a thesis in electrical engineering the requirements for

. ;

MODEL OF THE ELECTRICAL SYSTEM

OF A HEV

by

ARIF AL AMIN, B.Sc.E.

A THESIS

IN

ELECTRICAL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

ELECTRICAL ENGINEERING

Approved

May, 2000

T^ ACKNOWLEDGEMENTS

CQ-|0 ." I am deeply indebted to Dr. Micheal Parten, my advisor for his in-depth

mental and engineering resource to this project. His experience and most of all his

sincerity have enabled this project to become a reality and a truly clrallenging

experience.

1 would also like to thank Mr. Paul Leonard and Mr. Todd Bell for their

sincere help during the testing period of the project.

TABLE OF CONTENTS

ACKNOWLEDGEMENTS ii

ABSTRACT v

LIST OF TABLES vi

LIST OF FIGURES vii

CHAPTER I. AN OVERVIEW OF HYBRID ELECTRIC VEHICLE AND ITS

MODELLING 1 1.1 Alternative Fuel Vehicles 1

1.1.1 Electric Vehicles as Possible Alternatives to Petroleum Fuel Vehicles 1

1.1.2 Hybrid Electric Vehicle 3 1.1.3 Configuration of Hybrid Electric Vehicles 4

1.1.3.1 Series hybrid vehicle 4 1.1.3.2 Parallel hybrid vehicle 5

1.2 Operation of the Electrical System of an Electric or Hybrid Vehicle 5 1.2.1 Energy System 5 1.2.2 Power System 6 1.2.3 Drive Train 6 1.2.4 Charger System 7 1.2.5 Auxiliary System 7

1.3 Goals for Modeling All-Electric and Hybrid Electric Vehicle..7 1.4 Forward Facing Model of Hybrid Electric Vehicle 9 1.5 Approach to Model the Vehicle 11

II. MODELING OF AN AC INDUCTION MOTOR 12 2.1 AC Induction Motor 13 2.2 Basics of Induction Machine 13

2.2.1 Types and Construction of an Induction Machine 13 2.2.2 Rotating Electric Field and Slip 14

2.3 Lumped Parameter Circuit of an Induction Motor 15 2.4 Block Diagram of the Model 19 2.5 Estimation of Parameters 29 2.6 Simulink Block for Parameter Estimation 31

III. MODEL OF THE MOTOR CONTROLLER 36 3.1 Introduction Machine Drive 36

III

3.1.1 A Basic Topology of the Machine Drive System 36 3.2 Defining Inputs and Outputs of the Motor Controller Model..38 3.3 Approach to Model the Vehicle Motor Controller 39

3.3.1 Closed-Loop Speed Control System 39 3.3.2 Constant Terminal Volts/Hz Operation of the Motor..40 3.3.3 Controlled Slip Operation 44

3.4 Operation of the Motor Controller 46 3.4.1 Constant Torque Operation !f. 46 3.4.2 Constant Power Operation 46 3.4.3 High Speed Motoring 47

3.5 Simulink Block of the Motor Controller 48

IV. VEHICLE DYNAMICS MODEL 55 4.1 Modeling Equation for Vehicle Dynamics 55 4.2 Aerodynamic Resistance 56 4.3 Effect of Rolling Resistance 59 4.4 Model of the Vehicle 62

4.4.1 Inputs and Outputs of the Vehicle 62 4.4.2 Simulink Model of the Vehicle 64

V. SIMULATION RESULTS OF THE MODELS 68 5.1 Simulation of the Electrical System of a Vehicle 68 5.2 Simulation of a Model Vehicle 69 5.3 Simulation Results 71

5.3.1 Motor Simulation Results 71 5.3.2 Vehicle Dynamics Simulation 75

5.4 Simulation of the Overall Vehicle Model 78 5.4.1 Simulation for Urban Driving Cycle 83 5.4.2 Simulation for Highway Driving Cycle 85

5.5 Validation of Simulation Results 88 5.6 Limitations of the Model 99

VI. CONCLUSION 101

REFERENCES 103

IV

ABSTRACT

A computer simulation of power train components of an Electric Vehicle or Hybrid

Electric Vehicle is required as an analysis tool for engineers in automotive industry.

Two components, motor controller and AC induction motor, are investigated in detail

because of the importance in the analysis and design. Detail analysis of the equations

that are used in the models are provided and methods for characterizing the models

for different systems components are described. Commercial dynamic simulation

software (SIMULINK) is utilized, which has a graphical environment based on

nonlinear state block diagrams.

LIST OF TABLES

4.1. Typical values of rolling resistance coefficients for different surfaces 61

5.1 Motor specification 70

5.2 Specification of motor controller >^ 70

5.3 Parameters of the vehicle 71

5.4 Circuit parameters of motor for modeling 72

VI

LIST OF FIGURES

1.1 Block diagram of EV 2

2.1 Circuit representing the induction motor 16

2.2 Inputs and outputs to the motor model 20

2.3 Flow of variables in the model 21

2.4 Simulink model of an ac induction type motor 22

2.5 Inside of Induction motor block 23

2.6 Inside of the Motor block 24

2.7 The equations used in the model 25

2.8 Inside the torque block 26

2.9 Inside of the current block 27

2.10 Inside of correction block 28

2.11 Simulink block for parameter estimation 32

2.12 Simulink model inside the parameter estimation block 33

2.13 Flow of variable in the simulink models for parameter calculation 34

2.14 Simulink model inside the magnetizing block 35

3.1 Block diagram of a modern electric drive 37

3.2 Block diagram of the model of motor controller 38

3.3 Closed-loop speed control of a drive system 39

3.4 Closed-loop speed control with volts/hertz and slip regulation 42

3.5 Induction motor drive with direct control of rotor frequency 45

3.6 Variation of torque, current, and slip with speed for a constant slip, constant volt/hz controlled motor .48

VII

3.7 Simulink block for motor controller 49

3.8 Inside of the motor controller block 50

3.9 Inside of the voltage conversion block 51

4.1 Different values of aerodynamic drag coefficient for vehicles

of various models 58

4.2 Block diagram of the vehicle dynamics model 63

4.3 Simulink block of vehicle dynamics model 64

4.4 Inside of the vehicle dynamics block 65

4.5 Inside of the vehicle block 66

4.6 Inside of the basic block 67

5.1 Block diagram of the model of electrical system of a vehicle 68

5.2 Electrical system ofthe "Future Car 1999" 69

5.3 Torque versus speed curve ofthe motor 72

5.4 The torque speed curve ofthe motor from the manufacturer 73

5.5 Stator rms current versus speed 74

5.6 Torque versus slip ofthe motor 74

5.7 Power factor versus speed ofthe motor 75

5.8 Power train force (NM) available for the vehicle 76

5.9 Aerodynamic drag force (NM) versus speed(MPH) ofthe vehicle 76

5.10 Acceleration (m/sec^) versus time 77

5.11 Complete block for the electrical system of the vehicle 79

5.12 The feedback block ofthe vehicle model 80

5.13 Inside the vehicle block. The connection ofthe individual blocks

to get the complete block 81

5.14 Inside of the power calculation block 82

5.15 Reference driving cycle( urban ) in MPH 83

5.16 Output speed ofthe vehicle in MPH 83

V I I I

5.17 Acceleration (m/sec^) versus time 83

5.18 Torque versus time for urban driving cycle 84

5.19 Stator rms current ( A) for urban driving cycle 84

5.20 Stator phase voltage for the vehicle 85

5.21 The highway driving cycle as reference 85

5.22 Output Speed of the vehicle 86

5.23 Acceleration (m/sec^) for the driving cycle 86

5.24 RMS stator phase voltage ofthe motor for highway driving 87

5.25 Stator rms current for highway driving cycle 87

5.26 Speed response and acceleration for a reference speed of 0-60 mph at an acceleration of 2.4384 m/sec^ 88

5.27 Torque delivered by a motor versus speed ofthe vehicle for a

reference speed of 0-60 mph at an acceleration of 2.4384 m/sec 89

5.28 Stator current and stator voltage and stator frequency ofthe motor 90

5.29 Power output of a motor for the speed command of 0-60 mph in 9 seconds..91

5.30 Efficiency ofthe power train for the speed command of 0-60 mph in 9 sec..91

5.31 Ampere-hour demanded by the motor to maintain the input speed profile... 92 5.32 Speed response ofthe vehicle for an input of 0-60 mph within 9 seconds

when the DC input is 265 volts 93 5.33 Torque delivered by the motor versus time for an input of 0-60 mph

within 9 seconds when the DC input is 265 volts 94

5.34 Power output of a motor for the speed command of 0-60 mph in 9 seconds when the DC input is 265 V 94

5.35 The demand stator rms voltage and the controller output ac rms voltage when the DC voltage input is 312 V 95

5.36 The demanded stator rms voltage and the controller output ac rms voltage when the DC voltage input is 265 V 96

5.37 The demanded stator rms voltage and controller output rms voltage when the DC input voltage is 225 V 96

5.38 Speed response ofthe vehicle for an input of 0-60 mph within 9 seconds when the DC input is 265 V 97

5.39 Torque delivered by the motor versus time for an input 0-60 mph within 9 seconds when the DC input is 225 V 98

IX

5.40 Power output of a motor for the speed command of 0-60 mph in

9 seconds when the DC input is 225V 98

5.41 Oscillation ofthe torque response at starting (2 seconds) 99

5.42 The torque versus speed response ofthe vehicle for an input of 0-60 mph in 9 seconds without using PI control 100

5.43 The torque delivered by the motors for an input of 0-60 mph/vithout using PI contoller 100

CHAPTER I

AN OVERVIEW OF HYBRID ELECTRIC VEHICLE AND ITS MODELING

1.1 Altemative Fuel Vehicles

The transportation system is vital to the economy of the United States but at

the same time gasoline and diesel ftaeled vehicles are the greatest source of air

pollution. With the number of vehicles continuously increasing, air pollution in urban

areas is becoming of greater concern. Also U.S. dependency on gasoline products

from foreign countries is increasing daily. To attack the air quality problem and as a

response to fuel dependency, research to achieve fuel diversity with cleaner,

altemative fuels and develop vehicles that uses these fuels is going on nationwide.

This effort is dedicated toward achieving a truly diverse transportation landscape that

will provide consumer competitive choices in transportation technology, fuels and

fueling options, while meeting the cleaner air goals.

1.1.1 Electric Vehicles as Possible Alternatives to Petroleum Fuel Vehicles

Electric vehicles (EVs) are vehicles that are powered by an electric motor

instead of an internal combustion engine. EVs use electricity as "ftiel" instead of

gasoline or some other combustible fuel. Figure 1.1 shows the block diagram ofthe

electric vehicle. Electric cars have been around since the inception ofthe automobile.

In the early race for dominance, the internal combustion engine (ICE) won quickly as

the best power system for cars because as a source of energy, the battery was no

match for the high energy content, ease of handling, and cheap and abundant supply

of petroleum motor ftiel. As the easily recoverable petroleum deposits are not endless

and the cities are becoming choked with combustion by products, the ICE is

becoming a victim of its own success. So today, nearly a century later, it seems that

electric cars may be the ultimate winner.

Energy Storage System (Rechargeable batteries)

Fig 1.1 : Block diagram of EV

EVs have made dramatic improvements with respect to consumer

acceptability over the last few decades. Batteries have been developed that have

higher output and storage capacity while reducing overall weight. Motor technology

has also improved, resuhing in higher efficiencies, and power to weight ratio.

Lightweight and strong materials such as carbon fiber composites are being used in

vehicle bodies to reduce weight. All these developments helped to make electric

vehicles much more acceptable.

