in Fig. 4

The torque control loop has three levels of digital output, which possess the following relation

1

0

-1

Te Te Te

Te Te Te Te

Te Te Te

H for E HB

H for HB E HB

H for E HB

(13)

Fig. 3 Inverter voltage vectors and corresponding stator flux

variation in time t



Fig. 4 Trajectory of stator flux vectors

The feedback flux and torque are calculated from the machine terminal voltages and currents.

The signal computation block computes the sector number in which the flux vector currently

lies. There are six active voltage vectors each spanning 60. The voltage vector table receives

H , TeH and sector S i and generates the appropriate control for the inverter from a look-up

table.

2.2 Flux and Torque Estimator

Flux and torque estimators are used to determine the actual value of torque and flux linkages.

Into this block enters the VSI voltage vector transformed to the d-q stationary reference frame.

The three-phase variables are transformed into the d-q axes variables using the following

transformation

2 1 1

3 3 3

1 10

3 3

a

qs

b

ds

c

ii

ii

i

(14)

The d-q axes stator flux linkage is estimated by computing the integral of difference between

the respective d-q input voltage and the voltage drop across the stator resistance

ds d ds sv i r dt (15)

qs q qs sv i r dt (16)



The resultant stator flux linkage can be expressed as

2 2

ds qs (17)

The location of the stator flux linkage should be known so that the appropriate voltage vector is

selected depending upon the flux location.

1tanqs

e

ds

(18)

The electromagnetic torque can be expressed as

3

2 2e ds qs qs ds

PT i i

(19)

2.3 Torque and Flux Hysteresis Comparator

The estimated torque and stator flux linkage are compared with the reference torque and stator

flux linkage. The error signal is processed in a comparator. If the actual flux is smaller than the

reference value, the comparator output is at state 1 else it will be at state -1. The states for Flux

are as shown in Fig. 5

1

1

state

Fig. 5 Flux hysteresis states

The states for Torque are as shown in Fig. 6

1

1

state

0

Fig. 6 Torque hysteresis states



2.4 Switching Table

The hysteresis comparator states TeH and H together with the sector number S i are used

by the switching table block to choose appropriate voltage vector. The switching table

implemented is according to Table I. A high hysteresis state increases the corresponding

quantity and vice-versa. The selected voltage vector is synthesised and then sent to the VSI.

Table I. Switching Table of inverter voltage vectors

H TeH 1S 2S 3S 4S 5S 6S

1

1 V2 V3 V4 V5 V6 V1

0 V0 V7 V0 V7 V0 V7

-1 V6 V1 V2 V3 V4 V5

-1

1 V3 V4 V5 V6 V1 V2

0 V7 V0 V7 V0 V7 V0

-1 V5 V6 V1 V2 V3 V4

2.5 Voltage Source Inverter

The VSI synthesises the voltage vectors commanded by the switching table. In DTC, this is

quite simple since no pulse width modulation is employed, the output devices stay in the same

state during the entire sample period. The connection of power switches in a VSI with three

phase windings of an Induction Motor is shown in Fig. 7

3S 5S1S

4S2S 6S

aV cVbV

dcV

A B C

N

Fig. 7 Schematic of Voltage Source Inverter



The power switches of the VSI are 180 conducting mode, which implies that only three

switching signals , and a b cS S S are needed to uniquely determine the status of six switches. If

the upper switch in upper leg of certain phase is on, the switching signal for this phase is

designated as S=1 and S=0 represents the on state of a switch in the lower leg of the inverter.

In this manner, there are six effective space vectors and two zero space vectors existing in the

ordinary operation for the inverter. Assuming that the voltage space vectors are located along

a-axis of the a,b,c reference frame with phase a voltage Va applied alone, then the inverter

output voltage vector under different switching states can be expressed as

22 1 120

3

dc

i a b c

VV S a S a S where a (20)

According to the above equation, the inverter output voltage space vectors represent in terms

of switching states where six effective voltage space vectors 1 6V V which are apart in space

by 60electrical angle. The vectors 0 7 and V V are located at the centre of the space-vector

plane.

The inverter keeps the same state until the output of the hysteresis controllers changes their

outputs at sampling period. Therefore, the switching frequency is usually not fixed; it changes

with rotor speed, load and bandwidth of the flux and torque controllers.



