M zelechowski sách ĐIỀU KHIỂN TRỰC TIẾP MOMEN DTC SVM M zelechowski

Warsaw University of Technology
Faculty of Electrical Engineering
Institute of Control and Industrial Electronics

Ph.D. Thesis

Marcin Żelechowski, M. Sc.

Space Vector Modulated – Direct
Torque Controlled (DTC – SVM)
Inverter – Fed Induction Motor Drive

Thesis supervisor
Prof. Dr Sc. Marian P. Kaźmierkowski

Warsaw – Poland, 2005



Acknowledgements
The work presented in the thesis was carried out during author’s Ph.D. studies at the
Institute of Control and Industrial Electronics in Warsaw University of Technology,
Faculty of Electrical Engineering. Some parts of the work were realized in cooperation
with foreign Universities:
•

University of Nevada, Reno, USA (US National Science Foundation grant –
Prof. Andrzej Trzynadlowski),

•

University of Aalborg, Denmark (Prof. Frede Blaabjerg),

and company:
•

Power Electronics Manufacture – „TWERD”, Toruń, Poland.

First of all, I would like to express gratitude Prof. Marian P. Kaźmierkowski for the
continuous support and help during work of the thesis. His precious advice and
numerous discussions enhanced my knowledge and scientific inspiration.
I am grateful to Prof. Andrzej Sikorski from the Białystok Technical University and
Prof. Włodzimierz Koczara from the Warsaw University of Technology for their
interest in this work and holding the post of referee.
Specially, I am indebted to my friend Dr Paweł Grabowski for support and
assistance.
Furthermore, I thank my colleagues from the Intelligent Control Group in Power
Electronics for their support and friendly atmosphere. Specially, to Dr Dariusz Sobczuk,
Dr Mariusz Malinowski, Dr Mariusz Cichowlas, and Dariusz Świerczyńki M.Sc.
Finally, I would like thank to my whole family, particularly my parents for their love
and patience.



Contents
Pages
1. Introduction

1

2. Voltage Source Inverter Fed Induction Motor Drive

2.1. Introduction
2.2. Mathematical Model of Induction Motor
2.3. Voltage Source Inverter (VSI)
2.4. Pulse Width Modulation (PWM)
2.4.1. Introduction
2.4.2. Carrier Based PWM
2.4.3. Space Vector Modulation (SVM)
2.4.4. Relation Between Carrier Based and Space Vector Modulation
2.4.5. Overmodulation (OM)
2.4.6. Random Modulation Techniques
2.5. Summary

6
6
6
12
17
17
18
22
28
31
35
39

3. Vector Control Methods of Induction Motor
3.1. Introduction
3.2. Field Oriented Control (FOC)
3.3. Feedback Linearization Control (FLC)
3.4. Direct Flux and Torque Control (DTC)

3.4.1. Basics of Direct Flux and Torque Control
3.4.2. Classical Direct Torque Control (DTC) – Circular Flux Path
3.4.3. Direct Self Control (DSC) – Hexagon Flux Path
3.5. Summary

40
40
40
45
49
49
53
61
64

4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
4.1. Introduction
4.2. Structures of DTC-SVM – Review
4.2.1. DTC-SVM Scheme with Closed – Loop Flux Control
4.2.2. DTC-SVM Scheme with Closed – Loop Torque Control
4.2.3. DTC-SVM Scheme with Close – Loop Torque and Flux Control
Operating in Polar Coordinates
4.2.4. DTC-SVM Scheme with Close – Loop Torque and Flux Control
in Stator Flux Coordinates
4.2.5. Conclusions from Review of the DTC-SVM Structures
4.3. Analysis and Controller Design for DTC-SVM Method with
Close – Loop Torque and Flux Control in Stator Flux Coordinates
4.3.1. Torque and Flux Controllers Design – Symmetry Criterion Method
4.3.2. Torque and Flux Controllers Design – Root Locus Method
4.3.3. Summary of Flux and Torque Controllers Design

