Contribution to the Improvement of Sensorless DTC-SVM for

Three-Level NPC Inverter-fed Induction Motor Drive

DJAMILA CHERIFI , YAHIA MILOUD

Department of Electrical Engineering,

University of Dr.Tahar Moulay,

P. O. B. 138, 20000 Ennasr, Saida,

ALGERIA

Abstract: - This paper deals with the high performance of multi-level direct torque control (DTC) for induction

machines without speed and stator flux sensors. The estimation is performed using a sliding mode observer,

which is known for its robustness in high and low-speed operations, the control is based on a backstopping

speed controller. This control technique was introduced years ago to circumvent the problems of sensitivity to

parametric variations, it presents a high dynamic but their major problems are the variable switching frequency,

the size and complexity of the switching tables, and undulations of the torque. The proposed approach is to

replace switching tables with constant switching frequency control using three-level spatial vector modulation

(SVM). Theoretical elements and simulation results are presented and discussed. As a result, the flux and

torque ripple of three-level DTC-SVM control is greatly reduced compared to the flux and torque ripple of

DTC-classic control. The advantages of the training system have been validated by the simulation results.

Key-Words: - squirrel cage motor, multi-level DTC, sliding mode observer (SMO), multi-level SVM, three-

level NPC inverter, backstepping control.

Received: March 24, 2023. Revised: October 16, 2023. Accepted: November 11, 2023. Published: December 31, 2023.

1 Introduction

Currently, the induction motor is very popular

because it has certain advantages over the DC motor

in industrial applications, such as reliability and

simple structure, this is what makes it used in all

applications, [1], [2], [3]. This motor is used

industrially due to its low cost, [4].

However, controlling this motor is very difficult

given the performance required. This control

problem comes down to the complicated and non-

linear mathematical structure of the cage motor, and

the dependence of these output parameters on those

of the input ones, [5], different types of robust

control have been developed to solve these

problems. Rotor flux orientation vector control was

developed to eliminate the internal coupling of the

machine. However, although it gives a good

performance of the induction machine, FOC has a

certain number of drawbacks: poor robustness

concerning variations in rotor parameters,

dependence on an estimated angle, and the

requirement for an expensive mechanical sensor.

Direct torque control (DTC) comes to overcome the

inherent drawbacks of vector control, [6], [7], [8].

DTC is among the best controls applied to

asynchronous motors. Classic DTC is structured by

hysteresis controllers, resulting in high ripples in

torque and variable switching frequency, [9], [10].

This research work proposes a technique to improve

the results of conventional DTC by introducing the

three-level SVM to eliminate torque ripples and

have fast dynamics compared to conventional DTC

and also to achieve constant switching frequency

and good motor performance.

PID regulators are not robust for controlling non-

linear systems, they are sensitive to parametric

variations. In this research work, we have addressed

the control by backstepping controller for the robust

regulation of the speed of the IM. it is a robust

controller and insensitive to variations in system

parameters, internal and external disturbances, and

non-linearities.

The rotor speed of the IM must be measured by a

speed sensor, which poses the problem of cost and

maintenance. To overcome this problem the speed

must be estimated using the motor currents and

voltages. Several methods have been proposed for

speed and position estimation of induction motors,

[11], [12].

This research concerns direct multilevel torque

control without speed and flux sensors. The strategy

proposed in this work is based on the robust sliding

mode observer and three-level space vector

modulation.

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2 Induction Motor Model

A dynamic model of the induction motor in the

stator coordinates frame can be expressed by:















































sss

s

sss

s

r

s

rs

s

srs

s

r

s

rs

s

srs

s

iRu

dt

d

iRu

dt

d

u

LLLL

R

ii

dt

di

u

LLLL

R

ii

dt

di







1

(1)

with

r

s

sL

R

L

R







The torque equation is:

 

 

ssssem iipT 

(2)

The mechanical relationship given by:



fTT

dt

d

JLem

(3)

Vector expression of the voltage delivered by

the voltage inverter is:













 V

3

2

3

4

3

2

dc



j

c

j

bas eSeSSV



(4)

Vdc : represents the direct voltage.

