08PFL-554
Plug-in Hybrid Electric Vehicle Control Strategy: Comparison
between EV and Charge-Depleting Options
Phillip B. Sharer, Aymeric Rousseau, Dominik Karbowski, Sylvain Pagerit
Argonne National Laboratory
Copyright © 2008 SAE International
ABSTRACT
The U.S. Department of Energy (DOE) has invested
considerable research and development (R&D) effort
into Plug-in Hybrid Electric Vehicle (PHEV) technology
because of the potential fuel displacement offered by the
technology. DOE’s PHEV R&D Plan [1], which is driven
by the desire to reduce dependence on foreign oil by
diversifying the fuel sources of automobiles, describes
the various activities required to achieve the goals. The
U.S. DOE will use Argonne’s Powertrain Systems
Analysis Toolkit (PSAT) to guide its analysis activities,
stating, “Argonne’s Powertrain Systems Analysis Toolkit
(PSAT) will be used to design and evaluate a series of
PHEVs with various 'primary electric' ranges,
considering all-electric and charge-depleting strategies.”
PSAT was used to simulate three possible chargedepleting (CD) PHEV control strategies for a power split
hybrid. Trip distance was factored into the CD strategies
before the cycle was started. The results are examined
in this paper to determine if any of the three strategies
could reduce the power split configuration’s fuel
consumption beyond what a simple all-electrical strategy
followed by a charge-sustaining (CS) strategy could
afford. The results show that the improvements for this
configuration are small and depend on the ratio of the
engine efficiency when operating in CS mode to the
engine efficiency when operating in CD mode.
INTRODUCTION
PSAT [2, 3] is designed to serve as a single software
tool that can be used to meet the requirements of
automotive engineering throughout the development
process, from modeling to control. Because of time and
cost constraints, designers cannot build and test each of
the many possible powertrain configurations for
advanced vehicles. PSAT, a forward-looking model,
offers the ability to quickly compare several powertrain
control strategies.
To satisfy the California Air Resources Board (CARB)
requirement for zero emission credit, an all electric range
(AER) PHEV must drive all-electrically over repetitions of
the Urban Dynamometer Driving Schedule (UDDS). The
constraint to drive all-electrically imposes certain size
limitations on the battery and the electric motor, which
also affect vehicle cost. To minimize the cost of the
electric powertrain in these hybrids, a CD control
strategy can be used that would turn the engine on
during high power demand. Besides lowering the power
requirements for the battery and electric machines, there
has been some interest in using CD strategies to also
reduce fuel consumption when the vehicle AER is
exceeded. If the control strategy expects that the AER
will be exceeded, the strategy can start planning from
the beginning of the trip to conserve battery energy for
later use near the end of the trip. Such forward-planning
control is expected to increase powertrain efficiency. For
clarity, the following question can be asked: Given a
PHEV with an AER of 16 km, what control strategy
would minimize the vehicle’s fuel consumption when the
vehicle is driven beyond its AER? (A trip distance of
16 km was chosen because a UDDS cycle is 7.5 mi and
10 mi [16 km] is the nearest multiple of 10 to a single trip
on the UDDS.) Of course, if the vehicle is driven for a
shorter distance than 16 km, the best strategy to
minimize fuel consumption would be an all-electric
strategy that would turn the engine on only when the
electrical system could not provide the power needed by
the vehicle to follow the drive cycle. To understand the
different control options for such a situation, a power
split hybrid was simulated by using PSAT. This power
split hybrid had a powertrain structurally equivalent to
that usesd in the Toyota Prius. The power split
powertrain is schematically shown in Figure 1.
Traction
Motor
ring
Generator
sun
Engine
carrier
Figure 1: Power Split Schematic
By using a set of automatic sizing routines developed to
size vehicle components with the PSAT model, this
power split hybrid was sized with the following
performance constraints.
•
•
•
•
Acceleration 0–60 mph < 9 s
Gradeability of 6% at 65 mph
Maximum speed > 100 mph
Ability to follow the UDDS in all-electrical mode
Four control strategies were simulated and compared on
the basis of energy consumption and fuel consumption
for this study:
1.
2.
3.
4.
Electric Vehicle/Charge-Sustaining (EV/CS)
Differential Engine Power
Full Engine Power
Optimal Engine Power
The term “EV mode,” as used in this paper, is a
misnomer, for the EV strategy was really a CD strategy
that was tuned to keep the engine off during the UDDS
cycle. Thus, the term “EV mode” implies not only certain
characteristics for the strategy, but it also implies certain
characteristics for the operation under which it had been
simulated. Thus, the definition of “EV mode” used in this
paper is a CD strategy that had been tuned to run the
vehicle all-electrically on a UDDS cycle.
The power equations used by the vehicle control
strategy during EV mode are as follows
Peng = {0
for Seng = Off
(1)



