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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Name of Student

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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

VIII

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

XII

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⁄

XVI

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

5

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.

https://circuitdigest.com/power-electronics

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.

https://en.wikipedia.org/wiki/Semiconductor

https://en.wikipedia.org/wiki/Servo_system

https://en.wikipedia.org/wiki/Servo_system

https://en.wikipedia.org/wiki/Bearing_(mechanical)

https://en.wikipedia.org/wiki/Armature_(electrical_engineering)

https://en.wikipedia.org/wiki/Commutator_(electric)

https://en.wikipedia.org/wiki/Watt

https://en.wikipedia.org/wiki/Brush_(electric)

https://en.wikipedia.org/wiki/Electromagnetic_interference

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

https://en.m.wikipedia.org/wiki/Electric_motor

https://en.m.wikipedia.org/wiki/Magnet

https://en.m.wikipedia.org/wiki/Magnet

https://en.m.wikipedia.org/wiki/Magnetic_field

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.

https://circuitdigest.com/article/all-you-want-to-know-about-electric-vehicle-batteries

https://circuitdigest.com/power-electronics

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)


𝑉𝑑𝑐(sin(

𝑛

3𝜋 − 𝛼)) (3.52)


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.

71

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 4-5 shows the pulse generated from direvier circuit based on SVPWM for IGBT 5

and IGBT 2 of third leg.


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

72

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.

73

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.

75

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.

84

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


87.9 deg @ 20.5


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

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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

https://www.researchgate.net/figure/Torque-speed-characteristics-during-constant-%20%20%20%20torque-and-constant-power-regions_fig1_319611796

https://www.researchgate.net/figure/Torque-speed-characteristics-during-constant-%20%20%20%20torque-and-constant-power-regions_fig1_319611796

https://www.quora.com/Why-do-electric-engines-have-a-wider-torque-range

https://www.researchgate.net/figure/Torque-speed-envelope-of-a-BLDC-%20Motor_fig17_322116711

https://www.researchgate.net/figure/Torque-speed-envelope-of-a-BLDC-%20Motor_fig17_322116711

https://www.researchgate.net/figure/Classical-torque-speed-characteristics-of%20SRM_fig1_304012280

https://www.researchgate.net/figure/Classical-torque-speed-characteristics-of%20SRM_fig1_304012280

https://circuitdigest.com/article/different-types-of-motors-used-in-electric-vehicles

https://www.electriccarsandbikes.com/different-types-of-motors-in-electric-vehicles/

https://www.electriccarsandbikes.com/different-types-of-motors-in-electric-vehicles/

http://www.validyne.com/blog/application-note-basics-of-air-velocity-pressure-and-flow/

http://www.validyne.com/blog/application-note-basics-of-air-velocity-pressure-and-flow/

https://www.embitel.com/blog/embedded-blog/brushless-dc-motor-vs-pmsm-how-these-motors-and-motor-control-solutions-work

https://www.embitel.com/blog/embedded-blog/brushless-dc-motor-vs-pmsm-how-these-motors-and-motor-control-solutions-work

https://unidrivingsystem.en.alibaba.com/product/60856014476-807811033/10kW_PMSM_Motor_Driving_Kit_for_Electric_Vehicle.html?fullFirstScreen=true



https://www.cardekho.com/bajaj/re60/specs#leadForm

https://autoportal.com/newcars/bajaj/re60/specifications/

https://www.bajajauto.com/bajajqute/technology-specs.aspx#Dimensions

https://www.globalbajaj.com/global/english/brands/intracity/qute/specifications/

https://www.engineeringtoolbox.com/electrical-motors-hp-torque-rpm-d_1503.html

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



https://www.mrright.in/ideas/appliances/inverter/how-to-choose-the-right-inverter-battery-for-your-home/

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;





f_tot=0;


Tot_effcen.M=0.98;

adnsty=1.2; %Kd/m3


Vo=0; %air velocity in m/s


apangle=0;

Vkph=0;

Vkph1=0;


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);


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;





f_tot=0;


tot_effcen.m=0.98; %efficincy

adnsty=1.2; %kd/m3

af=1.56; %frontal area of the car (m2)


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);


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;


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




Vkph=0;

Vkph1=0;


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



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]


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


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

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