4.4. Speed Controller Design
4.5. Summary

66
66
66
66
68
69
70
71
71
75
78
88
94
98


Contents
5. Estimation in Induction Motor Drives
5.1. Introduction
5.2. Estimation of Inverter Output Voltage
5.3. Stator Flux Vector Estimators
5.4. Torque Estimation
5.5. Rotor Speed Estimation
5.6. Summary

99
99

100
104
110
110
112

6. Configuration of the Developed IM Drive Based on DTC-SVM
6.1. Introduction
6.2. Block Scheme of Implemented Control System
6.3. Laboratory Setup Based on DS1103
6.4. Drive Based on TMS320LF2406

113
113
113
115
118

7. Experimental Results
7.1. Introduction
7.2. Pulse Width Modulation
7.3. Flux and Torque Controllers
7.4. DTC-SVM Control System

122
122
122
125
129

8. Summary and Conclusions

138

References

141

List of Symbols

151

Appendices

156

A.1. Derivation of Fourier Series Formula for Phase Voltage
A.2. SABER Simulation Model
A.3. Data and Parameters of Induction Motors
A.4. Equipment
A.5. dSPACE DS1103 PPC Board
A.6. Processor TMS320FL2406


1.

Introduction
The Adjustable Speed Drives (ADS) are generally used in industry. In most drives

AC motors are applied. The standard in those drives are Induction Motors (IM) and

recently also Permanent Magnet Synchronous Motors (PMSM) are offered. Variable
speed drives are widely used in application such as pumps, fans, elevators, electrical
vehicles, heating, ventilation and air-conditioning (HVAC), robotics, wind generation
systems, ship propulsion, etc. [16].
Previously, DC machines were preferred for variable speed drives. However, DC
motors have disadvantages of higher cost, higher rotor inertia and maintenance problem
with commutators and brushes. In addition they cannot operate in dirty and explosive
environments. The AC motors do not have the disadvantages of DC machines.
Therefore, in last three decades the DC motors are progressively replaced by AC drives.
The responsible for those result are development of modern semiconductor devices,
especially power Insulated Gate Bipolar Transistor (IGBT) and Digital Signal Processor
(DSP) technologies.
The most economical IM speed control methods are realized by using frequency
converters. Many different topologies of frequency converters are proposed and
investigated in a literature. However, a converter consisting of a diode rectifier, a dclink and a Pulse Width Modulated (PWM) voltage inverter is the most applied used in
industry (see section 2.3).
The high-performance frequency controlled PWM inverter – fed IM drive should be
characterized by:
•

fast flux and torque response,

•

available maximum output torque in wide range of speed operation region,

•

constant switching frequency,

•

uni-polar voltage PWM,

•

low flux and torque ripple,

•

robustness for parameter variation,

•

four-quadrant operation,


1. Introduction
These features depend on the applied control strategy. The main goal of the chosen
control method is to provide the best possible parameters of drive. Additionally, a very
important requirement regarding control method is simplicity (simple algorithm, simple
tuning and operation with small controller dimension leads to low price of final
product).
A general classification of the variable frequency IM control methods is presented in
Fig. 1.1 [67]. These methods can be divided into two groups: scalar and vector.
Variable
Frequency Control

Scalar based
controllers

U/f=const.
Volt/Hertz

Vector based
controller

i s = f (ωr )

Feedback
Linearization

Field Oriented

Stator Current

Rotor Flux
Oriented

Direct
(Blaschke)

Stator Flux
Oriented

Indirect
(Hasse)

Direct Torque
Control

Direct Torque
Space - Vector
Modulation

Open Loop
&o&
NFO (Jonsson)

Circle flux
trajectory
(Takahashi)

Passivity Based
Control

Hexagon flux
trajectory
(Takahashi)

