FUZZY - PID SPEED CONTROL OF PMSM DRIVE FOR EV (QUTE …
Transcript of FUZZY - PID SPEED CONTROL OF PMSM DRIVE FOR EV (QUTE …
FUZZY - PID SPEED CONTROL OF PMSM DRIVE FOR EV (QUTE
BAJAJ) APPLICATION
By:
Getachew Teshome Teferi
A Thesis Paper Submitted to The Department of Electrical Power and Control
Engineering
School of Electrical Engineering and Computing
In Partial Fulfilment of The Requirement of The Degree of Master of Science
in Electrical Power and Control Engineering
(Specialization in Power Electronics)
Office of Graduate studies
Adama Science and Technology University
Adama, Ethiopia
July,2020
FUZZY - PID SPEED CONTROL OF PMSM DRIVE FOR EV (QUTE
BAJAJ) APPLICATION
Getachew Teshome Teferi
Advisor: Tafesse Asrat (PhD)
A Thesis Paper Submitted to The Department of Electrical Power and Control
Engineering
School of Electrical Engineering and Computing
In Partial Fulfilment of The Requirement of The Degree of Master of Science
in Electrical Power and Control Engineering
(Specialization in Power Electronics)
Office of Graduate studies
Adama Science and Technology University
Adama, Ethiopia
July,2020
I
Approval of Bord of Examiners
We, the undersigned, members of the board of examiners of the final open defence by
Getachew Teshome Teferi have read and evaluated his thesis entitled “Fuzzy - PID Speed
Control of PMSM Drive for EV (QUTE BAJAJ) Application” and examined the
candidate. This is therefore to certify that the thesis has been accepted in partial fulfilment
of the requirement of the Degree of Master of Science Electrical Power and Control (Power
Electronics).
Name Signature Date
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Advisor
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External Examiner
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Internal Examiner
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Chair Person
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Head of Department
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School Dean
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Post graduate Dean
II
DECLARATION
I hereby declare that this MSc. Thesis is my original work and has not been presented for a
degree in any other university, and all sources of material used for this thesis have been duly
acknowledged.
Name: ____________________________________
Signature: ________
This MSc Thesis has been submitted for examination with my approval as thesis advisor.
Name: ____________________________________
Signature: ________
Date of submission: …………..
III
ADVISOR’S APPROVAL SHEET
To: Electrical Power and Control Engineering department
Subject: Thesis Submission
This is to certify that the thesis entitled “Fuzzy - PID Speed Control of PMSM Drive for EV
(QUTE BAJAJ) Application” submitted in partial fulfilment of the requirements for the degree
of Masters of Master of science Electrical Power and Control (Power Electronics) the
Graduate program of the department of Electrical Power and Control, and has been carried out
Getachew Teshome Teferi Id. No PGR/18156/11 under our supervision. Therefore, we recommend
that the student has fulfilled the requirements and hence hereby he can submit the thesis to the
department.
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Advisor Signature Date
IV
ACKNOWLEDGEMENT
First, I would like to thank more my God. Then I want to express a sincere acknowledgement
to my advisor, Dr. Tafesse Asrat for giving me the opportunity to research under his guidance
and supervision. I received motivation, comments, encouragement and continuous guidance
from him during my graduate studies.
My thanks are extended to my Lecturer Dr. P. Palanivel for his contribution and assistance
and fruitful ideas. I further wish to thank all of them who had guided me through all the
technical difficulties throughout the research. This research would not have been successful
without the valuable guidance and constructive criticisms throughout the research.
V
ABSTRACT
This thesis explores speed control of PMSM drive using fuzzy - PID controller strategy which
is used to drive and control the speed and torque of PMSM. These controllers will replace
the conventional PID controller which have the disadvantage of convectional PID controller
which may not accommodate the uncertainties and disturbances. In addition to this the
controller is not really suited for nonlinear plants and not assure the desired performance
for a changing environment/ operating points, and thus present low robustness. Thus fuzzy
- PID improve the drawback for its proper performance. The conventional approach to these
issues is to tune the proportional and integral gains manually by observing the response of
the system. The tuning of the PID parameters must be made on-line and automatic in order
to avoid tedious tasks in manual control. The well-known Ziegler-Nichols method to tune the
coefficients of a PID controller is very simple to implement and tune, but cannot guarantee
to be always effective. For this reason, this thesis proposed the design of an on-line self-
tuning PID controller scheme using fuzzy logic controller. PMSM have the potential to
providing high torque-to-current ratio, high power-to-weight ratio, high efficiency and
robustness. Due to the above favourable point PMSMs are commonly used in latest variable
speed AC drives, particularly in city Electric Vehicle applications and PMSM became at the
top of ac motors in high performance drive systems such as EV like QUTE BAJAJ which
requires frequent start and stop. Electric vehicle is a best solution for reduction global
warming and climate change science it is not providing harmful gases. This thesis also will
describe the methodology and process of modelling the PMSM drive including data analysis
using MATLAB-Simulink will implemented. This project will improve time domain
specifications (Rise Time, Peak Time, Peak Value, Peak Overshoot, Settling Time and Steady
State Error) of PMSM improved by using the fuzzy- PID speed controller over convectional
controller. The obtained results for conventional and proposed approaches will compared.
Keywords - Conventional PID, Electric vehicle, Fuzzy Logic controller, On-line self-tuning
PID Controller, permanent magnet synchronous motor.
VI
Contents
DECLARATION .................................................................................................................. II
ADVISOR’S APPROVAL SHEET .................................................................................... III
ACKNOWLEDGEMENT ................................................................................................... IV
ABSTRACT ......................................................................................................................... V
LIST OF FIGURES .............................................................................................................. X
LIST OF TABLES ........................................................................................................... XIII
LIST OF ACRONYMS .................................................................................................... XIV
LIST OF SYMBOLS ......................................................................................................... XV
CHAPTER ONE .................................................................................................................... 1
1. INTRODUCTION ............................................................................................................. 1
1.1. Background of Study .................................................................................................. 1
1.2. Statement of Problem ................................................................................................. 4
1.3. Objective ..................................................................................................................... 5
1.3.1. General Objective ................................................................................................ 5
1.3.2. Specific Objectives .............................................................................................. 5
1.4. Significance of Study ................................................................................................. 5
1.5. Motivation .................................................................................................................. 6
1.6. Scope .......................................................................................................................... 6
1.7. Limitation ................................................................................................................... 7
1.8. Thesis Outline ............................................................................................................. 7
CHAPTER TWO ................................................................................................................... 8
2. LITERATURE REVIEW .................................................................................................. 8
2.1. Introduction ................................................................................................................ 8
2.2. The drive train of Electric Vehicles .......................................................................... 10
VII
2.3. Types of electric motor ............................................................................................. 13
2.3.1. DC Motor ........................................................................................................... 14
2.3.2. Induction Motor ................................................................................................. 15
2.3.3. BLDC Motor ..................................................................................................... 16
2.3.4. Switched Reluctance (SR) Motor ...................................................................... 17
2.3.5. PMSM ................................................................................................................ 17
2.3.6. Performance of Different Electric Motor for EV Propulsion ............................ 19
2.3.7. Comparison of PMSM with IM and BLDC ...................................................... 22
2.4. Electric Vehicle Batteries ......................................................................................... 25
2.4.1 Advantages of lithium-ion batteries for vehicle ................................................. 25
2.5. PMSM drives ............................................................................................................ 25
2.5.1. Permanent Magnet Materials ............................................................................. 26
2.5.2. Classification of Permanent Magnet Motors ..................................................... 26
2.6. Closely related works on PMSM motor control ....................................................... 28
CHAPTER THREE ............................................................................................................. 33
3. METHODOLOGY .......................................................................................................... 33
3.1. Introduction .............................................................................................................. 33
3.2. Materials ................................................................................................................... 33
3.3. Methods .................................................................................................................... 33
3.4 Electric Vehicle Dynamics ........................................................................................ 35
3.4.1. Motive force, Motive Power and Motive Torque of the Vehicle ...................... 36
3.4.2 Vehicle Specification and Traction Selection .................................................... 44
3.5. Dynamic Modelling of PMSM Drive ....................................................................... 45
3.5.1. Arbitrary Reference Frame Concept.................................................................. 45
3.5.2. Three Phases to Two Phase Transformation .................................................... 46
3.5.3. Transfer Function of PMSM.............................................................................. 51
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3.6. Space Vector Pulse Width Modulation .................................................................... 52
3.6.1. Implementation of SVPWM .............................................................................. 54
3.7. Controller Design ..................................................................................................... 60
3.7.1. Introduction to Fuzzy Logic Controller ............................................................. 60
3.7.1. Fuzzy Logic Controller ...................................................................................... 61
3.7.2. PID Controller ................................................................................................... 63
3.7.3. Fuzzy Logic based self-tuning PI Controller ..................................................... 64
3.8 Software Simulation Modelling and Design ............................................................. 67
3.8.1. MATLAB/SIMULINK model ........................................................................... 67
CHAPTER FOUR ............................................................................................................... 69
4. RESULTS AND DISCUSSIONS ................................................................................... 69
4.1. MATLAB Simulation Result of SVPWM ............................................................... 69
4.1.1. Clarke Transformation Output........................................................................... 69
4.1.2. Switching Pattern of SVPWM Inverter ............................................................ 69
4.1.3. Generated Gate Signal ....................................................................................... 70
4.2. Fuzzy Controller Output ........................................................................................... 71
4.2.1. Fuzzy Logic Output ........................................................................................... 71
4.3. OUTPUT VOLTAGE .............................................................................................. 73
4.3.1. Phase Voltage .................................................................................................... 73
4.3.2. Line to Line Voltage .......................................................................................... 73
4.4. Speed Output of PMSM ........................................................................................... 74
4.4.1 Rotor Speed and Reference Speed of PI Controller ........................................... 74
4.4.2. Rotor Speed and Reference Speed of Fuzzy Controller .................................... 76
4.4.3. Rotor Speed and Reference Speed of Fuzzy-PI Controller ............................... 78
4.4.4. Rotor Speed of Fuzzy-PI Controller for PMSM ................................................ 80
4.5. Torque and Current Response of PMSM ................................................................. 81
IX
4.5.1. Torque Output ................................................................................................... 81
4.5.2. Current Output ................................................................................................... 82
4.6. Steep Response of PMSM ........................................................................................ 84
CHAPTER FIVE ................................................................................................................. 87
5. CONCLUSION AND RECOMMENDATION .............................................................. 87
5.1. Conclusion ................................................................................................................ 87
5.2. Recommendation ...................................................................................................... 88
References ........................................................................................................................... 89
X
LIST OF FIGURES
Figure 2-1: Motor Classification. ........................................................................................ 13
Figure 2-2: (a) DC motor (b) Torque versus speed characteristics of DC motor. ............... 14
Figure 2-3: Torque and power versus characteristic of Induction motor. ........................... 15
Figure 2-4: (a) BLDC motor and (b)Torque speed envelope of a BLDC Motor. ............... 16
Figure 2-5: (a) SRM motor and (b)Classical torque-speed characteristics of SRM motor. 17
Figure 2-6: Torque-speed characteristic of a PMSM drive. ................................................ 18
Figure 2-7: Battery in terms of Power density and Energy density. ................................... 25
Figure 2-8: Rotor configurations studied: (a) Surface PM (SPM) synchronous machine. (b)
Surface inset PM (SIPM) synchronous machine. (c) Interior PM (IPM) synchronous
machine. (d) Interior PM synchronous machine with circumferential orientation.............. 28
Figure 3-1: Flow chart of research methodology. ............................................................... 34
Figure 3-2: Block diagram of the proposed control system. ............................................... 35
Figure 3-3: EV drives. ......................................................................................................... 35
Figure 3-4: External force acting on moving EV. ............................................................... 36
Figure 3-5: Aerodynamic dragging force versus speed of the car in 𝑘𝑚ℎ𝑟. ....................... 38
Figure 3-6: Motive force versus approaching angle of the vehicle. .................................... 39
Figure 3-7: Motive force in N versus speed of the vehicle in 𝑘𝑚ℎ𝑟................................... 40
Figure 3-8: The motor power consumption with respect to approaching angle. ................. 41
Figure 3-9: Consumed power versus speed of vehicle in 𝑘𝑚ℎ𝑟. ........................................ 42
Figure 3-10: Torque developed by motor versus speed of vehicle in 𝑘𝑚ℎ𝑟. ...................... 44
Figure 3-11:Three-phase and two-phase stator windings. ................................................... 47
Figure 3-12: PMSM Dynamic stator q-axis and d-axis equivalent circuit. ......................... 49
Figure 3-13: PMSM equivalent circuits from steady state equations. ................................. 49
Figure 3-14: Transfer function block diagram of PMSM.................................................... 52
Figure 3-15: Three Phase Inverter. ...................................................................................... 53
XI
Figure 3-16: Basic switching vectors, sectors and a reference vector. ................................ 55
Figure 3-17: Voltage space vector and its components in (abc axis). ................................. 56
Figure 3-18: Reference voltage as a combination of adjacent vectors in sector I. .............. 58
Figure 3-19: Space Vector PWM switching patterns for the first two sectors. ................... 58
Figure 3-20: PID control System. ........................................................................................ 64
Figure 3-21: Member ship for (a) Speed error input to FLC (b) change in speed error input
to FLC (c) speed limit output of FLC. ................................................................................. 66
Figure 3-22: Block diagram of FL-PID controller schematic representation. ................... 687
Figure 3-23: MATLAB Simulink model of fuzzy- PID of PMSM. .................................... 68
Figure 3-24:MATLAB Simulink model of fuzzy- PID of PMSM mathematical model. ... 68
Figure 4-1: αβ-transformation output voltage. .................................................................... 69
Figure 4-2: Voltage for three phases (PWM Duty cycles). ................................................. 70
Figure 4-3: Gate signal for IGBT 1 and IGBT 4. ................................................................ 70
Figure 4-4: Gate signal for IGBT 3 and IGBT 6. ............................................................... 71
Figure 4-5: Gate signal for IGBT 5 and IGBT 2. ............................................................... 71
Figure 4-6: Output of fuzzy rule viewer. ............................................................................. 72
Figure 4-7: Fuzzy surface viewer. ....................................................................................... 72
Figure 4-8: Phase voltage 𝑉𝑎𝑛, 𝑉𝑏𝑛 and 𝑉𝑐𝑛. .................................................................... 73
Figure 4-9: Line voltage 𝑉𝑎𝑏. ............................................................................................. 73
Figure 4-10: Line voltage 𝑉𝑎𝑐............................................................................................. 74
Figure 4-11: Line voltage 𝑉𝑏𝑐. ............................................................................................ 74
Figure 4-12: Rotor speed Vs reference speed of PI controller. ........................................... 75
Figure 4-13: Zoom out of rotor speed Vs reference speed of PI controller......................... 75
Figure 4-14: The difference between rotor speed Vs reference speed of PI controller. ...... 75
Figure 4-15: Zoom out of the difference between rotor speed Vs reference speed of PI
controller. ............................................................................................................................. 76
Figure 4-16: Rotor speed Vs reference speed of Fuzzy controller. ..................................... 76
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Figure 4-17: Zoom out of rotor speed Vs reference speed of fuzzy controller. .................. 77
Figure 4-18: The difference between rotor speed Vs reference speed of fuzzy controller. 77
Figure 4-19: Zoom out of the difference between rotor speed Vs reference speed of fuzzy
controller. ............................................................................................................................. 77
Figure 4-20: Rotor speed Vs reference speed of Fuzzy-PID controller. ............................. 78
Figure 4-21: Zoom out of rotor speed Vs reference speed of fuzzy-PID controller. .......... 78
Figure 4-22: The difference between rotor speed Vs reference speed of fuzzy- PID controller.
............................................................................................................................................. 79
Figure 4-23: Zoom out of the difference between rotor speed Vs reference speed of fuzzy-
PID controller. ..................................................................................................................... 79
Figure 4-24: Rotor speed of Fuzzy-PID controller. ............................................................. 80
Figure 4-25: zoom out view of Rotor speed of Fuzzy-PID controller. ............................... 81
Figure 4-26: Electromagnetic torque Vs load torque. ......................................................... 82
Figure 4-27: I abc current response. .................................................................................... 82
Figure 4-28: I dq current response. ...................................................................................... 83
Figure 4-29: Electromagnetic torque developed by PMSM. ............................................... 83
Figure 4-30: I dq current response of PMSM. ..................................................................... 84
Figure 4-31: Steep response of PMSM motor. .................................................................... 84
Figure 4-32: Error between steep input and steep output of PMSM. .................................. 85
XIII
LIST OF TABLES
Table 2-1: Electric vehicle available in world. .................................................................... 11
Table 2-2: Advantage and disadvantage of different Electric Motor used for EV propulsion.
............................................................................................................................................. 19
Table 2-3: Electric propulsion systems evaluation. ............................................................. 21
Table 2-4: Comparison of IM and PMSM.. ........................................................................ 22
Table 2-5: Comparison of BLDC and PMSM motors. ........................................................ 23
Table 2-6: Control method of PMSM done by different researcher.................................... 31
Table 3-1: The coefficient of friction for different types of surface. .................................. 40
Table 3-2: Electric Bajaj specification. ............................................................................... 44
Table 3-3: PMSM motor specification. ............................................................................... 45
Table 3-4: Switching vectors, phase voltages and output line to line voltages. .................. 54
Table 3-5: Switching Time Calculation at Each Sector. ..................................................... 59
Table 3-6: Rule Base for Fuzzy Logic Controller. .............................................................. 67
Table 4-1: Comparison of PID, Fuzzy logic and Fuzzy-PID controller. ............................. 80
Table 4-2: Comparison of dynamic performance for PID and Fuzzy- PID controller. ....... 85
XIV
LIST OF ACRONYMS
AC Alternating current
BLDC Brushless DC motor
DC Direct current
DSP Digital signal processing
EV Electric vehicle
FLC Fuzzy logic control
FOC Field-oriented control
IM Induction motor
MATLAB Matrix Laboratory
PI controller Proportional integral controller
PMSM Permanent-magnet synchronous motor
SRM Switched Reluctance motor
SVPWM Space vector pulse width modulation
VCPWS Vector control pulse width modulation
XV
LIST OF SYMBOLS
Symbol Description Unit
B viscous damping coefficient Nm. s
𝐹𝐴 Aerodynamics drag force N
𝐹𝐺 Gradient resistance N
𝐹𝑅 Rolling resistance force N
𝐹𝑇 Total tractive force N
𝑖𝑑 d-axis current in synchronous frame A
𝑖𝑞 q-axis current in synchronous frame A
J moment of inertia of the motor 𝐾𝑔𝑚2⁄
𝐿𝑑 d-axis inductance H
𝐿𝑞 q-axis inductance H
P Number of magnetic poles -
𝑅𝑠 Motor phase resistance Ω
𝑇𝑒 Electromagnetic torque Nm
𝑇𝑙 Load torque Nm
𝑉𝑑 d-axis voltage in synchronous frame V
𝑉𝑞 q-axis voltage in synchronous frame V
ω𝑟 motor electrical angular velocity 𝑟𝑎𝑑𝑠𝑒𝑐⁄
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ω𝑒 machine angle velocity of rotor 𝑟𝑎𝑑𝑠𝑒𝑐⁄
𝜆𝑑 d-axis flux linkage in synchronous frame 𝑊𝑏
𝜆𝑞 q-axis flux linkage in synchronous frame 𝑊𝑏
𝜆𝑚 PM flux linkage in synchronous frame 𝑊𝑏
1
CHAPTER ONE
1. INTRODUCTION
1.1. Background of Study
In recent years, the ac motors are extensively applied in home appliances as well as industrial
applications such as electric vehicles, wind generation systems, industrial robots, air
conditioners, washing machines, etc. There are two main categories of the ac motors: IMs
and PMSM. Nowadays, the IMs are used in about 70% of industrial electric motors due to
their simplicity, ruggedness, and low production costs [1] [2]. Despite that, the PMSMs are
gradually taking over the IMs owing to their low inertia, high-power density, low
noise, high power density, and high energy efficiency which makes the PMSM is best suited
to mitigate worldwide shortage of energy and development of new clean energy which is
important to society. However, the PMSM system is not easy to control because it is a
nonlinear multivariable system and its performance can be highly affected by parameters
variations in the run time [3] [4].
The idea of using electricity instead of fossil fuels for propulsion system of vehicle is not
new. Scientists and manufacturers have attempted to design and improve EV from long time
ago. As the result Rodert Anderson built the first electric carriage in 1839. In 1870 Davied
Salomon developed an electric car with light electric motor. The batteries were heavy at the
time therefore its performance was poor [5]. But, nowadays with the improvement of battery
technology EV have better performance. Engine based vehicle is ono of environmental
pollutant machines. Fossil fuel is expected to be totally finished after few decades. The only
solution to continues the transportation is to replace the engine-based vehicle by electric
based vehicle. EV is essential and simple to use for the developing country like Ethiopian
which are on their way generating large MW of electric power.
Motor is the propelling part of EV. In this study PMSM motor is selected for EV propulsion.
The invention of modern PM with high energy density led to the development of dc machines
with PM field excitation in 1950s. Introduction of PMs to replace the electromagnetic poles
with windings requiring an electric energy supply source resulted in compact dc machines.
Likewise, in synchronous machines, the conventional electromagnetic field poles in the rotor
are replaced by the PM poles and by doing so the slip rings and brush assembly are avoided.
2
With the advent of high switching power transistor and silicon-controlled rectifier devices
in the later part of 1950s, the replacement of the mechanical commutator with an electronic
commutator in the form of an inverter was achieved. These two developments contributed
to the development of PMSMs and BLDC.
Permanent magnet synchronous motors are electrical motors that are widely used in motion-
control applications in the low-to-medium power ratings such as robotics, house
appliances, adjustable speed drives, and electric vehicles. This popularity is justified by
numerous advantages over commonly used motors. The absence of the external rotor
excitation eliminates losses on the rotor, and makes PMSM highly efficient and high torque
to inertia ratio so that it gives fast response. In addition, the absence of the rotor winding
render slip rings on the rotor and brushes obsolete, and thus reduces the maintenance cost.
The replacement of the rotor winding with PM in PMSM makes it compact structure or
smaller in size that results a high-power density. The heat loss in the rotor of PMSM that
affects the machine operation is also negligible [6] [7].
