Proceedings of the American Control Conference
Chicago, Illinois June 2000
Energy Management in a Parallel Hybrid Electric Vehicle
With a Continuously Variable Transmission
Paul Bowles'
Scientific Research Laboratory
Ford Motor Company
Huei Peng
Department of Mechanical Engineering and Applied Mechanics
University of Michigan
Xianjie B a n g
Scientific Research Laboratory
Ford Motor Company
makes sense to combine PHEV and CVT technology into
a single vehicle.
1. Abstract
The combining of two different power sources in an
PHEV implies that a strategy is necessary for regulating
power flow in the vehicle [ 11. The issue of energy
management is discussed and an appropriate strategy is
presented. The simulation model used in this paper is a
dynamic, modular, forward-type simulation. That is the
model consists of a driver sub-model trying to follow a
predetermined velocity profile, a dynamic vehicle model,
and a PHEV control module that essentially acts as the
interface between the driver and vehicle models. The
relationships between these components are shown in
Figure 1. The PHEV control module controls the vehicle
such that the driver power demands are met, while
minimizing fuel consumption. The simulation was
implemented in the Matlab / Simulink environment.
This paper describes a control strategy for the energy
management of a post-transmission parallel hybrid electric
vehicle (PHEV) equipped with a continuously variable
transmission (CVT). Results are presented highlighting
the dynamic behavior of the model, as well as the fuel
consumption normalized to a base case. A dynamic,
forward simulation of a complete compact class vehicle
including driver model and computer controller was
written in Matlab / Simulink. Modeled vehicle
components include: internal combustion engine, engine
clutch, CVT, electric motor, lead-acid battery, vehicle
driveline, hydraulic brakes, and the vehicle and tire
dynamics.
2. Introduction
Vehicle Driver
Model
Hybrid Electric Vehicles (HEVs) offer the potential
to considerably increase the fuel economy of a vehicle,
while reducing the overall emissions of a conventional
powertrain [3]. Parallel Hybrid Electric Vehicles (PHEV)
are HEVs configured such that the electric motor
powertrain and the conventional powertrain can provide
tractive power to the drive wheels simultaneously [2].
Computer
Control Module
PHEV with CVT
Dynamic Model
Figure 1: Major Model Components
3. Energy Management in a Post-Transmission
PHEV with CVT
Figure 2 shows a post-transmission PHEV and the
possible sources of wheel motive power. Power can be
supplied by the engine, the motor, or by both at the same
time.
A Continuously Variable Transmission (CVT)
provides an infinite number of transmission gear ratios
within the limits of the device. This is in contrast to an
automatic or manual transmission that typically offers
between four and six gear choices. CVTs offer the same
potential as the PHEV to increase the fuel economy of a
vehicle while minimizing emissions [4]. It therefore
'
Paul Bowles was a graduate student in Mechanical Engineering at the University of Michigan during the completion of
this work.
0-7803-5519-9/00 $10.00 0 2000 AACC
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TRANSMISSION
Figure 2: PHEV Motive Power Sources
Figure 4: Possible Power Paths from Engine to Wheels
When discussing the issue of PHEV power
management, it is important to note that all of the vehicle’s
power ultimately comes from fuel. The battery is
recharged by using the electric motor as a generator, thus
transforming mechanical power into electrical power. In
theory, the battery could also be recharged by somehow
plugging the vehicle into a wall outlet. In practice,
requiring consumers to do this would make the PHEV a
very tough sell for automakers, so it is assumed that this is
never done. Regenerative braking involves recapturing
some of the energy normally lost through the hydraulic
brakes. This energy is only available for storage because
the vehicle was first put in motion by the enginehotor
power plant. Figure 3 shows the two methods of
recharging the battery.
Loolung at Figure 4,it should be clear that converting
the mechanical energy at the driveline into electric energy
and again into chemical energy for storage, only to repeat
the process in reverse, is significantly less efficient than
allowing the power to flow directly from the engine to the
wheels. We must keep in mind, however, that the energy
stored in the battery is available for use at any time, and
that the operating conditions under which the energy is
stored may not be the same as the conditions under which
the energy is released. This is particularly useful under
the two following conditions:
1. During start-up or at slow speeds, when the engine
cannot be operated at an efficient point, and;
2. When the driver power demand is so high that the
engine is unable to meet it and the electric motor is
required to provide additional torque.