Electric vehicles have several unique features. EVs have no tail pipe emission

and the more advanced electric vehicle motors emit almost no sound. Most advanced

electric vehicles use single speed AC motors with no transmission. Acceleration is

smooth and seamless. Although great improvements have been made in EV

technology, they still fail in several areas as far as consumer acceptance is concerned.

The major factor that has slowed the acceptance of EVs is their limited range.

Today's electric vehicles use less expensive lead acid batteries or advanced prototype

batteries. Lead acid powered electric vehicles only have about 50 mile range between

charges. Advanced batteries hope to achieve about 100 mile range between charges

and are very expensive. In order to achieve these distances between charges, recharge

is not a trivial task. Recharge requires considerable time ranging between 2-6 hours.

These downsides of the electric vehicle lead to an investigation of alternatives. The

hybrid electric vehicle is a possible solution to the problem of fully electric cars.

1.1.2 Hybrid Electric Vehicle (HEV)

A hybrid electric vehicle (HEV) is simply a battery electric vehicle with an

on-board auxiliary power unit. The on-board APU produces mechanical or electrical

power. The output of this APU system is combined whh the electric motor to mn the

vehicle. Hybrid electric vehicle provides roughly two or three times the fuel economy

of its intemal combustion engine vehicle. HEV s are more complex than a battery

powered vehicle. Hybrid electric vehicles can be recharged just like electric vehicles.

Thus this type of configuration allows the owner to operate the vehicle as a zero

emission, battery EV for urban driving, while allowing the comfort of switching to

hybrid mode for long trip or in situations where recharging is not readily available.

Initially, HEVs are not expected to compete directly with standard vehicles on

performance alone (e.g., acceleration and range), but they are expected to offer

benefits that a standard vehicle does not offer. Compared to today's standard vehicles,

for example, HEVs will reduce local/regional pollution, by means of:

• increased vehicle mileage (2X) per gallon of ftiel.

• Lower emissions per vehicle mile traveled.

• Propulsion systems that can be cycled off during stop-and-go driving,

producing no emissions.

• Fuels or fuel systems with reduced fuel evaporation and refueling

losses.

1.1.3 Configuration of Hybrid Electric Vehicles

1.1.3.1 Series hybrid vehicle

A series hybrid vehicle has one prime mover, an electric motor, powered by a

battery pack and/or an engine turning an electric generator. The motor converts

electrical power to mechanical power for propulsion. Electrical power for the motor is

available from an electrical energy storage device and/or auxiliary power unit (APU).

The APU consists of an intemal combustion engine and a generator. The engine

converts the heat energy potential of fuel into mechanical power. The mechanical

power of the engine is converted to electrical power in the generator and used by the

drive motor to move the vehicle. The electric power created by the generator can also

be used to recharge the electrical energy storage device.

1.1.3.2 Parallel hybrid vehicles kP

In a parallel hybrid electric vehicle, there are two prime movers—an ICE and an

electric motor. The engine converts the heat energy potential of ftael into mechanical

power. The sum of the engine power and motor power is available at the wheels. A

controller determines the load share of each device depending on the total required

power, the operating efficiency, and the limitations of each device. Control can be

optimized for ftael, economy, performance, emissions, and range.

1.2 Operation ofthe Electrical System of an Electric or Hybrid Electric Vehicle

The main operating components of an all-electric or hybrid electric vehicle are

described briefly here to get an overview ofthe whole system. The electrical part of

the EV or HEV is an addition to conventional vehicles.

1.2.1 Energy System

The energy storage system ofthe vehicle is a battery pack consisting of

rechargeable batteries. This stored energy is used to power the motor. A battery

controller might be used to monitor and govern the operation ofthe battery pack. The

batteries can not be used for a long period of time because they can be overdepleted.

In a series HEV, the battery pack is charged onboard by an altemative power source

(for example, an intemal combustion engine). The number of batteries is limited by

the weight and space restrictions ofthe vehicle and also the higher the number of

batteries, the longer the recharging time.

1.2.2 Power System

Motor controllers are the "brains" ofthe system because they regulate the

flow ofthe electricity from storage batteries to the motor. As the main component in

the power system, the function of motor controller actually is to make the stored

energy compatible with the motor. If the vehicle uses an AC motor, it acts as an

inverter to convert the DC voltage from the batteries to AC voltage to the AC motors.

If the motor is a DC motor, the controller acts as a DC to DC converter. The motor

controller also takes all user inputs to control the vehicle accordingly. Motor

controllers also help to restore energy in the batteries by regenerative braking ofthe

motors when the vehicle is decelerating or coasting.

1.2.3 Drive Train

The drive train is the muscle ofthe car, an electric motor that converts the

electric power into the rotational, mechanical power, which is delivered to the wheels

through the transaxle, propelling the vehicle. In a parallel HEV both the electric

motor and the ICE can power the wheels.

1.2.4 Charger System

A charger converts AC electricity from utility power lines to DC current that

can be accepted by the EV batteries to restore their power after being depleted. Some

vehicles carry a charger onboard, while other vehicles use chargers located offboard

at recharging sites. Electric current is transmitted to the vehicle via the charger inlet.

The primary concern for chargers is their charging time and size.

1.2.5 Auxiliary System

Vehicles have heat and air conditioning, power brakes and steering, radios and

CD players and other familiar features. These auxiliary systems mn primarily from

battery-stored electricity.

1.3 Goals for Modeling All-Electric and Hybrid Electric Vehicle:

Interactions of various subsystems of a full electric or hybrid electric vehicle

makes the overall system complicated. Moreover the experience in the design of EVs

or HEVs is not well established. So, continuous research and development is going on

in an effort to make a state ofthe art analysis and design tool.

Models ofthe various components ofthe systems illustrate the important

design variables that an auto designer would consider in producing high efficiency

vehicle. To provide an insight and understanding ofthe real system, especially the

complex dynamics from the interaction of simple physics, component models are

very useful. System level transient performance is of primary interest while selecting

the components of a vehicle. That is why it is important to create a useftil analysis

tool that meets this need. An analysis tool is also required for the vehicle system that

has the ability to easily change the system level configuration (power train layouts)

and predict the results of that change.

The components ofthe system are costly and they should be carefully chosen

from a limited number of options available commercially. A model is needed which

has the ability to easily test different versions of components within the same system

configuration to compare the effects on overall system performance. With detail

knowledge ofthe inside parameters ofthe components ofthe system, an overall

system can be designed with great deal of accuracy if a simulation tool is available.

Therefore optimization and sensitivity analyses could be performed on the

components and system level. With all these in mind this thesis can be described as

an effort to take a modular approach to model the electrical system ofthe complete

system of EVs or HEVs.

This thesis describes a system level model that was developed from known

characteristics and parameters of a vehicle along with actual test results. The effect of

changes made in the vehicle system can be simulated which will ease the decision of

making any change to the complex vehicle system that costs time and money.

Modifications can first be simulated to determine their benefit before costly changes

are made to the vehicle. Thus the design can be optimized and the main goal, to

develop an efficient HEV, can be achieved using simulation.

The model of the HEV is based upon a combination of previous work and

known mathematical relationship regarding vehicle performance. Experimental and

designed data is used to simulate the vehicle performance. The established relations

and data are modeled using the MATLAB Simulink simulation software package.

Simulink provides a graphical interface that makes model construction and debugging

very simple. The control over the speed and accuracy of the simulation is easy in

Simulink, which has a wide number of simulation algorithms.

1.4 Forward Facing Model of Hybrid Electric Vehicle

Efforts from different research institutes and universities have been made to

model hybrid electric vehicles. NREL's ADvanced Vehicle SimulatOR ( ADVISOR )

is a set of models and data for use with MATLAB and Simulink. This tool provides a

backbone for the detailed simulation and analysis of user defined drivetrain

components. But the difference lies in the purpose and approach in which the models

are developed. The models, in general, use simple physics and measured components

to model existing vehicles to predict the fuel use, tail pipe emission, acceleration

performance, and gradeability.

The user ofthe model defines the overall vehicle data and prescribes a speed

versus time trace along with road grade. The model will answer the questions about

the vehicles capability to follow the trace, ftael required, peak power consumption,

efficiency of transmission, and the torque and speed profile. This is the reason the

models are only an analysis tool. ADVISOR is an analysis tool that requires speed as

input, and determines what drivetrain torque, speeds, and powers would be required

to meet the vehicle speed. Because of this information flows backwards through the

drive train, ADVISOR is called a backward facing vehicle simulation. / /

Forward facing vehicle simulation requires a model ofthe motor drive system

(motor controller) which requires speed and responds with an accelerator or brake

position to which the drivetrain responds with a torque. The model of this thesis is an

effort to make a part ofthe vehicle model forward facing. The performance can be

evaluated at each point in the drivetrain. The basic goal ofthe type of forward facing

model is to design the components so that a proper control system can be established.

The control system can be designed and simulated for its performance with this type

of model.

Ofthe various system components of a hybrid electric vehicle, the motor and

the motor drive system are given a priority here and discussed in detail. The goal of

this thesis is to design an AC motor and motor drive that meets the specific

requirements of a vehicle. The control algorithm used in the model is very simple and

the control system model is suited for design ofthe system down to the hardware and

PC card level implementation. The motor model is also developed in such a way that

the motor can be designed using this model.

This thesis discusses only the electrical system ofthe vehicle that allows it to

be very detailed about the voltages and currents. Instead of evaluating only the power

10

flow this model evaluates the current and voltages at different points, which is the

primary concern ofthe electrical system design.

1.5 Approach to Model the Vehicle

This thesis models the electrical system ofthe car which will include the

motor controllers and the motors. These two main components ofthe car can be

called the "power converter system." In order to simulate the performance of these

two systems, the vehicle dynamics model is also necessary which is the load ofthe

power converter system ofthe car. The details ofthe motor model is discussed in

Chapter II. In Chapter III simulation ofthe motor controller is discussed. Chapter IV

is about the modeling ofthe vehicle itself Chapter V is for the result ofthe

simulation where the model is verified with some available test data.

11

CHAPTER II

MODELING OF AN AC INDUCTION MOTOR

2.1 AC Induction Motor

For many years induction motors have provided the most common form of

electromechanical drives for those industrial, commercial, domestic applications that

can operate at essentially constant speed. The induction machine is chosen for its

simplicity, reliability and low cost. These factors are combined with good efficiency,

good overload capacity and minimal or no service requirement. When the facts of

wide availability and simple installation by relatively little trained person is added,

the choice of an induction machine seems well founded.

Motors that could be chosen for a vehicle are permanent magnet brushless DC

motor, induction motors. Permanent magnet DC motors are costly. They also provide

relatively low torque to weight ratio. AC induction motors are bmshless and have

robust rotor construction, which permits reliable maintenance free operation at high

speed. The simple rotor construction also results in a lower cost motor and a higher

power/weight ratio.

2.2 Basics of Induction Machine

2.2.1 Types and Construction of an Induction Machine

A polyphase induction machine has a cylindrical stator with distributed kP

winding displaced symmetrically in slots around inner periphery. Based on the rotor

structure induction motors are of two types: (a) squirrel cage and (b) wound rotor

machine.

The squirrel cage rotor consists of a series of rotor conductors evenly spaced

around periphery ofthe motor having their ends short-circuited by conductors in the

form of end rings. The number of poles in a squirrel cage rotor is always equal to the

number of poles on the stator in which it operates. The wound rotor is provided with

polyphase winding that are similar to those ofthe stator. The rotor is wound for the

same number of poles as the stator.

