Enhanced Control of A Photovoltaic Water Pumping System by DTC-SVM

‫الجمهورية الجزائرية الديمقراطية الشعبية‬
People's Democratic Republic of Algeria

‫وزارة التعليم العالي و البحث العلمي‬
Ministry Of Higher Education & Scientific Research
‫جامعة الوادي‬
University of Eloued
‫كلية التكنولوجيا‬
Faculty of Technology
‫قسم الهندسة الكهربائية‬
Department of Electrical Engineering
A thesis submitted for the fulfillment of

the degree of
Master in Electrical Engineering
Option: Electrical Drive
Theme
Enhanced Control of a Photovoltaic Water Pumping

System by DTC-SVM
Presented by
Hocine Ihab AZZA and Ahmed MESAI BELGACEM
Board of Examiners:
Dr. Zohier TIR Suprvisor MCA

Dr. Youcef Bekkakra President MCA
Dr. Ismail Laib Examiner MCA
2019/2020
Dedication
I dedicate this thesis to my father,
I also dedicate it to my mother who has taken the biggest part of
sacrificing for our education. May Allah protect them.
To my brothers and sisters. To my nephews and nieces.
To all my friends, in my life.
Hocine Ihab AZZA
I
Dedication
I dedicate this thesis to my parent “MESAI BELGACEM
Elhadi” and "BEN ALI Teffaha", who have taken the biggest part
of sacrificing for my education. May Allah protect them.
To my brother: Abdelbaki.
To my sisters: Ikram and Sondos.
To all my friends, in my social and academic life.
Ahmed MESAI BELGACEM
II
Acknowledgments
First of all, I would like to thank God “Allah” the Most Gracious and the
Most Merciful, for blessing me with knowledge and giving me strength, courage,
patience, and serenity during all these years of study.
I would like to express my thanks to everyone that makes the achievement of

this work. My great gratitude goes to my supervisors: Dr. Zohier Tir for his
continuous support, guidance, encouragement throughout my project, his extensive
knowledge, and diligent working.
I also wish to thank the President of the jury Dr. Bekkakra Youcef and Dr.
Laib Ismail for serving as my committee members and taking the time to revise my
thesis. I am thankful that in the midst of all their activities, they accepted to be
members of the reading committee.
Last but not the least, I am grateful to my parents for their prayers,
guidance, and support throughout my education. Their inspiration and
encouragement have been invaluable.
III
Abstract ----------------------------------------------------------------------------------------------------------
‫تحسين التحكم في نظام ضخ المياه الكهروضوئي بناء على تقنية التحكم المباشر في عزم الدوران مع تعديل طول النبضة‬
(DTC-SVM) ‫الشعاعي‬
‫ مثل المواقع المعزولة في الصاااحراء فما يعد نظام ضاااخ‬،‫ العديد من ا ألماكن تعاني من مشاااافل في اامدا ا المياه‬،‫ حاليا‬- ‫ملخص‬
‫ والذي يحتاج االى صاايانة ألقل مقارنة بأأنظمة الطاقة ا ألخرى حيث يتكون هذا النظام‬،‫المياه ابلطاقة الشاامس ااية المس ااتقل ألحد ال لول المقترحة‬
‫ متصااال بعاكص مصااادر وهد مزو بمحرم حثي مقترن بمضااا ة ذا طر مرفزي الهدف والغرض من هذه المذكرة هو‬،‫من مولد كهروضاااوئي‬
‫ ولضمان‬،‫( للتحكم في المحرم الالتزامني الذي يساتمد تغذيته عن طريق النظام الكهروضوئي‬DTC) ‫اساات دام تقنية التحكم المباشار في العزم‬
(DTC-SVM) ‫ مع تعديل طول النبضاة الشعاعي‬DTC ‫التشاغيل ا ألمثل للطاقة لهذا النظام عند ظروف مناخية مختلفة بمعية تقنية التحكم‬
‫ لانشاااء المروع المناس ا نقدم بين يديكم هذا المحتوى والذي ننناقش فيه النتائج المتحصاال عليها لهذا‬P&O ‫حيث يتم اس اات دام خواريمية‬
. ‫ وفل ذلك تم ابساتعمال برانمج ماتالب للم افا‬، ‫النظام وهذا للتحقق من أل اءه ووو ته‬
‫ مض ة‬،‫ ا أللواح الكهروضوئية‬،‫ تعديل الفضاء الشعاعي‬،‫ مموج مصادر الجهد‬،‫ التحكم المباشار في العزم‬،‫ المحرم الالتزامني‬:‫الكلما المفتاحية‬
.‫ الطاقة المتجد ة‬، ‫( تتبع النقطة القصوى للطاقة‬MPPT) ، ‫ الطاقة الشمساية‬،‫الطر المرفزي‬
Enhanced Control of a Photovoltaic Water Pumping System by

DTC-SVM
Abstract - This thesis proposes an improved provide a (DTC) technique to control the used
motor in the photovoltaic system. The main contribution of this work ensures an optimum power
operation (MPPT) of this system for different climate conditions, the (P&O) algorithm is used to
generate the appropriate reference for direct torque control technique with space vector modulation
(DTC-SVM). This is achieved by the stand-alone solar water pumping system is one of the proposed
solutions for them, and it needs less intervention than other renewable energy systems by applying a
system consists of a photovoltaic generator, which is connected to a voltage source inverter supplying
an induction motor coupled to a centrifugal pump. To validate the whole system's performance, we
presented and discussed the result using the MATLAB/SIMULINK software environment. The solar
water pumping system is stable and gave satisfactory results, the DTC - SVM control is reduced the
torque and flux ripples, with a fewer harmonics of induction motor current, where the electromagnetic
torque of the induction motor tracked the load torque that was produced by the pump and controlled
by DTC-SVM.
Keywords: Induction Motor, Direct Torque Control, Voltage Source Inverter, Space Vector
Modulation, Photovoltaic, Centrifugal Pump, Solar Energy, Maximum Power Point Tracking.
IV
List of figures ------------------------------------------------------------------------------------------------------------
List of figures
Figure I.1. Photovoltaic Water Pumping System [7]. 4
Figure I.2. Solar Thermal Panel and Solar Photovoltaic Panel [9] 5
Figure I.3. Solar radiation’s components (DNI and DHI) [10]. 6
Figure I.4. The main components of the photovoltaic system [8]. 7
Figure I.5. Types of the photovoltaic solar cell [17]. 8
Figure I.6. The serial connections of PV modules [19]. 8
Figure I.7. The parallel connections of PV modules [19]. 9
Figure I.8. Shaded PV cells with Bypass Diodes protection [19]. 9
Figure I.9. PV cells with Bypass and Blocking Diodes protection [19]. 10
Figure I.10. Component and operational principle of PV cells [12]. 10
Figure I.11. Standard Stand-Alone PV system [19]. 11
Figure I.12. Standard Grid-Connected PV system [19]. 12
Figure I.13. Standard Hybrid PV system [21]. 12
Figure I.14. Typical I–V and P–V curves for a PV cell’s output [22]. 13
Figure I.15. I–V Characteristic curve of a PV module [12]. 13
Figure I.16. I–V Characteristic Curve of a PV Module at Constant Received Solar Radiation and Variable
Temperature [12]. 14
Figure I.17. The cycle of the Perturb and Observe algorithm [21]. 15
Figure I.18. Surface Centrifugal Pump [24]. 16
Figure II.1. Cross-section of an Induction Machine [31]. 18
Figure II.2. Squirrel-cage Rotors [32]. 19
Figure II.3. Induction Motor equivalent structure [6]. 19
Figure II.4. The passage of three-phase to a two-phase system using PARK transformation [6]. 21
Figure II.5. Three-phase voltage inverter [6]. 23
Figure II.6. The switching states of the output voltage represented by space vectors [6]. 24
Figure II.7. Vectors of Output Voltage in the complex plane (d-q axes) [4]. 25
Figure II.8. The possible range of the voltage reference vector in the SVM [4]. 26
Figure II.9. The process of generating the reference voltage vector in the first sector [4]. 27
Figure II.10. Switching sequence of the first sector [41]. 28
Figure III.1. General block diagram of SVM direct torque control [6]. 30
Figure III.2. DTC-SVM scheme with a closed flux control [5]. 31
Figure III.3. DTC-SVM scheme with closed torque control [5]. 31
Figure III.4. DTC-SVM scheme operated in stator flux polar coordinates [5]. 32
Figure III.5. DTC-SVM scheme operated in stator flux Cartesian coordinates [5]. 32
Figure III.6. The global control scheme of stator flux oriented DTC- SVM [6]. 33
Figure III.7. The flux control loop. 34
Figure III.8. The torque control loop. 35
Figure III.9. The speed control loop. 36
Figure III.10. Block diagram of the current model flux estimator [5]. 37
Figure III.11. Flux estimator based on current and voltage models [49]. 38
Figure III.12. Block diagram of speed estimator based on MRAS [52]. 39
Figure III.13. Simulation result of starting up and the steady-state case. 40
Figure III.14. Simulation result of low and reversing speed case. 41
Figure III.15. Simulation result of DTC-SVM using rotor speed estimation based on MRAS. 42
Figure IV.1. Block diagram of the PV array-fed IM drive [3]. 45
Figure IV.2. Reference speed generation 𝜔1 [1]. 47
Figure IV.3. Feedforward speed component [1]. 48
Figure IV.4. Block simulation of the Photovoltaic Water Pumping System using DTC-SVM control. 48
V
List of figures ------------------------------------------------------------------------------------------------------------
Figure IV.5. Simulation result of the varying in the load torque produced by the pump. 49
Figure IV.6. Simulation result of Photovoltaic Water Pumping System using DTC-SVM. 49
VI
List of tables -----------------------------------------------------------------------------------------------------
List of tables
Table I.1. Types of PV cell with their Efficiency and Expected lifetime [12]. ........................................... 7
Table II.1. Output voltage vectors corresponding to the switching states [41]. ......................................... 25
VII
Nomenclature ---------------------------------------------------------------------------------------------------
List of Abbreviations
AC Alternative Current.
DC Direct Current.
DHI Direct horizontal irradiance.
DNI Diffuse normal irradiance.
DSC Direct Self Control.
DTC Direct Torque Control.
IM Induction Motor.
MPPT Maximum Power Point Tracking.
MRAS Model Reference Adaptive System.
PI Proportional-Integral.
P&O Perturb and Observe.
PWM Pulse Width Modulation.
PV Photovoltaic.
SFOC Stator Filed Oriented Control.
SHE Selected Harmonic Elimination.
SPWM Sinusoidal Pulse Width Modulation.
SVM Space Vector Modulation.
SVPWM Space Vector Pulse Width Modulation.
VSI Voltage Source Inverter.
VIII
Nomenclature ---------------------------------------------------------------------------------------------------
List of Symbols
𝑉𝑠𝛼 𝑉𝑠𝛽 𝛼 and 𝛽 components of stator voltage.
𝑖𝑠𝛼 𝑖𝑠𝛽 𝛼 and 𝛽 components of stator current.
𝜓𝑠𝛼 𝜓𝑠𝛽 𝛼 and 𝛽 components of stator flux.
𝜓𝑟𝛼 𝜓𝑟𝛽 𝛼 and 𝛽 components of rotor flux.
𝜓𝑠 , 𝜓𝑟 Stator flux, Rotor flux.
𝑅𝑠 𝑅𝑟 Stator and rotor resistances respectively.
𝐿𝑠 𝐿𝑟 Stator and rotor inductances respectively.
𝑇𝑒 , TL Electromagnetic torque, Torque Load.
𝜎 Blondel’s coefficient.
𝑀𝑠𝑟 Stator-rotor mutual inductance
𝑝 Number of poles pairs.
𝜔𝑟 Rotor speed.
𝜔𝑠 Synchronous speed.
𝐽 Inertia moment.
𝑓 Coefficient of friction.
𝑉𝑑𝑐 Dc-bus voltage.
𝑆𝜓𝑠 , 𝑆𝑇𝑒 Flux logic output, Torque logic output.
ℎ𝜓𝑠 , ℎ 𝑇𝑒 Hysteresis band of stator flux and torque.
𝜃s Flux angle.
𝛿 Load angle between the stator and rotor flux vectors.
𝑇𝑠 Sampling time.
𝑇1 𝑇2 Reference voltages vectors corresponding durations.
𝐾𝑝 𝐾𝑖 Proportional and integral gains.
𝑉𝑠𝑑 𝑉𝑠𝑞 Direct and quadratic stator voltage components.
𝑉𝑟𝑑 𝑉𝑟𝑞 Direct and quadratic rotor voltage components.
𝑇p , K1 Load pump, Proportional constant of the pump.
𝑇, 𝑆 Temperature, Insolation.
𝜔ref Reference speed.
IX
Table of Contents -----------------------------------------------------------------------------------------------
Table of Contents
General Introduction........................................................................................................................ 2
CHAPTER I State of the Art of Solar Photovoltaic Water Pumping System .......................... 3
I.1 Introduction ........................................................................................................................ 4
I.2 Photovoltaic water pumping system ................................................................................... 4
I.3 Solar energy and photovoltaic system ................................................................................ 5
I.3.1 Solar energy: why renewable energy? ............................................................................ 5
I.3.2 Types of solar radiation .................................................................................................. 5
I.3.3 Photovoltaic solar energy ............................................................................................... 6
I.3.4 Photovoltaic cells: .......................................................................................................... 6
I.3.5 Photovoltaic effect ........................................................................................................ 10
I.3.6 Different types of PV systems ...................................................................................... 11
I.3.7 PV output characteristics and parameters ..................................................................... 13
I.3.8 Effect of solar irradiation and temperature ................................................................... 13
I.3.9 Maximum Power Point Tracking control techniques ................................................... 14
I.4 Water Pumping System .................................................................................................... 15
I.4.1 Motor technology ......................................................................................................... 15
I.4.2 Pump technology .......................................................................................................... 15
I.5 Conclusion ........................................................................................................................ 16
CHAPTER II Induction Motor Modeling and Space Vector Modulation ............................ 17
II.1 Introduction ...................................................................................................................... 18
II.2 Description and mathematical model of induction motor ................................................ 18
II.2.1 Description of the induction motor ............................................................................... 18
II.2.2 Modeling assumptions .................................................................................................. 19
II.2.3 Equivalent representation and vector formulation ........................................................ 19
II.2.4 Park transformation ...................................................................................................... 21
II.2.5 Two-phase models of induction machine ..................................................................... 22
II.3 Voltage Source Inverter (VSI) .......................................................................................... 23
II.4 Pulse Width Modulation (PWM)...................................................................................... 24
II.4.1 Space Vector Pulse Width Modulation ........................................................................ 24
II.5 Conclusion ........................................................................................................................ 28
CHAPTER III DTC-SVM Control for Induction Motor ...................................................... 29
III.1 Introduction ...................................................................................................................... 30
III.2 Direct Torque Control with Space vector modulation ...................................................... 30
III.3 Structures of DTC-SVM................................................................................................... 30
III.3.1 DTC-SVM strategy using closed-loop flux control...................................................... 30
X
Table of Contents -----------------------------------------------------------------------------------------------
III.3.2 DTC-SVM strategy using closed-loop torque control .................................................. 31