It has both the advantages of reliable operation of AC motor and the advantages of excellent
speed control performance of DC motor which is very suitable for engineering application
Therefore, researchers always desire to design a high performance controller which has a
simple algorithm, fast response, high accuracy, and robustness against the motor parameter
and load torque variations. Control of PMSM motor drives is most important due to
continuous and frequent use in various systems. The governing of AC motor drives can be
mainly divided into ‘scalar’ and ‘vector’ controls. Scalar control is easy to perform and
provide a satisfactorily steady-state response, stable though the changes are stagnant. To get
high accurate and good robust, as well as steady-steady response, ‘vector’ control advances
are to be employed with closed-loop feedback control. The field-oriented control
fundamental depends on the instantaneous control of stator current space vectors. The
research on FOC is effective, with the objective of organizing many progressive features for
highly accurate control, such as sensor less operation, and utilization of accessible
specification adjustments.
The Direct torque control can be applicable to power electronic converter-fed electrical
machines. Direct torque control takes a different look at the machine and the associated
power electronic converter. First, it is recognized that, regardless of how the inverter is
controlled, it is by default a voltage source rather than a current source. Next, it distributes
3
with one of the important characteristics of the vector control, indirect flux, and torque
control by means of two stator current factors [8].
In PID controller the proportional, integral and derivative parameter expressed as 𝐾𝑝, 𝐾𝑖
and 𝐾𝑑. All these parameters are the effect of closed loop control system. It effects the rise
time, settling time, overshoot and steady state error. Proportional, integral plus Derivative
(PID) controller is usually preferable, but due to fixed proportional gain and integral and
derivative time constant the performance of PID controller is affected by parameter
variation, load disturbance and speed variations. The low transient response of PID
controller and high response time is overcome by fuzzy controller [9]. In PID controller the
proportional gain is used to decrease rise time and integral and derivative gain is used to
maintain the error as small as possible.
For widespread industrial applications, such as high-performance motor drives, accurate
motor speed control is required in which regardless of sudden load changes and parameter
variations. Hence, the control system must be design very carefully to attain the optimum
speed operation under the environmental variations, load variations and structural
perturbations. Alternative control strategies have been studied extensively in attempts to
provide accurate control capability. Among many kinds of control schemes, fuzzy logic
controller (FLC) is one of the good solution for plants having difficulties in deriving
mathematical models or having performance limitations with conventional linear control
schemes the FL became a pleasing approach to high performance controllers for nonlinear
systems and has been practical to electrical drives [10].
Theoretically, FL is based on human reasoning, providing algorithms which can convert a
set of linguistic rules based on expert knowledge into an automatic control strategy. There
is no need of mathematical models to deal with a problem, but skill is needed to create the
rules in a particular FL controller [10]. This collaboration is practical as most of the industrial
system that are using conventional PID controller can insert a FLC to their control system
for optimization purposes without changing much of the system topology and scrapping the
conventional controller.
In the vector-controlled motor (PMSM) drive, the outer speed loop provides the PMSM
reference value of the current for the inner current loop and any disturbance in the speed
controller output would cause erroneous currents, thus degrading the system performance.
Hence, proper operation of the speed controller is of great importance for the appropriate
4
drive performance. The use of proportional plus integral plus derivative (PID) controller
suffers from performance degradation under system disturbances due to the fixed
proportional gain and integral and derivative time constant. This problem can be overcome
with fuzzy logic controller since it the error have different values of member ship value [11].
1.2. Statement of Problem
All vehicles rely on the combustion of hydrocarbon fuels to derive the energy necessary for
their propulsion. Combustion is a reaction between the fuel and the air that releases heat and
combustion products. The heat is converted to mechanical power by an engine and the
combustion products are released into the atmosphere. The combustion of fuel in combustion
engines is never ideal. Besides carbon dioxide and water, the combustion products contain a
certain amount of nitrogen oxides (NOx), carbon monoxides (CO), and unburned
hydrocarbons (HC), in addition to this fossil fuels release Sulfur dioxide (SO2) emissions
contribute to acid rain, carbon dioxide which adds to the greenhouse effect and increases
global warming all of which are toxic to human health.
Fossil fuels are non-renewable energy resources and their supply is limited. Eventually they
will run out. Now a days due to draw back fossil fuel-based vehicle Electric vehicle are
predicted to be the next widely used in transportation and technology to minimize energy
conflict and air pollution. Three phase PMSM are widely used in this electric vehicle and
also in industrial and commercial application because it has highly efficient at low speed
which helps the car used to stop easily at low speeds which improves battery utilization
which is main problem of EV and driving range. In addition to this it has also high torque/
volume ratio, smaller size and lighter weight which helps to have better geometrical
integration to reduce total weight of vehicles in addition to this no torque ripple during the
commutation, less core loss, higher maximum achievable speed, low noisy. For vast
application of PMSM for electric vehicle we need to design an effective drive system. The
existing driving system requires mathematical modelling which make it difficult and tidies
as well as they have not efficient during transient conditions. The main advantage of fuzzy
logic control method as compared to conventional control techniques resides in fact that no
mathematical modelling is required for controller design and easily designed as well as no
stability problem. The performance of the FLC is superior only under transient conditions
while the performance of the PID controller is superior under the steady-state condition. The
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merits of FLC and PID controller can be obtained with a hybrid fuzzy-PID controller. This
study is intended to answer the following basic questions:
How to analyse the propulsion power and other specifications of a motor for EV
propulsion?
How to design efficient and simple control system?
How to model PMSM motor drive for EV propulsion?
How to model PMSM motor drive by using MATLAB/code?
1.3. Objective
1.3.1. General Objective
The general objective of this thesis is modelling and analysing efficient FUZZY - PID speed
control (which is artificial intelligent technique, in conjunction with convectional field-
oriented control) method for three phase PMSM drive for four-wheel Qute Bajaj electric
vehicle application. It is expected that this control scheme can track the reference speed well
under parameter uncertainties and load torque disturbance.
1.3.2. Specific Objectives
Toward achieving the general objective mentioned, the following five specific objectives
will be accomplished in this thesis:
Review of performance of deferent types of motor used for Electric vehicle.
To analyse vehicle dynamics and its mathematical model.
To model three phase PMSM for electric vehicle application.
To model a Fuzzy Logic-PID speed control of the PMSM drive system.
Design three phase inverter for PMSM.
To simulate the modelled system using MATLAB software.
1.4. Significance of Study
Now a day’s energy source is shifting from non-renewable energy source to renewable
energy source. At this time in the world especially in developing country like Ethiopia most
energy source is non-renewable but this energy source is limited. Therefore, this energy
shortage is the main problem in transportation industry. To minimize this problem, we need
renewable energy source in transportation area. Since the electric vehicle is used the DC
6
source this thesis is important to support the trend started by centre of transportation vehicle
engineering in ASTU. In addition to forming clean environment this thesis has contribution
in driving system to have better performance during transient and steady state conditions.
High efficiency (That is no current in the rotor means no copper loss) and reliability.
They have high torque to inertia (lower weight). That is better dynamic performance
than conventional one.
Heat loss is significant science, no heat generated in rotor side.
Low torque ripple generated in a motor which improves performance of vehicle.
1.5 . Motivation
As the future of Transportation tending to be Electrical Vehicles & Electric Train it is very
interesting to do research around this area. The one who is being a professional EV drive
system expert is adeptly beneficial because huge market is coming. The battery technology
is getting better from time to time which gives hope for the easy use and future prospect of
EV. PMSM motor is getting popularity rapidly since it used in a broad power range from
hundreds KWs to MWs. PMSM is increasingly used in Transportation, Public life,
Information and office equipment, Défense forces, Medical and health care equipment,
Aerospace. This is due to its higher efficiency, no torque ripple when motor is commutated,
higher torque, more reliable and less noisy, than other asynchronous motors. In addition to
this it has high performance in both high and low speed of operation and have large
operational life. The ratio of torque delivered to the size of PMSM motor is higher, making
it very interesting in the application where space and weight are critical factors like electric
vehicle application.
1.6. Scope
The scopes of the project are limited as follows:
Mathematical model a Permanent Magnet Synchronous motor (PMSM)
To develop fuzzy- PID controller based on field-oriented control of vector control in
order to control speed of PMSM.
To test the performance of PID, Fuzzy logic and Fuzzy Logic based PID controller
and comparing those controllers by using simulation result. The design analysis of
speed control of a PMSM realized in MATLAB/Simulink software.
7
The study does not include about battery source design and other part of EV.
1.7. Limitation
The comparison of the motor for electric vehicle propulsion is taken from literature because
of time constraint and difficult to get PMSM motor, SR motor and BLDC motor around. The
content was to implement the speed control and torque control of PMSM motor using fuzzy-
PID controller. However, due the unavailability of rated PMSM motor hardware
implementation of the research work could not be conducted.
1.8. Thesis Outline
This thesis is organized into five chapters.
Chapter 1: The first chapter presents introduction of PMSM motor drive, statement of
problem, objective of study, motivation, scope and limitation of the research.
Chapter 2: The second chapter includes literature reviews on background of PMSM motor
drive and different control mechanism.
Chapter 3: This chapter includes the analysis of data’s PMSM motor drive modelling and
proposed system development are covered.
Chapter 4: This chapter discusses on simulation of the drive system on MATLAB/Simulink
including simulation result for proposed system.
Chapter 5: finally, in this chapter draws the conclusions from the work done in this thesis
and recommends further possible research direction in the future.
8
CHAPTER TWO
2. LITERATURE REVIEW
In this chapter the background and varieties of modulation techniques, advantage of PMSM
motor is compared with the other electric motor. In addition to this PMSM today world wide
application, the existing controlling mechanism and other related application of PMSM
motor are also reviewed and discussed.
2.1. Introduction
With the advancement in solid state power electronics devices various inverter control
techniques employing PWM are becoming increasingly popular in AC motor drive
application. This PWM-based drive is used to control frequency and magnitude of voltage
applied to motor. Varies PWM strategy, control schemes and realization techniques have
been developed in the past three decades. PWM strategy plays an important role in
minimization of harmonic and switching losses in converters, especially where three-phase
application is required [11] [12].
The first modulation techniques where developed at mid- 1960 by Kirnnich Heinrick, and
Bowes. The research in PWM schemes has intensified in last two decades. The main aim of
any modulation techniques is to obtain a variable output with a maximum fundamental
component and minimum harmonics [12].
The carrier- based PWM methods were developed first and widely used in most applications.
One of the earliest modulation signals for carrier based PWM is sinusoidal PWM. The
SPWM techniques is based on the cooperation of carrier signal and pure sinusoidal
modulation signal. It was introduced by Schonung and Stemmler in 1964. Utilization of DC
voltage for traditional PWM is only 78 % of DC input voltage. A better filtered sinusoidal
output waveform can be obtained by using a high switching frequency and by varying the
amplitude and frequency of a reference or modulating voltage. In SPWM technique it
maintains the pulses in different widths instead of maintaining in equal widths as in multi
pulse width modulation where the distortion factor and lowest order harmonics are
significantly reduced. The frequency of the modulating wave decides the frequency of the
output voltage. The peak amplitude of modulating wave decides the modulation index and
9
controls the RMS value of output voltage. By changing the modulation index, the RMS value
of the output voltage can be varied [13] [14].
Improving the utilization rate of the input voltage has been research focus on power
electronics. This underutilization of the DC input voltage led to development of THIPWM.
In 1975, Buja developed improved SPWM techniques, which added third- order harmonics
content in sinusoidal reference signal. In three phase systems the Third harmonic injection
PWM is preferred because third harmonic component will not be present in three phase
systems. In utilization of DC source, the THIPWM is better since this method increase
utilization rate 15.5 % of DC input voltage more compared with SPWM. The modulation
range in THIPWM can be extended by injecting the tripled harmonics [13] [14] [15].
Another method to increase the output voltage about that of SPWM technique is the
SVPWM technique which introduced in the mid-1980 and was greatly advanced by Van Der
Broeck in 1988. With the development of microprocessor, SVPWM has become one of the
most important PWM methods for three phase inverters [16]. The SVPWM method is
frequently used in vector-controlled applications. SVPWM refers to a special switching
sequence of the upper power switches of a three-phase power inverter. It has been shown to
generate less harmonic distortion in the output voltages and/or currents applied to the phases
of a power system and to provide more efficient use of supply voltage compared with other
modulation technique [17].
This method is used for adjustable speed drives. This technique can increase the fundamental
up to 27.3% when compared with SPWM. SVPWM uses the rotating synchronous reference
frame [18]. The SVPWM refers to a special switching sequence of the upper three switches
of a three-phase inverter. To implement the space vector PWM the voltages in the abc
reference frame to be transformed in to the stationary dq reference frame which consists of
horizontal and vertical axis. The main objective of the SVPWM is to approximate the
reference voltage vector by using the eight switching patterns. In SVPWM by using sectors
it can identify the location of reference vector and the switches can be operated as per sectors
identified [14].
The SVPWM technique utilize the DC bus voltage more efficiently and generate less
harmonic distortion compared with SPWM. The maximum peak fundamental magnitude of
SVPWM technique is about 91 % of inverter capacity [19].
10
2.2. The drive train of Electric Vehicles
The electric Vehicle drive train available in the world market are given in Table 2-1. From
this table PMSM, IM and BLDC motor are most popular from manufacturer point of view.
In order to select an appropriate motor which can mostly fulfil the EV motor technology
requirement, an overall comparison of electric motor is needed based on EV requirement.
The most important requirement of electric vehicle on electric motor drives is:
High instant power and high-power density.
High torque at low speeds for starting and climbing, as well as high power at high
speed for cruising.
Very wide speed range including constant-torque and constant-power regions.
Fast torque response.
High efficiency over wide speed and torque ranges.
High efficiency for regenerative braking.
High reliability and robustness for various vehicle-operating conditions.
Downsizing, weight reduction, and lower moment of inertia.
Fault tolerance
Reasonable cost
Suppression of electromagnetic interface (EMI) of motor controllers
1. two
11
Table 2-1: Electric vehicle available in world. [20] [21]
No EV name Propulsion
system
Electric Vehicle picture Country
1
PSA Peugeot-Citroën /
Berlingo
DM
France
2
Holden /ECOmmodore
SRM
Australia
3
Nissan/Tino
PMSM
Japan
4
Honda/Insight
PMSM
Japan
5
Toyota/Prius
PMSM
Japan
6
Renault/Kangoo
IM
France
7
Chevrolet/Silverado
IM
USA
8
DaimlerChrysler/Durango
IM
Germany /
USA
12
9
BMW/X5
IM
Germany
10
Nissan Leaf
BLDC
Japan
11
Mitsubishi i- MiEV
BLDC
Japan
12
BYD E6
BLDC
China
The rapid development in the field of Power electronics and control techniques has created
a space for those various types of electric motors to be used in Electric Vehicles as shown
in above Table 2-1. In addition, electrical motor used in EV should have important
characteristics like simple to design, high specific power, low maintenance cost and good /
essay to control. etc. In EVs, only traction motor delivers torque to the driven wheels. Thus,
the EV motor performance is completely determined by the torque speed or power speed
characteristic of the traction motor.
An EV, in order to meet its operational requirement, such as the initial acceleration and
ability to move in uphill road with minimum power mentioned above, operation entirely in
constant power is needed. Operation entirely in constant power is, however, not possible for
any practical vehicle. It can be observed that the EV motor drive is expected to be capable
of offering a high torque for starting and acceleration, and a high power at high speed for
cruising.
13
2.3. Types of electric motor
Nowadays, several types of electric motors are used for electric vehicle propulsion. But all
types of motor are not equally used duo to drawback in some of its characteristic. The
classification of electrical motor is summarized in the following Figure 2-1.
Figure 2-1: Motor Classification.
Out of the different motor listed above PMSM, IM, SRM, BLDCM and DC motor is used
widely in different electric vehicle company.
Universal Motor
Reluctance Motor
Hysteresis Motor Series
Electrical motors
AC motor DC motor
Commutator Homopolar Synchronous Asynchronous
Induction motor
PMSM
BLDCM
Wound Field Permanent Magnet
Compound
Shunt
14
2.3.1. DC Motor
DC motors have been prominent in electric propulsion because their torque–speed
characteristics suit the traction requirement well, decoupling of flux and torque, and their
speed controls are simple. However, dc motor drives have a bulky construction, low
efficiency, low reliability, and higher need of maintenance, mainly due to the presence of
the mechanical commutator (brush), even if interesting progress has been made with slippery
contacts. As current flows through the commutator through the armature windings, the
electromagnetic field repels the nearby magnets with the same polarity, and causes the
winging to turn to the attracting magnets of opposite polarity. As the armature turns, the
commutator reverses the current in the armature coil to repel the nearby magnets, thus
causing the motor to continuously turn. The fact that this motor can be driven by DC voltages
and currents makes it very attractive for low cost applications [22] .
In DC brushed motor, brushes along with commutators provide a nexus between external
supply circuit and armature of the motor. Brushes can be made up of carbon, copper, carbon
graphite, metal graphite and are mostly rectangular in shape. Wearing of commutators due
to continuous cutting with brushes is one of the main drawbacks of DC brushed motors.
Also, friction between brushes and commutators, limits the maximum motor speed [23].
(a) (b)
Figure 2-2: (a) DC motor (b) Torque versus speed characteristics of DC motor.
Moreover, the development of rugged solid-state power semiconductors made it increasingly
practical to introduce AC induction and synchronous motor drives that are mature to replace
dc motor drive in traction applications [20] [23].
15
2.3.2. Induction Motor
Induction motors are of simple construction, reliability, ruggedness, low maintenance, low
cost, and ability to operate in hostile environments. The absence of brush friction permits
the motors to raise the limit for maximum speed, and the higher rating of speed enable these
motors to develop high output. Speed variations of induction motors are achieved by
changing the frequency of voltage. FOC of induction motor can decouple its torque control
from field control. This allows the motor to behave in the same manner as a separately
excited dc motor. This motor, however, does not suffer from the same speed limitations as
in the dc motor. Extended speed range operation beyond base speed is accomplished by flux
weakening, once the motor has reached its rated power capability [20] [23] [24].
Existence of break-down torque in the constant power region, reduction of efficiency and
increment of losses at high speeds, intrinsically lower efficiency in comparison to permanent
magnet motors due to the presence of rotor winding and finally low power factor are among
the shortcomings of induction motors. Many efforts have been made by researchers to solve
these problems, such as: usage of dual inverters to extend the constant power region,
incorporating doubly- fed induction motors to have excellent performance at low speeds and
reducing rotor winding losses at the design stage [21] .
Figure 2-3: Torque and power versus characteristic of Induction motor.
16
2.3.3. BLDC Motor
A Brushless DC motor is an upgraded version of a brushed DC Motor. The development
of semiconductor electronics in the 1970s allowed the commutator and brushes to be
eliminated in DC motors and the absence of brushes gives BLDC motors to have the ability
to rotate at high-speed and increased efficiency. In brushless DC motors, an electronic servo
system replaces the mechanical commutator contacts. The elimination of the sliding contact
allows brushless motors to have less friction and longer life; their working life is only limited
by the lifetime of their bearings. A typical brushless motor has permanent magnets which
rotate around a fixed armature, eliminating problems associated with connecting current to
the moving armature. An electronic controller replaces the brush/commutator assembly of
the brushed DC motor, which continually switches the phase to the windings to keep the
motor turning [20] [25].
Brushless motors offer several advantages over brushed DC motors, including high torque
to weight ratio, more torque per watt (increased efficiency), increased reliability, reduced
noise, longer lifetime (no brush and commutator erosion), elimination of ionizing sparks
from the commutator, and overall reduction of electromagnetic interference (EMI). BLDC
motor is defined as rotating self-synchronous machine with a permanent magnet rotor and
known rotor shaft positions for electronic commutation. The advantage of this motor as
compared to the other motors is that this motor provides higher torque at the peak values of
current and voltage [26] [27].
(a) (b)
Figure 2-4: (a) BLDC motor and (b)Torque speed envelope of a BLDC Motor.
17
2.3.4. Switched Reluctance (SR) Motor
Switched reluctance motor produces torque by variable reluctance method. When stator coils
are energized, variable reluctance is set up in the air gap between the stator and the rotor.
Rotor tends to move to a position of least reluctance thus causing torque. The advantages of
these motors are that they have simple and rigid construction, high fault tolerance and
excellent torque-speed characteristics. It can operate under a wide constant power region.
This type of motor is not seen commonly in electric vehicles as they have high noise, high
torque ripple needs special convertor topology and have an electromagnetic interference [20]
[27] [28].
The torque-speed characteristics of SRM drives match very well with the EV load
characteristics. The SRM drive has high speed operation capability with a wide constant
power region. The motor has high starting torque and high torque-inertia ratio. The rotor
structure is extremely simple without any windings, magnets, commutators or brushes [28].
(a) (b)
Figure 2-5: (a) SRM motor and (b)Classical torque-speed characteristics of SRM motor.
2.3.5. PMSM
A permanent magnet motor is a type of brushless electric motor that uses permanent
magnets rather than winding in the field. This motor is also similar to BLDC motor which
has permanent magnets on the rotor. Similar to BLDC motors these motors also have traction
characteristics like high power density and high efficiency. The difference is that PMSM has
18
sinusoidal back EMF whereas BLDC has trapezoidal back EMF. Permanent Magnet
Synchronous motors are available for higher power ratings. PMSM is the best choice for
high performance applications like cars, buses. Despite the high cost, PMSM is providing
stiff competition to induction motors due to increased efficiency than the latter. PMSM is
also costlier than BLDC motors. Most of the automotive manufacturers use PMSM motors
for their hybrid and pure electric vehicles [20] [27].
The basic construction of PMSM is same as that of synchronous motor. The only difference
lies with the rotor. Unlike synchronous motor, there is no filed winding on the rotor of
PMSM. Field poles are created by using permanent magnet. These Permanent magnets are
made up of high permeability and high coercivity materials like Samarium-Cobalt and
Neodium-Iron-Boron. Neodium-Iron-Boron is mostly used due to its ease of availability and
cost effectiveness. Theses permanent magnets are mounted on the rotor core. PMSM
requires AC (Sinusoidal in nature) to achieve the best performance. This type of drive
current also reduces the noise produced by the motor.
In order to increase the speed range and improve the efficiency of PM brushless motor, the
conduction angle of the power converter can be controlled at above the base speed. The
torque-speed characteristic of a PM brushless motor with conduction angle control is given
in Figure 2.6 below. The speed range may be extended three to four times over the base
speed. However, at very high-speed range the efficiency may drop, the motor may suffer
from demagnetization [21] [29] [30].
