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sustainability
Article

Energy Management for Plug-In Hybrid Electric
Vehicle Based on Adaptive Simplified-ECMS
Yuping Zeng 1,2 , Yang Cai 1, *
1

2

*

ID

, Guiyue Kou 1 , Wei Gao 1 and Datong Qin 2

Jiangxi Province Key Laboratory of Precision Drive & Control, Nanchang Institute of Technology,
Nanchang 330099, China; zengyp198410@163.com (Y.Z.); kouguiyueng@sina.com (G.K.);
gaowei0761@126.com (W.G.)
State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China;
datongqin@163.com
Correspondence: yangcai@nit.edu.cn; Tel.: +86-0791-8212616

Received: 21 May 2018; Accepted: 12 June 2018; Published: 17 June 2018




Abstract: When searching for the optimal solution, Equivalent Consumption Minimum Strategy
(ECMS) has to calculate and compare the total equivalent fuel rate of huge candidates covered all
over the control domain for each time instant. Therefore, this strategy still has a heavy computation
burden problem; it is a challenge for ECMS to be implemented online for real-time control. To reduce
ECMS’s calculation load, this paper proposes an adaptive Simplified-ECMS-based strategy for a
parallel plug-in hybrid electric vehicle (PHEV). A convex piecewise function is applied to fit the total
equivalent fuel rate with respect to the motor torque, which is the control variable. Then, the ECMS
problem is simplified to calculate and compare only five candidates’ total equivalent fuel rate to
determine the optimal torque distribution. Particle swarm optimization (PSO) algorithm is applied to
optimize the equivalent factor, and the MAPs of this factor under different driving cycles, driving
distances and initial SOC are obtained. Based on this, the adaptive Simplified-ECMS-based strategy
is proposed. Simulations were performed, and the results show that the Simplified-ECMS-based
strategy can obviously shorten the calculation time compared to ECMS-based strategy, and the
adaptive Simplified-ECMS-based strategy can decrease fuel consumption of plug-in hybrid electric
vehicle by 16.43% under the testing driving cycle, compared to CD-CS-based strategy. A road test on
the prototype vehicle is conducted and the effectiveness of the Simplified-ECMS-based strategy is
validated by the test data.
Keywords: plug-in hybrid electric vehicle (PHEV); energy management strategy (EMS); equivalent
consumption minimization strategy (ECMS); particle swarm optimization algorithm (PSO)

1. Introduction
Plug-in hybrid electric vehicles (PHEVs) assume an essential role in decreasing fuel consumption,
pollutant emissions, and carbon footprint [1]. Indeed, the application effect of PHEVs is strongly
influenced by many optimization tasks, i.e., charging station’s locating optimization [2–4], charging
time optimization [4], the PHEV taxi system’s optimization [5], battery size optimization [6], and power
optimization during driving. This power optimization is actually the major part of the blended energy
management strategy (blend- energy management strategy (EMS)), which is a crucial technology
for PHEVs [7]. The main blend-EMSs encompass dynamic programming (DP)-based-EMS [8–11],
derivative-free algorithms (DFA)-based-EMS [12–15], quadratic programming (QP)-based-EMS [16],
pontryagin’s minimum principle (PMP)-based-EMS [17,18], equivalent consumption minimization
(ECMS)-based-EMS [19–21].

Sustainability 2018, 10, 2060; doi:10.3390/su10062060

www.mdpi.com/journal/sustainability

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DP-based-EMS is able to compute global optimal solutions for PHEVs. However, it is hard to apply
to real-time control for its high computational burden, As a result, DP-based-EMS is widely utilized in
offline analysis to benchmark alternative EMSs, inspire RB strategies design, and serve as training data
for machine learning algorithms, etc. [12,22]. DFA-based-EMS mainly concern metaheuristic algorithms
inspired in nature and DIRECT deterministic method [12], The main DFA-based-EMSs employed
by PHEVs are simulated annealing (SA)-based-EMS [13], genetic algorithm (GA)-based-EMS [16],
and particle swarm optimization (PSO)-based-EMS [14]. Above EMSs do not require derivative
calculations, but these EMSs solve optimization problems with large search space of likely solutions,
which causes a high computation load. The aforementioned EMSs have a heavy computation
burden problem, some studies explore simplifying technique, instantaneous optimization method
or local optimization method to improve computationally efficient, including QP-based-EMS [16],
PMP-based-EMS [18], and ECMS-based-EMS [21]. Hu et al. designed QP-based-EMS for a series
plug-in hybrid electric bus, and demonstrated its decreasing computational time and the feasibility of
real-time control [6]. Nevertheless, this EMS’s limitation lies in its strictly convex terms requirement,
which requires that both cost function and inequality constraints are expressed in convex form,
and equality constraints are affine [23]. So QP-based-EMS is not suit for PHEVs with complex
configuration. PMP-based-EMS has transformed the global optimization problem to an instantaneous
Hamiltonian optimization problem, which makes its real-time control possible. However, it is still a
challenge for optimizing the Hamiltonian real-time due to the massive computational load required [17].
ECMS-based-EMS was first introduced for a parallel single shaft hybrid powertrains with a constant
equivalent factor by Paganelli et al. [24]. ECMS is derived from the pontryagin’s minimum principle.
Making some assumptions, simplifications and equations derivation about PMP-based EMS, the local
optimization algorithm of ECMS is obtained. These simplifications really improve the algorithm of
ECMS’s computationally efficiency. However, ECMS online implementation requires further reduction
of the computational time, since candidates of the control variable cover all over the control domain,
calculating and comparing the total equivalent fuel of these huge candidates to determine the optimal
solution is still a challenge.
Through above analysis, we know that further simplification of optimization algorithm and further
reduction of the computational time are very necessary to apply blend-EMSs to PHEVs’ real-time control.
ECMS-based-EMS is more likely to be applied to PHEVs with complex configuration’s real-time control
than other blend-EMSs. Therefore, we select ECMS algorithm to further simplify it. Firstly, the models
of engine’s fuel rate and battery’s consumption rate are approximately fitted by the piecewise function.
Then, the total equivalent fuel rate can be expressed by a convex piecewise function. Finally, according
to the properties of convex functions, the ECMS problem is simplified to calculate and compare total
equivalent fuel rate of only five candidates to identify the optimal torque distribution, instead of calculating
and comparing the total equivalent fuel rate of huge candidates, who cover all over the control domain.
After gaining the Simplified-ECMS-based strategy, we introduce the particle swarm optimization (PSO)
genetic algorithm to optimize the Simplified-ECMS algorithm’s equivalent factor, instead of optimizing
this factor by trial and error method. The MAPs of this factor under different driving patterns, driving
distances and initial SOC are obtained through off-line optimization based on this genetic algorithm.
Finally, the adaptive Simplified-ECMS-based EMS is implemented based on the equivalent factor MAPs.
The original contribution of this paper is related to the following aspects. First, a Simplified-ECMSbased strategy is proposed to simplify ECMS problem and reduce calculation burden. Second,
the particle swarm optimization (PSO) genetic algorithm is introduced to optimize the equivalent
factor, rather than obtaining the factor by trial and error method. Finally, by integrating the two major
contributions mentioned above as well as other works, the adaptive Simplified-ECMS-based EMS is
proposed for the EMS of the PHEV.
The outline of this paper is as follows. The structure and parameters of a parallel continuously
variable transmission (CVT)-based PHEV powertrain are described in Section 2. The model of the
powertrain system is provided in Section 3. Simplified-ECMS-based strategy is proposed in Section 4.

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The adaptive Simplified-ECMS-based strategy is presented in Section 5. Road test is conducted in
Sustainability 2018, 10, x FOR PEER REVIEW
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Section 6 to validate the effectiveness of the Simplified-ECMS-based strategy. Finally, conclusions are
discussed
in6Section
7. the effectiveness of the Simplified-ECMS-based strategy. Finally, conclusions are
Section
to validate
discussed in Section 7.

2. Structure and Parameters of the Powertrain System
2. Structure and Parameters of the Powertrain System

This study focused on a single-shaft parallel CVT-based PHEV. Figure 1 shows the powertrain
This study
focused on
single-shaft
parallel CVT-based
PHEV.
1 shows
the powertrain
of this vehicle
that includes
anainternal
combustion
engine (ICE),
anFigure
integrated
starter
and generator
this vehicle
that
includes
an internal
combustionvariable
engine (ICE),
an integrated
starter
and
generator
motorof(ISG
motor),
battery,
clutch,
a continuously
transmission
(CVT)
and
final
drive (FD).
motor
(ISG
motor),
battery,
clutch,
a
continuously
variable
transmission
(CVT)
and
final
drive
(FD). and
The vehicle runs in different operating modes by controlling the state of the engine and motor
The vehicle runs in different operating modes by controlling the state of the engine and motor and
the separation and combination of the clutch. According to the state of engine, the working mode of
the separation and combination of the clutch. According to the state of engine, the working mode of
vehicle can be divided into two modes: engine on mode, and engine off mode. During the engine on
vehicle can be divided into two modes: engine on mode, and engine off mode. During the engine on
mode,mode,
the clutch
is closed,
the the
engine
provides
positive
of the
themotor
motor can
the clutch
is closed,
engine
provides
positivepower,
power,and
andthe
theoutput
output power
power of
be positive
(driving),
negative
(generating)
or
zero
(idle).
During
the
engine
off
mode,
the
clutch is
can be positive (driving), negative (generating) or zero (idle). During the engine off mode, the clutch
open,isonly
the
motor
runs,
and
this
mode
can
be
subdivided
into
motor
driving
mode
and
braking
open, only the motor runs, and this mode can be subdivided into motor driving mode and braking
mode.
The The
basicbasic
parameters
of of
the
PHEV
in Table
Table1.1.
mode.
parameters
the
PHEVare
areshown
shown in

ENGINE

CVT
ISG
CLUTCH MOTOR

FINAL
DRIVE

Figure 1. Parallel CVT-based PHEV powertrain system.

Figure 1. Parallel CVT-based PHEV powertrain system.
Table 1. Basic parameters of the PHEV.