III.3.3 DTC-SVM strategy using closed-loop flux and torque control in polar coordinates ... 32
III.3.4 DTC-SVM with closed-loop torque and flux control in stator flux coordinates .......... 32
III.4 Stator Flux Field-Oriented DTC-SVM ............................................................................. 33
III.4.1 Flux control design ....................................................................................................... 34
III.4.2 Torque control design ................................................................................................... 35
III.4.3 Speed control design..................................................................................................... 36
III.5 Flux, Torque, and Speed Estimation for Induction Motor Drives .................................... 36
III.5.1 Flux vector estimator .................................................................................................... 36
III.5.2 Torque estimation ......................................................................................................... 38
III.5.3 Rotor speed estimation based MRAS ........................................................................... 39
III.6 Simulation Results ............................................................................................................ 39
III.7 Conclusion ........................................................................................................................ 43
CHAPTER IV Photovoltaic Pumping System using DTC-SVM Control for Induction Motor44
IV.1 Introduction ...................................................................................................................... 45
IV.2 System Description........................................................................................................... 45
IV.3 System Design .................................................................................................................. 46
IV.3.1 Selection of DC-Link voltage ....................................................................................... 46
IV.3.2 DC-link capacitor voltage ............................................................................................. 46
IV.3.3 Design of water pump................................................................................................... 46
IV.4 System control .................................................................................................................. 47
IV.4.1 Reference speed estimation of induction motor ........................................................... 47
IV.5 Simulation Results ............................................................................................................ 48
IV.6 Conclusion ........................................................................................................................ 50
General Conclusion ........................................................................................................................ 52
XI
GENERAL
INTRODUCTION
GENERAL INTRODUCTION --------------------------------------------------------------------------------
General Introduction
In recent years, energy production has been a major challenge, where the energy demand
increases depend on the increase in population growth, and in the remote places have more demand
than others, especially for extracting the water [1]. Most of the electric power production depends
on non-renewable resources such as petroleum, coal, natural gas, and nuclear power sources. These
sources pose a big danger and threat to the environment. On the other hand, the use of renewable
energy such as the sun’s insolation, wind, and geothermal heat to produce electrical energy does
not pollute the environment and preserve it, which is the perfect way to provide water in isolated
areas [2].
In this thesis, the objective of our study is the implementation of a solar photovoltaic water
pumping system based on DTC-SVM control for an Induction motor connected with a centrifugal
pump [3], this system absorbs and stores the water from the well into a tank.
The present work is structured as follows:
In the first chapter, we present a theoretical overview of the photovoltaic and pumping
systems, where we present some methods and techniques that allow us to extract the available
maximum power that can be produced taking into account the influences of the temperature and
insolation variation on the efficiency of the PV systems.
In the second chapter, we present the modelling of the essential parts of the studied system
starting from the Induction Motor (IM) to the Voltage Source Inverter (VSI) and ending with the
theoretical overview of the Space Vector Pulse Width Modulation (SVPWM or SVM) [4].
In the third chapter, we present the Direct Torque Control (DTC) incorporated with the
SVM technique for induction motor drive. Yet, an accurate flux estimator is used to estimate the
non-measurable state variables [5], [6]. Finally, we close this chapter by implementing the SVM-
DTC technique using Simulink/Matlab with the discussion of the obtained results.
In the last chapter, we implement numerically the whole studied system that followed by
comments on the obtained results under different conditions.
2
CHAPTER I
State of the Art of Solar
Photovoltaic Water Pumping
System
CHAPTER I -------------------------- State of the Art of Solar Photovoltaic Water Pumping System
I.1 Introduction
The most common problems that face the rural owners are the absence of water and
electricity, and the difficulty to provide the fuel in some places, knowing that it causes pollution.
These entire problems negatively affect the pumping needs of the local community and irrigation,
but when we can provide electricity, we can also provide water. The use of solar energy to pump
the water from the well is a good choice in exchange for traditional pumping systems that use
electricity and fuel energy. The PV pumping system is environmentally friendly, has low-cost
energy from a renewable source, and it does not need frequent maintenance or fuel, using a
photovoltaic system that produces electrical energy to feed a motor equipped with an external
water pump. This water pumping supply system can be used in remote, and society places.
Therefore, the water supply system based on photovoltaic technology is very important in our lives,
so we have to study and develop the PV pumping systems more than before. In this chapter, we
will present a state of the art of that system, and explain many basics and some technologies and
methods that can make us use this system perfectly.
I.2 Photovoltaic water pumping system

The most common problem in remote places and the most isolated communities that are far
from waterways and electricity grid. To ensure the water supply anywhere, we have to use a stand-
alone power supply, and photovoltaic solar energy is one of the most common of these energies.
This combination is called "Photovoltaic Water Pumping System" as presented in Figure I.1. This
system is the perfect way to fix the water supply's problems, by extracting and pumping the
water from a well even in rural areas and places, and that is the system’s goal. The photovoltaic
water pumping system can be used in many domains, including residential, farming (irrigation,
breeding, and agriculture), water purification, or firefighting. It combines two principle parts that
are the photovoltaic system and the pumping system.
Figure I.1. Photovoltaic Water Pumping System [7].
4
I.3 Solar energy and photovoltaic system

I.3.1 Solar energy: why renewable energy?
Solar energy is a concept that refers to the radiation and heat of the sun exploited by various
techniques of energy conversion, such as solar thermal collectors and photovoltaic cells, … etc.
The biggest advantage of solar energy is that its source is stemming from the Sun which means is
an endless source. Moreover, the sun shines every place on the earth that what makes it applicable
to everyone. The other important advantages that these technologies present their lightness and
viability for residential installation. Simply, everyone can install it, in his backyard or rooftop.
Although the absence of solar irradiance is the most disadvantage that makes sometimes these
technologies useless, also the solar energy may vary in its intensity from one place to another,
which make its effectiveness is not the same on every place (effect of the temperature and the
radiance), which will be discussed in the following sections of this chapter. Generally, we can
divide the solar energy into two processes which are [8]:
1. Photovoltaic effect, which is the conversion of the sun's visible light into electricity.
2. Solar thermal, which is the transfer and the storage of the sun's heat for electricity heating
purposes.
Our work is based on photovoltaic solar energy, which will explain in this chapter. Figure
I.2 presents the difference between the two kinds of solar energy systems, which are the solar
photovoltaic panel, and the solar thermal panel.
Figure I.2. Solar Thermal Panel and Solar Photovoltaic Panel [9]
I.3.2 Types of solar radiation

Solar radiation is classified into two types which are terrestrial radiation or extra-terrestrial
radiation, depending on its location inside or outside the earth’s atmosphere respectively [8].
5
As shown in Figure I.3, the terrestrial radiation is also divided into two types: the first one
is when the radiation comes from the sun directly and it is called direct normal irradiance (DNI),
the second, the scattered radiation coming to the Earth's through the clouds, the ground or/and
other objects surface known as diffuse horizontal irradiance (DHI), and some of them are re-
scattered again by the atmosphere, they have also the same name diffuse horizontal irradiance
(DHI). As well known, the Solar radiation is described as a flux of energy expressed in power per
unit area (usual watts per square meters) [10], [11].
Figure I.3. Solar radiation’s components (DNI and DHI) [10].
I.3.3 Photovoltaic solar energy

Photovoltaic solar energy is an innovative technique for transforming the most available
solar energy to electrical energy without the use of internal combustion or rotating components
[12]. That is happened using a solar panel based on the photovoltaic effect, it is defined by the
hitting of the solar radiation on a photovoltaic cell that produces a direct current DC [13]. The
absorption of solar radiation depends on the properties of the material of the solar cell [14]. The
principal components of a photovoltaic system are solar cells (module, panel, and array) that
receives the sun’s radiation, and inverter, and electrical wires, and sometimes a storage battery
[15].
I.3.3.1 Inverter
The inverter becomes a key device when the consumes requires the alternating currents
AC, as well known, the principle of its work is to convert the energy provided by the PV systems
as DC form to AC form [12].
I.3.4 Photovoltaic cells:

The photovoltaic solar cells are working as a generator of the electric current after receiving
the solar radiation. The PV module is considered as PV cells in series. Also, the PV array is some
6
incorporated modules, which are connected in series or/and parallel. The series or/and parallel
connection of the modules is related to the voltage or the current output that is needed by
consumers. Figure I.4 shows the main components of the photovoltaic system [8].
Figure I.4. The main components of the photovoltaic system [8].
There are many different types of photovoltaic cell technology, its association series or
parallel, and its protection strategies. We will explain all that in the next paragraphs.
I.3.4.1 Type of PV cells technologies
The most common types of photovoltaic solar cells are the monocrystalline (single-
crystalline), polycrystalline (multicrystalline), and noncrystalline (Amorphous) silicon cells [16].
Table I.1 presents the types of PV cells with their Efficiency and Expected lifetime.
Type of cell Efficiency (%) Expected lifetime (years) References

