I

MASTER OF SCIENCE IN ELECTRICAL AND ELECTRONIC ENGINEERING

PERFORMANCE IMPROVEMENT OF DC ELECTRIC TRACTION MOTORS USING

A NOVEL SWITCHING TECHNIQUE

S.M.FERDOUS

DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING ISLAMIC UNIVERSITY OF TECHNOLOGY (IUT)

GAZIPUR-1704, BANGLADESH OCTOBER, 2012

II

CERTIFICATION OF APPROVAL The thesis titled “Performance Improvement of DC Electric Traction Motors using a Novel Switching Technique” submitted by S.M.Ferdous, student no. 092606 of Academic Year 2009-2010 has been found as satisfactory and accepted as partial fulfillment of the requirement for the Degree of Masters of Science in Electrical and Electronic Engineering on 01 October, 2012. Board of Examiners

1. ………………………….. Dr. Md. Ashraful Hoque Chairman Professor (Supervisor) Department of Electrical and Electronic Engineering. Islamic University of Technology (IUT) Board Bazar, Gazipur-1704, Bangladesh.

2. ………………................ Dr. Md. Shahid Ullah Member Professor and Head (Ex-Officio) Department of Electrical and Electronic Engineering. Islamic University of Technology (IUT) Board Bazar, Gazipur-1704, Bangladesh

3. ………………................

Dr. Md. Ruhul Amin Member Professor Department of Electrical and Electronic Engineering. Islamic University of Technology (IUT) Board Bazar, Gazipur-1704, Bangladesh

4. ………………................ Dr. Muhammad Fayyaz Khan Member Professor (External) Department of Electrical and Electronic Engineering. United International University (UIU), Dhanmondi, Dhaka, Bangladesh.

III

DECLARATION OF CANDIDATE It is hereby declared that this thesis or any part of it has not been submitted elsewhere for the award of any Degree. ………………….................. Dr. Md. Ashraful Hoque Supervisor and Professor Department of Electrical and Electronic Engineering. Islamic University of Technology (IUT) Board Bazar, Gazipur-1704, Bangladesh.

………………………………. S.M.Ferdous Student No. 092606 Academic Year 2009-2010

IV

TABLE OF CONTENTS LIST OF FIGURES...................................................................................................VII LIST OF TABLES.......................................................................................................X ACKNOWLEDGEMENTS .......................................................................................XI ABSTRACT ..............................................................................................................XII CHAPTER 1. INTRODUCTION

1.1 ELECTRIC TRACTION 1 1.1.1 ELECTRIC TRACTION DRIVE 1 1.1.2 ADVANTAGES OF ELECTRIC DRIVE 3 1.1.3 DISADVANTAGES OF ELECTRIC DRIVE 3

1.2 CHARACTERIZATION OF ELECTRIC MOTORS FOR TRACTION APPLICATION

1.3 GENERAL FEATURES OF TRACTION MOTORS 5 1.3.1 MECHANICAL FEATURES 7 1.3.2 ELECTRICAL CHARACTERISTICS 8

1.4 MOTORS USED FOR ELECTRIC PROPULSION SYSTEMS FOR EV AND HEV DESIGN 9

1.5 STATEMENT OF THE PROBLEM AND PURPOSE OF THE WORK 12 1.6 OUTLINE OF METHODOLOGY 15 1.7 THESIS ORGANIZATION 20

CHAPTER 2. MODELLING AND ANALYSIS OF COMPOUND MOTOR

2.1 DC COMPOUND MOTOR 21 2.2 ANALYSIS AND CHARACTERIZATION OF A COMPOUND

MOTOR FOR TRACTION 22 2.3 SPECIFCATION AND DESIGN OF THE MOTOR 24 2.4 MATHEMATICAL MODELLING OF THE MOTOR 27 2.5 LINEARIZED TRANSFER FUNCTION AND ITS BLOCK

DIAGRAM REPRESENTATION 29 2.6 CALCULATION OF OUTPUT PARAMETERS 32

V

CHAPTER 3. DYNAMICS OF TRACTION LOAD AND MODELLING OF ELECTRIC VEHICLE

3.1 INTRODUCTION 33 3.2 TRACTIVE EFFORT 33

3.2.1 ROLLING RESISTANCE FORCE 34 3.2.2 AERODYNAMIC DRAG 35 3.2.3 HILL CLIMBING FORCE 36 3.2.4 ACCELERATION FORCE 37 3.2.5 TOTAL TRACTIVE EFFORT 40

3.3 MODELLING VEHICLE ACCELERATION 41 3.3.1 ACCELERATION PERFORMANCE PARAMETER 43 3.3.2 MOTOR TORQUE MODELLING 44 3.3.3 TRACTION LOAD MODELLING 47

3.4 MODELLING AND SIMULATION OF PERFORMANCE PARAMETERS 50

3.5 MODELLING AND SIMULATION OF PERFORMANCE PARAMETERS USING WINDING CHANGE OVER TECHNIQUE 51

3.6 SUMMERY 54 CHAPTER 4. DESIGN OF CONVERTER AND CONTROLLER FOR ELECTRIC VEHICLE PROPULSION

4.1 INTRODUCTION 55 4.2 CONVERTER DESIGN 55 4.3 OPERATION OF CLASS C DC-DC CONVERTER 56 4.4 SIMULATION OF THE CONVERTER 57 4.5 SUMMERY 65

CHAPTER 5. SIMULATION OF THE OVERALL SYSTEM

5.1 INTRODUCTION 66 5.2 SYSTEM SIMULATION IN SIMULINK 66 5.3 SUMMERY 71

CHAPTER 6. CONCLUSION

6.1 SUMMERY 72 6.2 SUGGESTION FOR FUTURE WORK 73 6.3 CONCLUDING REMARKS 73

VI

REFERENCES 75

APPENDIX -A 78

APPENDIX -B 79

VII

LIST OF FIGURES FIG.1.1 Traction Characteristic of an Electrical Motor 4 FIG.1.2 A Typical Characteristic of a Vehicle (Traction Load) 5 FIG 1.3 Acceleration and Final Speed (Balancing Speed) of electric

vehicle. The point of balancing speed is the operating speed of the motor which determines the final speed of the vehicle

8

FIG.1.4 Tractive effort and power versus vehicle speed with different speed

12

FIG.1.5 Tractive power versus speed ratio, X 15 FIG.1.6 Tractive effort along with Motor Power, base speed and final

speed 20

FIG.1.7 Different Torque-Speed Characteristics of a DC Machine of same power rating (175W) with three separate configuration. 22

FIG.1.8 Power and Torque profile of a DC machine for three different configurations 24

FIG.1.9 Torque and speed profile of a DC machine for three different configurations to show the possibility of achieving a higher starting torque and higher final vehicle speed if change over in configuration takes place.

25

FIG.1.10

Torque and Power profile of the motor as a function of speed due to change in its configurations by the feature of winding change over

28

FIG.2.1 Compound Motor Connected in Long Shunt Configuration 30

FIG.2.2 Non-linear block diagram representation of the compound motor 33

FIG.2.3 Non-linear block diagram representation of the compound motor, assuming field current is constant 34

FIG.2.4 Linearized Block diagram of the compound motor 35

FIG.2.5 Linearized Block diagram of the compound motor assuming field current is constant 40

FIG.3.1 The forces acting on a vehicle moving along a slope 41

FIG.3.2 Arrangement for connecting a motor to a drive wheel using a belt system with step up gear mechanism to increase the amount of torque

45

VIII

FIG.3.3 The simplified diagram of the designed system of connecting the motor with the driving axle of the vehicle with a geared mechanism.

48

FIG.3.4 The initial acceleration and final velocity of the vehicle 49

FIG.3.5 The torque-velocity curve of the motor and vehicle respectively 50

FIG.3.6 The torque profile of the load as seen from the motor shaft 51

FIG.3.7 Axle Torque of the vehicle with respect to its speed. It is exactly in the same nature of the motor-vehicle speed curve of Fig. (3.5). 52

FIG.3.8 Axle torque profile though out the entire time of run of the vehicle 53 FIG.3.9 Armature Current vs Vehicle Speed 54

FIG.3.10 Armature current of the motor with respect to time. The current taken by the motor is very small during steady-state operation. 55

FIG.3.11 Simulated Speed and acceleration characteristic of the vehicle with the feature of winding change over facility. 56

FIG.3.12 Comparative analysis showing the differences in terms of final speed between the two types of motor 57

FIG.3.13 Torque speed characteristic of the motor with winding change over facility. The sharp rise in torque is due to sudden change in current consumed by the armature due to disconnecting the series field.

58

FIG.3.14 Current profile of the motor during its entire period of operation 59

FIG.4.1 Block Diagram Representation of the Motor Controller 60

FIG.4.2 Class C DC-DC converter 62

FIG.4.3 Simulation of Class C DC-DC converter in forward motoring mode in LTSpice 64

FIG.4.4 Output current, voltage and PWM signal of the converter 66

FIG.4.5 Motor current without hysteresis current controller 67

FIG.4.6 Limitation on starting current by the control action of hysteresis controller 68

FIG.4.7 Output voltage of the converter at a Duty cycle of 90%. 69

FIG.4.8 Simulated Boost Converter during Regenerative braking 70

IX

FIG.4.9 Output Voltage and Current of the Boost converter during Braking 70

FIG.4.10 Generation of Reference signal to vary the duty cycle of the

converter 71

FIG.4.11 Boost Converter Input Power due to the kinetic energy stored in the vehicle 72

FIG.4.12 Boost Converter Output Power. The amount of energy which is equal to the area under the curve, is feed back to the source 72

FIG.5.1 Simulation of the entire electromechanical system using SIMULINK 73

FIG.5.2 Speed of the vehicle with winding change over technique 74

FIG.5.3 Motor Current vs Time 74 FIG.5.4 Motor Torque Vs Time 75

FIG.5.5 Motor Power Vs Time 75

FIG.5.6 Speed of the vehicle operated with Series Motor 76

FIG.5.7 Current vs Time for the series motor 76

FIG.5.8 Power Vs Time for the Series Motor 76

X

LIST OF TABLES Table 1.1: ENERGY STORAGE CAPABILITY OF DIFFERENT TYPES

OF FUELS 8 Table 1.2: TYPICAL TORQUE DENSITY VALUE OF DIFFERENT MOTOR TYPES. 12

XI

ACKNOWLEDGEMENTS

I would like to first acknowledge my supervisor, Dr. Md. Ashraful Hoque, for his

support and advice throughout my graduate program. His power electronics courses and

his dedication to his students gave me the best experience during the program. I would also

like to express my sincere appreciation to my other thesis committees, Dr. Md. Shahid

Ullah and Prof. Dr. Md. Ruhul Amin for review of this thesis in detail and their important

feedback.

I would like to thank my colleagues and friends, Mr. Ahmed Mortuza Saleque and

Mr. Ahmed Al Mansur for their effective ideas and feedbacks are incorporated in this

thesis. Also, thanks to lab assistants, technicians for their support and willingness to help

me out during various stages of my thesis.

Finally, I take the opportunity to express my greatest admiration for my parents

who constantly motivated and encouraged me to keep working towards this goal. I also

thank all my other family members for all the support given during difficult times.

S.M.Ferdous

XII

ABSTRACT

A motor capable of operating in a wide constant power range would suit most for any kind of traction application. At the same time it must be capable of producing sufficient amount of torque to meet up the initial starting load demand and acceleration characteristics. In this thesis a novel concept of controlling a DC motor is proposed where a DC compound motor is being used for a traction purpose with a provision of winding switch over technique which will enable the motor to operate in three common forms- Compound, Series and Shunt configurations respectively. These three separate and independent configurations will enable the motor to operate in such a way that, it would suit most to match the Torque-Speed characteristics or the load profile of any conventional traction load. A detail investigation of the motor as well as the load characterization with the proposed method has been presented in the paper in terms of torque, speed and power consumption. A 2 Quadrant Class C DC-DC converter is designed as the main component of the motor controller which will help the motor to operate at variable speed during motor mode operation where as using the same converter regeneration is also possible during braking. Several controller circuits are developed for the purpose such as winding change over controller, speed sensor, PWM signal generator with variable duty cycle, Hysteresis current controller for current limiting purpose and magnetic contactors for forward and reverse motion of the motor. Mathematical model of the DC Compound motor is developed which is highly non-linear in nature and its characteristics. Hence the system is linearized and transfer function with associated block diagram is obtained. Both MATLAB codes and SIMULINK were used to analyze and represent the system. The response curve for Speed, Torque, Current and Power were obtained. The converter is simulated using LTSpice for various duty cycles to observe the adaptability and compliance of it when integrated with the system for variable speed operation. Significant improvements in vehicle performance were observed such as higher staring torque, rapid acceleration with smaller acceleration time and the most important achievement is to attain a higher final vehicle speed which is not possible to obtain using any other types of motor with such power ratings. This point simply implies the fact that, this novel switching technique maximizes and utilizes the full capacity of the motor which is capable of operating at high torque and low speed during starting where as at low torque and high speed at rated condition. But obviously, for a higher speed operation the load torque demand and the power consumption will be more. That means a higher speed operation along with improved vehicle performance will be achieved at the expense of larger energy consumption. The results suggest that, though conventional DC motors are no more being used for modern traction purpose, but yet it may be proven as an eligible candidate for automotive traction once again using this new technique as the results showed considerable performance improvement.

