MASTER’S THESIS
2004:072 CIV
JOEL TJÄRNBERG
Development of Control Strategies and
Transmission Model for Attribute Simulations of a Diesel HEV with Split-Power CVT
MASTER OF SCIENCE PROGRAMME Department of Applied Physics and Mechanical Engineering
Division of Computer Aided Design
Development of Control Strategies and Transmission Model for Attribute Simulations
of a Diesel HEV with Split-Power CVT
Thesis for the degree Master of Science in Mechanical Engineering Joel Tjärnberg
University Examiner Supervisors at VCC
M.Sc. and Ph.D. student Peter Åström Ph.D. Per Mattsson
Computer Aided Design M.Sc. Fredrik Axelsson
Luleå university of technology P/T Attribute Simulation
SE-971 87 Luleå, Volvo Car Corporation
Sweden Dept 97524, HM1
SE-405 31 Göteborg,
Sweden
VOLVO
Volvo Car Corporation
Abstract
In the year 2002/2003, the mechanical engineering and design project SIRIUS, performed at Luleå university of technology, was assigned to develop the electromechanical continuously variable transmission (CVT) Pergear, for use in a hybrid electric vehicle (HEV).
The concept was developed by Ph.D. Per Mattsson and had until then only been simulated and evaluated without regard concerning packaging and authentic mechanical solutions.
It became obvious that the powertrain concept, i.e. combustion engine, electric machines, gearbox etc, was somewhat space consuming to be installed in a production vehicle. With this in mind, a strategy involving a smaller combustion engine and thereby a more compact transmission needed to be investigated.
Other desirable factors needed investigation and development, e.g. creating a physical simulation model for the transmission, investigating control possibilities and developing fundamental control strategies.
To investigate these questions and to develop the transmission concept the master thesis project presented in this thesis was initiated. The thesis involves for instance the development of engine control, electric charge fundamentals, physical model simulations and comparisons to conventional vehicles.
The model was to be used for performance and fuel consumption simulations, but also to eventually evaluate dimensions of electric machines and the hybrid battery.
The results obtained using the vehicle model is presented in this thesis while also the modeling strategies along with driveability issues are discussed.
The concept has proven to be a worthy competitor both concerning fuel economy and performance.
Acknowledgements
This master thesis project has been carried out at the powertrain division, dept. 97524 Powertrain Attribute Simulation, at Volvo Car Corporation, Göteborg. The work has been supervised and guided by Ph.D. Per Mattsson and M.Sc. Fredrik Axelsson. The priceless support, knowledge and interest received from these supervisors were essential for the progress of this project.
My examiner M.Sc. and Ph.D. student Peter Åström at the division of Computer Aided Design at Luleå university of technology is also greatly acknowledged for his efforts during this thesis project.
Göteborg, February 2004
Joel Tjärnberg
Table of contents
ABSTRACT
ACKNOWLEDGEMENTS
TABLE OF CONTENTS...1
THESIS AIM AND LIMITATIONS ...3
1 NOMENCLATURE AND VARIABLES ...4
2 CONCEPT DESCRIPTION ...5
2.1 Changes in concept ...5
2.2 Concept layout ...5
3 MECHANICAL ANALYSIS ...6
3.1 Torque analysis ...6
3.1.1 Mode 1 ...7
3.1.2 Mode 2 ...7
3.1.3 Mode 3 (lockup mode)...8
3.1.4 Charge control torque equations ...9
3.2 Speed analysis...10
3.2.1 Speed ratios at mode shifts...11
4 VEHICLE MODEL / STRATEGIES ...13
4.1 General...13
4.2 Hardware and mechanics...14
4.2.1 Engine speed ...14
4.2.2 Drag losses ...14
4.2.3 Electric machines ...15
4.2.4 Modes...15
4.3 Software and control...16
4.4 Strategies...17
4.4.1 Engine control strategy - Variogram...17
4.4.2 Electric propulsion ...20
4.4.3 Lockup mode (mode 3) ...21
4.4.4 Mode hysteresis ...22
4.4.5 Charge control strategy ...23
4.4.6 SOCogram ...25
5 SIMULATION OF THE VEHICLE ...26
5.1 Performance simulations...26
5.1.1 Traction force characteristics ...26
5.1.2 Acceleration 0-100 km/h...29
5.1.3 Acceleration 80-120 km/h...30
5.2 Fuel consumption cycles ...32
5.2.1 EC00 drive cycle...33
5.2.2 US drive cycle...37
5.2.3 Miscellaneous cycles...41
6 SIMULATION RESULTS AND COMPARISON ...42
6.1 General...42
6.1.1 Performance ...42
6.1.2 Fuel consumption cycles...43
6.2 Model behavior during fuel consumption cycles...44
6.3 Result comparison with conventional vehicles. ...48
7 DISCUSSION AND FUTURE WORK ...49
8 REFERENCE LIST ...50
APPENDIX A ...51
APPENDIX B ...53
APPENDIX C ...54
APPENDIX D ...55
APPENDIX E ...56
APPENDIX F...57
Thesis aim and limitations
The purpose with this master thesis project was to simulate the hybrid electric vehicle with special attention towards driveability, performance and fuel consumption.
With focus on driveability rather than fuel economy, an approach using a variogram was chosen. A variogram is common for controlling transmissions with continuously variable speed ratios and specifies the combustion engine speed at a present accelerator pedal position and vehicle velocity.
An elementary charge control strategy was also desired as well as a complete physical model capable of simulating the earlier mentioned abilities.
The final goal was not to create a complete control strategy capable of being implemented in a prototype vehicle.
The model containing the control strategy must be able to simulate the essential drive cycles, used for fuel economy predictions as well as essential performance tests. Fuel consumption and performance must then be predicted with sufficient accuracy.