Table 1. Basic parameters of the PHEV.
Components
Parameters
Value
Curb
weight
(kg)
Components
Parameters
Value1395
2)
Frontal
area
(m
Curb weight (kg)
1395 2.265
Basic parameters of the vehicle
Air
dragarea
coefficient
2.2650.301
Frontal
(m2 )
Basic parameters of the vehicle
Air
drag coefficient
0.3010.307
Wheel
radius (m)
Wheel radius (m)
0.307
Wheel
rolling
resistance
coefficient
0.0135
Wheel rolling resistance coefficient
0.0135
Peak power (kW)
90
Peak power (kW)
90
Engine
Engine
Maximum
torque
(Nm)
Maximum torque
(Nm)
155 155
Peakpower
power
(kW)
Peak
(kW)
30 30
ISG ISG
motor
motor
Maximum
torque
(Nm)
Maximum torque
(Nm)
113 113
Capacity
(Ah)
Capacity
(Ah)
30 30
Rated
voltage
(V)(V)
316 316
Rated
voltage
Battery
Battery
Initial SOC
0.95
Initial SOC
0.95
Minimum SOC
0.25
Minimum SOC
0.25
CVT
The range of speed ratio
0.422–2.432
CVT
The range of speed ratio
0.422–2.432
FD
Speed ratio
5.24
FD
Speed ratio
5.24

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3. Powertrain System Modeling
3.1. Vehicle Dynamic Model
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This study mainly focuses on the energy management strategy and the evaluation of the power,
3. Powertrain
System
Modeling under energy management strategy, so the vehicle dynamics
economy, and
emission
performance
model only3.1.
relates
to longitudinal dynamics of vehicle, without involving vehicle’s vertical dynamics
Vehicle Dynamic Model
and lateral dynamics. Assume that the vehicle speed is v and the road slope angle is α, then the
This study mainly focuses on the energy management strategy and the evaluation of the power,
wheel-sideeconomy,
power Pand
be expressed
as:under energy management strategy, so the vehicle dynamics
r can
emission
performance
model only relates to longitudinal dynamics of vehicle, without involving vehicle’s vertical dynamics
dv
and lateral dynamics. Assume that the vehicle speed is cv d A
and 2the road
Pr = (mg f r cos(α) + mg sin(α) +
v + m slope
) · r angle
· ωr is  , then the
wheel-side power Pr can be expressed as:
21.15
dt

(1)

A 2
dv
where m is the vehicle mass; cdPris (the
aircd resistance;
r is the
mgf r coefficient
cos( )  mg sin(of
) 
v  m )  r A
r is the windward area;
(1)
21.15
dt
radius of the tire; f r is the rolling resistance coefficient; g is the gravitational acceleration; ωr is wheel’s
where m is the vehicle mass; cd is the coefficient of air resistance; A is the windward area; r
angular velocity.
f r ispowertrain
is the radius
of the tire;
the rolling resistance
the gravitational
A simplified
structure
of the
systemcoefficient;
is shown ginisFigure
2, poweracceleration;
is provided by the
engine andthe
motor separately or jointly, and it is transferred through the CVT and final drive to
r is wheel’s angular velocity.
the axle shaft of
the wheels.
Assume
Ir is the
joint
inertiainof
differential
gears
andbywheels;
Iout is
A simplified
structure
of the that
powertrain
system
is shown
Figure
2, power is
provided
the
engine of
andfinal
the motor
or jointly,
andwheel;
it is transferred
through
CVT and
final drive
to
the joint inertia
driveseparately
and CVT’s
driven
Iin is the
joint the
inertia
of CVT’s
driving
wheel,
the axle shaft of the wheels. Assume that I r is the joint inertia of differential gears and wheels; I out
engine and motor; ωr , ωout and ωin are the angular
velocity of the drive shaft, output axle of CVT and
is the joint inertia of final drive and CVT’s driven wheel; I is the joint inertia of CVT’s driving
input axle of CVT; η0 is the efficiency of the final drive; ηcvt isin the efficiency of CVT, which is obtained
wheel, engine and motor; r , out and in are the angular velocity of the drive shaft, output axle
by looking up table by CVT’s output torque and gear ratio. The power transmitted by the drive shaft
of CVT and input axle of CVT;  0 is the efficiency of the final drive; cvt is the efficiency of CVT,
of the vehicle
is iswritten
which
obtainedas:
by looking up table by CVT’s output torque and gear ratio. The power transmitted

by the drive shaft of the vehicle is written as:

dωout
dωr
dout )η0 = Irdω
rr dt + Pr
dt
( Pout  I out out
)0 =I r r
 Pr

( Pout − Iout ωout

dt

Pin , Tin , , win
Treq  Te  Tm

dt

Pr , T r , , w r

Pout , Tout, , wout

I in

icvt

i0

I out

Engine
Motor
Driving wheel of CVT

(2)
(2)

Final drive
Driven wheel of CVT

Ir
Vehicle wheels
Differential gears

Figure 2. A simplified structure of the powertrain system.

Figure 2. A simplified structure of the powertrain system.
Then the CVT’s output power Pout can be written as:

dr
1 be written
Then the CVT’s output power Pout
can
as: dout
P = (I 
 P)
+I 
out

The

0

r

r

dt

r

out

out

dt

1
dωr
dωout
The CVT’s input power
as: Pr ) + Iout ωout
Pin can
Pout =
( Ibe
+
r ωwritten
r
η0
dt
dt
I out out dout
dr
1
1
Pin =
Pout =
(I r r
 Pr)
+
0cvt as: dt
cvt
dt
CVT’s input power Pin canbe
cvt written
The require power need to be distributed between engine and motor can be expressed as:
1
dωr
Iout ωout dωout
1
Pout =
( Ir ωr
+dPrin) +
Pin =
ηcvt
ηP0reqηcvt
ηcvt
dt
=Pe +Pm =Pin dt
I inin
dt

(3)

(3)
(4)

(5)

(4)

The require
need to be distributed between engine and motor can be expressed as:
where Ppower
e is the output power of engine; Pm is the output power of motor.
Preq = Pe + Pm = Pin + Iin ωin

dωin
dt

where Pe is the output power of engine; Pm is the output power of motor.

(5)

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The require torque need to be distributed between engine and motor can be expressed as:
Sustainability 2018, 10, x FOR PEER REVIEW

Treq = Te + Tm =

9550Preq
Nm

5 of 24

(6)

The require torque need to be distributed between engine and motor can be expressed as:

where Treq is the require torque, which is distributed between
9550 Preq engine and motor; Te is the output torque
Treq  Te  Tm 
(6)
N mthe speed of the motor.
of the engine; Tm is the output torque of the motor; Nm is
where T

is the require torque, which is distributed between engine and motor; Te is the output

req
3.2. Engine’s Fuel Rate
Model

torque of the engine; Tm is the output torque of the motor; N m is the speed of the motor.

The engine’s fuel consumption map is shown in Figure 3. It is a fuel consumption curve
3.2. Engine’s Fuel Rate Model
with the abscissa
giving the engine speed and the ordinate giving the engine torque. The specific
The engine’s
fuel consumption
map isin
shown
in Figure
fuel·consumption
curve
with the
fuel consumption
in Figure
3 is expressed
be with
unit3. It
g/is(akW
h).Then the
instantaneous
fuel
abscissa giving the engine speed and the ordinate giving the engine torque. The specific fuel
consumption,
which is also known as fuel rate with unit g/s, can be expressed as:
consumption in Figure 3 is expressed in be with unit g / (kW h) .Then the instantaneous fuel
consumption, which is also known
as fuelPrate
with unitTg/s,
can be expressed as:
.
e · be
e · Ne · be
=
mice =
10
 be6 Te3.44
 Ne  b×
3.6 ×Pe10
e 10
mice
=
3.6 106 3.44 1010

(7)
(7)

where Ne is the speed of the engine.

where N e is the speed of the engine.
160

Engine toruqe(Nm)

140
240

120
100

254
80

260
270
280

60

300

40
400

20

360

330

Max torque curve
Specific fuel consumption [g/kwh]
Best efficiency by speed

500
700

0

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

Engine speed(rpm)
Figure 3. The engine’s fuel consumption map with respect to its torque and speed.

Figure 3. The engine’s fuel consumption map with respect to its torque and speed.
According to the engine’s fuel consumption map, the relationships between the fuel rate mice
and the engine torque Te at the given speed N were fitted by a piecewise function which is made

.

According to the engine’s fuel consumption map, the relationships between the fuel rate mice and
up of two quadratic functions, and the dividing point of the piecewise function is the best efficiency
the engine point
torque
at fitting
the given
Ninwere
fitted
bycorresponding
a piecewisefitting
function
which
is made
, ethe
result speed
is shown
Figure
4. The
formula
is expressed
as up of two
ToptT
quadratic functions,
and
the
dividing
point
of
the
piecewise
function
is
the
best
efficiency
point Topt ,
follows:
the fitting result is shown in Figure 4. The corresponding
fitting formula is expressed as follows:
2
line e1:ce10  ce11Te  ce12Te

where

when Te min  Te  Topt




m = line e2:ce 20  ce 21Te  ce 22Te 2 2when Topt  Te  Te max

line ice
e1 : ce10 + ce11 Te + ce12 Te when Temin ≤ Te ≤ Topt

.
0,
whenT  0
mice =
line e2 : ce20 + ce21eTe + ce22 Te 2 when Topt ≤ Te ≤ Temax


when
Te = 0
ce1i and ce 2i (0,
) are constants.
i  0,1,2

(8)

(8)

Based on Equations (1–6), the Treq is a constant at a certain speed, the engine torque Te can be

where ce1i expressed
and ce2i (i
0,T 1,2)
as =
, thenconstants.
Equation (8) is expressed as follows:
Te =
Tm are
req
Based on Equations (1–6), the Treq is a constant at a certain speed, the engine torque Te can be
expressed as Te = Treq − Tm , then Equation (8) is expressed as follows:
.

mice



2

 line e1 : c10 + c11 Tm + c12 Tm when Treq − Topt ≤ Tm ≤ min( Treq − Temin , Tmax
=
line e2 : c20 + c21 Tm + c22 Tm 2 when max Treq − Temax , Tmin ) ≤ Tm ≤ Treq − Topt

 0, when T = T
m
req

(9)

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line e1:c10  c11Tm  c12Tm 2 when Treq  Topt  Tm  min(Treq  Te min ,Tmax )


mice = line e2:c20  c21Tm  c22Tm 2 when max(Treq  Te max , Tmin )  Tm  Treq  Topt
Sustainability 2018, 10, 2060

0,
whenTm  Treq



(9)

6 of 24

where
( i=
is isthe
 0,1,2
where cc1i1i, ,cc2i2i (i
0, 1,)2)are
areconstants;
constants;TeTminemin
theengine’s
engine’sminimum
minimumoutput
outputtorque;
torque; TTeemax
is the
the
max is
engine’s
maximum
output
torque;
T
and
T
are
the
minimum
and
maximum
output
torque
of
engine’s maximum output torque; Tmin
minimum and maximum output torque of
min and Tmax
max are
the motor,
motor, respectively.
respectively.
the
7

Fitted fuel rate under 1000rpm
Fitted fuel rate under 2000rpm
Fitted fuel rate under 3000rpm
Fitted fuel rate under 4000rpm
Fitted fuel rate under 5000rpm
The actual fuel rate tested
The best efficiency point at the
current speed

6

Fuel Rate (g/s)

5

4

3

2

1

0

0

20

40

60

80

100

120

140

160

Engine Torque (Nm)

Figure
Figure 4.
4. Fuel
Fuel rate
rate of
of engine.
engine.

