2012 IEEE International Conference on Control Applications (CCA)
Part of 2012 IEEE Multi-Conference on Systems and Control
October 3-5, 2012. Dubrovnik, Croatia
A Series-Parallel Hybrid Electric Vehicle Control Strategy Including
Instantaneous Optimization of Equivalent Fuel Consumption
Branimir Škugor, Danijel Pavković, Member, IEEE and Joško Deur, Senior Member, IEEE

vicinity of its optimal fuel efficiency (which is closely related
to the operation near the maximum engine torque), while at the
same time keeping the battery SoC within the predefined
bounds. The RB controller is then extended with the ECMS
control approach, which determines the fuel consumption-wise
optimal engine operating point (i.e. the engine speed). The
resulting engine speed operating point is then smoothly
adjusted with respect to the battery SoC request, so that the
battery SoC drift is effectively avoided. The proposed RB and
ECMS-based control strategies are verified by means of
computer simulations for the NEDC, UDDS and HWFET
certification driving cycles.
Abstract — Control strategy for a series-parallel hybrid
electric vehicle powertain aimed at operating the engine in its
optimal fuel efficiency operating region is proposed in the paper.
An instantaneous optimization algorithm based on the equivalent
consumption minimization strategy (ECMS) is used in order to
improve the hybrid vehicle fuel efficiency, and it is combined
with a battery state-of-charge (SoC) controller to honor
predefined SoC bounds. The effectiveness of the proposed control
strategy is verified by means of computer simulations for three
characteristic certification driving cycles.
I. INTRODUCTION
Hybrid electric vehicle (HEV) powertrain is traditionally
controlled by a heuristic (rule-based) control strategy which
aims to keep the internal combustion engine (ICE) within an
optimal fuel efficiency operating region [1]. In order to
improve the fuel efficiency of parallel HEVs, an instantaneous
fuel consumption optimization strategy, based on the so-called
equivalent consumption minimization strategy (ECMS), can be
used instead [2, 3], or in combination with the rule-based
controller [4, 5]. In the ECMS approach, the battery power
flow is reflected to “additional” fuel consumption rate, and the
fuel consumption optimization is carried out over the whole
engine operating range. However, the results in [6] have shown
that the locally-optimal ECMS approaches cannot easily
account for the battery state-of-charge (SoC) sustainability (i.e.
SoC can be prone to drift). Therefore, the approach in [6]
proposes to penalize the battery-related equivalent
consumption in the so-called adaptive ECMS optimization cost
function, significantly increases the complexity of the control
strategy and it may still be sensitive to the quality/accuracy of
the penalty factor adaptation.
In order to avoid the above SoC sustainability issues, this
paper proposes to integrate a rule-based (RB) controller with
the ECMS approach in a novel manner incorporating explicit
SoC control, and to apply the resulting concept to a more recent
and more complex series-parallel HEV powertrain. In the
series-parallel hybrid powertrain, the engine operating point
can be chosen with a relatively high degree of freedom, due to
the implementation of the so-called electrical continuous
variable transmission (eCVT) concept [7]. In this approach the
core RB controller is aimed at operating the engine in the
II. PROCESS MODEL
This section outlines the series-parallel hybrid electric
powertrain including the kinematic model and the controloriented battery dynamics model.
A. Series-parallel transmission
The principal schematic of the common, one-mode seriesparallel hybrid electric vehicle powertrain [8, 9] is shown in
Fig. 1a. The hybrid vehicle powertrain comprises the internal
combustion engine as the primary power source and two
electric machines. The M/G1 electrical machine is typically
operated in the generator mode (thus being able to keep the
engine in the desired optimal operating point), while the M/G2
operates as a traction motor (during normal driving), or a
generator (during regenerative braking intervals) [9]. The
electrical power can also be supplied from the battery (e.g.
when the driver demand is increased), or it can be stored within
the battery during regenerative braking or low-power demand
intervals.
Fig. 1b shows the HEV transmission bond graph model,
which is convenient for mathematical model derivation and
power flow analysis [9]. The mechanical power flows are
illustrated in Fig. 1b by the bonds which determine the amount
of power () and its direction. The junction points 0 and 1
represent the speed and torque summation points, respectively,
the transformer elements (TF) denote the speed/torque
transformation (through a gearbox), and the modulated gyrator
(MGY) elements represent the mechanical-electrical power
transformation. The internal combustion engine and the battery
are modeled in Fig. 1b by the source effort bond element (SE).