1 Nomenclature and variables
a Acceleration A Vehicle front area
C d Aerodynamic resistance coefficient CV Continuously variable
EC European cycle
f r Coefficient of rolling friction F Force
g Gravity
GVW Gross vehicle weight I Ratio, gear or speed
ICE Internal combustion engine J Inertia
m Vehicle mass
M Torque
PG Power generator
ρ Density
SOC State of charge
SP Set point
TM Traction motor v Vehicle velocity W,ω Rotational speed WOT Wide open throttle
ZXX Name of gear, number of teeth on gearwheel
2 Concept description
Since the concept is thoroughly described in previous publications, mentioned below, the concept description presented here should be regarded as an up to date notification of the concept.
Layout and mechanical arrangements are not of great importance in this publication.
However, knowledge regarding name conventions etc. is necessary to fully understand the model structure and physical calculations. Power flow figures of the concept can be seen in appendix F.
2.1 Changes in concept
Modification of the concept, since it was presented in Development of a Two-Mode Split Power Hybrid Transmission1, concerns the use of a mechanical brake, used to decelerate and hold the internal combustion engine. The function of this brake is not desired, why it has been replaced by a freewheel or one-way clutch, connected between the ICE shaft and the gearbox housing, see fig. 2.1. Using a one-way clutch will prevent the ICE from rotating in a negative direction. This solution is assumed to save a substantial amount of space and is therefore regarded as advantageous.
Furthermore, the use of clutches in order to create a parking brake effect has been ignored. However, since this fact does not affect the results of this project it has been left out of the documentation.
2.2 Concept layout
Figure 2.1 describes the concept layout.
Fig. 2.1. Concept layout
1 See reference list, reference 1, chapter 7.
Clutch
Clutch
Z1
Z6
Z5
Z4
Z7,1
Z2,2
Z3,2
Z7,2
Z2
Z7,3
Z3
Z8
Zout
Traction Motor Drive shaft
Power Generator Battery
Internal Combustion Engine (ICE)
One-way clutch
3 Mechanical analysis
In order to create a physical model of the system, all relevant physical relations such as torque, speed, losses etc must be examined. The primary analysis consists of speed and torque analysis. The torque analysis is an updated version originally based on the analysis performed in Evaluation and Simulation of a Two-Mode Split Power Hybrid Vehicle2 report. The speed analysis is based on elementary planetary gear theory3. Information concerning gear sizes can be found in appendix E.
3.1 Torque analysis
The analytical torque analysis has been performed using fig. 3.1, which is a free body diagram of forces and torques in the epicyclic gear train and the remaining gearbox.
It should be observed that the equations regarding Mout for all modes is stated negative compared to the free body diagram. This is because of definition made in the vehicle model. This is important for the charge control torque equations, section 3.1.4.
Fig 3.1 Free body diagram of transmission.
2 See reference list, reference 2, chapter 7.
3 See reference list, reference 5, chapter 7.
One-way clutch
Z32
Z1
Z6
Z3
Z2
F8
F7
Z72
Z73
Z22
Z8
F4
F3
F1
F2
F5
F6
Zout
Z71
M6
M8
M1
Mout
3.1.1 Mode 1
In mode 1, the clutch arrangement is such that Z22 is rotating freely, i.e. the clutch in line with this gearwheel is neither connected to gearwheel nor to ground. The clutch on the secondary shaft connects Z73 to shaft (see appendix F). Because of this arrangement, no torque is applied on Z2, thus
2 0
1=F =
F
The following equilibrium equations can then be derived:
( )
0
2 0 0 0
0 0
8 8 8
6 3 1
4 32 5
71 8 73 7 72 5
7 6 3 6
1 4 1
=
⋅ +
+ =
⋅ + +
⋅
=
⋅ +
⋅ +
⋅
=
⋅ +
=
⋅
−
=
⋅
−
Z F M
Z F Z
F Z F
Z F Z F Z F
Z F M
Z F M
Z F M
out out
Combining the above equations with the planetary constrain
4
3 F
F =
results in equations
73 32 72 6 1 6
8 71
8 1
Z Z Z Z Z M Z
Z M Z
Mout ⋅ out
⋅
+
⋅ +
⋅
= and
6 1 6
1 Z
M Z M = ⋅
for mode 1.
3.1.2 Mode 2
In mode 2, the clutch parallel to Z22 locks this gear to shaft. This together with the release of Z73 initiates mode 2. The clutch releasing Z73 will now be in neutral position. Thereby the torque from the TM will be directed through the geartrain (appendix F).
The following equilibrium equations,
( )
0 0 0
2 0 0 0
2 0 ) (
8 8 8
22 6 2 1
6 3 6
32 5 6 1 3 4 3 2
72 5 73 7
7
1 4 3 2 2 1 1
=
⋅ +
=
⋅
−
⋅
=
⋅
−
=
⋅ + +
⋅ + +
⋅
=
⋅ +
⋅
=
⋅ +
=
⋅ + −
⋅ +
−
Z F M
Z F Z F
Z F M
Z Z F
F Z F Z F
Z F Z F
Z F M
Z Z F
F Z F M
out out
combined with planetary constraints
4 3
2 1
F F
F F
=
=
and constraint for free rotating gearwheel Z71.
8
6 F
F =
results in equations
( ) ( )
73 3272 6
6 1 6 3 2 6
3 1
6 6
1 Z Z
Z Z Z
Z M Z
Z Z Z Z Z M Z M
Mout out
⋅
⋅ ⋅
+ ⋅ +
+
⋅ ⋅
⋅
−
⋅
=
and
( )
6 1 6 8
2
22 2 3 8
1 Z
M Z Z
Z Z Z M Z
M + ⋅
⋅
⋅
⋅ +
−
= for mode 2.
3.1.3 Mode 3 (lockup mode)
Mode 3 is primarily used to minimize the electric losses when the TM does not develop any rotational speed but must produce torque. By locking the clutch parallel to Z73 so that the shaft is grounded, the TM can not rotate and the clutch will maintain the torque (appendix F). The clutch parallel to Z22 normally locks gear to shaft as in mode 2, but can also lock shaft to ground in order to keep the fix gear ratio in an alternative way using only one clutch.