From the basic understanding ofthe winding ofthe stator and rotor, induction

machine is basically an electric transformer whose magnetic circuit is separated by an

air gap into two relatively movable portions, one carrying the primary and the other

carrying the secondary winding. Poly-phase alternating sinusoidal voltage is supplied

to the primary, which is coupled to the stator to produce a revolving magnetic field.

The field crosses the air gap and sweeps past the shorted conductors in the rotor.

Thus, current is induced in the rotor conductors which in turn interacts with the

magnetic field to produce torque in the direction of field rotation.

2.2.2 Rotating Electric Field and Slip

The electric field in the air gap ofthe induction machine has a constant

magnitude and shape and rotates at a constant angular velocity. Ideally it is preferable

to have the turns of each phase winding distributed sinusoidally in space around the

stator periphery. The sum ofthe fields produced by the currents in all three phase

winding would also be sinusoidaly distributed in angular space. So the field has a

constant magnitude and shape and rotates at a constant angular velocity [10,198].

3 „ . = ^ /„ cos(<«,/ + a„ - e) A.turn 2.1

Equation 2.1 is an expression for 3 describes a mmf that is sinusoidaly distributed

in space and rotating with time. In equation 2.1 ^^. is the angular speed ofthe stator

mmf in electrical radians per sec. The rotating field travels past a pair of poles for

each complete fime cycle of excitation. Therefore the rotating field travels around the

air gap at a speed of

revolutions/ = frequency{Hz) /second pole/

/ 2

So the synchronous speed ofthe field in revolutions per minute is

f^ -1^24. 2.2 ' p

In mechanical radians per second the synchronous speed is

2_

P

2 -> s mechanical x electrical

14

When the rotor is rotating at a steady speed of /y mechanical radians per second, mi

the relative speed between the rotor and the synchronously rotating field 3 , is

Slip speed = ^ -co • 2.4 sm mi

The normalized slip speed is defined as slip and determined by the Allowing

expression.

Q) —0)

s = sm "mi 2 . 5

0) sm

So the slip speed can be expressed as ^^ and the slip frequency as ^f • When

motoring, co <co > ^^^ "^Giox conductors moving backwards at a speed equal to the

slip speed { sco ) relative to the rotating field. The induced voltage in the rotor

windings will be ofthe slip frequency ^y.

2.3 Lumped Parameter Circuit of an Induction Motor

The lumped parameter cicuit model of an induction motor is shown in Figure

2.1. The stator phase voltage, y , at frequency ^ . is considered as the reference for

phasors. Thus

If the stator resistance is ignored, this will also be the induced voltage £ .Thus the

magnetizing current will be

7 =_Ji_ A. 2.6

15

C^-t- -Wv

t '. R,

E <

<

P.

i'

-^

: t IR

JCOJAR

< •

4> CO.

R R

Figure 2.1: Circuit representing the induction motor [10, 198]

This magnetizing current produces a sinusoidally distributed flux density. The stator

flux linkage, representing a sinusoidally distriubuted flux in the stator rotating at

stator frequency is expressed by

A . = A. 2.7

The stator flux linkage consists of two components in the air gap, a flux linkage

A^ representing the leakage flux and a flux linkage A, representing the flux that

crosses the air gap into the rotor core. The leakage flux path is dominated by the air

paths between the tooth tips, the air gap and between the end windings. The leakage

flux will be directly proportional to the mmf causing it. So the leakage flux can be

given by equation 2.8 where leakage inductance I^ is a constant for leakage flux path

between the stator and the rotor.

16

Ai^=LJ^ Wb. 2.8

The remaining part ofthe induced voltage is jcoA,^, which represents the effect ofthe

rotor resistance and the mechanical load seen by the stator. The rotor system as seen

CD / *^ R / by the stator is modeled as a resistance per phase of i?, y, _ .. or y . A

part ofthe power crossing the air gap is used in the losses in the rotor resistance and

the rest ofthe air gap power is the mechanical output. R,^ is the effect ofthe rotor

resistance seen by the stator. The remaining part ofthe total resistance y is the

effect ofthe mechanical output power per phase.

R ^^/ - R = R ^V ^^ /{co,-(o,y ^x ^« /(CO,-coJ

Torque is the power crossing the air gap divided by the synchronous mechanical

speed Thus

3P„ T =

g

p

^p (-li^)ii,f 2co, CO, - co^

^o^sii, ^h.f^^a^^L,y N.m

_ ^PRR ^S

^sl,p

2

— N.m 2.9

17

Near synchronous speed the rotor frequency co^^p is much less than the ratio

Ri /j and the expression for torque is approximated by

3/7 A > , Up

2 R. 2.10

Maximum torque is generated at co^,^p = y, . The expression for maximum torque

is

3/7 A':

2 L, 2.11

The above calculations were made on the simple assumption that the stator resistance

is negligible. But actually there is a considerable voltage drop in the stator resistance

and the stator current and the torque should be corrected.

The corrected value ofthe stator voltage Vsuorreci) is

V = E + R I '^ S(correct) ^S ^ ^^stator ^s

The corrected torque and the stator current can be calculated according to the solution

ofthe model circuit [10, 203].

T = T * Corrected calculated

f E ^" V

\ S{correct) J

2.12

/ = / * •' S(correct) •* S{calailaled)

^ E ^

V, \ S{correct) )

2.13

18

2.4 Block Diagram ofthe Model

In this case, the induction machine is a part ofthe electrical system of a hybrid

electric vehicle. In order for the model ofthe motor to be compatible with the model

ofthe motor controller, which is basically a variable voltage and variable frequency

drive, the inputs to the motor are stator voltage and stator frequency. The outputs are

torque, speed, stator current, slip. Torque will be the input to the vehicle model,

which is the available shaft torque to the vehicle. The other outputs are needed to see

the performance ofthe motor.

The motor model is basically divided into three different blocks. The block

diagram of Figure 2.3 shows these three different blocks. The simulink blocks are

build according to this plan in which the equations ofthe lumped parameter circuit of

the induction machine is used. The primary block ofthe simulink model is shown in

Figure 2.4. The inside details ofthe simulink model are given in Figure 2.5 to

Figure 2.10

19

Stator voltage

Stator frequency

r >

U ^

> 1 /

M

O

T

O

R

3 PHASE AC

INDUCTION TYPE

^ ^

1^

> \^

r^ >

\y

r^

^

Torque

Stator r.iirrent

RPM

Slip

Figure 2.2 : Inputs and outputs to the motor model.

20

Rotor Resistance i?,

Leakage Inductance L,

Mutual Inductance

'M

Number of Poles P

Stator Phase Voltage V,

Stator Phasem frequency f.

A

V

A V

V

A V

A

T

O

R

U

A

RPM

Mechanical Load

^ SHp5

Torque T

Angular speed of stator co^

Angular speed of rotor CO.

A V

Magentizing Current, /^

O <y <y

CURRENT

E Stator Phase

^ Torque T /

Stator Phase A .V

E 5L^

CORRECTION

Figure 2.3 : Flow of variables in the model

21

In Figure 2.5 the torque ofthe motor is applied to the load and the mechanical speed

is obtained. The mechanical speed is converted into the electrical speed and fed back

to the motor block. RPM and slip is calculated in this block. Figure 2.6 shows inside

ofthe motor block, which consists ofthe three basic blocks that were shown in Figure

2.3. The inside of these blocks are shown in Figure 2.8 to Figure 2.10. The equations

used in these models are shown in Figure 2.7.

Stator

60

frequency f in HZ

stator vo

132.8

tage pe r phase

^

w

Torque

Stator Frequency

slip

Stator Current

power factor

stator phase voiatge

RPM

fc-w

1 1

Torque

^

k w

1 1

slip

1 1

stator current

^

pov

1 1

fverfat nor

w

spec

1 1

•d in F iPM

w

P Tonq

o ue vs dip

w F ^ W

Toq

o j e vsj 3pe(

Induction aiotor

Figure 2.4: Simulink model of an ac induction type motor

22

f(u)

Fen

t

Mu

x

Mux

a in

o

o

c o a -a

o

c

(N

CO

o o E c o o 3

TO c

23

o o

o o

o — «

(U

CO

24

di ii

^

•^ f o »s rs fS <s c c o o ^ ^ ^ r f

cq cq 3 3 O" O"

u u

a (.1

r4 c

03 3

a*

c --T 2' 3 :C

I

j2 3

3

u

m f S 1 - ^

<s 3 o

• * ^

CQ 3

r-rt

. (N C o rt D rr

W

bJ. ^

c _o o t o U

I J

O

a>

C

• « — >

cr

3 op

25

o o

cr

-a . .-

CO

CX3

CO

c o

3 _U (0 O 0) 3 E o

26

r«» c u

fl c

3 o o re

r

00 c o

1

o u

c u

X

^ o npo

Q.

IV ^

-> f(

u)

^

Fcn

4

t

Fcn

5

J

o a.

c o 75 3 O re o "c 0)

o o re w

o O

c (L) 3 o CD

on C

ON (N <U V-c

3 CO

27

^

o _o jS c o o OJ ; - • U

O

o o

rs "to C

(N

l - r

3

Hi

c o

o O

28

2.5 Estimation of Parameters

All ofthe parameters ofthe motors used in HEVs are usually not available from

the manufacturers. Simulations are frequently done to determine the motor to use, in

which case, the motor is not available for measurements. So the parameters ofthe motors

can be roughly calculated from its rated operating conditions and then simulations can be

performed using these parameters to get specific characteristics. The parameters can be

optimized using the simulation results. The following discussion is about the procedure to

determine the parameters from the standard name-plate data and the operating points of

the motor.

The motor name-plate data will provide the maximum operating speed ofthe

motor in RPM. This speed is used to calculate the maximum stator frequency.

The number of poles of a machine can be known from specification and then the stator

frequency is calculated according to the following relationship.

_ PjPole) * SpeedjRPM) J Staler {max) ~ 1 OH

The Stator phase voltage for the rated load is also available. The stator phase

voltage is assumed to be equal to the induced emf, the flux linkage,

A, = - ^ . 2.15

The starting torque and maximum torque value is available from the torque speed

profile. Using the statrting torque and the maximum torque the rotor resistance and the

leakage inductance can be estimated.

29

The leakage inductance is obtained from the maximum torque expression and this

value is later used to calculate the rotor resistance.

^ / . = 3/7 A'^

2 T 2.16

max

The torque can be expressed as a frinction of stator flux linkage, slip speed and

other circuit parameters.

T = 3pR, Alv

2co. 'R.^ 2.17

\ 0) J \ r J + 4

At the moment of starting, the rotor is at standstill. This means that slip is 100%,

the slip speed is equal to the stator speed.

Q) = CO r " ^ 5

So the starting torque can be calculated from the following equation.

T ^pR, A\v

Start 2co, 'R.^ 2.18

v^.sy + 4

Knowing the starting torque, the rotor resistance can be calculated. The following

equation is used in the simulink block to calcualte the rotor resistance.

^R.^

R.,= 2a>, \^sj

+ 4

3/?r, Start A's 2.19

30

Using the circuit parameters calculated above the rotor current can be calculated

as

2.20 !« = R^co,

CO r

E,

•+y^y. ,•4

The stator phase current is available from the motor specification. It can be

calculated from the rated power ofthe motor. So the magnetizing current can be

determined and the magnetizing inductance is estimated from the magnetizing current.

h=h + L 2.21

/,. = I, cos (9 + JI^ sin 0 - JI^ 2.22

/^ = I„ s'mO-^l's -{l„ COS0Y 2.23

where 0 = —!— 2.24 Rn

E, •M - J »

<y.v

A.V

h, 2.25

So the parameters can be calculated approximately and these values can be used to model

the motor.