3.3. Battery’s Consumption Rate Model
3.3. Battery’s Consumption Rate Model
The consumption rate of the battery can be expressed as:
The consumption rate of the battery can be expressed as:
Ib
d
. 
L  d SOC   SOC
(10)
I
dt
Q
L = − SOC = −SOC = −0 b
(10)
dt
Q0
where Q0 is the rated capacity of the battery, I b is the current of battery, which can be expressed
where Q0 is the rated capacity of the battery, Ib is the current of battery, which can be expressed as:
as:
p
2 − 4P R
Voc − V2 oc
V

Voc  4 Pb Rib i
Ib = oc
(11)
(11)
Ib =
2Ri
2 Ri
where Voc is the open circuit voltage of the battery; Ri is the internal resistance of the battery; according
where Voc is the open circuit voltage of the battery; Ri is the internal resistance of the battery;
to reference [25], the open circuit voltage and the internal resistance can be considered as constants
according
to reference
the internal resistance
can be in
considered
when the value
of SOC[25],
is inthe
the open
rangecircuit
of [0.2,voltage
1], andand
the temperature
(degree Celsius)
the rangeas
of
constants
when
the
value
of
SOC
is
in
the
range
of
[0.2,
1],
and
the
temperature
(degree
Celsius)
in
25 and 45. In this paper, we assume that the battery’s SOC and the temperature meet above conditions,
the
range
of 25circuit
and 45.
In this
paper,
we assume
that the
battery’s SOC
the temperature
meet
then,
the open
voltage
and
the internal
resistance
is considered
to beand
constants.
Pb is the output
above
then, can
the be
open
circuit by:
voltage and the internal resistance is considered to be
power conditions,
of battery, which
calculated
constants. Pb is the output power of battery, which can be calculated by:
1
Tm · Nm
Pb = Ub Ib = Pm 1+ Paux =Tm  N m
+ Paux
(12)
η
m Paux
Pb  U b I b  Pmm  Paux = 9550η
(12)
m
9550m
where Pm is the motor power; ηm is the motor efficiency, which is shown in Figure 5; Paux is the power
where
motor power;
Pm is theauxiliary
 m is the motor efficiency, which is shown in Figure 5; Paux is the
of the electrical
equipment.
power
of the electrical
auxiliary equipment.
Therefore,
the consumption
rate of the battery can be expressed as:
Therefore, the consumption rate of the battery
q can be expressed as:

Voc −
d
L = − SOC =
dt

2 − 4( Tm · Nm + P
Voc
aux ) Ri
9550ηm

2Ri Q0

(13)

Therefore, the consumption rate of the battery can be obtained by taking motor torque and motor
efficiency in every motor speed in to Equation (13). The result is shown in Figure 6.

T N
Voc  Voc2  4( Tm  Nm  Paux ) Ri
2
m m
9550
(13)
d
L   d SOC  Voc  Voc  4( 9550m  Paux ) Ri
(13)
m
2 Ri Q0
L   dt SOC 
dt
2 Ri Q0
Therefore,
the2060
consumption rate of the battery can be obtained by taking motor torque and motor
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2018, 10,
7 of 24
Therefore,
the
consumption
rate
of
the
battery
can
be
obtained
by
taking
motor
torque
and
motor
efficiency in every motor speed in to Equation (13). The result is shown in Figure 6.
efficiency in every motor speed in to Equation (13). The result is shown in Figure 6.

Motor
efficiency
Motor
efficiency

0.95
0.95
0.9
0.9
0.85
0.85
0.8
0.8
0.75
0.75
0.7
200
0.7
200 100
100

0
0

–100
–100 –200
Motor torque (Nm)
–200
Motor torque (Nm)

4000
4000

0
0

6000
6000

2000
2000
Motor speed (rpm)
Motor speed (rpm)

Figure 5. Efficiency of the ISG motor.
Figure 5. Efficiency of the ISG motor.
Figure 5. Efficiency of the ISG motor.
-3

x 10
2 x 10 -3
2

-d(soc)/dt
-d(soc)/dt

1.5
1.5
1
1

Consumption rate at 1000rpm
Consumption rate
rate at
at 2000rpm
1000rpm
Consumption
Consumption
rate
at
2000rpm
Consumption rate at 3000rpm
Consumption rate
rate at
at 4000rpm
3000rpm
Consumption
Consumption rate
rate at
at 5000rpm
4000rpm
Consumption
Consumption rate at 5000rpm

0.5
0.5
0
0

–0.5
–0.5
–1–150
–1–150

–100
–100

0
50
–50
0
50
(Nm)
–50 Motor torque

100
100

150
150

Motor torque (Nm)

Figure 6. The consumption rate of the battery.
Figure 6.
6. The
The consumption
consumption rate
rate of
of the
the battery.
battery.
Figure

As shown in Figure 6, the consumption rate of the battery can be fitted by a piecewise function
As shown
in of
Figure
6, the consumption
rate
of
the battery
can
be fitted
by a piecewise
function
which
made up
two quadratic
functions.rate
The of
dividing
pointcan
of the
piecewise
the zero
Asisshown
in Figure
6, the consumption
the battery
be fitted
by a function
piecewiseisfunction
which torque
is madepoint,
up ofand
twothe
quadratic
functions.
Thein
dividing
point
of the piecewise
function
is the zero
motor
fitted result
is shown
Figure 7,
its corresponding
analytic
function
can
which is made up of two quadratic functions. The dividing point of the piecewise function is the zero
motor
torque
point,
and
the
fitted
result
is
shown
in
Figure
7,
its
corresponding
analytic
function
can
be expressed as:
motor torque point, and the fitted result is shown in Figure 7, its corresponding analytic function can
be expressed as:
be expressed as:
(
2
line m1 : Cb10 + Cb11 Tm + Cb12 Tm
when Tm ≤ 0
L=
(14)
2
line m2 : Cb20 + Cb21 Tm + Cb22 Tm
when Tm ≥ 0

where Cb1i and Cb2i (i = 0, 1, 2) are constants.

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2

line m1: Cb10  Cb11Tm +Cb12Tm
L
2

line m2: Cb 20  Cb 21Tm +Cb 22Tm

when Tm  0

(14)

when Tm  0

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where Cb1i and Cb 2i ( i  0,1, 2 ) are constants.
x 10

2

Fitted consumption rate at 1000rpm
Fitted consumption rate at 2000rpm
Fitted consumption rate at 3000rpm
Fitted consumption rate at 4000rpm
Fitted consumption rate at 5000rpm
The actual consumption rate

1.5

1

-d(soc)/dt

-3

0.5

0

–0.5
––1150

–100

–50

0

50

100

150

Motor torque/Nm

Figure 7. The fitted consumption rate of the battery.
Figure 7. The fitted consumption rate of the battery.

4. Simplified-ECMS-Based Strategy
4. Simplified-ECMS-Based Strategy
In the plug-in hybrid electric vehicle, the fuel energy from the ICE and the electrical energy from
In the plug-in hybrid electric vehicle, the fuel energy from the ICE and the electrical energy from
the battery are used. To make these two types of energy consumption comparable, the equivalent
the battery are used. To make these two types of energy consumption comparable, the equivalent fuel
fuel consumption is derived from the electrical energy consumption of the battery. Then, the concept
consumption is derived from the electrical energy consumption of the battery. Then, the concept of the
of the ECMS is achieving the goal of minimizing the total of engine fuel consumption and the
ECMS is achieving the goal of minimizing the total of engine fuel consumption and the equivalent fuel
equivalent fuel consumption for each time step.
consumption for each time step.
In the plug-in hybrid system, the control variable is the ISG motor’s torque Tm (t) . The state
In the plug-in hybrid system, the control variable is the ISG motor’s torque Tm (t). The state
variable is the battery’s SOC. Based on the principle of ECMS, the mathematical problem of
variable is the battery’s SOC. Based on the principle of ECMS, the mathematical problem of minimizing
minimizing the total equivalent fuel rate is formulated as follows:
the total equivalent fuel rate is formulated as follows:
m )  min(mice  mbat )
 J  min(

. eq
.
.
 min(m
J
=
) = min(mice + mbat )

eq
T
(t)

T

req
e (t)  Tm (t)




Treq(t) = Te (t) + Tm (t)


SOCf  SOCobj
 SOC
 f = SOCobj
Temin (t)  Te (t)  Temax (t)
 Temin
≤ Te (t) ≤ Temax (t)

T (t)(t)

 T (t)  T (t)


 mmin
T
(
t
)
≤ Tmm (t) ≤mmaxTmmax (t)

mmin

 SOCmin  SOC  SOCmax

SOC
min ≤ SOC ≤ SOCmax

(15)
(15)

mbat is the equivalent fuel
where .meq is the total equivalent fuel rate;. mice is the engine’s fuel rate;
.
where meq is the total equivalent fuel rate; mice is the engine’s fuel rate; mbat is the equivalent fuel rate
rate of battery; SOCf is the SOC value at the driving end; SOCobj is the target SOC value at the
of battery; SOCf is the SOC value at the driving end; SOCobj is the target SOC value at the driving end;
SOCmin
driving
and
is the
upper
and of
lower
limitsrespectively.
of the SOC, respectively.
max is
min and
SOCmax end;
and SOC
the SOC
upper
lower
limits
the SOC,

 , then,
Suppose that
thatthe
theequivalent
equivalent
factor
the consumption
ratebattery
of thecan
battery
can be
factor
is λ,isthen,
the consumption
rate of the
be converted
converted
to the equivalent
rate by
of battery by
to the equivalent
fuel rate offuel
battery
( line m1: C  C T +C T 2 when T  0

b10
b11 m
b12 m
m
line
T 2 when
Tm ≤ 0
mbat =  L=
 m1 : λCb10 + λCb11 Tm + λC
2 b12 m
mbat = λ · L =
line m2: Cb 20  Cb 21Tm +Cb 22Tm when
2 Tm  0
.

line m2 : λCb20 + λCb21 Tm + λCb22 Tm

when Tm ≥ 0

Based on Equations (9) and (16), the total equivalent fuel rate is formulated as follows:
Based Ton Equations
(9) and (16), the total equivalent fuel rate is formulated as follows:
T <0
(1) If req opt , then

(16)
(16)

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(1) If Treq − Topt <, then

.

meq


line e2 + line m1 : c20 + λCb10 + (c21 + λCb11 ) Tm + (c22 + +λCb12 ) Tm 2 when max Treq − Temax , Tmin ) ≤ Tm < Treq − Topt



2


 line e1 + line m1 : c10 + λCb10 + (c11 + λCb11 ) Tm + (c12 + λCb12 ) Tm when Treq − Topt ≤ Tm < 0

2 when 0 ≤ T ≤ min( T
line
e1
+
line
m2
:
c
+
λC
+
(
c
+
λC
)
T
+
(
c
+
λC
)
T
=
m
req − Temin , Tmax
10
11
12
b20
b21 m
b22 m
(


2

line m1 : λCb10 + λCb11 Tm + λCb12 Tm when Tm = Treq < 0


 λ·L =
2 when T = T
line m2 : λCb20 + λCb21 Tm + λCb22 Tm
m
req ≥ 0

(17)

(2) If Treq − Topt ≥ 0, then

.

meq


lin e2 + line m1 : c20 + λCb10 + (c21 + λCb11 ) Tm + (c22 + λCb12 ) Tm 2 when max Treq − Temax , Tmin ) ≤ Tm < 0



2


 lin e2 + line m2 : c20 + λCb20 + (c21 + λCb21 ) Tm + (c22 + λCb22 ) Tm when 0 ≤ Tm < Treq − Topt

2 when T
lin
e1
+
line
m2
:
c
+
λC
+
(
c
+
λC
)
T
+
(
c
+
λC
)
T
=
req − Topt ≤ Tm ≤ min( Treq − Temin , Tmax
10
11
12
b20
b21 m
b22 m
(


2

line m1 : λCb10 + λCb11 Tm + λCb12 Tm when Tm = Treq < 0


 λ·L =
2 when T = T
line m2 : λCb20 + λCb21 Tm + λCb22 Tm
m
req ≥ 0

(18)