Pmc = min PLoad , Pmc  Seng = Off
max 


(2)
A brief description of each strategy appears in the next
section.
STRATEGY DESCRIPTIONS
EV/CS STRATEGY - The EV/CS control strategy was
included as the baseline strategy for comparison. Given
a UDDS trip distance of 32 km, the controller drove the
first 16 km by using energy from the battery, which
depleted the battery state-of-charge (SOC) from 90%
SOC to 30% SOC. The engine turned on only if the road
load exceeded the power capability of either the battery
or the motor, although the battery and motor had been
sized for the UDDS cycle. Therefore, the engine never
turned on during these simulations, because the
electrical system limits were never reached. The
remaining 16 km were then driven by using a
combination of the engine and battery while the SOC
was maintained. This is the CS operation of the strategy.
Figure 2 gives a representative SOC trajectory for the
EV/CS strategy.
+
S eng

 On


 On
=
Off


Off



for  Pload ≥ Pmc , Seng = Off 
max




for  Pload ≥ 0.9 Pmc , Seng = On 
max




for  Pload ≤ 0.9 Pmc , Seng = On 
max




for  Pload ≤ Pmc , S = Off 
max


(3)
If the SOC was high, the vehicle operated in EV mode,
as shown in Figure 2. When the power demand at the
road exceeded the maximum power that the motor could
deliver, the engine turned on, delivering the additional
power needed to follow the drive cycle. Note that when
the engine turned on, the term EV mode was no longer
applicable, and so the vehicle switched to CD mode.
When the SOC dropped low enough, the strategy
switched to CS mode (also shown in Figure 2). The
strategy during the CS mode was the basic split strategy
in PSAT. A brief overview of the power equations
describing its operation are provided below.
90
Pess dmd = K p ( SOC t arg et − SOC ) +
80
70
0

Peng = 
P
+
 load Pessdmd
SOC
EV
60
Ki
( SOC t arg et − SOC )
s
for Seng = Off
for Seng = On
(4)
(5)
50
The battery power
40
CS
30
20
0
2000
4000
6000 8000 10000 12000 14000
time (s)
Figure 2: Illustration of SOC Trajectory
for an EV Operation and CS Operation
Pessdmd maintained the SOC of the
battery during CS operation. The engine operated along
its optimal efficiency curve. Once the power of the
engine was known, the torque and speed were also
known, as shown in Figure 3.
Table 1 summarizes the different values for the engine
start threshold that were used as the trip distance
increased for the Differential Engine Power control
strategy.
Table 1: Differential Engine Power
Strategy Engine Start Threshold
Parameter Values
Nominal
Distance (km)
16
32
48
64
96
Figure 3: Transforming Engine Power Demand to
Engine Speed and Torque Demands
Once the engine torque and speed (as well as the
desired wheel torque and speed) were known, the
electric machine torques and speeds could also be
calculated. Not only did the engine follow this optimal
efficiency curve when operating in CS mode, but it also
followed this curve when the engine turned on during
high power transients while in EV mode.
DIFFERENTIAL ENGINE POWER STRATEGY - The
Differential Engine Power strategy was identical to the
EV/CS strategy, except that the power threshold at
which the engine turned on was set lower than the
maximum power of the electrical system. This change is
shown in equations 6 and 7.
0