2.6 Simulink Block for Parameter Estimation

A simulink block was designed to assist in the parameter estimation. The inputs to

the block are the available set of known operating values like line to line voltage, stator

phase current and supply frequency. The number of poles assumed. The maximum torque

and the starting torque are obtained from the torque speed profile. Using these inputs the

31

simulink block provides a rough values ofthe circuit parameters that are used to model

the machine. Several different operating conditions can be tried to get the parameters.

Then an ideal set of parameters can be selected to be used in the simulation. The simulink

block diagram is shown in the Fig. 2.11.

Fig. 2.12 shows the inside ofthe parameter estimation block. Fig. 2.13 shows the

flow of variables in the simulation ofthe block which is implemented in the block shown

in Fig. 2.12. Fig. 2.14 shows the inside ofthe magnetizing block which calculates the

current according to equation 2.20.

f

stator

\

1

opera

Max

statt

A .

)0le2

60

freq

230

745

ting 1

167

torq

25

Dr cu

72 •

uency

=JPM

ue

rrent

^ ^

^ w

w

^ w

•-•

^ w

^ w

starting torque

pole

staor freq

sync speed

Flux linkage

line to line Voltage

operating RPMeakage inductance

MAx torque

stator current

starting torque

Rotor Resistance

Lm

Subsystem

>CO Timr

sync speed sync speed

Flux linkage

0.3522

flux linkage

0.002229

••CID leakage inductance

Leakage inductance

— • O.-lfiH

^OD rotor resistance

Rotor Resistance

— •

Lm

0.03474

Mutual inductance

Figure 2.11 Simulink block for parameter estimation

32

V*-

}

Fen

t X X 3 3 "5 -5

8

Mux

T —

M 3

.^ C u

c u

3

.»-

CO

c u.

t 3 <S .

X 3

o o

c o

(U t-l

J3 ex o

c

o £ c

00

(N

L-i

9 O) 3 E o

c 'tr re W

33

c o

3 JJ a o t - i

B

ui

a.

o c

r3 >

O >

m

3 CO

34

o o CO

c

u c CO r3

U

C

o

^ d

00

(N

3 CO

35

CHAPTER III

MODEL OF THE MOTOR CONTROLLER

3.1 Induction Machine Drive

3.1.1 A Basic Topology ofthe Machine Drive System

Electric drives have numerous applications ranging from mdimentary motion

control to high precision machine tools. The machine has to do certain mechanical work

in terms of operating a load. An electric machine, with a drive system, should match the

load requirements, within the voltage and current limitations ofthe machine. Machines

commonly used with a drive are DC machines, synchronous and induction machines.

Since induction machines are rugged, economical, and have no sliding contacts to wear,

they have an edge on other motors in numerous applications. The difficulty of using

induction machines in variable speed drives is that they quite difficult to control since

their torque speed characteristics are complex and nonlinear.

A power semiconductor converter can control the flow of electric power between

the motor and the power source according to the load requirements. A converter is a

voltage or frequency changer. The control unit of a converter that is used to match a

changing load requirement within the range of motor capabilities can be a low power,

low voltage, unit using a microprocessor or digital signal processor.

36

Electric power source

^

C=B

Power semiconductor converter

^

C=3

Electric machine

Sensors

Control unit

n Sensors

^

Power source performance command

Drive command interface Energy flow for motoring

Energy flow for regenerative braking

Figure 3.1 Block diagram of a modem electric drive [11,2]

The inputs to the control unit are the drive commands and the power source performance

commands, which are used to adjust the operating point ofthe drive or torque and speed

ofthe machine.

The controller uses direct feedback sensors. To reduce the converter's harmonic

content, separate sensors are used to measure the voltage and current ofthe power source.

The electric machine is bilateral. Power flows from the source to load during motoring

and from the load to source during regenerative braking.

37

3.2 Defining Inputs and Outputs ofthe Motor Controller Model

The control algorithm to model the motor controller in this thesis uses the constant

volts/Hz and controlled slip operation of an induction machine. The DC voltage input to

the controller is converted to the stator rms phase voltage. The model uses feedback from

the drive shaft as its input to implement a closed-loop control system for the motor.

Speed command (Driving cycle)

Feed back signal (Vehicle speed)

DC voltage (Battery or Fuel Cell)

V

V

Motor Controller V Stator voltage

V Stator frequency

Figure 3.2 Block diagram ofthe model of motor controller

The command signal, which is the accelerator pedal input for the motor controller is

simulated by a driving cycle input to the controller. The outputs ofthe controller are

stator voltage and frequency, which is required for the specific control method used for

38

this model. The block diagram of Figure 3.2 shows the inputs and output considered for

modeling the motor controller of an electric vehicle.

kP

3.3 Approach to Model the Vehicle Motor Controller

3.3.1 Closed-Loop Speed Control System

When transient performance characteristics are not important and the motor

operates at steady speed for long periods, open-loop speed control of an induction motor

with an adjustable frequency provides satisfactory adjustable speed drive. But a feedback

control system is necessary for precise operation when the load is rapidly changing.

When rapid acceleration and deceleration is demanded, closed-loop speed control

systems provide a stable steady state operation. So for fast dynamic response, a

closed-loop control system is required.

Command speed (n*)

Speed Controller Torque

Controller

[—<SH Power converter and motor

Actual speed (n) Actual torque (T)

Load

Fig. 3.3 Closed-loop speed control of a drive system [9, 264]

39

The block diagram shown in Figure 3.3 has two loops for a closed-loop control system of

an induction motor drive. In the inner torque loop, the commanded torque is compared

with the actual torque measured from the electrical quantities of the machine for an error

signal. This error signal is used for a compensating transfer function. With satisfactory

torque control an outer loop is added to this to give an adjustable speed drive. The

reference is an analog signal whose magnitude and polarity represent the desired motor

speed and direction. The commanded speed is compared with actual speed. The resulting

speed error signal becomes the torque command signal for the inner loop.

3.3.2 Constant Terminal Volts/Hz Operation ofthe Motor

The steady state performance ofthe induction motor is analyzed from the lumped

parameter circuit model shown in Figure 2.1.The basic properties ofthe drive can be

approximated adequately by ignoring the stator resistance and leakage inductance. As a

first approximation, ignoring stator resistance drop, the fundamental frequency stator

voltage for any operating stator frequency, co^, is equal to the air gap induced emf, Es, in

the stator winding.

V,=E,=jco,K, 3.1

A , = - ^ 3.2 j^s

40

To obtain maximum torque with minimum current and therefore minimum winding loss,

the machine is normally operated at or near the rated stator flux linkage or rms value of

A . Thus a constant air gap flux is obtained when y is constant. / ^s

If the voltage drop across the stator leakage impedance is small, the air gap flux is nearly

constant when the ratio y . has a flxed value. This is called the constant terminal

volt/Hz operation. Figure 3.4 shows a block diagram of this operation. An inverter

provides the linear output voltage and frequency. But some compensation due to stator

resistance drop is necessary, particularly at low speed, when the motor performance

deteriorates at low frequencies with the air gap flux decreasing because of a voltage drop

across the stator leakage impedance. This problem is tackled by implementing a terminal

voltage /frequency characteristic in which the voltage is boosted above its frequency

proportional value at low frequency in order to compensate for the stator IR drop. Two

techniques are used to do this. For nonlinear characteristics, the terminal voltage and the

frequency are proportional at higher frequencies but a voltage boost is needed at lower

frequencies. Another approach is to maintain a linear relationship in which a constant

voltage component (V ) is added to the frequency proportional component, ko)^. V^ and

k are chosen so that voltage boost is required at zero frequency.

41

Voltage controller

-o\^ co„ -

Fig. 3.4 Closed-loop speed control with volts/hertz and slip regulation [5, 433]

The steady state torque equations can be derived from the model of an induction

machine.

T = 2 CO,

N.m 3.3

If the leakage inductance is neglected, the rotor current can be approximated by

7 . ^ ^ Rj^co,

jco,K,co^

RR^S

Ro A

42

The torque may be expressed by the following equation

TJ-^K\?i^ N.m 3.5

2 ' R,

The approximate speed-torque relationship [10,418] for the machine is therefore

2.

P

2_

P = - 0 ) , -

' 2_y R,j KPJ 3A 5 rad/sec 3.6

The relationship shows that for a constant airgap flux the torque speed relationship

depends on the stator frequency.

But as the voltage rating ofthe controller has a maximum available value, there is

a maximum stator frequency for which the rated flux linkage can be maintained. Up to

this frequency and its corresponding speed, flail load torque can be produced. But as the

speed is increased above the pull out speed ofthe motor, the machine is operated at

constant power with a reduced torque. The stator flux linkage is reduced in this region of

operation.

If the maximum stator frequency is cOf, and the operating stator frequency is

CO, > cOf,, then with a constant stator voltage of V, the rms stator flux linkage is given

approximately by

43

- V, COf, -

Ac. = — = —A... ,,. 3.7 ' i'(max) CO, CO,

And the maximum torque produced for a given stator flux linkage A is

j.jp'^\ '-•' 4 L,

0>H

\^SJ T., • 3.8

3.3.3 Controlled Slip Operation

As long as the rotor frequency does not exceed the breakdown value,

corresponding to the maximum torque, the induction machine operates at high power

factor and high efficiency. Beyond that point, the motor power factor and torque per

ampere is low. So in an adjustable speed motor drive, the motor should be operated at

low slip frequencies for stable operation with high power factor and torque/stator current.

To achieve this, a controlled slip technique is used. Slip is defined as

(co. -co„,)

CO,

where co, and ct)„, are the synchronous and actual shaft speeds. Slip speed is defined as,

COr = COs - 0)„, = SCO,

CO, =co„, +co^. 3.10

So a command rotor speed, <2;*r, is implemented by a control system in which co,„ is

measured by a tachometer and is added to co*r to generate the inverter frequency

command co\. Thus, direct control of slip speed is possible. Figure 3.5 shows the block

diagram of controlled slip operation.

44

3 phase ac supply

Static frequency converter

co;

1 \

CO,

Rotor

Frequency command

CO.

Induction I M I motor

Tachometer

Figure 3.5 Induction motor drive with direct control of rotor frequency [9, 283]

The torque dependency for an induction machine on slip speed can be seen from the

following sets of equations.

T = ^P RR T2

2 CO.

2 ' Ro

~ K ' ' A 2 = ^ ' A > . 3.11

For a constant air gap flux and small rotor slip, torque is directly proportional to O)^ (slip

speed).

45

3.4 Operation ofthe Motor Controller

3.4.1 Constant Torque Operation

In the constant torque operation the air gap flux is maintained constant by

applying the constant terminal volts/Hz operating principle. The stator voltage can only

be increased up to a certain value due to the limitations imposed by the motor stator

winding or the power electronic devices used in the machine drive. Thus this limiting

voltage and frequency defines the base speed ofthe motor which is the normal operating

speed ofthe motor at its rated voltage and current

3.4.2 Constant Power Operation:

Above the base speed, the stator voltage remains constant and the motor is

operated using controlled slip drive. The air gap flux is reduced but slip is increased to

maintain the stator current at its limit and the torque varies inversely with the stator

frequency. The induction machine torque at small slip is given by the equation

T^K'''k\co^. 3.12

In high frequencies the air gap flux can be assumed to be proportional to the terminal

volts/Hz ratio [9, 285]. Thus

- i2 v.. T = K

^v 0),

^r

If rotor speed is increased linearly with stator speed (—- = k), the output torque varies CO,

inversely with the stator speed CD, , giving a constant horse power characteristic.