According to Equations (17) and (18), the total equivalent fuel rate is a piecewise function,
which is composed of four continuous convex quadratic function. Based on the property of convex
function, the total equivalent fuel rate is also a convex function, therefore the minimum value of the
total equivalent fuel rate can only be obtained at points of the demarcation of the convex piecewise
function. As shown in Equations (17) and (18), the demarcation points of the piecewise function are

Tm = max Treq − Temax , Tmin ) ,Tm = Treq − Topt , Tm = 0, Tm = min( Treq − Temin , Tmax and Tm = Treq .
Thus, the optimal control variable can only be obtained from above five points. The optimal solution
can be determined by comparing the value of the total equivalent fuel rate of the five points. Based on
above conclusion, the simplified equivalent fuel consumption minimization strategy (Simplified-ECMS)
is proposed.
The concept of the Simplified-ECMS is achieving the optimal solution by comparing the total
equivalent fuel rate of above five points for each time instant, instead of comparing the values
of every step point in the control domain, which is the principle of normal ECMS. Therefore,
the Simplified-ECMS can greatly reduce the amount of calculation and shorten the time of calculation.
The procedure flow chart of the Simplified-ECMS is shown in Figure 8.
To validate the effect of the Simplified-ECMS-based strategy, three energy management strategies are
simulated under ten repeated NEDC driving cycles: CD-CS-based, ECMS-based and Simplified-ECMSbased. The initial SOC is set 0.95, the final SOC is set 0.25. The simulation is operated on a desktop
computer with 4 gigabits of RAM and 2.3 GHz of core i3 processor. In this section, the equivalent factor is
determined by trial and error method.
The simulated SOC variation trajectories under three control strategies mentioned above are
shown in Figure 9, the figure shows that the SOC of Simplified-ECMS-based strategy and ECMS-based
strategy declines with the increasing of driving distance, and it reaches the target SOC value at
the driving end, these two SOC curves are close, which shows that the optimization effect of
Simplified-ECMS-based strategy is very close to the ECMS-based strategy.
Figure 10 is the engine working points under three control strategies. According to the figure,
most engine working points of Simplified-ECMS-based strategy coincide with the points of ECMS-based
strategy, and these two strategies’ engine working points are almost in engine’s economic zone, while
CD-CS-based strategy’s engine working points are only a few parts in the economic zone.

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40
30
40
20
30
10
20
0
100
0
0

200

400

600

Driving cycle
200
400
600
Driving cycle
Demand torque calculation
Demand torque calculation Braking energy
No recovery control:
Treq  0
energy
No Braking
u * = max(Tcontrol:
req , Tm min )
recovery
Treq Yes
0
*
u = max(Treq , Tm min )
Yes
Calculate five demarcation
points:
Tm1  max(
 Te max , Tm min )points:
Calculate
fiveTreq
demarcation
TTmm21  Tmax(
req
req TT
eopt Te max , Tm min )
TTmm32 0Treq  Teopt
TTmm43  min(
0 Treq  Te min , Tm max )
TTmm54 Tmin(
req Treq  Te min , Tm max )
Tm5  Treq

Calculate the total equivalent fuel
rate
of above
Calculate
the five
total points:
equivalent fuel
meq (Tof
meq (Tm 2 ),five
meq (Tmpoints:
rate
m1 ),above
3 ), meq (Tm 4 ), meq (Tm 5 )
meq (Tm1 ), meq (Tm 2 ), meq (Tm3 ), meq (Tm 4 ), meq (Tm 5 )

Obtain the optimal control variable:

u Obtain
 arg min
(meqoptimal
(Tm1 ), meq (control
Tm 2 ), meq (Tvariable:
m 3 ), meq (Tm 4 ), meq (Tm 5 ))
the

u   arg min (meq (Tm1 ), meq (Tm 2 ), meq (Tm3 ), meq (Tm 4 ), meq (Tm5 ))
Tm , N m 


TTem, ,NNe m


Te , N e 
Figure 8. The procedure flow chart of the Simplified-ECMS.

Figure 8. The procedure flow chart of the Simplified-ECMS.
Figure 8. The procedure flow chart of the Simplified-ECMS.

1

CD-CS-based
ECMS-based
CD-CS-based
Simplified-ECMS-based
ECMS-based

1
0.9
0.9
0.8

Simplified-ECMS-based

SOCSOC

0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2

0

2000

0

2000

4000

10,000

12,000

4000

6000
8000
Time (s)
6000
8000
Time (s) trajectories.
Figure 9. SOC variation

10,000

12,000

Figure 9. SOC variation trajectories.

Figure 9. SOC variation trajectories.

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160
140
120

240

254
260

Torque (Nm)

100

270
280

80

300

60
40
20
0

CD-CS-based
ECMS-based
Simplified-ECMS-based
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000

Speed (rpm)

Figure 10. Engine working points under three strategies.

Figure 10. Engine working points under three strategies.
Table 2 is the engine’s fuel consumption and calculation time of three control strategies under

Table
2 is theNEDC
engine’s
fuelcycles.
consumption
and calculation
of three control strategies
under
ten repeated
driving
The fuel consumption
fromtime
the Simplified-ECMS-based
strategy
ten repeated
driving
cycles.are
The
fuelbut
consumption
from the Simplified-ECMS-based
strategy
and theNEDC
ECMS-based
strategy
close,
the fuel consumption
of the Simplified-ECMS-based
strategy
is obviously
less than
consumption
the consumption
CD-CS-based strategy;
the calculation time of
and the
ECMS-based
strategy
aretheclose,
but the of
fuel
of the Simplified-ECMS-based
theis
Simplified-ECMS-based
is obviouslyofshorter
than the ECMS-based
strategy,
it is close totime
strategy
obviously less than strategy
the consumption
the CD-CS-based
strategy;
the calculation
the
time
of
the
CD-CS-based
strategy,
which
is
a
real-time
control
strategy.
Therefore,
the
of the Simplified-ECMS-based strategy is obviously shorter than the ECMS-based Simplifiedstrategy, it is
ECMS-based strategy can obtain excellent fuel economy, and can obviously shorten the calculation
close to
the time of the CD-CS-based strategy, which is a real-time control strategy. Therefore,
time. We can conclude that Simplified-ECMS-based strategy is more appropriate for real-time control
the Simplified-ECMS-based strategy can obtain excellent fuel economy, and can obviously shorten
than ECMS-based strategy.
the calculation time. We can conclude that Simplified-ECMS-based strategy is more appropriate for
real-time control than
ECMS-based
strategy.
Table
2. Fuel consumption
and calculation time under three control strategies.
Result
CD-CS ECMS
Simplified-ECMS
Table 2. Fuel consumption
and calculation
time under
three control strategies.
fuel consumption (L)
4.812
3.964
3.967
calculation
time * (s)CD-CS
72.88
966.89
146.44
Result
ECMS
Simplified-ECMS
Final SOC
0.2502
0.250
0.2501
fuel consumption (L)
4.812
3.964
3.967
Note: * The calculation was completed on a desktop computer with 4 gigabits of RAM and 2.3 GHz
calculation time * (s)
72.88
966.89
146.44
of core i3 processor.
Final SOC
0.2502
0.250
0.2501
Note:
* The calculation
was completed on Strategy
a desktop computer with 4 gigabits of RAM and 2.3 GHz of core
5. Adaptive
Simplified-ECMS-Based
i3 processor.

The key for the implementation of the Simplified-ECMS-based strategy is to find the right
equivalent
factor, which is considered
to be a balancer balancing electrical energy consumption and
5. Adaptive
Simplified-ECMS-Based
Strategy
fuel energy consumption. A large number of scholars have conducted discussions about equivalent

The
keyThere
for the
implementation
ofequivalent
the Simplified-ECMS-based
to find factor
the right
factor.
are mainly
two kinds of
factor were proposed, strategy
the fixed is
equivalent
equivalent
factor,
which
is
considered
to
be
a
balancer
balancing
electrical
energy
consumption
and fuel
[24,26] and the adaptive equivalent factor. The former relies on prior knowledge about the driving
energycycle,
consumption.
A itlarge
scholars have conducted
discussions
abouthas
equivalent
factor.
which deters
fromnumber
real-timeofimplementation.
The adaptive
equivalent factor
fairly ideal
A commonly
used approach
obtaining
the adaptive
factor
is [24,26]
using a and
There performance.
are mainly two
kinds of equivalent
factorfor
were
proposed,
the fixedequivalent
equivalent
factor
feedbackequivalent
controller, such
as The
a PI controller
[21,27],
fuzzyknowledge
PI controller about
[28], a PID
[29] and
the adaptive
factor.
former relies
onaprior
the controller
driving cycle,
which
a
fuzzy
logic
controller
[30],
this
method
mainly
based
on
the
SOC
reference,
which
is
calculated
from
deters it from real-time implementation. The adaptive equivalent factor has fairly ideal performance.
the predicted driving horizon [25,31]. The parameters of the PI/PID and the law of fuzzy controller
A commonly
used approach for obtaining the adaptive equivalent factor is using a feedback controller,
are hard to be chosen, and the computation load of fuzzy logic controller is still heavy, therefore,
such as a PI controller [21,27], a fuzzy PI controller [28], a PID controller [29] and a fuzzy logic
above feedback controllers are still difficult to be applied in the real vehicle. In this section, the
controller [30], this method mainly based on the SOC reference, which is calculated from the predicted
equivalent factor optimization model is established, then, the equivalent factor is optimized off-line
driving
[25,31].
The
parameters
of the
PI/PID
and the
lawdifferent
of fuzzy
controller
hard to be
byhorizon
the particle
swarm
optimization
(PSO)
genetic
algorithm
under
driving
cycles,are
therefore,
chosen, and the computation load of fuzzy logic controller is still heavy, therefore, above feedback
controllers are still difficult to be applied in the real vehicle. In this section, the equivalent factor
optimization model is established, then, the equivalent factor is optimized off-line by the particle swarm
optimization (PSO) genetic algorithm under different driving cycles, therefore, the best equivalent