Monocrystalline 17-22.7 25-30 International Energy Agency
Polycrystalline 10-14 20-25 Cotar and Flicik
Amorphous 6 15-20 Cotar and Flicik
Table I.1. Types of PV cell with their Efficiency and Expected lifetime [12].
 The monocrystalline silicon cell is produced by a homogeneous crystallinity, and it has high
carrier mobility, high efficiency (17-22.7%), and high lifetime (25-30 years), but it is expensive
compared with other types.
 The polycrystalline silicon cell has an irregular direction of its crystalline. Its photoelectric
efficiency is lower than the single-crystalline silicon cell also it has a low cost compared to the
monocrystalline cell.
 In terms of the non-crystalline silicon cell, it makes from non-crystalline silicon materials
usually used to make thin-film solar cells. Non-crystalline silicon PV cell has low efficiency
7
but it is not expensive. They are usually used in weak light devices for example the cells of
calculators.
According to the provided data in Table I.1, the optimum value of the efficiency and the
lifetime refers to the monocrystalline silicon solar cells. Figure I.5 shows these three types of
solar cells.
Figure I.5. Types of the photovoltaic solar cell [17].
I.3.4.2 Series, parallel and mixed combinations of PV modules
To provide the appropriate values of current and voltage, the solar modules must be
properly connected between them to achieve the required value of current and/or voltage. So, there
are two principals possibilities of the interconnection, which are the parallel or series combinations,
and the mixing between them [8], [18].
 In the case of combinations of modules in series, the increase in voltage depends on the number
of the series modules, in such case, the maximum power and current of the own modules are
the same as shown in Figure I.6, when three solar modules are connected in series, where own
solar module characterized by 6 volts and 3 Amps, in this case, the voltage and current of
system output will be 18 volts and 3 Amps, respectively.
Figure I.6. The serial connections of PV modules [19].
 In the case of combinations of modules in parallel, the increase in current depends on the
number of the parallel modules, in such case, the maximum power and voltage of the own
modules are the same, as shown in Figure I.6, when three solar modules are connected in
8
parallel, where own solar module characterized by 6 volts and 3 Amps, in this case, the voltage
and current of system output will be 6 volts and 9 Amps, respectively.
Figure I.7. The parallel connections of PV modules [19].
 A mixed combination allows us to increase the voltage and current at the same time.
I.3.4.3 Solar modules protection [20]
The solar modules are composed of many solar cells in which are connected in series,
unfortunately, many risks can arise this PV module, this can damage it, perhaps like these risks:
hotspot shaded cell or its connection with a battery without protections … etc. The Hotspot
occurred when there is one low current cell in a string of at least several high short circuit current
solar cells. This causes the shaded cell to produce a low current that flows through the good cells
causing them to produce a higher voltage, which causes to be reverse biased and possibly increase
local overheating.
I.3.4.3.1 Use of bypass diode

The key function of a bypass diode is to bypass the current from the shaded cell. For making
the PV module still working even with the reduction in the output power. Generally, they use two
bypass diodes for each module with 36 cells, and these bypass diodes can be combined in parallel
with several cells. Figure I.8 shows the bypass diode role in the PV module.
Figure I.8. Shaded PV cells with Bypass Diodes protection [19].
9
I.3.4.3.2 Use of blocking diodes

In night conditions where the solar radiations are missed; no voltage is generated by the
solar panels, the battery’s voltage producing a current which flows through the panels in the
opposite direction. So to avoid this, blocking diodes are used to stop this problem as presented in
Figure I.9.
Figure I.9. PV cells with Bypass and Blocking Diodes protection [19].
I.3.5 Photovoltaic effect

The photovoltaic cell based on silicon consists of two thin layers of semiconductor, which
are doped differently, see Figure I.10. where the sun’s radiation fall on, the upper layer (2) is
negatively doped with phosphorous, while the other lower layer (3) is positively doped with boron.
Then, in the part between them, it knows as a p-n junction (1), where some electrical charges
combine that where an opposite electrical field is created [12].
Figure I.10. Component and operational principle of PV cells [12].
10
where: (1) is p-n junction, (2) is the negatively doped layer, (3) is the positively doped
layer, (4) is the negative electrode, (5) is the positive electrode, (6) is load.
I.3.6 Different types of PV systems

Solar PV systems are generally classified based on their operating requirements and the
design of their connections. This PV Solar system can be classified as [8], [20], [21]:
I.3.6.1 Stand-Alone PV systems
A stand-alone PV installation is required in the off-grid PV system. This design is perfect

for isolated and remote areas where electricity is required. Figure I.11 illustrates a standard stand-
alone PV system.
Figure I.11. Standard Stand-Alone PV system [19].
The PV system provides electricity from the sun's radiation. Therefore, they can only
supply power during the day. That is why the battery banks are very important in this PV system
type. Battery banks play a role of storing the generated power during the day, so that allows them
to supply the consumers anytime.
I.3.6.2 Grid-Connected PV system:
As shown in Figure I.12, the well-known grid-connected PV system is usually composed

of solar panels, charge controllers, battery banks, switchboards, smart inverter, and grid. This PV
11
system can be used either to fully supply the power to the network grid or to supply local load
requirements.
Figure I.12. Standard Grid-Connected PV system [19].
I.3.6.3 Hybrid PV system
As shown in Figure I.13, the hybrid systems usually refer to any two combines input
sources or more, in which the PV solar may be combined with renewable or non-renewable energy
sources. This type of system usually used a battery bank also for stocking the power coming from
the PV system.
Figure I.13. Standard Hybrid PV system [21].
12
I.3.7 PV output characteristics and parameters

The PV cell's output is characterized using the current-voltage (I–V) and power–voltage
(P–V) curves, these curves can represent the outputs of PV modules when their solar cells have
uniform conditions. Figure I.14 shows typical I–V and P–V curves for a PV cell output [22].
Figure I.14. Typical I–V and P–V curves for a PV cell’s output [22].
I.3.8 Effect of solar irradiation and temperature [12]

I.3.8.1 Solar Irradiation effect
Throughout the day, solar irradiance has a higher variation more than the temperature, and
it influences on the efficiency of the PV cells. As shown in Figure I.15, the electrical current
generated depends directly on the absorbed solar radiation.
Figure I.15. I–V Characteristic curve of a PV module [12].

I.3.8.2 Temperature effect
As presented in Figure I.16, the voltage of the PV panel is influenced by the temperature
variation. Using the same previous PV panel, the (𝑉𝑀𝑃𝑃 ) value is less roughly during hot summer
days by 10 V, and in the winter days is roughly higher than the STC (Standard Test Conditions)
value by 10 V. However, the PV system current just barely increases with the temperature.
13
Figure I.16. I–V Characteristic Curve of a PV Module at Constant Received Solar Radiation and
Variable Temperature [12].
I.3.9 Maximum Power Point Tracking control techniques

To exploit the majority of power that can be provided by the solar cell, a maximum power
point of this can be tracked through a specific technique. The strategies of MPP tracking vary from
one to other on many sides, like the range of performance, price, difficulty, used sensors, or their
robustness control in specific conditions (variation in irradiation or temperature or both). The most
common algorithms used for Maximum Power Point Tracking (MPPT) are “Hill Climbing/Perturb
and Observe (P&O)” and “Incremental Conductance (InCond)”, these two techniques are based
on “Hill Climbing” concept, and this concept is based on the moving of the operation power point
of the PV array to the increasing direction of the power [21].
I.3.9.1 Hill Climbing/Perturb and Observe
The operation of the P&O algorithm is based on the voltage and current sensors to provide
an appropriate duty cycle to power converter according to the requirements of consumers. Also,
such type of algorithm is known by its low cost computational. In this algorithm, the sign of the
last disturbance and the sign of the last increment in the power is used to decide the next order. If
the power value increase, the next perturbation should be kept in the same direction of the last one,
else if the power value decrease, the next perturbation should be changed in the opposite direction
of the last one. The cycle repeats until the MPP is satisfied.
Figure I.17 shows the orders of this process,
14
Figure I.17. The cycle of the Perturb and Observe algorithm [21].
I.4 Water Pumping System

It called also “Pump motors”, they are widely used in irrigation systems, pools, and water
pumping systems like pump water from groundwater sources.
These pumps comprise the following two principal components motor and pump, as their name
indicates. The motor that produces the required pumping power and the pump uses the motor’s
power to pump the water from the well. The power source of our project is photovoltaic solar
energy.
I.4.1 Motor technology

The most common types of motor that uses in Solar water pumps are:
 DC motors
 AC motors
The solar pump which uses an AC motor requires an inverter, in another case when the DC
motor is needed, the boost-buck converter is required [23]. Generally, the AC motors are used in
large scale systems in the contrary the DC motor is exploited in the small scale systems.
I.4.2 Pump technology

The most important component in the solar-powered pumping system is the pump. It can
be divided into two categories; centrifugal and positive displacement pump. We will explain the
centrifugal pump, which is included in our work.
15
I.4.2.1 Centrifugal pumps
As presented in Figure I.18, A centrifugal pump is a hydraulic mechanical system that

works to flow up the water helping the rotational mechanical energy provided by motor drive,
known as the impellers. This pump has one or multiple impellers that increase the water’s pressure
and velocity by spinning the water to subject it to centrifugal force, the water reaches to the rapidly
rotating impeller and is directed to the pump's outlet by this force through the vane tips of the
impeller along its circumference.
Figure I.18. Surface Centrifugal Pump [24].
To get a high-lift centrifugal pump, this pump must consist of several stages, each stage
consisting of an impeller. Lifting capacity increases with the increasing each stage adds to the
pump. Each stage adds pressure and friction, where the friction causes a decrease in the efficiency
of each stage [24].
I.5 Conclusion
In this chapter, the description of the principal parts of the photovoltaic water pumping
system is presented. Yet, the solar energy and photovoltaic system are well discussed, and the
sun’s radiation types are defined. Then, the most basics of the photovoltaic cells and their materials
technology are presented also, the PV effect, and its different types system. Efficiency of the PV
system are clarified depends on the solar radiations and temperature effects. To obtain the
maximum power at the output of the pump system, the common type of MPPT algorithm named
P&O is well explained in this chapter as well as its principle of operation. In the final of this
chapter, the main components of the water pumping system are presented so as the type of the
motors and pumps those can be used.
16
CHAPTER II
Induction Motor Modeling
and Space Vector
Modulation
CHAPTER II ------------------------------- Induction Motor Modeling and Space Vector Modulation
II.1 Introduction
In this chapter, the induction motor modeling is described considering some assumptions,
then, the Park transformation is exploited to make the motor easy to study. Therefore, a voltage
source inverter is analyzed. Finally, both techniques of Pulse Width Modulation (PWM) and Space
Vector Modulation (SVM) are also presented.
II.2 Description and mathematical model of induction motor

II.2.1 Description of the induction motor
The induction machines are usually used as motors for industrial applications due to their
robustness and reliability. The induction motor has two main parts, one of them is the stator (a
stationary part) and the second part is the rotor (a rotary part), the both parts are separated by an
air gap between them [25]–[28].
The stator is containing three-phase winding in which may be connected in a star or delta
connection. This three-phase winding is used to create a rotating magnetic field. As shown in
Figure II.1, the stator is shown in green and the rotor in blue [29].
The rotor of the used induction motor is the type of squirrel-cage rotor as presented in
Figure II.2 [30]. As known, almost 90% of induction motors that uses in industrials are squirrel
cage motor due to its simple construction, its robustness, and its reliability in service.
Figure II.1. Cross-section of an Induction Machine [31].
18
Figure II.2. Squirrel-cage Rotors [32].
II.2.2 Modeling assumptions

The model of the three-phase induction machine has been simplified by using these several
hypotheses : [33]–[35]
 The MMFs created by the different circuits of stator and rotor are spread to have sinusoidal
repartitions.
 The magnetic fields are supposed unsaturated.
 The skin effect does not exist.
 The machine has a constant air gap, which made the slotting effect is not taken account.
These hypotheses will make the modeling of the induction machine less complex, which
allows developing the control methods easily.
II.2.3 Equivalent representation and vector formulation