1

CHAPTER 1 INTRODUCTION

1.1 ELECTRIC TRACTION

The act of drawing or the state of being drawn i.e. the propulsion of vehicle is called

the Traction and the system of traction involving the use of electricity is called

Electric Traction System. There are various systems of traction prevailing in the

world such as steam engine drive, internal combustion engine drive, diesel electric

drive, battery electric drive, straight electric drive and the most recent trend of hybrid

electric drive. These systems of traction may be classified broadly into two main

groups namely-

(i) The traction systems which do not involve the use of electricity at any

stage and called non-electric traction system such as steam engine drive, internal

combustion engine drive etc.

(ii) The traction systems which involve the use of electricity at some stage or

the other and called electric traction system such as diesel electric drive, straight

electric drive, battery driven drive etc.

System of electric traction can further be divided into two main groups-

(i) The group consisting of vehicles which receive power from a distribution

network fed at suitable points from either a central power station or substations

suitably spaced such as tramways, trolley bus, electric railways etc.

(ii) The group consisting of self contained locomotives such as diesel electric

trains, ships, petrol electric trucks and Lorries, battery driven road vehicles.

1.1.1 ELECTRIC TRACTION DRIVES

Electric drives are more reliable, flexible and suitable for traction purpose rather than

conventional engine driven vehicle. But storage of electrical energy is the main

obstruction in this technology as batteries stores a much less amount of energy

compare to the energy stored in fuels. Therefore the mileage of an electric vehicle is

2

much less than conventional vehicle. The problem can be solved by increasing the

capacity of the batteries, which is not a good solution considering the both technical

and economical viability. One possible solution can be obtained by reducing the

power consumption of the traction motor. To reduce the power rating of the motor

with a given vehicle performance and energy storage, the motor is required to have a

long constant power range to meet the load torque and demand [1]

The ideal characteristic of an electric motor drive for traction application are high

torque at low speed region for fault acceleration, hill climbing and obstacle

negotiation and low torque at high speed for normal driving. To minimize the power

of the motor as well as the energy storage power rating as a given vehicle

performance, the motor drive is required to have long constant power rage

application [1]. The essential requirements for electric traction are-

• Traction equipment should be robust and sturdy enough to withstand

continuous vibrations, dust and humid environment.

• Power to weight ratio of the traction motor should be high so that it occupies

less space.

• High tractive effort at starting,

• It should be possible to overload the motor for a short period.

• Ability of traction motors to apply regenerative braking during descent.

• Coefficient of adhesion should be high.

• The traction motors must be capable of withstanding voltage fluctuations and

interruptions of power supply.

• The motors should be amenable to simple speed control methods.

It is widely agreed that vehicles electrification will lead to revolutionary

improvements on vehicle performance, energy resource conservation and pollutant

emissions. Now a day’s research and development of vehicle electrification are

widely proceeding in civilian vehicle, military vehicle, construction vehicle, rail

vehicle farm vehicle etc. As the key component, electric motor drive and energy

storage system play the most vital role for developing good performance electric

drive train and rapid mass transport vehicles. Proper characteristics, optimal

parametric design and smart configuration and combination can yield in a compact,

reliable, high efficiency drive system.

3

1.1.2 ADVANTAGES OF ELECTRIC DRIVES FOR TRACTION

• As it has no smoke, electric traction is most suited for the underground

transportation system. At the same time, it is proven to be the most

environment friendly form of transportation system. A better safety margin

can be expected from this kind of system.

• Due to high starting torque developed, it is possible to achieve high

acceleration rates 1.5 to 2.5 kmphps (i.e. 0-50 kmph in 10-12 Sec).

• Electric drives for traction purpose are available in wide range of torque,

speed and power. Electric motors have high efficiency, low losses and

considerable amount of overloading capacity. They are adaptable to almost

any operating condition.

• Electric drives can be used operate in all four quadrants of speed torque plane

which is very suitable for forward and backward movements of the vehicle as

well as braking.

• Better flexibility in operation and less maintenance (about 50% less compare

to engine driven system) [6].

• Saving in energy is another attractive feature for electric traction as almost

30-40% of energy can be saved by the unique distinctive feature of

regenerative braking.

1.1.3. DISADVANTAGES OF ELECTRIC TRACTION

The main disadvantage of any EV is the lack of ability to store sufficient amount of

energy to run the vehicle. Other than Main line urban and sub-urban locomotive

traction system where the drive receives its power from main line, any battery/fuel

cell operated EVs hold a very small amount of energy to run the motor as well as the

vehicle compare to any engine driven vehicle. This one single disadvantage is so

severe that, despite all the attractive features, the EVs are still lagging behind with

respect to engine driven vehicles for commercial and practical application. It is due

to the fact that, the energy density of any fuel is far greater than any electrical energy

4

storage system such as battery or recently developed fuel-cells. The following Table

1.1 can visualize a clear idea on this subject.

TABLE 1.1: ENERGY STORAGE CAPABILITY OF DIFFERENT TYPES OF FUELS AND

ELECTROCHEMICAL/ELECTROMECHANICAL SYSTEMS [6]

Sl.

No. Name of the Fuel

Energy contain

(Wh/kg)

Energy Contain

(Wh/Litre)

1 Gasoline 12300 9348

2 Natural gas 9350 7480

3 Methanol 6200 4904

4 Kerosene 5300 4500

5 Coal 8200 -

6 Battery (Lead-Acid) 35 -

7 Typical rechargeable Battery 40-100 -

8 Electrochemical Capacitor 5-15 -

9 Flywheel 15 -

10 Spring 0.1-.0.3 -

11 Solar Thermal 900 Wh/day -

12 Solar PV 500 Wh/day -

The other limitations are –

• Small capacity of the battery and the necessity of frequent charging. the

charging time is more or less very long.

• Speed range/mileage is limited.

• Limited battery life. Needs to be replaced after 3-4 years at a regular interval.

• Regular maintenance is required.

• Batteries are costly and their frequent and regular replacement may not be

proven economically viable and cost effective.

• Hazardous and harmful chemicals are present in batteries. Proper dumping

and recycling of these chemicals must be done properly. Otherwise severe

environmental pollution can be caused which is harmful for any living

organism.

5

1.2 CHARACTERIZATION OF ELECTRIC MOTORS FOR TRACTION

APPLICATION

Ideal profile of torque speed characterization of EV is divided into two parts i.e. the

constant torque region and the constant power region. The vehicle performance is

completely determined by the profile of tractive effect verses vehicle speed. For a

power source with a given power rating, the profile of tractive effort versus vehicle

speed should be constant power in the speed range that is the tractive effect drops

hyperbolically with the increase of the vehicle speed as shown in Figure 1.1.

Figure 1.1. Traction Characteristic of an Electrical Motor. [1]

The detailed design of EV and HEV in [5]. The electric motor in its normal mode of

operation can provide constant rated torque up to its base speed. At this speed the

motor reaches its maximum power limit. The operation beyond the base speed up to

the maximum speed is limited to this constant power region (Fig.1). The range of

constant power operation depends primarily on the particular motor types and its

control strategy. However, some electric motors deviate from the constant power

operation, beyond certain speed and enter the natural mode before reaching the

maximum speed. The maximum available torque in the natural mode of operation

decreases inversely with the square of the speed. Although machine torque in the

natural mode decreases inversely with the square of the speed, for some extremely

high speed motors the natural mode of operation is an appreciable part of its torque

speed profile. Inclusion of this natural mode for such motors may result in a

reduction of the total power requirement [2]. However power electronic controls

6

allow the motor to operate at any point in the torque-speed plane. It is the profile of

this envelops which determines the drive selection criteria and design.

A typical traction load characteristic curve is shown in Figure 1.2.

Figure 1.2. A Typical Characteristic of a Vehicle (Traction Load)

By analyzing the characteristics of a traction load or a vehicle as shown in Fig.2 one

can conclude that, the required torque or tractive effort decreases with increase in

vehicle speed but again increases after a certain value where the resistance forces

acting upon the vehicle become more dominant at high speed. The detail traction

load characteristics will be analyzed and modeled in the upcoming chapters.

The overall characteristic curve of the traction motor along with traction load is

shown in Figure 1.3 to explain the acceleration and operating point (load matching)

of both the drive and the load.

7

Figure 1.3. Acceleration and Final Speed (Balancing Speed) of electric vehicle. The point of balancing speed is the operating speed of the motor which determines the

final speed of the vehicle. [12]

1.3 GENERAL FEATURES OF TRACTION MOTORS

The primary requirements of electric motors used for traction purpose are-

1.3.1 MECHANICAL FEATURES

• A traction motor must be robust and capable to withstand continuous

vibrations since service conditions are extremely severe.

• The weight of a traction motor should be minimum in order to increase the

payload capacity of the vehicle. This is achieved by using high speed motors,

upper limit being fixed by excessive centrifugal stresses.

• The traction motor is located underneath a motor coach. The space

underneath a motor is limited by the size of driving wheels and the track

gauge. The traction motor, therefore, must be small in overall dimensions

specially in its overall diameter.

• The traction motor must be totally enclosed type, particularly when mounted

beneath the locomotive or the motor coach, to provide protection against

ingress of dirt, dust, water and mud etc.

8

• For magnetic circuit of traction motor cast iron, which cannot suitable

continuous vibration, is not suitable. Use of cast steel or fabricated steel,

which gives more mechanical strength, is made in place of cast iron. Those

parts of the motor, which are not highly stressed, must be made of pressed or

fabricated steel plates and light alloys.

1.3.2 ELECTRICAL CHARACTERISTICS

• High starting torque. A traction motor must be capable of developing high

starting torque, specially when the train is to be accelerated at a reasonably

high rates such as in case of urban and sub-urban services.

• Simple speed control The traction motor must be amenable to simple speed

control as the an electric train or vehicle have to be started and stopped very

often.

• Self relieving property The speed-torque characteristic of the motor should be

such that the speed may fall with the increase in load. The motors having such

characteristics are self protective against excessive overloading as power

output of a motor is proportional to the product of torque-speed.

• Possibility of Dynamic and Regenerative braking The traction motor should

be amenable to easy and simple methods of dynamic and regenerative braking

along with mechanical braking.

• Overload capacity Traction motors should be capable of taking excessive

loads as it is subjected to very arduous and heavy duties.

• Parallel running In traction work, usually more than one motor (two or four

motors per car) are required. Traction motors, therefore, should be of such

speed-torque and current-torque characteristics that, when they are operated

in parallel and mechanically coupled, they share the loads almost equally.

No such motors meet the all the requirements mentioned above. Most suitable

motors for DC traction systems are series and compound motors whereas for ac

traction systems single phase series and three phase induction motors are

employed.

9

1.4 MOTORS USED FOR ELECTRIC PROPULSION SYSTEMS FOR EV AND

HEV DESIGN

An electric propulsion system is comprised of three main elements: power electronic

converter, motor and its controller. Traditionally, DC motors drives have the proper

characteristics for traction application, and were popularly used couple of decades

ago. They offer the provision of extended speed range operation through field

weakening under the constant power operating region. However, DC motor drives

have bulky construction, low efficiency, need of maintenance and low reliability,

mainly due to the presence of mechanical commutator and brush. With the coming

era of power electronics and advanced microprocessor control technology, other

advanced motor drives are mature to replace DC motor drive in traction application.

At present permanent magnet brushless DC motors (BLDC), Induction motors and

Switch Reluctance motors are considered to be the most potential candidates for the

vehicle propulsion application.

For traction application, the torque density is the most important criterion of the

electric motors, which reflects the volume and weight of machines at given demand.

Table 1.2 lists the typical torque density values for different motor types. [1].

TABLE 1.2: TYPICAL TORQUE DENSITY VALUES FOR DIFFERENT MOTOR TYPES [1]

Machine Type T/Volume envelop (N-m/m3)

T/Cu mass N-m/kg-Cu

Permanent Magnet 28860 28.7-48

Induction motor 4170 6.6

Switch Reluctance 6780 6.1

Table 1.2 shows that the PM machines provide the highest torque density and

therefore will potentially have the lowest weight for given torque and power rating.

However, the fixed flux limits its extended speed range as the feature of field

weakening like brushed DC motors are not available. The induction motor and switch

reluctance motor have the similar torque densities.