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factor MAPs are obtained, finally, the adaptive Simplified-ECMS-based strategy is implemented based
the
bestequivalent
equivalentfactor
factorMAPs.
MAPs are obtained, finally, the adaptive Simplified-ECMS-based strategy
on the
is implemented based on the equivalent factor MAPs.
5.1. Equivalent Factor
5.1. Equivalent Factor
As we known, the equivalent factor can be used to adjust the electrical energy consumption and
As we known,
the equivalent
factor can
be SOC
used is
to high,
adjustmore
the electrical
fuel energy
consumption.
For example,
if the
electricalenergy
energyconsumption
is consumedand
by
fuel
energy
consumption.
For
example,
if
the
SOC
is
high,
more
electrical
energy
is
consumed
by
reducing the equivalent factor, otherwise, more fuel energy is consumed by increasing the equivalent
reducing
the equivalent
factor,
otherwise, more
fuel
energythe
is consumed
increasing
the
equivalent
factor. Based
on knowing
the preliminary
change
between
equivalentby
factor
and the
SOC,
we can
factor.
Based
on
knowing
the
preliminary
change
between
the
equivalent
factor
and
the
SOC,
we
establish an initial function, which preliminarily defines above changes, and modify it accordingcan
to
establish
an initial
function,
which
preliminarily
defines
changes,
and modify
it according
to
different driving
cycles,
driving
distances
and initial
SOC.above
The initial
function
is expressed
as
different driving cycles, driving distances and initial SOC. The initial function is expressed as
λ(t, SOC) = k · f (SOC )
(19)
 (t,SOC)=k  f (SOC)
(19)
where
the
initial
where f f((SOC
isthe
the initial
initial function;
function; kkis is
thecorrection
correctioncoefficient
coefficientofofthe
theinitial
initialfunction.
function. The
The initial
SOC)) is
function is
is shown
shownin
inFigure
Figure11,
11,asasshown
shown
the
figure,
value
of initial
function
increases
function
inin
the
figure,
thethe
value
of initial
function
increases
withwith
the
the
decreasing
of
SOC,
and
the
rate
of
increasing
is
different
when
the
SOC
in
different
regions.
decreasing of SOC, and the rate of increasing is different when the SOC in different regions. For
For example,
when
is lower
than
0.25,
value
theinitial
initialfunction
functionincreases
increasesfastest
fastest with
with the
the
example,
when
SOCSOC
is lower
than
0.25,
thethe
value
ofofthe
decreasing of
of SOC,
decreasing
SOC, which
which can
can defer
defer SOC
SOC further
further declining.
declining.
2
1.8
1.6

f

1.4
1.2
1
0.8
0.6
0.4

0

0.1

0.2

0.3

0.4

0.5

SOC

0.6

0.7

0.8

0.9

1

Figure
Figure 11.
11. The
The initial
initial function’s
function’s value
value versus
versus the
the battery’s
battery’s SOC.
SOC.

5.2.
5.2. Off-Line
Off-Line Optimization
Optimization Based
Based on
on PSO
PSO Algorithm
Algorithm
After
After determining
determining the
the initial
initial function,
function, the
the equivalent
equivalent factor
factor entirely
entirely depends
depends on
on the
the correction
correction
k , therefore, the energy distribution of the engine and the battery can be dynamically
coefficient
coefficient k, therefore, the energy distribution of the engine and the battery can be dynamically
k becomes a
adjusted
coefficient k.k Then,
. Then,
thecorrection
correction
coefficient
adjusted by
by only
only altering
altering the
the correction
correction coefficient
the
coefficient
k becomes
a key
key
parameter
of
the
adaptive
Simplified-ECMS-based
strategy,
and
the
key
parameter
of this
parameter of the adaptive Simplified-ECMS-based strategy, and the key parameter of this strategy
strategy
is optimized
by PSO algorithm
because
its optimization
is a nonlinear
global optimization
is optimized
by PSO algorithm
because its
optimization
is a nonlinear
global optimization
process,
process,
thefunction
fitness function
is expressed
as
the fitness
is expressed
as
 F  minR t.m (t)dt

0 ice
min ktm

F
=

{k} 0 ice (t)dt

0.25 

SOC (t)  0.95
0.25≤ SOC (t) ≤ 0.95

T
(t)
 Te (t)  Temax (t)
emin

Temin

 (t) ≤ Te (t) ≤ Temax (t)


T
(t)
Tmmax (t)
 mmin
Tmmin
(t) ≤TTmm (t)
(t)≤
Tmmax (t)

(20)
(20)

The flow chart of k optimization is shown in Figure 12, the simulation is performed under ten
The flow chart of k optimization is shown in Figure 12, the simulation is performed under ten
repeated NEDC driving cycles, the initial SOC is 0.95, the parameters of PSO are set: the size of
repeated NEDC driving cycles, the initial SOC is 0.95, the parameters of PSO are set: the size of particle
particle swarm is 100, the maximum number of iterations is 100, the initial inertia weight 0.9, the final
inertia weight is 0.4.

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swarm is 100, the maximum number of iterations is 100, the initial inertia weight 0.9, the final inertia
Sustainability 2018, 10, x FOR PEER REVIEW
13 of 24
weight
is 0.4.
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2018, 10, x FOR PEER REVIEW
13 of 24
The
optimization
result
is
shown
in
Figure
13,
the
optimal
value
of
k
is
4.38,
and
the
optimal
fuel
The optimization result is shown in Figure 13, the optimal value of k is 4.38, and the optimal
consumption
is
3.945
L.
Comparison
results
of
two
equivalent
factor
determining
methods
are
given
k
The
optimization
result
is
shown
in
Figure
13,
the
optimal
value
of
is
4.38,
and
the
optimal
fuel consumption is 3.945 L. Comparison results of two equivalent factor determining methods are
in
Table
the equivalent
determining
by PSO
can saved
fuel
consumption
by 0.55%
fuel
consumption
3.945factor
L. Comparison
results
of
two
factor
determining
methods
are
given
in 3,
Table
3, theisequivalent
factor
determining
byalgorithm
PSOequivalent
algorithm
can saved
fuel consumption
by
compared
to
the
trial
and
error
method.
given
in
Table
3,
the
equivalent
factor
determining
by
PSO
algorithm
can
saved
fuel
consumption
by
0.55% compared to the trial and error method.
0.55% compared to the trial and error method.
PSO
PSO
Start
Start

Matlab/Simulink
Matlab/Simulink

Generate particle swarm
Generate particle swarm

Assign a value to k
Assign a value to k

Update operation of Particle swarm
Update operation of Particle swarm

Run vehicle simulation model based
on
Simplified-ECMS-based
strategy
Run
vehicle simulation model
based
on Simplified-ECMS-based strategy

No
No
Terminating
condition
satisfied?
Terminating
condition satisfied?
Yes
End Yes

Calculate fitness function
Calculate fitness function

End

Figure 12. The flow chart of k optimization.
Figure 12.
12. The
The flow
flow chart
chart of
of kkoptimization.
Figure
optimization.

Fuel
consumption
Fuel
consumption
(L)(L)

6
6
5.5
5.5
5
5

4.5
4.5
4
4

3.5
3.50
0

20
40
60
20 Number
40 of iterations
60
Number of iterations

80
80

100
100

Figure 13. The optimization result.
Figure13.
13.The
Theoptimization
optimizationresult.
result.
Figure
Table 3. Comparison results of two equivalent factor determining methods.
Table3.3.Comparison
Comparisonresults
resultsof
oftwo
twoequivalent
equivalentfactor
factordetermining
determiningmethods.
methods.
Table
Equivalent Factor Determined
Equivalent Factor Determined
Results
Equivalent
Factor
Equivalent
Factor
Determined
by Trial and
ErrorDetermined
Method
by PSO
Algorithm
Results
Equivalent
Factor
Determined
Equivalent
Factor
Determined
by
Trial
and
Error
Method
by
PSO
Algorithm
Fuel consumption
(L)
3.967
3.945
Results
by Trial and Error Method
by PSO Algorithm
Fuel consumption
(L)
3.967
3.945
Final SOC
0.2501
0.2502
Fuel consumption
3.967
3.945
Final SOC (L)
0.2501
0.2502
Final SOC

0.2501

0.2502

Saving
Saving
0.55%
Saving
0.55%
--0.55%
--—

Equivalent factor is mainly affected by driving distance and initial SOC in certain driving cycle
Equivalent
is mainly
affected
by driving
distance
and
initial
SOCaffected
in certain
cycle
k is
[32], then,
based factor
on Equation
(19),
correction
coefficient
also
mainly
bydriving
the driving
Equivalent
factor
is
mainly
affected
by
driving
distance
and
initial
SOC
in
certain
driving
cycle
[32],
k
[32],
then,
based
on
Equation
(19),
correction
coefficient
is
also
mainly
affected
by
the
driving
distance and the initial SOC in certain driving cycle, Above k optimization is based on the given
then,
based
on
Equation
(19),
correction
coefficient
k
is
also
mainly
affected
by
the
driving
distance
and
k optimization
distancedistance
and the initial
SOC inSOC,
certain
driving
cycle,
Above
on the given
driving
and initial
Next,
under
NEDC
driving
cycle, the is kbased
optimization
is
the
initial
SOC
in
certain
driving
cycle,
Above
k
optimization
is
based
on
the
given
driving
distance
k
driving
distance
and
initial
SOC,
Next,
under
NEDC
driving
cycle,
the
optimization
implemented one by one in different driving distance and initial SOC through off-line optimization,is
implemented
one byofone
in different
drivingk distance
initial
SOC through
and
the MAP figure
correction
coefficient
under theand
NEDC
driving
cycle, asoff-line
shown optimization,
in Figure 14,
k
and
the
MAP
figure
of
correction
coefficient
under
the
NEDC
driving
cycle,
as
shown
in Figure 14,
is obtained.
is obtained.

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and initial SOC, Next, under NEDC driving cycle, the k optimization is implemented one by one
in different driving distance and initial SOC through off-line optimization, and the MAP figure of
correction coefficient k under the NEDC driving cycle, as shown in Figure 14, is obtained.
Sustainability 2018, 10, x FOR PEER REVIEW

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8
7

k

6
5
4

3
0.2

150
100

0.4
0.6

50

0.8
SOC

1 0

Driving distance (km)

k.
Figure
Figure14.
14.The
TheMAP
MAPfigure
figureofofcorrection
correctioncoefficient
coefficient k.

As shown in Figure 14, when the driving distance is less than the pure electric mileage, k is a
As shown in Figure 14, when the driving distance is less than the pure electric mileage, k is a
constant, and its value is minimum, the reason is that electrical energy is enough in this condition, a
constant, and its value is minimum, the reason is that electrical energy is enough in this condition,
small k makes driving using battery power as more as possible; when the driving distance is larger
a small k makes driving using battery power as more as possible; when the driving distance is larger
than the pure electric mileage, k increases with the increasing driving distance in certain initial
than the pure electric mileage, k increases with the increasing driving distance in certain initial SOC,
SOC, which can blend electric energy with the trip distance adding. k reduces with the increasing
which can blend electric energy with the trip distance adding. k reduces with the increasing initial
initial SOC in certain driving distance, then, the opportunity of motor participation increases under
SOC in certain driving distance, then, the opportunity of motor participation increases under this way.
this way.