Torque distribution in mode 3 is the same as in mode 2, i.e.
( ) ( )
73 3272 6
6 1 6 3 2 6
3 1
6 6
1 Z Z
Z Z Z
Z M Z
Z Z Z Z Z M Z M
Mout out
⋅
⋅ ⋅
+ ⋅ +
+
⋅ ⋅
⋅
−
⋅
=
3.1.4 Charge control torque equations
As the power generator torque is always (in hybrid mode) used to control the ICE speed, the remaining power source, i.e. the traction motor, must be used to control the battery charge set points. However, if the traction motor is used in this purpose without influence of any other source, the output torque Mout will be altered, which implies a deviation in traction force. As this is not a desirable situation, a method for balancing the electric machines is needed. Read more about charge control in the charge control strategy section 4.4.5.
Using the mode equations both for Mout and M1 for each separate mode, three separate equations can be derived, one for each mode. These equations describe the interaction between PG and TM in order to maintain a constant output torque, i.e. ∆Mout =0, during various charge levels. These are as follows
(
6 1)
72 8
32 6 71 8
6 Z Z Z Z
Z Z M Z
M ⋅ ⋅ +
⋅
⋅ ⋅
∆
−
=
∆
for mode 1
(
6 1)
8 2
6 3 22 8
6 Z Z Z Z
Z Z M Z
M ⋅ ⋅ +
⋅
⋅ ⋅
∆
=
∆
for mode 2 and
(
2 3) (
6 1)
3 16 3 1
6 Z Z Z Z Z Z
Z M Z
M + ⋅ + − ⋅
⋅ ⋅
∆
−
=
∆
for mode 3.
Mout is in mode 3 directly dependent of the engine shaft torque M1 because of the direct connection (non CVT) to the output shaft. Although, both in mode 1 and 2 the engine torque need to be increased in order to maintain a constant output torque while charging. This is solved using the torque relations between PG and engine in mode 1 and in mode 2 the PG, TM and engine. This result in equations
(
1 6)
72 8
1 32 71 8
1 Z Z Z Z
Z Z M Z
M ⋅ ⋅ +
⋅
⋅ ⋅
∆
−
=
∆
for mode 1
( ) ( )
⋅
⋅
− + +
⋅
⋅
⋅
⋅ ⋅
∆
=
∆
8 2
22 3 2 6 1 8 2
1 3 22 8
1 Z Z
Z Z Z Z
Z Z Z
Z Z M Z
M
for mode 2 and
( ) ( )
6 3
1 3 1 6 3 2 6
1 Z Z
Z Z Z Z Z M Z
M ⋅
⋅
− +
⋅
⋅ +
∆
−
=
∆
for mode 3.
3.2 Speed analysis
Two relevant speed relations, concerning the planetary gear train, can be derived using the free body transmission diagram in fig. 3.2.
Fig. 3.2 Free body diagram concerning rotational speed.
( ) ( )
21
6 1 3
1 3 6
2 3 1
3 1 2
Z Z Z Z
−
− =
−
−
− =
−
ω ω
ω ω
ω ω
ω ω
Using eq 1 and 2 separately, the following four speed equations can be derived
( ) ( )
36 1 1 6
32 73
6 1 72
6 Z
Z Z
Z Z
Z Z Z Zout
out − ⋅
⋅
⋅
+
⋅
⋅ ⋅
=ω ω
ω
which is adaptable for all modes (1, 2 and 3).
( )
48 73
71
8 Z Z
Z Zout
out ⋅
⋅ ⋅
=ω ω
for mode 1 separately
Z1
Z5
Z6
Z4
Z71
Z22
Z32
Z72
Z2
Z73
Z3
Z8
Zout
ω8
ωout
ω6
ω1 ω2
ω3
( ) ( )
52 8
22 2
3 1 32
73
72 3
8 Z Z
Z Z Z Z
Z
Z Z Z out
out ⋅ ⋅
+ ⋅ +
⋅
⋅
⋅ ⋅
−
= ω ω
ω
for mode 2 separately, and
( ) ( )
632 73 2 3
72 3
1 Z Z Z Z
Z Z Z out
out + ⋅ ⋅
⋅
⋅ ⋅
=ω ω
for mode 3 separately.
3.2.1 Speed ratios at mode shifts
The two changes of mode (from mode 1 to mode 2 and from mode 2 to mode 3) are prescribed using the overall speed ratio, i.e.
ω1
ω ω
ω out
engine wheel
Itot = =
Using equation (3) and (5) separately with the conditions
0 0
8 6
=
= ω ω
the following expressions can be stated.
(
1 6)
72 73 32 1
1 Z Z Z Z
Z Z Z
out out
+
⋅
⋅
⋅
= ⋅ ω ω
which is the overall speed ratio when engaging mode 2 from mode 1, and
( )
72 3
32 73 2 3
1 Z Z Z
Z Z Z Z
out out
⋅
⋅
⋅
⋅
= + ω ω
which is the ratio for engaging mode 3 from mode 2.
These values of Itot will allow the clutches to engage synchronously. This is essential since the concept prescribes non-synchronized clutches.
If the overall speed ratio (Itot) is plotted in a graph, versus the variator speed ratio (Ivar), the result will be asymptotes where Ivar reaches infinity, which will occur at the speed ratio calculated from the equations above as depicted in fig. 3.3.
Fig. 3.3 Speed plot with overall and variator speed ratios.
In figure 3.3, the speed ratios at different modes are illustrated. The plot is reversed compared to earlier concepts, i.e. those presented in Evaluation and Simulation of a Two-Mode Split-Power Hybrid Vehicle and Continuously variable split-power transmission with several modes4, because of the gear separating the TM from the secondary shaft.
The vertical asymptotes describe the variator speed ratio at electric propulsion, i.e. Itot
is infinite because of no speed on the combustion engine. This implies that when an electric mode has been chosen, it is impossible to change mode unless Itot reaches the value of the horizontal asymptote, which would require a finite value of Itot, i.e. the ICE has to be started.