3.0 INDUCTION MOTOR MODELLING

The main objective of DTC is to control the induction motor. The per-phase equivalent circuit of

an induction motor is valid only in steady-state condition. In an adjustable speed drive like the

DTC drive, the machine normally constitutes an element within a feedback loop and hence its

transient behaviour has to be taken into consideration.

The induction motor can be considered to be a transformer with short circuited and moving

secondary. The coupling coefficients between the stator and rotor phases change continuously

in the course of rotation of rotor [5]. Hence the machine model can be described by differential

equations with time-varying mutual inductances.

For simplicity of analysis, a three phase machine which is supplied with three-phase balanced

supply can be represented by an equivalent two-phase machine as shown in Fig. 8

rd

sq

sd

rrq

Fig. 8 Two phase equivalent of a symmetric three-phase machine

The time-varying inductances are to be eliminated so as to obtain the dynamic model of the

induction motor [10]. The time-varying inductance that occur due to an electric circuits in relative

motion and electric circuits with varying magnetic fields can be eliminated by transforming the

rotor variables associated with fictitious stator windings. For transient studies of adjustable

speed drives, the machine as well as its converter is modelled on a stationary reference frame

[1,6,11].

Consider a symmetrical three-phase induction machine with stationary as-bs-cs axes at 120

apart. The three-phase stationary reference frame (as-bs-cs) variables can be transformed into

two phase stationary frame (ds-qs) variables by the following transformation matrix



0

1 11

2 2

2 3 30

3 2 2

1 1 1

3 3 3

as

s

dq bs

cs

v

v v

v

(21)

The voltage equations pertaining to the two phase machine in terms of flux linkages in the d-q

axes can be expressed as

1 ds e

qs s qs ds

b b

dFv R i F

dt

(22)

1 ds e

ds s ds qs

b b

dFv R i F

dt

(23)

1 qr e b

qr s qr ds

b b

dFv R i F

dt

(24)

1 dr e b

dr s qr qr

b b

dFv R i F

dt

(25)

Since the machine is singly fed,

0dr qrv v (26)

The flux linkage equations pertaining to two axes model can be expressed as

qs e s

b qs ds mq qs

b ls

dF Rv F F F

dt x

(27)

ds e s

b ds ds md ds

b ls

dF Rv F F F

dt x

(28)

qr e r s

b qr dr mq qr

b lr

dF Rv F F F

dt x

(29)

dr e r s

b dr dr mq dr

b lr

dF Rv F F F

dt x

(30)

The stator and rotor currents with respect to the two axes model can be expressed as

qs mq

qs

ls

F Fi

x

(31)



ds md

ds

ls

F Fi

x

(32)

qr mq

qr

lr

F Fi

x

(33)

dr md

dr

lr

F Fi

x

(34)

The electromagnetic torque can be obtained from the flux linkages and currents as

3 1

2 2e ds qs qs ds

b

PT F i F i

(35)

The mechanical speed of the rotor can be computed from the expression

2 r

e L

dT T J

P dt

(36)

s

qsv

' s

qrv

s

qsi

sr lsx '

lrx

' s r

dr

b

'

rr

' s

qrE ' s

qri

s

dsv

' s

drv

s

dsi

sr lsx '

lrx '

rr

' s

drE ' s

dri

' s rqr

b

0

s

sv

0

s

si

sr lsx

0

s

rv

'

rr

'

0

s

ri

'

lrx

q-axis

d-axis

zero sequence

mx

mx

Fig. 9 Equivalent circuit of Induction Motor in stationary reference frame



4.0 IMPLEMENTATION OF DTC IN SIMULINK

The building blocks of classical DTC drive are as shown in Fig. 10

Flux

Hysteresis

Controller

Torque

Hysteresis

Controller

Switching

Table

VSIInduction

Motor

Flux and Torque

Estimator

aS

cS

bS

e

*

s

*

eT

eT

s

dcV

Fig. 10 Building blocks of classical DTC drive

The different blocks which are to be implemented in SIMULINK are

Induction Motor

Flux and Torque Estimator

Flux and Torque hysteresis controllers

Switching Table

Voltage Source Inverter

4.1 Induction Motor

The induction motor is modelled in stationary reference frame with its d-axis along the axis of

the a-phase. The equations pertaining to the induction motor in the stationary reference frame