5.3. Implementation of the Adaptive Simplified-ECMS-Based Strategy
5.3. Implementation of the Adaptive Simplified-ECMS-Based Strategy
Determining the correction coefficient k in actual driving conditions is a key issue for
Determining
the correction
coefficient k in
actual In
driving
conditions
is aofkey
issuethefork
implementing
adaptive
Simplified-ECMS-based
strategy.
the real-time
control
PHEV,
implementing
adaptivebySimplified-ECMS-based
the real-time
controlburden.
of PHEV,
the k
could
not be obtained
PSO algorithm on-line strategy.
due to theIngreat
computational
However,
could
not
be
obtained
by
PSO
algorithm
on-line
due
to
the
great
computational
burden.
However,
the value of k in different driving distances, initial SOC and driving cycles can be obtained by PSO
k in which
the value of
different
distances,
initial
and driving
cyclesflowchart
can be obtained
by PSO
algorithm
off-line,
hasdriving
been done
in Section
5.2.SOC
Therefore,
the control
of the adaptive
algorithm off-line, whichstrategy
has been
done
in Section
5.2.15.
Therefore,
thecorrection
control flowchart
of the
adaptive
Simplified-ECMS-based
can
be set
in Figure
Firstly, the
coefficient’s
MAPs
(like
Simplified-ECMS-based
strategy
can
be
set
in
Figure
15.
Firstly,
the
correction
coefficient’s
MAPs
Figure 14) under different driving cycles are obtained by global off-line optimizer based on the
PSO
(like FigureSecondly,
14) underidentify
differentthe
driving
cycles
are obtained
by global
based
on the
algorithm.
type of
the real
driving cycle
basedoff-line
on the optimizer
recognition
algorithm.
PSO
algorithm.
Secondly,
identify
the
type
of
the
real
driving
cycle
based
on
the
recognition
Thirdly, the driving distance is gained by vehicle’s navigation system. Fourthly, extract the optimal
algorithm. coefficient
Thirdly, the
driving
distance
is through
gained by
vehicle’s
navigation
system.cycle,
Fourthly,
extract
correction
k from
above
MAPs
the
obtained
type of driving
the driving
the optimal
coefficient
from above MAPs through
theisobtained
of driving
cycle,
distance
andcorrection
the initial SOC.
Finally,kSimplified-ECMS-based
strategy
applied totype
distribute
the engine
the
driving
distance
and
the
initial
SOC.
Finally,
Simplified-ECMS-based
strategy
is
applied
and motor’s torque, and out put the optimal engine and motor’s torque to vehicle power system. to
distribute the engine and motor’s torque, and out put the optimal engine and motor’s torque to
vehicle power system.

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15 of 24

Recognition algorithm
40
30
20
10
0
0
200
400
600
Real-time driving cycle

Cycle features
extraction

Navigation system

The type of
drive cycle

Driving distance 

Initial SOC 

MAP of correction
coefficient k

(t)Accelerator

Vref  t 

correction coefficient k

(t) Brake
 (t)

Driver

(t)

Torque
requirement

Global off-line optimizer
based on PSO algorithm

Treq (t)

Simplified-ECMSbased strategy

Tm , N m 


Te , N e 

V(t)
Vehicle power
SOC(t)
system

Figure
Figure15.
15.The
Theflow
flowchart
chartofofthe
theadaptive
adaptiveSimplified-ECMS-based
Simplified-ECMS-basedstrategy.
strategy.

5.4.Simulation
SimulationValidation
Validationofofthe
theAdaptive
AdaptiveSimplified-ECMS-Based
Simplified-ECMS-BasedStrategy
Strategy
5.4.
Anotherkey
key
business
applying
the adaptive
Simplified-ECMS-based
is pattern
driving
Another
business
for for
applying
the adaptive
Simplified-ECMS-based
strategystrategy
is driving
pattern recognition.
methods
ofpattern
the driving
pattern
or system
recognition
recognition.
Generally, Generally,
the methodsthe
of the
driving
or system
recognition
mainly
include amainly
fuzzy
include
a
fuzzy
logic
controller
[33,34],
cluster
analysis
[35],
k-means
clustering
method
[36],
support
logic controller [33,34], cluster analysis [35], k-means clustering method [36], support vector machine
vector[37],
machine
(SVM)
[37],
extended
support
vector
machine
(SVM)
[38], neural
[39],
(SVM)
extended
support
vector
machine
(SVM) [38],
neural
network
[39], learning
vectornetwork
quantization
learning[40]
vector
quantization
network
[40]
genetic
programming
for system
recognition
network
and genetic
programming
(GP)
forand
system
recognition
[41,42]. In(GP)
this paper,
extreme
learning
[41,42]. (ELM)
In this is
paper,
learning
(ELM) is used for driving pattern recognition.
machine
used extreme
for driving
patternmachine
recognition.

5.4.1.
5.4.1.Driving
DrivingPattern
PatternRecognition
RecognitionBased
Basedon
onELM
ELM
ELM
ELMisisan
aneasy
easyand
andeffective
effectivealgorithm
algorithmfor
forsingle
singlelayer
layerfeed
feedforward
forwardneural
neuralnetwork,
network,was
wasfirst
first
introduced
introducedby
byHuang
Huangetetal.
al.[43].
[43].The
Thestructure
structureofofELM
ELMmodel
modelisisshown
shownininFigure
Figure16.
16.
The
Thetarget
targetofofdriving
drivingpattern
patternrecognition
recognitionisistotoanalyze
analyzethe
thevelocity
velocityinformation
informationand
andclassify
classify
practical
driving
patterns
as
similar
standard
driving
cycles.
Recognized
driving
cycles
practical driving patterns as similar standard driving cycles. Recognized driving cyclesshould
shouldbe
be
included
includedininthe
therepresentative
representativedriving
drivingcycle
cyclegroup.
group.Six
Sixrepresentative
representativestandard
standarddriving
drivingcycles,
cycles,shown
shown
ininTable
Table4 4and
andFigure
Figure17,
17,were
wereselected
selectedininthis
thispaper
papertotocover
covermost
mostofofthe
thedifferent
differentstreet
streettypes
typesand
and
driving
16, the
drivingbehaviors.
behaviors.Therefore,
Therefore,ininFigure
Figure16,
theoutput
outputlayer
layerhas
hassix
sixneurons
neuronsthat
thatrepresent
representabove
abovesix
six
typical
. , x11], wwijij isisthe
typicaldriving
drivingcycles.
cycles.The
Theinput
inputvector
vectorof
ofthe
theinput
inputlayer
layerisisXX==[x1,
[x1,x2,
x2,. .…,
theweight
weight
between
betweenthe
theith
ithneuron
neuronofofthe
theinput
inputlayer
layerand
andthe
thejth
jthneuron
neuronofofthe
thehidden
hiddenlayer.
layer.To
Toidentify
identifythe
the
driving
drivingpattern,
pattern,the
theeleven
elevenfeatures
featureswere
wereextracted
extractedfrom
fromthe
thevehicle
vehiclespeed
speedduring
duringthe
thetime
timeinterval,
interval,
and
andthe
theeleven
elevenneurons
neuronsofofthe
theinput
inputlayer
layermatched
matchedthese
theseeleven
elevencharacteristic
characteristicparameters:
parameters:average
average
speed (v), maximum speed (vmax ), maximum acceleration (amax ), average acceleration (a), maximum
speed ( v ), maximum speed ( vmax ), maximum acceleration ( amax ), average acceleration ( a ),
deceleration (dmax ), average deceleration (d), idle time factor ri (idle time/total time), acceleration
ri (idle time/total time),
maximum
( d max ), average
deceleration
( d time
), idle
timer factor
time
factor rdeceleration
time),
deceleration
factor
a (acceleration time/total
d (deceleration time/total time),
ra (acceleration
acceleration
deceleration
time factor rd (deceleration
uniform
time time
factorfactor
rc (uniform
time/total time/total
time) and time),
idle times
( f i ).
time/total time), uniform time factor rc (uniform time/total time) and idle times ( f i ).

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 jk

wij

 jk

wij

Average speed

Driving cycle 1

Driving cycle 1

Average speed

Driving cycle 2

Max speed

.
.

. speed
Max
Idle.times

.
.

.
.
.

.
.
.
.
.
.

.
.
.

Driving
. cycle 2
Driving cycle 6

.
..

.
.
.

Driving cycle 6
Output layer

Input layer
Idle times

Input layer

.
.

.
..

The hidden layer

Output layer

Figure 16. The structure of ELM model.

Figure 16. The The
structure
of ELM model.
hidden layer
Table 4. Representative standard driving cycles.

VelocityVelocity
(km/h) (km/h)VelocityVelocity
(km/h) (km/h)
VelocityVelocity
(km/h) (km/h)

VelocityVelocity
(km/h) (km/h) VelocityVelocity
(km/h) (km/h)VelocityVelocity
(km/h) (km/h)

Figure 16. The structure of ELM model.
Table 4.
Representative standard driving cycles.
Driving Cycle Type
Name
Driving Cycle Number
Table 4. Representative standard driving cycles.
NYCC
DrivingCycle
CycleNumber
1
Driving Cycle Type
Name
Driving
Urban Road
NewYorkBus
Driving
Cycle
2
Driving Cycle Type
Name
Driving
Cycle
Number
NYCC
Driving Cycle 1
Urban Road
ECE_EUDC_LOW
Driving
Cycle
31 2
NYCC
Driving
Cycle
NewYorkBus
Driving Cycle
Suburb
Urban Road
Road
UDDS
Driving
NewYorkBus
DrivingCycle
Cycle42
ECE_EUDC_LOW
Driving Cycle 3
HWFET
Driving
ECE_EUDC_LOW
DrivingCycle
Cycle53
Suburb Road
UDDS
Driving Cycle 4
Highway
Suburb Road
US06_HWY
Driving
UDDS
DrivingCycle
Cycle64
HWFET
Driving
Cycle5 5
HWFET
Driving Cycle
Highway Road
Highway Road
US06_HWY
Driving Cycle 6
NYCC
NewYorkBus
US06_HWY
Driving Cycle 6
50
40
40
30
30
NYCC
NewYorkBus
20
50
20
40
40
10
10
30
30
0
0
300
300
600
200
200
Time (s)
Time
(s)
10
10 cycles
(a) Urban driving
0 0 ECE_EUDC_LOW
UDDS
300
300
600 1000 0
80
Time (s)
Time (s)
80
(a) Urban driving cycles
60
60
ECE_EUDC_LOW
UDDS
40
100
40
80
20
80
20
60
0600
0
400
800
1200
400
800
40
400
Time (s)
Time (s)
20
20
(b) Suburban driving
cycles
00
0
400
800
1200
0
400
800
HWFET
US06_HWY
Time (s)
100
Time (s)
80
(b) Suburban120
driving cycles
60
80
HWFET
US06_HWY
100
40
120
40
80
20
60
80
0
00
200
400
600 800
200
400
Time
(s)
40
Time (s)
20
(c) Highway driving
0
00 cycles
0
200
400
600 800
200
Time
(s)17. Six typical driving cycles. Time (s)
Figure
(c) Highway driving cycles

600
600

1200
1200

400
400

The training samples can be Figure
obtained
based
ondriving
characteristic
17. Six
typical
cycles. parameters of the six typical
Figure 17.parameters
Six typical driving
cycles.
driving cycles. If only the characteristic
of whole
driving cycle are taken as training
samples,
the
accuracy
of
training
and
recognition
is
difficult
to
guarantee
for too little
sample
data.
The training samples can be obtained based on characteristic parameters
of the
six typical
Therefore,
it
is
preferable
to
divide
each
driving
cycle
into
the
appropriate
number
of
120
s
driving
cycles.
If only can
the be
characteristic
parameters
of whole driving
cycle are
taken
training
The
training
samples
obtained based
on characteristic
parameters
of the
six as
typical
driving
samples,
accuracy
of training
and recognition
is difficult
to guarantee
too little
sample data.
cycles.
If onlythethe
characteristic
parameters
of whole
driving
cycle arefor
taken
as training
samples,
Therefore,
is preferable
to divide each
driving
into the
number
of Therefore,
120 s
the accuracy
of it
training
and recognition
is difficult
to cycle
guarantee
for appropriate
too little sample
data.