TRANSMISSION
In other words, we wish to route power to the battery
for use either when the engine cannot be operated
efficiently or cannot meet the driver power demand. This
allows both the engine and motor to be sized smaller than
would be necessary if either one had to supply the entire
vehicle’s power directly. We also wish to recapture as
much energy as possible through regenerative braking, as
this energy is essentially free.
Dim loading c€cn@nc
Figure 3: Battery Recharging Paths
The HEV control problem can be summarized as
follows. Assuming that the motive power demand (from
the driver) must be met, and that certain driveability
requirements must also be considered, how do we balance
the power from the engine and from the motor? Also,
knowing that the motor is powered by a battery that is
charged by one of the two methods shown in Figure 3,
when is regenerative braking to be used, and when should
the engine be loaded to charge the battery?
4.
Energy Extraction from the Engine / CVT
From Figure 4,we see that the power flow through
the engine and CVT is unidirectional. While the engine
and CVT friction can be used to brake the vehicle, no
mechanical energy can be converted back into gasoline.
The answer to the question of when regenerative
braking should be used is relatively straightforward.
Assuming that there exists the capacity in the battery to
store the energy, we would want to use regenerative
braking as much as possible. Whatever energy is not
recaptured is essentially wasted by using the hydraulic
brakes.
Furthermore, the CVT gives us an additional degree
of freedom over a conventional transmission to exactly
choose the transmission gear ratio. This is in contrast to a
manual or automatic transmission where the choice of
gear ratio is limited to the number of gears, generally four
or five. This implies that we have two degrees of freedom
to control the amount of power that is delivered to the
wheels from the engine / CVT part of the vehicle: the
engine throttle angle and the CVT gear ratio. If we have
two degrees of freedom in the control of the engine /
CVT, then it should be possible to minimize one quantity
(e.g. fuel consumption) subject to one constraint (e.g. the
vehicle or driveshaft speed).
The real power management problem is whether to
route power from the engine directly to the wheels or store
it temporarily in the battery for use at a later time. These
two power paths are shown in Figure 4,ignoring the
possibility of regenerative braking.
Both of these facts set up the following optimization
sub-problem. How can we maximize fuel efficiency
56
est Case Enginemrane Ange (&g)
(minimize fuel consumption) subject to the following
constraints:
1. The engine I CVT subsystem delivers the power
requested by the PHEV controller.
2. The engine is operated within its operating limits.
3.
The CVT is operated within its operating limits.
This problem is complicated by the fact that the
driveline speed (CVT output speed) cannot be controlled
by the engine I CVT subsystem.
The goal is to determine what engine throttle angle
and CVT gear ratio should be used to minimize fuel
consumption while producing a given amount of power at
a known vehicle (or driveline) speed. Fuel minimization
is accomplished by processing the steady-state engine fuel
consumption map along with the torque loss data for the
CVT. For a given vehicle speed and desired power
output, we calculate the solution to the aforementioned
optimizationproblem, assuming such a solution exists. If
a solution does not exist, this simply means that we have
reached the limitations of this vehicle.
Vehicle spaed (MPH)
Figure 6: Engine Throttle Angle for Minimum Fuel
Consumption
The plot of the CVT gear ratio (Figure 5 ) provides
some insight into the general behavior of the system. At
low requested power levels, the best CVT gear ratio is
quite low and gets lower as speed increases. While this
may seem strange, it can be explained by the fact that the
engine I CVT subsystem produces low levels of power
most efficiently at low engine speeds. There is, however,
a minimum engine speed below which it is not able to
provide significant power; this limit is around 1000 rpm.
In order to maintain a low engine speed as the vehicle
speed increases, the CVT gear ratio must drop. At very
low speeds (about 10 mph), the CVT must be operated at
a gear ratio above two, as anything less could stall the
engine. If we look at different levels of power output
along the 25 mph line we notice the general trend that
increasing the power output results in a higher gear ratio.