10

It is obvious that, in case of DC machines with separate field winding would

certainly exhibit more torque density than PM motors. But at the same time, due to

its bulky constructional features (as it is fitted with commutator, brush assembly and

field winding), it will be heavier than PMDC motor. Most of the PMDC motors have

the brushless commutation technique using electronic circuitry. If the same brushless

commutation technique is introduced in the conventional DC motors fitted with

separate field winding, it may have been proven to be the best option for electric

traction system. But due to the presence of field winding (which is not present in case

of PMDC motor) the weight and size of this type of DC motor would be more

compare to PMDC motor; even if it has brushless commutation technique.

More Detail operating characteristics of several types of motors employed for electric

traction are discussed in brief in the following.

A. Permanent Magnet Brushless DC Motor Drive

As mentioned above, since the magnetic field is excited by high-energy

permanent magnets (PMs), the overall weight and volume can be significantly

reduced for given output torque, resulting in higher torque density. Because of

the absence of rotor winding and rotor copper losses, their efficiency is

inherently higher than that of induction motors.

However, This motor inherently has a short constant power range due to its

rather limited field weakening capability, resulting from the presence of the PM

field, which can only be weakened through production of a stator field

component, which opposes the rotor magnetic field.

Recently, the use of additional field windings to extend the speed range of

PM brushless DC motors has been developed [7]. The key is to control the

field current such a way that the air-gap field provided by PMs can be weakened

during high-speed constant-power operation. Due to the presence of both PMs

and the field windings, these motors are so-called PM hybrid motors. The PM

hybrid motor can achieve a speed ratio of around 4. The optimal efficiency

profiles of a PM hybrid motor drive are shown in Fig. 9[7, 8].

However, the PM hybrid motors have the drawback of relative complex

structure. The speed ratio is still not enough to meet the vehicle performance

11

requirement, especially to off-road vehicle. Thus a multi-gear transmission is

required.

B. Induction Motor (IM) Drive

Field orientation control (FOC) of induction motor can decouple its torque control

from filed control. This allows the motor to behave in the same manner as a

separately excited DC motor. Extended speed range operation with constant power

beyond base speed is accomplished by flux weakening. However, the presence of

breakdown torque limits its extended constant power operation. At the critical

speed, the breakdown torque is reached. Any attempt to operate the machine at

the maximum current beyond this speed will stall the machine.

Nevertheless, a properly design induction motor, e.g. spindle motor, with field

orientation control can achieve field weakened range of about 3-5 times its base

speed [9]. This approach, however, results in an increased breakdown torque,

and thereby resulting in over sizing of the motor. A special winding changeover

technique of a field orientation controlled induction motor is also reported

which demonstrates long field weakening operation[ 10]. This approach,

however, requires winding tap changing and contactors. A contactless control

scheme for extending the speed range of a four-pole induction motor was presented

in [9]. This scheme uses two inverters, each of half the rated power rating that, in

theory, can extend the constant power

Operating range to 4 times the base speed, for a motor, that would otherwise be

limited to 2 times the base speed. It may be mentioned here that the torque control in

induction motor is achieved through PWM control of the current. in order to retain

the current control capability in the extended speed constant power range, the

motor is required to enter the field weakening range before reaching the base

speed, so that it has adequate voltage margin to control the current[l2]. This would,

however, oversize the motor slightly. Current regulation with synchronous current

regulator [I31 may be preferred choice. It can regulate current with lower voltage

margin. The availability of a long field weakened range, obviously, makes the

induction very suitable for vehicle application.

12

C. Switched Reluctance Motor (SRM) Drive

Switched reluctance motor (SRM) is gaining much interest as a candidate of

electric propulsion for electric vehicle (EV) and hybrid electric vehicle (HEV)

because of its simple and rugged construction, simple control ability of extremely

high speed operation and hazard free operation. These prominent advantages are

more attractive for traction application than other kinds of machines

SRM can inherently operate with extremely long constant power range. The serial

design and simulation results, performed in the SRM research group at Texas

A&M University, show that the speed ratio can reach up to 6-8 times. This long

constant power range makes SRM highly favorable for vehicle traction application.

1.5 STATEMENT OF THE PROBLEM AND PURPOSE OF THE WORK

Electric motor driven small vehicles (Auto-Rickshaws) namely “Easy bike” or “Polly

bike” are extensively used in Bangladesh all over the country. They are three

wheeled vehicles providing the purpose of transportation. Although the vehicles are

not designed in Bangladesh and not even been tested to suit the environment of

Bangladesh, a detail study is needed to be carried out in this field as it seems to be an

emerging practice throughout the whole country.

Electric drives are more reliable, flexible and suitable for traction purpose rather than

conventional engine driven vehicles. But storage of electrical energy is the main

obstruction in this technology as batteries stores a much less amount of energy

compare to the energy stored in fuels. Therefore the mileage of an electric vehicle is

much less than conventional vehicle. The problem can be solved by increasing the

capacity of the batteries, which is not a good solution considering the both technical

and economical viability. One possible solution can be obtained by reducing the

power consumption of the traction motor. To reduce the power rating of the motor

with a given vehicle performance and energy storage, the motor is required to have a

long constant power range to meet the load torque and demand [1]. By analyzing the

different characteristics of different types of motors, it has been found that, DC series

13

motors are the most suitable type of motor for traction. But for a reliable operation

the motor rating must be increased to such a value which would increase the total

cost of the system. On the other hand DC motors has some disadvantages like – field

control method is not flexible, speed of the motor is less than other types of up to a

certain region and finally, effective regenerative braking is not possible as the motor

becomes unstable during regenerative braking.

An optimum performance can be obtained by using a compound motor, where there

should be a provision of switching between the series and shunt winding. That

means, the motor is started as series motor with shunt connection being opened to get

a high starting torque. The motor will operate in series connection for the constant

torque region. After the period of acceleration that is, in the constant power region

the motor will be added with a shunt connection and gradually as the speed is

increased the series connection will be opened. As a result a smooth operation in the

field current control region (the constant power region) can be achieved and it has

been predicted that a higher final velocity, Vf can be gained, which indicates that the

vehicle would run at a final velocity compare to the previous condition.

The objective of the thesis will be to design a control circuit to verify the theory that

has been stated above. Only a few studies have been carried out in this topic by

several researchers. To strengthen the theory, the family of curves shown in figure 2

should be closely observed [1].

Fig.1.4 : Tractive effort and power versus vehicle speed with different speed

14

Fig. 1.4 shows that with higher value of speed ratio (i.e. low base speed) the power

rating of the motor will be less. But the final speed of the vehicle will be very less

which implies that the vehicle will move with a very low speed. By observing the

Torque- Speed Characteristics of DC motors, it has been found that the speed of a

shunt motor will be much higher than the series motor within a particular region. As

the full load torque of a vehicle is much less than the starting torque the (the value of

the load torque changes hyperbolically), conversion of the motor from series to shunt

will match the load torque and the same time speed of the vehicle will be increased.

In addition to these, the final speed of the vehicle can be increased by 2-3 times

which will certainly be a great outcome from the project. Figure 1.5 shows the

relation between the power rating and speed ration of a traction motor.

Fig.1.5 : Tractive power versus speed ratio, X [1]

From figure 1.5 we can conclude the rating and size of the motor will be lowered for

high speed ratio, which will result in a lower vehicle speed. This speed can be

achieved by introducing a shunt winding with a provision of switching the field

winding from series to shunt as the motor accelerates. This will yield a high speed

performance along with improved gradeability of the vehicle.

As a whole as per several studies carried out in the field of EV and HEV design and

analysis, the ideal desirable characteristic from an electric vehicle when operated at

prolonged constant power range are–

15

• Longer constant power range operation of the motor effectively reduces the

motor power rating.

• Reduced Power consumption.

• Improved, fast and rapid acceleration.

• Gradeability of the vehicle is improved.

• Single and simple gear transmission.

• Reduction in size and capacity of battery.

• Design of the vehicle is compact, robust, highly efficient and reliable.

So, if any motor chosen and designed for the purpose of electric traction is capable of

prolonging its constant power range operation, it would suit most for the traction

application as its characteristics would exactly represent the characteristics expected

from a traction motor. A figure in terms of Power, Tractive Effort, Speed and

Traction load would provide a detail idea as shown in Figure 1.6.

Figure 1.6. . Tractive effort along with Motor Power, base speed and final speed.

1.6 OUTLINE OF METHODOLOGY

A Compound motor provided with winding change over facility should outdo the

performance of DC series motor. This will enable the motor to operate at three

different configurations – Compound, Series and Shunt where later it would be

shown that, only two configurations are suffice to obtain the desirable performance,

i.e. the compound and shunt. This is due to the fact that, whatever the characteristics

desired from series configuration can very well be achieved from the compound

16

configuration. This would suit the traction characteristics more. Switching between

the windings will prolong the constant power range operation of the motor.

An experimental investigation on the Torque-speed characteristics would provide the

justification of the claim as shown in Figure 1.6.

Figure 1.7. . Different Torque-Speed Characteristics of a DC Machine of same power rating (175W) with three separate configuration.

The torque and power characteristics of the machine due to different configurations

are shown in Figure 1.8. As seen from the figure, the compound motor would provide

the maximum amount of starting torque but it is capable to sustain that torque only

for a small base speed. For series configuration it provides smaller starting torque but

relatively higher base speed. Finally, for shunt configuration, as we all know it is a

constant speed motor that is completely different from the previous two

configurations, it would provide the largest base speed but there is a reduction in its

starting torque significantly. This switching of windings prolongs the constant power

operating range of the motor. This is due to the fact that inclusion of all the three

configurations of the DC Motor optimizes the performance and hence exhibits all

types of characteristics that can be obtained from several DC motors. In other word,

the winding change over techniques integrated all the three configurations available

17

for a self excited motor which includes all possible combination of the motor. Thus

the motor exhibit such characteristics which are highly expected for an ideal traction

motor and very much suitable for traction application.

Figure 1.8. . Power and Torque profile of a DC machine for three different configurations

According to the traction load characteristic, it can be very easily obtained from

Figure 1.9 that, winding change over feature would enable the vehicle to operate at a

higher final velocity. The overall speed, torque and power profile due to winding

change over are given in Figure.10.

18

Figure 1.9. . Torque and speed profile of a DC machine for three different configurations to show the possibility of achieving a higher starting torque and

higher final vehicle speed if change over in configuration takes place.

Figure 1.10. Torque and Power profile of the motor as a function of speed due to change in its configurations by the feature of winding change over.

19

It is to be noted that, the accelerating torque for acceleration is very high due to

compound configuration where as the winding change over enables the vehicle to

attain a relatively higher speed due to change over into shunt configuration.

A controller circuit will be needed to perform the switching action between the two

separate windings. The purpose of the controller circuit would be to sense the load

condition and depending on that, perform the switching action. At constant torque

region the motor should operate at in series connection. At the end of acceleration

period (as the required tractive effort will be much less compare to the starting

condition) the switching must be taken place to increase the speed of the motor as

well as the vehicle.

1.6.1 PERFORMANCE IMPROVEMENT BY WINDING CHANGE OVER

TECHNIQUE IN A COMPOUND MOTOR

• An Optimum performance would be obtained using a DC Compound motor

with winding change over technique

• High starting Torque with Low speed

• Due to winding change over a high final speed is attained with a drop in Load

Torque.

• Very smooth regenerative braking is possible as the machine will be

configured as Shunt Motor during the time of regenerative braking which is

very much stable for this kind of operation.

• Reduced Power rating of the motor to achieve same performance.

• Single gear transmission instead of Multi gear transmission system.

• Reduced sizing of the on board energy storing device or conversely mileage

of the vehicle will be increased with the storage battery of same size and

capacity.

• Saving in energy is increased as the kinetic energy of the vehicle will be used

to charge the battery through regenerative braking which implies as almost

30-40% of energy can be saved by the system.

20

1.7 THESIS ORGANIZATION

Chapter 1 describes the introduction of electric traction systems, types and different

features of it. General criteria of traction motor has been discussed from where it has

been found that, a motor with constant power range operation is certainly the best

choice for traction application. Finally a brief overview of the proposed method is

discussed and its applicability for electric traction is analyzed.

Chapter 2 describes the modeling, analysis and design of the compound motor that

will be used for traction purpose. Different characteristic equations have been

developed and simulated to predict the performance of the motor. The non-linear

model of the motor is developed and finally using the linearization technique, the

model is linearized and hence transfer function of the motor is obtained.

Chapter 3 describes in detail the dynamics of a traction load and hence the modeling

of the electric vehicle is done. From initial acceleration to final speed operation of the

vehicle had been calculated, simulated and presented along with all the necessary

mathematical calculation and analysis.

Chapter 4 discusses the modeling and Simulation of 2 quadrant Class C DC-DC

converter used for motor control. The novel integration of PWM voltage and

Hysteresis current controller is discussed in detail and simulated using LTSpice. All

the necessary controller circuit required for the operation of the vehicle along with

the winding change over controller, Speed Sensing, braking, speed controller and

others are designed, discussed and analyzed.