As presented in Figure II.3, the induction machine is described by three symmetrical
windings for each of the stator and the rotor phases whose axes are equitably distant between
themselves by an electrical angle equal to 2/3. Also, the three-rotor windings rotating at the
mechanical speed (ωr).
Figure II.3. Induction Motor equivalent structure [6].
19
By applying the Kirchhoff’s laws on both circuits of the stator and the rotor, one can get :
II.2.3.1 Voltage equations
𝑑
[𝑣𝑠𝑎𝑏𝑐 ] = [𝑅𝑠 ][𝑖𝑠𝑎𝑏𝑐 ] + [𝜓𝑠𝑎𝑏𝑐 ] ( II.1)
𝑑𝑡
𝑑
[𝑣𝑟𝑎𝑏𝑐 ] = 0 = [𝑅𝑟 ][𝑖𝑟𝑎𝑏𝑐 ] + [𝜓𝑟𝑎𝑏𝑐 ] ( II.2)
𝑑𝑡
II.2.3.2 Flux equations
[𝜓𝑠𝑎𝑏𝑐 ] = [𝐿𝑠 ][𝑖𝑠𝑎𝑏𝑐 ] + [𝑀𝑠𝑟 ][𝑖𝑟𝑎𝑏𝑐 ] ( II.3)

[𝜓𝑟𝑎𝑏𝑐 ] = [𝐿𝑟 ][𝑖𝑟𝑎𝑏𝑐 ] + [𝑀𝑠𝑟 ]𝑇 [𝑖𝑠𝑎𝑏𝑐 ] ( II.4)
where:
𝑣𝑠𝑎 𝑖𝑠𝑎 𝜓𝑠𝑎

[𝑣𝑠𝑎𝑏𝑐 ] = [𝑣𝑠𝑏 ] ; [𝑖𝑠𝑎𝑏𝑐 ] = [𝑖𝑠𝑏 ] ; [𝜓𝑠𝑎𝑏𝑐 ] = [𝜓𝑠𝑏 ] ( II.5)
𝑣𝑠𝑐 𝑖𝑠𝑐 𝜓𝑠𝑐
𝑣𝑟𝑎 𝑖𝑟𝑎 𝜓𝑟𝑎

𝑣 𝑖 𝜓
[𝑣𝑟𝑎𝑏𝑐 ] = [ 𝑟𝑏 ] ; [𝑖𝑟𝑎𝑏𝑐 ] = [ 𝑟𝑏 ] ; [𝜓𝑠𝑎𝑏𝑐 ] = [ 𝑟𝑏 ] ( II.6)
𝑣𝑟𝑐 𝑖𝑟𝑐 𝜓𝑟𝑐
The subscripts s and r refer to the stator and the rotor, respectively, and the indices a, b,
and c refers to the three phases. All resistances and inductances matrices are symmetric as seen
below:
𝑅𝑠 0 0 𝑅𝑟 0 0
[𝑅𝑠 ] = [ 0 𝑅𝑠 0 ] ; [𝑅𝑟 ] = [ 0 𝑅𝑟 0] ( II.7)
0 0 𝑅𝑠 0 0 𝑅𝑟
𝐿𝑠 𝑀𝑠 𝑀𝑠 𝐿𝑟 𝑀𝑟 𝑀𝑟
[𝐿𝑠 ] = [𝑀𝑠 𝐿𝑠 𝑀𝑠 ] ; [𝐿𝑟 ] = [𝑀𝑟 𝐿𝑟 𝑀𝑟 ] ( II.8)
𝑀𝑠 𝑀𝑠 𝐿𝑠 𝑀𝑟 𝑀𝑟 𝐿𝑟
𝑅𝑠 and 𝑅𝑟 , 𝐿𝑠 and 𝐿𝑟 are the resistances and self-inductances of the stator and the rotor,
respectively.
𝑀𝑆 and 𝑀𝑟 are the mutual inductance between two stator and rotor phases.
The mutual inductance between the stator and the rotor is considered as sinusoidal functions
of the rotor position 𝜃 as following:
2𝜋 4𝜋
𝑐𝑜𝑠(𝜃) 𝑐𝑜𝑠(𝜃 + ) 𝑐𝑜𝑠(𝜃 + )
3 3
4𝜋 2𝜋
[𝑀𝑠𝑟 ] = [𝑀𝑟𝑠 ]𝑇 = 𝑀𝑠𝑟 𝑐𝑜𝑠(𝜃 + ) 𝑐𝑜𝑠(𝜃) 𝑐𝑜𝑠(𝜃 + ) ( II.9)
3 3
2𝜋 4𝜋
[𝑐𝑜𝑠(𝜃 + 3
) 𝑐𝑜𝑠(𝜃 + 3
) 𝑐𝑜𝑠(𝜃) ]
20
𝑀𝑠𝑟 is the maximal mutual inductance between the stator and the rotor phases.
II.2.3.3 Mechanical equations
The mechanical equation of IM is described as :
𝑑𝜔𝑟
𝐽 = 𝑇𝑒 − 𝑇𝐿 − 𝑓𝜔𝑟 ( II.10)
𝑑𝑡
𝜔𝑟 , 𝑇𝑒 and 𝑇𝐿 are the rotor speed, the electromagnetic torque, and the load torque respectively.
𝐽 is the inertia moment,
f is the friction coefficient.
II.2.4 Park transformation

To simplify the control and the study of an AC machine, one of the uses is Park
transformations by which the three-phase stationary frame (a, b, c) can be transformed into the
two-phase direct-quadrature frame (d, q) [6], [36]. The Park transformation’s representation, in
general, is given as:
𝑥𝑑 𝑥𝑎
[𝑥𝑞 ] = 𝑃(𝜃) [𝑥𝑏 ] ( II.11)
𝑥0 𝑥𝑐
2𝜋 4𝜋
𝑐𝑜𝑠(𝜃) 𝑐𝑜𝑠 (𝜃 − ) 𝑐𝑜𝑠(𝜃 − )
3 3
𝑃(𝜃) = 𝑛 [ 𝑠𝑖𝑛(𝜃) 2𝜋 4𝜋
𝑠𝑖𝑛(𝜃 − ) 𝑠𝑖𝑛(𝜃 − )] ( II.12)
3 3
1/2 1/2 1/2
Where θ is the angle between the axis-a and the axis-d, k is defined as a constant.
Figure II.4 has illustrated the passage of a three-phase stationary system (a,b,c) to the equivalent
two-phase fixed system (α, β) then to the rotating frame (d, q).
Figure II.4. The passage of three-phase to a two-phase system using PARK transformation [6].
21
II.2.5 Two-phase models of induction machine

one can simplify the three-phase model of the IM by applying Park transformation, where
all their equations are rewritten in the two-phase rotating frame (d, q).
II.2.5.1 Voltage and flux equations in (d, q) frame
After applying the Park transformation on the equations of the induction machine
( II.1-II.4) get the following (d, q) equations:
𝑣𝑠𝑑 𝑖𝑠𝑑 𝜓𝑠𝑑

[ 𝑣 ] = [𝑃(𝜃𝑠 )][𝑣𝑠𝑎𝑏𝑐 ] ; [𝑖 ] = [𝑃(𝜃𝑠 )][𝑖𝑠𝑎𝑏𝑐 ] ; [ 𝜓 ] = [𝑃(𝜃𝑠 )][𝜓𝑠𝑎𝑏𝑐 ] ( II.13)
𝑠𝑞 𝑠𝑞 𝑠𝑞
𝑣𝑟𝑑 𝑖𝑟𝑑 𝜓𝑟𝑑

[ 𝑣 ] = [𝑃(𝜃𝑠 )][𝑣𝑟𝑎𝑏𝑐 ] ; [𝑖 ] = [𝑃(𝜃𝑠 )][𝑖𝑟𝑎𝑏𝑐 ] ; [ 𝜓 ] = [𝑃(𝜃𝑠 )][𝜓𝑟𝑎𝑏𝑐 ] ( II.14)
𝑟𝑞 𝑟𝑞 𝑟𝑞
So, the voltage equations can be written as the following:

𝑑𝜓𝑠𝑑
𝑣𝑠𝑑 = 𝑅𝑠 𝑖𝑠𝑑 + − 𝜔𝑠 𝜓𝑠𝑞
𝑑𝑡
𝑑𝜓𝑠𝑞
𝑣𝑠𝑞 = 𝑅𝑠 𝑖𝑠𝑞 + + 𝜔𝑠 𝜓𝑠𝑑
𝑑𝑡
𝑑𝜓𝑟𝑑
( II.15)
𝑣𝑟𝑑 = 𝑅𝑟 𝑖𝑟𝑑 + − (𝜔𝑠 − 𝑝𝜔𝑟 )𝜓𝑟𝑞
𝑑𝑡
𝑑𝜓𝑟𝑞
{ 𝑣𝑟𝑞 = 𝑅𝑟 𝑖𝑟𝑞 + 𝑑𝑡
+ (𝜔𝑠 − 𝑝𝜔𝑟 )𝜓𝑟𝑑
where:
𝑑𝜃𝑠 𝑑𝜃𝑟
𝜔𝑠 = ; 𝜔𝑟 = ( II.16)
𝑑𝑡 𝑑𝑡
The flux equations can be written as the following:

𝜓𝑠𝑑𝑞 = 𝐿𝑠 [𝑖𝑠𝑑𝑞 ] + 𝑀𝑠𝑟 [𝑖𝑟𝑑𝑞 ]
{ ( II.17)
𝜓𝑟𝑑𝑞 = 𝐿𝑟 [𝑖𝑟𝑑𝑞 ] + 𝑀𝑠𝑟 [𝑖𝑠𝑑𝑞 ]
II.2.5.2 Mechanical equations
The rotor motion is followed by the dynamic equation as

𝑑𝜔𝑟
𝐽 = 𝑇𝑒 − 𝑇𝐿 − 𝑓𝜔𝑟 ( II.18)
𝑑𝑡
The electromagnetic torque is given by:

𝑀𝑠𝑟
𝑇𝑒 = 𝑝 (𝜓𝑟𝑑 𝑖𝑠𝑞 − 𝜓𝑟𝑞 𝑖𝑠𝑑 ) ( II.19)
𝐿𝑟
or, in another expression:

𝑇𝑒 = 𝑝(𝜓𝑠𝑑 𝑖𝑠𝑞 − 𝜓𝑠𝑞 𝑖𝑠𝑑 ) ( II.20)
22
As well-known in the literature, the model of the induction machine expressed in the rotating frame
(d, q) is often used for the field-oriented control design.
II.3 Voltage Source Inverter (VSI)

An inverter is a static converter ensuring DC to AC conversion. it periodically changes the
connections between the input and the output to obtain alternating voltage and current at the output
[37]. The schematic of the two-level voltage source inverter is presented in Figure II.5, as shown,
the inverter is supplied by a DC link voltage Vdc which is provided by a rectifier or another DC
source, The converter consists of the three legs with IGBT transistors with parallel free-wheeling
diodes in the most applications [5], [6].
Figure II.5. Three-phase voltage inverter [6].
To avoid a short-circuit of the source, it is necessary to respect the following states as:
̅𝑖 is OFF.
𝑆𝑖 = 1, 𝑇𝑖 is ON and 𝑇
̅𝑖 is ON.
𝑆𝑖 = 0, 𝑇𝑖 is OFF and 𝑇
with: i= a, b, c.
The output voltages inverter depend on switching states by the following matrix [38]:
𝑉𝐴 2 −1 −1 𝑆𝑎
𝑉𝑑𝑐
[𝑉𝐵 ] = 3 [−1 2 −1] [𝑆𝑏 ] ( II.21)
𝑉𝐶 −1 −1 2 𝑆𝑐
The voltage vector is generated by the following equation [6]:

2𝜋 4𝜋
2
𝑉𝑠 = √3 𝑉𝑑𝑐 [𝑆𝑎 + 𝑆𝑏 𝑒 −𝑗 3 + 𝑆𝑐 𝑒 −𝑗 3 ] ( II.22)
The inverter output voltage constitutes a cyclic and symmetric sequence of vectors [39], There
are eight possible positions of the switches states, two states are zero vectors (V0, V7) and six states
23
are active vectors (V1 to V6) [5], [6]. The states of the output voltage are represented by space
vectors as shown in Figure II.6.
Figure II.6. The switching states of the output voltage represented by space vectors [6].
II.4 Pulse Width Modulation (PWM)