Peng =  P − P
eng
 Load
threshold



min PLoad , Pmc 
max
Pmc = 


Peng

threshold

+
S eng

 On


 On
=
Off

Off

Peng
for Seng = Off
for Seng = On
for Seng = Off
(6)


for  PLoad ≥ Peng
, Seng = Off 
threshold




for  PLoad ≥ 0.9 Peng
, Seng = On 
threshold


for (PLoad ≤ 0.9 Pthreshold , Seng = On )


for  PLoad ≤ Peng
, S = Off 
threshold


FULL ENGINE POWER STRATEGY - The Full Engine
Power strategy calculated the engine power differently,
as shown in Equation 9. The main difference between
this strategy and the EV/CS strategy was that when the
engine turned on, it supplied the full road load demand
while the motor power went to zero. The goal is to force
the engine to operate at a higher power and,
consequently, at a higher efficiency. If the marginal gain
in efficiency is large enough, it will compensate for the
increased operating power of the engine. Equations for
engine power, motor power, and engine on state for this
strategy are shown below.
 0
Peng = 
 PLoad
for Seng = Off
for Seng = On



min PLoad , Pmc 
Pmc = 
max 


0

(7)
for Seng = On
Engine
Threshold (W)
38,000
11,500
7,500
N/A
N/A
+
S eng

 On


 On
=
Off


Off

for Seng = Off
(9)
(10)
for Seng = On


, Seng = Off 
for  PLoad ≥ Peng
threshold




for  PLoad ≥ 0.9 Peng , Seng = On 
threshold




for  PLoad ≤ 0.9 Peng , Seng = On 
threshold




for  PLoad ≤ Peng , Seng = Off 
threshold


(11)
(8)
was chosen so that the engine supplied enough
threshold
additional energy during the trip that the CD range was
extended beyond the 16-km EV range.
Table 2 shows the control strategy values of the engine
start threshold as trip distance was increased from 16
km to 96 km.
Table 2: Full Engine Power Strategy
Engine Start Threshold Parameter
Values
Nominal
Distance (km)
16
32
48
64
96
low load, thus moving the average operating point of the
engine to a higher average efficiency. This concept is
illustrated in Figure 4.
Engine
Threshold (W)
38,000
17,438
13,379
11,447
8,800
OPTIMAL ENGINE POWER STRATEGY - The last
strategy is the Optimal Engine strategy. This strategy
borrowed the idea of the previous strategy, Engine Full
Power strategy, of operating the engine at high power,
except that this strategy attempted to restrict the engine
operating region close to the peak efficiency of the
engine. The equations for this strategy are shown below.
 0
Peng = 
 Poptimal
for Seng = Off
for Seng = On



min PLoad , Pmc 
Pmc = 
max 

 PLoad − Poptimal

+
S eng

 On


 On
=
Off


Off

for Seng = Off
(12)
Figure 4: How a CD Strategy Lowers Fuel
Consumption when Compared to an EV/CS Strategy
Operation
(13)
The top part of Figure 4, labeled “EV/CS strategy,”
shows the characteristic operation of an EV/CS control
strategy over a trip that consists of three repetitions of a
conceptual cycle composed of two trapezoids of speed
versus time. The first cycle is completed entirely in EV
mode with the engine off, whereas the second and third
cycles are completed in CS mode with the engine
turning on and off. As a result, the engine has an
for Seng = On


for  PLoad ≥ Peng
, Seng = Off 
threshold




for  PLoad ≥ 0.9 Peng , Seng = On 
threshold




for  PLoad ≤ 0.9 Peng , Seng = On 
threshold




for  PLoad ≤ Peng , Seng = Off 
threshold


(14)
Table 3: Optimal Engine Power
Strategy Engine Start Threshold
Parameter Values
Nominal
Distance (km)
16
32
48
64
96
Engine
Threshold (W)
38,000
15,593
13,039
11,216
8,910
EXPLANATION FOR HOW A CD STRATEGY
LOWERS FUEL CONSUMPTION WHEN
COMPARED TO AN EV/CS STRATEGY
A PHEV benefits from a predetermined route because its
control strategy can schedule the blending of power from
the engine and the battery. By ”knowing” the route, the
PHEV control strategy can conserve battery energy
during high load and use it to propel the vehicle during
low
η engine
on
average efficiency of
and an average efficiency of
the low-speed trapezoid
high
on
η engine
the high-speed
trapezoid.
If E is the energy required at the wheels for the lowspeed trapezoid and 2 E is the energy required at the
wheels for the high-speed trapezoid, the total fuel energy
required from the engine during the EV/CS control
strategy is then
EV / CS
=0+0+
Eengine
fuel
E
η
low
engine
+
2E
η
high
engine
+
E
η
low
engine
+
2E
high
ηengine
(15)
The bottom part of Figure 4, labeled “CD strategy,”
shows one possible operation for a CD control strategy.
The same reasoning used for the EV/CS example can
be applied to this trip to compute the energy required
from the engine during the CD control strategy
operation, which is
CD
= 0+
Eengine
fuel
2E
η
high
engine
+0+
2E
η
high
engine
+0+
2E
high
η engine
(16)
Taking the ratio of equations 15 and 16 gives
EV / CS
Eengine
fuel
CD
engine
fuel
E
high
1  ηengine  2
=
+
low
 3
3  ηengine