The kinematic relationships between the engine, M/G1 and
M/G2 torques and speeds are given by the following sets of
equations (Fig. 1b, [9]):
This work has been supported by the Croatian Science Foundation
through the, grant No. 09/128, and logistically by the AVL Company
through the AVL-Cruise Academic Software License agreement.
B. Škugor (corresponding author), D. Pavković, and J. Deur are with the
University of Zagreb, Faculty of Mechanical Engineering and Naval
Architecture, Zagreb, Croatia. Corresponding author phone: +385-(0)16168325; fax: +385-(0)1-6168351. E-mails: branimir.skugor@fsb.hr;
danijel.pavkovic@fsb.hr; josko.deur@fsb.hr.
978-1-4673-4504-0/12/$31.00 ©2012 IEEE
 e  (h  1) mg1 ,
310
(1)
 mg1  (h  1)e  hmg 2 ,
(2)
cd  mg 2 / io ,
(3)
 cd  io ( mg 2  h(h  1) 1 e ) ,
(4)
v
where the torque (.) and speed (.) variables are defined in Fig.
1a, h is the (fixed) planetary gear ratio, and io is the final drive
ratio.
Fig. 2 shows the simplified block diagram representation of
power flows and corresponding efficiencies mg1, mg2, batt of
the M/G1 and M/G2 machines and the battery, respectively.
The reference power flow directions denote the case when the
M/G1 machine operates as a generator, the M/G2 machine
operates as a traction motor, and the battery is being discharged
(Fig. 1b).
Fig. 3 shows the efficiency maps of the engine and
electrical machines, along with the engine and electrical
machines maximum torque curves (denoted by bold lines). The
data are adopted from the AVL Cruise simulation software and
adapted for the particular implementation by using the data and
experimental results given in [7] and [10].
e, e
ICE
SE
r
io
cd, io cd
t1
-1
Diff.
c
mg1, mg1
M/G1
(b)
t1
mg2, mg2
M/G2
B. Battery model
Fig. 4a shows an equivalent battery circuit used to build the
control-oriented battery model. It includes a nonlinear opencircuit voltage vs. SoC dependence Uoc(SoC) taken from the
AVL Cruise data library (Fig. 4b). In this particular application,
the battery internal resistance R(SoC, i) [11] is only made
dependent on the battery operating mode (i.e. R = Ric for
charging, and R = Ridc for discharging).
The battery SoC rate depends on the battery current i and
the battery charge capacity Qmax:
dSoC
i (t )
,

dt
Qmax
Battery /
Ultracapacitor
(a)
t2
t2
s
kgy1
ubat
M/G1
..
MGY i
0 i
SE
Rmg1
bat
mg1
.. r1
1
R
img2
M/G2
MGY: kgy2
s= mg1
s= mg1
e
e
h+1
h..
TF
TF: h PG
1
mg2
0
r
r
1
r2
mg2
R Rmg2
i..o-1
TF
cd
cd
Fig. 1. Principal schematic of considered series-parallel hybrid powertrain (a),
and corresponding kinematic bond graph model (b).
Fig. 2. Block diagram illustration of vehicle power flow (battery discharging).
(5)
while the battery power is given as:
Pbatt  U oc ( SoC )i(t )  R ( SoC , i)i 2 (t ) .
(6)
By combining (5) and (6), the final control-oriented battery
model can be obtained [3]:
U oc2 ( SoC )  4 R ( SoC , i ) Pbatt  U oc
dSoC
.

dt
2Qmax R ( SoC , i )
(7)
The battery power Pbatt in (7) is calculated according to the
following electrical power balance equation (cf. Fig.3):
k
k
Pbatt   mg
2mg 2 mg 2   mg 1mg 1 mg1 ,
2
1
(8)
where the coefficients k1 and k2 are equal to -1 in the case of
electrical machine operating as a motor, while they equal +1 in
the case of generator operation.