The PWM is a technique that allows obtaining the appropriate amplitude and a frequency
at the VSI output. Yet, this technique can eliminate harmonics and minimize switching losses [4].
There are many possible PWM techniques proposed in the literature.
The classification of common PWM techniques can be given as [40]:
 Sinusoidal PWM (SPWM)
 Selected harmonic elimination (SHE) PWM
 Minimum ripple current PWM
 Space vector PWM (SVM)
The SVM technique is one of the most popular PWM techniques due to the higher voltage
it can produce, easy to realize. Nowadays, the SVM technique is commonly used in several three-
phase inverters uses that why it is because it can produce a higher output voltage more than SPWM,
and provides lowers torque ripple, and less harmonic of distortion in the current of induction
motors, and lower switching losses [4], [41].
II.4.1 Space Vector Pulse Width Modulation
A three-phase two-level inverter provides eight possible switching states that are corresponding
to the eight output voltage vectors, 𝑉0 to 𝑉7, as shown in Table II.1. The six of these vectors 𝑉1 to
2
𝑉6 be called active voltage vectors, their magnitudes are equal to 3 𝑉𝑑𝑐 . The two other vectors
𝑉0 , 𝑉7 are called zero (non-active) voltage vectors where their magnitudes equal to zero. The zero
vectors are superfluous but they are used to minimize the switching frequency. When the space
24
active vectors joined together made a hexagon. This last one consists of six sectors stretching
(along) over 360 degrees, for each sector 60 degrees [42]. The space vectors are shown graphically
in Figure II.7.
Switch States Phase Voltage Space Voltage Vector

𝑺𝒂 𝑺𝒃 𝑺𝒄 𝑽𝒂𝒔 𝑽𝒃𝒔 𝑽𝒄𝒔 𝑽𝒏 (𝒏 = 𝟎 − 𝟕)
0 0 0 0 0 0 𝑉0 = 0∠0°
2 1 1 2
1 0 0 𝑉 − 𝑉𝑑𝑐 − 𝑉𝑑𝑐 𝑉1 = 𝑉𝑑𝑐 ∠0°
3 𝑑𝑐 3 3 3
1 1 2 2
1 1 0 𝑉 𝑉 − 𝑉𝑑𝑐 𝑉2 = 𝑉𝑑𝑐 ∠60°
3 𝑑𝑐 3 𝑑𝑐 3 3
1 2 1 2
0 1 0 − 𝑉𝑑𝑐 𝑉 − 𝑉𝑑𝑐 𝑉3 = 𝑉𝑑𝑐 ∠120°
3 3 𝑑𝑐 3 3
2 1 1 2
0 1 1 − 𝑉𝑑𝑐 𝑉 𝑉 𝑉4 = 𝑉𝑑𝑐 ∠180°
3 3 𝑑𝑐 3 𝑑𝑐 3
1 1 2 2
0 0 1 − 𝑉𝑑𝑐 − 𝑉𝑑𝑐 𝑉 𝑉5 = 𝑉𝑑𝑐 ∠240°
3 3 3 𝑑𝑐 3
1 2 1 2
1 0 1 𝑉 − 𝑉𝑑𝑐 𝑉 𝑉6 = 𝑉𝑑𝑐 ∠300°
3 𝑑𝑐 3 3 𝑑𝑐 3
1 1 1 0 0 0 𝑉7 = 0∠0°
Table II.1. Output voltage vectors corresponding to the switching states [41].
Figure II.7. Vectors of Output Voltage in the complex plane (d-q axes) [4].
25
In the SVPWM technique, it can produce a reference voltage of the output inverter by using
the two active voltages neighbors to 𝑉𝑠∗ and the zero vectors from the eight voltage vectors. This
technique has the same fundamental volt-second average as given the voltage reference vector 𝑉𝑠∗
along the modulation (switching) period 𝑇𝑠 . In the linear modulation range, the voltage reference
follows the circular trajectory. This last one will be a hexagon boundary when the inverter is
operating in the six-step mode [4].
In the SVPWM technique, the maximum value of the reference vector amplitude that can
be approximated is equal to the radius of the circle that can be inscribed within the hexagon. Thus,
the maximum obtainable fundamental output voltage is calculated from the right-angled triangle
(Figure II.8) as:
2 𝜋 1
𝑉𝑚𝑎𝑥 = (3) 𝑉𝑑𝑐 cos (6 ) = 𝑉 = 0.577𝑉𝑑𝑐 ( II.23)
√3 𝑑𝑐
Therefore, Modulation Index MI at this condition can be derived as:

𝑉𝑚𝑎𝑥 0.577𝑉𝑑𝑐
𝑀𝐼 = = 2 = 0.907 ( II.24)
𝑉1𝑠𝑤 .𝑉
𝜋 𝑑𝑐
𝑉𝑚𝑎𝑥 : Maximum phase voltage,

2
𝑉1𝑠𝑤 : Fundamental peak value ( 𝜋 𝑉𝑑𝑐 ) of the square-phase voltage wave.
This means that the maximum value of the peak voltage can be obtained from the SVPWM
technique corresponds to 90.7% of the output voltage in the square wave operation. In the
𝑉𝑑𝑐
sinusoidal PWM (SPWM) technique, the maximum value output voltage is , when using
2
SVPWM is (2𝑉𝑑𝑐 /3)/(𝑉𝑑𝑐 /2) = 1.154. The SVPWM method is 15.47% higher than the SPWM
method. Therefore, the dc-link utilization of the two-level inverter is better in the SVPWM method
compared to the SPWM [40], [41], [43].
Figure II.8. The possible range of the voltage reference vector in the SVM [4].
26
The first step in SVPWM implementation is the determination of the duration time of each
voltage vector. When the reference voltage in sector 1 is, the first vector 𝑉1 is applied during time
𝑇1 and the other vector 𝑉2 is applied during time 𝑇2 , then one of the zero vectors, 𝑉0 or 𝑉7, is
applied during time 𝑇0 , where the time of application zero vector 𝑇0 is remaining time over 𝑇s
period, 𝑇0 = 𝑇s − 𝑇1 − 𝑇2 . Through these steps, it is possible to generate the reference output
voltage vector over the modulation period 𝑇s . Hence, using the equal volt-second principle, for
sector 1:
𝑉𝑠∗ 𝑇𝑠 = 𝑉1 𝑇1 + 𝑉2 𝑇2 + 𝑉0 𝑇0 ( II.25)
𝜋
As an example, in the first sector 1 (0 ≤ 𝜃 ≤ ), Equation (II.25) can be decomposed into
3
two components the real and imaginary as:

2 2 𝜋
|𝑉𝑠∗ | cos(𝜃) 𝑇𝑠 = 𝑉𝑑𝑐 𝑇1 + 𝑉𝑑𝑐 cos ( ) 𝑇2
3 3 3
{ 2 𝜋
( II.26)
∗
|𝑉𝑠 | sin(𝜃) 𝑇𝑠 = 𝑉𝑑𝑐 sin ( ) 𝑇2
3 3
Solving equations (II.26) for the duration times 𝑇1 and 𝑇2 :

√3|𝑉𝑠∗ | 𝜋
𝑇1 = sin ( 3 − 𝜃) 𝑇𝑠 ( II.27)
𝑉𝑑𝑐
√3|𝑉𝑠∗ |
𝑇2 = sin(𝜃) 𝑇𝑠 ( II.28)
𝑉𝑑𝑐
𝑇0 = 𝑇𝑠 − 𝑇1 − 𝑇2 ( II.29)
Figure II.9 shows the generation of the voltage reference process in the first sector.
Figure II.9. The process of generating the reference voltage vector in the first sector [4].
The calculation times for the reference voltage vector in all sectors give the following,
where 𝑘 = 1, 2, … 6 is the sector number:
√3|𝑉𝑠∗ | 𝜋
𝑇1 = sin (𝑘 3 − 𝜃) 𝑇𝑠 ( II.30)
𝑉𝑑𝑐
27
√3|𝑉𝑠∗ | 𝜋
𝑇2 = sin (𝜃 − (𝑘 − 1) 3 ) 𝑇𝑠 ( II.31)
𝑉𝑑𝑐
𝑇0 = 𝑇𝑠 − 𝑇1 − 𝑇2 ( II.32)
After the duration time of calculation, the next step in SVM implementation is the selection
of the switching sequence. To obtain a better harmonic performance and constant switching
frequency, each leg should change its state only once in each switching period, which is called the
symmetrical SVM technique. In this technique, the total switching time interval 𝑇𝑠 is dividing into
two parts. The first part begins with the zero vector (000) is applied for 1/4th of the total time 𝑇0 ,
followed by two neighbor active state vectors for their half duration times and then again zero
vector (111) is applied for 1/4th of the total time 𝑇0 . In the second part, the switching sequence is
a mirror image of the first one [4], [41], [43].
As an example in the sector 1, the switching sequence in the first part:
𝑉0 (000) → 𝑉1 (100) → 𝑉2 (110) → 𝑉7 (111)
In the second part is reversed:
𝑉7 (111) → 𝑉2 (110) → 𝑉1 (100) → 𝑉0 (000)
The switching pattern for the sector I is showing the voltages leg in one switching period
𝑇𝑠 , see Figure II.10.
Figure II.10. Switching sequence of the first sector [41].
II.5 Conclusion
In this chapter, the mathematical behavior of IM is described in the framework of the bi-
phase space vectors (d-q) reference for propose to control and estimate the variables of them. Also,
the SVPWM structure and its basic principles have been well discussed. As well-known that the
SVPWM (or SVM) technique is commonly used in many applications in industrials thanks to its
capability to produce a higher output voltage of 15.5% compared to classical techniques named
SPWM. In the next chapters, the SVM strategy will be used as the main part to drive the motor-
pump system.
28
CHAPTER III
DTC-SVM Control for
Induction Motor
CHAPTER III --------------------------------------------------- DTC-SVM Control for Induction Motor
III.1 Introduction
Over 30 years ago, Takahashi and Depenbrock have invented a control technique for
electric motor drives called the Direct Torque Control (DTC) [44]. This classical technique is
focused to replace the technique of Field-Oriented Control (FOC), but it has some drawbacks such
as variable switching frequency, high torque ripple. To improve that, there are several control
structures are proposed in the literature, and one of them, a DTC-SVM technique that is
characterized by its constant switching frequency and low torque ripple ... etc. In this chapter, a
technique of DTC-SVM is described and discussed using it as part of the electric motor drive. All
that is verified numerically exploiting the Simulink/MATLAB.
III.2 Direct Torque Control with Space vector modulation

The DTC which incorporates the technique of space vector modulation is a choice to
overcome the drawbacks which are inherently included in the classical DTC, this technique of
control allows us to reduces the torque and current ripples [45]. As archived in the literature, the
DTC-SVM is proposed firstly by Habetler in 1992 [46]. Figure III.1 shows a general block diagram
of DTC-SVM.
Figure III.1. General block diagram of SVM direct torque control [6].
Different structures of DTC-SVM methods are presented in the next section.
III.3 Structures of DTC-SVM

III.3.1 DTC-SVM strategy using closed-loop flux control
The DTC-SVM scheme with a closed flux control is shown in Figure III.2, the principle of
operation of this strategy is based on driving the stator flux vector toward the corresponding
reference vector defined by the input commands [46].
30
The d-q components of stator flux are defined as:
𝐿 𝐿 𝑑𝜓𝑟𝑐
𝜓𝑠𝑑𝑐 = 𝐿 𝑠 (𝜓𝑟𝑐 + 𝑅𝑟 𝜎 ) ( III.1)
𝑀 𝑟 𝑑𝑡
2 𝐿𝑟 𝑇
𝜓𝑠𝑞𝑐 = 𝑝𝑚 𝜎𝐿𝑠 𝜓𝑒𝑐 ( III.2)
𝑠 𝑀𝑠𝑟 𝑟𝑐
Figure III.2. DTC-SVM scheme with a closed flux control [5].
III.3.2 DTC-SVM strategy using closed-loop torque control