(a) Typical characteristic (b) With conduction angle control.
Figure 2-6: Torque-speed characteristic of a PMSM drive.
19
2.3.6. Performance of Different Electric Motor for EV Propulsion
Among all Electric motor used for electric propulsion all are not equally used due to its
advantage and disadvantage of electric motors.
Table 2-2: Advantage and disadvantage of different Electric Motor used for EV propulsion.
[20] [31] [32].
Electric Motor Advantage Disadvantage
DC Motor
Maximum torque at low speed
Good controllability
Linear torque
current curve
Low torque ripple
Bulky structure
Low reliability
Requires maintenance
Low overloading
capability
Low heat dissipation
IM
Excellent dynamics with proper
control
High speed operation possible
Low price and simple construction
Durable
Several suppliers available
Complicated control
Always lagging power factor
Low efficiency with lighter loads
SRM
Have simple and rigid construction
High fault tolerance
Excellent torque-speed
Wide constant power region
High starting torque
High torque-inertia ratio
High noise
High torque ripple
Need special convertor topology
Have an electromagnetic
interference
Complex control mechanism
20
BLDC
High power density and torque-to-
inertia ratio
Good heat dissipation good over
loading capability
Expensive
Torque ripple
Danger of demagnetization of the
magnets
Poor field weakening
PMSM
Smooth torque possible
High efficiency
High torque/volume
High pull-out torque possible
Good heat dissipation
Good overloading capability
Good field weakening
Expensive
Danger of demagnetization of the
magnets
The core element of the EV, apart from Electric Vehicle Batteries, which replaces the
Internal Combustion engines is an Electric motor. The rapid development in the field
of Power electronics and control techniques has created a space for various types of electric
motors to be used in Electric Vehicles. The electric motors used for automotive applications
should have characteristics like high starting torque, high power density, good efficiency,
etc including they need to operate in a harsh environment with the humidity of up to 85%
and the ambient temperature between -40 and 135 degree Celsius. The traction system
commonly used in EV are evaluated based on the factors that listed in Table 2-3, a score out
of 5 is given for each comparation point to each motor. It is concluded that based on this
compression factor IM, BLDC and PMSM motor are more suitable.
Due to the drawback of convectional DC motor BLDC Motors have replace the Brushed DC
Motors, PMSM motors have come across as a better alternative to AC Induction motor. The
following Table 2-3 is describing the comparison between different motors used in EV
applications by using different parameters as a measurement.
21
Table 2-3: Electric propulsion systems evaluation. [20] [33] [34] [35]
Propulsion system
Characteristic
DC IM BLDC PMSM SRM
Power density 2.5 3.5 5 5 3.5
Efficiency 2.5 3.5 5 5 3.5
Controllability 5 5 4 4 3
Reliability 3 5
4 4 5
Technological
maturity
5 5 4 4 3
Cost 4 5 3 3 4
Weight 2 3.5 4.5 4.5 5
Power to weight ratio 2.5 3.2 4.5 4.5 3.2
Speed range 4 4 4.5 5 4.5
Maintenance 3 4 4.5 4.5 4.5
Torque ripple 4 4 3.5 5 3
Total 37.5 45.7 46.5 48.5 42.2
As we observed from above Table 2-3 PMSM and BLDC motors have high power density
due to presence of high-power density permanent magnet. Moreover, they have highest
efficiency because of the absence rotor losses. DC and IM have best controllability and their
flux and torque control can be easily decoupled. The IM has the best reliability due to its
robust and rigid construction.
22
2.3.7. Comparison of PMSM with IM and BLDC
Table 2-4: Comparison of IM and PMSM. [36] [37]
PMSM Advantages in EV
If PMSM is compared to
IM, it has high efficiency
at low speeds.
Advantages for city cars where frequent start-
stops occur at low speeds. This also improves
battery utilization and driving range.
High torque/ volume ratio,
smaller sizes and lighter weight.
It has better geometrical integration into engine
cabinet and reduces total weight of vehicle.
Current rating is lower than IM. Lower current rating for inverter and improved
battery utilization.
Lower rotor inertia Better dynamic characteristic
IM Advantages in EV
For the magnetizing current is
supplied by stator, IM has
flexible efficiency control.
If state of charge is near maximum limit,
efficiency of IM can be reduced by motor drive
system in order to limit the return of
regenerative energy. Efficiency optimization at
light load conditions is possible by control of
flux reference.
IM field weakening is
controlled by reduction of
magnetizing current.
Efficiency of IM is competitive against IPMSM
at high speed region on torque-speed curve.
Cost competitive both in
terms of material and
production technology.
Economical Unlike PMSM, material cost is
independent of magnet price changes.
As we sea from Table 2-4 the high efficiency of PMSM at low speeds improves battery
utilization and driving range. PMSM has better geometrical integration into engine cabinet
and reduces total weight of vehicle.
23
There are a number of similarities in the overall drive scheme of the PMSM and the BLDCM
presented [38]. Table 2-5 gives the brief comparison of Brushless DC Motor i.e. BLDC
drives and PMS Motor.
Table 2-5: Comparison of BLDC and PMSM motors.[38]
BLDCM PMSM
Trapezoidal back emf Sinusoidal back emf
Stator flux position commutation
each 60º
Continuous stator flux position
variation
Only two phases ON at the same
time
Possible to have three phases ON at
the same time
Torque ripple at the commutation No torque ripple at the commutation
Low order current harmonics in the
audible range
Fewer harmonics due to sinusoidal
excitation
High core losses due to harmonic
content Less core loss
Better for lower speed Higher maximum achievable speed
Noisy Low noisy
Doesn’t work with distributed
winding
Work with low-cost distributed
winding
Less efficient and lower torque Higher efficiency and higher torque
Rectangular current waveforms Sinusoidal or quasi- sinusoidal
current waveforms
Used in Toyota Prius (2005) Used in Toyota Prius, Nissan Leaf,
Soul EV
24
PM motors are classified on the basis of the flux density distribution and the shape of current
excitation. They are PMSM and PM brushless motors (BLDC). The PMSM has a sinusoidal
shaped back EMF (it is an induced voltage in the stator by the motion of the rotor).
Generally, the PMSM is designed to develop sinusoidal back EMF waveforms and has a:
Sinusoidal distribution of magnet flux in the air gap
Sinusoidal current waveforms, and
Sinusoidal distribution of stator conductors.
BLDC has a trapezoidal-shaped back EMF and is designed to develop trapezoidal back EMF
waveforms. It has:
Rectangular distribution of magnet flux in the air gap
Rectangular current waveform
Concentrated stator windings
Advantages of PMSM over DC motor, Induction motor and BLDC motor [39] [40]
Advantages of PMSM over DC motor Advantages of PMSM over IM
• Less audible noise • Higher efficiency
• Longer life • Higher power factor
• Sparkless (no fire hazard)
• Higher speed
• Higher power density and smaller
size
• Higher power density for medium
power applications, resulting in
smaller size
• Better heat transfer • Better heat transfer
Advantages of PMSM over BLDC motor
• Higher efficiency than Brushless DC Motors
• No torque ripple when motor is commutated
• Higher torque and better performance
• More reliable and less noisy, than other asynchronous motors
• High performance in both high and low speed of operation
• Low rotor inertia makes it easy to control
• Efficient dissipation of heat
25
2.4. Electric Vehicle Batteries
Batteries have been the major energy source for EV. Lithium-ion batteries become the most
popular battery for plug-in and full-battery electric vehicles (PHEVs and BEVs). While other
types of batteries, including lead-acid and nickel-metal hydride (in the first generation of the
Toyota Prius hybrid) will continue to retain considerable market share in the short term,
lithium-ion batteries are expected to dominate the world market.
2.4.1 Advantages of lithium-ion batteries for vehicle
Lithium-ion batteries are the most suitable existing technology for electric vehicles because
they can output high energy and power per unit of battery mass, allowing them to be lighter
and smaller than other rechargeable batteries. Compared to lead acid and nickel metal
hydride batteries lithium-ion batteries have advantages includes high-energy efficiency, no
memory effects, and a relatively long cycle life [41] [42].
Figure2-7: Battery in terms of Power density and Energy density.
2.5. PMSM drives
The synchronous motors require AC supply for the stator windings and DC supply for the
rotor windings. The motor speed is determined by the AC supply frequency and the number
Power density (W/kg)
Maximum power per
unit of battery mass
Energy density (Wh/kg)
Maximum stored energy per unit of battery mass
26
of poles of the synchronous motor, the rotor rotates at the speed of the stator revolving field
at synchronous speed, which is constant. The variations in mechanical load within the
machine’s rating will not affect the motor’s synchronous speed. One of the types of
synchronous motor is the PMSM. The PMSM consists of conventional three phase windings
in the stator and permanent magnets in the rotor [43].
The purpose of the field windings in the conventional synchronous machine is done by
permanent magnets in PMSM. The conventional synchronous machine requires AC and DC
supply, whereas the PMSM requires only AC supply for its operation. One of the greatest
advantages of PMSM over its counterpart is the removal of dc supply for field excitation.
The PMSMs involve adjustment of the stator supply frequency, proportionally as the rotor
speed is varied, so that the stator field always moves at the same speed as the rotor. The
rotating magnetic fields of the stator (armature) and the rotor (excitation) system are then
always in synchronous motion producing a steady torque at all operating speeds. This is
analogous to the D.C motor in which the armature and excitation fields are synchronous but
stationary for all operating speeds. PMSM requires the very accurate measurement of rotor
speed and position and the very precise adjustment of the stator frequency. Rotor position
sensing is done by an encoder, resolver… etc which forms part of a control loop of an
adjustable frequency inverter feeding the stator winding.
2.5.1. Permanent Magnet Materials
Materials to retain magnetism were introduced in electrical machine research in the 1950s.
There has been a rapid progress in these kinds of materials since then. The properties of the
permanent magnet material affect directly the performance of the motor and proper
knowledge is required for the selection of the materials and for understanding PM motors.
The materials such as alnico-5, ferrites (ceramics), samarium-cobalt, and neodymium boron
iron are available as PMs for use in machines. The particular choice of magnets and other
design factors is important, but does not directly influence the basic principles of power
converter control [6].
2.5.2. Classification of Permanent Magnet Motors
The PMSM are classified based on the direction of field flux are as follows,
a) Radial field
27
b) Axial field
In radial field, the flux direction is along the radius of the machine. The radial field PM
motors are the most commonly used. In axial field, the flux direction is parallel to the rotor
shaft. The axial field permanent magnet motors are presently used in a variety of numerous
applications because of their higher power density and quick acceleration.
In PMSMs, the magnets can be placed in different ways on the rotor. Depending on the
placement they are called either as Surface Permanent Magnet Motor (SPM) or Interior
Permanent Magnet (IPM) Synchronous Motor.
Surface mounted PM motors have a surface mounted permanent magnet rotor. Each of the
PM is mounted on the surface of the outer periphery of rotor laminations. This arrangement
provides the highest air gap flux density as it directly faces the air gap without the
interruption of any other medium such as part of rotor laminations. Drawbacks of such an
arrangement are lower structural integrity and mechanical robustness as they are not tightly
fitted into the rotor laminations to their entire thickness. This configuration is used for low
speed applications because of the limitation that the magnets will fly apart during high-speed
operations. It has practically equal inductances in both quadrature and direct axes. For a
surface permanent magnet motor, q axis inductance 𝐿𝑞 equal to the d axis inductance 𝐿𝑑.
Interior mounted PM Motors have interior mounted permanent magnet rotor. Each
permanent magnet is mounted inside the rotor. The interior PM rotor construction is
mechanically robust and therefore suited for high-speed applications. The manufacturing of
this arrangement is more complex than the surface mount. By designing a rotor magnetic
circuit such that the inductance varies as a function of rotor angle, the reluctance torque can
be produced in addition to the mutual reaction torque of synchronous motors. These motors
are considered to have saliency with q axis inductance 𝐿𝑞 greater than the d axis inductance
𝐿𝑑.
In this thesis IPM radial flux machine with classical winding and lamination has been chosen
due to the following reasons:
SPMSM uses magnetic torque and IPMSM uses both magnetic torque and reluctance
torque, so it can obtain to produce same power density as a SPMSM even with fewer
magnets used.
The topology of a axial flux machine with classical winding and lamination has been
chosen because of the well-known and established technology.
28
Based on the PM volume and output density of the motor, an IPMSM can obtain the
same output with relatively few magnets.
The surface PMSM used for applications which require low speed operations and
interior PMSM are used for applications which require high speed.
(a) (b)
(c) (d)
Figure2-8: Rotor configurations studied: (a) Surface PM (SPM) synchronous machine. (b)
Surface inset PM (SIPM) synchronous machine. (c) Interior PM (IPM) synchronous
machine. (d) Interior PM synchronous machine with circumferential orientation.
2.6. Closely related works on PMSM motor control
Researcher reported several papers on PMSM motor speed control by using several methods
and algorithms.
29
Authors in [37] proposes “Design and implementation of a loss optimization control for
electric vehicle in-wheel permanent-magnet synchronous motor direct drive system” As a
main driving force of EV, the losses of in-wheel PMSM direct drive system can seriously
affect the energy consumption of EVs. These authors propose a loss optimization control
strategy for in-wheel PMSM direct drive system of EVs which optimizes the losses of both
the PMSM and the inverter. Moreover, there are strongly nonlinear characteristics for the
power devices, this paper creates a nonlinear loss model for three-phase half-bridge inverters
to obtain accurate inverter losses under space vector pulse width modulation (SVPWM).
Authors in [44] proposes “Field Oriented Control of PMSM Using Improved Space Vector
Modulation Technique” these authors, design external device that regulates and controls the
performance of Permanent Magnet Synchronous Motor. With the fluctuations accessed in
the motor, rotor magnets structured from ferrite core experience turbulent flow and
hysteresis loss. This study concentrates on producing the pulse orientation from FOC to
PMSM is that subjected to monitoring and control the PMSM, and made it feasible by PI
controllers. It is popularized that control properties of PID controller is far superior in
consideration with PI controller but it has not accurate due to the non-linearities of the
system.
Authors in [45] proposes “Vector Control of Permanent Magnet Synchronous Motor for Fan
of New Energy Vehicle” these authors, design vector control of PMSM based on the analysis
of the mathematical model of permanent magnet synchronous motor and the common
control strategy, and the overall system architecture of the control system is analysed based
on the specific control algorithm. The control system uses special motor control chip
MC9S12ZVMC128 as the system controller and uses vector control (FOC) as the control
algorithm. These authors describe architecture of controller software detail, using the state
machine model to control the motor running in different stages, including start-up stage,
motor open detection and treatment of closed loop phase and fault ring stage. The
experimental results show that, permanent magnet synchronous motor can operate
efficiently and stably but its cost is very high which makes it not used widely.
Authors in [46] proposes “Simulation of PMSM Vector Control System with Fuzzy
Self-Adjusting PID Controller Using MATLAB” these authors divides PMSM control
system into several independent functional modules such as PMSM body module, inverter
module and coordinate transformation module and SVPWM production module. According
to this author the PMSM system is a nonlinear time-varying complex system. The results of
30
traditional PI control are not satisfactory to the higher degree of accuracy condition. The
fuzzy control system has the prominent advantage in complex, time lag, time varying and
non-linear system control and the mathematical model of the controlled object is not
required. The fuzzy-PID controller has the advantages of both PID control and fuzzy control,
so it can get better control performance.
Authors in [47] proposes “Real-Time Robust Controlled Driving System with Permanent-
Magnet Synchronous Motor” these authors propose robust vector control of a permanent
magnet synchronous motor (PM-SM) using a fix point DSP based computing architecture
with speed control systems are analysed for different operating conditions.
Authors in [48] proposes “Adaptive Fuzzy Logic compensator for PMSM Torque control
system” these authors indicate PMSM is a fundamental section of the automatic screw
machine. It presents a torque control system with an adaptive fuzzy logic compensator for
torque control and torque evaluation at the same time. The process of the study can add to
the efficiency of torque control system and reduce the calibration time of the automatic screw
machines.
Authors in [49] proposes “Speed Control of PMSM Drive Using Adaptive Fuzzy Logic
Controller” these authors design speed controller with a parallel combination of two
controllers- fuzzy PD controller and a fuzzy PI controller forms the adaptive fuzzy PID
controller and has the combined advantages of both. Switching action take place between
the two controllers based on the error in the speed. Even this system is having the advantage
of both fuzzy PD and a fuzzy PI controller it is not applicable due to its complexity and cost.
Generally, from literature the PID controller is widely adopted to control the PMSM systems
in industrial applications owing to its simplicity, clear functionality, and effectiveness.
However, a big problem of the PID controller is its sensitivity to the system uncertainties.
Thus, the control performance of the conventional PID method can be seriously degraded
under parameter variations. Some groups of researchers try to overcome this disadvantage
by proposing the hybrid PID controllers or new tuning rules [50]. In, a hybrid control
system, which contains a fuzzy controller in the transient and a PID controller in the steady
state, is proposed.
In [51], the fuzzy rules are employed for tuning the PI gains. Unfortunately, these methods
use offline-tuning rules, which lack the adaptability to deal with the time-varying system
uncertainties. An adaptive PI controller with an online-tuning rule is presented in [8].
31
Although this controller does not require the exact knowledge of any motor parameter, but
the authors do not show the results under parameter uncertainties.
Table 2-6: Control method of PMSM done by different researcher.
Per
form
ance
Res
ponse
tim
e an
d
sta
bil
ity
T
orq
ue
and S
pee
d
Spee
d c
ontr
ol
in m
axim
um
torq
ue
per
am
per
e
Eff
ecti
ve
redu
ctio
ns
of
har
monic
loss
es, to
rque
ripple
s, a
nd E
M n
ois
es
Spee
d c
ontr
ol
Dynam
ic p
erfo
rman
ce o
f
moto
r st
arti
ng
Met
hod/
Tec
hniq
ues
SV
PW
M T
echniq
ues
by u
sing
Fuzz
y-P
I C
ontr
ol
F
ault
tole
rant
oper
atio
n o
f m
oto
r
dri
ves
Opti
mal
fie
ld-o
rien
ted c
ontr
ol
thro
ugh l
inea
r quad
rati
c re
gula
tor
Anal
yti
cal
Model
ling o
f C
urr
ent
H
arm
onic
Com
ponen
ts
C
urr
ent
model
pre
dic
tiv
e
co
ntr
oll
er
A
dap
tive
inte
gra
l bac
kst
eppin
g
c
ontr
oll
er
Conver
ter
3-p
has
e In
ver
ter
PW
M I
nver
ter
SV
PW
M
Tec
hniq
ues
VS
I by S
VP
WM
Tec
hniq
ue
SV
PW
M
Tec
hniq
ues
SV
PW
M
Tec
hniq
ues
Auth
or’
s
T. T
. L
iu [
51
]
C
. J. G
aja
nayak
e
[52]
Ch
rist
ian
Joez
er
Mei
rin
ho [
53]
W. L
ian
g, J. W
an
g
[54]
M. T
an
g,
S. Z
hu
an
g [
55]
W. W
an
g, F
. T
an
[56]
No
.
1.
2.
3.
4.
5.
6.
32
S
pee
d c
ontr
ol
Torq
ue
per
am
per
e an
d
fast
rev
ersa
l
Torq
ue
and S
pee
d
Spee
d o
f P
MS
M
Spee
d, ro
bust
nes
s an
d
anti
-inte
rfer
e ab
ilit
y
Spee
d, st
ator
curr
ent
and
torq
ue
Torq
ue
and s
pee
d
Spee
d, to
rque
and f
lux
ripple
s
Hyst
eres
is C
urr
ent
Contr
oll
er
Sta
tor
curr
ent
contr
oll
ing
Hybri
d f
uzz
y P
I
Tak
agi
Sugen
o F
uzz
y L
ogic
Contr
ol
Vec
tor
Contr
ol
Tec
hnolo
gy w
ith
PI
contr
oll
er
Mag
net
ic f
ield
-ori
ente
d c
ontr
ol
algori
thm
Adap
tive
contr
ol
bas
ed o
n t
he
input-
ou
tput
feed
bac
k
linea
riza
tion
Vec
tor
Contr
ol
Tec
hnolo
gy
wit
h f
uzz
y c
ontr
oll
er
V
SI
inver
ter
SP
WM
inv
erte
r
SP
WM
SV
PW
M i
nver
ter
SV
PW
M i
nver
ter
SV
PW
M i
nver
ter
SV
PW
M i
nv
erte
r
Vec
tor
contr
ol
PW
M
R. P
. N
ath
wan
i [5
7]
Kau
shik
Jash
[58]
An
an
tham
oort
hy N
P
[50]
Ah
mad
Asr
i [5
9]
Tin
gti
ng L
iu [
60]
Li
Yu
[61]
Gaja
nan
Rath
od
[62]
S. S
ak
un
thala
[8]
7.
8.
9.
10.
11.
12.
13.
14.
This thesis focused on analysis and speed control characteristics of PMSM based on space
vector pulse width modulation for controlling speed and torque of PMSM by using fuzzy-
PID controller. This method is proposed to improve the performance of convectional
controller and it adopts electric vehicle for transportation industry to reduce the problem of
limitation in non-renewable energy source and global warming.
33
CHAPTER THREE
3. METHODOLOGY
3.1. Introduction
This chapter include the methodology that have been followed in this thesis work. The
characteristic and property of material and software used are explained. In addition, data
analysis, mathematical modelling of PMSM motor drive, and PMSM motor drive system
setup in MATLAB are presented. The analysis of the identified motor specification and
vehicle dynamics is performed.
3.2. Materials
MATLAB version R2018a software is used throughout this research study. MATLAB is the
general-purpose computing software which consist of a vast range of specialized toolbox.
This toolbox performs symbolic algebraic/ mathematical manipulative operation with a lot
of built in interactivity. It is a high-level mathematical package designed for doing numerical
computations and graphics. MATLAB also has powerful symbolic math ability. MATLAB
is undoubtedly popular among computer and multi-disciplinary scientist, engineers and
particularly with experts in the area of computational mathematics and Engineering [63].
3.3. Methods
The following method is used to study the general and specific objectives of this thesis. First
the closely related works are reviewed. Then the necessary data used throughout this study
is collected from Quet Bajaj manufacturing company in India through their site and Hora
trading company. Then the collected data is analysed for the purpose of understanding and
developing the system modelling. The modelling PMSM motor drive with its speed
controller is developed. Then the system is simulated by using both MATLAB/Simulink/
codes. The result of the simulation is compared for different control algorithms in the case
of inverter driving techniques and speed controller schemes. In general, the method followed
throughout the research study can be summarized as the following flow chart.