DTC focuses on the adjustment of flux and

torque by selecting voltage vectors and maintaining

these two quantities in hysteresis bands to have high

control precision, [13].

The flux estimate is:

22 ˆˆˆ

 

sss 

(5)

The two estimated flux components are :















t

sss

t

sss

dtiRv

s

0

)(

ˆ

)(

ˆ











(6)

With:























s

sarctg ˆ

ˆ

(7)

The torque is estimated by:

 

 

ssssem iipT ˆˆ 

(8)

Compared with two-level DTC, three-level DTC

motor drives have a special aspect, that relates to

improving electromagnetic performance, including

reducing torque ripple and improving low-speed

performance, in a similar manner to that of two-level

DTC, [14], [15].

3 The Composition of a Multilevel

Inverter with NPC Structure (3

levels)

The three phases of the multilevel structure of the

NPC inverter are shown in Figure 1. This structure is

composed of two identical capacitors with a

common midpoint denoted “M”. The inverter has

three arms A, B, and C. Each consists of four fully

controllable switches with four anti-parallel diodes

to ensure the reversibility of currents in the load, and

two clamp diodes to develop the multilevel voltage,

which are connected to the midpoint of the DC bus,

[16], [17], [18].

Fig. 1: Structure of a three-phase inverter with NPC

structure -3 level-

Controlling the switches (considered perfect) of

an arm, three different voltage levels can be imposed

on the phase, as shown in Figure 2:

M

2

dc

V

2

dc

V

A

B

C

T1

b

D1b

T2

b

D2c

T3

b

D3b

T4c

D4b

T1a

D1a

T2a

D2a

T3a

D3a

T4a

D4a

D1c

T3c

D3c

T4

b

D2b

T1c

T2c

D4c

VA

n

VC

Load

VB

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Fig. 2: Switching and passage of energy in phase

"A" switches.

3.1 SVM Multilevel of NPC inverter

Modeling of the 3 level voltage inverter showed that

for the different drive combinations, the inverter can

generate only 27 voltage vectors in the plane (α, β),

(33=27), three of which are zero (Figure 3). It is

therefore necessary to apply feasible voltage vectors

for adequate durations over this interval Ts, [19],

[20].

The different vectors form an exagon of six

triangles (A to F), and each triangle is also

composed of four other triangles, thus giving in the

totality of the vector diagram to 24 regions, [21],

[22], as shown in Figure 4.

The vector PWM technique applied to multi-level

inverters follows the following calculation steps:

1- Determination of the duty cycles Ta, Tb, and Tc

for each region.

2- Determination of the switching period of each

switch.

Load

M

2

dc

V

2

dc

V

T1a

D1a

T2a

D2a

T3a

D3a

T4a

D4a

Load

M

2

dc

V

2

dc

V

T1a

D1a

T2a

D2a

T3a

D3a

T4a

D4a

 

00,1,1,0 

Load

M

2

dc

V

2

dc

V

T1a

D1a

T2a

D2a

T3a

D3a

T4a

D4a

 

2

1,1,0,0 dc

V



 

2

0,0,1,1 dc

V



Fig. 3: Diagram of the placement of the

different voltage vectors

α

Vz

V1L

V2L

V3L

V4L

V5L

V6L

β

V1S

V2S

V3S

V4S

V5S

V6S

V1M

V2M

V3M

V4M

V5M

V6M

11-1

01-1

-11-1

10-1

1-1-1

1-10

1-11

0-11

-1-11

-101

-111

-110

A

B

C

D

E

F

110

-10-1

010

00-1

011

-100

100

0-1-1

-1-1-1

111

000

001

-1-10

101

0-10

Fig. 4: Three Level Inverter Vector Diagram

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3.2 Calculation of Ta, Tb, and Tc for each

Region

The calculation is done in the region (A). The

projection of the reference vector (Vref) onto the first

region of the sector (A) is shown in Figure 5, [21],

[22].