46

T = K'"-^ 3.13 CO, 'S

3.4.3 High Speed Motoring

When the slip frequency finally approaches a value corresponding to the pull out

torque, the slip is kept just under its pull-out torque value as the stator frequency is

further increased the output torque varies inversely with the speed squared. A family of

motor torque-speed characteristics at different stator frequencies in the constant torque,

constant horsepower and high speed motoring regions can be plotted. It can be found that

the maximum torque or breakdown torque is constant below base speed and decreases

inversely with speed squared above base speed. The operating characteristic is shown.

The slip is held constant below base speed but increased with supply frequency to get a

constant horsepower characteristic upto twice base speed.

Figure 3.6 shows the variation in motor voltage current, slip frequency and

torque, as a function of speed for the operating characteristic discussed above. At base

speed, the motor is supplied with rated voltage and frequency, and draws rated current,

the developed torque is half of the pullout torque. In the constant horsepower region the

stator current stays constant at rated value but rotor frequency or slip speed is increased

to the pull-out value.

47

Stator voltage /

Motor torque \

1.0 2.0

Per-unit speed 3.0

Figure 3.6 Variation of torque, current, and slip with speed for a constant slip, constant volt/hz controlled motor [9, 287].

3.5 Simulink Block ofthe Motor Controller

The simulink model ofthe motor controller is shown in Figure 3.7. The inside ofthe

motor controller block is shown in Figure 3.8. The inside ofthe voltage conversion block

of Figure 3.8 is shown in Figure 3.9. The motor controller model should be characterized

for a particular motor used in the system. As discussed in the previous sections of this

chapter, the motor controller is a constant slip, constant air-gap flux motor drive system.

The closed-loop control system, which is used here, is shown in Figure 3.4.

48

CD O CN

o o

•t—> c o CJ

o o B

o o

t ^

l - c

CO

49

Q! c 0) 3 cr 0)

•OJ

Ai o c re

Y

0)

i k

3

O

> ^ 0)

"o

c 8 0) C3) ra ^

IS "O c a E «> •o 4> o> (0

o > o eg O)

i ^

« Ol

Ola

> o

sta

re tJ

i ; 3 Q. C

O o

c o e?

c:

O)

o >

t

1 \

i

^^ iO V

(s+0

in

vri

\1

^

k

(U

jLU

dip

li

L "

M

t + 1 t

•C3

f

0)

^ s

cont

CI. •pj

1 "

E 3

w

0) 0)

L »

0) CJ)

re

E

9l 0! re • \y o

01 3 a. c O Q

o

(U

c o o U l

o o B — (

oo

(U Ul CX)

50

9 0)

^ at O re re ^ Vi o

> H

i

0) t : > c

0) Q. C3. O

u

t <

• ^ o £• o re JQ

i

5(s+

0.02

)

i

(A

a>

t 4- I

4 41

</) >

0) T3

9 • o at 0) re •o ~ c o re >

E o Q re

(1) C3> re

91

o o

c

Ul OJ > c o CJ

 OJ

ro

u

51

The speed controller is a PI controller. The transfer flinction ofthe speed controller is

A:,(l + - i - ) 3.14 T,s

where the constants Kp and 7] are the proportional and integration constants. Values of

the constants are to be determined according to the Ziegler-Nichols tuning rules based on

a step response ofthe system and set in the slip controller block of Figure 3.8.

The slip limiter is designed to fix a maximum allowable operating speed ofthe

motor. Generally the speed ofthe motor needs to be less than the speed which

corresponds to the peak torque ofthe motor. Thus the motor is forced to operate in the

stable region. So the saturation limit is set at kco^^j^ ( co^^j^ is the maximum safe stator

angular speed) where the value of k is less than one ( 0.8-0.9). This safe value should be

calculated fi-om the motor parameters. This value is the saturation value ofthe block slip

limiter in Figure 3.8, which limits the stator frequency in the stable range of operation.

Equation 3.15 is used to obtain the command stator speed.

error _ speed + feedback _ speed = (l - 5) * command _ statorfrequency

Aco„, +co^ =(\-s)co's

col =- *i^^n,+^r) \-s

CO*, = Gain *{Aco„,+0)^) 3.15

The value of Gain in equation 3.15 depends on the operating slip ofthe motor. This

value has to be set in the simulink block Gainjslip in Figure 3.8.

52

The voltage controller block is a voltage versus frequency equation where the air

gap flux is kept constant.

" sator _ phase ^ "^ ^S^ i

= ^S^S+^S^S

The stator rms current, h^^M-^h

A s As-s ^ s J'^M ^R

CO. + J'^L

Kator phase =^S^S+Rs ( " 7 ^ + " ^

JHf ^ CO.

A.V

+ J^L

3.16

In equation 3.16,

A^ = Rated air gap flux in Wb

co^ = Rated slip speed ofthe motor.

Z,„, Rjf, L,, R, = Circuit parameters of the motor.

The values of these constants are used to develop equation 3.16 that is used in the

voltage controller block in Figure 3.8 to calculate the stator voltage for the corresponding

frequency calculated by the slip limiter. The upper saturation limit ofthe voltage limiter

is the maximum allowable stator phase voltage ofthe motor. This value is set in the block

voltage limiter in Figure 3.8. Thus, not allowing the demanded voltage to exceed the

maximum limit ofthe stator voltage.

The output ofthe voltage limiter block is an input to the voltage conversion block.

The inside ofthe voltage conversion block is shown in Figure 3.9. The rms fundamental-

53

frequency component ofthe line to neutral or phase voltage of an inverter can be

expressed by equation 3.17

J2 ^ 6 = — v . = 0.45 V, ^ 3.17

where

V, = rms phase voltage produced by the inverter

V, = DC voltage input to the inverter.

The DC link voltage is boosted by the chopper to get the desired AC output voltage.

V =V *n4S*/o' ' Stator phase ' IXJ _input '-'•^-> '^boost

~'^DCJnput '^ boost 3 . 1 8

Equation 3.18 is used to calculate the desired constant to convert the DC to AC voltage.

V Stator _ phase = V,^ _ .„^„, * k 3 . 1 9

r demanded_Stator_phase ^^ ''^ 1X2 input 3 . .ZU

The difference between the demanded stator voltage and the stator voltage is used to

calculate the required boost constant.

AF =V * Ak 3 21 ^'^ Stator _ phase '^ DC _input " ' ^ - ' • ^ ^

The feedback loop is stabilized using a PI controller and AV„^,„^ ^f,^^^ is used to

determine the desired constant ofthe chopper/inverter block. The saturation limit ofthe

alpha boost block in Figure 3.9 is set to a„„ . This sets a limit to the total

convertion^oost constant ofthe motor controller.

5 4

CHAPTER IV

VEHICLE DYNAMICS MODEL

4.1 Modeling Equation for Vehicle Dynamics

Vehicle modeling is derived from the basic equation of solid body motion, as

given in the following equation.

F = ma

The dynamic model sums the specific forces acting upon the vehicle. The forces

acting upon the vehicle are the forces produced by the powertrain, the aerodynamic drag

forces, the force produced by the rolling resistance ofthe tires, and the gravitational

forces due to the incline ofthe road. These forces are combined to get a simple modeling

equation which provides an accurate method for describing the straight line motion ofthe

vehicle [14, 169].

F z= F + F + F + m a 41 powertrain drag rolling-res gravity vehicle tot

aV •' powertrain drag nilling-res . ^ ~ 7 ~ ~ tot ~ Ci^^i^.jiy ' T . Z

Cit ^vehicle

The individual forces are calculated using the known vehicle parameters. The

different equations for various vehicle forces are given below.

= ^tireC''"/ / ' lir

F powertrain

' lire

55

^drag ry 'Pair - ^ drag "^ front ' ^

P'ntlling -resis tan ce = ' " • C , , - g COS (^„,^, , ) 4 . 3

«,«,v=g.sin(^„,„J 4.4

The forward force ofthe vehicle is calculated using the torque output from the

transmission (r„„,), the fire efficiency (77,; ) and the radius ofthe fires (r,.^^). The other

forces are discussed briefly in the following sections.

4.2 Aerodynamic Resistance

At moderate and high speed the power required to over come the aerodynamic

resistance becomes significant. The aerodynamic resistance is generated by two sources:

one is the air flow over the exterior ofthe vehicle body and the other is the flow through

the engine radiator system and the interior ofthe vehicle for purpose ofthe HVAC

system. The extemal aerodynamic drag is more than 90% ofthe total aerodynamic

resistance of a passenger car.

Aerodynamic resistance is usually expressed in the following form.

f'aentdyanmic=--P'CD-^f''' 4 . 5

where p is the mass density of air, C,) is the coefficient of aerodynamic drag that

describes the combined effect of all the factors, A^ is the characteristics area ofthe

vehicle, numerically taken as the frontal area which is the projected area of travel in the

direction of travel, and v is the speed ofthe vehicle relative to wind.

56

Aerodynamic resistance is proportional to the square ofthe speed which means

that the power required to overcome the resistance increases with the cube of speed. Thus

if the speed is doubled, the power required to overcome the aerodynamic drag increases

eightfold. Atmospheric condifions affect the air density and hence aerodynamic drag

significantly. The commonly used standard conditions are a temperature of 60° F and a

barometric pressure 76 cm in Hg. In performance calculafions the mass density of air is

taken as 1.23 kg/cm . The frontal area ofthe vehicle may be determined from a

photograph taken from the front if the drawing is not available. The coefficient of drag

may be obtained by wind tunnel tesfing of scale models or full-scale vehicles. The

deceleration method of road testing, commonly known as coast down test, may also be

used to determine the aerodynamic drag coefficient. The values of aerodynamic drag

coefficient and the frontal area may be roughly assumed from typical data sheets. Figure

4.1 shows drag coefficient for different vehicle models.

57

crv^Hrv^ Cp= 0.311 Cj,= 0.38

(a) (b)

—rv3 <<y—<p Cjj= 0.387 Cj = 0.416

(c) (d)

C =0.458 C =0.475 D

(e) (')

Figure 4.1 Different values of aerodynamic drag coefficient for vehicles of various models [14, 176]

58

4.3 Effect of Rolling Resistance

The major vehicle resistance force on level ground is the rolling resistance of

fires. At low speed, off highway level ground operation, the rolling resistance is the

primary mofion resisfing force. When a fire is rolling, as the rubber goes through periodic

compression and expansion, rubber consumes energy. The fire distortion results in a shift

ofthe center of normal pressure in the direction of rotation which in turn results in rolling

resistance moment. In a free rolling tire, there exists a horizontal force at the tire ground

contact patch which is known as rolling resistance and the ratio of rolling resistance to

the normal load on the tire is defined as the coefficient of rolling resistance. Other

mechanisms that account for rolling resistance are the slip in the longitudinal and lateral

direction, air drag on the inside and outside of tire and energy loss on a bump.

A number of factors affect the rolling resistance of a pneumatic tire.They include:

1. construction and material of tire.

2. surface conditions ofthe road. On hard, smooth surfaces rolling resistance is lower

than on rough road. On wet surface rolling resistance is higher than on dry surfaces.

3. Tire inflation resistance affects the flexibility ofthe tire. On hard surfaces, the rolling

resistance generally increases with the increase in inflation pressure. The higher

inflation pressure decreases the deflection ofthe tire, resulting in low hysteresis loss.

4. Rolling resistance depends on the driving speed because the work in the deforming

the tire and the vibration in the tire structure increases with the increase in speed.