Closed Loop
Flux & Torque
Control

Fig. 1.1. General classification of induction motor control methods

The scalar control methods are simple to implement. The most popular in industry is
constant Voltage/Frequency (V/Hz=const.) control. This is the simplest, which does not
provide a high-performance. The vector control group allows not only control of the
voltage amplitude and frequency, like in the scalar control methods, but also the

instantaneous position of the voltage, current and flux vectors. This improves
significantly the dynamic behavior of the drive.
However, induction motor has a nonlinear structure and a coupling exists in the
motor, between flux and the produced electromagnetic torque. Therefore, several
methods for decoupling torque and flux have been proposed. These algorithms are
based on different ideas and analysis.

2


1. Introduction
The first vector control method of induction motor was Field Oriented Control
(FOC) presented by K. Hasse (Indirect FOC) [45] and F. Blaschke (Direct FOC) [12] in
early of 70s. Those methods were investigated and discussed by many researchers and
have now become an industry standard. In this method the motor equations are
transformed into a coordinate system that rotates in synchronism with the rotor flux
vector. The FOC method guarantees flux and torque decoupling. However, the
induction motor equations are still nonlinear fully decoupled only for constant flux
operation.
An other method known as Feedback Linearization Control (FLC) introduces a new
nonlinear transformation of the IM state variables, so that in the new coordinates, the
speed and rotor flux amplitude are decoupled by feedback [81, 83].
A method based on the variation theory and energy shaping has been investigated
recently, and is called Passivity Based Control (PBC) [88]. In this case the induction
motor is described in terms of the Euler-Lagrange equations expressed in generalized
coordinates.
In the middle of 80s new strategies for the torque control of induction motor was
presented by I. Takahashi and T. Noguchi as Direct Torque Control (DTC) [97] and by
M. Depenbrock as Direct Self Control (DSC) [4, 31, 32]. Those methods thanks to the
other approach to control of IM have become alternatives for the classical vector control

– FOC. The authors of the new control strategies proposed to replace motor decoupling
and linearization via coordinate transformation, like in FOC, by hysteresis controllers,
which corresponds very well to on-off operation of the inverter semiconductor power
devices. These methods are referred to as classical DTC. Since 1985 they have been
continuously developed and improved by many researchers.
Simple structure and very good dynamic behavior are main features of DTC.
However, classical DTC has several disadvantages, from which most important is
variable switching frequency.
Recently, from the classical DTC methods a new control techniques called Direct
Torque Control – Space Vector Modulated (DTC-SVM) has been developed.
In this new method disadvantages of the classical DTC are eliminated. Basically, the
DTC-SVM strategies are the methods, which operates with constant switching
frequency. These methods are the main subject of this thesis. The DTC-SVM structures

3


1. Introduction
are based on the same fundamentals and analysis of the drive as classical DTC.
However, from the formal considerations these methods can also be viewed as stator
field oriented control (SFOC), as shown in Fig. 1.1.
Presented DTC-SVM technique has also simple structure and provide dynamic
behavior comparable with classical DTC. However, DTC-SVM method is characterized
by much better parameters in steady state operation.
Therefore, the following thesis can be formulated: “The most convenient industrial
control scheme for voltage source inverter-fed induction motor drives is direct
torque control with space vector modulation DTC-SVM”
In order to prove the above thesis the author used an analytical and simulation based
approach, as well as experimental verification on the laboratory setup with 5 kVA and
18 kVA IGBT inverters with 3 kW and 15 kW induction motors, respectively.

Moreover, the control algorithm DTC-SVM has been introduced used in a serial
commercial product of Polish manufacture TWERD, Toruń.
In the author’s opinion the following parts of the thesis are his original achievements:
•

elaboration and experimental verification of flux and torque controller design for
DTC-SVM induction motor drives,

•

development of a SABER - based simulation algorithm for control and
investigation voltage source inverter-fed induction motors,

•

construction and practical verification of the experimental setups with 5 kVA and
18 kVA IGBT inverters,

•

bringing into production and testing of developed DTC-SVM algorithm in Polish
industry.