This is because the engine produces high power more
efficiently at high speeds. As the vehicle speed increases
we hit the upper engine speed limit and consequently the
gear ratio must drop to allow the engine to power the
vehicle.
After this process is complete for the entire operating
space (desired power versus speed) we have two maps.
One map is the desired engine throttle angle required to
minimize fuel consumption while delivering a certain
amount of power to the driveline at a given vehicle speed.
The second map is similar but contains the corresponding
CVT gear ratio that minimizes fuel consumption.
The CVT gear ratio and engine throttle angle maps
are shown in the following figures. The CVT gear ratio
range is approximately 0.5 through 2.5.
Best Case CVT Gear Patio
Note that the engine I CVT can only produce power
up to the maximum power curve. This curve is speed
dependent. Should the driver power request be higher
than the maximum power curve, the motor would have to
assist the engine in meeting the demand.
5. Charge-Sustaining Strategy
10
20
.
30
40
50
Vehicle Speed (MPH)
60
70
The charge-sustaining strategy implemented here is as
follows. At low power levels, the motor provides all
power to the vehicle. When the driver requested power
crosses a preset threshold, the ‘engine on power level’, the
engine is engaged and replaces the motor in powering the
vehicle. Should the power request rise above the
maximum power that the engine I CVT is able to deliver,
the motor is again called upon to deliver the difference in
power up to its capacity. When the battery state of charge
Figure 5: CVT Gear Ratio Curves for Minimum Fuel
Consumption
57
falls below a low limit, the vehicle attempts to charge the
battery at a preset power, the 'recharge level'. The
corresponding amount of power is added to the driver
power request and is satisfied by the engine, if possible.
motoring and regenerative functions. Negative values in
this trace represent both regenerative braking (shown as
positive in Figure 8), as well as additional charging of the
battery.
6. Drive Cycle Simulation Results and Discussion
The battery high and low state of charge limits were
set to 65% and 60% respectively. This was done to
ensure that there would be several charging and
discharging periods over a single FUDS cycle, which aid
in fuel economy comparisons (see Appendix). In practice,
a larger battery state of charge range would be used,
allowing the vehicle to be driven at low power levels for a
longer period of time without recharging the battery. A
wider range in state of charge limits also.means that the
vehicle has greater range at zero emissions (with the
engine off). Despite these facts, restricting the battery
state of charge to a narrow range does not inhibit us from
observing the benefits of hybridization as well as changes
in the control strategy set points.
This section presents results obtained through
simulation of the vehicle over a Federal Urban Drive
Cycle (FUDS) cycle. Figure 7 and Figure 8 show the
dynamic simulation response when the 'engine on power
level' is set to 15kW and the battery rate of recharge is set
to 30kW. The traces shown in Figure 7 are vehicle speed
(mph), vehicle speed error (&sec), driver accelerator
pedal (% of max), engine power requested (kW) and
motor power requested (kW). In Figure 8, the traces
shown are battery state of charge (%), brake line pressure
(psi), regenerative braking power (kW), CVT gear ratio
and battery terminal voltage (V).
Table 1 contains a summary of the normalized fuel
economies obtained through many such dynamic
simulations. The 'engine on' power levels were chosen to
avoid engine operation in its inefficient range. Three rates
of recharge were investigated.
0
203
400
6W
800
1wO
1200
0
2p0
4Qo
6p0
800
loo0
1200
The simulation without a normalized miles/gallon
rating was not able to maintain the battery state of charge.
Having an engine on power level of 20kW consumed so
much battery energy that a lOkW rate of recharge was
unable to sustain the charge over a FUDS cycle.