The battery model in Fig. 4a can be used for calculation of
the battery charging/discharging efficiency needed in the
ECMS approach in Section III. For the case of battery
charging, the so-called “local” battery power efficiency (see
Fig. 3. Efficiency maps and maximum torque curves of ICE and electrical
machines M/G1 and M/G2.
311
e.g. [1]) can be used, because it effectively takes into account
the battery roundtrip (charging/discharging) power losses:
P (t ) U oc (t )  Ridc i(t )
c  d
,
(9)

Pc (t ) U oc (t )  Ric i(t )
where Pc(t) and Pd(t) are battery charging and discharging
power requirement, respectively. On the other hand, when
battery discharging is considered, a straightforward efficiency
relationship may be used:
 d  (1  i 2 (t ) Ridc / Pbatt ) 1 ,
Fig. 4. Quasi steady-state battery model (a), and open-circuit battery voltage vs.
state-of-charge dependence (b).
(10)
because in that case the round-trip losses do not exist.
C. Driver model
A driver model corresponding to a ”virtual” proportionalintegral (PI) vehicle speed controller [12] is shown in Fig. 5. It
is implemented herein for the generation of the driveline torque
command cdR based on the predefined (desired) vehicle speed
vdc profile over a certification driving cycle and for the assumed
zero road grade case. The driver torque limit, which
corresponds to the transmission torque limit, is used within the
driver model saturation algorithm. The aerodynamic and
rolling resistance effects may be treated as slowly-varying
disturbances when designing the driver “controller”.
III. CONTROL SYSTEM
Fig. 5. Driver as a part of vehicle model.
This section presents the HEV powertrain control system
structure, which includes (i) the core rule-based engine
controller that provides the basic reference (target) values for
M/G1 electrical machine and engine control, and (ii) a
superimposed controller based on the equivalent consumption
minimization strategy (ECMS).
A. Basic structure
The series-parallel hybrid powertrain combines
two torque development paths, first through the
engine and second through the M/G2 machine, (Fig.
1b, Eqs. (1) and (4)), while at the same time allowing
for the independent control of the engine speed via
the M/G1 machine. Thus, it is possible to keep the
engine in the vicinity of the optimal operating region
(characterized by optimal fuel consumption), which is
located around the engine maximum output torque
curve (see Fig. 3a, [4, 7, 13]). This type of "enginecentric" control is typically realized through
utilization of the so-called rule-based (RB) controller,
wherein the engine operating point is determined
based on the driver demand and the battery power
demand [7].
The block diagram of a RB controller, inspired by
the Toyota Prius power flow analysis from [7] is
shown in Fig. 6. The controller utilizes the driver
power demand Pd = τcdR ωmg2/io and the battery power
demand (-PbattR) commanded by the SoC controller in
order to determine the engine power demand Pe*. It is
further used to obtain the engine torque demand eR0
and the engine speed reference ωeR0 (needed for the
low level engine control strategy) based on the requirement that
the engine operates on the nearly optimal maximum engine
torque output curve Pe* =eemax(e), where the emax(e) curve
is approximated by a third-order polynomial.
The RB control strategy in Fig. 6 also comprises a typical
engine start/stop logic (cf. [7]) which turns the engine off at
low power demands (Pe* < Poff), thus avoiding low power
Fig. 6. Rule-based (RB) control algorithm.
312
engine operation which corresponds to lower engine
efficiencies (especially at low engine speed values, see Fig. 3a).
The engine is again restarted only when the engine power
demand exceeds the predefined threshold Pon (either due to
increased driver demand Pd or due to SoC controller requesting
battery charging).