According to the figure, the vectors concerned

are V0 ou V7 ou V14, V1, and V2, [21], [22].

  





a m

ca

a

mT T

TT

T

ref dtVdtVdtVdtV

0

021

0

....

(9)

21 ... VTVTVT carefm 

(10)

 

































































3

sin

3

cos

..

6

1

.

0

1

..

6

1

.

sin

cos

..





ETETVT carefm

(11)

 

2

1

..

6

.

6

cos.. carefm T

E

T

E

VT 



(12)

 

2

3

..

6

sin.. crefm T

E

VT 



(13)

cbam TTTT 

(14)

 

2

3

.sin...

22



refma VTT

E

 



sin.

..22

E

VT

Trefm

c

(15)

We replace the expression of (Tc) in (12) we find:

   

2

1

.sin

..22

.

6

.

6

cos..



E

VT

E

T

E

VT refm

arefm 

















3

sin

..22

E

VT

Trefm

a

(16)



























3

sin

.22

1E

V

TTTTT ref

mcamb

(17)

We take:

E

V

Kref

.22



So:

















3

sin. ma TKT

,



























3

sin.1 KTT mb

,

 



sin. mc TKT 

Similarly, the switching times for the other

regions of sector A are found. The switching times

for the rest of the sectors (from B to F) are

calculated in the same way.

3.3 Calculation of Switching Times for each

Switch

Figure 6 shows the waveforms showing the order of

switching states for Region 1 in the sector (A).

With: (Si1, Si2): are respectively the switching

times of the switches at the top (Ki1, Ki2) for arm i.

With: (i=a, b, c)

Fig. 6: Switching times for the switches at the top of

inverter in region 1 of utility (A).

The previous figure helps us calculate the

switching time

422844

.2 11 bca

a

bca

aTTT

S

TTT

S













(18)











 844444

.2

2bcabca

aTTTTTT

S

(19)

Vref

Vref_α

Vref_β

β

α

1

2

3

4

V1 (100)

V’1 (0-1-1)

V15 (1-1-1)

V7 (111)

V0 (000)

V14 (-1-1-1)

V2 (110)

V’2 (00-1)

V9 (10-1)

V16 (11-1)

Fig. 5: Projection of the reference vector into the

first region of sector A

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 

bcaaa TTTSS  2

1

12

(20)

4284

.2 11 bc

b

bc

bTT

S

TT

S













(21)











 84444

.2

2bcabc

bTTTTT

S

 

bcabb TTTSS  2

1

12

(22)

4

1b

cT

S

(23)











 8444

.2

2bcab

cTTTT

S

 

bcacc TTTSS  2

1

12

(24)

Similarly, the switching times of the switches are

calculated for the other cases.

The advantage of multilevel DTC without a

speed sensor is that it will give good results

compared to two-level SVM and conventional DTC

4 Sliding mode observer (SMO)

The mathematical model of the IM is the basis for

constructing the observer. It uses imposed inputs

and measured outputs whose correction terms are

discontinuous function sign for torque and speed

estimation.

The state vectors are: "

s



" and "

s

i

"

SMO based on this equation, [23], [24] :







































s

r

rs

s

rs

s

r

s

u

L

j

TL

i

TT

i

dt

d

ujiR

dt

d









11111

(25)

where:

r

s

sR

L

T

R

L

T ,

note the existence of the back-EMF

s

r

j



in

(25). So we move on to the next model







































)sgn(

11

ˆ

11

ˆ

11

ˆ

)sgn(

ˆ

SK

L

u

L

j

TL

i

TT

i

dt

d

SKujiR

dt

d

s

r

rs

s

rs

s

r

s









(26)

The corrector obtained is

 

ss

i

pii

s

K

KS 











 ˆ

(27)

4.1 Gain Selection

Based on the Lyapunov function, we give the gain

of the observer which ensures the stability:



















 



sr

r

sr

rT

e

T

e

Ks

s

max

(28)

flux error is expressed by





s

e

4.2 Rotor Speed Estimation of IM

ωr calculated by (29), this is among the advantages

of this type of observer :

2

s

r

2

r

gls.