Chapter 5 provides the complete simulation of the entire electromechanical system

using Simulink. The response of the motor along with the vehicle is determined and

optimized. Finally, the obtained result is compared with the characteristics of a

conventional DC series motor to show the superiority and effectiveness of the

proposed method compare to any conventional vehicle traction system.

Chapter 6 concludes the overall thesis with some recommendations for future work.

21

CHAPTER 2 MODELLING AND ANALYSIS OF COMPOUND

MOTOR

2.1 INTRODUCTION

DC drives are widely used in application requiring adjustable speed, good speed

regulation and frequent starting, braking and reversing. In case of traction application

DC series motors are dominating long since. But in this study it will be shown that, a

compound motor can be more efficient in traction purpose if it is modified and added

with some special features. Generally compound motors are of two types-

Cumulative and Differential compound motor where the Differential compound

motor is seldom used. For this particular thesis work where a compound motor is

chosen for vehicle propulsion system, it is obvious that, Cumulative compound motor

will be the best choice between these two types. Comparing to DC series motor a

compound motor can exhibit a more stable operation and also provides a finite and

safe no load speed (which is not possible in case of DC series motor as its no load

operation would produce a dangerously high speed due to very low value of field

flux) that depends on the strength of the shunt field. The slope of the Speed-Torque

characteristic depends upon the strength of the series field. Cumulative compound

motors are used in those applications where a dropping characteristic is similar to

that of a series motor and at the same time a no load speed is limited within a safe

value. The best application of such motor is loads with intermittent duty cycle where

load varies from almost no-load (constant speed operation of the vehicle at steady

state) to very heavy load (during starting). In these applications a fly wheel may be

mounted on the motor shaft for load equalization. Apart from load equalization, use

of compound motor permits the use of a motor with smaller size and less power

rating.

22

A cumulative compound motor has a definite no load speed and so it does not "run away"like

series motor when load is removed.It also developed a high starting torque when load is

increased. This makes it suitable for such applications like rolling mills, shears and punching

presses. It is also a preferred motor for application of such as cranes and elevators that requires

(a) high starting torque, (2) are prone to sudden load change and (c) present a possibility of going

from no load to full load.

2.2 CHARACTERIZATION AND CONFIGURATION OF THE COMPOUND MOTOR

General characterization of the motor :

𝐼𝐼𝑎𝑎 = 𝑉𝑉 − 𝐸𝐸𝐵𝐵𝑅𝑅𝑎𝑎 + 𝑅𝑅𝑠𝑠𝑠𝑠

𝐼𝐼𝑎𝑎 = 𝑉𝑉 − 𝐸𝐸𝐵𝐵RTotal

(2.1)

Field Current, 𝐼𝐼𝐹𝐹 = 𝑉𝑉𝑅𝑅𝐹𝐹

(2.2)

where, V = Supply Voltage

EB = Back EMF

RTotal = Total Resistance of the armature circuit = Ra+Rse

Ra = Resistance of the armature

Rse = Resistance of the series winding

RF = Resistance of the field winding.

𝐸𝐸𝐵𝐵 = 𝐾𝐾𝐵𝐵𝜑𝜑𝜑𝜑 = 𝑉𝑉 − 𝐼𝐼𝑎𝑎𝑅𝑅𝑇𝑇 (2.3)

where φ = Total Flux = φse+φsh

φse = Flux produced from Series field (Wb)= Kse Ia

φsh = Flux produced from Shunt field (Wb)= Ksh IF

23

ω = Angular velocity (rad/sec) = 2𝜋𝜋𝜋𝜋60

N = R.P.M of the motor

KB = Back EMF Constant

From Eq. (2.3)

ω = V − IaRT

KBφ=

V − IaRT

KB�ϕse + ϕsh�=

V − IaRT

KBKsh IF + KBKse Ia (2.4)

This Eq. (2.4) is known as Speed-Current characteristic of the motor.

Again, Torque developed by the motor is given by,

T = KTϕIa (2.5)

where, KT = Torque Constant

Now,

T = KTϕIa = KT�ϕse + φsh�Ia = KT(Ksh IF + Kse Ia)Ia = KTKsh IFIa + KTKse Ia2 (2.6)

This Eq. (2.6) is known as Torque-Current Characteristic of the motor.

Eq. (2.6) can re-written in the form,

T = C1Ia + C2Ia2 (2.7)

where, C1 = KTKsh IF and C2 = KTKse

Now, from Eq. (2.7), expression for the current can found in terms of developed torque as,

Ia =−C1 ± �C1

2 + 4C2T

2C2 (2.8)

24

Putting the value of Ia in Eq. (2.4),

ω =V −

−C1±�C12+4C2T

2C2RT

KBKsh IF + KBKse−C1±�C1

2+4C2T

2C2

ω =V −

−C1+�C12+4C2T

2C2RT

K1 + K2−C1+�C1

2+4C2T

2C2

where, K1 = KB Ksh IF and K2 = KB Kse . Here Negative sign is discarded as current cannot be

negative during motor mode operation.

By simple manipulation and rearranging, this equation can be written as,

ω =2C2V + C1RT − RT�C1

2 + 4C2T

2C2K1 − K2C1 + K2�C12 + 4C2T

(2.9)

This Eq. (2.9) is known as Torque-Speed characteristic of the motor.

2.3 SPECIFICATION AND DESIGNING OF THE MOTOR :

The motor considered for traction purpose is shown in Figure 2.1.

Figure 2.1. Compound Motor Connected in Long Shunt Configuration

25

The specification of motor is as follows :

Voltage, V = 60V, Ia(rated) = 40A , IF = 5A, Total Current, ITotal = 40+5=45A

Total armature Resistance, Rtotal = Rse+Ra = 0.15Ω; Field Resistance, RF = 12Ω

Rated power, P = 2500W

No load Speed of the motor, NNL = 1800 RPM

No load angular velocity, ωNL = 188.4 rad/sec

To overcome the maximum torque offered by the load (i.e. the vehicle itself) the motor must be

capable of developing a torque of 65Nm at rated condition. This particular value of torque will

be obtained when the traction load characteristic was analyzed (discussed in detail in chapter 3).

So, the rated torque of the motor should be 65N.m and must be developed at rated power. So, we

know,

P= Torque x Angular velocity = Tω

so, ωrated = PratedTrated

= 250065

= 38.46 rad/sec

This primarily calculated value will be used to design and calculate different parameters of the

motor.Now, from Eq. (2.3)

ω = 38.46 =EB

KBϕ

KBϕ = EB

ω=

V − IaRT

ω=

60 − (40 × 0.15)38.1

= 1.42 (2.10)

From Eq. (2.5)

T = 65 = (KTϕ)40

KTϕ =6540

= 1.625 (2.11)

26

Dividing Eq. (2.11) by (2.10),

KTϕKBϕ

=1.6251.42

= 1.1444

KT = 1.144KB (2.12)

Rewriting Eq. (2.10) and (2.11),

KBϕse + KBφsh = 1.42 (2.13)

KTϕse + KTφsh = 1.625 (2.14)

Putting the the value of KT from Eq.(2.12)into Eq.(2.14),

1.144KBKse Ia + 1.144KBKsh IF = 1.625 (2.15)

Let us assume 70% of the total flux is provided by the series field and 30% of the flux are

provided by the shunt field. So, we can write,

1.144KBKsh IF = 1.625 × 0.3 = 0.4875

KBKsh =0.4875

1.1444 × 5= 0.0852 (2.16)

Similarly,

1.144KBKse Ia = 1.625 × 0.7 = 1.1375

KBKse =1.1375

1.1444 × 40= 0.02485 (2.17)

Dividing Eq. (2.16) by Eq. (2.17),

KB Ksh

KBKse=

0.08520.02485

= 3.4286

Ksh = 3.4286Kse

φshIF

= 3.4286ϕseIa

27

φsh = 3.4286 ×5

40× ϕse = 0.4286ϕse

φsh = 0.4286ϕse (2.18)

Let, ϕse = 0.01Wb = 10 mWb

So, φsh = 0.01 × 0.4286 = 0.004286Wb = 4.286 mWb

Now from Eq. (2.13),

KB�ϕse + φsh� = 1.42

KB =1.42

0.01 + 0.004286= 99.4 V/rad. Wb

And from Eq. (2.12),

KT = 1.144KB = 1.144 × 99.4 = 113.75 N. m/A. Wb

Other constants can now be calculated as,

Ksh = φshIF

=0.004286

5= 0.0008572 Wb/A

Kse =ϕseIa

=0.0140

= 0.00025 Wb/A

2.3 MATHEMATICAL MODEL AND TRANSFER FUNCTION OF COMPOUND MOTOR :

From Figure 2.1 the following set of Equations can be written;

V = LTdia

dt+ IaRT + EB (2.19)

V = LFdiF

dt+ IFRF (2.20)

EB = KB�ϕse + φsh�ω (2.21)

28

T = KTϕIa = KT�ϕse + φsh�Ia (2.22)

= KTKsh IFIa + KTKse Ia2 (2.23)

where, LT = La + Lse =Inductance of Armature+Inductance of Series field=Total Inductance

LF =Inductance of Field winding; RF =Resistance of Field Winding.

TL is the torque required to drive the load then, then the developed torque balance equation can

be written as;

T = Jdωdt

+ Bω + TL (2.24)

where, J = Moment of Inertia of the Load (N.m-S2/rad)

B = Viscous friction constant (N.m/rad/s)

Using Eq. (2.19) to Eq. (2.24) the electromechanical model of the motor can be obtained. But

due to the product of variable type non-linearities present in Eq. (2.23), it is not possible to

obtain a transfer function of this model. However, these equations can be linearized by

considering a small perturbation at the operating point. Before deriving the linearized transfer

fuction, let us develop a complete block diagram of the motor considering the non-linearities

which is shown in Figure 2.2.

Figure 2.2. Non-linear block diagram representation of the compound motor

29

Assuming the field current is constant, this block diagram can be further simplified into the

following based on Eq. (2.4) and Eq. (2.6).

Figure 2.3. Non-linear block diagram representation of the compound motor, assuming field current is constant

2.4 LINEARIZED TRANSFER FUNCTION AND ITS BLOCK DIAGRAM

REPRESENTATION :

All the system parameters can be defined around their operating point as follows;

V = V0 + ΔV; EB = EB0 + ΔEB; Ia = Ia0 + ΔIa ; IF = IF0 + ΔIF;

T = T0 + ΔT; TL = TL0 + ΔTL ; ω = ω0 + Δω

The following basic equations will be needed to describe and represent the electromechanical

system of compound motor along with its load.

V = LTdia

dt+ IaRT + EB

EB = KBKsh IFω + KBKse Iaω

V = LFdiF

dt+ IFRF

30

T = KTKsh IFIa + KTKse Ia2

T = Jdωdt

+ Bω + TL

Recognizing that, ΔIa0 Δω and (ΔIa)2 are very small and hence tending to zero, all the above

Equations can be linearized to;

∆V = RTΔIa + LTd(ΔIa)

dt+ ΔEB (2.25)

ΔEB = KBKse (Ia0Δω + ΔIaω0) + KBKsh (IF0Δω + ΔIFω0) (2.26)

∆V = RFΔIF + LFd(ΔIF)

dt (2.27)

ΔT = 2KTKse Ia0ΔIa + KTKsh (IF0ΔIa + Ia0ΔIF) (2.28)

ΔT = Jd(∆ω)

dt+ B(Δω) + ΔTL (2.29)

These five equations are sufficient to establish the block diagram of a DC Compound motor

drive as shown in Figure. 2.4.

Figure 2.4. Linearized Block diagram of the compound motor

31

A further simplification in the block diagram can be possible by rearraging the blocks as shown

in the following Figure. 2.5.

Figure 2.5. Linearized Block diagram of the compound motor assuming field current is constant

After using the block diagram simplification technique, the final linearized transfer function of

the motor is obtained as,

T(s) = C1(SLF + RF − C2) + C3(SLT + RT + C4)

(Js + B)(SLF + RF)(SLT + RT + C4) + C1C5 (2.30)

where;

C1 = (2KTKse Ia0 + KTKsh IF0)

C2 = KBKsh ω0

C3 = KTKsh Ia0

C4 = KB Kse ω0

C5 = (KBKse Ia0 + KBKsh IF0)

32

which can be re-written in the generalized form as;

T(s) = s + b0

s3 + a2s2 + a1s + a0 (2.31)

where,

b0 = RFC1 + RTC3 + C3C4 − C1C2

LFC1 + LTC3 (2.32)

a0 = BRFRT + BRFC4 + C1C5

JLFLT (2.33)

a1 = JRFRT + JRFC4 + BLFRT + BLFC4 + BLTRF

JLFLT (2.34)

a2 = JLFRT + JLFC4 + JRFLT + BLFLT

JLFLT (2.35)

2.5 CALCULATION OF OUTPUT PARAMETERS :

Maximum Allowable Armature current is twice than its rated value i.e. (40x2=80A). For current

control/limiting purpose, hysteresis controller is used and as the current will switch between two

certain limits of upper and lower level of current defined by the hysteresis controller, it is a good

approximation to consider the starting current as 1.6 times the rated current. As a result the

starting torque of the motor will be around 1.5 times to its rated value. Using Eq. (2.5) the

starting torque of the machine can be calculted as-

Tstarting = KTϕIa(starting ) = 113.75 × 14.286 × 10−3 × 1.5 × 40 = 97.5 N. m

where, Ia(starting ) = 1.5 × Ia(rated )

Maximum power consumed during starting,

Pmax (starting ) = 60 × (1.5 × 40 + 5) = 3900W

During No load condition, NNL= 1800 rpm, ωNL= 188.4 rad/sec

ωrated = PratedTrated

= PratedKT ϕIa (rated )

= 250065

= 38.46 rad/sec; Nrated = 9.55X38.46= 367.3 rpm

33

CHAPTER 3 DYNAMICS OF TRACTION LOAD AND MODELING

OF ELECTRIC VEHICLE

3.1 INTRODUCTION

Modeling of electric vehicles will make it more convenient to predict its performance

and characteristics. The primary parameter to be modeled is vehicle performance. By

performance we mean acceleration and top speed, an area where electric vehicles

have a reputation of being very poor. It is necessary that any electric vehicle has a

performance that allows it, at the very least, to blend safely with ordinary city traffic.