it is preferable to divide each driving cycle into the appropriate number of 120 s overlapping shorter

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overlapping shorter periods and then to extract their characteristic parameters. Table 5 shows the
NYCC driving cycle divided into ten time periods. Using this method, characteristic parameters of
the six driving
cycles
in different
are taken
as training
samples.
periods
and then
to extract
their periods
characteristic
parameters.
Table
5 shows the NYCC driving cycle

divided into ten time periods. Using this method, characteristic parameters of the six driving cycles in
Recognition
characteristics of the six typical driving cycles.
different periods areTable
taken5.as
training samples.
Driving Cycle
1
1 Cycle
Driving
11
11
1
11
11
11
1
11
11
1
1

v
11.41
7.07
v
22.64
11.41
7.07
10.23
22.64
6.26
10.23
10.84
6.26
10.84
16.45
16.45
19.04
19.04
6.04
6.04
8.81
8.81

vmax

amax

44.6
v36.9
max
42.5
44.6
36.9
36.1
42.5
25.4
36.1
44.6
25.4
44.6
40.6
40.6
42.5
42.5
22.1
22.1
33.8
33.8

2.68
2.50
amax
2.68
2.68
2.50
2.24
2.68
1.43
2.24
1.83
1.43
1.83
2.50
2.50
2.68
2.68
1.61
1.61
1.48
1.48

a
0.62
0.74
a
0.68
0.62
0.74
0.62
0.68
0.38
0.62
0.62
0.38
0.62
0.70
0.70
0.77
0.77
0.50
0.50
0.46
0.46

dmax

ri
ra
rd
rc
fi
d
−0.64 0.351 0.326 0.304 0.020 18
−0.72
5
r0.433
ra0.283 rd 0.258 rc 0.025fi
d
i
−0.63
0.033
0.442
0.483
0.042
−0.64
0.351
0.326
0.304
0.020
18 2
−0.72
−0.54 0.433
0.308 0.283
0.3250.2580.3580.0250.0085 4
−0.63
0.033
0.442
0.483
0.042
2
−0.47
0.542
0.2420.3580.1920.0080.0254 5
−0.54
0.308
0.325
−0.90 0.542
0.437 0.242
0.3360.1920.2270.0250.0005 2
−0.47
−0.90
−0.58 0.437
0.108 0.336
0.4080.2270.4580.0000.0252 3
−0.58
0.108
0.408
0.458
0.025
3
−0.65 0.142
0.142 0.383
0.3830.4330.4330.0420.0423 3
−0.65
−0.58
−0.58 0.433
0.433 0.292
0.2920.2580.2580.0170.0175 5
−0.71
0.417
0.333
0.242
0.008
3
−0.71 0.417 0.333 0.242 0.008 3

Table 5. Recognition characteristics of the six typical driving cycles.

−2.64
d−2.06
max
−−2.64
2.64
−−1.39
2.06
−2.64
−1.48
−1.39
−−2.49
1.48
−2.49
−2.06
−2.06
−−2.64
2.64
−−1.39
1.39
−2.46
−2.46

Unlike
neural
networks
whose whose
weights weights
need to beneed
tuned to
using
backpropagation
Unlike conventional
conventional
neural
networks
be the
tuned
using the
algorithm,
in
ELM
the
weights
between
the
input
layer
and
the
hidden
layer
and
the biases
of and
the
backpropagation algorithm, in ELM the weights between the input layer and the hidden
layer
hidden
layer
assigned.
In default,
sigmoidInfunction
chosen as
the activation
function.
the biases
of are
the randomly
hidden layer
are randomly
assigned.
default,issigmoid
function
is chosen
as the
Then,
the
ELM
only
needs
to
set
the
number
of
hidden
layer
nodes.
In
this
work,
this
number
is
activation function. Then, the ELM only needs to set the number of hidden layer nodes. In this work,
determined
through
gradually
increasing
the
number
of
hidden
neurons
from
10
to
150
in
interval
of
this number is determined through gradually increasing the number of hidden neurons from 10 to
10.
accuracy
against
the numberagainst
of hidden
forhidden
ELM onneurons
the testfor
sets,
which
150The
in interval
ofof
10.recognition
The accuracy
of recognition
the neurons
number of
ELM
on
is
randomly
extracted
from
training
samples,
is
shown
in
Figure
18.
It
is
seen
that
the
highest
accuracy
the test sets, which is randomly extracted from training samples, is shown in Figure 18. It is seen that
has
achieved
when
number
of hidden
is between
70 and
100. In
paper,7080and
hidden
the been
highest
accuracy
hasthe
been
achieved
when neurons
the number
of hidden
neurons
is this
between
100.
neurons
are
chosen
to
create
the
training
model.
In this paper, 80 hidden neurons are chosen to create the training model.
100
90

Accuracy (%)

80
70
60
50
40
30
20
10
0

20

40

60

80

100

120

The number of hidden neurons

140

Figure 18.
18. Accuracy
Accuracy vs.
vs. number
number of
of hidden
hidden neurons
neurons for
for ELM.
ELM.
Figure

5.4.2. Simulation Validation of the Adaptive Simplified-ECMS-Based Strategy
5.4.2. Simulation Validation of the Adaptive Simplified-ECMS-Based Strategy
To validate the effect of the adaptive Simplified-ECMS-based strategy, the CD-CS-based and the
To validate the effect of the adaptive Simplified-ECMS-based strategy, the CD-CS-based and the
adaptive Simplified-ECMS-based strategy are simulated in Matlab/Simulink. The testing driving
adaptive Simplified-ECMS-based strategy are simulated in Matlab/Simulink. The testing driving
cycle, made up of Manhattan, SC03, UDDS, Japanese1015, WVUCITY and HWFET driving cycle, is
cycle, made up of Manhattan, SC03, UDDS, Japanese1015, WVUCITY and HWFET driving cycle,
structured in Figure 19a. The speed profiles from 0 to 1090 s, from 1090 to 1691 s, from 1691 to 3061
is structured in Figure 19a. The speed profiles from 0 to 1090 s, from 1090 to 1691 s, from 1691 to 3061
s, from 3061 to 3721 s, from 3721 to 5129 s, from 5129 to 5895 s, from 5895 to 7303 s, from 7303 to 8673
s, from 3061 to 3721 s, from 3721 to 5129 s, from 5129 to 5895 s, from 5895 to 7303 s, from 7303 to

Sustainability 2018, 10, 2060

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Sustainability 2018, 10, x FOR PEER REVIEW

18 of 24

velocity/(km/h)

8673
s, from
and from
to 9763
s represent
Manhattan,
SC03,
UDDS,Japanese1015,
Japanese1015,WVUCITY,
WVUCITY,HWFET,
HWFET,
s, and
86738673
to 9763
s represent
Manhattan,
SC03,
UDDS,
WVUCITY,
UDDS,
and
Manhattan
driving
cycle,
respectively.
The
speed
profiles
of
Manhattan,
WVUCITY, UDDS, and Manhattan driving cycle, respectively. The speed profiles of Manhattan, SC03,
SC03,
UDDS,
Japanese1015,
WVUCITY
and
HWFET
are
obtained
from
ADVISOR
(2002,
National
Renewable
UDDS, Japanese1015, WVUCITY and HWFET are obtained from ADVISOR (2002, National
Energy
Laboratory,
Golden, CO,Golden,
USA). CO, USA).
Renewable
Energy Laboratory,
The
ELM
is
used
to
identify
the
patterns,
and
thethe
recognition
result
is shown
in Figure
19b.
The ELM is used to identify thedriving
driving
patterns,
and
recognition
result
is shown
in Figure
From
this result
and combining
withwith
the speed
curve
of test
cycle,
ELMELM
can can
recognize
the
19b. From
this result
and combining
the speed
curve
of driving
test driving
cycle,
recognize
types
of
the
test
driving
cycle
well.
The
simulation
results
of
above
strategies
under
the
testing
driving
the types of the test driving cycle well. The simulation results of above strategies under the testing
cycle
arecycle
shown
Figures
driving
areinshown
in 20–22,
Figuresrespectively.
20–22, respectively.
100
90
80
70
60
50
40
30
20
10
00

1000 2000 3000 4000 5000 6000 7000 8000 9000 10,000

Time (s)
(a)The testing driving cycle

Type of the driving cycle

6
5
4
3
2
1
0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10,000
Time (s)
(b) The recognition result
Figure
result.
Figure 19.
19. The
The testing
testing driving
driving cycle
cycle and
and recognition
recognition result.

Figure 20 is the SOC variation trajectories from the CD-CS-based and the adaptive SimplifiedFigure 20 is the SOC variation trajectories from the CD-CS-based and the adaptive Simplified-ECMSECMS-based strategy. With the CD-CS-based strategy, the vehicle is driven mainly by electricity
based strategy. With the CD-CS-based strategy, the vehicle is driven mainly by electricity before it is
before it is fully depleted, so the SOC declines quickly in charge depleting stage, but the electrical
fully depleted, so the SOC declines quickly in charge depleting stage, but the electrical energy of the
energy of the vehicle, which is using the adaptive Simplified-ECMS-based strategy, is blended over
vehicle, which is using the adaptive Simplified-ECMS-based strategy, is blended over the whole driving
the whole driving trip, therefore it can make the SOC dropping more slowly.
trip, therefore it can make the SOC dropping more slowly.

19 of 24
19 of 24

Sustainability 2018, 10, x FOR PEER REVIEW

19 of 24

SOC
SOC

Sustainability 2018, 10, 2060
Sustainability 2018, 10, x FOR PEER REVIEW

1
CD-CS-based
1
adaptive
Simplified-ECMS-based
0.9
CD-CS-based
adaptive Simplified-ECMS-based
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10,000
0.2
(s) 7000 8000 9000 10,000
0 1000 2000 3000 4000 Time
5000 6000

Time (s)

Figure20. SOC variation trajectories.
Figure 20. SOC variation trajectories.
Figure20. SOC variation trajectories.

The engine operating points under the test driving cycle are shown in Figure 21. It can be seen
points
test
driving
cycle
areare
shown
in Figure
21. in
It
can
seen
that
The
engineoperating
operating
pointsunder
underthe
the
test
driving
cycle
shown
inengine
Figure
21.
It be
can
bebrake
seen
that The
the engine
adaptive
Simplified-ECMS-based
strategy
intelligently
controls
the
low
the
adaptive
Simplified-ECMS-based
strategy
intelligently
controls
engine
in
the
low
brake
specific
that
the fuel
adaptive
Simplified-ECMS-based
intelligently
controls the
engine
in the low
brake
specific
consumption
(BSFC) regions forstrategy
any power
level. In contrast,
CD-CS-based
strategy
fuel
consumption
(BSFC)
regions
for
any
power
level.
In
contrast,
the
CD-CS-based
strategy
operates
specific
consumption
(BSFC)region.
regions
anyextent,
powerthe
level.
In contrast,
theprove
CD-CS-based
strategy
operatesfuel
the engine
over a wider
Tofor
some
comparisons
can
that the proposed
the
engine
over
a equivalent
wider
To
someaccording
extent,
can of
prove
that
the proposed
method
operates
the
engine
overregion.
a wider
region.
To
somethe
extent,
the comparisons
can
prove
that
the proposed
method
can
tune
factor
well
tocomparisons
the information
driving
cycle,
driving
distance
can
tune
equivalent
factor
well
according
to
the
information
of
driving
cycle,
driving
distance
and
method
canSOC,
tuneand
equivalent
well
according
to the information
driving
driving distance
and initial
also canfactor
explain
why
the proposed
method canofsave
fuel cycle,
consumption.
initial
SOC,SOC,
and also
why why
the proposed
method
can save
fuel consumption.
and initial
and can
alsoexplain
can explain
the proposed
method
can save
fuel consumption.
160
160
140

Torque
Torque
of engine
of engine
(Nm)
(Nm)

140
120
120
100
100
80

240
240

Adaptive Simplified-ECMS-based
CD-CS-based
Adaptive Simplified-ECMS-based
254
CD-CS-based
254

260
260

270
270

280
280

300
300

80
60
60
40
40
20
20
0
0

1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000

Speed
Engine
(rpm)
1000 1500 2000 2500
3000of3500
4000
4500 5000 5500 6000

Speed of Engine (rpm)
Figure 21. Engine working points under the test driving cycle.
Figure 21. Engine working points under the test driving cycle.
Figure 21. Engine working points under the test driving cycle.