(17)
If the average engine efficiency is the same for both the
high-speed and low-speed trapezoids, the ratio of fuel
energies is 1. If
high
low
ηengine
≥ ηengine
,
(18)
then the ratio of fuel energies is greater than 1, and the
CD strategy saves fuel over the EV/CS strategy. Many
details have been left out of this analysis. It has been
included simply to give a brief explanation of how a CD
strategy can outperform an EV/CS strategy by reducing
fuel consumption. The principle of saving battery energy
for later portions of the cycle allows the CD strategy to
increase the average engine efficiency, resulting in
overall lower fuel consumption. Again, this outcome
relies on the assumption that the speed versus time
cycle trace is known in advance for the control strategy
to schedule the engine use.
A further comment is that the driveline efficiency has
been left out of this analysis to simplify the equations.
The justification for this simplification is that in this study,
engine operation is manipulated either through
advancing or retarding the engine start event or by
changing the power operating point of the engine. For
this study, the behavior of the engine is the difference
between the EV/CS control strategy and the CD control
strategy. No attempt has been made in this study to
address optimizing the transmission and driveline of the
split configuration for this study. Thus, implicit in the
above analysis is the assumption that the transmission
and driveline efficiencies do not significantly change
between the EV/CS and CD strategies. Note that in this
study, EV modes interspersed with CS modes are
viewed as representing a CD mode.
SIMULATION SETUP
For this study, the three strategies described earlier in
this paper were simulated for fixed distances on trips
consisting of UDDS cycles. As explained, the PHEV was
designed to operate all electrically for a range of 16 km,
but the trip lengths simulated exceeded this distance.
Thus, to drive the longer trip distances in CD mode, the
strategies had to be changed. The threshold that
controls the engine start event was adjusted by using the
Matlab fzero routine until the PHEV met the longer trip
distance by supplementing battery energy with energy
from the engine. The objective function optimized was
the PSAT PHEV model with the engine start threshold
as the input variable. The simulation ran, depleting the
battery from 90% SOC to 30% SOC, at which time the
simulation would stop, because 30% SOC was assumed
to be the onset of CS mode. The distance predicted by
the simulation was then compared to the desired
distance to compute the error. The Matlab fzero function
ran until this error was sufficiently close to zero.
This method was convenient for this study but
impractical for real-world application. A prediction
algorithm would have to be used in a real control
strategy. Also, instead of using a single engine start
threshold, multiple engine-start thresholds could be used
(or even a continuous curve could be used). This study’s
main focus was on how a CD strategy compared with an
EV/CS strategy and how the CD fuel consumption
evolved as the range is extended. In Figure 5, example
SOC trajectories are drawn that are representative of the
typical output observed from the optimization routine. As
the engine start threshold varies, the curves slowly
converge to a shape that produces the desired trip
distance. This convergence to the desired trip distance is
also demonstrated in Figure 5.
Figure 5: Computing the Engine Start
Thresholds
Figure 6 graphs as a function of distance the Engine
Power On thresholds that were used by each of the
three control strategies. The Differential Engine Power
strategy could not reach the 64-km and 96-km trip
distances through manipulation of the engine start
threshold. This threshold was lowered until it equaled the
value this parameter has for the charge-sustaining
engine start threshold, at which point no further changes
in this parameter were made.
ECTotal =
E fuel (d ) + E ess
(20)
d
Taking the limit as the trip distance goes to infinity gives
lim ECTotal = lim
d →∞
E fuel (d ) + E ess
d →∞
d
As the electric consumption,
Figure 6: Full Engine Power Strategy Engine Start
Threshold Parameter Values
E fuel (d )
d
+ 0 (21)
E ess
, approaches 0, the
d
fuel consumption approaches the charge-sustaining
value, and the total energy consumption also
approaches the charge-sustaining value.
lim ECTotal = lim EC cs
d →∞
RESULTS
=
d →∞
(22)
Figure 7 shows the total energy consumption for each
control strategy and set of control parameters. Energy