34
2. three
Figure 3-1: Flow chart of research methodology.
Write a code and design the Simulink model
Observe the performance and discuss the result
Write the thesis documentation
End
Study about vehicle dynamics and PMSM
Modeling of PMSM
start
Collect journal paper for literature review and data
collection from site
Review collected paper and analyze data
Develop speed control algorithm of PMSM
35
The block diagram of the proposed system is shown Figure 3-2:
Figure 3-2: Block diagram of the proposed control system.
3.4 Electric Vehicle Dynamics
The drive train consist of six components: the electrical motor, power electronics, battery,
motor controller, battery controller, and vehicle interface. In the Figure 3.3 the vehicle
interface provides the interface for the sensors and controllers which communicate with
motor controller and battery controller. The motor controller normally controls the power
supplied to the motor, while the battery controller controls power from battery. The battery
is for energy storage and power electronics manipulate the voltage, current and frequency
provided to suit the motor requirements [64].
Figure 3-3: EV drives.
W
W ref Inverter SVPWM Park
inverse
transformati
PID
PID
FL
PMSM
Clark
transformation
Park
transformation
Battery
θ
Id*
Iq*
Id
Iq
Iabc Iαβ
Vdq Vαβ
Battery
Motor
controller
Battery
controller
Power
electronics
Veh
icle
Inte
rfac
e
Motor
36
In designing the EV various variables are to be considered. The design variable includes:
Electric motor rated speed.
Electric motor power ratting.
Maximum speed of electric motor.
Constant power region beyond the rated speed.
3.4.1. Motive force, Motive Power and Motive Torque of the Vehicle
The force propelling the electric vehicle has to overcome the rolling resistance force (FR),
gradient resistance (FG) and aerodynamics drag force (FA). In this thesis the car of gross
weight 700 kg is considered as per collected data in order to select the required motor power
rating and another specification of electric motor. The total force required for driving a
vehicle is calculated in equation (3.1) [65] [66].
Ftotal = FR + FA + FG (3.1)
The total force is the tractive force that the motor must overcome, in order to drive the vehicle
therefore the selected motor must produce the force greater than total force so that there is
no slipping of the wheels.
Figure 3-4: External force acting on moving EV.
The main force needs to overcome by the EV are discussed as the showing points:
3.4.1.1. Rolling resistance
Rolling Resistance is the opposing force that the vehicle has to overcome due to the rolling
motion between the wheels and the surface of motion of the vehicle. The rolling resistance
α
FA
m*g m*g*cosα
V
37
depends on the co-efficient of rolling friction which varies depending upon the material of
tyres and the roughness of the surface of motion [66].
FR = Crr ∗ M ∗ g ∗ cos𝛼 (3.2)
FR= 700*9.81*0.01*cos (8) = 68 N
Where Crr: Co-efficient of rolling resistance, (M*g): Gross vehicle weight in N, 𝛼:
Inclination angle. The power required to overcome rolling resistance of the 68 N @ 70
𝑘𝑚ℎ𝑟⁄ and 8𝑜 is:
pR = FR ∗ Vc(𝑚𝑠⁄ ) (3.3)
pR = 68 ∗ (70
3600) = 1.3 KW
3.4.1.2. Gradient resistance
Grade resistance is the form of gravitational force. It is the force that tends to pull the vehicle
back when it is climbing an inclined surface. This component either opposes the forward
motion (grade climbing) or helps the forward motion (grade descending). In vehicle
performance analysis, only uphill operation is considered. The angle between the ground and
slope of the path is represented as α, which is shown is Figure 3-4 [66].
FG = M ∗ g ∗ sin𝛼 (3.4)
FG= 700*9.81*sin (8) = 955.7 N
The climbing power is given by pG = FG ∗ Vc(𝑚𝑠⁄ ). Where Vc is the climbing velocity and
the power required to overcome gradient resistance of the 955.7 N @ 25 𝑘𝑚ℎ𝑟⁄ is:
pg = 955.7 ∗ (25
3600) = 6.63 KW
3.4.1.3. Aerodynamic drag force
A vehicle traveling at a particular speed in air encounters a force resisting its motion. This
force is referred to as aerodynamic drag. It mainly results from two components: shape drag
and skin friction.
Shape drag: The forward motion of the vehicle pushes the air in front of it. However, the
air cannot instantaneously move out of the way resulting in high air pressure in addition, the
air behind the vehicle cannot instantaneously fill the space left by the forward motion of the
vehicle. The motion has therefore created two zones of pressure that oppose the motion of
38
a vehicle by pushing it forward (high pressure in front) and pulling it backward (low pressure
in the back).
Skin friction: Air close to the skin of the vehicle moves almost at the speed of the vehicle
while air far from the vehicle remains still. In between, air molecules move at a wide range
of speeds. The difference in speed between two air molecules produces a friction that results
in the aerodynamic drag.
Aerodynamic drag is a function of vehicle speed V, vehicle frontal area Af, shape of the
vehicle, and air density ρ. Then aerodynamic drag force is given by:
FA = 1
2∗ Cd ∗ Af ∗ ρ ∗ (V + Vc)2 (3.5)
FA = 1
2∗ 0.2 ∗ 1.5 ∗ 1.23 ∗ (19.44)2= 68.7N
Where, Cd is the aerodynamic drag coefficient, ρ is the air density in 𝐾𝑔
𝑚3⁄ , V is the air
speed in 𝑚 𝑠⁄ and Vc is vehicle speed in 𝑚 𝑠⁄ [65]. In general, ρ is taken as 1.23 𝐾𝑔
𝑚3⁄ , Cd
lies between 0.2 and 1.5 and taken as 0.2. Af = 0.8*1.43*1.312= 1.5 𝑚2 from vehicle
specification given in Table 3.2. The above equation (3.5) shows that, the aerodynamic force
of the car is directly proportional to the square sum of the speed of the vehicle and speed of
air by substituting the values of constant in equation (3.5), the aerodynamics forces as the
speed of the vehicle varies from 0 to 70 𝐾𝑚ℎ𝑟⁄ (0 to 20 𝑚
𝑠⁄ ) can be plotted as shown
Figure 3-5 by taking the assumption that the speed of the air is zero.
Figure 3-5: Aerodynamic dragging force versus speed of the car in 𝑘𝑚ℎ𝑟⁄ .
Aerodynamic force (N)
39
3.4.1.4. Aerodynamic lift force
Aerodynamic lift force is caused by pressure difference between the velocity platforms roof
and underside, and is expressed as FL = 1
2∗ CL ∗ B ∗ ρ ∗ (V + Vc)2. Where B is vehicle
platform’s reference area, CL is the coefficient of lift lies between (0.1 - 0.16).
The power applied on the vehicle due to aerodynamic drag force and aerodynamic lift force
is calculated as by considering aerodynamic lift force is one fourth of aerodynamic drag
force:
pg = 90 ∗ (70
3600) = 1.75KW
3.4.1.5. Acceleration forces
These are the three main force which act on the vehicle when it travels at constant speed.
But while the vehicle is accelerating or decelerating the effect of force due to inertia also
acts up on the vehicle. Gradient forces increase as the approaching angle of the road increases
and aerodynamic force is constant if the speed of the vehicle is assumed to be constant. The
total motive force with each component of the vehicle is shown in Figure 3-6. In this Figure
3-6 the vehicle is assumed to move up a hill with constant speed of 25 𝐾𝑚ℎ𝑟⁄ and the
velocity of the air is also assumed to zero.
Figure 3-6: Motive force versus approaching angle of the vehicle.
The coefficient of friction of different types of surface used in the analysis of data is taken
from literature is given in Table 3-1 [65] [67].
Motive force (N)
_ _ _ _ _ Gradient force (N)
. . . . . . . Rolling force (N)
Drag force (N)
40
Table 3-1: The coefficient of friction for different types of surface.
Surface type Coefficient of friction
Concrete(good/fair/poor) 0.010/0.015/0.020
Asphalt(good/fair/poor) 0.012/0.017/0.022
Macadam(good/fair/poor) 0.015/0.022/0.037
Snow / dirt 0.025/0.037
Mud(firm/medium/soft) 0.037/0.090/0.150
Grass(firm/soft) 0.055/0.075
Sand(firm/soft/dune) 0.060/0.150/0.300
In similar ways when the vehicle is moving on straight rod the gradient force acting on the
vehicle will be zero. The total motive force with each component of force acting on the
vehicle is reduced and shown in Figure 3-7. In this Figure 3-7 the vehicle is assumed to be
moving within the range of an average speed from (0 to 70 𝐾𝑚ℎ𝑟⁄ ) with 0.5 𝑚
𝑠2⁄
acceleration on straight line. The kinetic friction and static friction of the road is assumed to
be 0.01 and 0.1 respectively .
Figure 3-7: Motive force in N versus speed of the vehicle in 𝑘𝑚ℎ𝑟⁄ .
Motive force (N)
_ _ _ _ _ Gradient force (N)
. . . . . . . Rolling force (N)
Drag force (N)
41
From analysis of equation (3.1) to (3.5) we can determine the maximum power need to be
generated by PMSM motor in order to propel the vehicle in all condition of motion.
Therefore, the maximum tractive power and force required to propel the vehicle will be:
Ptotal(max) = PR + PA + PG (3.6)
Ptotal(max) = 1.75𝐾𝑊 + 6.63 𝐾𝑊 + 1.3𝐾𝑊 = 9.68𝐾𝑊
From equation (3.1) the total force acting on the vehicle will be:
Ftotal = 68.7𝑁 + 955.7𝑁 + 90𝑁 = 1114.4𝑁
But PMSM motor with output power rating of 9.68KW should not be selected. The losses
due to transmission of power to the wheel must be included. Therefore, the mechanical
power output required to drive the vehicle is given by equation below:
Mtotal(max) =Ptotal(max)
𝜂 𝑜𝑓 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑔𝑒𝑎𝑟 𝑠𝑦𝑠𝑡𝑒𝑚 =
9.68 𝐾𝑊
0.98= 9.87𝐾𝑊
Approximately we use 10 KW maximum power PMSM motor. The maximum tractive power
supplied when the vehicle is clamping the hill of maximum approaching angle which is 8
degree with its full load at the speed of 25 𝐾𝑚ℎ𝑟⁄ . The reason why the speed of the vehicle
is reduced in the hill is to increase torque with limited power supply of battery and limited
power output of the motor.
Figure 3-8: The motor power consumption with respect to approaching angle.
42
If we need to use larger battery size and motor of larger power rating, the penalty of cost and
weight increment. In Figure 3-8 shows the power need to be supplied by motor to drive the
vehicle at constant speed of 25 𝐾𝑚ℎ𝑟⁄ with varies approaching angle. In this Figure 3-8 it
is assumed that the car is moving with constant speed of 25 𝐾𝑚ℎ𝑟⁄ and suddenly come to
face an inclined road of defined approaching angle. From Figure 3-8 we can see that 10 KW
power is enough for the car to propel over the maximum approaching angle of 8 degrees at
25 𝐾𝑚ℎ𝑟⁄ . It is known that as we increase the speed of a vehicle its power consumption also
increases. Therefore, its necessary to identify the maximum power and rated power of
defined vehicle with a load so that the speed as well as torque requirement will be fulfilled.
A vehicle with its full load with an initial speed of 0 𝑚 𝑠⁄ starts to move with an acceleration
of 0.5 𝑚 𝑠2⁄ on the straight-line road is considered. The speed versus consumed power of the
vehicle can be as shown in Figure 3-9.
Figure 3-9: Consumed power versus speed of vehicle in 𝑘𝑚ℎ𝑟⁄ .
From the above Figure 3-9, we can say that the vehicle can move with speed 80 𝐾𝑚ℎ𝑟⁄ with
power conception of 10 KW that is above maximum speed. It is also necessary to identify
the rated torque and maximum torque of the motor requirement in order to model the system.
Once the power output of the motor required to propel the vehicle is known the torque and
the speed of the vehicle can be corrected by the gear system.
43
3.4.1.6 Torque required on the drive wheel
The torque required on the drive wheel will be the one that the drive motor requires to
produce so as to obtain the desired drive characteristic. The torque is calculated as in two
methods for given vehicle and motor specifications of M = 700kg, V = 70/3.6= 19.44𝑚𝑠⁄ ,
ω= 2000*2*pi/60 = 209.33𝑟𝑎𝑑𝑠𝑒𝑐⁄ , Wheel radius (r) = 0.20 and from equation of power P
= 10KW [66] [67] [L1].
Method 1:
Torque (ideal) = P
ω=
10 kw
209.33𝑟𝑎𝑑𝑠𝑒𝑐⁄
= 47.78 Nm
Overall transmission efficiency of electric vehicle is considered to 0.89 [L3].
Torque (Actual)= Torque (ideal)* efficiency
Torque (Actual) = 47.78 ∗ 0.89 = 42.51 Nm
ω wheel =V
r =
19.44 𝑚𝑠⁄
0.2m = 97.2 1
𝑠𝑒𝑐⁄
Gear(Transmission) Ratio(G) =ω
ω wheel =
209.33 𝑟𝑎𝑑𝑠𝑒𝑐⁄
97.2 1𝑠𝑒𝑐⁄
= 2.15
Torque in wheels = Torque (ideal) ∗ 𝐺 = 47.78 ∗ 2.15 = 102.7 Nm
The Electric car making 70 kmph with E-motor of 10 KW Generates 42.51 Nm of Torque
in motor at 2000 rpm and has to generate 102.7 Nm of Torque in wheels in order to make
70 kmph. Thus, the Gear Ratio has to be 2.15.
Method 2:
Torque =P
ω =
P∗9.549
RPM =
10 kw∗9.549
2000 RPM = 47.75 𝑁𝑚
Where 9.549 is from conversion of revolution per minute to rad per second.
T = 𝐹𝑡𝑜𝑡𝑎𝑙 ∗ r
2.15 (3.7)
T = 1114.4 𝑁 ∗ 0.2
2.15= 102.65𝑁𝑚
Where T is torque in wheel, r is radius of drive wheel and G is gear ratio. This torque can be
obtained by directly mounting a motor with torque value on the differential of the vehicle or
by using chain drive magnify a lesser torque to this value before it drives the wheel.
44
Figure 3-10: Torque developed by motor versus speed of vehicle in 𝑘𝑚ℎ𝑟⁄ .
3.4.2 Vehicle Specification and Traction Selection
We have taken specification data from Bajaj Auto Limited (India) and Hora Bajaj as a source
Vehicle whose vehicle parameter and specification are shown in below Table 3-2:
Table 3-2: Electric Bajaj specification [L2].
Parameter Symbol Value
Maximum Power P 10 𝐾𝑤
Wheel base B 1.925 𝑚
Length × Width× Height L× W× H 2.75 × 1.31 × 1.65 m
Coefficient of rolling friction 𝐶𝑟𝑟 0.01
Vehicle mass M 700 𝐾𝑔
Air density Ρ 1.23 𝐾𝑔/𝑚3
Frontal area A 1.5 𝑚2
Aerodynamic drag coefficient 𝐶𝑑 0.25
Tyre radius R 0.2 𝑚
Gravitational acceleration G 9.81 𝑚 𝑠⁄
45
Based on the above calculation and Bajaj Quet electric vehicle data the PMSM motor
specification used in the thesis is given as in in the following Table 3-3:
Table 3-3: PMSM motor specification [L2].
Parameter Value
Pole 4
Maximum power 10 𝐾𝑤
Efficiency 98 % @ rated value
Speed 2000 𝑟𝑝𝑚
Frequency 50 𝐻𝑧
Voltage 400 𝑉
Power factor 0.98
Inductance (𝐿𝑞 𝑎𝑛𝑑 𝐿𝑑) 2.8mH and 1.4mH
Stator resistance 2.875 Ω
Moment of inertia (J) 0.0006329 𝐾𝑔 ∙ 𝑚2
Friction (B) 0.0003035 Nm ∙ 𝑚𝑠⁄
Full load torque 42.51 𝑁𝑚
3.5. Dynamic Modelling of PMSM Drive
3.5.1. Arbitrary Reference Frame Concept
Reference frame are important like observer platform, in that each of the platforms gives a
unique view of the system as well as dramatic simplification of the system equation. For
example, for the purpose of control, it is desirable to have the system variable as dc quantity,
although the actual variable is sinusoidal. This could be accomplished by having reference
46
frame revolving at the same angular speed as that of sinusoidal variable. As the reference
frame are moving at an angular speed to angular frequency of sinusoidal supply, so that the
differential speed between them is reduced to zero, resulting in the sinusoidal signal
behaving as dc signal from reference frame. So, by moving that line, it becomes easier to
develop small signal equation of nonlinear equation, as the operating point is described only
by DC values; this then leads to linearized system around operating point. Such advantages
are many from using reference frames instead of driving the transformation for each and
every particular reference frame; it is advantageous to drive general transformation for an
arbitrary rotating reference frame. Then any particular reference frame model can be derived
by substituting the appropriate frame speed and position.
3.5.2. Three Phases to Two Phase Transformation
Vector control reconstructs orthogonal components of the stator current in AC machine as
torque producing current and magnetic flux producing current. In order to create the
perpendicular components of the stator current of PMSM which is in the form of a vector,
concept of coordinate transformation is required Assume that the three-phase supply voltage
is balanced. The Clarke and Parke transformation are a transformation of coordinates from
the three-phase stationary coordinate system to the dq rotating coordinate system.
A dynamic model for the three-phase PMSM can be derived from the two-phase machine if
the equivalence between the three and two phases is established. The equivalence is based
on the equality of the MMF produced in the two-phase and three-phase windings and on
equal current magnitudes. Assuming that each of the three-phase windings has N turns per
phase, and equal current magnitudes, the two-phase windings will have 3
2 N turns per phase
for MMF equality [6].
For proper simulation and analysis of the system, a complete modelling of the drive model
is essential. The motor axis has been developed using d-q rotor reference frame theory. At
any particular time, t, the rotor reference axis makes an angle Ѳ𝑟with the fixed stator axis
and the rotating stator MMF creates an angle α with the rotor d axis. It is viewed that at any
time t, the stator MMF rotates at the same speed as that of the rotor axis.
The transformations are usually based on following assumptions:
Rotor flux is assumed to be concentrated across d-axis and zero flux along q-axis.
Rotor flux is assumed to be fixed at a given operating point
47
Rotor temperature alters the flux, but the variation with time is assumed to be
negligible
Permanent magnets behave linearly.
There are no field current dynamics.
Saturation is neglected.
Induced EMF is sinusoidal in nature.
Hysteresis losses and Eddy current losses are negligible.
Figure 3-11: Three-phase and two-phase stator windings [6].
Let the magnetomotive force MMF=f=NI
𝑓𝑞 =3
2𝑁𝑖𝑞 = cos Ѳ𝑟 𝑁𝑖𝑎 + cos(Ѳ𝑟 −
2𝜋
3)𝑁𝑖𝑏 + cos(Ѳ𝑟 +
2𝜋
3)𝑁𝑖𝑐 (3.8)
𝑓𝑑 =3
2𝑁𝑖𝑑 = sin Ѳ𝑟 𝑁𝑖𝑎 + sin(Ѳ𝑟 −
2𝜋
3)𝑁𝑖𝑏 + sin(Ѳ𝑟 +
2𝜋
3)𝑁𝑖𝑐 (3.9)
Removing N from both sides results a matrix equation to determine the d & q stator current
components in the rotor reference frame directly from 𝑖𝑎, 𝑖𝑏, & 𝑖𝑐 in the stationary reference
frame.
[𝑖𝑞
𝑖𝑑] =
2
3[cos Ѳ𝑟 cos(Ѳ𝑟 −
2𝜋
3) cos(Ѳ𝑟 +
2𝜋
3)
sin Ѳ𝑟 sin(Ѳ𝑟 −2𝜋
3) sin(Ѳ𝑟 +
2𝜋
3)
] [𝑖𝑎
𝑖𝑏
𝑖𝑐
] (3.10)
𝑖𝑞𝑑 = [𝑇𝑎𝑏𝑐] ∗ 𝑖𝑎𝑏𝑐 (3.11)
48
The transformation from the two-phase stator currents in rotor reference frame to three-phase
stator currents in stationary reference frame can be obtained as
𝑖𝑎𝑏𝑐 = [𝑇𝑎𝑏𝑐]−1 ∗ 𝑖𝑞𝑑 (3.12)
[𝑇𝑎𝑏𝑐]−1 = [
cos Ѳ𝑟 sin Ѳ𝑟
cos(Ѳ𝑟 −2𝜋
3) sin(Ѳ𝑟 −
2𝜋
3)
cos(Ѳ𝑟 +2𝜋
3) sin(Ѳ𝑟 +
2𝜋
3)
] (3.13)
PMSM is very similar to the standard wound rotor synchronous machine except that the
PMSM has no damper windings and excitation is provided by a permanent magnet instead
of a field winding. Hence the d, q model of the PMSM can be derived from the well-known
model of the synchronous machine with the equations of the damper windings and field
current dynamics removed [6] [7].
Here is the derivation of the electrical equations which are greatly simplified due to the
concept of rotating transformation. The two axis voltage equations for the stator winding
which are of an IPMSM (but is the same for SPMSM where 𝐿𝑑 and 𝐿𝑞 have the same value)
are given by equations: [68]
Voltage equation from the model are given by:
𝑉𝑞 = 𝑅𝑠𝑖𝑞 + 𝑤𝑟𝜆𝑑 + 𝜌𝜆𝑞 (3.14)
𝑉𝑑 = 𝑅𝑠𝑖𝑑 − 𝑤𝑟𝜆𝑞 + 𝜌𝜆𝑑 (3.15)
Flux linkage are given by:
𝜆𝑞 = 𝐿𝑞𝑖𝑞 (3.16)
𝜆𝑑 = 𝐿𝑑𝑖𝑞 + 𝜆𝑓 (3.17)
Substituting Eq. (3.16) and Eq. (3.17) into Eq. (3.14) and Eq. (3.15)
𝑉𝑞 = 𝑅𝑠 𝑖𝑞 + 𝑤𝑟 (𝐿𝑑𝑖𝑑 + 𝜆𝑓) + 𝜌𝐿𝑞𝑖𝑞 (3.18)
𝑉𝑑 = 𝑅𝑠𝑖𝑑 − 𝑤𝑟𝐿𝑞 𝑖𝑞 + 𝜌( 𝐿𝑑𝑖𝑑 + 𝜆𝑓) (3.19)
Arranging Eq. (3.12) and Eq. (3.13) in matrix form,
(𝑉𝑞
𝑉𝑑) = (
𝑅𝑠 + ρ𝐿𝑞 𝑤𝑟𝐿𝑑
−𝑤𝑟𝐿𝑑 𝑅𝑠 + ρ𝐿𝑑) (
𝑖𝑞
𝑖𝑑) + (
𝜆𝑓𝑤𝑟
𝜆𝑓 𝜌)
49
3.5.2.1. Equivalent Circuits
From the dynamic equation (3.12 and 3.13) the equivalent circuit of the PMSM can be
derived for the stator q-axis and d-axis coordinates. During steady state operation, the d-q
axis currents are constant quantities. Hence the dynamic equivalent circuit can be reduced
to the steady state circuit.