The thesis consist of eight chapters. Chapter 1 is an introduction. In Chapter 2
mathematical model of IM, voltage source inverter construction and pulse width
modulation techniques are presented. Chapter 3 describes basic vector control method
of IM and gives analysis of advantages and disadvantages for all methods. In this
chapter basic principles of direct torque control are also presented. Those basis are
common for classical DTC, which is presented in Chapter 3 and for DTC-SVM method.
Chapter 4 is devoted to analysis and synthesis of DTC-SVM control technique. The

flux, torque and speed controllers design are presented. In Chapter 5 the estimations

4


1. Introduction
algorithms are described and discussed. In Chapter 6 implemented DTC-SVM control
algorithm and used hardware setup are presented. In Chapter 7 experimental results are
presented and studied. Chapter 8 includes a conclusion. Description of the simulation
program and parameters of the equipment used are given in Appendixes.

5


2.

Voltage Source Inverter Fed Induction Motor Drive

2.1.

Introduction

In this chapter the model of induction motor will be presented. This mathematical
description is based on space vector notation. In next part description of the voltage
source inverter is given. The inverter is controlled in Pulse Width Modulation fashion.
In last part of this chapter review of the modulation technique is presented.

2.2.

Mathematical Model of Induction Motor

When describing a three-phase IM by a system of equations [66] the following
simplifying assumptions are made:
•

the three-phase motor is symmetrical,

•

only the fundamental harmonic is considered, while the higher harmonics of the
spatial field distribution and of the magnetomotive force (MMF) in the air gap
are disregarded,

•

the spatially distributed stator and rotor windings are replaced by a specially
formed, so-called concentrated coil,

•

the effects of anisotropy, magnetic saturation, iron losses and eddy currents are
neglected,

•

the coil resistances and reactance are taken to be constant,

•

in many cases, especially when considering steady state, the current and voltages

are taken to be sinusoidal.

Taking into consideration the above stated assumptions the following equations of
the instantaneous stator phase voltage values can be written:

U A = I A Rs +

dΨ A
dt

(2.1a)

U B = I B Rs +

dΨ B
dt

(2.1b)


2.2. Mathematical Model of Induction Motor
U C = I C Rs +

dΨ C
dt

(2.1c)

The space vector method is generally used to describe the model of the induction
motor. The advantages of this method are as follows:

•

reduction of the number of dynamic equations,

•

possibility of analysis at any supply voltage waveform,

•

the equations can be represented in various rectangular coordinate systems.

A three-phase symmetric system represented in a neutral coordinate system by phase
quantities, such as: voltages, currents or flux linkages, can be replaced by one resulting
space vector of, respectively, voltage, current and flux-linkage. A space vector is
defined as:

k=

[

]

2
1 ⋅ k A (t ) + a ⋅ k B (t ) + a 2 ⋅ k C (t )
3

(2.2)

where: k A (t ), k B (t ), k C (t ) – arbitrary phase quantities in a system of natural
coordinates, satisfying the condition k A (t ) + k B (t ) + k C (t ) = 0 ,
1, a, a2 – complex unit vectors, with a phase shift
2/3 – normalization factor.
Im
3
k
2

B

a 2 kC (t )
a

k

ak B (t )
Re

1
k A (t )

A

a2

C

Fig. 2.1. Construction of space vector according to the definition (2.2)

7


2. Voltage Source Inverter Fed Induction Motor Drive
An example of the space vector construction is shown in Fig. 2.1.
Using the space vector method the IM model equation can be written as:
U s = I s Rs +

dΨ s
dt

(2.3a)

U r = I r Rr +

dΨ r
dt

(2.3b)

Ψ s = Ls I s + Me jγ m I r

(2.4a)