consumption is fuel energy combined with battery
energy and is given by the equation below.
ECtotal =
m fuel × LHV + ∫ Voc × I ess dt
d
(19)
In Equation 19, the efficiency of the wall charger was not
taken into account.
From Figure 7, one can see that there was no
appreciable difference between the results of the EV/CS
strategy and the Differential Engine Power strategy. The
Differential Engine Power strategy used the engine
earlier than the EV/CS strategy; however, the strategy
ran the engine at lower power, which resulted in a lower
average efficiency for the engine. The results of the Full
Engine Power strategy had the greatest decrease in fuel
energy consumption. Figure 8 shows that this decrease
was as large as 9% for the 32-km trip distance. As trip
distance increased, the energy savings dropped to
around 2%, which is well within the error margin of the
simulation. The Optimal Engine Strategy performed
worse than the Full Engine Power strategy. This result
was unexpected, because the reduction in energy
consumption of a CD strategy over an EV/CS is
theorized to come from an increase in engine efficiency.
Figure 10 clearly shows that the Optimal Engine
Strategy had the highest engine efficiency, but this high
efficiency came at the cost of operating the engine at a
power much higher than that required by cycle. This
excess power unnecessarily charged the battery, which
brought down the overall efficiency of the vehicle.
Figure 7 also shows that as trip distance increases, the
energy consumption asymptotically approaches the
vehicle energy consumption in CS mode. Equation 20
expresses this relationship.
Figure 7: Vehicle Energy Consumption versus
Trip Distance for Each Control Strategy
In Figure 8, the percent increase in fuel energy
consumption, when compared to the EV/CS strategy, is
plotted versus the trip distance. Clearly, the Differential
Engine Power strategy and the Optimal Engine Power
strategy had no significant improvement over the EV/CS
strategy and, actually, for some trip distances, had
worse fuel energy consumption.
Figure 8: Percent Increase in Fuel
Consumption When Compared to the EV/CS
Strategy for Different Trip Distances
The fuel energy reduction for the three strategies shown
in Figure 8 can be attributed to four powertrain
characteristics and how these characteristics change as
trip distance is increased:
1.
2.
3.
4.
Engine Efficiency
Battery Percent Charging from the Engine
Transmission Efficiency
Regenerative Braking Percent Recovered
ENGINE EFFICIENCY - As expected, the Optimal
Engine Strategy had the highest average engine
efficiency, followed by the Full Engine Power Strategy,
as shown in Figure 9. Both of these strategies operated
the engine at high power and consequently high
efficiency. The Differential Engine Power strategy
actually showed a decrease in engine efficiency.
Figure 10: Percentage of Battery Charging That
Comes from the Engine as a Function of Trip
Distance for Each Control Strategy
Charging Fraction is defined by using Equation 23.
∫ − P u (− P )dt
ChF =
x100
(
)
P
u
P
dt
∫
ess
eng
Figure 9: Engine Efficiency as a Function of
Trip Distance for Each Control Strategy
The Differential Power Strategy decreased engine
efficiency, because the engine was operated at a lower
average load than it was for the other strategies. This
lower engine efficiency was identified as the primary
reason the Differential Engine Power Strategy consumed
more fuel than either the Full Engine Power Strategy or
the Optimal Engine Power Strategy.
BATTERY PERCENT CHARGING FROM THE ENGINE
- For a CD strategy, it is undesirable to have a significant
amount of battery charging from the engine. The path of
energy from the engine through the battery to the
wheels, which takes excess charging energy, is longer
and less efficient than the path of energy from the
engine directly to the wheels. Thus, a control strategy
that often charges the battery by using the engine is
expected to have greater fuel consumption. Figure 10
demonstrates the extent to which each strategy charges
the battery by using the engine by plotting the Charging
Fraction for each strategy as a function of trip distance.
ess
(23)
eng
Essentially, the Charging Fraction is defined as the ratio
of the battery energy during charging to the engine
energy at the engine’s output. Figure 10 shows that the
Optimal Engine Power strategy has the greatest
Charging Fractions of any of the CD strategies. To
operate the engine at high efficiency, the engine must be
operated at high power, which results in periods when