Another vitally important feature of electric vehicles that we must be able to predict

is their range. This can also be mathematically modeled, and computer programs

make this quite straightforward. The mathematics we will develop will allow us to

see the effects of changing things like battery type and capacity, as well as all other

aspects of vehicle design, on range. This is an essential tool for the vehicle designer.

We will go on to show how the data produced by the simulations can also have other

uses in addition to predicting performance and range. For example we will see how

data about the motor torque and speed can be used to optimize the compromises

involved in the design of the motor and other subsystems.

3.2 TRACTIVE EFFORT

The first step in vehicle performance modeling is to produce an equation for the

tractive effort. This is the force propelling the vehicle forward, transmitted to the

ground through the drive wheels.

Let us consider a vehicle of mass m, proceeding at a velocity v, up a slope of angle

ψ, as in Figure 3.1. The force propelling the vehicle forward, the tractive effort, has

to accomplish the following:

34

Figure 3.1: The forces acting on a vehicle moving along a slope. [6]

• To overcome the rolling resistance;

• To overcome the aerodynamic drag;

• To provide the force needed to overcome the component of the vehicle’s

weight acting down the slope.

• accelerate the vehicle, if the velocity is not constant.

3.2.1 ROLLING RESISTANCE FORCE

The rolling resistance is primarily due to the friction of the vehicle tyre on the road.

Friction in bearings and the gearing system also play their part. The rolling resistance

is approximately constant, and hardly depends on vehicle speed. It is proportional to

vehicle weight. The equation is:

Frr= µrrmg (3.1)

Where µrr is the coefficient of rolling resistance. The main factors controlling µrr are

the type of tyre and the tyre pressure. The free-wheeling performance of a vehicle

becomes much better if the tyres are pumped up to a high pressure, though the ride

may be less comfortable.

The value of µrr can reasonably readily be found by pulling a vehicle at a steady very

low speed, and measuring the force required. Typical values of µrr are 0.015 for a

35

radial ply tyre, down to about 0.005 for tyres developed especially for electric

vehicles.

3.2.2 AERODYNAMIC DRAG

This part of the force is due to the friction of the vehicle body moving through the

air. It is a function of the frontal area, shape, protrusions such as side mirrors, ducts

and air passages, spoilers, and many other factors. The formula for this component is:

Fad = 0.5CdρAv2 (3.2)

Where ρ is the density of the air, A is the frontal area, and v is the velocity. Cd is a

constant called the drag coefficient.

The drag coefficient Cd can be reduced by good vehicle design. A typical value for a

saloon car is 0.3, but some electric vehicle designs have achieved values as low as

0.19. There is greater opportunity for reducing Cd in electric vehicle design because

there is more flexibility in the location of the major components, and there is less

need for cooling air ducting and under-vehicle pipe work. However, some vehicles,

such as motorcycles and buses will inevitably have much larger values, and Cd varies

around 0.7 are more typical in such cases.

The density of air does of course vary with temperature, altitude and humidity.

However a value of 1.25 kg.m−3 is a reasonable value to use in most cases. Provided

that SI units are used (m2for A, m.s−1for v) then the value of Fad will be given in

Newton.

3.2.3 HILL CLIMBING FORCE

The force needed to drive the vehicle up a slope is the most straight forward to find.

It is simply the component of the vehicle weight that acts along the slope. By simple

resolution of forces we see that:

Fhc= mg sin (ψ) (3.3)

36

3.2.4 ACCELERATION FORCE

If the velocity of the vehicle is changing, then clearly a force will need to be applied

in addition to the forces shown in Figure 3.1. This force will provide the linear

acceleration of the vehicle, and is given by the well-known equation derived from

Newton’s second law,

Fla= ma (3.4)

However, for a more accurate picture of the force needed to accelerate the vehicle we

should also consider the force needed to make the rotating parts turn faster. In other

words, we need to consider rotational acceleration as well as linear acceleration. The

main issue here is the electric motor, not necessarily because of its particularly high

moment of inertia, but because of its higher angular speeds.

Figure 3.2: Arrangement for connecting a motor to a drive wheel using a belt system with step up gear mechanism to increase the amount of torque. [6]

Referring to Figure 7.2, clearly the axle torque = Fter , where r is the radius of the

tyre, and Fte is the tractive effort delivered by the power train. If G is the gear ratio of

the system connecting the motor to the axle, and Tm is the motor torque, then we can

say that:

Tvech = Tm × G

Tm = Fte r𝐺𝐺

(3.5)

37

Again, angular velocity of the motor,

ωm = G × ωvech = G vr

(rad/sec) (3.6)

Where, v = velocity of the vehicle in m/s

Torque required for this angular acceleration is,

Tm = JG ar (3.7)

Where, J is the moment of inertia of the motor. The force at the wheels needed to

provide the angular acceleration (Fωa) is found by combining this equation with Eq.

(3.7);

Fωa = J G2

r2 a (3.8)

We must note that in these simple equations we have assumed that the gear system is

100% efficient, it causes no losses. Since the system will usually be very simple, the

efficiency is often very high. However, it will never be 100%, and so we should

rewrite the equation by incorporating the gear system efficiency ηg. The force

required will be slightly larger, so equation (7.8) can be rewritten to:

Fωa = J G2

r2 a × ηg (3.9)

Typical values for the constants here are 40 for G/r and 0.025 kg.m2 for the moment

of inertia. These are for a 30 kW motor, driving a car which reaches 60 kph at a

motor speed of 7000 rpm. Such a car would probably weigh about 800 kg. The right

hand side in equation (7.8) will have a value of about 40 kg in this case. In other

words the angular acceleration force given by equation (7.8) will typically be much

smaller than the linear acceleration force given by equation (7.4). In this specific (but

reasonably typical) case, it will be smaller by the ratio:

40800

= .05 = 5%

It will quite often turn out that the moment of inertia of the motor J will not be

known. In such cases a reasonable approximation is to simply increase the mass by

5% in equation (7.4), and to ignore the Fωa term.

38

3.2.5 TOTAL TRACTIVE EFFORT

The total tractive effort is the sum of all these forces:

Fte= Frr+ Fad+ Fhc+ Fla+ Fωa (3.10) Where,

• Frris the rolling resistance force, given by equation (3.1);

• Fadis the aerodynamic drag, given by equation (3.2);

• Fhcis the hill climbing force, given by equation (3.3);

• Flais the force required to give linear acceleration given by equation (3.4);

• Fωa is the force required to give angular acceleration to the rotating motor,

given by equation (3.9).

We should note that Fla and Fωa will be negative if the vehicle is slowing down, and

that Fhc will be negative if it is going downhill.

3.3 MODELLING VEHICLE ACCELERATION

3.3.1 ACCELERATION PERFORMANCE PARAMETER

The acceleration of a vehicle is a key performance indicator, though there is no

standard measure used. Typically the time to accelerate from standstill to 60 mph, or

30 or 50 kph will be given. The nearest to such a standard for electric vehicles are the

0–30 kph and 0–50 kph times, though these times are not given for all vehicles. Such

acceleration figures are found from simulation or testing of real vehicles. For IC

engine vehicles this is done at maximum power, or ‘wide open throttle’ (WOT).

Similarly, for electric vehicles performance simulations are carried out at maximum

torque.

As discussed in Chapter 2 that the maximum torque of an electric motor is a fairly

simple function of angular speed. In most cases, at low speeds, the maximum torque

is a constant, until the motor speed reaches a critical value ωc after which the torque

falls. This critical value of speed is mostly known as the base speed of the motor i.e.

the speed up to which the motor is capable of maintaining the maximum or constant

torque that it produces. In the case of a brushed shunt or permanent magnet DC

motor the torque falls linearly with increasing speed. In the case of most other types

39

of motor, the torque falls in such a way that the power remains constant. The angular

velocity of the motor depends on the gear ratio G and the radius of the drive wheel r

as in equation (3.5) derived above. So we can say that:

For, 𝜔𝜔m< 𝜔𝜔base ; Tm = Tmax = 97.5 N.m

And for 𝜔𝜔m> 𝜔𝜔base ; Tm = T0 - K𝜔𝜔m = T0 – KG𝜔𝜔vech (3.11)

= T0 – KG𝑣𝑣𝑟𝑟 (3.12)

Where, 𝜔𝜔vech = angular velocity of the velocity (i.e. angular velocity of the axle) (rad/sec) 𝜔𝜔m = angular velocity of the motor (rad/sec) 𝑣𝑣 = velocity of the vehicle. (m/s)

Eq. (3.11) represents motor torque in terms of angular velocity of the vehicle where as Eq. (3.12) represents it in terms of linear velocity of the vehicle.

3.3.2 MOTOR TORQUE MODELLING

The generalized torque equation of the motor can be written as-

Tm = KTφIa = KTφVRT

− KT KBφ2

RTωm (3.13)

Motor angular speed, ωm = 2ωvech = 2 vr (3.14)

so, in terms of vehicle speed,

Tm = KTφIa = KTφVRT

− 2KT KBφ2

RT rv (3.15)

Putting all the values of the constants and other parameters,

𝑇𝑇𝑚𝑚= 650−15.384𝜔𝜔𝑚𝑚 (3.16) At base speed, 𝜔𝜔m = 𝜔𝜔base;

𝑇𝑇𝑚𝑚=𝑇𝑇𝑚𝑚𝑚𝑚𝑚𝑚 = 97.5 = 650−15.384𝜔𝜔𝑏𝑏𝑚𝑚𝑏𝑏𝑏𝑏

𝜔𝜔𝑏𝑏𝑚𝑚𝑏𝑏𝑏𝑏 = 551.3315.984

= 35.84 rad/sec (3.17)

𝑣𝑣 = 𝜔𝜔𝑚𝑚 × 𝑟𝑟2

= 0.15𝜔𝜔𝑚𝑚 = 0.15 x 35.84 = 5.376 m/s (3.18)

40

3.3.3 TRACTION LOAD MODELLING

Total tractive force required for the vehicle movement when it is moving in a road in a smooth flat plane,

Fte= Frr+ Fad+ Fla+ Fωa

as per Eq. (3.10). Hill climbing force can be considered zero because of assuming zero inclination.

Fte = 1.05m dvdt

+ μmg + Cd × 0.5ρAv2 (3.19)

Here the moment of inertia of the motor is not known, so we will adopt the expedient

suggested at the end of Section 7.2.5, and increase m by 5% in the linear acceleration

term only.

Torque required for the traction,

Tte = Fte x r (3.20)

The motor is coupled with the axle through a gear. If G is the gear ratio, then the total

load torque for traction referred to motor shaft can be written as-

Tm = Motor Torque = Tte𝐺𝐺

= Fte ×rG

= 𝑟𝑟𝐺𝐺

[𝑚𝑚𝑑𝑑𝑣𝑣𝑑𝑑𝑑𝑑

+ 𝜇𝜇𝑚𝑚𝜇𝜇 + 𝐶𝐶𝑑𝑑 × 0.5𝜌𝜌𝜌𝜌𝑣𝑣2 ] (3.21)

= 𝑟𝑟𝐺𝐺

[𝑚𝑚𝑟𝑟2

𝑑𝑑𝜔𝜔𝑚𝑚𝑑𝑑𝑑𝑑

+ 𝜇𝜇𝑚𝑚𝜇𝜇 + 𝐶𝐶𝑑𝑑 × 0.0625𝜌𝜌𝜌𝜌𝑟𝑟2𝜔𝜔𝑚𝑚2 ] (3.22)

where, 𝑣𝑣 = 𝜔𝜔𝑣𝑣𝑏𝑏𝑣𝑣ℎ𝑟𝑟 = 𝜔𝜔𝑚𝑚×𝑟𝑟2

= vehicle velocity

Let us put all the values in Eq. (3.22) to obtain a equation that will describe the

dynamics of traction load;

• The electric vehicle has a mass of 380 kg, with a typical passenger of mass 180

kg (for 3 passengers with average mass of 60kg) so total mass m = (180+200)

= 380 kg.