Ψ r = Lr I r + Me − jγ m I s

(2.4b)

These are the voltage equations (2.3) and flux-current equations (2.4).
To obtain a complete set of electric motor equations it is necessary to, firstly,

transform the equations (2.3, 2.4) into a common rotating coordinate system and
secondly bring the rotor value into the stator side and thirdly. These equations are
written in the coordinate system K rotating with the angular speed ΩK .
U sK = Rs I sK +

dΨ sK
+ j ΩK Ψ sK
dt

(2.5a)

U rK = Rr I rK +

dΨ rK
+ j(ΩK − pb Ωm )Ψ rK
dt

(2.5b)

Ψ sK = Ls I sK + LM I rK

(2.6a)

Ψ rK = Lr I rK + LM I sK

(2.6b)

The equation of the dynamic rotor rotation can be expressed as:

dΩm 1

= [M e − M L − BΩm ]
dt
J

(2.7)

where: M e – electromagnetic torque,
M L – load torque,

B – viscous constant.
In further consideration the friction factor will be negated (B = 0 ) .
The electromagnetic torque M e can be expressed by the following formulas:

8


2.2. Mathematical Model of Induction Motor

M e = − pb
M e = pb

(

ms
LM Im I *s I r
2

(

ms

Im Ψ *s I s
2

)

(2.8)

)

(2.9)

Taking into consideration the fact that in the cage motor the rotor voltage equals zero
and the electromagnetic torque equation (2.9) a complete set of equations for the cage
induction motor can be written as:
U sK = Rs I sK +
0 = Rr I rK +

dΨ sK
+ j ΩK Ψ sK
dt

dΨ rK
+ j(ΩK − pb Ωm )Ψ rK
dt

(2.10a)

(2.10b)

Ψ sK = Ls I sK + LM I rK

(2.11a)

Ψ rK = Lr I rK + LM I sK

(2.11b)

(

)

dΩm 1  ms

Im Ψ *s I s − M L 
=  pb
dt
J
2


(2.12)

Equations (2.10), (2.11) and (2.12) are the basis of further consideration.
The applied space vector method as a mathematical tool for the analysis of the
electric machines a complete set equations can be represented in various systems of
coordinates. One of them is the stationary coordinates system (fixed to the stator) α − β
in this case angular speed of the reference frame is zero ΩK = 0 . The complex space
vector can be resolved into components α and β .
U sK = U sα + jU sβ
I sK = I sα + j I sβ ,

(2.13a)
I rK = I rα + j I rβ

Ψ sK = Ψ sα + jΨ sβ , Ψ rK = Ψ rβ + jΨ rβ

(2.13b)
(2.13c)

In α − β coordinate system the motor model equation can be written as:
U sα = Rs I sα +

dΨ sα
dt

(2.14a)

9


2. Voltage Source Inverter Fed Induction Motor Drive

U sβ = Rs I sβ +

0 = Rr I rα +
0 = Rr I rβ +

dΨ sβ
dt

dΨ rα
+ pb ΩmΨ rβ
dt
dΨ rβ
dt

− pb ΩmΨ rα

(2.14b)

(2.14c)

(2.14d)

Ψ sα = Ls I sα + LM I rα

(2.15a)

Ψ sβ = Ls I sβ + LM I rβ

(2.15b)

Ψ rα = Lr I rα + LM I sα

(2.15c)

Ψ rβ = Lr I rβ + LM I sβ

(2.15d)

dΩm 1  ms
(Ψ sα I sβ − Ψ sβ I sα ) − M L 
=  pb
dt
J
2


(2.16)

The relations described above by the motor equations can be represented as a block
diagram. There is not just one block diagram of an induction motor. The lay-out
Construction of a block diagram will depend on the chosen coordinate system and input
signals. For instance, if it is assumed in the stationary α − β coordinate system that the
input signal to the motor is the stator voltage, the equations (2.14-2.16) can be
transformed into:
dΨ sα
= U sα − Rs I sα
dt
dΨ sβ