Eqns. (21) - (36) have been implemented through the basic building blocks of SIMULINK. The

model of Induction model in SIMULINK is as shown in Fig. 11

Fig. 11 SIMULINK model of Induction Motor



Fig. 13 SIMULINK model of flux comparator and hysteresis controller

4.2 Flux and Torque estimator

Eqns. (15)-(19) pertain to the flux and the torque estimator. The model of Flux and Torque

estimator in SIMULINK is as shown in Fig. 12

Fig. 12 SIMULINK model of flux and the torque estimator

4.3 Flux and Torque hysteresis Controller

The flux hysteresis controller is modelled according to Eqn. 12. The output of the comparator is

-1 or 1 according to the difference between reference flux and actual value of flux. The

SIMULINK model of the controller and flux hysteresis comparator is as shown in Fig. 13

According to Eqn. (13), the output of the torque hysteresis controller may be -1, 0 or 1. For the

identification of index in look-up table of SIMULINK, a constant bock is augmented with the

output of the hysteresis band controller. Hence the input to the 3-D look-up table is 1, 2 and 3

for states -1, 0 or 1 respectively. The SIMULINK model of torque comparator and controller is

as shown in Fig. 14



Fig. 14 SIMULINK model of torque comparator and hysteresis controller

4.4 Switching Table

The switching table of the inverter comprises of a 3-D look-up table and a 2-D look-up table.

The indices for the input to the 3-D look-up table is 1 and 2 for states -1 and 1 respectively for

flux controllers and 1, 2 and 3 for states -1, 0 or 1 respectively for torque controllers. The

SIMULINK model of the implementation of table is as shown in Fig. 15

Fig. 15 Implementation of look-up table in SIMULINK

4.5 Voltage Source Inverter

The three phase inverter which is coupled at the front-end of the motor can be implemented as

shown in Fig. 16

Fig. 16 SIMULINK model of three-phase VSI



The complete model of classical DTC scheme is as shown in Fig. 17

Fig. 17 Complete SIMULINK model of classical DTC scheme

5.0 SIMULATION RESULTS

5.1 Start-up with No Load

Torque control dynamic performance of developed DTC model is evaluated by applying a step

input of amplitude 3 Nm after 0.05 s to torque reference while the stator flux reference is

maintained at 1 Wb. The width of the hysteresis band is adjusted to 0.02 Wb for the flux

comparator and 0.2 Nm for the torque comparator. Maximum step size of 0.1 ms is used in

this simulation. The obtained torque response is as shown in Fig. 18. The equation of torque for

no load running with single inertia and negligible friction is shown below

r

e

dT J

dt

From Fig. 18, the estimated electromagnetic torque remains at zero at period before 0.05 s, so

the rotor does not rotate. At s, a step of 3 Nm is applied to the torque reference and the

electromagnetic torque immediately increases to reach the reference torque. This causes the

rotor to accelerate at a rate dictated by the rotor inertia.

From the torque response, the acceleration is given by

2330 /

0.1

erTd

rad sdt J



Fig. 18 Plot of estimated Torque at no-load

Fig. 19 shows the stator flux magnitude response has risen to its final value of 1.0 Wb that is

equal to the stator flux reference. The stator flux magnitude is also constrained within its

hysteresis band of 0.02 Wb.

Fig. 19 Plot of Stator Flux at no-load

In DTC scheme, a direct control of the stator current is not present and this may determine

over current when a step variation of torque and flux are applied to the input command. Due to

the uncontrolled current during start-up, the machine exceeds the rated current with stator

current amplitude, 4si A as shown in Fig. 20. It can be noted that even a small variation of

stator flux command will causes a large variation of the stator current. A control method to limit

the current amplitude can be applied. [3] has proposed to pre-flux the machine prior to apply



Fig. 21 Plot of stator flux at no load on step increase in torque

the torque demand to limit the starting current transient in DTC in order to prevent the damage

of the switch powers of inverter.