• To incorporate the angular acceleration of different rotating parts of the vehicle

along with motor, m is increased by 5% in the linear acceleration term only.

A value of 400 kg will thus be used from m in the final term of equation

(3.19).

41

• The drag coefficient Cd is estimated as 0.3, a reasonable value for a small

electric vehicle whose shape of the body is aerodynamically designed and

optimized.

• The frontal area of vehicle and rider = 1.2 m2.

• The tires and wheel bearings give a coefficient of rolling resistance,

µrr= 0.005 which is a typical value for specially designed tires for electric

vehicle.

• The motor is connected to the rear wheel using a 2:1 ratio belt system, and the

wheel diameter is 60 cm. Thus G = 2 and r = 0.3 m.

A typical figure of the motor coupled with the axle of the vehicle through a step up

gear mechanism is shown in Figure. (3.3).

Figure 3.3: The simplified diagram of the designed system of connecting the motor with the driving axle of the vehicle with a geared mechanism.

42

Putting all the values in Eq. (3.22) the final equation can be obtained as-

𝑇𝑇𝑚𝑚 = 9 𝑑𝑑𝜔𝜔𝑚𝑚𝑑𝑑𝑑𝑑

+ 2.95 + 𝐶𝐶𝑑𝑑 × 0.00075𝜔𝜔𝑚𝑚 2 (3.23)

Again, Eq. (3.23) can be written in terms of vehicle velocity as-

𝑇𝑇𝑚𝑚 = 60 𝑑𝑑𝑣𝑣𝑑𝑑𝑑𝑑

+ 2.95 + 𝐶𝐶𝑑𝑑 × 0.03321𝑣𝑣2 (3.24)

3.4 MODELLING PERFORMANCE PARAMETERS

When 𝜔𝜔m < 𝜔𝜔base; the motor will produce maximum amount of torque and this torque will be utilize to accelerate the vehicle. From Eq. (3.24);

𝑇𝑇𝑚𝑚 = 𝑇𝑇𝑚𝑚𝑚𝑚𝑚𝑚 = 97.5 = 60 𝑑𝑑𝑣𝑣𝑑𝑑𝑑𝑑

+ 2.95 + 𝐶𝐶𝑑𝑑 × 0.03321𝑣𝑣2

1.576 = 𝑑𝑑𝑣𝑣𝑑𝑑𝑑𝑑

+ 0.0005535𝑣𝑣2

𝑑𝑑𝑣𝑣𝑑𝑑𝑑𝑑

= 1.576 − 0.0005535𝑣𝑣2 (3.25)

When 𝜔𝜔m ≥ 𝜔𝜔base; i.e. v ≥ 5.376, motor torque 𝑇𝑇𝑚𝑚 is given by Eq. (3.16). Based on that, Eq. (3.24) can be written as-

Tm = 650−15.384ωm

= 650−15.3842

0.3𝑣𝑣= 650−102.56v =60 𝑑𝑑𝑣𝑣

𝑑𝑑𝑑𝑑+ 2.95 + 𝐶𝐶𝑑𝑑 × 0.03321𝑣𝑣2

This can be arranged into-

𝑑𝑑𝑣𝑣𝑑𝑑𝑑𝑑

= 10.271 − 1.628𝑣𝑣 − 0.000527𝑣𝑣2 (3.26)

The total vehicle traction acceleration and final speed can be modeled using Eq.

(3.25) and Eq. (3.26). There are many practical and simple ways of solving these

differential equations using a simple initial condition that v = 0 when t = 0.

However, the most versatile next step is to derive a simple numerical solution, which

can then easily be used in MATLAB.

The derivative of v is simply the difference between consecutive values of v divided

by the time step. Applying this to equation (3.25) gives us:

𝑑𝑑𝑣𝑣𝑑𝑑𝑑𝑑

=𝑣𝑣𝑛𝑛+1 − 𝑣𝑣𝑛𝑛

Δt= 1.576 − 0.0005535𝑣𝑣2

𝑣𝑣𝑛𝑛+1 = 𝑣𝑣𝑛𝑛 + Δt × (1.576 − 0.0005535𝑣𝑣𝑛𝑛2) (3.27)

43

Similarly, Eq. (3.26) can be arranged as-

𝑣𝑣𝑛𝑛+1 = 𝑣𝑣𝑛𝑛 + Δt × (10.271 − 1.628𝑣𝑣𝑛𝑛 − 0.0005535𝑣𝑣𝑛𝑛2) (3.28)

Eq. (3.27) holds valid for velocities up to the critical velocity of 5.376 ms−1, after

which we have to use equation (3.28), approximated in exactly the same way as we

have done for equation (3.27).

The MATLAB script file (discussed in Appendix-A) shows how to solve these

equations using this program. Figure 3.4 is a plot of the solution using a time step Δt

of 0.1s.

The simulated results are discussed in the following-

Figure 3.4: The initial acceleration and final velocity of the vehicle.

From the figure it is clearly evident that the vehicle takes just over 5 seconds to reach

its maximum speed of 22.5kmph. At this point the motor will rotate at a speed of

41.667 rad/sec which is very close to its rated speed (38.46 rad/sec).

44

Figure 3.5: The torque-velocity curve of the motor and vehicle respectively.

The maximum amount of torque obtained from the motor is around 95 N.m. This torque is responsible to accelerate the vehicle. This maximum torque of 95 N.m is maintained up to the base speed of the motor which corresponds to the vehicle speed of (5.376 x 3.6) = 19.3536kmph. After that, the torque begins to fall and eventually settles down to the balancing speed of the motor. At final or balancing speed, the torque falls very sharply as the acceleration phase is over and it requires only to overcome the rolling resistance and aerodynamic resistance of the vehicle when speed becomes constant (as Fla becomes zero at constant speed due to zero acceleration).

The total torque profile of the vehicle from zero to final speed can be visualized as shown in Figure 3.6-

Figure 3.6: The torque profile of the load as seen from the motor shaft.

45

The constant torque region provides the maximum torque which in turn provides a

linear constant acceleration up to base speed that is 19.35kmph speed of the vehicle.

After that, the torque falls naturally as it enters to the natural characteristic region of

its operation. Finally the motor torque matches with the load torque which falls

significantly and continues to operate at this value.

The axle torque i.e. the vehicle torque with respect to vehicle speed and time are

shown in Figure (3.7) and Figure (3.8) respectively. It may be noted here that, the

axle torque will be around 2 times greater than motor torque due to the presence of a

step up gear. At the same time, considering an efficiency of 98% for the gear

arrangement, the actual torque will be .98 times of it.

Figure 3.7: Axle Torque of the vehicle with respect to its speed. It is exactly in the

same nature of the motor-vehicle speed curve of Fig. (3.5).

46

Figure 3.8: Axle torque profile though out the entire time of run of the vehicle

Axle Torque of the vehicle with respect time to show the maximum starting torque

along with final steady state torque value of the vehicle. As the acceleration phase is

over around 7.5 seconds, the torque falls significantly and settles to a new lower

value where it remains constant for the rest of the period of it operation.

The final parameter of the motor to be discussed and analyzed is motor current. As

the current is proportional to motor torque, it will vary itself according to the

variation of torque during different periods of its operation.

The current-vehicle speed and current-time curves are shown in Figure (3.9) and

Figure (3.10) respectively.

47

Figure 3.9: Armature Current vs Vehicle Speed

Armature current of the motor varies with speed. Initially current is constant up to the

base speed and then starts to reduce as speed tends to become constant. Here the

average current value during starting is shown. In practice the starting current will be

very high which will be limited by using a current controller (will be discussed in the

next chapter). With the presence of controller, the current wave shape will not be like

this. But this result helps to final value of the current during Steady State operation

Figure 3.9: Armature current of the motor with respect to time. The current taken by the motor is very small during steady-state operation.

48

3.5 MODELLING PERFORMANCE PARAMETERS USING WINDING

CHANGE OVER TECHNIQUE

The analysis presented so far is presented for a conventional compound motor

employed to drive a vehicle. The analysis and simulation show that, the maximum

achievable speed of the vehicle is 22.5kmph. Now, the feature of winding change

over should be employed and the vehicle parameters like speed, torque and motor

parameters like motor current and torque should be simulated and observed. It was

claimed at the very beginning of the thesis that, using this technique, the final speed

of the vehicle will be much higher than the speed obtained by running the vehicle

using conventional motors (like series or separately excited DC Motors).

When the vehicle settles down to its final speed of 22.5kmph, the controller of the

motor will disconnect the series field of the compound motor from the circuit. As

result there will be a sudden rise in the armature current (which will eventually

limited by the current controller) as well as motor torque to accelerate the vehicle to a

higher value of speed. This phenomenon can be observed by using the same model

that has been developed in immediate earlier to simulate conventional compound

motor.

When the series field winding is disconnected the motor will be converted to a

simple DC shunt motor whose torque-speed characteristic is pretty straight forward

and very simple to analyze. Due to winding change over the motor is left with only

one i.e. the shunt winding and the total flux of the machine will now be produced

with the help of shunt winding only. So, the torque equation can be written as-

Tm = KTφshIa = KTφsh VRT

− KT KBφsh2

RT𝜔𝜔𝑚𝑚 = 195.013−1.385𝜔𝜔𝑚𝑚 (3.29)

= 195.013−9.2333v Now, in the similar way of Eq.(3.25), we can develop another equation using Eq.

(3.29). It must be noted that, this Eq. (3.29) will be coming into the consideration

when the vehicle speed is equal to its final speed that is 22.5kmph i.e. 6.25m/s.

When, 𝜔𝜔𝑚𝑚 ≥ 41.667 rad/sec (i.e. vehicle speed, v≥6.25m/s);

195.013−9.2333v = 60 𝑑𝑑𝑣𝑣𝑑𝑑𝑑𝑑

+ 2.95 + 𝐶𝐶𝑑𝑑 × 0.03321𝑣𝑣2

49

which can now be rearranged to write-

𝑑𝑑𝑣𝑣𝑑𝑑𝑑𝑑

= 3.0486 − 0.1465𝑣𝑣 − 0.000527𝑣𝑣2 (3.30)

For numerical simulation the Eq. (3.30) can be re-written as-

𝑣𝑣𝑛𝑛+1 = 𝑣𝑣𝑛𝑛 + Δt × (3.0486 − 0.1465𝑣𝑣𝑛𝑛 − 0.0005535𝑣𝑣𝑛𝑛2) (3.31)

Motor torque is simulated using the following equation –

𝑇𝑇𝑀𝑀(𝑛𝑛 + 1) = 2.95 + 60 �𝑣𝑣𝑛𝑛+1−𝑣𝑣𝑛𝑛Δ𝑑𝑑

� + 0.03321𝑣𝑣𝑛𝑛2 (3.31)

Axle or the vehicle torque for traction can be calculated as-

𝑇𝑇𝑑𝑑𝑏𝑏 (𝑛𝑛 + 1) = 5.9 + 120 �𝑣𝑣𝑛𝑛+1−𝑣𝑣𝑛𝑛Δ𝑑𝑑

� + 0.06642𝑣𝑣𝑛𝑛2 (3.32)

Armature current will be calculated based on two different conditions.

when, 𝑣𝑣 < 6.25 m/s; the armature current Ia is calculated as-

𝐼𝐼𝑚𝑚(𝑛𝑛 + 1) = �0.24+0.1138𝑇𝑇𝑀𝑀 (𝑛𝑛+1)−0.48750.057

(3.33)

when, 𝑣𝑣 ≥ 6.25 m/s; the armature current Ia is calculated as-

𝐼𝐼𝑚𝑚(𝑛𝑛 + 1) = 𝑇𝑇𝑀𝑀 (𝑛𝑛+1)0.4875

(3.34)

So, the modified MATLAB script file (shown in Appendix-B) according to the

modification done in the system due to winding changeover would yield the

following set of output curves for speed, torque and current. This set of results will

be used to compare the performance between the vehicle fitted with winding change

over facility and the vehicles operated with series and compound motor only without

winding change over facility. The different output and input parameters of the motor

as well as the vehicle obtained by simulation in MATLAB are shown as follows one

by one along with description and significance of the figures for interpretation.

50

Figure 3.10: Simulated Speed and acceleration characteristic of the vehicle with the

feature of winding change over facility.

A comparative diagram showing the speed without and with the winding change over

facility would be more helpful to justify the improvement in the performances of

vehicle. A diagram of such kind is shown in Figure 3.11 in the following-

Figure 3.11: Comparative analysis showing the differences in terms of final speed

between the two types of motor.

51

Fig. (3.11) clearly indicates that, the motor with winding change over facility would

provide the highest final speed. The difference in their final is around 47.5kmph.