Figure 3-12: PMSM Dynamic stator q-axis and d-axis equivalent circuit.
Figure 3-13: PMSM equivalent circuits from steady state equations.
3.5.2.2. Power Equivalence
The power input to the three-phase machine has to be equal to the power input of the two
phase machine to have meaningful interpretation in the modelling, analysis, and simulation.
Such an identity is derived in this section. The three-phase instantaneous power input is
given by equation (3.24) and input power remains constant for all reference frames.
𝑃𝑖𝑛 = 𝑉𝑎𝑏𝑐∗ 𝑡 𝑖𝑎𝑏𝑐 = (𝑉𝑎 𝑉𝑏 𝑉𝑐) (
𝑖𝑎
𝑖𝑏
𝑖𝑐
) (3.20)
𝑃𝑖𝑛 = 𝑉𝑎𝑖𝑎 + 𝑉𝑏𝑖𝑏 + 𝑉𝑐𝑖𝑐 (3.21)
𝑉𝑎𝑏𝑐 = [𝑇𝑎𝑏𝑐]−1𝑉𝑞𝑑 (3.22)
Substituting equation (3.22) to (3.21) results:
50
𝑃𝑖𝑛 = ([𝑇𝑎𝑏𝑐]−1𝑉𝑞𝑑)𝑡[𝑇𝑎𝑏𝑐]−1𝑖𝑞𝑑 (3.23)
𝑃𝑖𝑛 =3
2(𝑖𝑞 𝑉𝑞+𝑖𝑑𝑉𝑑) (3.24)
3.5.2.3. Electromagnetic Torque Equation
The electromagnetic torque is the most important output variable that determines the
mechanical dynamics of the machine such as the rotor position and speed. Therefore, its
importance cannot be overstated in all the simulation studies. It is derived from the machine
matrix equation by looking at the input power and its various components such as resistive
losses, mechanical power, and the rate of change of stored magnetic energy. Elementary
reasoning leads to the fact that there cannot be a power component due to the introduction
of reference frames. Similarly, the rate of change of stored magnetic energy could only be
zero in steady state. Hence, the output power is the difference between the input power and
the resistive losses in a steady state. Note that dynamically, the rate of change of stored
magnetic energy need not be zero. Based on these observations, the derivation of the
electromagnetic torque is made as follows [6] [69].
Substituting equation (3.14 and 3.15) to the power equation (3.24) gives:
𝑃𝑖𝑛 =3
2(𝑅𝑠𝑖𝑑
2 + 𝑅𝑠𝑖𝑞 2 ) +
3
2(𝑖𝑑𝜌𝜆𝑑 + 𝑖𝑞𝜌𝜆𝑞) +
3
2𝑤𝑟(𝑖𝑞𝜆𝑑 − 𝑖𝑑𝜆𝑞) (3.25)
The first term of the above equation is the power loss in the conductors, the second term is
the time rate of change of stored energy in the magnetic fields and the third term is the energy
conversion from electrical to mechanical energy. The torque can be derived from the third
term of the power equation and written as:
𝑃𝑚 = 𝑤𝑚𝑇𝑒𝑚 =3
2𝑤𝑟(𝑖𝑞𝜆𝑑 − 𝑖𝑑𝜆𝑞) (3.26)
The mechanical speed is related to electrical speed by
𝑤𝑟 = 𝑤𝑚 ∗ 𝑃 (3.27)
where
𝑃𝑚 is output mechanical power, 𝑤𝑚 is mechanical angular velocity of the rotor shaft, 𝑇𝑒𝑚 is
generated electromagnetic torque and P is number of pole pairs.
Substituting equation (3.27) to (3.26) results:
𝑇𝑒𝑚 =3
2∗ 𝑃(𝜆𝑑 𝑖𝑞 − 𝑖𝑑𝜆𝑞) (3.28)
51
Hereafter substituting the equation (3.16 and 3.17) in to equation (3.28) the torque equation
can also be expressed in the following way and equated to the mechanical equation (3.29):
𝑇𝑒𝑚 =3
2∗ 𝑃(𝜆𝑓𝑖𝑞 + (𝐿𝑑 − 𝐿𝑞)𝑖𝑑𝑖𝑞) (3.29)
The mechanical torque equation is,
𝑇𝑒𝑚 = 𝑇𝐿 + 𝑤𝑚𝐵𝑤 + 𝐽𝑑𝑤𝑚
𝑑t (3.30)
Solving for the rotor mechanical speed form equation (3.30)
𝑤𝑚 = ∫𝑇𝑒−𝑇𝐿−𝑤𝑚𝐵𝑤
𝐽 𝑑t (3.31)
𝑤𝑟 = 𝑤𝑚𝑃 (3.32)
The first term is called “mutual reaction torque” occurring between 𝑖𝑞 and the permanent
magnet, while the second term corresponds to “reluctance torque” due to the difference in
d-axis and q-axis reluctance (or inductance). If the motor is surface mounted PMSM which
means that 𝐿𝑑= 𝐿𝑞, due to the same reluctance paths in rotor d and q-axis, and
therefore the “reluctance torque” is equal to zero and total torque is low with IPMSM, so the
torque expression for SPMSM is:
𝑇𝑒𝑚 =3
2∗ 𝑃(𝜆𝑓𝑖𝑞) = 𝐾𝑡𝑖𝑞 (3.33)
Since the number of pole pairs and the magnetic flux linkages are constant, then the torque
is directly proportional to q-axis current 𝑖𝑞 and the torque equation (3.30) is now similar to
that in a separately excited DC motor, where 𝑖𝑞corresponds to the armature current of the
DC machine and torque can be controlled by controlling 𝑖𝑞. Constant torque control strategy
is derived from field-oriented control, where the maximum possible torque is desired at all
times like the dc motor. This is performed by making the torque producing current 𝑖𝑞 equal
to the supply current𝑖𝑠. This is achieved by controlling id to be equal to zero [6] [70].
3.5.3. Transfer Function of PMSM
Mathematical modelling of PMSM can derived in above equation (3.14) to equation (3.30)
and the transfer function between output and command input was derived by assuming all
the equations (3.14 and 3.15) and (3.29) are nonlinear and id is forced to zero according to
vector control of PMSM which leads to 𝑉𝑑 = − 𝑤𝑟𝐿𝑞𝑖𝑞 and independent of d-axis [71].
By applying Laplace transform in equations (3.18), (3.30) and (3.33)
52
𝑉𝑞(𝑠) = 𝑅𝑠 𝑖𝑞(𝑠) + 𝑤𝑟𝜆𝑓 + 𝐿𝑞𝑖𝑞(𝑠) = (𝑅𝑠 + 𝑠𝐿𝑞)𝑖𝑞(𝑠) + 𝑤𝑚𝑃𝜆𝑓 (3.34)
𝑇𝑒𝑚(𝑠) = 𝐾𝑡𝑖𝑞(𝑠) = 𝑤𝑚(𝑠)𝐵𝑤 + 𝐽𝑠𝑤𝑚(𝑠) + 𝑇𝑙 = (𝐵𝑤 + 𝐽𝑠)𝑤𝑚(𝑠) + 𝑇𝑙 (3.35)
𝑖𝑞(𝑠) =(𝐵𝑤+𝐽𝑠)𝑤𝑚(𝑠)+𝑇𝑙
𝐾𝑡 (3.36)
𝑉𝑞(𝑠) = (𝑅𝑠 + 𝑠𝐿𝑞)(𝐵𝑤+𝐽𝑠)𝑤𝑚(𝑠)+𝑇𝑙
𝐾𝑡+ 𝑤𝑚(𝑠)𝑃𝜆𝑓 (3.37)
𝑉𝑞(𝑠)𝐾𝑡 = ((𝑅𝑠 + 𝑠𝐿𝑞)((𝐵𝑤 + 𝐽𝑠) + 𝑇𝑙) + 𝐾𝑡𝑃𝜆𝑓)𝑤𝑚(𝑠) (3.38)
𝑤𝑚(𝑠)
𝑉𝑞(𝑠)=
𝐾𝑡
(𝑅𝑠+𝑠𝐿𝑞)((𝐵𝑤+𝐽𝑠)+𝑇𝑙)+𝐾𝑡𝑃𝜆𝑓 (3.39)
Figure 3-14: Transfer function block diagram of PMSM.
3.6. Space Vector Pulse Width Modulation
In the late 1960s and early 1970s, efforts were made to understand the dynamics of the ac
machines. It all started on the basis that independent control of flux and torque is the
characteristic of the separately excited DC motor drive that gives a very high dynamic and
steady-state performance. An equivalent control of that in AC motor drives, if found, can
overcome entirely the problems associated with the dynamic transients of the motor drive
[6]. SVPWM refers to the different combinations of the switching tubes of the bridge arm
of the three-phase inverter bridge and outputs different pulse sequences for controlling the
inverter to output three-phase sinusoidal voltage or three-phase sinusoidal current.
The output voltage could be fixed or variable at a fixed or variable frequency. A variable
output voltage can be obtained by varying the input DC voltage and maintaining the gain of
the inverter constant. On the other hand, if the DC input voltage is fixed and is not
controllable, a variable output voltage can be obtained by varying the gain of the inverter
𝑉𝑞(𝑠) 1
𝑅𝑠 + 𝑠𝐿𝑞 3
2𝑃𝜆𝑓
𝑃𝜆𝑓
𝑤𝑚(𝑠) 1
𝐵𝑤 + 𝑠𝐽
𝑇𝑙
53
which is normally accomplished by pulse width modulation (PWM) control within the
inverter.,
Figure 3-15: Three Phase Inverter.
There are 23 = 8 eight possible combinations of ‘on’ and ‘off’ states for the three upper
power transistors which determine eight phase voltage configurations. This PWM technique
controls the motor based on the switching of space voltage vectors, by which an approximate
circular rotary magnetic field is obtained. It approximates the reference voltage 𝑉𝑟𝑒𝑓 by a
combination of the eight switching patterns (𝑉0 – 𝑉7). The vectors (𝑉1 – 𝑉6) divide the plane
into six sectors (each sector: 60°). 𝑉𝑟𝑒𝑓 is generated by two adjacent non-zero vectors and
two zero vectors.
Principle of Space Vector PWM
Treats the sinusoidal voltage (reference voltage) as a constant amplitude vector
rotating at constant frequency.
This PWM technique approximates the reference voltage 𝑉𝑟𝑒𝑓 by a combination
of the eight switching patterns (V0 to V7).
Coordinate Transformation (abc reference frame to the stationary α-β frame). That is
a three-phase voltage vector is transformed into a vector in the stationary α-β
coordinate frame represents the spatial vector sum of the three-phase voltage.
The vectors (V1 to V6) divide the plane into six sectors (each sector: 60 degrees).
𝑉𝑟𝑒𝑓 is generated by two adjacent non-zero vectors and two zero vectors.
𝑉𝑏
𝑉𝑎
𝑉𝑐
𝐷1 𝐷3 𝐷5
𝐷6 𝐷4 𝐷2
𝑆1
𝑆4
𝑆3 𝑆5
𝑆6 𝑆2
A C B
A’ B’ C’
𝑉𝑑𝑐
54
The on and off states of the upper power devices are opposite to the lower one. So once the
states of the upper power transistors are determined, the states of lower one can be easily
determined. The eight switching vectors of the three upper power switches, output line to
neutral voltage (phase voltage), and output line-to-line voltages in terms of DC-link Vdc,
are given in Table 3-4 [72].
Table 3-4: Switching vectors, phase voltages and output line to line voltages.
Voltage
vectors
Switching
vectors
Line to neutral
voltage
Line to line
voltage
Vα
Vβ
A B C 𝑽an 𝑽bn 𝑽cn 𝑽ab 𝑽bc 𝑽ca
𝑉0 0 0 0 0 0 0 0 0 0 0 0
𝑉1 1 0 0 23⁄ −1
3⁄ −13⁄ 1 0 -1 𝒄 0
𝑉2 1 1 0 13⁄ 1
3⁄ − 23⁄ 1 0 -1 1
3⁄ 1√3
⁄
𝑉3 0 1 0 −13⁄ 2
3⁄ −13⁄ -1 1 0 −1
3⁄ 1√3
⁄
𝑉4 0 1 1 −23⁄ 1
3⁄ 13⁄ -1 0 1 2
3⁄ 0
𝑉5 0 0 1 −13⁄ −1
3⁄ 23⁄ 0 -1 1 −1
3⁄ −1√3
⁄
𝑉6 1 0 1 13⁄ −2
3⁄ 13⁄ 1 -1 0 1
3⁄ −1√3
⁄
𝑉7 1 1 1 0 0 0 0 0 0 0 0
(Note that the respective voltage should be multiplied by 𝑉𝑑𝑐)
3.6.1. Implementation of SVPWM
To implement the space vector PWM, the voltage equations in the abc reference frame must
be transformed into the stationary αβ reference frame that consists of the horizontal (α) and
vertical (β) axes, as a result, six non-zero vectors and two zero vectors are possible. Six
nonzero vectors (𝑉1 – 𝑉6) shape the axes of a hexagonal as depicted in Figure 3-16 and feed
55
electric power to the load or DC link voltage is supplied to the load. The objective of space
vector PWM technique is to approximate the reference voltage vector 𝑉𝑟𝑒𝑓 using the eight
switching patterns. One simple method of approximation is to generate the average output
of the inverter in a small period, 𝑇𝑍 to be the same as that of 𝑉𝑟𝑒𝑓in the same period [40].
Consider that voltage phasor 𝑉𝑟𝑒𝑓 is commanded. Its position is in between two switching
voltage vectors, say 𝑉1 and 𝑉2, and has a relative phase of α from 𝑉1, as shown in Figure
3-16. The commanded voltage phasor can only be realized with the use of the neighbouring
switching voltage vectors and, in this case, 𝑉1 and 𝑉2. Taking these switching vectors for a
fraction of time as it is not possible to take the fraction of them, and then combining them
through the load gives the desired command space voltage phasor [69] [73] .
Figure 3-16: Basic switching vectors, sectors and a reference vector.
Therefore, space vector PWM can be implemented by the following steps:
Determine 𝑉𝛼, 𝑉𝛽, 𝑉𝑟𝑒𝑓, and angle (α) to determine the specific sector.
Determine time duration 𝑇1, 𝑇2, 𝑇0 for the specific sector where 𝑇1, 𝑇2 are the
respective time for which the basic space vectors 𝑉1 and 𝑉2 should be applied within
the time period 𝑇𝑍 and 𝑇0 is the course of time for which the null vectors 𝑉0 and 𝑉7
are applied.
Determine the switching time of each transistor (𝑆1to 𝑆6).
𝑉1(100)
𝑉2(110) 𝑉3(010)
𝑉4(011)
𝑉5(001) 𝑉6(101)
𝑉7(111)
𝑉0(000) Vr
α 1
2
4
5
6
3
56
Step 1: Determine 𝑉𝛼, 𝑉𝛽, 𝑉𝑟𝑒𝑓, and angle (α) to determine the specific sector.
Using the co-ordinate transformation to 2-Ф stationary reference frame in Figure 3-17, the
𝑉𝛼, 𝑉𝛽, 𝑉𝑟𝑒𝑓, and angle (α) can be determined as follows:
𝑉𝛼 = 𝑉𝑎𝑛 − 𝑉𝑏𝑛 cos(60) − 𝑉𝑐𝑛 cos(60) (3.40)
𝑉𝛼 = 𝑉𝑎𝑛 −1
2𝑉𝑏𝑛 −
1
2𝑉𝑐𝑛
𝑉𝛽 = 0 + 𝑉𝑏𝑛 cos(30) − 𝑉𝑐𝑛 cos(30) (3.41)
𝑉𝛽 =√3
2𝑉𝑏𝑛 −
√3
2𝑉𝑐𝑛
Therefore, the above equations can be summarized in matrix form as follows:
[𝑉𝛼
𝑉𝛽] = [
1−1
2
−1
2
0√3
2
−√3
2
] [𝑉𝑎𝑛
𝑉𝑏𝑛
𝑉𝑐𝑛
] (3.42)
The reference space vector voltage crossing every sector is derived as:
|𝑉𝑟𝑒𝑓| = √𝑉𝛼2 + 𝑉𝛽
2 (3.43)
The current sector in which the 𝑉𝑟𝑒𝑓 vector found is determined by the equation (3.44)
α = tan−1 (𝑉𝛽
𝑉𝛼) = 𝑤𝑡 = 2𝜋𝑓𝑡, where f= fundamental frequency (3.44)
Figure 3-17: Voltage space vector and its components in (abc axis).
Step 2: Determine time duration T1, T2, T0
𝑎 , 𝑑𝑎𝑥𝑖𝑠
b
𝑞𝑎𝑥𝑖𝑠
c
α
𝑉𝛼
𝑉𝛽 𝑉𝑟𝑒𝑓
𝑠𝑒𝑐𝑡𝑜𝑟1
57
From Figure 3-18, the switching time duration for Sector 1can be calculated as follows:
∫ 𝑉𝑟𝑒𝑓 𝑇𝑍
0 𝑑𝑡 = ∫ 𝑉1
𝑇1
0 𝑑𝑡 + ∫ 𝑉2
𝑇1+𝑇2
𝑇1 𝑑𝑡 + ∫ 𝑉0
𝑇𝑍
𝑇1+𝑇2 𝑑𝑡 (3.45)
𝑇𝑍. 𝑉𝑟𝑒𝑓 = (𝑇1 ∙ 𝑉1 + 𝑇2 ∙ 𝑉2) (3.46)
The average voltage for the first sector which is made by vectors 𝑉0, 𝑉1, 𝑉2, and 𝑉7 is given
by equation (3.47). (Where, 0 ≤ α ≤ 60)
𝑇𝑍 ∙ |𝑉𝑟𝑒𝑓| ∙ [cos 𝛼sin 𝛼
] = (𝑇1 ∙2
3∙ 𝑉𝑑𝑐 ∙ [
10
] + 𝑇2 ∙2
3∙ 𝑉𝑑𝑐 ∙ [
cos𝜋
3
sin𝜋
3
]) (3.47)
𝑇1 = 𝑇𝑍 ∙ 𝑎 ∙sin(
𝜋
3−𝛼)
sin(𝜋
3)
(3.48)
𝑇2 = 𝑇𝑍 ∙ 𝑎 ∙sin(𝛼)
sin(𝜋
3) (3.49)
𝑇0 = 𝑇𝑍 − (𝑇1 + 𝑇2) , where 𝑇𝑍 =1
𝑓𝑍 and 𝑎 =
𝑉𝑟𝑒𝑓
2
3𝑉𝑑𝑐
(3.50)
Where
𝑇1, 𝑇2are the switching time durations of vectors 𝑉1 and 𝑉1 respectively.
𝑇0 is the time duration of the zero vector.
𝑇𝑍 is the time period which applied for one sector.
Switching time duration at any sector is given by the following equations:
𝑇𝑛 =√3 ∙𝑇𝑍∙|𝑉𝑟𝑒𝑓|
𝑉𝑑𝑐(sin(
𝜋
3− 𝛼 +
𝑛−1
3∙ 𝜋)) (3.51)
𝑇𝑛 =√3 ∙𝑇𝑍∙|𝑉𝑟𝑒𝑓|
𝑉𝑑𝑐(sin(
𝑛
3𝜋 − 𝛼)) (3.52)
𝑇𝑛 =√3 ∙𝑇𝑍∙|𝑉𝑟𝑒𝑓|
𝑉𝑑𝑐(sin
𝑛
3𝜋 ∙ cos 𝛼 − sin 𝛼 . cos
𝑛
3𝜋) (3.53)
𝑇𝑛+1 =√3 ∙𝑇𝑍∙|𝑉𝑟𝑒𝑓|
𝑉𝑑𝑐(sin(α −
𝑛−1
3∙ 𝜋)) (3.54)
𝑇𝑛+1 =√3 ∙𝑇𝑍∙|𝑉𝑟𝑒𝑓|
𝑉𝑑𝑐(− cos 𝛼 sin
𝑛−1
3𝜋 + sin 𝛼 cos
𝑛−1
3𝜋) (3.55)
𝑇0 = 𝑇𝑍 − (𝑇𝑛 + 𝑇𝑛+1) (3.56)
Where, n = 1 through 6(sector I to VI) and 0 ≤ α ≤ 60.
58
The method used to approximate the desired stator reference voltage with only eight possible
states of switches is to combine adjacent vectors of the reference voltage and to determine
the time of application of each adjacent vector as shown in Figure 3-18 for the first sector.
Figure 3-18: Reference voltage as a combination of adjacent vectors in sector I.
Step 3: Determine the switching time of each transistor (S1 to S6).
The SVPWM switching patterns for sector 1 and 2 are shown in Figure 3-19:
Figure 3-19: Space Vector PWM switching patterns for the first two sectors.
Based on Figure 3-19, the switching time at each sector is summarized Table 3-5.
𝑉𝑟𝑒𝑓
𝑉1
𝑉2
α
𝑇2
𝑇𝑍𝑉𝑑𝑐
𝑇1
𝑇𝑍𝑉𝑑𝑐
0
𝑠1
𝑠3
𝑠2
𝑠4
𝑠5
𝑠6
𝑉0 𝑉1 𝑉2 𝑉7 𝑉2 𝑉1 𝑉0
𝑇2 𝑇0
2 𝑇1 𝑇2 𝑇0 𝑇1
𝑇0
2
𝑠4
𝑠1
𝑠2
𝑠3
𝑠5
𝑠6
𝑉0 𝑉0 𝑉2 𝑉2 𝑉7 𝑉3 𝑉3
𝑇0
2
𝑇0
2 𝑇0 𝑇1 𝑇2 𝑇1 𝑇2
a). Sector 1 b). Sector 2
59
Table 3-5: Switching Time Calculation at Each Sector.