Table 1: FUDS Fuel Economy Comparisons
nme (s)
Level (kW)
Figure 7: FUDS Results 1
t
0
I
I
I
I
I
I
2W
440
6W
EM)
loo0
1200
J
Engine Only
11
11
11
15
15
15
20
I
20
20
I
I
I
I
N/A
10
15
30
10
15
30
10
I
15
30
I
I
I
Normalized
MPG
1.oo
1.69
1.71
1.74
1.73
1.68
1.81
N/A (SOC
didn't recover)
1.67
1.76
The observed normalized hybrid fuel economy was
relatively insensitive to the changes in engine on power
level and recharge level. This assumes that the recharge
level was matched appropriately with the engine on power
level to maintain the battery state of charge (not the case
for 20kW engine on level and 10 kW recharge). The
results imply that most of the benefits of hybridization
Time (s)
Figure 8: FUDS Results 2
Vehicle speed was controlled by the driver model to
within 2m/s. The commanded motor power trace shows
both positive and negative values, highlighting its
58
distance traveled by the vehicle and divide by the amount
of fuel consumed in traveling that distance. Hybrid
electric vehicles are more complicated, however, as the
possibility of energy storage in the battery is introduced.
The problem can be illustrated with a simple example.
Suppose we wish to evaluate the fuel economy of a
vehicle with a certain control strategy over a drive cycle
such as the FUDS, and that the initial battery state of
charge is 70%. Suppose that at the end of the FUDS, the
vehicle has consumed 0.30 gallons of fuel and has a final
battery state of charge of 68%. If we simply divide the
distance traveled by the fuel consumed, we will overstate
the fuel economy, as the depletion of the battery has not
been factored in.
occur at low engine on power levels. This means two
things:
I.
.
A major benefit of hybridization is regenerative
braking, which is the same for all of the hybrid cases
and non-existent for the engine only case.
2. The process of altering the power path from that of a
conventional vehicle to temporarily storing energy in
the battery is most beneficial at low power levels (less
than 11kW).
Recall that in the HEV presented here, all of the
vehicle’s power ultimately comes from the engine.
Furthermore, the HEV is an incremental change from the
conventional vehicle. There is therefore an inherent
limitation in the achievable fuel economy of the HEV; that
limit is the maximum fuel economy of the engine coupled
with the corresponding losses in the rest of the vehicle. In
light of this, it has been shown that the two major benefits
of post-transmission,parallel hybridization are the ability
to recapture energy through regenerative brakmg and the
ability to avoid low power, inefficient engine operation.
To overcome this problem, two identical drive cycles
were run in succession. Then, a window of time equal to
the length of a FUDS cycle was ’slid’along the time axis
until the battery state of charge at the start and end of the
sliding window cycle were equal. So long as the control
strategy keeps the state of charge between two boundaries,
eventually a point in the ‘double cycle’ will be reached
where the starting and ending battery states of charge are
equal. This is shown in Figure 9. Within the shifted
window, the vehicle has still traveled through a complete
FUDS cycle. We can therefore divide the distance
traveled within the window by the fuel consumed without
regard for the battery state of charge. By doing this, we
are forcing the vehicle to be in a charging mode at the
beginning of the shifted cycle and a discharging mode at
the end (or vice versa). Consequently, the vehicle is not
in exactly the same state at the start and end of the shifted
cycle, but it is similar enough to be used as an
approximation.
7. References
[ l ] Biscarri, Erbis L., Tamor, M.A. and Murtuza, Syed,
“Simulation of Hybrid Electric Vehicles with
Emphasis on Fuel Economy Estimation,”
International Congress and Exposition. SAEi
Technical Paper 981132.1998.
[2] Powell, B.K., Bailey, K.E., and Cikanek, S.R.,
“DynamicModeling and Control of Hybrid Electric
Vehicle Powertrain Systems”, IEEE Control Systems
Magazine, pp 17-33, October 1998.
Original
[3] Powell, B.K. and Pilutti, T.E., “A Range Extender
Hybrid Electric Vehicle Dynamic Model”,
Proceedings of the 331dIEEE Conference on Decision
and Control, Lake Buena Vista, FL,December 1994.
0
53
s
2i
[4] Sakaguchi, S., Kimura, E. and Yamamoto, K.,
“Development of an Engine-CVT Integrated Control
System.” SAE Technical Paper 1999-01-0754.
0
500
1000
1500
2000
Tme (s)
Figure 9: Shifted FUDS Time Window
8. Appendix - HEV Fuel Economy Calculation
In a conventional vehicle, calculation of the fuel
economy is straightforward. One simply takes the
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