the engine must charge the battery. This behavior is
undesirable and can lower the overall efficiency of the
powertrain. Because of this, the Optimal Engine Power
strategy has higher engine efficiency than the Full
Engine Power strategy, but it does not have significantly
lower fuel consumption. In other words, higher engine
efficiency comes at the penalty of excess battery
charging.
TRANSMISSION EFFICIENCY - The next factor
affecting fuel consumption is transmission efficiency,
which is defined for this study as follows:
η tx =
∫ P u ( P )dt
u (P )dt + ∫ P u (P )dt
tx
∫ Peng
eng
tx
ess
(24)
ess
Equation 24 considers the transmission to consist of the
two electric machines and the planetary gear set.
Therefore, the engine and battery are both inputs to the
transmission.
percentage of recoverable energy that was reclaimed
through regenerative braking decreased. Figure 13
illustrates why the percentage of energy recovered
decreased. In Figure 13, the maximum battery charging
power is plotted for the Differential Engine Power
strategy and for the Full Engine Power strategy for both
32 km and 48 km. Figure 13 clearly shows that the
charging power magnitude increases at a faster rate for
the 32-km trip than for the 48-km trip. This trend occurs
because the SOC drops faster for the 32-km trip than for
the 48-km trip. High SOC limits the battery charging
power. Therefore, the faster discharge of the battery
allowed an increase in regenerative braking.
Figure 11: Transmission Efficiency
Figure 11 shows that the Optimal Engine Power strategy
had a lower transmission efficiency than the other CD
strategies. Running the engine at high power implies
running the engine at high speed, which also implies a
greater speed ratio of engine speed to transmission
output speed. A large speed ratio causes more power
circulation in split-type transmissions than a small speed
ratio. This is another disadvantage of the Optimal Engine
Power strategy’s overly aggressive attempts to maintain
high engine efficiency.
REGENERATIVE BRAKING PERCENT RECOVERED Regenerative braking is the final characteristic
considered in this paper that influences the fuel
consumption for the strategies that are shown in
Figure 12.
Figure 13: Battery Maximum Charging Power
EXPLORING THE ALMOST ONE-TO-ONE TRADE-OFF
BETWEEN BATTERY CONSUMPTION AND FUEL
ENERGY CONSUMPTION - Figure 14 shows battery
energy consumption versus engine fuel consumption.
Figure 14: Operating Points of Battery
Consumption versus Fuel Consumption and Their
Location with Respect to the Constant Energy
Boundary
Figure 12: Regenerative Braking Percent Recovered
Both the Full Engine Power strategy and the Optimal
Engine Power strategy exhibited similar trends in
regenerative braking. As trip distance increased, the
EUDDS is the energy consumption required to follow
the UDDS cycle, and if χEUDDS is the fraction of total
If
energy required from the engine, then the following
expression can be written that divides the energy
consumption into a fraction that comes from the engine
and a fraction that comes from the battery:
ECUDDS = χECUDDS + (1 − χ )ECUDDS
(25)
FC eng
EC ess =
(26)
η essη
− (LHV )
pwt
η engη eng
pwt
η essη
ess
FC eng
(28)
pwt
Because the average battery efficiency and energy path
efficiency from the battery to the wheels is relatively
constant, the term,
ECUDDS
η essη ess
, is also roughly constant.
pwt
If the engine efficiency and the energy path efficiency
from the engine to the wheels are roughly constant, then
the plot in Figure 14 is obtained where the trade-off
between battery energy consumption and engine fuel
consumption is a straight line (the dotted line in
Figure 14). On this line, the energy exchange rate
between battery energy and engine energy is constant
as the wheel load fraction χ is varied. Because the
simulated points all lie close to this line, the results of the
simulation indicate that there is little benefit in terms of
fuel consumption to operating in CD mode over
operating EV/CS mode for this configuration and choice
of engine.
Ultimately, CD mode has lower fuel consumption than
EV/CS mode because the control strategy operating in
CD mode can increase the overall energy path efficiency
from the engine to the wheels. The CD control strategy
is able to reduce fuel consumption because it conserves
battery energy at the beginning of the trip and uses this
energy throughout the whole trip to improve the
efficiency of the engine, while the EV/CS strategy uses
all of its battery energy at the beginning of the trip.