Since the stator flux magnitude is constantly maintained in the hysteresis band, the locus

draws the figure of a circle as shown in Fig. 21

5.2 Dynamic Behaviour

The transient performance of the developed DTC model has been tested by applying a step

load torque command from +1 Nm to +3 Nm on the mechanical dynamics. The flux reference is

maintained at 1.0 Wb. The estimated electromagnetic torque tracks immediately after the step

command. This demonstrates that the developed DTC achieved high dynamic performance in

response to changes in demand torque. Fig. 22 shows the stator flux magnitude, emphasizing

the decoupled action of torque and flux control. It is observed that the variation of motor torque

does not influence flux. Thus, DTC system can assure independent flux and torque control.

Fig. 20 Plot of stator current at no load

Fig. 21 Plot of locus of stator flux at no load



5.3 Effect of Flux Hysteresis Band

The flux hysteresis band mainly affects the stator current distortion [1], [7]. Thus, for a fixed

torque hysteresis band, the distortion increases with the flux hysteresis band. The simulation

has been performed for different values of the flux hysteresis band amplitude and the results

are shown in Fig. 23 - Fig. 26. If small flux hysteresis band amplitude of 0.02 Wb is applied, the

stator flux vector locus approaches a circle and the phase stator current waveform is

sinusoidal. As the amplitude of the flux hysteresis band increases to 0.2 Wb, the stator flux

locus approaches to a hexagon shape and the stator current distortion has also increased.

Fig. 24 Plot of locus of stator flux with

hysteresis band of 0.02 Wb Fig. 23 Plot of d-q axes stator flux with

hysteresis band of 0.02 Wb

Fig. 25 Plot of d-q axes stator flux with


Fig. 26 Plot of locus of stator flux with




5.4 Effect of Torque Hysteresis Band

The selection of the width of the hysteresis band has important effects switching frequency and

thus the switching losses [1,7,8]. If the band is too small, a torque overshoot may cause and it

must be selected appropriately. It affects the torque error to exceed the hysteresis band. This

will result in a reverse voltage vector to be selected to reduce the torque. A reverse voltage

vector will reduce the torque rapidly and hence may in turn causes a torque undershoots.

Therefore, the torque ripple can become high if the torque hysteresis band is set too small.

Fig. 27 and Fig. 28 show the effects of the torque hysteresis band.

6.0 MODIFIED DTC SCHEME

In classical DTC scheme, the speed is determined according to the reference torque input. The

speed control is not possible because a step increase in reference speed will cause the motor

to accelerate quickly.

In order to improve the flux and speed tracking, it is possible to implement a speed controller in

closed loop using the DTC method [7,8]. For that, it becomes essential to know the rotor

mechanical speed. A speed controller may be employed and augmented with the classical

DTC scheme. In the speed mode operation, the estimated speed is compared with the speed

reference. The error is applied to speed controller, which supplies an electromagnetic torque

reference. The actual torque is compared and then the required signals are applied to the

inverter.

Fig. 27 Plot of torque with hysteresis band of

0.02 Nm Fig. 28 Plot of torque with hysteresis band of

1 Nm



The block diagram of the modified DTC scheme is as shown in Fig. 29

The SIMULINK model of modified DTC scheme is as sown in Fig. 21

Speed PI

ControllerState

Selector INVERTER Induction

Motor

Stator Flux and Torque

Observer

*

r

*

s

r

*

eT

eT

s

edcV

aS

bS

cS

Speed

Sensor

Fig. 29 Block diagram of modified DTC scheme

Fig. 30 SIMULINK model of modified DTC scheme



The values of PI controller for speed being set to 80, 0.3i iK T and the reference speed as

1200 rpm. The plot of speed response and torque response are shown in Fig. 31 and Fig. 32

respectively.

The behaviour in the speed control mode of the modified scheme is superior when compared

to the classical DTC scheme. The torque command is generated in accordance with the input

reference speed. The torque controller simulation results were very good as expected, an

excellent torque control response, either in steady-state or transient regime. The good results

continued steadily even when the system was subjected to overload operation.

Fig. 31 Plot of speed response with reference

speed of 1200 rpm Fig. 32 Plot of torque response with reference

speed of 1200 rpm



7.0 CONCLUSION

The DTC architecture allows the independent and decoupled control of torque and stator flux.

The implementation of the DTC model has been described and justified by simulation. The

merits of DTC can be summarised as

Fast torque response: This significantly reduces the speed drop time during a load

transient, bringing much improved process control and a more consistent product

quality.

Torque control at low frequencies: This is particularly beneficial to cranes or

elevators, where the load needs to be started and stopped regularly without any jerking.