Due to the torque limits of the M/G1 and M/G2 electrical
machines (especially at high speeds, see Figs. 3b and 3c), the
engine torque command eR0 needs to satisfy the following
expressions derived from (1) and (4):
 e  (h  1) mg1max ( mg1 )
(11)
 e  (h  1)(hio ) 1 cd  (h  1)h 1 mg 2 max ( mg 2 )
(12)
ICE constraints, case
240
160
eRl
40
0
0
1000
2000
e
mg1R
KR
5000
rate ( m eq ) to be optimized:
m eq  m fuel  m batt ,
(13)
Instead of using the constant (average) battery equivalent
fuel rate over the whole battery operating range (as proposed in
[3]), the battery equivalent fuel rate is made dependent on the
engine operating point in the following manner:
 Aek Pe  Aek batt Pbatt , for Pbatt  0
m eq  
1
 Aek Pe  Aek batt
Pbatt , for Pbatt  0
(14)
where Aek [g/J] is the instantaneous engine specific fuel
consumption (see Fig. 9 and cf. Fig. 3a), and Aek is the
average engine fuel consumption over the engine operating
range on the maximum output torque curve. The significance
of the above equation is that during battery charging, for which
the engine power is consumed, a negative equivalent fuel
consumption of the battery is obtained directly from the
instantaneous engine specific fuel consumption. On the other
hand, when the battery is being discharged, the discharged
energy cannot be directly related to the current engine specific
fuel consumption, but rather to a moving average of the past
consumption. This fact is reflected in (14) in an approximated
manner by using the average engine specific fuel consumption
Aek .
The goal of the ECMS is to find the optimum engine
operating point in terms of minimizing the cost function (13),
which relates to finding the optimum feasible engine speed e
mg1max
emax
Km
T s +1
mg1
1
+
Iemg1s
Torque lag
e
eR
mg1L
-
4000
defined ( m batt ) and added to the actual engine fuel
consumption rate ( m fuel ) to obtain the overall equivalent fuel
mg
+
3000
[rpm]
Fig. 7. Illustration of engine constraints.
mg1max
-
= 4500 rpm
80
C. Equivalent consumption minimization strategy
In order to further minimize the HEV fuel consumption, the
RB control system is extended by a strictly realized equivalent
consumption minimization strategy (ECMS). In the ECMS
approach, the so-called battery equivalent fuel rate [2, 3] is
+
mg2
eRu
120
B. Low-level control
The M/G1 machine needs to be speed-controlled, because it
is intended to keep the engine in a desired (optimal) operating
point. The structure of the M/G1 speed control loop is shown in
Fig. 8a, wherein a proportional-integral (PI) speed controller is
used. The PI speed controller is tuned according to the
symmetrical optimum tuning procedure [12], thus facilitating a
fast and well-damped response of the M/G1 speed control loop.
The engine low-level control system structure is shown in
Fig. 8b. The engine torque is primarily controlled by means of
the feedforward torque reference eR (corresponding to gas
pedal command in conventional vehicles), which is supplied
by the superimposed RB controller (see previous subsection).
The auxiliary, relatively slow (dynamically non-dominant)
proportional (P) feedback controller is included in order to
avoid drifting the engine speed away its target value under the
“boundary” conditions when the M/G1 machine torque is
saturated and cannot balance the engine torque (e.g. due to
dynamic/inertia effects or inaccuracies of torque limit curves).
If the engine speed drift tends to occur, the P controller simply
corrects (reduces) the engine torque reference eR.
KR
TR s
= 400 Nm,
Maximum ICE torque
Upper limit
Lower limit
200
In the case when the engine torque feedforward reference eR0
violates the upper limit (11) or lower limit (12), the engine
speed command ωeR0 is reset to the nearest boundary value
(ωeRl or ωeRu, Fig. 7) at which the engine torque demand
satisfies the conditions (11) and (12).
mg1R
cd
e
+
mg1
eR
+
Equivalent
inertia
a
b
Fig. 8. MG1 speed control loop (a), ICE speed control loop (b).
313
Kc
-
eR
+
1
e
Te s + 1 +
Torque lag
eL
-
1
IeICE s
Equivalent
inertia
e
the RB controller augments the driver power demand Pd
without consideration for the engine fuel efficiency, the ECMS
should be used to indirectly moderate the SoC controller power
request PbattR (see Section III.A). Due to the fact that the engine
power request P*e is effectively determined by the requirement
of engine operation at or near the maximum torque curve, the
overall control strategy should moderate the RB controller
output (i.e. the engine speed reference ωeR), while taking into
account the value of the battery SoC control error eSoC (Fig. 6).
For that purpose, a simple SoC control error weighting
approach is proposed herein:
 eRmod  ( eR  eopt )W (eSoC )  eopt ,
(17)
where eRmod is the modified engine speed reference, and
W(eSoC) is the SoC error weighting function defined as follows:
W (eSoC )  tanhbeSoC  tanh(eSoC )
Fig. 9. Engine specific fuel consumption plot Aek.