The DTC-SVM strategy using closed-loop torque control is mainly based on control of the
load angle 𝛿𝜓 using the PI controller. Also, the reference stator flux vector should be calculated
by knowing the stator flux position and the torque angle as [5], [47]:
𝜓𝑠𝑐 = 𝜓𝑠𝑐 𝑒 𝑗(θ𝑠 +∆𝛿𝜓 ) ( III.3)
Then, the reference stator flux vector is compared with the estimated value to obtain the flux error
𝛥𝜓𝑠 which is used to calculate the reference voltage vector 𝑉𝑠𝑐 . This strategy has a simple structure
because it has only one PI controller in which makes the DTC control easier to implement. The
block diagram of the DTC-SVM strategy using closed-loop torque control is given in Figure III.3.
Figure III.3. DTC-SVM scheme with closed torque control [5].
31
III.3.3 DTC-SVM strategy using closed-loop flux and torque control in polar coordinates
This method provides further development when both of the torque and the stator flux
magnitude are controlled. As shown in Figure III.4, the stator flux error 𝛥𝜓𝑠 is calculated through
both outputs 𝛥𝛾𝑠 and 𝑘𝜓 of the torque and flux controllers, respectively [38]. As:
∆𝜓𝑠 (𝑘) = 𝜓𝑠 (𝑘) − 𝜓𝑠 (𝑘 − 1) = ([1 + 𝑘𝜓 (𝑘)]𝑒 𝑗𝛥𝛾𝑠 (𝑘) − 1)𝜓𝑠 (𝑘 − 1) ( III.4)
assume that
𝑒 𝑗𝛥𝛾𝑠 (𝑘) = 1 + 𝑗𝛥𝛾𝑠 (𝑘) ( III.5)
Therefore, the stator flux error can be written as:
∆𝜓𝑠 (𝑘) = ([𝑘𝜓 (𝑘) + 𝑗𝛥𝛾𝑠 (𝑘)]. 𝜓𝑠 (𝑘 − 1)) ( III.6)
Figure III.4. DTC-SVM scheme operated in stator flux polar coordinates [5].
For improvement of the dynamic performance of the torque controller, the increment of
angle 𝛥𝛾𝑠 is composed of two parts: the static part 𝛥θ𝑠 that is delivered by the feed-forward loop
and the dynamic part, 𝛥𝛾𝑠𝑑 that is generated by the torque controller.
III.3.4 DTC-SVM with closed-loop torque and flux control in stator flux coordinates
The outputs of the PI flux and torque controllers can be considered as the reference stator
voltage components 𝑉𝑠𝑑𝑐 , 𝑉𝑠𝑞𝑐 . To fed the SVM-inverter, the command references 𝑉𝒔𝛼𝒄 , 𝑉𝑠𝛽𝑐 are
used after applying the transformation matrix (𝑑 − 𝑞 to 𝛼 − 𝛽). The DTC-SVM scheme with
closed-loop flux and torque control in stator flux coordinates is presented in Figure III.5 [5], [47].
Figure III.5. DTC-SVM scheme operated in stator flux Cartesian coordinates [5].
32
This strategy of direct torque control is selected to validate this project.
III.4 Stator Flux Field-Oriented DTC-SVM

The stator flux oriented direct torque control with space vector modulation depends on the
torque and flux closed-loop control in the stator flux coordinate system without any current
regulation. The stator flux oriented achieves a decoupling between flux and electromagnetic
torque. This method consists of two PI controllers, the first one uses the error between the reference
and the estimated values of the flux to produce a reference voltage signal 𝑉𝑠𝑑𝑐 , where the stator
flux vector becomes aligned with the d-axis, the second PI controller uses the error between the
reference and the estimated values of the electromagnetic torque to produce a reference voltage
signal 𝑉𝑠𝑞𝑐 , where the torque becomes aligned with the q-axis [49]. Figure III.6 shows the global
block diagram of the stator flux oriented DTC with SVM.
Figure III.6. The global control scheme of stator flux oriented DTC- SVM [6].
The stator flux oriented technique depends on the alignment of stator flux with the d-axis, where
the stator flux with the q-axis equal to zero, and it can be written as:
𝜓𝑠𝑑 = 𝜓𝑠
{𝜓 =0 ( III.7)
𝑠𝑞
Consequently, the voltage of the induction motor can be written as:

𝑑𝜓𝑠
𝑣𝑠𝑑 = 𝑅𝑠 𝑖𝑠𝑑 + 𝑑𝑡
𝑣𝑠𝑞 = 𝑅𝑠 𝑖𝑠𝑞 + 𝜔𝑠 𝜓𝑠
𝑑𝜓𝑟𝑑 ( III.8)
0 = 𝑅𝑟 𝑖𝑟𝑑 + − (𝜔𝑠 − 𝑝𝜔𝑟 )𝜓𝑟𝑞
𝑑𝑡
𝑑𝜓𝑟𝑞
{0 = 𝑅𝑟 𝑖𝑟𝑞 + 𝑑𝑡
+ (𝜔𝑠 − 𝑝𝜔𝑟 )𝜓𝑟𝑑
Where the flux equation can be described as the following:
33
𝜓𝑠 = 𝐿𝑠 𝑖𝑠𝑑 + 𝑀𝑠𝑟 𝑖𝑟𝑑

0 = 𝐿𝑠 𝑖𝑠𝑞 + 𝑀𝑠𝑟 𝑖𝑟𝑞
( III.9)
𝜓𝑟𝑑 = 𝐿𝑟 𝑖𝑟𝑑 + 𝑀𝑠𝑟 𝑖𝑠𝑑
{ 𝜓𝑟𝑞 = 𝐿𝑟 𝑖𝑟𝑞 + 𝑀𝑠𝑟 𝑖𝑠𝑞
Then the torque and the mechanical equations can be expressed as:
𝑇𝑒 = 𝑝𝜓𝑠 𝑖𝑠𝑞 ( III.10)
𝑑𝜔𝑟
𝐽 = 𝑇𝑒 − 𝑇𝐿 − 𝑓𝜔𝑟 ( III.11)
𝑑𝑡
III.4.1 Flux control design

The input of the flux PI controller is the error between the reference and the estimated
values of the flux and its output is a reference voltage signal 𝑉𝑠𝑑𝑐 .
Based on the motor model equations (III.8-III.9), one has:
𝑅𝑟 𝑑 𝑅𝑠 𝑅𝑟 (𝑅𝑟 𝐿𝑠 +𝑅𝑠 𝐿𝑟 ) 𝑑 𝑑 2
( + ) 𝑉𝑠𝑑 = [ + + ( ) ] 𝜓𝑠 + 𝑅𝑠 𝑖𝑠𝑞 (𝜔𝑠 − 𝑝𝜔𝑟 ) ( III.12)
𝜎𝐿𝑟 𝑑𝑡 𝜎𝐿𝑠 𝐿𝑟 𝜎𝐿𝑠 𝐿𝑟 𝑑𝑡 𝑑𝑡
with
𝑅𝑠 𝑖𝑠𝑞 (𝜔𝑠 − 𝜔𝑟 ) ≈ 0 ( III.13)
the equation (III.12) becomes as:
𝑅 𝑑 𝑅 𝑅 (𝑅𝑟 𝐿𝑠 +𝑅𝑠 𝐿𝑟 ) 𝑑 𝑑 2
(𝜎𝐿𝑟 + 𝑑𝑡) 𝑉𝑠𝑑 = [𝜎𝐿𝑠 𝐿𝑟 + + (𝑑𝑡) ] 𝜓𝑠 ( III.14)
𝑟 𝑠 𝑟 𝜎𝐿𝑠 𝐿𝑟 𝑑𝑡
Based on equation (III.14) and applying the Laplace transformation, the relationship between the
stator flux and stator voltage 𝑉𝑠𝑑 can be written as:
𝜓 (𝑠) 𝐴 +𝑠
𝐺𝜓𝑠 (𝑠) = 𝑉 𝑠 (𝑠) = 𝑠2 +𝐵𝜓 𝑠+𝐶 ( III.15)
𝑠𝑑 𝜓 𝜓
𝑅 𝑅𝑟 𝐿𝑠 +𝑅𝑠 𝐿𝑟 𝑅 𝑅
where, 𝐴𝜓 = 𝜎𝐿𝑟 𝐵𝜓 = 𝜎𝐿𝑠 𝐿𝑟
𝐶𝜓 = 𝜎𝐿𝑠 𝐿𝑟
𝑟 𝑠 𝑟
The flux control loop is shown in Figure III.7, where 𝐺𝑅𝜓 (𝑠) is a transfer function of the PI
controller.
Figure III.7. The flux control loop.
34
There are several methods to tune the gains of the PI controller 𝐾𝑝𝜓 and𝐾𝑖𝜓 , such analysis
by Bode diagrams and pole placement. The last one has been used in our work, one has:
𝐾𝑝𝜓 = 1647.8, 𝐾𝑖𝜓 = 12141.3.
III.4.2 Torque control design

The input of the PI torque controller is the error between the reference and the estimated
values of the electromagnetic torque and its output is a reference voltage signal 𝑉𝑠𝑞𝑐 .
Based on the motor model equations (III.8-III.9), one has:
𝑑
[(𝑅𝑟 𝐿𝑠 + 𝑅𝑠 𝐿𝑟 ) + 𝜎𝐿𝑠 𝐿𝑟 𝑑𝑡] 𝑖𝑠𝑞 =𝐿𝑟 𝑉𝑠𝑞 − 𝐿𝑟 𝜓𝑠 𝑝𝜔𝑟 + (𝜔𝑠 − 𝑝𝜔𝑟 )𝜎𝐿𝑠 𝐿𝑟 𝑖𝑠𝑑 ( III.16)
with,
(𝜔𝑠 − 𝑝𝜔𝑟 )𝜎𝐿𝑠 𝐿𝑟 𝑖𝑠𝑑 ≈ 0 ( III.17)
If both sides of the equation (III.16) are differentiated, one obtains:
𝑑 𝑑 2 𝑑𝑉𝑠𝑞 𝑑𝜔𝑟
[(𝑅𝑟 𝐿𝑠 + 𝑅𝑠 𝐿𝑟 ) 𝑑𝑡 + 𝜎𝐿𝑠 𝐿𝑟 (𝑑𝑡) ] 𝑖𝑠𝑞 = 𝐿𝑟 − 𝐿𝑟 𝜓𝑠 𝑝 ( III.18)
𝑑𝑡 𝑑𝑡
Based on equation (III.18) and applying the Laplace transformation, the relationship between the
torque and stator voltage 𝑉𝑠𝑞 is as the following:
𝑇 (𝑠) 𝐴 𝑠
𝐺𝑇𝑒 (𝑠) = 𝑉 𝑒 (𝑠) = 𝑠2 +𝐵 𝑇𝑠+𝐶 ( III.19)
𝑠𝑞 𝑇 𝑇
𝑝𝜓𝑠 𝑅𝑟 𝐿𝑠 +𝑅𝑠 𝐿𝑟 𝑝2 𝜓𝑠 2
where: 𝐴𝑇 = 𝐵𝑇 = 𝐶𝑇 =
𝜎𝐿𝑠 𝜎𝐿𝑠 𝐿𝑟 𝜎𝐿𝑠 𝐽
The torque control loop is shown in Figure III.8, where 𝐺𝑅𝑇 (𝑠) is a transfer function of the
PI controller.
Figure III.8. The torque control loop.
The gains of the controller are getting using the same last method, where the gains are
obtained as 𝐾𝑝𝑇 = 720.5, 𝐾𝑖𝑇 = 1647.8.
35
III.4.3 Speed control design

The speed regulation based on the PI controller has generated the reference of
electromagnetic torque. The input of this controller is the error between the speed reference and
measured speed. The measured speed can be obtained via the speed sensor or estimator.
Using the dynamic equation of an induction motor (III.11), in the transfer function of speed loop
is given as:
𝑟 𝜔 (𝑠) 1
𝐺𝜔𝑟 (𝑠) = 𝑇 (𝑠)−𝑇 = 𝐽𝑠+𝑓 ( III.20)
𝑒 𝐿 (𝑠)
Considering the load torque 𝑇𝐿 as a disturbance, the transfer function of the speed control in open
loop becomes:
𝜔𝑟 (𝑠) 1
𝐺𝜔𝑟 (𝑠) = = 𝐽𝑠+𝑓 ( III.21)
𝑇𝑒 (𝑠)
The speed control loop is shown in Figure III.9, where 𝐺𝑅𝑆 (𝑠) is a transfer function of the
PI controller.
Figure III.9. The speed control loop.
The gains of the PI speed controller are obtained as: 𝐾𝑝𝑠 = 1.2, 𝐾𝑖𝑠 = 24.6.
III.5 Flux, Torque, and Speed Estimation for Induction Motor Drives
III.5.1 Flux vector estimator