Because the energy consumption at the wheels is the
same whether the vehicle is in CS mode or CD mode,
ev / cs
cd
ECUDDS
= ECUDDS
η η
cs
pwt
EC
Expressing the battery energy consumption in terms of
engine energy consumption gives
ess
cd
cd
cd
η ess
pwtη ess Eess + η pwt ( d )η eng ( d ) Eeng
(30)
d
Removing like terms from each side gives
cs
eng
cs
Eeng
(27)
η essη ess
pwt
EC ess =
=
d
=η
cd
pwt
(d )η
cd
eng
(d )
cd
Eeng
d
(31)
This gives
(1 − χ )ECUDDS
ECUDDS
cs
cs
cs
η ess
pwtη ess Eess + η pwtη eng Eeng
d
Reflecting these fractions to their respective component
inputs gives the following two equations:
1 χECUDDS
=
LHV η engη eng
pwt
Expressing the above equation in terms of the energy
that went in to the system from the engine and from
battery gives
(29)
CD
fuel
=
cs
η cspwtη eng
η
cd
pwt
(d )η
cd
eng
(d )
EC CS
fuel
(32)
CONCLUSION
This study has demonstrated that basic information on
trip distance, combined with a simple control scheme,
can slightly decrease the fuel consumption of a PHEV
when the vehicle is driven beyond its all-electric-capable
range. A CD control strategy has an advantage over an
EV/CS control strategy because a CD strategy has the
flexibility to ration a vehicle’s battery energy throughout
an entire trip, assuming that trip distance has been
predetermined for the strategy through either user input
or algorithmic prediction. However, this result relies on a
significant simplification that a trip consists of repetitions
of the same driving cycle. If the average speed and
acceleration at the beginning of a trip significantly differ
from their values at the end of a trip, a fixed power
threshold, as used in this study to trigger the engine on
event, would not be a judicious choice. Instead of a fixed
power threshold, a real-time optimization routine would
need to continuously update the engine start threshold.
Thus, these results demonstrate that a rudimentary CD
control strategy outperforms an EV/CS control strategy
when comparing fuel consumption and total energy use
when trip distance and drive cycle are known.
CD distance was extended in this study by
supplementing the energy of the battery with energy
from the engine. Energy was added from the engine by
increasing (1) the time the engine was on during the trip
by lowering the engine on power threshold and (2) the
power at which the engine operated. The first method
was implemented in this study by changing a single
control parameter: the engine on power threshold. The
second method was implemented by switching between
three control strategies: Engine Differential Power,
Engine Full Power, and Engine Optimal Power.
Of the three CD control strategies simulated for this
study, two of them gave improvements over the baseline
EV/CS control strategy. Both of these strategies, Engine
Optimal Power and Engine Full Power, operated the
engine at higher power than the third strategy, Engine
Differential Power. Also as a result of operating the
engine at high power, the first two strategies operated
the engine at higher efficiency than did the Engine
Differential Power Strategy. A subsequent result was
that these strategies consumed less fuel and less energy
than the Engine Differential Power strategy.
Future studies can examine the robustness of this result
by using a stochastic trip generated by a Markov
process, in which the total trip length is held constant,
but the average cycle speed and acceleration change
randomly. An adaptive controller can then be compared
to the three CD strategies, which were simulated in this
study, along with the baseline EV/CS strategy.
Determining trip distance before the driving cycle may
not, alone, be sufficient to allow the CD strategies to
have a significant benefit over the EV/CS strategies
when the driving style fluctuates. The basic EV/CS
strategy may, therefore, turn out to be the best
compromise when handling uncertainty in trip speed and
acceleration.
Simple heuristics, such as delaying engine starts to
higher road load demand and choosing an engine
operating power that maximizes engine efficiency, are
not sufficient for the split configuration to yield a
significant reduction in energy consumption over the
EV/CS strategy. Rather, more intelligent heuristic
algorithms are needed to realize a greater reduction in
fuel consumption, and even then this reduction is limited
by the improvement in engine efficiency that can be
obtained over a CS strategy.
REFERENCES
1. U.S. DOE Plug-in Hybrid Electric Vehicle R&D Plan,
http://www1.eere.energy.gov/vehiclesandfuels/pdfs/
program/phev_rd_plan_02-28-07.pdf