= 200 Nm
eopt [x
1000 rev/min]
5
4
3
2
1
0
0
1000 rev/min]
cd
eR [x
= 100 Nm
eopt -
cd
cd
= 300 Nm
cd
= 400 Nm
Fig. 11 shows the comparative plots of the SoC error
weighting functions for different values of the arbitrary
shaping factor b. In the vicinity of the target SoC value (eSoC
≈ 0) the weighting function is close to zero, thus giving
emphasis on the fuel-optimal ECMS (see (17)). On the other
hand, for excessive SoC errors the weighting function tends
to unit value (W(eSoC) = 1) one, thus favoring the SoC
controller action. The larger the shaping factor b, the more
emphasized is the SoC error weighting.
2
1
0
-1
-2 0 30 60 90 120 150
30 60 90 120 150 180
180
v
[km/h]
vv [km/h]
v
a
b
Fig. 10. ECMS optimal speeds e with given torque demands vs. vehicle
velocity (a), difference between RB and ECMS optimal speeds with given
torque demands vs. vehicle velocity (b).
IV. SIMULATION RESULTS
This section presents the results of the proposed
RB+ECMS control strategy simulation studies for
characteristic certification driving cycles. For the purpose of
examination of various types of HEV control strategies, where
each strategy will generally end up with different final SoC
value, a simple equivalent consumption-based criterion is
proposed in order to account for the discrepancy in the final
SoC value.
(cf. Fig. 7) on the target maximum engine torque curve, i.e.:
eopt  min(m eq (e , e )) ,
(15)
subject to
 eRl   e   eRu , and  e   emax (e ) .
(18)
(16)
A. Compensation of final SoC value variations
Effectiveness of the above concept is illustrated by the
results of off-line searching for the optimal engine speed eopt
according (14)-(16) for a wide range of vehicle speeds. The
optimization results, shown in Fig. 10a, point out that the
engine speed may be kept at approximately constant low values
at low vehicle velocities (and low torque demands), while it
grows with the vehicle velocity, otherwise. More importantly,
Fig 10b shows the difference of engine speed references
provided by the ECMS and the RB controller for the case when
the SoC controller is inactive (the battery SoC is assumed to be
within the SoC controller deadzone). The presented results
indicate that the fuel-optimal ECMS approach results in
notably different engine speed references compared to those
obtained by the RB controller, thus pointing to a good potential
for further RB controller improvement via ECMS.
The final SoC discrepancy (SoC) from the target value
(SoCR = 50%) is transformed to the corrected fuel consumption
mf using a static map obtained by global control-variable
optimization method [15] for the same vehicle model and
driving cycle and various target values of the final SoC. The
corrected fuel consumption mf is then added to the actual
consumption mf in order to calculate the equivalent fuel
consumption mc,eq, thus facilitating unified comparison of
different variants of the control strategy. The fuel consumption
correction map obtained by the aforementioned optimization
approach for the NEDC cycle is shown in Fig. 12.
B. Results
The proposed, basic RB control strategy and the combined
RB-ECMS strategy have been verified by means of simulations
for the case of New European Driving Cycle (NEDC), Urban
Dynamometer Driving Schedule (UDDS), and Highway Fuel
Economy Test (HWFET) certification cycles. In all simulations
D. Incorporation of ECMS into RB strategy
The above ECMS intervention is integrated within the RB
controller in Fig. 6, in order to reduce the vehicle fuel
consumption. Since the low-level battery SoC controller within
314
place the engine operating points onto the engine maximum
torque curve. The responses in Fig. 14b show that both
strategies gradually discharge the battery over the initial portion
of the driving cycle (t < 500 s) corresponding to urban driving.
As the driving progresses (t > 500 s), the RB strategy puts the
emphasis on recharging the battery by means of engine power
(the engine is sporadically turned on), thus resulting in higher
RB fuel consumption compared to RB-ECMS that tries to
reach a good trade-off between consumption minimization and
SoC control. Finally, during highway driving conditions (t >
800 s), the RB and RB-ECMS strategies turn the engine on/off
in a similar manner, but the speed/torque operating points may
differ (see Fig. 14 and cf. Fig. 10b) since the ECMS component
tends to find the locally-optimal engine operating point.