5. Operafing tire temperature, tire radius and tractive force also have an effect on the tire

rolling resistance.

59

Considering the vehicle as a whole the total rolling resistance is the sum ofthe

resistance from all the wheels.

K.I,ing=Rrr+Rrf+C,,W 4 . 6

where: ^

R^^ = Rolling resistance ofthe rear wheels.

R^ = Rolling resistance ofthe front wheels.

C ^ = Rolling resistance coefficient.

W = Weight ofthe vehicle.

The multiple and interrelated factors affecfing the rolling resistance make it

virtually impossible to devise a formula that takes all the variables in account. Two

methods of calculating rolling resistance are discussed here.

The rolling loss of solid rubber tires led to the following equation.

Rrolling ^W \h C = - ^ ! = - = C — J - 4.7

W D\w

where:

Rroiimg - Rollirig resistance force.

W = Weight on wheel.

C = Constant reflecting loss and elastic

characteristics of tire material.

h = Tire section height

w = Tire section width.

D = Outside diameter.

60

This formula shows that the rolling resistance is load and tire structure sensitive.

The coefficient of rolling resistance can also be estimated at lower speed because

at low speed the rolling resistance coefficient rises approximately linearly with speed.

The following equation can be used where V is the speed in mph.

C . . = 0 . 0 1 ( U % ^ ) 4.8

At the most elementary level, the rolling resistance coefficient may be estimated

as constant. Table 4.1 lists some typical values that might be of that case

Table 4.1: Typical values of rolling resistance coefficients for different surfaces [16, 220]

Vehicle type

Passenger car

Heavy trucks

Tractors

Surface

Concrete

0.015

0.012

0.02

Medium hard

0.08

0.06

0.04

Sand

0.30

0.25

0.20

61

4.4 Model ofthe Vehicle

4.4.1 Inputs and Outputs ofthe Model

As described in the previous sections of this chapter the vehicle dynamics model

requires some characteristic parameters ofthe vehicle. The parameters are to be set in the

model described below. The primary input to the model is the torque produced by the

motor ofthe vehicle. Somefimes more than one motor can be used to enhance the power

ofthe vehicle. The number of motors is also be set in the model. The model basically

calculates the power train force applied to the vehicle, aerodynamic drag force and the

force due to rolling resistance, all three of which are outputs that can be seen inside the

first block if needed. The coefficient of rolling resistance is considered constant in this

model. The outputs of primary concern are the speed and the acceleration ofthe vehicle.

This block also outputs the angular speed ofthe shaft which is a feedback to the motor

drive system. The block diagram shown in Figure 4.2 shows the inputs and outputs to the

vehicle model.

62

Torque (developed per motor)

A V

Vehicle —N —y Speed and Acceleration

Parameters 1. Coefficient of aerodynamic drag 2. Rolling resistance coefficient 3. Axle ratio & tire efficiency 4. Tire radius 5. Frontal area 6. Grading of road 7. Ambient condition( air density)

A V

Different forces 1. Power train force 2. Aerodynamic drag force 3. Roiling resistance force.

Figure 4.2 Block diagram ofthe vehicle dynamics model

63

4.4.2 Simulink Model ofthe Vehicle

Figure 4.3 shows the simulink model ofthe vehicle dynamics system. Figure 4.4

to Figure 4.6 shows the inside details ofthe vehicle dynamics model of Figure 4.3.

148

Torque

Vehicle Dynamics Model

speed in MPH

Speed in M/Sec

wmech (rad/sec)

acderation in m/se

Figure 4.3 Simulink block of vehicle dynamics model

64

fol aerodynamic drag vs speed

to vehicle(NM)

vehicle

aerodynamic drag force(NM)

force due to rolling resitance(NM)

Figure 4.4 Inside ofthe vehicle dynamics block

65

lo of motors

Basic block

MPH

M/sec

>CD acderation m/sec^2

— • C D powertrain force in

— • C D aerodynamic drag force

• C D force due to rolling resistance

Figure 4.5 Inside ofthe vehicle block

66

C3>

C [TJ

E (0

T5

e a)

J4 o o - JD O CO CO

- D (U

JIS • 4 — •

<4-H

O (U

-a CO

C > — < VO

^ OJ < - l

3 CD

u.

67

CHAPTER V

SIMULATION RESULTS OF THE MODELS

5.1 Simulation ofthe Electrical Svstem of a Vehicle

The models developed in the previous chapters are coupled together to get the overall

model ofthe electrical system ofthe vehicle. The block diagram shown in Figure 5.1

shows the overall model ofthe electrical system of a totally electric vehicle.

r' I

Desirbd speeq

I DC Inout

I

/ Motor drive system

7y

voltage

V

frequency V

Motor

7 ^

torque Vehicle 1 vl, chicle

Fig 5.1 Block diagram ofthe model of electrical system of a vehicle.

The individual blocks should be characterized according to the specifications of a

particular system. The circuit parameters ofthe motor should be set in the model. The

circuit parameters can be obtained from tests or can be roughly assumed using the

68

parameter block discussed in Chapter II. The data for the vehicles also needs to be set.

For the motor controller the equation relating the voltage and stator frequency has to be

derived using the motor circuit parameters. The limit of slip speed also has to be defined

in the motor controller model. The overall block is now ready for sirnulation and the

vehicle model can be tested for an input driving pattern.

5.2 Simulation of a Model Vehicle

In order to verify the developed models, the hybrid electric vehicle developed at

Texas Tech University was chosen. The "Future Car, 1999" is a hybrid electric car which

is a research project currently going on in this university. The electrical system design of

this car is best shown in Figure 5.2.

Battery

Pack

Current Flow

Motor t.ControHer

Accelerator Pot

Motor Controller 3(DA

Figure 5.2 Electrical system ofthe "Future Car 1999"

Specifications ofthe AC induction motors used in this vehicle are given in Table 5.1

69

Table 5.1: Motor specification [3]

Motor manufacturer: Solectria

Model: AC40

Peak Torque (NM)

Maximum current( A, rms)

Continuous torque(Nm)

Continuous power (kw)

Peak efficiency

Nominal speed (krpm)

Peak electrical power (kw)

150

240

25

16

93%

4

78

Specifications ofthe motor controllers are given in the Table 5.2.

Table 5.2 Specification of motor controller [3]

Motor controller manufacturer: Solectria

Model : UMOC 440F '

Maximum Battery voltage:

RMS value of current

Vehicle type

Peak kW

312V

250A

CAR

78

70

The vehicle that was used in the " Future Car 1999" project is a 1997 Chevrolet

Lumina.The data for the model of vehicle dynamics is given in Table 5.3.

Table 5.3: Parameters ofthe vehicle.

Vehicle: Chevrolet Lumina

Year: 1997

Axle ratio

Tire efficiency

Overall gear efficiency

Tire radius(m)

Mass( Kg)

Drag Coefficient

Tire rolling resistance

coefficient

Frontal area( m ^

^

8.5

0.93

0.93

0.344

1950

0.32

0.0077

1.997

5.3 Simulation Results

5.3.1 Motor Simulation Results

The motor is best characterized by the following set of parameters. These

parameters are calculated using some operating points that are taken from Figure 5.3 and

the nameplate data on the motor.

71

Table 5.4 Circuit parameters of motor for modeling

Mutual inductance (H)

Rotor resistance( Ohms)

Number of pole

Leakage inductance(H)

Stator resistance( Ohms)

0.02

1.2

2

0.00095

0.4

The simulation ofthe motor is shown in Figures 5.3 to 5.6.

Figure 5.3 shows the simulated torque speed curve ofthe motor. The peak torque

and the starting torque are equal and equal to 145 Nm. The maximum speed ofthe motor

is 12 krpm. For simulation, the stator frequency is 200 Hz to obtain the synchronous

speed in that region.

E c o

c u D ty b« o

f -

Figure 5.3 Torque versus speed curve ofthe motor

72

<<g5 252X? , 312V OC Battery) ISO

30 -I

a

• i •

i

1

• 1

. ^ 1

psa- ^

^

I 1 1

> S ^ ; ^

-1 = ^ ^ 1 •

o snoo l aac - -«or3o Goc-o S p e e c h ('••f>nri">

Figure 5.4 The torque speed curve ofthe motor from the manufacturer (Solectria Corporation)

• oaac-

The simulated characteristics match the motor torque-speed curve supplied by the

manufacturer, which is shown in Figure 5.4. The torque speed curve in Figure 5.4 is

shown as a fiincfion of DC input voltage ofthe motor controller. In Figure 5.3, the

simulafion is done using the ac inputs ofthe motors only. Thus the motor is separately

characterized to produce the same output. As it is made independent ofthe motor

controller, it can produce the same output irrespective ofthe controller model used.

Figure 5.5 shows the AC rms value ofthe stator current ofthe motor. The peak

current is 250 ampere according to the specification. The simulation result is close

to the specification. Figure 5.6 shows the torque versus slip curve. Torque is constant up

to 97% slip.

73

2SO

2 0 0 -

X Y Plot

rre

3

</>

k . >.~N O O .

^ ^ f M

2 1 t>0 w

Aja

s

^

I b U

1 0 0

SO -

12000

Speed (rpm)

Figure 5.5 Stator rms current versus speed

3 cr o

160 -

140 -

1 2 0

eo -

BO

4 0

2 0 -

Figure 5.6 Torque versus slip ofthe motor

74

u ^

k.

u > »^ o

OH

1

0.9

0.8

0.7

0.6

.? 0.5 >-

0.4

0.3

0.2

0.1

n

-

1

X Y Plot

1 1

A^

> 1

-

\

\

"l -

1 _

I -

1-

2000 4000 6000 XAxis

8000 10000 12000

Figure 5.7 Power factor versus speed ofthe motor

5.3.2 Vehicle Dynamics Simulation

The peak torque ofthe motor is given as an input to the model and the outputs are

examined. Figure 5.8 shows the force available at the wheels ofthe vehicle. For the peak

torque ofthe motor (150 Nm) the power train force which is available for the vehicle is 3

Nm. This is determined considering the axle ratio ofthe vehicle and the axle efficiency.

75

4 5

as

3 -

Z 5 -

10 15 20 30 35 SO

o w

K C > C w 4. <

Time (second)

Figure 5.8: Power train force (NM) available for the vehicle

1

0.9

0.8

0.7

0 6

!5 0.5 >-

0.4

0 .3

0 2

0.1

n

X Y Plot

1 1 1

-

-

-

-

^ ^

-

-

' 20 40 60

XAxis 80 100 120

Speed (mph)

Figure 5.9 Aerodynamic drag force (NM) versus speed (MPH) of the vehicle

76

' ! ''

The aerodynamic drag force ofthe vehicle is shown in Figure 5.9. When the peak

torque is applied to the vehicle maximum acceleration attained is 3.2 m/s^. In case of

continuous torque (25 Nm) the maximum attainable speed is 120 MPH and maximum

acceleration is 0.54 m/s . Figure 5.10 shows acceleration ofthe vehicle when peak torque

is applied.

3 5

Z5 -

15 -

0 5

2 -

10 15 20 30 35 45 50

Time (sec)

Figure 5.10 Acceleration (m/sec^) versus time

77

5.4 Simulation ofthe Overall Vehicle Model

The overall model for the electrical system ofthe vehicle is shown in Figure 5.11.

The three component models are connected together as shown in Figure 5.13. Vehicle

speed is fed back to the motor and motor controller. The feedback block has an overall hP

gain that is to convert the output speed ofthe vehicle (MPH) to the electrical angular

speed (rad/sec) ofthe motor. The conversion block is shown in Figure 5.12. The power

calculation block shown in Figure 5.14 calculates the efficiency ofthe overall power

train.