2. Argonne National Laboratory, PSAT (Powertrain
Systems Analysis Toolkit), http://www.transportation.
anl.gov/.
3. Rousseau, A.; Sharer, P.; and Besnier, F.,
“Feasibility of
Reusable Vehicle Modeling:
Application to Hybrid Vehicles,” SAE Paper 2004-011618, SAE World Congress, Detroit, March 2004.
CONTACT
Phillip Sharer
Research Engineer
Center for Transportation Research
Argonne National Laboratory
630-252-9739
[email protected]
VARIABLE DESCRIPTIONS
Pmc
Mechanical power output for the traction
motor
Pload
Power required by the vehicle to follow the
cycle
Pmc
Maximum power the motor can deliver
max
ACKNOWLEDGMENTS
This work was supported by DOE’s FreedomCAR and
Vehicle Technology Office under the direction of Lee
Slezak. The submitted manuscript has been created by
UChicago Argonne, LLC, Operator of Argonne National
Laboratory (“Argonne”). Argonne, a U.S. Department of
Energy Office of Science laboratory, is operated under
Contract
No.
DE-AC02-06CH11357.
The
U.S. Government retains for itself, and others acting on
its behalf, a paid-up nonexclusive, irrevocable worldwide
license in said article to reproduce, prepare derivative
works, distribute copies to the public, and perform
publicly and display publicly, by or on behalf of the
Government.
Peng
Power delivered by the engine
S eng
Engine-on current state
+
S eng
Engine-on next state
On
Engine is on and consuming fuel
Off
Engine is off
Pessdmd
Power demand by the control for the battery
Kp
Battery SOC control proportional constant
SOCtarget
Target State of Charge for the battery
SOC
Battery instantaneous State of Charge
Ki
Battery SOC control integral constant
1
s
Integration factor
Peng
on
Peng
off
Peng
threshold
Charge-sustaining strategy engine on power
threshold – for hysteresis
Charge-sustaining strategy engine off power
threshold – hysteresis
Engine power on threshold for Differential
Engine Power, Full Engine Power, and
Optimal Engine Power strategies
Poptimal
Engine power at which it has peak efficiency
η
Average engine efficiency for a low-power
portion of a generic drive cycle
low
eng
high
η eng
Average engine efficiency for a low-power
portion of a generic drive cycle
E
Unit of energy to drive low-speed portion of
generic drive cycle
ev / cs
Eengine
fuel
E
CD
engine
fuel
Fuel energy consumed when operating in
charge depleting mode
Total mass of fuel consumed on a repeating
UDDS cycle trip
LHV
Lower heating value of the fuel
Voc
Open circuit voltage of the battery
I ess
Current for the battery
d
Trip distance
ECtotal
Total energy consumption, electrical plus
fuel energy
E fuel (d )
Total fuel energy consumed on a repeating
UDDS cycle trip
Eess
Total battery energy used on a trip from
90% SOC -> 30% SOC
ECCS
Energy consumption (unit of energy per
distance)
during
charge-sustaining
operation
χ
η eng
Average efficiency of the pathway from the
engine to the wheels through the
transmission
FCeng
Fuel consumption for the engine
ECess
Energy consumption for the battery
η ess
Average efficiency of the battery during a
trip
η ess
pwt
Average efficiency of the pathway from the
battery to the wheels through the
transmission
EV / CS
ECUDDS
Energy consumption at the wheels of the
vehicle to drive a UDDS cycle when
operating with the EV/CS strategy
CD
ECUDDS
Energy consumption at the wheels of the
vehicle to drive a UDDS cycle when
operating with the EV/CS strategy
CS
Eeng
Energy delivered by the engine on a trip
when operating with the charge-sustaining
strategy
Fuel energy consumed when operating in
EV/CS mode
m fuel
ECUDDS
η eng
pwt
Energy consumption at the wheels of the
vehicle to drive a UDDS cycle
Fraction of energy at the vehicle’s wheels
delivered by the engine
Average energy efficiency of the engine
during a trip
η cd
pwt (d )
cd
(d )
η eng
Average efficiency of the pathway from the
engine to the wheels when operating in
charge-depleting mode as a function of trip
distance
Average efficiency of the engine when
operating in charge-depleting mode as a
function of trip distance
EC CD
fuel
Fuel consumption in units of energy when
operating in charge-depleting mode
EC CS
fuel
Fuel consumption in units of energy when
operating in charge-sustaining mode
ChF
Charging Fraction Percentage of total
engine power used to charge the battery
Pess
Battery power
Ptx
Transmission output power. Net power at
the ring of the planetary gear set.
η tx
Transmission efficiency
u (x )
0 if x is negative, 1 if x is positive
u (Ptx )
u (− Pess )
1 when transmission output power is greater
than 0
1 when battery power is negative (i.e., when
battery is charging)