Thus obtained fuel consumption and SoC data are then
compared based on the equivalent consumption assessment
criterion explained in the previous subsection. The main
simulation results for the different driving cycles are
summarized in Tables I – III. The results show that for the case
of NEDC driving cycle the equivalent fuel consumption of the
RB-ECMS approach is about 3% lower compared to the RB
strategy. The comparative summary results for other driving
cycles show that the similar benefit of the ECMS utilization is
obtained in the case of HWFET cycle (2.9% fuel consumption
reduction), while it is somewhat lower for the UDDS cycle
(1.8% fuel consumption reduction).
mf [%]
Fig. 11. SoC control error weighting function.
Fig. 12. Equivalent fuel consumption vs. final SoC discrepancy calculation.
TABLE 1. Main simulation results for New European Driving Cycle (NEDC).
NEDC
RB
RB-ECMS
mf [g]
268.6
281.4
SoC [%]
47.6
51.9
mc,eq [g]
268.6
260.5
TABLE 2. Main simulation results for Highway Fuel Economy Test (HWFET).
HWFET
RB
RB-ECMS
Fig. 13. Vehicle speed profiles for different certification driving cycles.
mf [g]
474.1
543.0
SoC [%]
45.4
64.5
mc,eq [g]
474.1
460.4
TABLE 3. Main simulation results for Urban Dynamometer Driving Schedule
(UDDS).
UDDS
RB
RB-ECMS
the battery SoC reference (target) value is kept at 50%, while
the SoC controller deadzone width SoC is set to 10%.
Fig. 13 shows the vehicle speed reference profiles for the
NEDC, UDDS and HWFET driving cycles, based on which
the driveline torque command is calculated by the driver
model (see Subsection II.C). The NEDC cycle comprises a
relatively long interval of urban-like driving (frequent vehicle
starting and stopping), which is followed by a highway-like
driving (vehicle speed vv reaching 120 km/h) and final rapid
deceleration. The UDDS cycle is characterized by even more
frequent starting and stopping intervals with less emphasis on
high-speed driving compared to NEDC. The HWFET cycle,
on the other hand, is characterized by driving at relatively high
and approximately constant speed (i.e. vehicle speed is mostly
kept between 60 and 90 km/h).
Simulation results for the case of NEDC driving cycle are
shown in Fig. 14. The engine operating point plot in Fig. 14a
shows that both the RB controller and the RB-ECMS tend to
mf [g]
267.1
290.6
SoC [%]
44.5
51.0
mc,eq [g]
267.1
262.2
V. CONCLUSIONS
The paper has proposed a rule-based (RB) energy
management control strategy for the common series-parallel
HEV, which is aimed at operating the internal combustion
engine close to optimal efficiency region. In order to further
improve the fuel efficiency an exact equivalent consumption
minimization strategy (ECMS) has been incorporated into the
RB control system, where arbitration between the ECMS
instantaneous optimization and SoC feedback control is
realized by means of a smooth weighting function.
The proposed RB and RB-ECMS control strategies have
been validated by computer simulation for three characteristic
certification driving cycles (NEDC, UDDS and HWFET). The
315
[4]
e
[Nm]
[5]
[6]
[7]
e
[rad/s]
[8]
[9]
[Nm]
[10]
e
[11]
SoC [%]
[12]
[13]
mf [g]
[14]
[15]
[16]
Fig. 14. Simulation results for NEDC driving cycle: engine operating points
(a), and simulation traces (b).
presented simulation results have shown that RB-ECMS can
reduce the fuel consumption by up to 3% when compared to
the simpler RB strategy. The ECMS effectiveness has been
particularly emphasized in the case of NEDC driving cycle
characterized by moderate urban driving and short-duration
high-speed driving, whereas it has been somewhat less
effective for the more aggressive UDDS driving cycle.
It should be noted that the presented one-dimensional
instantaneous optimization (over the maximum engine torque
curve) can be readily modified for the two-dimensional
optimization case (simultaneous optimization of engine speed
and torque operating points over a wider engine map region),
in order to achieve further gains in fuel economy [16].
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