= U sβ − Rs I sβ

(2.17b)

dΨ rα
= − Rr I rα − pb ΩmΨ rβ
dt

(2.17c)

dt

dΨ rβ

= − Rr I rβ + pb ΩmΨ rα

(2.17d)

I sα =

L
1
Ψ sα − M Ψ rα
σLs
σLs Lr

(2.18a)

I sβ =

1
L
Ψ sβ − M Ψ rβ
σLr
σLs Lr

(2.18b)

dt

10

(2.17a)


2.2. Mathematical Model of Induction Motor
I rα =

1
L
Ψ rα − M Ψ sα
σLr
σLs Lr

(2.18c)

I rβ =

1
L
Ψ rβ − M Ψ sβ
σLr
σLs Lr

(2.18d)

dΩm 1  ms
(Ψ sα I sβ − Ψ sβ I sα ) − M L 
=  pb

dt
J 2


(2.19)

These equations can be represented in the block diagram as shown in Fig. 2.2.
ML
Rs
U sα

∫

Ψ sα

LM

LM

σLs Lr

Rr

∫

I sα

1

σ Ls

I rα

σLs Lr

pb

ms M e
2

1
J

∫

Ωm

1

σ Lr

Ψ rα

pb

∫
Rr

Ψ rβ
I rβ

1

σ Lr
LM

LM

σLs Lr

U sβ

∫

Ψ sβ

σLs Lr

1
σ Ls

I sβ

Rs

Fig. 2.2. Block diagram of an induction motor in the stationary coordinate system

α −β

This representation of the induction motor is not good for use to design a control

structure, because the output signals flux, torque and speed depend on both inputs. From
the control point of view this system is complicated. That is the reason why there are a

11


2. Voltage Source Inverter Fed Induction Motor Drive
few methods proposed to decouple the flux and torque control. It is achieved, for
example, by the orientation of the coordinate system to the rotor or stator flux vectors.
Both control systems are described further in Chapter 3.
The equations (2.17), (2.18), (2.19) and the block diagram presented in the Fig. 2.2
can be used to build a simulation model of the induction motor. It was used in a
simulation model, which is presented in Appendix A.2.

2.3.

Voltage Source Inverter (VSI)

The three-phase two level VSI consists of six active switches. The basic topology of
the inverter is shown in Fig. 2.3. The converter consists of the three legs with IGBT
transistors, or (in the case of high power) GTO thyristors and free-wheeling diodes. The
inverter is supplied by a voltage source composed of a diode rectifier with a C filter in
the dc-link. The capacitor C is typically large enough to obtain adequately low voltage
source impedance for the alternating current component in the dc-link.
DC side

PWM Converter
T1

U dc

2

S A+

C

T3
D1

SB +

D2

SB -

T5
D3

S C+

D4

S C-

D5

0

T2
U dc

2

S A-

C

T4

IA

UAB

A

RA
LA
EA

T6

IB

IC
B

RC
UB

LB
EB

LC

UC

EC
N

Fig. 2.3. Topology of the voltage source inverter

12

AC side

C

RB
UA

D6

IM


2.3. Voltage Source Inverter (VSI)
The voltage source inverter (Fig. 2.3) makes it possible to connect each of the three
motor phase coils to a positive or negative voltage of the dc link. Fig. 2.4 explains the
fabrication of the output voltage waves in square-wave, or six-step, mode of operation.
The phase voltages are related to the dc-link center point 0 (see Fig. 2.3).
a)

UA0

1

2

3

4

5

6

1
U dc
2

0

π

2π

ωt

π

2π

ωt

π

2π

ωt

π

2π

ωt

π

2π

ωt

1
− U dc
2

b)

UB0
1
U dc

2

0
1
− U dc
2

c)

UC0
1
U dc
2

0
1
− U dc
2

d)