Sector Upper Switches (𝑆1,𝑆3,𝑆5) Lower Switches (𝑆4, 𝑆6, 𝑆2)
1 𝑆1 = 𝑇1 + 𝑇2 +𝑇0
2
𝑆3 = 𝑇2 + 𝑇0
2
𝑆5 = 𝑇0
2
𝑆4 =𝑇0
2
𝑆6 = 𝑇1 + 𝑇0
2
𝑆2 = 𝑇1 + 𝑇2 +𝑇0
2
2 𝑆1 = 𝑇1 + 𝑇0
2
𝑆3 = 𝑇1 + 𝑇2 +𝑇0
2
𝑆5 = 𝑇0
2
𝑆4 = 𝑇2 + 𝑇0
2
𝑆6 =𝑇0
2
𝑆2 = 𝑇1 + 𝑇2 +𝑇0
2
3 𝑆1 =𝑇0
2
𝑆3 = 𝑇1 + 𝑇2 +𝑇0
2
𝑆5 =𝑇2 + 𝑇0
2
𝑆4 = 𝑇1 + 𝑇2 +𝑇0
2
𝑆6 =𝑇0
2
𝑆2 = 𝑇1 +𝑇0
2
4 𝑆1 =𝑇0
2
𝑆3 = 𝑇1 +𝑇0
2
𝑆5 = 𝑇1 + 𝑇2 +𝑇0
2
𝑆4 = 𝑇1 + 𝑇2 +𝑇0
2
𝑆6 = 𝑇2 +𝑇0
2
𝑆2 =𝑇0
2
5 𝑆1 = 𝑇2 +𝑇0
2
𝑆3 =𝑇0
2
𝑆5 = 𝑇1 + 𝑇2 +𝑇0
2
𝑆4 = 𝑇1 +𝑇0
2
𝑆6 = 𝑇1 + 𝑇2 +𝑇0
2
𝑆2 =𝑇0
2
6 𝑆1 = 𝑇1 + 𝑇2 +𝑇0
2
𝑆3 =𝑇0
2
𝑆5 = 𝑇1 +𝑇0
2
𝑆1 =𝑇0
2
𝑆3 = 𝑇1 + 𝑇2 +𝑇0
2
𝑆5 = 𝑇2 +𝑇0
2
60
KVA rating of the inverter
It stands for the Volt ampere rating. It is the voltage and current supplied by the inverter to
the equipment’s. If an inverter operates with 100% efficiency, then the power requirement
of the electrical items and power supplied by inverter is same. But we all know that 100%
or ideal conditions don’t exist in real. Most inverters have the efficiency range from 60 %
to 90%. This efficiency is also called power factor of an inverter and is simply the ratio of
power required by the appliances to power supplied by an inverter. Power factor of most
inverters ranges from 0.6 to 0.9.
The total power required to derive the vehicle is 10𝐾𝑊 and the rating of inverter required
is greater than the power required to drive the vehicle and calculated as follows:
VA rating of inverter =power consumed
𝑃𝑜𝑤𝑒𝑟 𝑓𝑎𝑐𝑡𝑜𝑟(efficiency) (3.57)
𝑉𝐴 𝑟𝑎𝑡𝑖𝑛𝑔 =10 𝐾𝑊
0.85= 11.76𝐾𝑉𝐴
By considering the inverter efficiency or power factor is taken as 0.85.
The inverter rating is expressed in KVA rather than KW since the inverters is made up
of actual power (kW) and reactive power (kVAR) which via the cos/sine rule specify the
apparent power (kVA) of the inverter [L3].
3.7. Controller Design
3.7.1. Introduction to Fuzzy Logic Controller
The fuzzy logic is a class of artificial intelligence with a recent history and application. The
concept of fuzzy logic was first introduced by 1965 by a computer scientist Lotfy Zadeh,
and presented not as a control methodology, but as a way of processing data by allowing
partial set membership rather than crisp set membership or non-membership. He argued that
human thinking is often fuzzy, vague, or imprecise in nature, and, therefore cannot be
represented by yes (1) or no (0). Fuzzy logic allows the programmer to deal with natural,
“linguistic sets” of states, such as very fast, fast, slow, etc. Fuzzy-logic provides a simple
way to arrive at a definite conclusion based upon vague, ambiguous, imprecise, noisy, or
missing input information. Its approach to control problems mimics how a person would
make decisions, much faster [74] [75].
61
3.7.1. Fuzzy Logic Controller
The basic concept behind FLC is to utilize the expert knowledge and experience
of a human operator for designing a controller an application processes whose input output
relationship is given by a collection of fuzzy control rules using linguistic variables instead
of a complicated dynamic model. The FLC initially converts the crisp error and change in
error variables into fuzzy variables and then are mapped into linguistic labels. Membership
functions are associated with each label as shown in which consists of two inputs and one
output. The inputs are speed error and change in speed error and the output is speed limit.
Fuzzy Inference System uses “IF... THEN...” statements, and the connectors present in the
rule statement are “OR” or “AND” to make the necessary decision to a solve control problem
rather than attempting to model a system mathematically [59].
A Fuzzy Logic Controller usually consists of [76]:
Fuzzification unit which maps measured inputs of crisp value into fuzzy linguistic
values to be used by a fuzzy reasoning mechanism.
Knowledge base (KB) which is the collection of expert control knowledge required
to achieve the control objective.
Fuzzy reasoning mechanism (inference engine) that performs various fuzzy logic
operations to infer the control action for the given fuzzy inputs.
Defuzzification unit which converts the inferred fuzzy control action into the
required crisp control values to be entered into the system process.
a) Fuzzification
Fuzzification is the process of making a crisp quantity fuzzy. It transforms the physical
values of the error signal, rate of change of error which is input to the fuzzy logic controller,
into a fuzzy set consisting of an interval for the range of the input values and an associate
membership function describing the degrees of the confidence of the input belonging to this
range. The conversion process is performed by a membership function. The purpose of this
fuzzification step is to make the input physical signal compatible with the fuzzy control rule
base in the core of the controller.
b) Knowledge Base
The knowledge base of a fuzzy logic controller consists of a data base and a rule Base. The
basic function of the data base is to provide the necessary information for the proper
62
functioning of the fuzzification, the rule base and the defuzzification units. This information
includes:
The meaning of the linguistic values of the membership functions of the Input
variables and the control output variables.
Physical domains and their normalized counterparts together with the normalization,
denormalization and scaling factors.
The type of the membership functions of a fuzzy set.
The rule base is the way that expert knowledge is described for fuzzy logic controller. The
basic function of the rule base is to represent the expert knowledge in a form of if-then rule
structure. The power of fuzzy rule-based systems is their ability to yield ‘‘good’’ results with
reasonably simple mathematical operations.
c) Inference Mechanism
In order to draw conclusions from a rule base, we need a mechanism that can produce an
output from a collection of IF-THEN rules. This is done using the computational rule of
inference. The Inference Mechanism provides the mechanism for referring to the rule base
such that the appropriate rules are fired. The two most commonly used inference procedures
in FLC are Mamdani's Max-Min and Max-Algebraic Product (or Max-Dot) composition.
Max-Min composition:
Consider a simple system where each rule comprises two antecedents and one consequent.
A fuzzy system with two non-interactive inputs x1 and x2 (antecedents) and a single output
y (consequent) are described by a collection of n linguistic IF-THEN rules.
IF x1 is A1(𝑘)
and x2 is A2(𝑘)THEN y(𝑘)is 𝐵(𝑘), k = 1, 2, …. n.
Where
A1(𝑘)
and A2(𝑘)
are fuzzy sets representing the 𝐾𝑡ℎ antecedent pairs and 𝐵(𝑘) are the fuzzy
sets representing the 𝐾𝑡ℎ consequent
Based on the Mamdani’s max-min composition method of inference, and for a set of
disjunctive rules, the aggregated output for the n rules will be given by:
μ𝐵(𝑘) (𝑦) = 𝑀𝑎𝑥 𝑀𝑖𝑛[μ𝐴1
(𝑘)(𝑖𝑛𝑝𝑢𝑡(𝑖)), μ𝐴2(𝑘)(𝑖𝑛𝑝𝑢𝑡(𝑗))] (3.58)
where i, j is input fuzzy set variables and y is output fuzzy set variable.
63
d) Defuzzification
Defuzzification unit in FLC is the inverse of the fuzzification process. It converts the fuzzy
controller output fuzzy variables in to a crisp real signal. There are several commonly used,
logically meaningful, and practically effective defuzzification formulas available, which are
by nature weighted average formulas in various forms. In this thesis a centre of gravity
defuzzification method is adopted for, which can reflect the overall inference information.
Centre of gravity method
This procedure is the most prevalent and physically appealing of all the defuzzification
methods. It is given by the algebraic expression in equation (3.59).
𝑥∗ =∑ 𝜇𝑥(𝑥)∗𝑥
∑ 𝜇𝑥(𝑥) (3.59)
Design Process of FLC
Identify controller Inputs and Outputs as the Fuzzy variables.
Break up Inputs and Outputs into several Fuzzy Sets and label them according to the
problem to be solved.
Assign or determine a membership function (MF) for each fuzzy set.
Choose appropriate scaling factors for the input and output variable to normalize to
[0,1] or [-1,1] interval range.
Fuzzify the inputs
Develop the fuzzy IF-THEN rules to solve the problem.
Choose Inference Mechanism.
Aggregate the fuzzy outputs of each rule.
Choose a DEFUZZIFICATION method.
3.7.2. PID Controller
In process control today, more than 95% of the control loops are of PID type, most loops are
actually PI control to improve the steady state performance and since derivative term
produces saturation effects and also amplifies the noise signals produced in the system. In
the control of dynamic systems, no controller has enjoyed both the success and the failure of
the PID control. There is actually a great variety of types and design methods for the PID
controller. The most used type of PID controller is PI controller. Each of these, P and I are
terms in a control algorithm, and each has a special purpose. In the field of electrical drives
64
PI regulators are employed for motor control. The variables to be controlled are position,
speed, torque, and current or voltage. The fact that the measurement of these signals can
contain considerable noise (high frequency) makes the PI structure without the derivative
part more suitable. And in fact, PI controller is enough for first order systems.
Figure 3-20: PID control System.
The output produced by this type of controller is consist three terms. In these three terms one
is the proportional to actuating signal and other is integral and derivative to have zero steady-
state error to a step input. Based on Ziegler Nichols tuned techniques the value of 𝑘𝑝, 𝑘𝑖 and
𝑘𝑑 are calculated from transfer function simulated wave form.
Output(t) = 𝑘𝑝𝑒(𝑡) + 𝑘𝑖 ∫ 𝑒(𝑡) 𝑑𝑡𝑡
0+ 𝑘𝑑
𝑑𝑒(𝑡)
𝑑𝑡 (3.60)
e(t) = set reference value – actual calculated value
where 𝑘𝑝, 𝑘𝑖 and 𝑘𝑑 is speed controller gain of proportional, integral and differential
controller respectively and its value is k𝑝 = 4.8, K𝑖 = 97 and k𝑑 = 0.
3.7.3. Fuzzy Logic based PID Controller
As we have seen in the above sections, to achieve a high-performance speed control of
PMSM Fuzzy Logic based PID Controller is proposed in speed loop (outer loop) of the
control system. This collaboration is practical as most of the industrial system that are using
conventional controller can insert a FLC to their control system for optimization purposes
without changing much of the system topology and scrapping the conventional controller.
As a result, fuzzy logic controller (FLC) is used to aid conventional method to enhance the
output performance by limiting the reference current for torque production for inner loop of
controller at different operating conditions.
R(s)
𝑘𝑖
𝑠
G(s)
𝑘𝑝
E(s) Y(s)
U(s)
PID controller
𝑘𝑑𝑠
65
The accurate mathematical model is not necessary to Fuzzy Logic based PID controller. The
practical experience is saved in the form of control rules, then the correct control decision is
made according to the practicable condition of control system(the magnitude, direction and
the change trend of the input signal deviation).The parameters 𝐼𝑞 can be adjusted on-line,
So the control performance of PMSM servo system can be improved [77].
a. The input variables and output variables
The Fuzzy Logic-PID controller uses the speed error and error change rate as fuzzy inputs,
and the reference current 𝐼∗𝑞 as fuzzy outputs.
The error and rate of change of error are defined as:
e(𝑘) = 𝑟(𝑘) − 𝑦(𝑘) (3.61)
ce(k) = e(k)− e(k−1)
𝑇𝑠 (3.62)
where
𝑟(𝑘) is the reference input speed signal, 𝑦(𝑘)is the output speed response, e(𝑘) is the error
signal, and 𝑐e(𝑘) is the rate of change in error.
b. Fuzzy language of input and output variables
For the system under study the universe of discourse for both inputs e(t) and ce(t) is
normalized to the range -100 to 100 as the range of the universe of discourse for the
membership functions is selected to be from -100 to 100 to include all error crated with
maximum speed of 70 km/hr, and the linguistic labels(fuzzy sets) are defined asNB
(Negative Big), NM( Negative medium), NS (Negative small), ZE (Zero), PS (Positive
small), PM (Positive medium), and PB (Positive Big) and are referred to in the rules bases
as NB,NM,NS,ZE,PS,PM,PB as it is shown in Figure 3-21. The linguistic labels of the
outputs Kp1 and KI1 in the range -1 to 1 are Zero, Medium small, Small, Medium, Big,
Medium big, very big and referred to in the rule bases as Z, MS, S, M, B, MB, VB.
As discussed in above section the FLC initially converts the crisp error and change in error
variables into fuzzy variables and then are mapped into linguistic labels. Membership
functions are associated with each label as shown in which consists of two inputs and one
output. The inputs are speed error and change in speed error and the output is speed limit.
Fuzzy Inference System uses “IF... THEN...” statements, and the connectors present in the
rule statement are “OR” or “AND” to make the necessary decision rules. Each of the inputs
66
and the output contain membership functions with all above seven linguistics and this
membership function used for input and output fuzzy sets are shown in Figure 3-21.
(a) (b)
(c)
Figure 3-21: Member ship for (a) Speed error input to FLC (b) change in speed error input
to FLC (c) speed limit output of FLC.
c) Fuzzy Rule
The mapping of the fuzzy inputs into the required output is derived with the help of a rule
base and the rule base is expressed as IF (antecedent)-THEN (consequent) rules as shown
as Table 3-6. This fuzzy rule is extracted from fundamental knowledge and human
experience about the process and used to limet Iq. Each control input has seven fuzzy sets
so that there are at most 49 fuzzy rules and this fuzzy rule are extracted from fundamental
knowledge and human experience about the process [78].
67
Figure 3-22: Block diagram of FL-PID controller schematic representation.
Table 3-6: Rule Base for Fuzzy Logic Controller.
ce\e NB NM NS ZE PS PM PB
NB ZE ZE MS MS S S M
NM ZE MS MS S S M B
NS MS MS S S M B B
ZE MS S S M B B MB
PS S S M B B MB MB
PM S M B B MB MB VB
PB M B B MB MB VB VB
3.8 Software Simulation Modelling and Design
3.8.1. MATLAB/SIMULINK model
The simulation consists of several steps. The Space Vector Generation using Clark & Park
transforms has been implemented. The inner current loop is present with two PID controllers
for d and q axis separately. Then outer speed loop is present with FL speed controller. The
drive system consists of the motor model, average value inverter fed by a 400 V dc supply.
The duty cycles are provided to inverter by the SVPWM block. The inverter drives the motor
to generate controlled rotor speed. Figure 3-23 and Figure 3-24 describes the overall
MATLAB Simulink model of the thesis.
Id*
FLW ref PID
PID
Iq*
W mes
Id Iq
68
Figure 3-23: MATLAB Simulink model of fuzzy- PID of PMSM.
Figure 3-24: MATLAB Simulink model of fuzzy- PID of PMSM mathematical model.
The above Figure 3-23 and Figure 3-24 shows a complete MATLAB/Simulink model of
SVPWM based PMSM with fuzzy-PID control. For complete mathematical model of
PMSM. The step by step subsystem model of the SVPWM method and mathematical model
of PMSM is given in appendix A.
69
CHAPTER FOUR
4. RESULTS AND DISCUSSIONS
4.1. MATLAB Simulation Result of SVPWM
The MATLAB/Simulink model simulation results are given for PMSM for the following
specification: number of poles [p]= 4, frequency=50Hz, stator resistance=0.6Ω; moment of
inertia= 0.011Kg-m/sec, friction factor= 0.014Nm/(rad/sec), q-axis and d-axis inductance is
2.8 mH and 1.4mH respectively.
4.1.1. Clarke Transformation Output
The voltage 𝑉𝑎, 𝑉𝑏 and 𝑉𝑐 in a power system can be converted to a stationary reference frame
𝑉𝛼 and 𝑉𝛽 using Clarke transformation as discussed in equation (3.42). In this transformation
𝑉𝑎 and 𝑉𝛼 have the same direction and different magnitude. As seen in Figure 4-1 the 𝛼𝛽-
transformation are demonstrated in two-dimensional plane which make it easier to use in the
calculation.
Figure 4-1: αβ-transformation output voltage.
4.1.2. Switching Pattern of SVPWM Inverter
The SVPWM based on a carrier with reduced switching ratio, is the better implementation
of SVPWM because, when the switching ratio is reduced the heat generated in switches also
reduced at the same time which improves the life time of switches and efficiency of the
inverter.
70
This pattern is compared with high frequency carrier signal to produce gating signal to
switch on and off all six switches in inverter in appropriate sequence. There is also extra
boost voltage compared with sinusoidal PWM as there is an addition of common mode
component in SVPWM compared with SPWM.
Figure 4-2: Voltage for three phases (PWM Duty cycles).
4.1.3. Generated Gate Signal
The generated output get signal based SVPWM techniques in order to switching the IGBT
of inverter to generate required three phase AC voltage to drive the PMSM is shown in the
below Figure 4-3 to Figure 4-5 the signal that generated from the driver circuit is out phase
in one leg as shown in Figure 4-3, Figure 4-4 and Figure 4-5 in different colure those pulse
is out of phase in on leg because to prevent short circuit which is the cause for damage of
the inverter. Therefore, the switches are on and off sequentially based on the pattern of sector
vectors to generate three phase sinusoidal waves.
Figure 4-3: Gate signal for IGBT 1 and IGBT 4.
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As shown in Figure 4-3 the IGBT in first leg is on and off at diffirent time interval to prevent
short circuit damage.
Figure 4-4 shows the pulse generated from direvier circuit based on SVPWM for IGBT 3
and IGBT 6 of second leg.
Figure 4-4: Gate signal for IGBT 3 and IGBT 6.
Figure 4-5 shows the pulse generated from direvier circuit based on SVPWM for IGBT 5
and IGBT 2 of third leg.
Figure 4-5: Gate signal for IGBT 5 and IGBT 2.
4.2. Fuzzy Controller Output
4.2.1. Fuzzy Logic Output
Fuzzy-PID controller used in this paper is based on two inputs and one output. These are
error (e), error change (de) are input for fuzzy controller and producing current control signal
which responsible for torque production are the output of the controller. A linguistic variable
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which implies inputs have been classified as: NB, NM, NS, ZE, PS, PM, PB and output have
been classified as Z, MS, S, M, B, MB, VB as discussed in chapter three. Then the controller
gives the decision according to rule base for fuzzy logic controller given in Table 3-6. The
fuzzy rule output and the surface of operation is given in Figure 4-6 and Figure 4-7
respectively.
Figure 4-6: Output of fuzzy rule viewer.
Figure 4-7: Fuzzy surface viewer.
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4.3. OUTPUT VOLTAGE
4.3.1. Phase Voltage
Phase Voltage that are generated from the inverter have three steps 0, ±1
3𝑉𝑑𝑐, ±
2
3𝑉𝑑𝑐 as
shown in below Figure 4-8 which are generated from the gate pulse on and off sequentially
based on SVPWM techniques.
Figure 4-8: Phase voltage 𝑉𝑎𝑛, 𝑉𝑏𝑛 and 𝑉𝑐𝑛.
4.3.2. Line to Line Voltage
Line to line voltage from the inverter is shown in Figure 4-9 to Figure 4-11 and it is the
voltage between two phase and represented as 𝑉𝑎𝑏 = 𝑉𝑎𝑛 − 𝑉𝑏𝑛 , 𝑉𝑎𝑐 = 𝑉𝑎𝑛 − 𝑉𝑐𝑛 and 𝑉𝑏𝑐 =
𝑉𝑏𝑛 − 𝑉𝑐𝑛 where 𝑉𝑎𝑛, 𝑉𝑏𝑛 and 𝑉𝑐𝑛 is phase voltage A, B and C respectively.
Figure 4-9: Line voltage 𝑉𝑎𝑏.
74
Figure 4-10: Line voltage 𝑉𝑎𝑐.
Figure 4-11: Line voltage 𝑉𝑏𝑐.
4.4. Speed Output of PMSM
4.4.1 Rotor Speed and Reference Speed of PID Controller
The rotor speed of PMSM and reference speed for PID controller in outer and inner loop is
given in Figure 4-12 at the starting time speed of PMSM is flow the reference speed and
rotor speed is gradually increases as the motor rotates. At the time speed or torque while
change the rotor speed while vary and at instant of time it tracks the reference speed as shown
in Figure 4-12 and the zoom view of this output from time 0.25 to 0.3 is given in Figure 4-
13. The speed difference between rotor speed and reference speed is given in Figure 4-14
and the zoom view of this speed difference from time 0.3 to 0.35 is given in below Figure
4-15.
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Figure 4-12: Rotor speed Vs reference speed of PID controller.
Figure 4-13: Zoom out of rotor speed Vs reference speed of PID controller.
Figure 4-14: The difference between rotor speed Vs reference speed of PID controller.
76
Figure 4-15: Zoom out of the difference between rotor speed Vs reference speed of PID
controller.
4.4.2. Rotor Speed and Reference Speed of Fuzzy Controller
The rotor speed of PMSM and reference speed for fuzzy controller in outer and inner loop
is given in Figure 4-16 at the starting time speed of PMSM is flow the reference speed and
rotor speed is gradually increases as the motor rotates. At the time speed or torque while
change the rotor speed while vary and at instant of time it tracks the reference speed as shown
in Figure 4-16 and the zoom view of this output from time 0.25 to 0.3 is given in Figure 4-
17. The speed difference between rotor speed and reference speed is given in Figure 4-18
and the zoom view of this speed difference from time 0.3 to 0.35 is given in below Figure
4-19.