Also with a winder, tension control can be achieved from zero through to maximum

speed. Compared to PWM flux vector drives, DTC brings the cost saving benefit that no

tachometer is needed.

Torque linearity: This is important in precision applications like winders, used in the

paper industry, where an accurate and consistent level of winding is critical.

Dynamic speed accuracy: After a sudden load change, the motor can recover to a

stable state remarkably fast. Standard applications account for 70% of all variable

speed drives installed throughout industry.

Closed loop control of DTC drive has also been achieved using PI controllers. The simulation

results show that the torque ripples are reduced considerably with good dynamic response.

The high speed of switching is fundamental to the success of DTC. The main motor control

parameters are updated times a second [12]. This configuration brings immense

processing speeds such that every 25 µs, the inverter semiconductor switching devices are

supplied with an optimum pulse for reaching or maintaining the accurate motor torque. This

allows extremely rapid response on the shaft and results in high performance of the drive

without encoder.

There have been more challenges in DTC of AC drives- the foremost being the accuracy of

stator flux estimation [9,12]. The accuracy of stator flux estimation decreases as the rotor speed

reduces in the low speed range. Advanced observers such as extended Kalman filters, sliding

mode observers as well as high frequency signal injection techniques can be used to further

improve the performance of DTC drive.



8.0 REFERENCES

[1] H. F. Abdul Wahab and H. Sanusi, ‘Direct Torque Control of Induction Motor’, American Journal Of Applied Sciences, 2008, vol. 8, Iss. 5, pp. 1083-1090

[2] I.Takahashi, T. Noguchi (1986), ‘A New quick-response and high efficiency control strategy of an induction machine’, IEEE Trans. Ind. Appl., vol. 22, pp. 830-832.

[3] C. Lascu, Ion Boldea, F. Blaabjerg, ‘A modified Direct Torque Control for Induction Motor Sensorless Drive’, IEEE Trans. Ind. Appl., vol. 36, no. 1, Jan/Feb 2000

[4] Andrzej M. Trzynadlowski, ‘Control of Induction Motor Drives’, Academic Press, 2/e, 2001

[5] Paul C. Krause: ‘Analysis of Electric Machinery’, McGraw Hill International Edition, 1987

[6] Bimal K. Bose: ‘Modern Power Electronics and AC Drives’, Pearson Education, 4/e, 2007

[7] X. Garcia, A. Arias, ‘New DTC schemes for induction motors fed with a three-level inverter’, AUTOMATIKA, 46(2005), 1-2, 73-81

[8] Takahashi, Y. Ohmori, ‘High Performance direct torque control of induction motor’, IEEE Trans. Ind. Appl., 1989, Iss. 25 (2), pp. 257-264

[9] Ion Boldea, S. A. Nasar: ‘Electric Drives’, CRC press, 2/e, Taylor and Francis, 2006

[10] Ion Boldea, S. A. Nasar: Induction machine Handbook, CRC Press, 3/e, Taylor and Francis, 2007

[11] Chee-Mun-Ong, ‘Dynamic Simulation of Electric Machinery’, Pearson Education, 2001

[12] Direct Torque Control Manual, ASEA Brown Boveri, 2002



APPENDIX

The test machine is a three phase, 50 Hz induction machine having the following parameters

rated

rated

rated

-3

Power rating, P 7500

Rated voltage, V 400

Rated current, I 16

Stator Resistance, 1.77

Rotor Resistance, 1.34

Stator leakage inductance, 13.93 10

Rotor leakage in

s

r

sl

W

V

A

R

R

L H

-3

-3

2

ductance, 12.12 10

Mutual Inductance, 369 10

No. of poles, 4

Moment of Inertia, 0.1

Viscous Friction coefficient, 0.1 /

Bus Voltage, 700

rl

m

m

dc

L H

L H

P

J kg m

B Ns rad

V V

SWITCHING TABLE VALUES

a

(:,:,1) [4 0 2; 5 7 3];

(:,:, 2) [5 7 6; 1 0 2];

(:,:,3) [1 0 4; 3 7 6];

(:,:, 4) [3 7 5; 2 0 4];

(:,:,5) [2 0

a

a

a

a

1; 6 7 5];

(:,:,6) [6 7 3; 4 0 1];a

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