4 See reference list, reference 3, chapter 7.
Mode 2 Mode 1
Itot=0,2178 Itot=0,4326
Itot=ωout/ω1
Ivar=ω8/ω6
4 Vehicle model / Strategies
4.1 General
When creating the vehicle model, the modeling interface VSim (Vehicle Simulation Tool) was used. As this is a graphical interface to Matlab®5s Simulink®6 modeler, the model was build using Simulink components and related, such as Stateflow®7 etc.
The transmission model is one of several integrated parts in a state feedback system.
When assembled, the system simulates a vehicles physical behavior during a certain drive cycle.
This implies that the transmission model and control must be able to simulate the transmission behavior continuously throughout the entire drive cycle.
The model will be used for both performance and fuel consumption cycles without any changes, only the driver parameters and drive cycle information will be altered.
The transmission model consists of two major parts. The first part is the gearbox, which computes the mechanical input and output of the transmission. The second part is the control unit, which contains control strategies such as variogram, mode control, charge control and other software related devices. The transmission control is integrated in a simulated electronic control unit, which can be loaded with information concerning all parts of the vehicle.
The aim and final use of the model was to be able to simulate various drive cycles and performance tests with sufficient accuracy to predict fuel consumption and achievable performance. In fig. 4.1, the models capability of following the drive cycle is illustrated.
Fig 4.1 Velocity set points (blue) and vehicle velocity (red).
5 See reference list, reference 4.1, chapter 7.
6 See reference list, reference 4.2, chapter 7.
7 See reference list, reference 4.3, chapter 7.
4.2 Hardware and mechanics
Using the derived torque and speed relations, all relevant information concerning the physical behavior of the gearbox can be calculated. The most important relation when controlling the system is the one between the rotational speeds of the wheels and the internal combustion engine. This relation gives information regarding mode shifts which is essential because they can only occur during certain conditions. The wheel speed together with accelerator pedal position delivers (by using the variogram) information about ICE speed set point. See more about ICE control strategies in section 4.4.1.
4.2.1 Engine speed
The ICE speed is calculated using engine produced torque, input torque to gearbox and ICE inertia using following equation
(
1) (
1)
1
1
1 ICEtorque M
J or S
M ICEtorque W J
ICE t
ICE
state ⋅ −
− ⋅
⋅
=
∫
where S is the Laplace transformation, in this case used for integration.
With this information, and using the torque relations for the present mode, the required torque from the PG to balance the engine speed can be calculated as
(
WSP Wstate)
M6 ∝∆ 1 − 1
which is done continuously using a proportional/integrating (PI) controller using the simplified block diagram illustrated in fig 4.2.
Fig 4.2 Simplified block diagram of PI controller.
These equations are always applied in mode 1 and 2, i.e. in CVT mode. In mode 3 the engine speed and torque are directly proportional to those delivered to the wheels.
Since the traction motor torque is controlled by the charge power level in the battery, it has been referred to as software controlled.
4.2.2 Drag losses
Since the gearbox is mechanically complex and no data is available regarding gear losses, the only losses taken under consideration are drag losses. The final drive is a standard component also used in a present manual gearbox at VCC. For that gearbox most part of the total drag losses comes from the final drive. Therefore, drag losses for
W1SP
W1state
M6SP
the final drive together with gear Z72 and Z32 are here approximated with the known total drag losses for that gearbox. Other losses taken under consideration are the ones introduced in the gears in connection with the TM, i.e. Z8, Z71 and Z22. Although these losses are merely estimated. These losses together cover the entire gearbox with exception for the planetary gear train which provides a relatively low drag loss.
The loss of torque due to drag are speed related and easy to update within the model if new data is available.
4.2.3 Electric machines
The electric motors are modeled using standard electric machines from the VSim component library.
These models contain limitations in torque and power. Here these limitations have been disconnected in order to plot the required torque and power for an accurate dimensioning of the machines.
The models contain loss maps, which calculate total loss with regards to motor speed and torque. The losses are divided into motor and inverter loss and can be updated separately.
Since there are no electric machines specified for this concept, no authentic data is known regarding motor losses. However, these losses are important for the simulation outcome when considering fuel consumption, performance and battery recharge.
4.2.4 Modes
The mode control is a simple discrete case switch, ruled by the total speed ratio (Itot).
It only controls the mode switch between mode 1 and 2 since it was easier and more consistent to place mode 3 selection in the mode hysteresis function, see section 4.4.4.
The mode control itself is software based. However, the shifting of modes alters the physical behavior of the model, e.g. torque and speed relations.
Since the concept uses non-synchronized clutches, it is essential to provide the clutch mechanism sufficient time to perform a mode change. This is solved using the mode hysteresis function. This function controls the speed of the gearbox in order to maintain synchronized clutch speed during the mode shift. This without altering output speed too heavily.
4.3 Software and control
Simulated modules regarded as software are
• Variogram
• Mode control
• Mode hysteresis
• Electric propulsion control
• Controller reset
• TM torque control/ battery charge control
The module variogram, contains a function for low velocity kickdown performance, which means that from near zero velocity the maximum engine speed line is elevated from the original kickdown line in order to develop more power at WOT acceleration from standstill.
The variogram is more thoroughly described in the strategy section 4.4.1.
The mode selector and hysteresis functions are in CV mode dominated by the overall speed ratio set by the variogram. The interaction can be described as:
The TM torque control is used for balancing the battery's SOC by adjusting the torque on the traction motor with regard to its speed, to fulfill a charge power set point of the battery. This set point is decided by a so called SOCogram, giving the power level as a function of accelerator and SOC. The following chart describes the process.