This is certainly being a great advantage for the latter one compare to the former one.

Figure 3.11: Torque speed characteristic of the motor with winding change over facility. The sharp rise in torque is due to sudden change in current consumed by the

armature due to disconnecting the series field.

The total torque profile of the motor is shown in Figure 3.12.

Figure 3.12: Torque profile of the motor during entire period of its operation.

52

Figure 3.13: Torque –speed characteristic of the vehicle when operated by a compound motor with winding change over facility.

Figure 3.14: Torque profile of the vehicle from starting to “winding change” over to steady state condition, when operated by a compound motor with winding change

over facility.

53

Figure 3.15: Speed-current characteristic of the motor. After winding change over, the value of the current remains very during the entire period of its acceleration.

Figure 3.16: Current profile of the motor during its entire period of operation.

A very high current is being consumed by the current at the moment of winding

change over. This is due to the sudden reduction in the flux of the motor as the series

winding is disconnected from the armature at this instant. To sustain the same

amount of torque, the current of the motor rises to a very high value due to

compensate the reduction of flux. As the motor speed approaches towards its final

speed, the current starts to decrease and eventually settles down to a steady value. It

54

must be noted with great importance that, such amount of high current must not be

allowed to flow in the circuit as it may damage the winding as well as the motor. In

practice this current will be limited by using a hysteresis current controller which will

restrict the current within twice the maximum of its rated value (i.e. 40x2=80A). In

other words, the controller will allow a current to flow through the armature which

may be at best twice than its rated value. Such a limitation will obviously affect the

performance of the motor. Due to such restriction in current the torque produced by

the motor will be less and as result the acceleration of the vehicle beyond the instant

of winding change over will be reduced. But this will not affect the final speed of the

motor. Due to limited amount of torque available, the vehicle will take a relatively

long time to reach its final speed.

3.6 SUMMERY

This chapter deals with the modeling and simulation of electric vehicle. It is obvious

that, a vehicle’s mathematical model is crucially important in the design of electric

vehicles as it allows the designer very quickly to try out different design options,

virtually at no cost at all. Even a quite simple mathematical model used in this

chapter is sufficient to predict the performance parameters of a real vehicle.

55

CHAPTER 4 DESIGN OF CONVERTER AND CONTROLLER FOR

ELECTRIC VEHICLE

4.1 INTRODUCTION

This chapter presents the design of the controller of the motor. Choppers, also

commonly known as dc-to-dc converters which are used to get a variable dc voltage

from a dc source of fixed voltage. Because of the use DC voltage widely in electric

transportation and traction system, chopper controlled DC drives find a ready

application in that field.

DC-DC Converters are widely used for traction motor controls in electric

automobiles, trolley cars, marine hoists, forklift trucks and mine haulers. They

provide smooth acceleration control, high efficiency and fast dynamic response. DC-

DC converters can be effectively used in regenerative braking of DC motors to return

energy back into the supply and this feature results in energy savings for the

transportation systems with frequent stops.

Self commutated devices, such as MOSFETS. power transistors, IGBT (insulated

gate bipolar transistor), GTO ( gate turn-off thyristor) and IGCT (insulated gate

commutated thyristor). are preferred over thyristors for building choppers because

they can be commutated by a low power control signal and do not need commutation

circuit. Further, they can be operated at a higher frequency for the same rating. The

operation at a high frequency improves motor performance by reducing current ripple

and eliminating discontinuous conduction.

4.2 CONVERTER DESIGN

For any traction application a two quadrant converter with a pair of reversing switch

is necessary. Otherwise it is not possible for the motor to operate at all four quadrants

as it is mandatory for any motor to be capable of operating in all the four quadrants

employed for traction application.

56

In this design a Two Quadrant Class C DC-DC converter along with a pair of

reversing switch are used. The converter has a novel integrated feature of both PWM

and Hysteresis controller, where the PWM controller is used for variable voltage

operation of the motor (to run the vehicle at different speed) and hysteresis controller

is used for the purpose of current control. The designed system is shown in brief in

the following block diagram-

Figure 4.1: Block Diagram Representation of the Motor Controller

4.3 OPERATION OF THE CLASS C DC-DC CONVERTER

A typical class C converter is made of one pair of diode and one pair of switch.

Generally, it is made from one buck and one boost converter. For normal motoring

mode the circuit operates as buck controller. During braking of the motor which is

also known as regenerative braking, the converter operates as a boost converter to

feed back the stored kinetic energy of the motor to the source and thus reducing its

speed. A typical circuit is shown in Fig. 4.2.

57

Figure 4.2: Class C DC-DC converter

The circuit shown in Figure 4.2 is a combination of one Buck and one Boost

converter. It is clear that, both transistors must not be turned on simultaneously as

that would short circuit the source V. They are turned on alternately and a short

interval (typically about 100µs) is allowed to elapse between the removals of one

signal and the application of the other.

For first quadrant operation, Tr1 and D1 perform the functions of Forward motoring

and provide variable speed operation of the motor up to the base speed. Gate drive

signal with variable duty cycle enables the converter to provide with a variable

voltage appearing across its terminals. This mode of operation is called Class A

operation where the converter is operating as buck converter. Both armature current

and field current are positive. The motor develops torque to meet the load demand.

For second quadrant operation, Tr2 and D2 perform the functions of Regenerative

braking and the converter must operate as Boost converter to feed the stored kinetic

energy of the motor back to the supply system or the battery. This mode of operation

is also known as Class B operation of chopper. The motor acts as a generator and

develops an induced voltage equal to the back EMF of the motor, EB. The armature

current is negative but the field current is positive. The kinetic energy of the motor is

returned to the supply. The motor speed would decrease with time. To maintain the

armature current at the same level the effective load resistance of the motor acting as

generator during this period, must be adjusted by varying the duty cycle of the DC-

DC converter.

58

4.4 SIMULATION OF THE CONVERTER

The converter circuit is simulated in LTSpice in motoring mode. The output wave

shape of the converter are shown in the following-

Figure 4.3: Simulation of Class C DC-DC converter in forward motoring mode in

LTSpice.

59

Figure 4.4: Output current, voltage and PWM signal of the converter

Figure 4.5: Motor current without hysteresis current controller.

The starting Current of the motor is around 345A which dangerously high enough to damage the motor.

60

Figure 4.6: Limitation on starting current by the control action of hysteresis controller

Hysteresis current controller limits the starting motor current within its maximum

limit. If the motor current exceeds twice the value of the rated current the controller

turns off the power supply and when the current falls to value sufficiently low

enough the controller again turns on the power supply.

Figure 4.7: Output voltage of the converter at a Duty cycle of 90%.

61

The variable output voltage can be obtained by varying the duty cycle of the

converter. Variation of duty cycle is possible by varying the reference voltage of the

PWM comparator. Gate driving pulses with variable duty cycle are generated to

operate the motor in different speed. This signal along with the output of the

hysteresis controller are fed to an AND gate where the output of hysteresis controller

dominates over the PWM signal. If the Current of the motor at any point due to

application of the voltage exceeds the certain limit the output of the hysteresis

controller goes zero setting an output zero for and gate too and eventually turns of the

power supply to the motor.

4.4 REGENERATIVE BRAKING

Regenerative braking will be obtained as the converter operates in the 2nd quadrant.

Gate signal with appropriate duty cycle must be generated to provide the switching.

The circuit must contain a duty cycle varying feature where the duty cycle of the

gating pulses will be varied by sensing the terminal voltage of the motor during

regenerative braking. The duty cycle must be varied to keep the output voltage of the

converter fixed as the voltage of the motor will be gradually decreasing during the

period of regeneration and as a result the speed of the motor will be decreasing. If the

voltage at the output of the converter is not kept fixed and higher than the source

voltage, it will not be possible to feed the energy back to the source as current will

stop continuing to flow.

Simulation of regenerative braking is done assuming the stored kinetic energy will

eventually be given up and the motor will to come to a stop with no voltage across its

terminal. So, source voltage must be gradually decreasing during braking and to keep

the output voltage constant, the reference voltage of the comparator should be

increased accordingly to increase the duty cycle of gate driving signal. The simulated

circuit is shown in Figure 4.8.

62

Figure 4.8: Simulated Boost Converter during Regenerative braking

63

Figure 4.9: Output Voltage and Current of the Boost converter during Braking

Figure 4.10: Generation of Reference signal to vary the duty cycle of the converter

64

Figure 4.11: Boost Converter Input Power due to the kinetic energy stored in the

vehicle

Figure 4.12: Boost Converter Output Power. The amount of energy which is equal to

the area under the curve, is feed back to the source

65

4.5 SUMMARY

This chapter has suggested such a design of the converter that is capable of varying

its output voltage and at the same time limits the excess current. The two quadrant

operation of the motor enables the motor to operate at both Forward motoring and

Forward regenerative braking. For reverse motoring reverse contacts are employed to

operate the motor in opposite direction.

66

CHAPTER 5 SIMULATION OF THE OVERALL SYSTEM

5.1 INTRODUCTION

The overall system is electromechanical which is simulated using SIMULINK.

Simulated figures in this chapter are divided into two parts. Here at first the

simulation of the total system would be presented for a compound motor with

winding change over technique. The simulated figures will contain the Speed of the

vehicle, Torque of the system, Current and output power. Next the same simulation

will be done for the overall vehicle and traction system when operated by a series

motor of same power. This portion is simulated to deduce a comparison between the

proposed method and the conventional method. According to simulated result it can

very be easily found out that, the proposed method offers a better performance

because the vehicle will be operating at a higher speed compare to the case when it is

operated by series motor. To simulate the entire system three subsystems have to be

integrated with the overall system. The entire system comprises of –

• Electronic DC-DC converter • Compound Motor • Mechanical System (Traction Load)

5.2 SIMULATION RESULTS

All three sub systems are integrated and co-ordinated together to perform the

simulation work. The entire simulation is done for a 60 seconds run of the vehicle.

The simulated block in SIMULINK is shown in Figure.5.1.

67

Figure 5.1: Simulation of the entire electromechanical system using SIMULINK

68

The system response is obtained as-

Figure 5.2: Speed of the vehicle with winding change over technique.

Figure 5.3: Motor Current vs Time

The motor current is being regulated by the Hysteresis controller, always remains in

the permissible limit of operation. Hysteresis controller will be in effect whenever the

current tries to exceed the limits.

69

Figure 5.4: Motor Torque Vs Time

Figure 5.5: Motor Power Vs Time

70

Now for the purpose of comparison the simulated results for a series motor driven

electric vehicle with same characteristics as before will be presented in the following.

Figure 5.6: Speed of the vehicle operated with Series Motor.

Figure 5.7: Current vs Time for the series motor

71

Figure 5.8: Power Vs Time for the Series Motor

5.3 SUMMERY

Simulation of the overall system clearly signifies the fact that, the proposed method

of winding change over feature can improve the performance of an electric vehicle

when operated with a DC motor. The conventional traction loads are operated with

DC series motor. Final Speed obtained for the vehicle with the proposed system is

around 72kmph whereas, with conventional DC series motor, the obtained maximum

speed is 54kmph. But one thing that also should be focused here that, as the proposed

method is operating at a speed 18kmph higher than the conventional method energy

consumed by the motor will be more as the resistance force due to aerodynamic drag

offered by vehicle increases with the square of the velocity and hence power required

increases with the cube of the velocity.

72

CHAPTER 6 CONCLUSION

7.1 SUMMARY

A Novel Switching technique along with a new concept is proposed for the purpose

of traction. The ideal characteristics of an electric motor drive for traction

application in an electric and hybrid electric vehicle are high torque at low speed

region for fast acceleration, hill climbing and obstacle negotiation, and low

torque at high speed for normal driving. A single DC motor cannot fulfill all these

ideal requirements. But according to the proposed method of using a compound

motor with winding change over, the characteristics will be very close to the ideal

one. To minimize the power rating of the motor drive, therefore, the energy

storage requirement, at a given vehicle performance, the electric motor drive is

required to have a long constant power range to meet the torque and speed

demand. Once again this proposed method enables the motor to maximize its

capability by prolonging its constant power. The effect of the motor characteristics

on the vehicle performance is analyzed, and the characteristics of three major

electric motors- induction motor, permanent magnet brushless DC motor and

switched reluctance motor are studied for literature review, where it has been

concluded that, though DC machines are now almost become obsolete, still it has the

maximum torque density and the most suitable characteristics for traction

application. This technique can further enhance that capability of the DC motor for

traction application as the result suggests an improvement in its performance

compare to the traditional one. Results show a better acceleration performance and

significant improvement in final speed of the vehicle. This technique minimizes the

power rating of the motor as it is operating at a longer constant power range due to

change over in its configurations. The high torque operation of the compound and

series configuration is utilized as well as the field long constant power range

operation of shunt configuration by field weakening is also being made use of. The

simulation results show that, the extended speed operation of the motor can reach up

73

to 3.5 times of the base speed which can never be obtained without the feature of

winding change over. At the same time it is also evident that, this method will

consume more power to run the vehicle and it is obvious that, the power consumption

will be more for higher speed of operation.