The input to the overall drive-train model is a specific driving cycle. The model is

tested for two types of driving cycles: (1) urban driving cycle and (2) highway driving

cycle. The output speed ofthe vehicle is compared with the input to find the accuracy of

the motor drive system. At the same time outputs ofthe motor controller, motor and the

vehicle dynamics model are observed to see how the individual components ofthe total

system are performing.

78

[cl g

reference driving cycle3

urban

reference driving cycle2

highway

reference driving cycle!

vehicle acceleration mlsec^l

Figure 5.11 Complete block for the electrical system ofthe vehicle

79

^*

o CO

~g o

II d .2 II

CJ ^

X ^ < -

.

CO

1

v.

1 "a

^ 2 ^ 5

^

-_ a S

"U ^ »» S

^

(N

II "5

-^

.-Ji»v * • * * > *

O c

^ (N

*

-i-o r-^ ^ C5 *

* ::^

' ^

2^ sp

eed

HD 

o o

J4 o

(N

CJ)

80

VI

9! 0 n D id 1

CM

\ I/I

0i t

(0

e

•c o> t O

O O

Z3 k-O. 0)

II O C

t 1 o

XI (L)

o o

00

o o

c o <fl

3

real

a) * ^

Cd P -o • • • ^

>

- — 1

(U j : :

o • • - >

o

O

H

CJ

_o

>

• » — '

op

81

i o Q.

l - i

u

o k .

ont

u k. O

e m

ot

»— • • ^

( ^ o

o Q. 3 Q. 3 o II

5 1

= =

k.

Slu

lu

• ^

* 3

2

II 'o 5

1

3

k . (U

p <

o k.

c o o o O E o a. 4-^ 3 CL

IT '

1

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*

2 a

^ "

1 \ J

1

Q

k. o o E u

J C .. CM

o OJ 00

o > k.

o

Cri II k.

^

1

o

1 ( J

" i

l _

o o E (U

k- - c

c -o lU c -a

" o

B II

11 i u. 5 3 1

a 3

2 o

1

a

1

C II

1

^ ^ 5

E ~, (/) k .

_a> ^ i ^

o k .

c o u k.

o ^-» o E

•T3 C CO

k M

o • ^ o E u

.£ C M

O

o c fD o

e O II

I k. %i

1

1

>..

t *

k .

ka 4 . ^

c o o U l

o o E 4J

•a a>

O k_

c o u k .

o o E r^

' ^ o • •' 3 a.

o >

U Q II X

J4 o

o Cd

• <

3 JJ Cd

CJ u, OJ

o O H

(-;

O

'w5 ^

;- Z3 CO

tin

82

5.4.1 Simulation for Urban Driving Cycle

The reference input to the vehicle model for a typical urban driving cycle is

shown in Figure 5.15. The response ofthe vehicle to this command is seen in Figure 5.16.

a. E

•a U o.

C/3

T i m e (<ipc^

o.

-a u Q.

c/0

Figure 5.15 Reference driving cycle (urban) in MPH

Time (sec)

Figure 5.16 Output speed ofthe vehicle in MPH

-

V

11

• " r " ' ' • ' ' • T

U \r.l\A(\A(\r\ 1 '^'' ' M

( ^ J V^

Time (sec)

Figure 5.17 Acceleration (m/sec^) versus time

83

The output shows that the vehicle follows the input without considerable error for this

sort of input.

Acceleration ofthe vehicle with respect to time is seen in the Figure 5.17. The

vehicle responded to the sudden change of speed at the beginning ofthe driving cycle.

The corresponding torque required for the vehicle is seen in the Figure 5.18. The torque

required to attain an acceleration as high as 1.5m/sec^ is nearly 60 Nm for the vehicle.

c

3 cr k-o

Time (sec)

Figure 5.18 Torque versus time for urban driving cycle

c

3

u

o

Time (sec)

Figure 5.19 Stator rms current (A) for urban driving cycle

84

Figure 5.19 and Figure 5.20 show the input to the motor supplied by the motor

controller. The RMS stator current is high at starting and becomes low when the motor

starts. The stator phase voltage is 108.5 volts when the vehicle is not running to give a

low fi-equency boost as demanded by the control topology followed in the motor

controller.

Time (second)

Figure 5.20 Stator phase voltage for the vehicle

5.4.2 Simulation for Highway Driving Cycle

The vehicle is also tested for a typical driving cycle of highway and the results are

shown in the figures below. The input reference speed is seen in Figure 5.21 and the

vehicle response is in Figure 5.22.

Q .

T3 CJ (U Q .

CO

Time (second))

Figure 5.21 The highway driving cycle as reference

85

a. E

• o &> u a .

00

Figure 5.22 Output Speed ofthe vehicle

The highway driving has not much sudden change of speed within a considerable

amount of time. The acceleration ofthe vehicle is shown in the Figure 5.23.

0) CO

c

k.

o o <

150

Time (second)

Figure 5.23 Acceleration (m/sec ) for the driving cycle

86

> ii vt

Si o. k.

o • • - •

CO

120 -

112

110 -

108

i 1

1 1

1 i

1 ._i

• T !

- .. . _ .,, , i i

Figure 5.24 RMS stator phase voltage ofthe motor for highway driving

The stator phase voltage and the stator phase current are shown in the Figures

5.24 and 5.25, respectively. The AC inputs to the motors do not vary much as the speed

ofthe vehicle in this particular time frame does not change considerably.

CO

E

c t 3

u

o

00

Time (second)

Figure 5.25 Stator rms current for highway driving cycle

87

5.5 Validation of Simulation Results

Texas Tech University's "Future Car, 1999" was road tested to determine the

acceleration ofthe vehicle. It was found that the vehicle got up to a speed of 60 MPH

vAthin 11 seconds with a fially charged battery pack with nominal pack voltage of 312

volts. Thus the acceleration was 2.4384 m/sec^, assuming constant acceleration

Simulafions can be done to compare this data with the outputs ofthe model.

The vehicle model is tested by a ramp input. The command speed ofthe vehicle is

60 mph within 9 seconds at an acceleration of 2.9 m/sec^. The outputs are shown in

Figure 5.26. The output speed follows the input closely. The output reaches 60 mph at

9.725 seconds and goes up to 63.734 mph (Peak) at 11.56 seconds resuhing in 6%

overshoot. The settling time is 24 seconds. The acceleration is 2.8 m/sec^ at starting. Due

to the starting transients, the acceleration has an undershoot for a very short amount of

time.

^ c Q . . =

SI aj CJ

00 <

k. 20 -

--

- • •

- • •

. r 1

// > y^/

y ^ '

f /

—r

' ^ / • • •

1

-•

I

f ^

•

1 1

• '

1

•

• 1

1

30

Time (sec)

Figure 5.26 Speed response and acceleration for a reference speed of 0-60 mph at an acceleration of 2.4384 m/sec^

88

r\ I r~ l o t 200

Speed (mph)

Figure 5.27 Torque delivered by a motor vs. speed ofthe vehicle for a reference speed of 0-60 mph at an acceleration of 2.4384 m/sec

The vehicle demands 120 Nm of torque from each motor for an acceleration of

2.55 m/sec^. This data is obtained from Equafion 4.1 and the parameters ofthe vehicle of

Table 5.3. The simulation result shown in Figure 5.27 shows that the starting torque is

140 Nm. After the startup transients are over, the torque is 130 Nm. After that, it varies in

between 130 Nm and 140 Nm up to the speed of 50 mph and then it starts decaying and

goes to zero when the vehicle starts coasting at a speed of 60 mph.

89

\

Time( sec)

Figure 5.28 Stator current (RMS ampere) and stator voltage (V) and stator fi-equency ofthe motor.

The stator phase voltage (V) and the rms stator current ofthe motor are shown in

Figure 5.28. The stator phase voltage has a peak of 400 volts when the vehicle demands

peak acceleration. For a starting voltage boost, the phase voltage starts at 118 volts. The

starting current is 255 ampere which is the peak current ofthe motor. The current

decreases sharply as expected in the case of an induction motors. Maximum current

required to supply the peak torque (140 Nm) is 145 amperes. For maintaining a constant

speed of 60 mph, the stator phase voltage and the stator currents are 340 Volts and 25

amperes, respectively. The stator fi-equency goes up to a peak of 200 Hz due to

overshoot, but settles at 120 Hz to maintain the constant RPM of the shaft while the

vehicle is coasting at 60 Mph.

The power delivered by a motor is shown in Figure 5.29. The rated maximum

power ofthe Solectria AC40 motors is 75 kW (100 HP). To attain an acceleration of 2.9

m/sec the motors have to deliver peak power. Figure 5.30 shows that each motor _

90

reaches its maximum power of 90 HP at 50 mph and delivers maximum power up to 60

mph. Thus the motors are closely following the rated data.

X T H-lOt 100

JO •T3 a> k .

OJ X

cu E

Speed (mph)

Figure 5.29 Power (HP) output of a motor for the speed command of 0 to 60 mph in 9 seconds.

1

0.9

0 8

0 . 7

0 6

0 5

0 .4

0 . 3

0 . 2

0 1

(

r

Efficiency

/

/

D 10

1

2 0

1

3 0 4 0

-

-

\

\

\

\

\

F ip f t f^H ( M ^ P H ) • 50 " 60 ' 7

Figure 5.30 Efficiency ofthe power train for the speed command of 0_to 60 mph in 9 seconds

91

30

25 -

20 —•

15 -

10 - •

1 1 1 T I • 1

Energy ( Amp-hrj ;

; ^^,^^-^1 ^

J \ ; 1 i T i l

1

me (sec)

5 —

100 200 300 40O 500 EDO

Figure 5.31 Ampere-hour demanded by the motor to maintain the input speed profile

The efficiency ofthe overall powertrain is calculated acoording to the equations

shown in Figure 5.14. Figure 5.30 shows the peak efficiency ofthe vehicle is 73% and

the efficiency is nearly constant for the constant acceleration upto the speed 60 MPH.

The efficiency is very low (9%) when the vehicle is coasting at 60 MPH.

The DC current demanded by the motor controller for a desired speed input is

calculated in the power calculation block of Figure 5.14. Thus the Amp-hr required by

the vehicle to maintain the commanded speed input is simulated in Figure 5.31. The

simulation is run for 1/6*" of an hour and the figure shows that the vehicle requires 27

Amp-hr of energy from the DC source. If the total energy storage ofthe battery pack is

known, this simulation can evaluate the overall drive time ofthe vehicle.

Simulation results shown in Figures 5.26 to Figure 5.31 were done assuming the

DC voltage input as ftilly charged battery pack voltage (312 V DC nominal).

92

The speed response and torque and power delivered by the motors vary with the DC

voltage input to the motor controller. The outputs are examined for a DC input voltage of

265V and 225 V in the following simulafions.

-

•" — r-

y/

/ /

«

'

r

y^ i

y'

»

-•''

! !

«(•<>

• '

C I l l r « i " M o r *

1 1

1 1

.._

Figure 5.32 Speed response ofthe vehicle for an input of 0-60 MPH within 9 seconds when the DC input is 265V.

Figure 5.32 shows the speed response ofthe vehicle for a command speed of 60

mph within 9 seconds when the DC input is 265 V. The response to this input is slow.

The output reaches 60 MPH at 12.25 seconds and settles down slowly. The acceleration

is 2.4 m/sec^ at starting. Thus, the response ofthe vehicle is slow with a reduced DC

voltage input to the motor controller. The effect of a reduced DC voltage input can also

be seen on the torque and power delivered by the motor in Figure 5.33 and Figure 5.34.