<Mode control>
• Wheel speed
• Engine speed (state)
• Accelerator
<Variogram>
<Mode
hysteresis> • Engine speed SP
• Mode
Electric charge power
<Battery> <SOCogram>
<TM torque control> <Traction Motor>
<Driver>
<Vehicle>
SOC
M6 SP
Acc/brake
Velocity
Power SP
4.4 Strategies
4.4.1 Engine control strategy - Variogram
The variogram, see fig. 4.3, is the connection between accelerator pedal, vehicle wheel speed and combustion engine speed. A given wheel speed together with accelerator pedal position generates the engine speed set point. The variogram can be seen as consisting of two parts, one for performance and one for continuous driving (cruising).
The performance part is represented with the kickdown line (100% accelerator). This line can be converted to the maximum performance line (110% acc.) by using full accelerator before exceeding a certain low velocity. These lines are the two upper lines in fig. 4.3. The max performance line is limited by the PG´s continuous power outlet/inlet in mode 1. It is optimized for acceleration 0-100 km/h. Therefore the mode shift is placed just above 100 km/h. In mode 2 the max performance line keeps the engine speed at maximum power.
Whenever driving at velocities exceeding the limit mentioned earlier and using lower pedal position than maximum, the kickdown line can be reached by using full accelerator. The engine speed will then follow the kickdown line, which is somewhat lower in speed compared to the max performance line. This line gives more of the impression of a non-CV transmission because of its continuous climb towards maximum velocity.
The kickdown line is positioned so that an 80-120 km/h acceleration situation is covered in mode 2. This is thanks to the mode hysteresis function which will not allow a downshift in mode unless a hysteresis interval is breached or a time interval is exceeded. See mode hysteresis, section 4.4.4 for further details.
The continuous driving part is created by drawing a maximum non-kickdown restriction line (99% accelerator). A minimum (0% accelerator) line is also introduced by using points for maximum velocity at certain discrete pedal positions (using only the standard pedal maps without altered engine torque, in mode 3). These points can be seen in the variogram along the mode 2,3 shift line. Remaining accelerator positions, (0% < accelerator < 99%), have been evenly distributed in the interval.
An example for understanding could be to consider the first point along the 2,3 mode shift line, i.e. the point situated furthest to the left in fig. 4.3. Since this is the maximum velocity using only ICE propulsion in mode 3 for accelerator pedal position 20% on a level surface, the 0.2 pedal line needs to coincide with the mode shift line in this point. When this constraint is decided, the 0% accelerator line can be positioned so that the distance between the 0% line and the 20% line (0.2) is 20% of the total length from 0% pedal line up until 99% pedal. This procedure is then used for all pedal positions between 0.2 up to 0.6 beyond which the torque characteristics will cease to increase with pedal position.
This results that at a given constant pedal position, mode 3 will be reached in a point where the combustion engine normally would (without the use a of hybrid power source) have leveled out in mode 3. See figure 4.3 for visualization of the variogram.
A big scale variogram with practical scales (rpm and km/h) is found in appendix B.
Variogram
1,1
0,0 1,0
0,99
0 50 100 150 200 250 300 350 400 450 500
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Wheel speed (rad/s)
Engine speed (rad/s)
Figure 4.3. Complete variogram with mode shift lines and mode hysteresis.
The variogram also contains information regarding electric propulsion in both mode 1 and 2. This information is represented by boundaries in which electric propulsion is initiated in mode 1 or 2 and where hybrid propulsion is engaged. Details can be seen in figure 4.4 and in the electric propulsion section 4.4.2.
It is not possible to change mode while using electric propulsion because of infinite overall speed ratio. The initiated electric mode must be used until hybrid propulsion is engaged. This means for example that if the accelerator pedal position is high at takeoff (>50%), mode 1 will be initiated. However, if the pedal position is decreased below 50%, mode 2 will not engage until hybrid propulsion occurs, and vice versa if the pedal position is low at takeoff and thereafter increased. At any point during electrical propulsion, hybrid mode can be reached by using full accelerator pedal. This is actually the situation when performing a 0-100 km/h acceleration. A high pedal position value triggers electric mode 1 and when full accelerator is reached, hybrid mode 1 is engaged.
The electric modes are only initiated if the SOC exceeds a lower value. If this is not the case, hybrid propulsion will be used to avoid the battery from discharging completely. This situation must be avoided since the battery must be able to supply sufficient power to the PG in order to start the ICE.
Furthermore, the electric modes are only accessible from standstill or when the accelerator pedal has been completely released along with that the wheel speed has fallen below a certain velocity set point.
In fig. 4.4 the different electric modes as well as remaining mode situations has been represented with colored fields.
Figure 4.4. Electric propulsion strategy
= Electric propulsion mode 1 (electric mode change not possible).
= Electric propulsion mode 2 (electric mode change not possible).
= Only electric propulsion in mode 2 (mode 1 hybrid).
= Strictly hybrid propulsion (mode according to overall speed ratio).
4.4.2 Electric propulsion
When the vehicle accelerates from zero speed and the driver does not use kickdown mode, the vehicle is accelerated using electric propulsion. This was seen in fig. 4.4 as two separate fields, the red and green, and also described earlier. In electric mode, the torque delivered from the electric machines is adjusted to match the torque presented at hybrid drive using the same accelerator pedal position. This results in a low threshold in traction force between electric mode and hybrid mode. Fig. 4.6 illustrates vehicle acceleration as a function of velocity for electric mode into hybrid mode for 30% accelerator pedal position.
Fig. 4.6 Transition from electric mode to hybrid propulsion at moderate acceleration.
To accomplish this behavior a calibration chart is used. The chart is created by comparing the traction force in electric mode and in hybrid mode and using the most suitable value for propulsion. Fig. 4.7 describes the calibration torque curve as a function of accelerator pedal.
Electric propulsion torque
0 20 40 60 80 100 120 140
0 0,2 0,4 0,6 0,8 1 1,2
Accelerator pedal [frac.]
Torque [Nm]
Fig. 4.7 Electric propulsion torque for TM and PG respectively as a function of accelerator pedal.