Figure 4-16: Rotor speed Vs reference speed of Fuzzy controller.
77
Figure 4-17: Zoom out of rotor speed Vs reference speed of fuzzy controller.
Figure 4-18: The difference between rotor speed Vs reference speed of fuzzy controller.
Figure 4-19: Zoom out of the difference between rotor speed Vs reference speed of fuzzy
controller.
78
4.4.3. Rotor Speed and Reference Speed of Fuzzy-PID Controller
The rotor speed of PMSM and reference speed when fuzzy logic is used in outer loop and
PID controller is used in inner loop is given in Figure 4-20 at the starting time speed of
PMSM is flow the reference speed and rotor speed is gradually increases as the motor rotates.
At the time speed or torque while change the speed rotor speed while vary and at instant of
time it tracks the reference speed as shown in Figure 4-20 and the zoom view of this output
from time 0.25 to 0.3 is given in Figure 4-21. The speed difference between rotor speed and
reference speed is given in Figure 4-22. and the zoom view of this speed difference from
time 0.3 to 0.35 is given in below Figure 4-23.
Figure 4-20: Rotor speed Vs reference speed of Fuzzy-PID controller.
Figure 4-21: Zoom out of rotor speed Vs reference speed of fuzzy-PID controller.
79
Figure 4-22: The between rotor speed Vs reference speed of fuzzy- PID controller.
Figure 4-23: Zoom out of the difference between rotor speed Vs reference speed of fuzzy-
PID controller.
From Figure 4-20 the speed of rotor ripples oscillates from 159.46 rad/sec (minimum) to
160.04 rad/sec (maximum) for the given reference speed of 160rad/sec (1500 rpm), 138.8
rad/sec (minimum) to 140 rad/sec (maximum) for the given reference speed of 140rad/sec
(1350 rpm) and 99.8 rad/sec (minimum) to 100.01 rad/sec (maximum) for the given
reference speed of 100rad/sec (950 rpm).
As we see from Figure 4-12 to Figure 4-23 the speed of PMSM will track the reference speed
within fraction of second and the difference in reference speed and rotor speed will
minimized as controller is changed from PID and fuzzy to Fuzzy to Fuzzy-PID. Generally,
by comparing difference in reference speed and rotor speed for Figure 4-12, Figure 4-16 and
Figure 4-20 fuzzy-PID controller have fast track to given reference speed and have small
error with change in reference speed and load torque.
80
In this study FUZZY-PID controller is used and its comparison of Conventional PID
controller, FL controller and FL-PID Controllers from simulation result is given in Table
4-1:
Table 4-1: Comparison of PID, Fuzzy logic and Fuzzy-PID controller.
Controller Transient state error
in %
Steady state
error
Variation during load and
reference speed change
Conventional PID 15% ± 0.015 11.43%
Fuzzy logic 8.75% ± 0.016 8.57%
Fuzzy-PID 4.87% ± 0.009 4.2%
As seen from Table 4-1 fuzzy-PID have small error during transient state, steady state and it
track the reference speed and load torque very fast over PID controller and fuzzy logic
controller since it has both advantage of fuzzy controller and PID controller. From the
simulation result we conclude the hybrid of fuzzy controller and PID controller have better
performance than Conventional PID and Fuzzy controller.
4.4.4. Rotor Speed of Fuzzy-PID Controller for PMSM
In section 4.4.1 to 4.4.3 the result of rotor speed for mathematical representation of PMSM
is expressed and in this section, we discuss the rotor speed of PMSM for Fuzzy-PID
controller.
Figure 4-24: Rotor speed of Fuzzy-PID controller.
Time (s)
Roto
r sp
eed (
rad/s
ec)
81
Figure 4-25: zoom out view of Rotor speed of Fuzzy-PID controller.
As shown in Figure 4-24 at the starting time speed of PMSM is flow the reference speed and
rotor speed is gradually increases as the motor rotates. The rotor speed is controlled
according to required speed of the Qute Bajaj to drive effectively. From comparison of Rotor
speed of Fuzzy-PID controller shown in Figure 4-20 and Figure 4-24 the speed curve for
mathematical model of PMSM have follow reference speed very fast because of
mathematical model is ideal representation of motor.
4.5. Torque and Current Response of PMSM
4.5.1. Torque Output
4.5.1.1. Torque Output for PMSM mathematical representation
The torque associated with permanent magnet synchronous motor is given in Figure 4-26
high more than load torque during starting time and then it follows the load torque and during
change in speed the torque also varies either increases or decreases depend on whether speed
is increases or decreases of fraction of time. The torque required by the QUTE BAJAJ is
around 47.75 Nm, after the motor rotate and start drive and the speed is at steady state the
torque comes to zero to minimize losses.
Time (s)
Roto
r sp
eed (
rad/s
ec)
82
Figure 4-26: Electromagnetic torque Vs load torque.
4.5.2. Current Output
The currents are obtained using reverse Park's transformation. It is clear that the current is
non sinusoidal at the starting and becomes sinusoidal when the motor reaches the controller
command speed at steady state. The magnitude of this current is depending on the motor
load during maximum load 47.75 Nm the current output also maximum and if motor load
also reduces the output current also reduces finally when motor load is zero the output
current also almost zero.
Figure 4-27: I abc current response.
The corresponding dq component of current is given in Figure 4-28. Since field-oriented
control is used the value of id is zero and since iq is responsible for torque producing it have
the value different from zero and its output response curve looks like the torque curve with
different magnitude.
83
Figure 4-28: I dq current response.
4.5.1.2. Torque Output for PMSM
The electromagnetic torque developed by motor is high during starting time beyond the
required to start safely with high starting torque and it follows the load torque variation as
shown in Figure 4-29.
Figure 4-29: Electromagnetic torque developed by PMSM.
The corresponding dq component of current is given in Figure 4-30. Since field-oriented
control is used the value of id is zero which indicated in red line and since iq is responsible
for torque producing it have the value different from zero indicated in blue lines.
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Figure 4-30: I dq current response of PMSM.
4.6. Step Response of PMSM
The step response of PMSM from MATLAB implementation of transfer function is given in
Figure 4-31:
Figure 4-31: Steep response of PMSM motor.
The error between step input and step output is given in Figure 4-32 and it indicate that the
steady state error is very low and below 1%:
85
Figure 4-32: Error between steep input and steep output of PMSM.
From the steep response of PMSM the dynamic performance of the motor is given in Table
4-2
Table 4-2: Comparison of dynamic performance for PID and Fuzzy- PID controller.
PID PID – online
tuned
Fuzzy-PID
Gain Parameters k𝑝 = 4.8
K𝑖 = 97
k𝑑 = 0
k𝑝 = 0.33633
K𝑖 = 0.15904
k𝑑 = 0.0001607
k𝑝 = 0.036366
K𝑖 = 0.15904
k𝑑 = 0.0001607
Rise time (s) 0.107 0.0907 0.0861
Settling time (s) 0.63 0.567 0.55
Overshoot % 9.85 9.72 9
Peak Time (s) 1.1 1.1 1.09
Phase margin 83.6 deg @ 15.4
𝑟𝑎𝑑𝑠𝑒𝑐⁄
79 deg @ 17.7
𝑟𝑎𝑑𝑠𝑒𝑐⁄
87.9 deg @ 20.5
𝑟𝑎𝑑𝑠𝑒𝑐⁄
Closed loop stability stable stable stable
86
From the comparison of Table 4-2 Fuzzy- PID controller have good dynamic performance
than convectional controller which have the advantage in reducing time required for settling
and have low overshot than convectional controller.
Generally, from the simulation and result fuzzy-PID controller have good dynamic and
steady state performance. Therefore, for a drive system which requires efficient and vast
control mechanism like electric vehicle fuzzy- PID controller is very important. In addition
to this PMSM motor is very useful in future transportation industry since it is very energy
efficient motor, high power density and smaller size which is a main requirement of EV.
87
CHAPTER FIVE
5. CONCLUSION AND RECOMMENDATION
5.1. Conclusion
In this thesis space vector pulse width modulation based Permanent Magnet Synchronous
Machines with fuzzy-PID control model is designed and simulated through MATLAB
software. As PMSM is increasingly used in high-performance applications in industry, such
applications need speed controllers with high accuracy, high performance, flexibility and
efficiency.
Based on the study on control strategies of PMSM system, a compound control strategy
combining Fuzzy control and PID control is designed, establish the Fuzzy-PID control
simulation Model and conduct simulation analysis in MATLAB/Simulink Compare the
simulation results of traditional PID control, fuzzy control and Fuzzy-PID control. The
simulation results show that fuzzy-PID controller have improvements in terms of steady-
state error, small settling time, low overshoot, and fast recovery from load torque changes
and parameter variations compared to the traditional PID controller with fixed gains and
fuzzy controller. Since, PID controller is still widely used in industry; the developed FLC
can be applied to the available PID controller for optimization purposes once the
implementation is carried out successfully.
The modulation techniques chosen in this thesis is SVPWM, has good DC link voltage
utilization (less switching losses), low current ripple, less THD which improves the
efficiency of the system to overcome the EV problem of battery system and this future make
it suitable for high voltage, high power application such as renewable power generation. A
design procedure for QUTE BAJAJ EV drive system is presented based on the vehicle
dynamics. This methodology helps to calculate the motor power rating and load torque to
drive the wheel according to vehicle dynamics and the mathematical model of Permanent
Magnet motor drive system using field-oriented control is also developed.
88
5.2. Recommendation
In this thesis there are several ideas that can be discussed and analysed but some work is not
included in this thesis due to time limitation and this is included in recommendation for
future work.
The main recommendations for this thesis are summarized as:
If all equipment’s are available, the developed fuzzy-PID speed controller can be
implemented and tested for Quet- Bajaj application to verify the theoretical
conclusion.
This thesis done by using rotor position sensor but it is possible to implement fuzzy-
PID sensor less speed control of PMSM can also be (with no rotor position sensor)
implemented.
This thesis done by using fuzzy-PID logic but there is other latest control and tuning
method of artificial intelligent like artificial neural network, Adaptive Neuro-Fuzzy,
particle swarm optimization in addition to fuzzy controller.
The performance comparison of designed PMSM motor Quet- Bajaj is compared
with existing benzene based Quet- Bajaj.
Acknowledgement: This research thesis was founded by Adama Science and Technology
University under the grant number of ASTU/SM-R/075/19, Adama, Ethiopia
89
References
[1] J. W. Jung, V.Q. Leu, T.D. Do, E.K. Kim, H. H. Choi, “Adaptive PID Speed Control
Design for Permanent Magnet Synchronous Motor Drives,” IEEE Transactions on
Power, vol. 30, no. 2, 2015.
[2] X. Zhang, L. Sun, K. Zhao, L. Sun, “Nonlinear speed control for PMSM system using
sliding-mode control and disturbance compensation techniques,” IEEE Transactions
on Power Electron, vol. 28, no. 3, p. 1358–1365, Mar. 2013.
[3] M. Sekour, K. Hartani, A. Draou, and A. Allali, “Sensor less fuzzy direct torque control
for high performance electric vehicle with four in-wheel motors,” J. Electr. Eng.
Technol, vol. 8, no. 3, p. 530–543, May 2013.
[4] T. Fei, M. Yunfei, J. Hongjie, E.al, “Challenges on primary frequency control and
potential solution from EVs in the future electricity system,” Appl Energy, vol. 62, no.
4, pp. 194-353, 2017.
[5] Etal, A. Tashakori, “Direct Torque controlled Drive Train for Electric Vehicle,”
Proceedings of the world congress on Engineering, vol. 2, p. 1, July 2012.
[6] R. Krishnan, “Permanent Magnet Synchronous and Brushless DC Motor Drives,” in
Electrical and Computer Engineering Department, Virginia Tech Blacksburg,
Virginia, U.S.A, 2010.
[7] R. Krishnan, Electric Motor Drives Modeling Analysis and Control, U.S.A: Virginia
Tech Blacksburg: CRC Press Taylor & Francis Group, 2001.
[8] S.Sakunthala, R.Kiranmayi, P.Nagaraju Mandadi, “Investigation of PI and Fuzzy
Controllers for Speed Control of PMSM Motor Drive,” International Conference on
Recent Trends in Electrical, Control and Communication, pp. 133-136, 2018.
90
[9] M.Umabharathi, S.Vijayabaskar, “Speed control of Permanent Magnet Synchronies
Motor Using Evolutionary Fuzzy PID Controller,” World Academy of science,
Engineering and Technology, International Journal of Electrical and Information
Engineering , vol. 9, no. 12, pp. 1485- 1491, 2015.
[10] Bhagyashree Shikkewal, Vaishali Nandanwar, “Fuzzy Logic Controller for PMSM,”
International Journal of Electrical and Electronics Engineering , vol. 1, no. 3, pp. 73-
78, 2012.
[11] B. Basnet, “DSP Based Implementation of Field Oriented Control for Induction Motor
Drives,” International Journal of Innovations in Engineering and Technology (IJIET),
vol. 8, no. 2, pp. 65- 69, April 2017.
[12] R.K. Pongiannan, N. Yadaiah, “FPGA Based Three Phase Sinusoidal PWM VVVF
Controller,” International Conference on electrical Energy System, pp. 34-39 , 2011.
[13] Hardik Shahane, Shekhar Onkarkar, Prashik Khandekar, Zalendra Bhagat, Resham
Tondare, “Review of Different PWM Techniques,” International Journal of
Engineering Research in Electrical and Electronic Engineering, vol. 4, no. 3, pp. 206
-208, March 2018. .
[14] R. Kameswara Rao, P. Srinivas, M.V. Suresh Kumar, “Design and Analysis of Various
Inverters Using Different PWM Techniques,” The International Journal Of
Engineering And Science, pp. 41-51, 2014 .
[15] H. Quan, Z.Gang, C.Jie, Z.Wu, Z. Liu, “Study of A Novel Over-modulation Technique
Based on SVPWM,” in 2011 International Conference on Computer Distributed
Control and Intelligent Environmental Monitoring, Beijing, China, 2011.
[16] Keliang Zhou, Danwei Wang, “Relationship Between Space- Vector Modulation and
Three PHase Carrier Based PWM :Comprehensive Analysis,” IEEE TRANSACTIONS
ON INDUSTRIAL ELECTRONICS, vol. 49, no. 1, pp. 186- 196, 2012.
[17] Sandeep Kumar Singh, Harish Kumar, Kamal Singh, Amit Patel, “A Survey and Study
of Different Types of PWM Techniques Used In Induction Motor Drive,” [IJESAT]
91
[International Journal of Engineering Science & Advanced Technology], vol. 4, no. 1,
pp. 18- 22, Feb 2014.
[18] Preeti Soni, Kavita Burse, “Analysis of Voltage Source Inverters using Space Vector
PWM for Induction Motor Drive,” IOSR Journal of Electrical and Electronics
Engineering (IOSR-JEEE), vol. 2, no. 6, pp. 14-19, Sep-Oct. 2012.
[19] K. Vinoth Kumar, Prawin Angel Michael, Joseph P. John and Dr. S. Suresh Kumar,
“Simulation and Comparision of SPWMand SVPWM Control for Three phase
Inverter,” ARPN Journal of Engineering and Applied Sciences, vol. 5, no. 7, pp. 61-
74, JULY 2010.
[20] Mounir Zeraoulia, Mohamed El Hachemi Benbouzid, Demba Diallo, “Electric Motor
Drive Selection Issues for HEV Propulsion Systems: A Comparative Study,” IEEE
Transactions On Vehicular Technology, vol. 55, no. 6, pp. 1756- 1764, November
2006.
[21] C.C.Chan, “The state of the art of electric and hybrid vehicles,” Proceedings of the
IEEE, vol. 90, no. 2, pp. 247-275, February 2012.
[22] G. D. et, “Motor control law and comfort law in the Peugeot and Citroen electric
vehicles driven by a dc commutator motor,” IEEE Power Electronics and Variable
Speed Drives Conference, pp. 370-374, September 21-23, 1998.
[23] J.B.Gupta, Theory and Performance of Electrical Machines, S.K.Kataria and sons ,
2014.
[24] X. D. Xue, K. W. E. Cheng, and N. C. Cheung, “Selection of Electric Motor Drives
for Electric Vehicle,” in Australasian Universities Power Engineering Conference,
Australasian , June 30, 2012.
[25] M.V.Ramesh, J.Amarnath, S.Kamakshaiah, B.Jawaharlal, Gorantla.S.Rao, “Speed
Torque characteristics of Brushless DC motor in either direction on load using ARM
controller,” Journal of Energy Technologies and Policy, vol. 2, no. 1, pp. 31- 48, 2011.
92
[26] D. van Niekerk, M. Case, D.V. Nicolae, “Brushless Direct Current Motor Efficiency
Characterization,” IEEE, pp. 226- 231, 2015.
[27] Ansh Thattil, Sumit Vachhani, Darshan Raval, Piyush Patel, Priyanka Sharma,
“Comparative Study of using Different Electric Motors for EV,” International
Research Journal of Engineering and Technology (IRJET), vol. 6, no. 4, pp. 4601-
4604, Apr 2019.
[28] Cheng He, Chen Hao, Wang Qianlong, Xu Shaohui, Yang Shunyao, “Design and
Control of Switched Reluctance Motor Drive for Electric Vehicles,” in in 14th
International Conference on Control, Automation, Robotics & Vision Phuket,
Thailand, 13-15th November 2016.
[29] Masayuki Terashima, Tadashi Ashikaga,Takayuki Mizuno, Kazuo Natori, Noboru
Fujiwara, Masayuki Yada, “Novel motors and controllers for high- performance
electric vehicle with four in-wheel motors,” IEEE Trans Industrial Electronics, vol.
44, no. 1, pp. 28-38, February 2007.
[30] P.Ramesh, RachaPrathyusha, “Field Oriented Control of Permanent Magnet
Synchronous Motor,” International Journal of Computer Science and Mobile
Computing, vol. 3, no. 3, pp. 269-275, March- 2014.
[31] P. Jussi, “Induction Motor Versus Permanent Magnet Synchronous Motor In Motion
Control Applications,” in Lappeenranta University of Technology, Finland, December,
2006.
[32] G. Luthra, “Comparison Of Characteristics Of Various Motor Drives Currently Used
In Electric Vehicle Propulsion System,” International Journal of Mechanical And
Production Engineering, vol. 5, no. 6, pp. 38- 41, Jun-2017.
[33] ian Zhao,Yangwei Yu, Brushless DC Motor Fundamentals Application Note, MPS
Proprietary Information, July 2011.
[34] Merve YILDIRIM, Mehmet POLAT, Hasan KÜRÜM, “A survey on comparison of
electric motor types and drives used for electric vehicles,” in 16th International Power
93
Electronics and Motion Control Conference and Exposition, Antalya, Turkey, 21-24
Sept 2014.
[35] Wenping Cao, Abid Ali Shah Bukhari, Lassi Aarniovuori, “Review of Electrical Motor
Drives for Electric Vehicle Applications,” Mehran University Research Journal of
Engineering & Technology, vol. 38, no. 3, pp. 525-540, July 2019.
[36] M. Karamuk, “A Survey on Electric Vehicle Power Train System,” Electro motion,
Istanbul, pp. 315- 324, Septemper 2011.
[37] Q. Guo, C. Zhang, L. Li, D. Gerada, J. Zhang, M. Wang,, “Design and implementation
of a loss optimization control for electric vehicle in-wheel permanent-magnet
synchronous motor direct drive system,” Applied Energy, p. 1317–1332, 2017.
[38] S.Sakunthala, R.Kiranmayi, P.Nagaraju Mandadi, “A Study on Industrial Motor
Drives : Comparison and Applications of PMSM and BLDC Motor Drives,” IEEE,
International Conference on Energy, Communication, Data Analytics and Soft
Computing, pp. 86- 89, 2017.
[39] Bhim Singh, Sanjeev Singh, “State of the Art on Permanent Magnet Brushless DC
Motor Drives,” Journal of Power Electronics, vol. 9, no. 1, pp. 1- 17, January 2009.
[40] Ambarisha Mishra, Pramod Agarwal, S.P. Srivastava, “A comprehensive analysis and
implementation of vector control of permanent magnet synchronous motor,” Int. J.
Power and Energy Conversion, vol. 5, no. 1, pp. 1- 24, 2014.
[41] Marcy Lowe, Etal, Lithium-ion Batteries for Electric Vehicles, the U.S. Value Chain,
2010.
[42] Abuelsamid, Sam, “general-motors-talks-about-battery-development,” 14 03 2015.
[Online]. Available: https://www.autoblog.com. [Accessed 13 04 2020].
[43] P. Bimbra, Electric Machinery. 7th ed, India: Khanna Publishers, 2011.
94
[44] Yeshwant Joshi, Kapil Parikh, Vinod Kumar Yadav, “Field Oriented Control of
PMSM Using Improved Space Vector Modulation Technique,” International Journal
of Digital Application & Contemporary research, vol. 2, no. 8, March 2014.
[45] L. Yong, “Vector Control of Permanent Magnet Synchronous Motor for Fan of New
Energy Vehicle,” International Journal of Innovative Science, Engineering &
Technology, vol. 4, no. 2, pp. 302- 314, February 2017.
[46] Kiran Boby, Acy M Kottalil, N.P.Ananthamoorthy, “Simulation of PMSM Vector
Control System with Fuzzy Self-Adjusting PID Controller Using MATLAB,”
International Journal of Scientific and Research Publications, vol. 3, no. 3, pp. 1- 4,
March 2013.
[47] Iulian M.T. BIROU, Calin C. RUSU, Sorin Gh. PAVEL, Virgil MAIER, “Real-Time
Robust Controlled Driving System with Permanent-Magnet Synchronous Motor,” in
International Conference and Exposition on Electrical and Power Engineering, Iasi,
Romania, 16-18 October 2014.
[48] Pewmaikam C, Srisertpol J, and Khajorntraidet C, “Adaptive Fuzzy Logic
compensator for PMSM Torque control system,” International Journal of modelling
and optimization, vol. 2, no. 2, pp. 141- 146, April 2012.
[49] Vishnu Mahesh, Sreelekha, “Speed Control of PMSM Drive Using Adaptive Fuzzy
Logic Controller,” International Journal of Innovative Research in Electrical,
Electronics, Instrumentation and Control Engineering, vol. 1, no. 2, pp. 156- 160,
March 2018.