UAB
U dc

2
U dc
3
1
U dc
3

0
1
− U dc
3
2
− U dc
3
− U dc

e)

UA
2
U dc
3
1
U dc
3

0
1
− U dc
3
2
− U dc
3

Fig. 2.4. The output voltage waveforms in six-step mode

The phase voltage of an inverter fed motor (Fig. 2.4e) can be expressed by Fourier
series as [16, 66]:
UA =

∞
∞
1
U dc ∑ sin (nωt ) = U m (n ) ∑ sin (nωt )
π
n =1 n
n =1

2

(2.20)

where:
U dc - dc supply voltage,

13


2. Voltage Source Inverter Fed Induction Motor Drive
U m (n ) =

2
U dc - peak value of the n-th harmonic,
nπ

n = 1+6k, k = 0, ±1, ±2,…

Derivation of the formula (2.20) is presented in Appendix A.1.
U1 (100)

a)
Udc

Udc

A

B

C

U3 (010)

c)

B

C

A

B

C

A

B

C

A

B

C

Udc

A

B

C

U5 (001)

U6 (101)

f)

Udc

Udc

A

B

C

U0 (000)

g)

A

U4 (011)

d)

Udc

e)

U2 (110)

b)

U7 (111)

h)

Udc

Udc

A

B

C

Fig. 2.5. Switching states for the voltage source inverter

From the equation (2.20) the fundamental peak value is given as:
U m (1) =

14

2

π

U dc

(2.21)


2.3. Voltage Source Inverter (VSI)
This value will be used to define the modulation index M used in pulse width
modulation (PWM) methods (see section 2.4).
For the sake of the inverter structure, each inverter-leg can be represented as an ideal
switch. The equivalent inverter states are shown in Fig. 2.5.
There are eight possible positions of the switches in the inverter. These states
correspond to voltage vectors. Six of them (Fig. 2.5 a-f) are active vectors and the last
two (Fig. 2.5 g-h) are zero vectors. The output voltage represented by space vectors is

defined as:
2
j ( v −1)π 3
 3 U dc e
Uv = 
0


v = 1...6
(2.22)

v = 0,7

The output voltage vectors are shown in Fig. 2.6.
Im
U3 (010)

U4 (011)

U2 (110)

U1 (100)

U0 (000)

Re

U7 (111)

U5 (001)

U6 (101)

Fig. 2.6. Output voltage represented as space vectors

Any output voltage can in average be generated, of course limited by the value of the
dc voltage. In order to realize many different pulse width modulation methods are
proposed [13, 27, 30, 38, 46, 47, 51, 52, 105] in history. However, the general idea is

15


2. Voltage Source Inverter Fed Induction Motor Drive
based on a sequential switching of active and zero vectors. The modulation methods are
widely described in the next section.
Only one switch in an inverter-leg (Fig. 2.3) can be turned on at a time, to avoid a
short circuit in the dc-link. A delay time in the transistor switching signals must be
inserted. During this delay time, the dead-time TD transistors cease to conduct. Two
control signals SA+, SA- for transistors T1, T2 with dead-time TD are presented in Fig.
2.7. The duration of dead-time depends of the used transistor. Most of them it takes 13µs.

SA+
t
SATD

TD

t

Ts

Fig. 2.7. Dead-time effect in a PWM inverter

Although, this delay time guarantees safe operation of the inverter, it causes a serious
distortion in the output voltage. It results in a momentary loss of control, where the
output voltage deviates from the reference voltage. Since this is repeated for every
switching operation, it has significant influence on the control of the inverter. This is
known as the dead-time effect. This is important in applications like a sensorless direct
torque control of induction motor. These applications require feedback signals like:
stator flux, torque and mechanical speed. Typically the inverter output voltage is needed
to calculate it. Unfortunately, the output voltage is very difficult to measure and it
requires additional hardware. Because of that for calculation of feedback signals the
reference voltage is used. However, the relation between the output voltage and the
reference voltage is nonlinear due to the dead-time effect [8]. It is especially important