4.4.3 Lockup mode (mode 3)
Because of the strategy to let the vehicle velocity level out in mode 3 for various accelerator pedal positions, a useful behavior is presented. Whenever the driver desires to cruise at a constant speed, the gearbox can position itself in mode 3 and thereby reduce losses as described earlier. These levels can be seen in the variogram as dots along the mode 3 shift line. These are used as intersections for the pedal lines across the mode shift line. This leads to lockup mode when vehicle velocity exceeds
~60 km/h and the driver wishes to cruise at constant speed. Fig. 4.5 shows lockup behavior for a drive cycle starting at 40 km/h and discretely increasing with steps of 10 km/h towards 130 km/h. The first level at 40 km/h is electric mode thus the overall speed ratio is infinite (according to the speed ratio diagram, fig 3.3). At 50 km/h the variogram does not allow mode 3 lockup. At 60 km/h and upwards, the lockup mode is used which can be seen by the blue Itot characteristic coincides with the green line.
This dotted green line indicates the mode 3 lockup speed ratio. Whenever a new speed is desired the driver increases the accelerator pedal position and the transmission exits mode 3 and enters mode 2. This can be seen as the dropouts in Itot.
Fig. 4.5 Mode 3 lockup behavior for varying vehicle velocities.
Since mode 3 is not a CV mode, there is no direct need of using electric machines in this mode for gearbox functionality. However, since the PG is essential in all CV modes there can be a lack of power when entering mode 3 if the PG is not used there as well. There are two obvious alternatives to eliminate this lack. One is to compensate electric torque in order to maintain constant traction force when entering mode 3. The second is to regard the entrance in mode 3 as the cruising velocity for the current accelerator pedal position as described above. The second alternative is used in the simulations since the entry to mode 3 is time based and can be overridden by the drivers pedal handling. The compensation strategy on the other hand, is hazardous as it would gradually discharge the battery.
4.4.4 Mode hysteresis
Since the mode shifts involve movement of mechanical clutches, there must be a time interval in which these shifts take place. In order to perform a mode shift, the clutches must rotate at a synchronous speed. This is achievable if the speed of the combustion engine can be forced to follow the mode shift line. This is the task for the mode hysteresis function. When the engine speed reaches the mode shift line, the control signal is altered so that the set point value will follow the mode shift line. It will do so until the original signal, i.e. the value from the original pedal line in the variogram exits the mode shift zone. This zone is represented by the dotted lines on each side of the mode shift line, fig. 4.8.
In figure 4.8, three cases can be observed. The red line describes acceleration using full accelerator pedal from standstill and moving across the mode shift from mode 1 to mode 2. The altered signal is climbing along the mode shift line until the original signal exits the shift zone.
The blue line is a deceleration using the same pedal position. This situation can occur when driving up a steep hill. Here a greater leap in speed will occur but is also tolerated because this can be regarded as a downshift.
The green line represents an 80-120 km/h acceleration and here the other advantage of the mode hysteresis is visible. Since the acceleration requires the highest possible engine speed for high power, however without wasting time on mode shifts, the mode shift line is the highest possible value permitted in this case. Therefore, when trying to reach the kickdown line in speeds near 80 km/h the mode hysteresis will instead hold the engine set point at the mode shift line and thereby maintain highest engine speed without changing mode.
Fig. 4.8 Mode hysteresis behavior for various situations.
1,1
0,0 1,0
0,99 Modeshift zone 1,2
Modeshift zone 2,3
When the driver has leveled the vehicle at a constant speed within an interval similar to highway velocity conditions, the overall speed ratio will coincide with the mode 3 shift line. If the driver chooses to remain at this speed, the lockup mode will engage after a short period of time. This mode will be held until the driver alters the accelerator pedal position in such a way that the hysteresis is breached. An essential factor for lockup is the road inclination. If the vehicle approaches a slope and the driver uses the accelerator to remain at constant speed while the transmission is locked in mode 3, a certain amount of inclination is possible to overcome before the mode shift interval will be breached. Table 4.1 shows inclination values for some typical velocities causing the lockup mode to disengage. The limits can be extended or lessened by using the PG.
Vehicle velocity Positive inclination limit Negative inclination limit
70 km/h 1,3% 1,0%
90 km/h 1,6% 1,0%
110 km/h 2,0% 1,5%
Table 4.1 Inclination limits for mode 3 disengagement.
4.4.5 Charge control strategy
While charging or discharging the battery, power is added or removed from the mechanical system. This is necessary but unwanted because of the inconsistent behavior it provides at similar driving situations under varying charge power. To reduce, or to some extent eliminate this behavior, a control strategy has been developed.
The strategy involves the torque relations for all power sources, i.e. ICE, PG and TM.
When increasing torque on one of them separately, another one has to be increased or decreased in order to maintain a constant torque on the wheels. Since the PG has no d.o.f. and instead is proportional to the ICE torque, the remaining source of control is the TM. When additional torque is added to the TM, a proportional part is added to the ICE control system. By doing this, the torque level on the PG is also altered and a fixed torque relationship between the electric machines can be achieved. This results in a negligible torque loss or gain on the driving wheels for reasonably low accelerator positions. This process is graphically described in figure 4.9.
Fig. 4.9 Flowchart describing wheel torque compensation during battery charge.
The torque relations for maintaining constant driving torque are to be found in the torque analysis section 3.1.4.
Using this strategy, the total power from the battery (Pbatt) can be controlled, which leads to control of the SOC because of the relation
∫
= t sys batt
V SOC P
where Vsys is system voltage.
The torque compensation function is applied only when torque would be lost, i.e.
when charging the battery and not when discharging. It must also be disabled during regenerative braking.
The system can of course be operated without the constant torque feature. The result of this action would be a proportional loss of torque on the wheels when power is added to the battery, which could be hazardous in some traffic situations.
The limitation is when the ICE reaches its maximum torque value for its present revolution speed. At this point the vehicle will lose traction force and/or the battery must decrease its charge level. However, the strategy using torque compensation has been selected for the model because of its ability to maintain a consistent behavior in traction force.