[50] Ananthamoorthy NP, Baskaran K, “Speed and torque control of permanent magnet
synchronous motor using hybrid fuzzy proportional plus integral controller,” Journal
of Vibration and Control, vol. 21, no. 3, p. 563–579, 2015.
[51] T. T. Liu, Z. G. Yan, K. Chen,S. G. Li, “Fuzzy-PI Control Strategy for PMSM Used
in Electric Vehicles,” Journal of Mechanical Engineering Research and
Developments, vol. 39, no. 3, pp. 763-771, 2016.
95
[52] Chandana Jayampathi Gajanayake, Bicky Bhangu, Sivakumar Nadarajan, Gamini
Jayasinghe, “Fault Tolerant Control Method to Improve the Torque and Speed
Response in PMSM Drive with Winding Faults,” in IEEE PEDS 2011, Singapore, 5 -
8 December 2011.
[53] Christian Joezer Meirinho, Arthur Bartsch, Jose de Oliveira ,Mariana Santos Matos
Cavalca, “An Optimal MIMO Control Approach for PMSM Drives,” in University of
Santa Catarina State, Joinville, Brazil, 2017.
[54] Wenyi Liang, Jianfeng Wang, Patrick Chi-Kwong Luk, Weizhong Fang, Weizhong
Fei, “Analytical Modeling of Current Harmonic Components in PMSM Drive With
Voltage-Source Inverter by SVPWM Technique,” IEEE Transactions On Energy
Conversion, pp. 1- 8, 2014.
[55] Meiling Tang, Shengxian Zhuang, “On Speed Control of a Permanent Magnet
Synchronous Motor with Current Predictive Compensation,”
www.mdpi.com/journal/energies, pp. 1- 15, 26 December 2018.
[56] Weiran Wang, Fei Tan, Jiaxin Wu, Huilin Ge, Haifeng Wei, Yi Zhang, “Adaptive
Integral Backstepping Controller for PMSM with AWPSO Parameters Optimization,”
www.mdpi.com/journal/energies, pp. 1- 24, 5 July 2019.
[57] Rajesh P. Nathwani, Hitesh M. Karkar, “Vector Control of PM Synchronous Motor
Drive System Using Hysteresis Current Controller,” International Journal of
Engineering Development and Research, vol. 2, no. 2, pp. 1610- 1616, 2014.
[58] Kaushik Jash, Pradip Kumar Saha, Goutam Kumar Panda, “Vector Control of
Permanent Magnet Synchronous Motor Based On Sinusoidal Pulse Width Modulated
Inverter with Proportional Integral Controller,” Journal of Engineering Research and
Applications, vol. 3, no. 5, pp. 913- 917, Sep-Oct 2013.
[59] Ahmad Asri, Abd Samat, N. Fazli, N.A. Salim,Abdul Malek Saidina Omar,
Muhammad Khusairi Osman , “Speed Control Design of Permanent Magnet
Synchronous Motor using Takagi Sugeno Fuzzy Logic Control,” Journal of Electrical
System, vol. 13, no. 4, pp. 689- 695, 2017.
96
[60] Tingting Liu, Guojin Chen, Shigang Li, “Application of Vector Control Technology
for PMSM Used in Electric Vehicles,” The Open Automation and Control Systems
Journal, vol. 6, pp. 1334-1341, 2014.
[61] Li Yu, Chunyang Wang, Hongwei Shi, Ruihao Xin, Lingxin Wang, “Simulation of
PMSM Field-Oriented Control Based on SVPWM,” in 29th Chinese Control And
Decision Conference, China, 2017.
[62] Gajanan Rathod, A. G. Thosar, Dhote.V.P, Rakesh Zalke, “PM Synchronous Motor
Drive for Electric Vehicles By Using an Adaptive Controller,” in Proceedings of 2018
ICETIETR, India, 2018.
[63] Seifedine, Kadry, “Learning Basic Mathematics Using MATLAB,” International
Journal of Information Technology and Management, 2014.
[64] Swaraj Ravindra Jape, Archana thosar, “Comparison of electrical motor for electric
vehicle application,” International Journal of Research in Engineering and
Technology, vol. 6, no. 9, pp. 3- 5, 2017.
[65] Mehrdad Ehsani, Yimin Gao, Sebastien E. Gay, Ali Emadi, Modern Electric, Hybrid
Electric, and Fuel Cell Vehicles Fundamentals, Theory, and Design, United States of
America : CRC PRESS, 2005.
[66] T.Porselvi, Srihariharan .M. K, Ashok.J, Ajith Kumar.S, “Selection of Power Rating
of an Electric Motor for Electric Vehicles,” International Journal of Engineering
Science and Computing, vol. 7, no. 4, pp. 6469- 6472, 2017.
[67] S. Chauhan, “Motor Torque Calculations For Electric Vehicle,” International Journal
Of Scientific & Technology Research, vol. 4, no. 8, pp. 126-127, August 2015.
[68] Sinan Ünsal, İbrahim Alişkan, “Investigation of Speed Control Performances of The
Fuzzy Logic Controllers Having Different Membership Functions and Inference
Methods,” Anadolu University Journal of Science and Technology A- Applied Sciences
and Engineering, vol. 18, no. 4, pp. 831-841, 15 August 2017.
97
[69] E. Simon, “Implementation of a Speed Field Oriented Control of 3-phase PMSM
Motor using TMS320F240,” Texas Instruments Application Report, Texas, 2010.
[70] Wengliang Liu, Pengfei Xu, “Design of PMSM Speed Control system based on
simulink Model,” in IOP Conf. Series: Materials Science and Engineering, China,
2019.
[71] Y.V.P. Karteek1, N. Prema Kumar, “Transfer Function Model Based Analysis of
Permanent Magnet Synchronous Motor with Controllers,” International Journal of
Innovative Research in Electrical, Electronics, Instrumentation and Control
Engineering, vol. 4, no. 11, pp. 8- 14, November 2016.
[72] E.Prasad, B.Suresh, K.Raghuveer, “Field Oriented Control of PMSM Using SVPWM
Technique,” Global Journal of Advanced Engineering Technologies, vol. 11, no. 2, pp.
39- 45, 2012.
[73] Gentao Dong, Jianfei Yang, Xin Qiu , Xun Liu, Cao Wei, “Space Vector Flux
Weakening Control of PMSM Drivers,” in 2018 2nd International Conference on
Power and Energy Engineering , China, 2018.
[74] T. J. Ross, Fuzzy Logic with Engineering Applications, University of New Mexico,
USA: John Wiley & sons, Ltd, 2010.
[75] Praveen Kumar, Anurag Singh Tomer, “Modeling & Simulation of PMSM Drives with
Fuzzy Logic Controller,” International Journal of Modern Engineering Research, vol.
3, no. 4, pp. 2492-2497, Jul - Aug. 2013 .
[76] A. Salam Waley, Chengxiong Mao, C. Dan Wang, “Artificial Optimal Fuzzy Control
Strategy for Electric Vehicle Drive System by Using Permanent Magnet Synchronous
Motor,” International Journal of Engineering and Technology, vol. 9, no. 1, pp. 50-
57, February 2017.
[77] Salam Waley Shneen, Hussien Hadi Kareem, Hassan Ali Abdulmajeed, “Fuzzy-PI
Control for Speed of PMSM Drive System,” Journal of Scientific and Engineering
Research, pp. 31- 35, 2019.
98
[78] Ali Rohan, Furqan Asghar, Sung Ho Kim, “Design of Fuzzy Logic Tuned PID
Controller for Electric Vehicle based on IPMSM Using Flux-weakening,” Jouranal of
Electrical Engineering Technology, pp. 451- 459, 2018.
99
Reference link:
[L1] Reference link for Figure 2.2, Figure 2.3, Figure 2.4, Figure 2.5, Figure 2.6 (accessed
on January 23 to February 29).
1. https://www.researchgate.net/figure/Torque-speed-characteristics-during-constant-
torque-and-constant-power-regions_fig1_319611796
2. https://www.quora.com/Why-do-electric-engines-have-a-wider-torque-range
3. https://www.researchgate.net/figure/Torque-speed-envelope-of-a-BLDC-
Motor_fig17_322116711
4. https://www.researchgate.net/figure/Classical-torque-speed-characteristics-of
SRM_fig1_304012280
[L2] Reference link for material datasheet used in this thesis (accessed on January 23 to
march 15)
1. https://circuitdigest.com/article/different-types-of-motors-used-in-electric-vehicles
2. https://www.electriccarsandbikes.com/different-types-of-motors-in-electric-
vehicles/
3. http://www.validyne.com/blog/application-note-basics-of-air-velocity-pressure-
and-flow/
4. https://www.embitel.com/blog/embedded-blog/brushless-dc-motor-vs-pmsm-how-
these-motors-and-motor-control-solutions-work
5. https://unidrivingsystem.en.alibaba.com/product/60856014476-
807811033/10kW_PMSM_Motor_Driving_Kit_for_Electric_Vehicle.html?fullFirs
tScreen=true
6. https://www.cardekho.com/bajaj/re60/specs#leadForm
7. https://autoportal.com/newcars/bajaj/re60/specifications/
8. https://www.bajajauto.com/bajajqute/technology-specs.aspx#Dimensions
9. https://www.globalbajaj.com/global/english/brands/intracity/qute/specifications/
[L3] Reference link for different formulas used in this thesis (accessed on May 23)
1. https://www.engineeringtoolbox.com/electrical-motors-hp-torque-rpm-d_1503.html
2. https://www.quora.com/How-can-we-calculate-required-torque-on-wheels-to-
move-a-vehicle-from-rest-so-that-we-can-reverse-calculate-the-torque-of-motor-
that-should-be-installed-on-vehicle
3. https://www.mrright.in/ideas/appliances/inverter/how-to-choose-the-right-inverter
100
Appendix A: MATLAB code for analysing Figure
MATLAB code for analysis of Aerodynamic force Vs speed of car in Km/hr (Figure
3.5)
adnsty=1.23; %Kd/m3
Af=1.56; %area in m2
Vo=0; %air velocity in m/s
Cw=0.25; %Aerodynamics drag coefficient
Vkph=0;
d_Vkph=1e-2; %unit step increment
Vkph_final=80; %final value in km/hr
x=1;
n=1;
while (Vkph<Vkph_final),
vmps=Vkph*(1000/3600);
FA=0.5*adnsty*Cw*Af*(vmps+Vo)^2;
if Vkph<=50*d_Vkph;
statfric=0.1;
else
statfric=0;
end
Vkph=Vkph+d_Vkph
if x>16,
FAn(n)=FA;
Vkphn(n)=Vkph;
n=n+1;
x=1;
101
end
x=x+1;
end
figure(1);
plot(Vkphn,FAn,'K')
axis([0 80 0 100]);
grid
xlabel('speed of the car in Km/hr')
ylabel('Aerodynamic force(N)')
MATLAB code for analysis of motive force Vs approaching angle of the vehicle
(Figure 3.6)
m=700; %friction coefficient
g=9.81; %gravitational acceleration
a=0.5; %acceleration (m/sec)
r=0.2; %radius of the wheel in meter
k_friction = 0.01; %coafficinet of friction by considering the asphalt road
f_tot=0;
vkph=70; % speed of the rotor in km/hr
tot_effcen.m=0.98; %efficincy
adnsty=1.2; %kd/m3
af=1.56; %frontal area of the car (m2)
vo=0; %air velocity in m/s
cw=0.25; %Aerodynamics drag coefficient
apangle =0;
apangle1=20;
102
d_apangle=1e-2; %unit step increment
apangle_final=20; %final value in degree
x=1; n=1;
while (apangle<apangle_final);
vmps=vkph*(1000/3600);
theta=apangle *(2*pi/360);
Fa=0.5*adnsty*cw*af*(vmps+vo)^2;
if apangle<=100*d_apangle;
statfic=0.001;
else
statfic=0
end
Frolling=m*g*(k_friction+statfic)*cos(theta);
Fgradient=m*g*sin(theta);
F_tot=Frolling+Fgradient+Fa+m*a;
apangle=apangle+d_apangle;
if x >16,
F_totn(n)=F_tot;
Frollingn(n)=Frolling;
Fgradientn(n)=Fgradient;
F_an(n)=Fa;
apanglen(n)=apangle;
n=n+1;
x=1;
end
x=x+1;
103
end
figure(1);
plot(apanglen,F_totn,'k',apanglen,Fgradientn,'b--', apanglen,Frollingn,'k:',apanglen,F_an,'r')
axis([0 20 0 2500]);
grid
xlabel('Approaching angle')
ylabel('motive force(N)')
MATLAB code for analysis of motive force Vs speed of car in Km/hr (Figure 3.7)
m=700; %friction coefficient
fric=0.01;
g=9.81; %gravitational acceleration
a=0.5; %acceleration (m/sec)
r=0.2; %radius of the wheel in meter
k_friction = 0.01; %coafficinet of friction by considering the asphalt road
f_tot=0;
vkph=70; % speed of the rotor in km/hr
Tot_effcen.M=0.98;
adnsty=1.2; %Kd/m3
Af=1.56; %area in m2
Vo=0; %air velocity in m/s
Cw=0.25; %Aerodynamics drag coefficient
apangle=0;
Vkph=0;
Vkph1=0;
d_Vkph=1e-2; %unit step increment
104
Vkph_final=70; %final value in km/hr
x=1;
n=1;
while (Vkph<Vkph_final),
vmps=Vkph*(1000/3600);
theta=apangle*(2*pi/360);
FA=0.5*adnsty*Cw*Af*(vmps+Vo)^2;
if Vkph<=50*d_Vkph;
statfric=0.1;
else
statfric=0;
end
Fac=m*a;
Frolling=m*g*(k_friction+statfric)*cos(theta);
Fgradient=m*g*sin(theta);
F_tot=Frolling+Fgradient+FA+Fac; %Total force (Nm)
Vkph=Vkph+d_Vkph
Vkph1=Vkph1+d_Vkph;
if x>16,
F_totn(n)=F_tot;
Fgradientn(n)=Fgradient;
Frollingn(n)=Frolling; %power in KW
FAn(n)=FA;
Facn(n)=Fac;
Vkphn(n)=Vkph;
n=n+1;
105
x=1;
end
x=x+1;
end
figure(1);
plot(Vkphn,F_totn,'K',Vkphn,Fgradientn,'K',Vkphn,Frollingn,'K:',Vkphn,FAn,'r',Vkphn,Fa
cn,'r--')
axis([0 70 0 1000]);
grid
xlabel('speed of the car in Kmp')
ylabel('motive force(N)')
MATLAB code for analysis of power conception Vs approaching angle (Figure 3.8)
m=700;
g=9.81; %gravitational acceleration
a=0.5; %acceleration (m/sec)
r=0.2; %radius of the wheel in meter
k_friction = 0.01; %coafficinet of friction by considering the asphalt road
f_tot=0;
vkph=25; % speed of the rotor in km/hr
tot_effcen.m=0.98; %efficincy
adnsty=1.2; %kd/m3
af=1.56; %frontal area of the car (m2)
vo=0; %air velocity in m/s
cw=0.25; %Aerodynamics drag coefficient
apangle =0;
106
apangle1=20;
d_apangle=1e-2; %unit step increment
apangle_final=20; %final value in degree
x=1;
n=1;
while (apangle<apangle_final);
vmps=vkph*(1000/3600);
theta=apangle *(2*pi/360);
Fa=0.5*adnsty*cw*af*(vmps+vo)^2;
if apangle<=100*d_apangle;
statfic=0.001;
else
statfic=0;
end
Frolling=m*g*(k_friction+statfic)*cos(theta);
Fgradient=m*g*sin(theta);
F_tot=Frolling+Fgradient+Fa;
Power=F_tot*vmps;
apangle=apangle+d_apangle;
if x >16,
Powern(n)=Power/1000;
apanglen(n)=apangle;
n=n+1;
x=1;
end
x=x+1;
107
end
figure(1);
plot(apanglen,Powern,'k')
axis([0 20 0 14]);
grid
xlabel('Approaching angle')
ylabel('power(Kw)')
MATLAB code for analysis of power conception Vs speed of car in Km/hr (Figure
3.9)
m=700;
g=9.81; %gravitational acceleration
a=0.5; acceleration (m/sec)
R=0.2;%radius of the wheel in meter
K_friction=0.01; %coefficient of friction by considering the asphalt road
F_tot=0;
adnst=1.2; %Kd/m3
Af=1.56; %area in m2
vo=0; %air velocity in m/s
Cw=0.25; %Aerodynamics drag coefficient
Vkph=0;
Vkph1=0;
d_Vkph=1e-2; %unit step increment
Vkph_final=80; %final value in km/hr.
x=1;
n=1;
108
while(Vkph<Vkph_final);
Vmps=Vkph*(1000/3600);
fadyna=0.5*adnst*Cw*Af*(Vmps+vo)^2;
if Vkph<=100*d_Vkph;
statfric=0;
else
statfric=0;
end
F_tot=m*g*(K_friction+statfric)+fadyna+m*a;%total forse(Nm)
Power=F_tot*Vmps/0.95;%required input power(Waat)
Vkph=Vkph+d_Vkph;
Vkph1=Vkph1+d_Vkph;
if x>16,
Powern(n)=Power/1000;%power in KW
Vkphn(n)=Vkph;
n=n+1;
x=1;
end
x=x+1;
end
figure(1);
plot(Vkphn,Powern,'r');
axis([0 80 0 14]);
grid
xlabel('Speed of the of the car Km/hr)')
ylabel('power (KW)')
109
MATLAB code for analysis of torque developed by motor Vs speed of car in Km/hr
(Figure 3.10)
m=700;
g=9.81;
a=0.5;
R=0.2; %radius of the wheel in meter
K_friction=0.01; %coefficinet of friction by considering the asphalt road
F_tot=0;
adnst=1.2; %Kd/m3
Af=1.56; %area in m2
vo=0; %air velocity in m/s
Cw=0.25; %initial condition
Vkph=0;
Vkph1=0;
d_Vkph=1e-2;%unit step increment
Vkph_final=80;%final value in km/hr.
omega=209.33;
x=1;
n=1;
while(Vkph<Vkph_final);
Vmps=Vkph*(1000/3600);
fadyna=0.5*adnst*Cw*Af*(Vmps+vo)^2;
if Vkph<=100*d_Vkph;
statfric=0;
91
else
statfric=0;
110
end
F_tot=m*g*(K_friction+statfric)+fadyna+m*a;%total forse(Nm)
Power=F_tot*Vmps/0.98;%required input power(Waat)
Torque=Power/omega;
Vkph=Vkph+d_Vkph;
Vkph1=Vkph1+d_Vkph;
if x>16,
torquen(n)=Torque;
Vkphn(n)=Vkph;
n=n+1;
x=1;
end
x=x+1;
end
figure(1);
plot(Vkphn,torquen,'b');
axis([0 80 0 60]);
grid
xlabel('Speed of the of the car Km/hr)')
ylabel('Torque developed by motor(NM)')
111
Appendix B: MATLAB Simulink model for mathematical model of PMSM
Figure A1: MATLAB Simulink model for mathematical model of PMSM
Figure A2: MATLAB Simulink subsystem model for qdr2abc
Figure A3: MATLAB Simulink subsystem model for Inverter
112
Figure A4: MATLAB Simulink subsystem model for phase voltage formation
Figure A5: MATLAB Simulink subsystem model for subsystem1
113
Figure A6: MATLAB Simulink subsystem model for PARK transform
Figure A7: MATLAB Simulink subsystem model for mathematical model of PMSM
Figure A8: MATLAB Simulink subsystem model for qdr2abc
114
Appendix C: MATLAB Simulink model of PMSM
Figure A9: MATLAB Simulink modelling of PMSM
Figure A10: The SVPWM sub system in Figure A9
Figure A11: MATLAB Simulink subsystem model for CLARK transformation (abc2αβ)
115
Figure A12: MATLAB Simulink subsystem model for sector judgment
Figure A13: MATLAB Simulink subsystem model for calculating X, Y, Z
Figure A14: MATLAB Simulink subsystem model for calculating operating time of the
fundamental vector
116
Figure A15: MATLAB Simulink subsystem model for inverter switch operating time
Figure A16: MATLAB Simulink subsystem model for generating SVPWM
117
Appendix D: Data sheet and characteristic selected component used in thesis
Table Al: Absolute maximum electrical ratings of STGW39NC60VD IGBTs
Symbol Parameter Value Unit
VCES Collector-emitter voltage (VGE = 0) 600 V
IC (1) Collector current (continuous) at 25 °C 60 A
IC (1) Collector current (continuous) at 100 °C 30 A
ICL (2) Turn-off latching current 220 A
ICP (3) Pulsed collector current 220 A
IF Diode RMS forward current at 25 °C 30 A
IFSM Surge non repetitive forward current
(tp=10 ms sinusoidal) 120 A
VGE Gate-emitter voltage ± 20 V
PTOT Total dissipation at TC = 25 °C 190 W
Tj Operating junction temperature – 55 to 150 °C
The typical output characteristics of STGW39NC60VD IGBTs
Figure A17: Output characteristics and Transfer characteristics of
118
Figure A18: Collector-emitter on voltage vs collector current
Table A2: Quet Bajaj specification used in this thesis [L2]
Parameter Symbol Value
Maximum Power P 10 𝐾𝑤
Length L 2752mm
Width W 1312 mm
Height H 1652 mm
Wheel base B 1925 mm
Wheel Track T 1143 mm
Vehicle mass m 700 𝐾𝑔
Air density ρ 1.23 𝐾𝑔/𝑚3
Frontal area A 1.5 𝑚2
Aerodynamic drag coefficient 𝐶𝑑 0.25
Tyre radius R 0.2 𝑚
Maximum Speed V 70 Kmℎ𝑟⁄
119
Table A3: PMSM motor specification for EV [L2]
Name:10kW PMSM Motor Driving Kit for Electric Vehicle
Model Number:10kw PMSM Motor
Type: Synchronous Motor
Application: Electric Car Vehicle or Boat
Parameter Symbol Value
Phase Φ Three-phase
pole p 4
Frequency f 50 Hz
Voltage V 400 V
Rated Power P 10kW
Max. Power Pmax 22kW
Rated Torque T 53 Nm
Max. Torque Tmax 140 Nm
Rated Speed RPM 2000 r/min
Max. Speed RPM 8000 r/min