93

I •••|««r'

Torque ( Nm| variation with time when OC Input I * ZG5 V

Figure 5.33 Torque delivered by the motor versus time for an input of 0-60 MPH within 9 seconds when the DC input is 265V.

A T t - I O I 1 0 0

- 2 0

P o w e r (HP) - I 1 1 1 1

Pov/cr de l i ve red b y the motor (HP) v s s p e e d ( M P H )

S p e e d ( M P H )

10 2 0 3 0 4 0 5 0 6 0 7 0

Figure 5.34 Power (HP) output of a motor for the speed command of 0 to 60 mph in 9 second when the DC input is 265 V.

In Figure 5.33 the starting torque is 160 Nm but the torque delivered by the motor

decreases fast. Up to 9 seconds the vehicle demands constant acceleration and constant

torque. But with a reduced DC input the torque developed by the motor goes down to 60

Nm within 10 seconds.

94

Figure 5.34 illustrates that the power delivered by the motor is also less. The peak power

delivered by the motors with the fiill battery pack voltage (nominal 312 V) was 90 HP

shown in Figure 5.29. Figure 5.34 illustrates that the peak power delivered by the motor

is reduced to 80 HP. k^

The motor controller converts the DC voltage to AC voltage. But when the DC

voltage is reduced the motor controller cannot supply the required AC voltage to

maintain the command speed and acceleration. In the motor controller model, chopper

frequency is controlled to step up the DC battery voltage. But the chopper frequency has

a maximum value. In the simulation it is set as 3. So the stator AC voltage has a

maximum limit depending on the DC input voltage. For a DC input of 312 V, the AC

voltage supplied by the motor controller is equal to the maximum AC voltage demanded

by the motor (440 V). But the AC voltage reduces when the DC input voltage is reduced.

Figure 5.35 shows the demanded AC voltage and the supplied AC voltage when the DC

input is 312 V. Figure 5.36 compares the two values when the DC input voltage is 265

volts.

3 5 0 '•• i

• /

I l r '«<a#«««i l» ' -« l -^vlMl iar ^ • f l l l # « « | r ' 0%*%%% **•%%%••%% A C ! ^ ^ • • I f # « a | r

I • • • • V t •*«»••

25

Figure 5.35 The demanded stator rms voltage and the controller output ac rms voltage when the DC voltage input is 312 V.

95

Figure 5.35 illustrates that the AC voltage output ofthe controller is same as the

demanded stator voltage. Figure 5.36 shows the difference between the required stator

voltage and supplied rms voltage for a DC input of 265 volts.

h^


It is seen that the maximum demanded voltage is 400 V as before. But the

controller could produce only 370 volts at the peak demand, which affected the vehicle

performances, shown in Figure 5.32 to Figure 5.34.

V..H^M- I ^

40 «5


96

Figure 5.37 shows the difference between the demanded stator voltage and the

actual output voltage ofthe motor controller when the DC input is 225 volts. The

maximum voltage the motor controller can supply is 314 volts while the demanded

voltage is higher than that (peak 400V, steady 340 V). The vehicle's speed performance

is seen in the Figure 5.38. The acceleration is 2.9m/sec at starting, but never remains

constant. Acceleration decreases fast and the vehicle finally starts coasfing after 15

seconds.

60 Trrrr - t - > — —

^«|•r'«'•t r f . « | f l i a l i r . %i«lit'li I K ! • l i | i i i l i.^ X ^ * * V

50

40

30

20

10

•.|l>-t-ll I Iw l i ' l l l

I •« l i r _J

10 15 20 25 30 35 40 45 50

Figure 5.38 Speed response ofthe vehicle for an input of 0-60 MPH within 9 seconds when the DC input is 265V

The torque delivered by the motor is shown in Figure 5.38. the starting torque is

high but the torque starts decreasing from 6 second, which indicates that the vehicle

cannot maintain constant acceleration. As the demanded stator voltage and the output

stator voltage is different the controller cannot maintain the constant torque, constant slip

operation. Power delivered by the motor is shown in Figure 5. 40. The maximum power

97

produced by the motor is 65 HP, which is less than that produced with a DC input of 312

volts.

140

120

100 -

80 -

60

40

20 -

0 -

•20

y 1 1 ! 1 1 • •«i|iar- | N l M | :

• ••\ : j-

- i -V i

i i i

" • • • • 1

1 • • r i | i i f v x laii iv %i/l«fit tUf 1 H! m i

i 1

1 1 1

iMl I*. X / * . Viall^.

-

1 • l l i f 1 •^r-i 1

1 10 15 20 25 30 35 40 45 50

Figure 5.39 Torque delivered by the motor versus time for an input of 0-60 MPH within 9 seconds when the DC input is 225V.

X Y HlOt

100

80 -

60 -

40 -

I'liwt-r I til'

S|ii-r-it I MI'll)

-20' 10 20 30 40 50 60 70

Figure 5.40: Power (HP) output of a motor for the speed command of 0 to 60 mph in 9 second when the DC input is 225 V.

98

5.6 Limitations ofthe Model

There is about 6% overshoot in the speed response ofthe system and torque

oscillation at starting. Figure 5.41 shows that the settling time ofthe torque response is

about 1 second. The PI controller in the motor controller is incorporated to obtain a better

speed response and reduced oscillation. The response without the PI controller is shown

in Figure 5.42 and Figure 5.43. Figure 5.42 shows that without the PI controller in the

motor controller model the output speed takes a longer time to settle to the steady state

value. The figure shows that the output settles at the steady state value at 22"^ second.

The PI controller improved the performance ofthe system, while it is accelerating fast

because without the PI controller the output cannot quite follow the command speed. The

torque response without using the PI controller is shown in Figure 5.43. Although it is

free of oscillation, but it takes longer to reach to the steady value of 120 Nm for constant

acceleration. That is the reason for the slow response ofthe output.

s

3 a* o

^^0

1 2 0

lOO

eo

so

4 0

2 0

O

- 2 0

- 4 0

1 » 1 1 1

i \^,ff~/^~~ tzvf\ ^ :::T::::I:.:

1 1 1 1

1

1 i

i \ -

- ^ ' 1 -

i 1 .._ 1 J

Time( sec)

Figure 5.41 Oscillafion ofthe torque response at starting (2 seconds)

99

Q.

ii ii

a. CO

1 1 ^ ' -y T 1 1

I 1

1

1 1

1

- / • \ 1 ^ ^ : 4? -

t 1 1 L 1 ;

Time (sec)

Figure 5.42 The torque versus speed response ofthe vehicle for an input of 0-60 MPH in 9 seconds without using PI control.

The motors used for the vehicle are large and very powerful. The inertia ofthe

rotor has to be taken into account while the motor is accelerating. That might be a reason

for the oscillation ofthe motor while it is accelerating. Also the control system used here

is very simple. It is difficult to control such a huge load and motor with a simple control

algorithm. The real system is computer controlled.

This model uses the vehicle speed as a feedback, which makes the control worse

due to the poor error signals. This problem can be fixed by using a better controller. The

proportional and integral constants should be determined accurately to obtain the best

result from the control system.

-

-

, / /

y'

/

r - • • T T

, * •

• \

\

-

"

:

Time (sec)

Figure 5.43 The torque delivered by the motors for an input of 0-60 MPH without using the PI controller.

100

CHAPTER VI

CONCLUSION

In the near fijture the automotive industry and automotive engineers will be

involved in wide spread research and development of electric and hybrid electric

vehicles. Simulafion tools are very necessary in the design of a variety of new vehicles.

This allows computer selection of power trains, sizing of components and evaluating

performance, cost and reliability. This thesis is a part ofthe research that is aimed to

develop a toolkit for vehicle simulation. The approach to model the power train

components is design oriented so that fiiture work can be done to develop a fully design

tool for powertrain components.

The simulation results obtained from the models are showing practical values.

The differences with the rated operating conditions and the simulation results are due to

the characterization ofthe machines. The model parameters should be experimentally

taken. This thesis lacks the experimentation part. More experiments should have to be

done to get the input voltage waveform ofthe motors, the torque required at different

speed, the efficiency ofthe motors, which will help to characterize the motor and motor

controller. Although the models developed in this thesis are simple, it successfially

simulated the performance ofthe vehicle. The models are not simulating the dynamic

performance well.

The motor and motor controller models that are developed in this thesis are

characterized using the specifications supplied by manufacturers. The simulated results

should be compared with test results to validate the models. The motor controller uses

101

feedback, which requires a speed sensor. The hardware implementation of this sort of

motor controller is very difficult because ofthe noises in the system. The feedback signal

might get distorted enough to make the control system very inefficient. For this reason

the vector control method should also be tried to avoid the use of speed sensors. The AC

rms stator phase voltage, rms stator current and frequency should be measured and

compared with the results ofthe outputs of motor controller model. The power required

by the vehicle for different speed should be measured and compared with the output of

the motor.

The model has to be made more interactive and should have a graphic user

interface. Thus it would be more convenient to change the parameters ofthe components

to characterize them. The motor controller model should have a PWM converter modeled

in it so that it can be cormected to an energy storage system.

102

REFERENCES

I. Future Car Competition at http://cp358.dhcp.ttu.edu/index.html

2 The Math Works Inc. at http://www.mathworks .com/

3. Data Sheet for UMOC 440F, Solectria Corporafion, Wilmington,^A.

4. Trzynadlowski, Andrzej M., The Field Orientafion Principle in Control of Induction Motors, Kluwer Academic Publishers, Norwell, MA, 1994.

5. Chee-Mun Ong, Dynamic Simulation of Electric Machinery (Using MATLAB SIMULINK), Prenfice Hall PTR, Englewood Cliffs, NJ, 1998.

6 Electric and Hybrid electric vehicle modeling and simulation at http://ev.inel.gov/simpleV/simpleV.html

7. Computer modeling in the Design and Evaluation of Electric and Hybrid Vehicles at http://education.lanl.gov/resources/h2/aceves/education.html

8. http://www.ucsusa.org/transporation/zeroingout.htm

9. Murphy, J.M.D. and F.G. Tumbull, Power electronic control of AC motors, Oxford, New York, 1988.

10. Gordon, Slemon R., Electric machines and drives, Addison Wesley Pub Co., Reading, Mass, 1992.

II. Bordea, I., and S. A. Nasar, Vector control of AC drives, CRC Press, Boca Raton, FL, 1992.

12. Nasar, S. A., Handbook of Electric Machines, McGraw-Hill, New York, 1987.

13. Beaty, Wayne H., and James L Kirthluy Jr., Electric Motor Handbook, McGraw-Hill, New York, 1998.

14 Wong, J. Y., Theory of Ground Vehicles, John Willey & Sons, Somerset, New Jersey, 1993.

15. Milliken, William F. and Douglas L. Milliken, Race Car Vehicle Dynamics, SAE International, Warrendale, PA, 1995.

16 Gillespie, Thomas D., Fundamentals of vehicle dynamics. Society of Automotive

103

http://cp358.dhcp.ttu.edu/index.html

http://www.mathworks

http://ev.inel.gov/simpleV/simpleV.html

http://education.lanl.gov/resources/h2/aceves/education.html

http://www.ucsusa.org/transporation/zeroingout.htm

Engineers, Warrendale, PA, 1992.

17. Hybrid Electric Vehicle Program at http://www.hev.doe.gov

18 Leonard Paul, Future Car Project, Project Lab V report, (1999).

hi'

104

http://www.hev.doe.gov

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master's degree at Texas Tech University or Texas Tech Uni\£fersity Health Sciences

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y^

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