The classical stator flux estimator is based on a voltage model. Such estimator may be
directly obtained through the motor model equation as:
𝜓̂𝑠𝛼𝛽 = ∫(𝑉𝑠𝛼𝛽 − 𝑅𝑠 𝑖𝑠𝛼𝛽 ) 𝑑𝑡 ( III.22)
2 2
𝜓̂𝑠𝛼𝛽 = √𝜓̂𝑠𝛼 + 𝜓̂𝑠𝛽 ( III.23)
However, in terms of practical implementation, this type of estimator is prone to several sensitivity
problems concerning the dc-drift which arise when the pure integrator is used [50]. Therefore,
there were several methods proposed to avoid such a problem, one of them, the flux estimator that
36
was proposed by Lascu and Boldea. The Figure III.11 is presented the flux estimator based on
current and voltage models [51].
From the rotor voltages and fluxes (II.15 and II.17) equations, the rotor fluxes can be expressed
as:
𝐿 𝑑𝜓 𝐿
𝜓𝑟𝑑 = 𝑀𝑠𝑟 𝑖𝑠𝑑 − 𝑅𝑟 𝑑𝑡𝑟𝑑 + (𝜔𝑠 − 𝜔𝑟 ) 𝑅𝑟 𝜓𝑟𝑞
𝑟 𝑟
{ 𝐿𝑟 𝑑𝜓𝑟𝑞 𝐿𝑟
( III.24)
𝜓𝑟𝑞 = 𝑀𝑠𝑟 𝑖𝑠𝑞 − 𝑅 𝑑𝑡 − (𝜔𝑠 − 𝜔𝑟 ) 𝑅 𝜓𝑟𝑑
𝑟 𝑟
The rotor fluxes can be written also as:

𝑀 1
𝜓𝑟𝑑 = 𝑠𝑟 𝑖𝑠𝑑 + (𝜔𝑠 − 𝜔𝑟 )𝜓𝑟𝑞
1+𝑇𝑟 𝑠 1+𝑇𝑟 𝑠
{ 𝑀 1 ( III.25)
𝜓𝑟𝑞 = 1+𝑇𝑠𝑟 𝑠 𝑖𝑠𝑞 − 1+𝑇 𝑠 (𝜔𝑠 − 𝜔𝑟 )𝜓𝑟𝑑
𝑟 𝑟
where 𝑇𝑟 = 𝐿𝑟 /𝑅𝑟 is the rotor time constant.

the d-q rotor flux components are:
𝑀
𝜓𝑟𝑑 = 1+𝑇𝑠𝑟 𝑠 𝑖𝑠𝑑
{ 𝑟 ( III.26)
𝜓𝑟𝑞 = 0
𝑖
the stator flux 𝜓𝑠𝛼𝛽 calculated in stator coordinates as:
𝑖 𝑀𝑠𝑟 𝑖 𝐿𝑠 𝐿𝑟 −𝑀𝑠𝑟 2
𝜓𝑠𝛼𝛽 = 𝜓𝑟𝛼𝛽 + 𝑖𝑠𝛼𝛽 ( III.27)
𝐿𝑟 𝐿𝑟
𝑖
where 𝜓𝑟𝛼𝛽 is the estimated rotor flux from (III.26) in a stationary reference frame.
The Block diagram of the current model stator flux estimator is shown in Figure III.10.
Figure III.10. Block diagram of the current model flux estimator [5].
𝑖
After obtaining 𝜓𝑠𝛼𝛽 from the open-loop current model, the voltage model is used to estimate the
stator fluxes. To correct the value of estimated stator flux should add a compensation term, 𝑈𝑐𝑜𝑚𝑝
37
regarding the control action of a PI controller, which evaluates the error between the stator fluxes
𝑖
generated by the voltage and current model of the estimator 𝑒𝜓𝑠𝛼𝛽 = (𝜓𝑠𝛼𝛽 − 𝜓𝑠𝛼𝛽 )
1
𝜓𝑠𝛼𝛽 = 𝑠 (𝑉𝑠𝛼𝛽 − 𝑅𝑠 𝑖𝑠𝛼𝛽 − 𝑈𝑐𝑜𝑚𝑝 ) ( III.28)
1
𝑈𝑐𝑜𝑚𝑝 = (𝐾𝑝 + 𝐾𝑖 𝑠 )𝑒𝜓𝑠𝛼𝛽 ( III.29)
The coefficients 𝐾𝑝 and 𝐾𝑖 may be calculated such that, at zero frequency, the current
model stands alone, while at high frequency the voltage model prevails. the PI controller gains are
obtained by the following relations
𝐾𝑝 = 𝜔1 + 𝜔2 , 𝐾𝑖 = 𝜔1 × 𝜔2 ( III.30)
To achieve a good performance of the flux estimator, the parameters 𝜔1and 𝜔2 to be

between 2 < 𝜔1 < 5 and 20 < 𝜔2 < 30 , respectively [51].
After obtaining the stator flux 𝜓𝑠𝛼𝛽 , the rotor flux 𝜓𝑟𝛼𝛽 is determined as :
𝐿𝑚 𝐿𝑠 𝐿𝑟 −𝐿𝑚 2
𝜓𝑟𝛼𝛽 = 𝜓𝑠𝛼𝛽 + 𝑖𝑠𝛼𝛽 ( III.31)
𝐿𝑟 𝐿𝑟
Figure III.11. Flux estimator based on current and voltage models [49].
III.5.2 Torque estimation

The estimation torque is depended on the current measurement accuracy and stator flux
estimation method as:
3
𝑇𝑒 = 2 𝑝(𝜓𝑠𝛼 𝑖𝑠𝛽 − 𝜓𝑠𝛽 𝑖𝑠𝛼 ) ( III.32)
38
III.5.3 Rotor speed estimation based MRAS

In this project, the Model Reference Adaptive Systems (MRAS) is used to estimate the
speed of the induction motor due to its simple structure and robustness. The complete MRAS speed
estimator structure can be divided into three components (Figure III.12): Reference model,
Adaptive model, and an Adaptive mechanism. The reference model is independent of the speed
whereas the adaptive model is dependent to speed. The error vector is generated after comparing
the two outputs of the adaptive model and the reference model. This error is processed in the
adaptation mechanism to estimate the value of rotor speed. The estimated speed is as feedback to
the adaptive model [52].
Figure III.12. Block diagram of speed estimator based on MRAS [52].
The error between the reference model and the adaptive model can be expressed by:
𝑒𝜓𝑟 = 𝜓̂𝑟𝛽 𝜓𝑟𝛼
𝛼 𝛼 ̂
− 𝜓𝑟𝛽 𝜓𝑟𝛼 ( III.33)
In addition, the adaptive model can be written as:

1 𝐿
𝛼
𝜓𝑟𝛽 = − 𝑇 𝜓̂𝑟𝛽 + 𝑇𝑚 𝑖𝑠𝛽 + 𝜔 𝛼
̂𝑟 𝜓𝑟𝛼
𝑟 𝑟
{ 1 𝐿 ( III.34)
𝛼
𝜓𝑟𝛼 = − 𝑇 𝜓̂𝑟𝛼 + 𝑇𝑚 𝑖𝑠𝛼 − 𝜔 𝛼
̂𝑟 𝜓𝑟𝛽
𝑟 𝑟
where, 𝜓̂𝑟𝛼 and 𝜓̂𝑟𝛽 are the rotor fluxes estimated components for the reference model.
𝛼 𝛼
𝜓𝑟𝛼 𝑎𝑛𝑑 𝜓𝑟𝛽 are the rotor fluxes components for the adaptive model.
The estimated speed is expressed by:
1
𝜔
̂𝑟 = (𝐾𝑝 + 𝐾𝑖 𝑠 ) 𝑒𝜓𝑟 ( III.35)
III.6 Simulation Results

The DTC-SVM control for three phases 1.5 kW induction motor is implemented using
MATLAB/Simulink. The different operating conditions are verified to validate the presented
technique, the discussion of this result is comparing to the classical DTC that is presented at [6].
39
 The test at starting up and the steady states:
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Figure III.13. Simulation result of starting up and the steady-state case.
40
The speed step reference is 1000 rpm with a load torque 9 N.m. Figure III.13 shows the starting
up and the steady state's condition, and it shows the rotor speed, torque, stator phase current 𝑖𝑠𝛼 ,
stator flux components, flux magnitude, and the circular trajectory.
Figure III.13 (a) illustrates the speed responses of DTC- SVM with their reference speed
applying the torque load at (t=1s). In the starting up part, the figure shows a fast and good speed
response, where its controller loop rejects the torque load in the steady-state part.
Figure III.13 (c) shows the torque response and its reference when inserting the torque load,
this response is identical with its reference, where the results of the error equal to zero. It can be
noticed easily that has lower ripples compared with classical DTC. Then, in Figure III.13 (g, h)
illustrates the stator phase current with its zoom. It shows a smoother sinusoidal current which
refers to low harmonics. Next, Figure III.13 (b, d, and e) present the stator flux magnitude, circular
trajectory, and components. In these figures, the flux magnitude response is fast at the starting up;
the flux components 𝜓𝑠𝛼 𝑎𝑛𝑑 𝜓𝑠𝛽 have a good waveform. Therefore, the trajectory has a good
circle form and fewer ripples level. Figure III.13 (f) shows the stator flux vector position.
 The test at low and reversing speed:
(a)
(b)
Figure III.14. Simulation result of low and reversing speed case.
41
Figure III.14 (a) presents the test of operating at low and reversing speed response of the
studied technique, one shows that the speed value is starting from 200 rpm (1-3 second) to 600
rpm (4-6 second), then applying a reversing speed from 600 rpm to -600 rpm (6 to 10 seconds),
one shows the robustness of the presented technique is verified. It can be noticed easily that the
speed has an overshoot at the starting up at low-speed region. Also, in the region of reversing
speed, and one can be seen that the speed of the motor presents a good fast response. As seen in
Figure III.14 (b), the torque response follows its trajectory in a good way, In general, the DTC-
SVM technique provides a good dynamic more than the classical DTC.
 Test of MRAS estimator:
(a) (b)
(c) (d)
Figure III.15. Simulation result of DTC-SVM using rotor speed estimation based on MRAS.
Figure III.15 shows the behavior of IM using a rotor speed estimation based on MRAS.
Figure III.15 (a, b, and d) shows the rotor speed, the torque, and the stator flux magnitude,
respectively.
42
III.7 Conclusion
This chapter presents a study of IM behavior using Direct Torque Control with Space Vector
Modulation. The DTC-SVM strategy uses three PI controllers for electromagnetic torque, stator
flux, and speed control is presented. For better performance of the speed regulation loop, an anti-
windup PI controller is used. Then, the MRAS estimator instead of the hardware sensor is
presented to minimize the total cost of the system. For more, the DTC-SVM based on the MRAS
estimator for IM is numerically studied via the Simulink/Matlab environment.
43
CHAPTER IV
Photovoltaic Pumping System
using DTC-SVM Control for
Induction Motor
CHAPTER IV ------- Photovoltaic Pumping System using DTC-SVM Control for Induction Motor
IV.1 Introduction
In this chapter, we present an overview of the solar photovoltaic water pumping system
firstly, then the system design and system control will present and describe, which are the modeling
of the pumping system for the design part and the modeling of the P&O algorithm for the control
system. Finally, we will simulate the solar water pumping system using Simulink Matlab software,
then testing it under different insolation and temperature values to make sure of the effectiveness
of this system by discussing the system results.
IV.2 System Description