<TM>
(Torque level controls battery charge power)
TM+PG => Mout
<PG>
(Torque increases to maintain control of ICE speed.
<Wheels>
(Torque not depending on battery charge level)
<ICE>
(Torque increased to compensate battery charge power) Multiplied with scale
factor, for the present mode.
M8
control- signal
M1 SP M8
M6
Mout
M1
4.4.6 SOCogram
To acquire a set point for battery power, the SOCogram (earlier mentioned in software and control) is used. This is a continuous chart where power is given as a function of accelerator pedal and SOC. A discrete SOCogram for mode 1 is presented in fig. 4.10. As the chart is easier to describe discretely, the function will later be interpolated by the model to act continuously.
The lines in fig. 4.10 represent discrete pedal positions starting at 0 from the top to 1,1 at the bottom. The deviant line is representing the power level when using regenerative braking. This line, with power added from zero accelerator pedal, produces a constant power, for reasonable SOC levels, when applying the brakes.
Figure 4.10 Discrete SOCogram for hybrid mode 1.
It can be observed that the lines, especially pedal 1.1, levels out at a fix power level above a certain SOC. This is because this power is sufficient to accelerate the vehicle from zero to 100 km/h within a specified time range. This limits the vehicles maximum performance to a SOC exceeding a certain level, which should not be fallen short of if high performance is desired.
The SOCogram is also used to prevent the battery from fully discharging or overcharging. For example, this affects the regenerative braking. When the battery is full, no power can be added to the battery and no regenerative braking can occur.
Another noticeable behavior is the power lines below 30% SOC. The strictly positive power will prevent the battery from discharging by applying, even at a high accelerator pedal position, a positive charge power. Visualization of SOCogram for both mode 1 and 2 can be found in appendix C.
Chargecontrol diagram, hybridmode1
-35000 -30000 -25000 -20000 -15000 -10000 -5000 0 5000 10000 15000 20000 25000 30000 35000
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
State of charge [frac.]
Battery power [W]
Regenerative braking
0% acc
110% acc
5 Simulation of the vehicle
After verifying the new model, i.e. comparing it to previous work, and making sure that the physical relations such as losses etc behave as expected, the model is ready to be used in simulations.
The simulations can be divided into performance tests and fuel consumption cycles. In these cases, other important variables can be stored, e.g. battery power and electric motor torque. These data can later be used when dimensioning battery and electric machines.
5.1 Performance simulations
Performance simulations mostly cover acceleration situations like vehicle acceleration 0-100 km/h and 80-120 km/h.
An additional feature is the vehicles capability of handling slopes, e.g. slope takeoff and maximum possible inclination at 90 km/h. Continuous top speed is also investigated.
All performance simulations have been carried out using two different levels of the vehicle mass. This is because the actual mass for this kind of vehicle is not known.
However it should end up within the range of the values used in the simulations.
The requirements set for a standard vehicle concerning acceleration should be exceeded due to the possibility to use electric energy stored in the battery. Therefore the acceleration requirements have been set to correspond with a somewhat stronger engine than the one used in the simulation. However, this is not the case for top speed, since this is not an acceleration test and must be performed continuously.
During performance simulations, for instance a 0-100 km/h acceleration, several important measures can be calculated. This is done by a Matlab script which calculates accelerations, speeds, maximum takeoff, inclination etc. The outcome from this script can be observed in the result section.
5.1.1 Traction force characteristics
When describing vehicle performance, the traction force plot is very informative. In fig. 5.1, traction force calculated on the wheels can be compared for different accelerator pedal positions. The case simulated is acceleration from standstill until top speed and/or mode 3 is reached (for lower accelerator pedal positions).
Fig. 5.1 Traction force during acceleration from standstill, 1700 kg vehicle weight.
The increasing dotted lines show total road load in form of rolling resistance, air resistance and slope. Since rolling resistance and air resistance is velocity dependent, the lines are monotonically increasing. The vertical spread is because of climb, which is not velocity dependent. These climb angles or inclinations are given in percentage.
See appendix D for calculations concerning road load. The simulations performed in fig. 5.1 are done with SOC start value at 0.75.
As described in earlier sections, kickdown (accelerator pedal = 1), automatically engages hybrid mode. Starting from standstill, this is seen using accelerator pedal 1.1 in fig. 5.1. Lower accelerator pedal results in electric mode until a certain speed is reached and therefore a somewhat constant torque characteristic is seen up until that point. Electric propulsion is preferred if high and constant initial takeoff traction is desired. However, if maximum possible peak traction is wanted, hybrid propulsion is necessary. The drop in traction force, easily seen at 20 km/h using pedal 0.9, is a consequence when starting the ICE.
In the case of WOT acceleration, characteristics curves can be produced to illustrate the difference in acceleration depending on SOC start value. Because of lower SOC, the SOCogram will force the TM to charge the battery and therefore reduce the torque delivered to the wheels. Torque is reduced because of the fact that the engine can not compensate torque loss when using WOT. Fig. 5.2 contains acceleration curves for various SOC levels, using 1700 kg as vehicle weight.
When driving with GVW, i.e. vehicle weight 2000 kg, the traction force using WOT and varying SOC start values is visualized in figure 5.3. The level curves represent inclination percentage for GVW.
Fig. 5.2 Acceleration characteristics using WOT and different values for SOC.
Fig. 5.3 Traction force using WOT, GVW and varying SOC.
5.1.2 Acceleration 0-100 km/h
When performing a 0-100 km/h acceleration, the engine speed is controlled by the maximum performance line (accelerator pedal 1.1) in the variogram. This implies that no electric propulsion will be used and that the combustion engine produces maximum power possible (limited by the PG).
To achieve maximum performance, the SOC level should exceed 70%. This is the lower limit when maximum acceleration performance is desired on a level surface. If SOC level is below 70%, the torque delivered by the TM will be reduced and therefore limiting the acceleration performance.
