a thesis in electrical engineering the requirements for
TRANSCRIPT
. ;
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
*55 c:
> — «
(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 <u
t—•
C 4 - .
o
CO
C > — (
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
<u CO
> 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
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81
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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^
Figure 5.36 The demanded stator rms voltage and the controller output ac rms voltage when the DC voltage input is 265 V.
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
Figure 5.37 The demanded stator rms voltage and the controller output ac rms voltage when the DC voltage input is 225 V.
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
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
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y^