7.2 FUTURE WORKS

As stated earlier, the proposed method demands a relatively larger amount of power,

the most important task still left is to calculate the energy consumption of the vehicle

for per Kilometer of operation. This would provide the final concluding remark of

this study.

From this the Mileage of the vehicle for a given battery capacity can be very easily

determined which has not been done yet. At the same time for nominal operation of

the vehicle, the battery size and its capacity has to be determined.

Comparative study with other types motor can be done and then the motor with

optimum performance for traction application can be chosen.

Microcontroller can be used as the prime controller of the entire system which should

perform all the necessary control action and this would make the system more

optimum, flexible and adaptable to any operating condition.

Advanced algorithms like Fuzzy logic or Neuro-Fuzzy controller may be introduced

for system operation. These adaptive advanced algorithms may also be used to

replace the brushed DC motor by a Brushless DC motor which would be more

advanced and efficient compare to the conventional one.

7.3 CONCLUDING REMARKS

Long constant power range of vehicle traction motor can effectively reduce

the required motor power rating for the given vehicle acceleration performance

and at the same time, the gradeability of the vehicle can he enhanced

significantly, thereby, reduce the required power capacity of the on-board

energy storage, such as the batteries. It can also simplify the transmission system

74

by allowing use of a single-gear transmission. Consequently, the whole drive

train can he designed with compactness, high efficiency and good reliability.

Of the three major candidates of traction motors, permanent magnet brushless

DC motor has the highest torque density. However, the constant power range is

very limited due to the difficulty of the field weakening. The constant speed

range of variable speed induction motor drives is also limited to maximum of 4

times of its base speed, even using special winding changeover technique. On the

other hand, switched reluctance motor drives inherently have favorable speed-

torque characteristic for traction application. This design and simulation shows

that the extended speed constant power range can reach about 3 (3.5 times the

based speed), much higher than other kinds of electric motors, with high

operating efficiency.

75

REFERENCES [1] Mehrad Ehsani, Yimin Gao, Sebastiaen Gay, “Characteristics of Electric

motor Drives for Traction Application” IEEE transaction on vehicular technology, 2003.

[2] Y. Wong, Theory of Ground Vehicle, John Wiley & Son, Inc., 1978. Page 132-133.

[3] Yimin-Gao, and M. Ehsani, “A Mild Hybrid Drive Trainfor 42 V Automotive Power System--Design, Control and Simulation”, SAE 2002 World Congress, Detroit, MI., Paper No. 2002-02-1082

[4] M. H. Rashid, Power Electronics Handbook. Academic Press, 2001.

[5] Z. Rahman, K.L. Butler and M. Ehsani, “Effect of Extended-speed, Constant-

power Operation of Electric Drives on the Design and Performance of EV Propulsion System“, SAE Future Car Congress, Apr. 2000, Paper No. 2001-01-0699

[6] John, Larmanie. “Electric Vehicle Technology Explained”, John Wiley and

Sons. [7] M.Ehsani, Yimin Gao, “ Application of Electric Peaking Hybrid Propulsion

system to a Full Size Passenger Car with Simulation Design Verification”, IEEE Transaction on Vehicular Technology, Vol. 48, No.6, Nov, 1999.

[8] Z. Rahman, “ K.L.Butler, M.Ehsani, “ Effect of Extended Speed, constant

Power Operation of Electric Drives on the Design and Performance of EV Propulsion System.” , SAE Future Car Congress, Apr. 2000. Paper No. 2001-01-0699.

[9] M.H.Rashid, “Power Electronics- Circuits, Devices and Applications,”

Prentice-Hall of India. [9] S.M. Bashi, N. Marium, S.B. Noor & H.S. Athab, “Three- Phase Single

Switch Power Factor Correction Circuit with Harmonic Reduction”, Journal of Applied Sciences 5(1); 80-84,2005, ISSN 1607-8926 © 2005 Asian Network for Scientific Information.

[10] A.R. Prasad, P.D. Ziagos & S. Manias, “An Active Power Factor Correction Technique for Three-Phase Diode Rectifier”, IEEE Trans. on Power Electronics, vol. 6, no.1, pp.83-92, January1991.

[11] E. Ismail & R.W. Erickson, “A Single Transistor Three-Phase Resonant Switch for High Quality Rectification”, M. Sc Thesis, Dept of Electrical & Computer Engineering, University of Colorado, Boulder 80309-0425,1992.

76

[12] O. Gercia, J.A. Cobos, R. Prieto, P. Alou & J. Ueeda, “An Alternative to Supply DC Voltage with High Power Factor”, IEEE Trans. on Industrial Electronics, vol.46, no.4, pp.703-709, August 1999.

[13] R. Redl, ” Low Cost Line Harmonic Reduction”, Professional Education Seminar Workshop, IEEE Applied Power Electronic Conf.,1995.

[14] J.C. Salmon, “Techniques for Minimizing the Input Current Distortion of Current Controlled Single-Phase Boost rectifiers”, IEEE Trans. on Power Electronic, vol.8,no.4,pp.509-520, October 1993.

[15] J.A.G. Marafao, J.A. Pomillio, “A high quality three phase rectifier complying with IEC 61000-3-40 standards”, School of Electrical & Computer Engineering, University of Campinas, Brazil, G. Spiazzi, dept of Electronics & Informarics, University of Padova, Italy.

[16] M.J. Kocher & R.L. Steigerwald, “An AC to DC Converter with High Quality Input Waveforms”, IEEE Trans. on Industrial Applications, 1A-19, pp.586-599,1983.

[17] Y. Jane & M. Jovanovic,”A New Input Voltage Feed forward Harmonic Injection Technique with Nonlinear Gain Control for Single Switch, Three-Phase, DCM Boost Rectifier”, IEEE Trans. On Power Electronics, vol.28, no.1, pp.268-277, March, 2000.

[18] Q. Huang, “Harmonic Reduction in a Single Switch Three Phase Boost Rectifier with Harmonic Injected PWM”, M.Sc. Thesis, Dept. of Electrical Engineering, Virginia Polytechnic Institute & State University.

[19] R. Erickson, “Fundamental of Power Electronics”, Khuwer 1997,ch-17.

[20] J. Chen, D. Maksimovie & R. Erickson, “A New Low Stress Buck-Boost Converter for Universal Input PFC Applications”, Colorado Power Electronics Center, dept. of Electrical & Computer Engineering, University of Colorado at Boulder, Boulder, CO80309-0425,USA.

[21] C. Qiao & K.M. Smedley, “Unified Constant Frequency Integration Control of Three Phase Standard Bridge Boost Rectifier”, Dept. of Electrical & Computer Engineering, University of California, Irvine.

[22] Mao. H. D. Boroyevich & F.C Lee, “Analysis & Design of High Frequency Three-Phase Boost Rectifiers”, APEC96, pp.538-544.

[23] R.W. Erickson, “Some Topologies of High Quality Rectifiers” Keynote paper, First International Conference on Energy, Power & Motion Control, May-6,1997, Tel Aviv, Israel.

77

[24] L. Ressetto, Dept of Electrical Engineering, G.Spiazzi & P. Tenti, Dept. of Electronics & Informatics, “Boost PFC with 100Hz Switching Frequency Providing Output Voltage Stabilization & Compliance with EMC Standards”, University of Padova, Italy.

[25] M.H. Rashid, “Power Electronics”, Prentice Hall of India,2004, 3rd edition.

[26] J.A. Gomes, Marafao, J.A. Pomilio, G. Spiazzi, “Improved Three Phase High Quality Rectifier with Line Commutated Switches”, IEEE transactions on power Electronics, vol.19, no.3, May 2004.

[27] K.D. Purton & R.P. Lisner, “Average Current Mode Control in Power Electronic Converters Analog versus Digital”, Dept. of Electrical & Computer System Engineering, Monash University, Australia.

[28] R. Ghosh & G. Narayan, “Input Voltage Sensorless Average Current Control Technique for High Power Factor Boost Rectifiers Operated in Discontinuous Conduction Mode”, Power Electronics Group, Dept. of Electrical Engineering, Indian Institute of Science, Bangalore-560012, IEEE2005.

[29] Simonetti, D.S.L., J. Ueeda, “single Switch Three Phase Power Factor Pre regulator Under Variable Switching Frequency & Discontinuous Input Current”, Conference Record IEEE PESC,pp:657-662,1993.

[30] Lolar, J.W., H.Ertl & F.C. Zach, “Space Vector Based Analytical Analysis of the Inpur Current Distortion of a Three-Phase Discontinuous Mode Boost Rectifier system”, Conference Record, IEEE PESC, pp:696-703,1993.

[31] C.M. Wang, “ZCS-PWM Boost Rectifier with High Power Factor & Low Conduction Losses”, Lunghwa University of Science & Technology, Taiwan, IEEE Trans. on Aerospace & Electronic System,vol.40,no.2,April 2004.

[32] Y. Jang & M.M. Jovanovic, “A New Technique for Reducing Switching Losses in Pulse Width Modulated Boost Converter”, Delta Peoducts Corporation, Power Electronics Laboratory, P.O.Box 12173,5101 Davis Drive, Research Tringle park, NC 27709.

[33] E.H. Ismail & R. Erickson, “A New Class of Low Cost Three-Phase High Quality Rectifiers with Zero Voltage Switching”, IEEE Trans. on Power Electronics, vol.12no.4, July1997.

[34] Q.Huang & F.C. Lee, “Characterization & Control of Three-Phase Boost Rectifier at Light Load”, Proceedings of the Virginia Power Electronics center seminar 1996, pp.29-34.

78

Appendix-A MATLAB SCRIPT FILE FOR SIMULATING VEHICLE PERFORMANCE

PARAMETERS WITHOUT WINDING CHANGE OVER TECHNIQUE

t=linspace(0,100,1001); vel=zeros(1,1001); d=zeros(1,1001); T=zeros(1,1001); Tv=zeros(1,1001); I=zeros(1,1001); dT=0.1; for n=1:1000 if vel(n)<5.376 vel(n+1)=vel(n)+dT*(1.51-(0.000527*(vel(n)^2))); elseif vel(n)>=5.376 vel(n+1)=vel(n)+dT*(10.271-(1.628*vel(n))-(0.000527*(vel(n)^2))); end d(n+1)=d(n)+0.1*vel(n); T(n+1)=2.95+(60*((vel(n+1)-vel(n))/dT))+(0.03321*(vel(n)^2)); Tv(n+1)=2*T(n+1); end for n=1:1000 I(n+1)=((sqrt(0.24+(0.1138*T(n+1))))-.4875)/0.057; end vel=vel.*3.6; figure(1) plot(t(1:1001),vel); axis([0 50 0 30]); xlabel('Time/seconds'); ylabel('velocity/kph'); title('full power Acceleration'); hold figure(2) plot (vel,T); hold figure(3) plot(t(1:1001),T); figure(4) plot(vel,I); figure(5) plot(t(1:1001),I); figure(6) plot (vel,Tv); hold figure(7) plot(t(1:1001),Tv);

*************************************

79

Appendix-B MATLAB SCRIPT FILE FOR SIMULATING VEHICLE PERFORMANCE

PARAMETERS WITH WINDING CHANGE OVER TECHNIQUE

t=linspace(0,100,1001); vel=zeros(1,1001); d=zeros(1,1001); T=zeros(1,1001); Tv=zeros(1,1001); I=zeros(1,1001); dT=0.1; for n=1:1000 if vel(n)<5.376 vel(n+1)=vel(n)+dT*(1.51-(0.000527*(vel(n)^2))); elseif vel(n)>=5.376 && vel(n)<6.25 vel(n+1)=vel(n)+dT*(10.271-(1.628*vel(n))-(0.000527*(vel(n)^2))); elseif vel(n)>=6.25 vel(n+1)=vel(n)+dT*(3.0486-(0.1465*vel(n))-(0.000527*(vel(n)^2))); end d(n+1)=d(n)+0.1*vel(n); T(n+1)=2.95+(60*((vel(n+1)-vel(n))/dT))+(0.03321*(vel(n)^2)); Tv(n+1)=2*T(n+1); end for n=1:1000 if vel(n)<6.25 I(n+1)=((sqrt(0.24+(0.1138*T(n+1))))-.4875)/0.057; elseif vel(n)>=6.25 I(n+1)=T(n+1)/.4875; end end vel=vel.*3.6; figure(1) plot(t(1:1001),vel); axis([0 50 0 30]); xlabel('Time/seconds'); ylabel('velocity/kph'); title('full power Acceleration'); hold figure(2) plot (vel,T); hold figure(3) plot(t(1:1001),T); figure(4) plot(vel,I); figure(5) plot(t(1:1001),I); figure(6) plot (vel,Tv); hold figure(7) plot(t(1:1001),Tv);