ˆ

R

-

ˆ

d

ˆ

d

1

ˆ

-

ˆ

r

em

rp

T

dtdt



 

















(29)

based on

s



and

s

i

,

r



estimated, as is well

demonstrated by this equation:

M

iLLL srssr

r

...

ˆ









(30)

5 Speed Controller based on

Backstepping

In this part, the Backstepping controller is used to

control the induction motor speed for sensorless

control.

Lyapunov's theory allows us to build a robust

controller, [25], [26], [27] :

     

 

)(

1tftTtT

Jdt

td Lem 



(31)

where:

         

tctbTtaTt

dt

td Lem 



(32)

The parameters of the motor are expressed by a,

b, and c:

J

f

c

J

b

J

a ,

1

,

1

We derive the speed error by this equation:

     

ttte ref 

(33)

We calculate the derivative of the speed error

by:

     

ttte ref  



(34)

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We can write:

       

tctbTtaTte Lemref  



(35)

The Lyapunov function is :

   

tetV 2

2

1



(36)

We derive the Lyapunov function and we find:

               

 

tctbTtTattetetetV Lemref  



.

(37)

The derivative of the Lyapunov function V is

negative. This is expressed by the definition of a

constant "K" in equation (36)

   

0. 2 teKtV



(38)

The general formula for reference torque

*

em

T

is

expressed by:

         

 

teKtctTbt

a

tT Lrefem ...

1

* 

(39)

6 Simulation Results and Discussion

The Global structure of multilevel DTC-SVM

without speed sensor and stator flux based on the

robust sliding mode observer and with motor torque

estimation is shown in Figure 7.

The three-phase squirrel cage motor of 1.5 kW,

parameters are indicated in Table 1.

Table 1. IM motor parameters

Item

Symbol

Data

IM Mechanical

Power

Nominal speed

Nominal

Frequency

Pole pairs number

Stator resistance

Rotor resistance

Stator self-

inductance

Rotor self-

inductance

Mutual

inductance

Moment of inertia

Friction

coefficient

PW



f

P

Rs

Rr

Ls

Lr

Lm

J

F

1.5 Kw

1420 rpm

50 Hz

2

4.85

3.805

274 mH

258 mH

0.031 kg.m2

0.00114kg.m2/s

Fig. 7: Global scheme of sensorless DTC of

induction motor with multilevel SVM based on rotor

speed and stator flux observers

6.1 Performance of DTC with Three-Level

SVM Sensorless Induction Motor based

on SM Observer

Figure 8 gives the good behavior of IM when

estimating the speed by the SMO with high

dynamics, also there is negligible sensitivity to load

disturbances.

The electromagnetic torque response was very

fast. The load torque has no influence on the stator

flux in the plane (α, β), which proves that the

decoupling between torque and flux has been well

achieved.

0 1 2 3

-100

-50

0

50

100

Time (s)

Speed (rad/s)

ref

mes

obs

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E-ISSN: 2224-350X

441

Volume 18, 2023

0 1 2 3

-5

0

5

Time (s)

Speed error (rad/s)

0 1 2 3

0

0.5

1

1.5

Time (s)

Stator flux (Wb)

-2 -1 0 1 2

-2

-1

0

1

2

Flux axis alpha (Wb)

Flux axis beta (Wb)

0 1 2 3

-20

-10

0

10

20

Time (s)

Electromagnetic Torque (N.m)

0 1 2 3

0

0.5

1

Time (s)

Stator flux (Wb)

sd

sq

1 1.05 1.1 1.15 1.2

-2

-1

0

1

2

Time (s)

Stator flux components (Wb)

1.4 1.45 1.5 1.55 1.6

-10

-5

0

5

10

Time (s)

Zoomestator current is (A)

Fig. 8: Different simulation results of the proposed

structure drives: rotor speed, speed error, stator flux,

torque, flux, flux circular trajectory

6.2 Robustness Tests

a. Trapezoidal speed profile

This test concerns the profile of the reversal of the

direction of rotation from -100 rad/s to 100 rad/s, as

shown in Figure 9 it gives a good control results.