Solar water pumping systems are very important for many applications. Initially, these
systems were pumped using DC motors connected to a pump. However, it was replaced by
induction motors due to their better performance, economical and robust. The induction motor is
supplied by a photovoltaic (PV) arrays through power converters.
In most of these systems, single-stage and two-stage IM feeding methods were used. In
two-stage consisting of a DC-DC converter and a voltage source inverter, the maximum power of
the PV panels is usually extracted by maximum power point tracking algorithm (MPPT) using the
DC-DC converter. In single-stage, the maximum power point (MPP) of the system is extracted by
the VSI converter itself. The induction motor is controlled by DTC-SVM control, where the
switching states of the inverter are set by the SVM technique. Figure IV.1 has presented the scheme
of the PV array-fed IM drive [3].
Figure IV.1. Block diagram of the PV array-fed IM drive [3].
45
IV.3 System Design

This design system constitutes a single-stage PV array followed by a VSI fed three-phase
induction motor drive operated pump. The PV array operates at maximum power point tracking
along with SVM gating logic for effective utilization, the DC-link voltage has been calculated. An
Induction motor and voltage source inverter are previously discussed.
IV.3.1 Selection of DC-Link voltage

In order to determine the DC-link voltage of VSI that has to be higher than the peak
amplitude voltage, which is given to the motor. It can be estimated as [1]:
𝑉𝑑𝑐 > 𝑉𝐿 √2 ( IV.1)
where, 𝑉𝐿 is a line voltage across the motor terminals.
hence, the value of dc-link voltage is kept 𝑉𝑑𝑐 .
IV.3.2 DC-link capacitor voltage

The DC-link capacitor can provide sufficient energy at the time of transients, such as a
decrease in radiation and an increase in the load [2]. The DC-link capacitor is determined using
the following relation:
6𝑎𝑉𝑝 𝐼 𝑡
𝐶𝐷𝐶−𝑙𝑖𝑛𝑘 = (𝑉 2 −𝑉 2 ( IV.2)
𝑑𝑐 𝑑𝑐1 )
where
𝑉𝑑𝑐 is the DC-link voltage.
𝑉𝑑𝑐1 = 𝑉𝐿 √2 is the minimum allowable DC-link voltage during the transient condition.
𝑡 is the time required to recover the minimum DC-link allowable voltage.
𝐼 is the motor phase current, 𝑉𝑝 is the phase voltage, 𝑎 = 1.2 is an overloading factor.
IV.3.3 Design of water pump

The most popular pumps are centrifugal pumps and they are used for various applications.
These pumps have a nonlinear proportional relationship between the rotor speed and load torque.
We can describe them as following [1]:
𝑇𝑝 = 𝐾1 𝜔𝑟2 ( IV.3)
𝜔𝑟 is the speed of the induction motor.
where 𝐾1 is proportionality constant of the pump. It can be determined as:
46
𝑇𝑝
𝐾1 = 𝜔2 ( IV.4)
𝑟
IV.4 System control

The studied system control constitutes two parts: the first one is the MPPT control. It is
achieved by three-phase VSI using the P&O algorithm. The second part is motor speed control,
which is executed by direct torque control of the drive with the SVM switching scheme.
IV.4.1 Reference speed estimation of induction motor

The reference speed of the induction motor can be estimated by two components. The first
one is estimated by the DC-link voltage PI controller. The reference PV voltage is given through
∗
MPPT, thus obtained at 𝑘 𝑡ℎ sampling instant, is the DC-link voltage reference 𝑉𝑑𝑐 and it is
compared with the PV voltage as follows [1]:
∗
𝑉𝑑𝑐𝑙(𝑘) = 𝑉𝑑𝑐(𝑘) − 𝑉𝑝𝑣(𝑘) ( IV.5)
Figure IV.2 shows the schematic for speed estimation 𝜔1, the error signal 𝑉𝑑𝑐𝑙(𝑘) is fed to
the DC link voltage PI controller and the resulting speed error signal at the 𝑘 𝑡ℎ sampling instant
and is given as follows:
𝜔1(𝑘) = 𝜔1(𝑘−1) + 𝐾𝑝𝑑𝑐 {𝑉𝑑𝑐𝑙(𝑘) − 𝑉𝑑𝑐𝑙(𝑘−1) } + 𝐾𝑖𝑑𝑐 𝑉𝑑𝑐𝑙(𝑘) ( IV.6)
where 𝐾𝑝𝑑𝑐 and 𝐾𝑖𝑑𝑐 are the gains of the DC-link voltage PI controller.
P&O
Figure IV.2. Reference speed generation 𝜔1 [1].
Figure IV.3 shows the converted speed term from the PV by the next relation and that gives
the second reference speed by affinity law of pump. It can be obtained as:
𝑃𝑝𝑣 = 𝐾1 𝜔23 ( IV.7)
where 𝐾1 is proportionality constant of the pump.
47
Figure IV.3. Feedforward speed component [1].

Hence, the reference speed of the motor is estimated as follows:
𝜔𝑟𝑒𝑓 = 𝜔1 + 𝜔2 ( IV.8)
This reference speed is used for control of VSI feeding induction motor drive.
IV.5 Simulation Results

The photovoltaic water pumping system is simulated and modeled in Simulink (MATLAB
environment), and the simulation results are shown under conditions of varying the insolation and
temperature. The pump load is automatically changed as the rotor speed is varied. Figure IV.4
shows the block simulation of the Photovoltaic Water Pumping System using DTC-SVM control.
Figure IV.4. Block simulation of the Photovoltaic Water Pumping System using DTC-SVM
control.
48
 In the case of the varying in the load pump value by the rotor speed, the result is given as
follows:
Figure IV.5. Simulation result of the varying in the load torque produced by the pump.
Figure IV.5 clearly shows the changing of IM load torque, which is produced by the pump,
automatically with the rotation speed. Where the load pump increase when the increase of rotor
speed. DTC-SVM can control this load torque of the pump that is applied to the induction motor.
 In the case of the varying in the solar radiation value according to the temperature value, the
result is given as follows:
Figure IV.6. Simulation result of Photovoltaic Water Pumping System using DTC-SVM.
49
Figure IV.6 shows rotor speed and electromagnetic torque with a load pump. In the first case,
we put the input of the insolation is 1000 𝑤/𝑚2 form (0-1 second) then is 500 𝑤/𝑚2 form (1-2
seconds) with a constant temperature equal to 25 °𝑐. In the second one, we put the values of the
same interval of the insolation with another constant temperature equal to 45 °𝑐.
In the first case, when it is operating at a temperature of 25 °𝑐 and insolation 1000 𝑤/𝑚2 ,
which is the ideal part in this case, where it is the ideal case for the system, which is given
maximum speed (1480 rpm) and load pump. It can be seen when decreasing the insolation to
become 500 𝑤/𝑚2 and the temperature is keeping 25 °𝑐, in this case, the speed (1076 rpm) and
torque load decrease according to the insolation. In the second case, it can be seen when increasing
the temperature to become 45 °𝑐 and the insolation is keeping 1000 𝑤/𝑚2 , in this part, the speed
(1411 rpm) and torque load decrease according to the temperature. Next, it can be seen when
keeping the temperature at 45 °𝑐 with decreasing the insolation to become 500 𝑤/𝑚2 , in this part,
the speed (1031 rpm) and torque load decrease according to both the insolation and temperature.
Generally, increasing the temperature or decreasing insolation led to decrease in the speed and
torque load, which means it affects negatively the efficiency of the PV array.
IV.6 Conclusion
This chapter presents the photovoltaic water pumping system. Firstly, this system is a
standalone system that can be described as an induction motor connected to a pump that is fed by
a photovoltaic array through a voltage source inverter. Then the modeling of the system design
and system control, which are the modeling of the pump and the reference speed estimation MPPT.
Secondly, this studied system is simulated in MATLAB/Simulink. Thus, the simulation system
shows satisfactory results. These results indicate that the MPPT algorithm can achieve the
objective under the variation in the input temperature and solar irradiance. It is clear that the
photovoltaic water pumping system is entirely appropriate and suggested in sunny places like
South Algeria. Many applications use this system owing to the virtues of simple structure, cost-
effectiveness, control, and fairly good efficiency.
50
GENERAL CONCLUSION
GENERAL CONCLUSION -----------------------------------------------------------------------------------
General Conclusion
The work presented in this thesis concerns the modeling and simulation of a photovoltaic
pumping system. This system allows supplying the water to isolated sites where no energy source
is available. The selected photovoltaic model was simulated in an environment by MATLAB for
different temperatures and insolation, the purpose of this simulation is to determine their influence
on the system performance, to validate the motor driving efficiency (DTC-SVM), and checking its
performance. Where we can conclude depending on our system simulation results some benefices
and notices.
Firstly, for selecting the switching states of this system inverter we have used the SVM
technique, which provides a constant switching frequency that allows having a reset for the inverter
(on/off), it can give a higher voltage value 15% more than SPWM technique. Secondly, the DTC-
SVM control is reduced the torque and flux ripples, with a less harmonics of induction motor
current that what can give it a good sinusoidal waveform, and give generally a high performance
at the starting up and the steady states under the reversing and low speed operating conditions more
then the classical DTC. Finally, through the results obtained, the solar water pumping system is
stable and gave satisfactory results under different conditions of temperature and insolation, where
the electromagnetic torque of the induction motor tracked the load torque that was produced by
the pump and controlled by DTC-SVM.
52
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Enhanced Control of A Photovoltaic Water Pumping System by DTC-SVM

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‫الجمهورية الجزائرية الديمقراطية الشعبية‬

People's Democratic Republic of Algeria

A thesis submitted for the fulfillment of

Enhanced Control of a Photovoltaic Water Pumping

Dr. Zohier TIR Suprvisor MCA

I dedicate this thesis to my father,

I also dedicate it to my mother who has taken the biggest part of

sacrificing for our education. May Allah protect them.

To my brothers and sisters. To my nephews and nieces.

To all my friends, in my life.

Hocine Ihab AZZA

I dedicate this thesis to my parent “MESAI BELGACEM

of sacrificing for my education. May Allah protect them.

To my sisters: Ikram and Sondos.

To all my friends, in my social and academic life.

Ahmed MESAI BELGACEM

I would like to express my thanks to everyone that makes the achievement of

Enhanced Control of a Photovoltaic Water Pumping System by

III.3.2 DTC-SVM strategy using closed-loop torque control .................................................. 31

The present work is structured as follows:

I.2 Photovoltaic water pumping system

Figure I.1. Photovoltaic Water Pumping System [7].

I.3 Solar energy and photovoltaic system

I.3.2 Types of solar radiation

Figure I.3. Solar radiation’s components (DNI and DHI) [10].

I.3.3 Photovoltaic solar energy

I.3.4 Photovoltaic cells:

Figure I.4. The main components of the photovoltaic system [8].

I.3.4.1 Type of PV cells technologies

Type of cell Efficiency (%) Expected lifetime (years) References

Figure I.5. Types of the photovoltaic solar cell [17].

I.3.4.2 Series, parallel and mixed combinations of PV modules

Figure I.6. The serial connections of PV modules [19].

Figure I.7. The parallel connections of PV modules [19].

I.3.4.3 Solar modules protection [20]

I.3.4.3.1 Use of bypass diode

Figure I.8. Shaded PV cells with Bypass Diodes protection [19].

I.3.4.3.2 Use of blocking diodes

I.3.5 Photovoltaic effect

Figure I.10. Component and operational principle of PV cells [12].

I.3.6 Different types of PV systems

I.3.6.1 Stand-Alone PV systems

A stand-alone PV installation is required in the off-grid PV system. This design is perfect

Figure I.11. Standard Stand-Alone PV system [19].

I.3.6.2 Grid-Connected PV system:

As shown in Figure I.12, the well-known grid-connected PV system is usually composed

Figure I.12. Standard Grid-Connected PV system [19].

I.3.6.3 Hybrid PV system

Figure I.13. Standard Hybrid PV system [21].

I.3.7 PV output characteristics and parameters

I.3.8 Effect of solar irradiation and temperature [12]

Figure I.15. I–V Characteristic curve of a PV module [12].

I.3.9 Maximum Power Point Tracking control techniques

I.3.9.1 Hill Climbing/Perturb and Observe

Figure I.17 shows the orders of this process,

I.4 Water Pumping System

I.4.1 Motor technology

I.4.2 Pump technology