Fig. 5.4 illustrates the vehicle acceleration and velocity characteristics during a 0-100 km/h acceleration. In fig. 5.5, showing engine speed and vehicle velocity, the engine startup can be seen in the beginning of the simulation.
The 0-100 km/h acceleration is performed using only mode 1. It is important not to involve a mode shift in such an important acceleration situation. This is controlled by the variogram.
Fig. 5.4 Acceleration during 0-100 km/h, vehicle weight 1700 kg.
Fig. 5.5 Engine speed during 0-100 km/h, vehicle weight 1700 kg.
It is seen here in fig. 5.5, that the engine speed is controlled by the performance line in the variogram. The characteristic of the curve is such that speed for maximum power is regarded as an asymptote and the mode shift into mode 2 will be reached just above 100 km/h.
5.1.3 Acceleration 80-120 km/h
The 80-120 km/h performance simulation is carried out using mode 2. Also here a mode shift would result in an increased acceleration time. However, when the driver levels out at 80 km/h, preceding the test, mode 3 is reached. This mode must be released and mode 2 be engaged when the driver initiates the acceleration.
As seen in fig. 5.6 and 5.7, the lockup mode is used when leveling at 80 km/h and then released at acceleration. At this point the engine speed starts to increase.
The actual performance acceleration starts at time = 0 and then takes place in the indicated area in which mode 2 is active.
Figure 5.6 represents vehicle acceleration and velocity during the test, while fig. 5.7 represents engine speed as well as velocity.
It can be seen in figure 5.7 that the engine momentarily passes the maximum revolution speed permitted in mode 2 for the vehicle velocity in question. However, the mode hysteresis function identifies the drive situation and forces the engine speed to return to the mode shift line.
Fig. 5.6 Acceleration during 80-120 km/h acceleration cycle
Fig. 5.7 Engine speed during 80-120 km/h acceleration cycle.
5.2 Fuel consumption cycles
The primary continuous drive cycles examined are the European drive cycle (EC00) and the US cycle. The European cycle is divided into city traffic, highway and both of them together as combined. This is also the case for the US cycle. It is divided the same way, FTP75, highway and combined.
When running a long drive cycle it is important to be aware of the influence of battery SOC. It is possible to run a drive cycle with very low fuel consumption if a large amount of battery energy is used. Nevertheless, the opposite behavior will appear if the battery is charged a lot during the cycle.
The SOCogram contains the primary set points for battery charge power and will prevent the battery from reaching its extremes in SOC. For instance, the city part of EC00 tends to drain battery charge level rapidly because of great amount of time in electric mode. This rapid drainage is counteracted by the SOCogram. In fig. 5.10 (EC00 section) the SOC behavior during EC00 city traffic, run four continuous times, can be seen. When this power compensation occurs the power must be delivered by the ICE and thereby the fuel consumption is increased.
As a result of this, a number of simulations must be made to ensure a trustworthy understanding of total fuel consumption.
Table 5.1 shows suitable fuel consumption drive cycles for such an investigation.
The ICE startup temperatures used when simulating highway separately, have been simulated and chosen as the temperature after a complete EC city cycle or FTP75 in the US cycle.
EC00 City Highway Combined
1700
Kg • Varying SOCstart
• Cold engine startup
• Varying SOCstart
• 65°C engine startup
• Varying SOCstart
• Cold engine startup
US FTP75 Highway Combined
1700
Kg • Varying SOCstart
• Cold engine startup
• Varying SOCstart
• 90°C engine startup
• Varying SOCstart
• Cold engine startup
Table 5.1 Suitable fuel consumption drive cycles.
5.2.1 EC00 drive cycle
When simulating fuel consumption during EC00, two different approaches have been used. One approach using different start values of SOC when simulating the different cycles, and one approach where consumption is measured when running a continuous cycle consisting of multiples of the original cycle.
Because the EC00 combined (fig. 5.8) is a frequently used standard cycle concerning fuel consumption, the single EC cycle is important to examine. As this cycle starts with a cool engine and progressively increases in temperature, the fuel consumption differs from the average obtained in multicycle simulation.
Fig. 5.8 EC00 combined drive cycle, velocity set points.
The main idea is to measure fuel consumption when the SOC start and end value is somewhat similar after a completed cycle.
When using the strategy of different SOC start values, an inter- or extrapolation is used to determine the fuel consumption when ∆SOC =0. This is visualized in regression plots 5.9, 5.11 and 5.13.
5.2.1.1 EC00 city traffic
EC00 City
y = -25,714x + 7,1178
0 1 2 3 4 5 6 7 8
0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2
delta SOC
Fuel consumption
Fig. 5.9 Linear regression plot for ∆SOC = 0.
Here it can be seen, according to the trend line equation, that the fuel consumption at
=0
∆SOC is 7,12 l/100km. However, a non-descending SOC value is not expected in city traffic due to much electric propulsion, thus this linear extrapolation is questionable.
Compared to a value measured during a multicycle simulation (SOC behavior seen in figure 5.10) the results are in disagreement. Although, the fuel consumption, 4.95 l/100km, calculated using multicycle is somewhat low because of the loss of battery charge in the first part of the simulation. The temperature of the engine will also increase and after about one cycle it will operate under normal thermal conditions.
Red circle indicates a new cycle.
Fig. 5.10 SOC behavior during EC00 city cycle (multicycle strategy).
5.2.1.2 EC00 highway
EC00 Highway
y = -11,914x + 4,737
0 1 2 3 4 5 6 7 8
-0,25 -0,2 -0,15 -0,1 -0,05 0 0,05 0,1
delta SOC
Fuel consumption
Fig. 5.11 Linear regression plot for ∆SOC = 0.
For a reasonable SOC start value, the SOC value should increase during the highway cycle. The interpolated consumption of 4,74 l/100km is comparable to the value obtained in the simulations using multicycle strategy, for which the consumption 4,69 l/100km is obtained. In fig. 5.12 the SOC during this multicycle can be seen.
Fig. 5.12 SOC behavior during EC00 highway cycle (multicycle strategy).