16


2.4. Pulse Width Modulation (PWM)
for the low speed range when voltage is very low. The dead-time may also cause
instability in the induction motor [52].
Therefore, for correct operation of control algorithm proper compensation of deadtime is required. Many approaches are proposed to compensate of this effect [2, 3, 8, 29,
54, 64, 76].
The dead-time compensation is directly connected with estimation of inverter output
voltage. Therefore, compensation algorithm, which is used in final control structure of
the inverter is presented in Chapter 5.

2.4.

Pulse Width Modulation (PWM)

2.4.1. Introduction

In the voltage source inverter conversion of dc power to three-phase ac power is
performed in the switched mode (Fig. 2.3). This mode consists in power semiconductors
switches are controlled in an on-off fashion. The actual power flow in each motor phase
is controlled by the duty cycle of the respective switches. To obtain a suitable duty
cycle for each switches technique pulse width modulation is used. Many different
modulation methods were proposed and development of it is still in progress [13, 27,
30, 38, 46, 47, 51, 52, 105].
The modulation method is an important part of the control structure. It should
provide features like:
•

wide range of linear operation,

•

low content of higher harmonics in voltage and current,

•

low frequency harmonics,

•

operation in overmodulation,

•

reduction of common mode voltage,

•

minimal number of switching to decrease switching losses in the power
components.

The development of modulation methods may improve converter parameters. In the
carrier based PWM methods the Zero Sequence Signals (ZSS) [46] are added to extend
17


2. Voltage Source Inverter Fed Induction Motor Drive
the linear operation range (see section 2.4.2). The carrier based modulation methods
with ZSS correspond to space vector modulation. It will be widely presented in section
2.4.4.
All PWM methods have specific features. However, there is not just one PWM
method which satisfies all requirements in the whole operating region. Therefore, in the
literature are proposed modulators, which contain from several modulation methods.
For example, adaptive space vector modulation [79], which provides the following
features:
•

full control range including overmodulation and six-step mode, achieved by the
use of three different modulation algorithms,

•

reduction of switching losses thanks to an instantaneous tracking peak value of
the phase current.

The content of the higher harmonics voltage (current) and electromagnetic
interference generated in the inverter fed drive depends on the modulation technique.
Therefore, PWM methods are investigated from this point of view. To reduce these
disadvantages several methods have been proposed. One of these methods is random
modulation (RPWM). The classical carrier based method or space vector modulation
method are named deterministic (DEPWM), because these methods work with constant
switching frequency. In opposite to the deterministic methods, the random modulation
methods work with variable frequency, or with randomly changed switching sequence
(see section 2.4.6).

2.4.2. Carrier Based PWM

The most widely used method of pulse width modulation are carrier based. This
method is also known as the sinusoidal (SPWM), triangulation, subharmonic, or
suboscillation method [16, 52]. Sinusoidal modulation is based on triangular carrier
signal as shown in Fig. 2.8. In this method three reference signals UAc, UBc, UCc are
compared with triangular carrier signal Ut, which is common to all three phases. In this
way the logical signals SA, SB, SC are generated, which define the switching instants of
the power transistors as is shown in Fig. 2.9.

18


2.4. Pulse Width Modulation (PWM)
Udc
UAc

SA

UBc

SB

UCc

SC
A

B

C

Ut
Carrier

N
Fig. 2.8. Block scheme of carrier based sinusoidal PWM

U dc 2

Ut

UAc UBc

0

− U dc 2

UCc

1

SA

0
1

SB
SC

UA

0
1
0

2 3Udc
1 3Udc0
0

−1 3Udc
− 2 3Udc
U dc

U AB

0

− U dc

0

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Fig. 2.9. Basic waveforms of carrier based sinusoidal PWM

19