0 1 2 3

-100

0

100

Time (s)

Speed (rad/s)

ref

mes

obs

0 1 2 3

-2

-1

0

1

2

Time (s)

Speed error (rad/s)

Fig. 9: Approach proposed with variable speed and

rotation reversal

WSEAS TRANSACTIONS on POWER SYSTEMS

DOI: 10.37394/232016.2023.18.43

Djamila Cherifi , Yahia Miloud

E-ISSN: 2224-350X

442

Volume 18, 2023

b. Low-speed test

In this simulation, the small speed value chosen to

drive the motor is 10 rad/s, is shown in Figure 10.

The results prove that the approach studied is

very effective in all speed regions and the estimation

was well done for 10 rad/s and gives a static error

equal to zero, with rapid rejection of load

disturbance.

0 1 2 3

0

5

10

Time (s)

Speed (rad/s)

ref

mes

obs

0 1 2 3

-1

-0.5

0

0.5

1

Time (s)

Speed error (rad/s)

-2 -1 0 1 2

-2

-1

0

1

2

Flux axis alpha (Wb)

Flux axis beta (Wb)

0 1 2 3

0

0.5

1

1.5

Time (s)

Stator flux (Wb)

Fig. 10: Results of low-speed test

c. Resistive parameter change

We amplified Rs by half of its nominal value, and

the result as found was shown in Figure 11 which

demonstrates that the change in this parameter does

not influence the performance of the training, the

observer at a good estimation of the speed and the

speed regulation loop by Backstepping clearly

shows its robustness.

0 1 2 3

0

50

100

Time (s)

Speed (rad/s)

ref

mes

obs

0 1 2 3

-2

0

2

4

Time (s)

Speed error (rad/s)

0 1 2 3

0

0.5

1

1.5

Time (s)

Stator flux (Wb)

-2 -1 0 1 2

-2

-1

0

1

2

Flux axis alpha (Wb)

Flux axis beta (Wb)

Fig. 11: Study of the influence of the increase in Rs

on the proposed sensorless control drives

7 Conclusion

The research presented in this paper addresses the

DTC with multilevel SVM command of

asynchronous motor for sensorless control of speed

and flux, the used observation based on sliding

mode, using an algorithm robust adjustment system

based on the backstepping controller for the servo-

control and speed regulation of the machine.

The essential aim of this research work is to

improve the performance of a drive system based on

an induction motor controlled by DTC using

WSEAS TRANSACTIONS on POWER SYSTEMS

DOI: 10.37394/232016.2023.18.43

Djamila Cherifi , Yahia Miloud

E-ISSN: 2224-350X

443

Volume 18, 2023

multilevel inverters and the digital and robust

control approach by SVM.

1. Eliminated the disadvantage of variable

switching due to hysteresis comparators which

causes high ripples

2. Replacement of classical control laws by non-

linear ones to ensure the stability and robustness of

the system,

3. Eliminated the high number of sensors by

inserting a sensorless algorithm

This allows us to say that the study control

system provides effective improvements to the DTC

control of the IM, we then see:

1. elimination of flux and torque ripples

2. good speed regulation in all chosen ranges

3. robustness to parameter variations and load

disturbances.

4. decoupling between flux and torque of the

motor.

5. Sliding mode observer shows good

accuracy and excellent estimation of speed

and flux

For the continuation of research relating to this

work, we propose as perspectives:

• Application of other complete order observers.

• Development of control strategies for dual-

supply induction motors

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The authors equally contributed in the present

research, at all stages from the formulation of the

problem to the final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The authors have no conflicts of interest to declare.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

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WSEAS TRANSACTIONS on POWER SYSTEMS

DOI: 10.37394/232016.2023.18.43

Djamila Cherifi , Yahia Miloud

E-ISSN: 2224-350X

445

Volume 18, 2023