The fuel consumption variation trajectories from the CD-CS-based strategy and the adaptive
The fuel consumption
variation
trajectories
fromasthe
CD-CS-based
strategy
andCD–CS-based
the adaptive
Simplified-ECMS-based
strategy
are totally
different,
shown
in Figure 22.
With the
The
fuel
consumption
variation
trajectories
from
the
CD-CS-based
strategy
and
the
Simplified-ECMS-based
strategy
are totally
different,
as shownbefore
in Figure
With
the CD–CS-based
strategy, the vehicle is driven
almost
completely
by electricity
it is22.
fully
depleted,
soadaptive
the fuel
Simplified-ECMS-based
strategy
are
totally
different,
as
shown
in
Figure
22.
With
the
CD–CS-based
strategy,
the vehicle
is driven
almost completely
by electricity
beforeprovides
it is fullythe
depleted,
so theafter
fuel
consumption
in the charge
depletion
stage is close
to zero. Engine
main power
strategy,
the
vehicle
is
driven
almost
completely
by
electricity
before
it
is
fully
depleted,
so
the
fuel
consumption
in
the
charge
depletion
stage
is
close
to
zero.
Engine
provides
the
main
power
after
electricity is fully depleted, therefore, the fuel consumption increases rapidly after the charge
consumption
thedepleted,
chargethe
depletion
stage
close
to zero.
Engine
provides
the event
main
after
electricity
is in
fully
therefore,
the isfuel
consumption
increases
rapidly
after power
the charge
depletion stage.
However,
electrical
energy
is blended
over
the
whole
driving
when
using
electricity
is
fully
depleted,
therefore,
the
fuel
consumption
increases
rapidly
after
the
charge
depletion
depletion
stage.
However, the electrical
energy Correspondingly,
is blended over the
whole
driving eventaccumulates
when using
the adaptive
Simplified-ECMS-based
strategy.
the
fuel consumption
stage.
However,
the
electrical
energy
is
blended
over
the
whole
driving
event
when
using
the
adaptive
the
adaptive
Simplified-ECMS-based
strategy.
Correspondingly,
the
fuel
consumption
accumulates
with the increasing of the driving distance. The fuel consumption underthe CD-CS-based strategy
is
with
increasing
of the driving
distance.
The fuel Simplified-ECMS-based
consumption underthe CD-CS-based
strategy
is
1.874the
L. The
fuel consumption
under
the adaptive
strategy is 1.566
L, this
1.874
L. The
fueltoconsumption
under
the adaptive
Simplified-ECMS-based
strategy is 1.566 L, this
strategy
do help
reduce the fuel
consumption
significantly.
The adaptive Simplified-ECMS-based
strategy do help to reduce the fuel consumption significantly. The adaptive Simplified-ECMS-based

Sustainability 2018, 10, 2060

20 of 24

Simplified-ECMS-based strategy. Correspondingly, the fuel consumption accumulates with the increasing of
the driving distance. The fuel consumption underthe CD-CS-based strategy is 1.874 L. The fuel consumption
2018, 10,
x FOR PEER REVIEW
20 ofthe
24 fuel
underSustainability
the adaptive
Simplified-ECMS-based
strategy is 1.566 L, this strategy do help to reduce
consumption
significantly.
The
adaptive
Simplified-ECMS-based strategy reduces the fuel consumption
by
Sustainability
2018, 10,the
x FOR
PEER
REVIEW
20 of
24
strategy reduces
fuel
consumption
by 16.43% under the testing driving cycle, comparing to
CD16.43%
under
the
testing
driving
cycle,
comparing
to
CD-CS-based
strategy.
CS-based strategy.
strategy reduces the fuel consumption by 16.43% under the testing driving cycle, comparing to CDCS-based strategy.
2
1.874L

Fuel consumption
(L) (L)
Fuel consumption

1.8
2

CD-CS-based
Adaptive Simplified-ECMS-based
CD-CS-based
Adaptive Simplified-ECMS-based

1.6
1.8
1.4
1.6

1.874L
1.566L
1.566L

1.2
1.4
1
1.2
0.8
1
0.6
0.8
0.4
0.6
0.2
0.4
0
0.2 0

10

20

30

40

50

60

70

60

70

Driving distance (km)
0

0

10

20

30

40

50

Figure 22. Fuel consumption variation trajectories.

Driving distance (km)
Figure 22. Fuel consumption
variation trajectories.
Figure
22. Fuel consumption variation trajectories.
6. Road Test on the Prototype
Vehicle

6. Road Test on the Prototype Vehicle

TheTest
Simplified-ECMS-based
Strategy for PHEVs has been experimentally validated on a
6. Road
on the Prototype Vehicle

prototype
PHEV. The parameters
of the prototype
vehicle
are shown
in Table 1. The
prototype
The
Simplified-ECMS-based
Strategy
for PHEVs
has been
experimentally
validated
on avehicle
prototype
The in
Simplified-ECMS-based
Strategy
for PHEVs
has beenonexperimentally
validated
on a
is The
shown
Figure 23.
control
software
is developed
Development
Production
PHEV.
parameters
of The
the vehicle’s
prototype
vehicle
are shown
in Table 1.theThe
prototypeto
vehicle
is shown
prototype
PHEV.
The
parameters
of
the
prototype
vehicle
are
shown
in
Table
1.
The
prototype
vehicle
(D2P,
DEV+PROD,
Germany
E.ON,
Essen,
Germany)
and
Matlab/Simulink
platforms.
in Figure 23. The vehicle’s control software is developed on the Development to Production (D2P,
is shown in Figure 23. The vehicle’s control software is developed on the Development to Production
DEV+PROD,
GermanyGermany
E.ON, Essen,
and Matlab/Simulink
platforms.
(D2P, DEV+PROD,
E.ON,Germany)
Essen, Germany)
and Matlab/Simulink
platforms.

Figure 23. The prototype vehicle.
Figure
23. The prototype
vehicle.
The results of the road test have
been
in Figure
24. The velocity curve of the vehicle is
Figure
23.presented
The prototype
vehicle.
shown in Figure 24a. The vehicle speed ranges from 0 to 61.58 km/h, the velocity of the test is low,
The results
ofthe
theprototype
road test have
been
in Figure
24. The velocity
curve
the vehicle
is
the reason
is that
PHEV
canpresented
only be tested
on campus,
for the sake
of of
safety,
the road
shown
in
Figure
24a.
The
vehicle
speed
ranges
from
0
to
61.58
km/h,
the
velocity
of
the
test
is
low,
The
results
of
the
road
test
have
been
presented
in
Figure
24.
The
velocity
curve
of
the
vehicle
test is only carried out at the low speed. The curves of five candidates’ total equivalent fuel rate are
the
reason
is that24a.
the prototype
PHEV
caninclude
only
bethe
tested
campus,
for(driving
the sake
of
safety,
the
road
is shown
ininFigure
Thedriving
vehicle
speed
ranges
from
0control
to
61.58
km/h,
themode
velocity
of the
test is
shown
Figure
24b.
The
modes
starton
mode
is equal
to 0),
test
is
only
carried
out
at
the
low
speed.
The
curves
of
five
candidates’
total
equivalent
fuel
rate
low, the
reasondriving
is thatmode
the prototype
PHEV
can to
only
be tested
on campus,
for the
sake
ofaresafety,
the electric
(driving mode
is equal
1), engine
driving
mode (driving
mode
is equal
shown
in Figure
24b. mode
The driving
modes include
controland
mode (driving
mode
is equal
to 0),
to 2),test
hybrid
driving
(driving
is equalthe
to start
3),
driving
mode
(driving
mode
is fuel
the road
is only
carried out
at the mode
low speed.
The
curves
of fivecharging
candidates’
total
equivalent
the
electric
driving
mode
(driving
mode
is
equal
to
1),
engine
driving
mode
(driving
mode
is
equal
equal
to
4),
and
the
regenerative
braking
mode
(driving
mode
is
0.5).
a1
is
the
start
stage,
so
driving
rate are shown in Figure 24b. The driving modes include the start control mode (driving mode is
to
2), hybrid
driving
(driving
mode
is equal in
to 3), driving
charging
modeIn(driving
is
mode
is equal
to mode
0, the
vehicle
operates
start and
control
mode.
the a2mode
stage,
equalequal
to 0),
electric
driving
mode
(driving
modethe
ismode
equal
to
1),a1engine
driving
(driving
to the
4), and
the regenerative
braking
mode (driving
is 0.5).
is the start
stage,mode
so driving
mode is equal to 0, the vehicle operates in the start control mode. In the a2 stage,

Sustainability 2018, 10, 2060

21 of 24

mode is equal to 2), hybrid driving mode (driving mode is equal to 3), driving and charging mode
(driving mode is equal to 4), and the regenerative braking mode (driving mode is 0.5). a1 is the start
stage, so driving mode is equal to 0, the vehicle operates in the start control mode. In the a2 stage,
. Sustainability. 2018, 10, x FOR
. PEER REVIEW
.
.
.
21 of 24
min(meq ( Tm1 ), meq ( Tm2 ), meq ( Tm3 ), meq ( Tm4 ), meq ( Tm5 )) = meq ( Tm5 ) , this means the fifth candidate
has the minimum
equivalent fuel rate. Therefore, the vehicle operates in the electric driving mode,
min (meq (Tm1 ), mtotal
eq (Tm 2 ), meq (Tm 3 ), meq (Tm 4 ), meq (Tm 5 ))=meq (Tm 5 ) , this means the fifth candidate has the minimum
and driving mode is equal to 1. Other stages can be analyzed in the same way. The engine and motor’s
total equivalent fuel rate. Therefore, the vehicle operates in the electric driving mode, and driving
toque distribution
testing
is shown
in Figurein24c.
and
motor’s
output
mode is equalduring
to 1. Other
stages
can be analyzed
the The
sameengine
way. The
engine
and total
motor’s
toque torque’s
response
to the require
inFigure
Figure24c.
24d,
From
theand
figure,
thetotal
totaloutput
output
torque of the
distribution
duringtorque
testing is
is shown
shown in
The
engine
motor’s
torque’s
to the
require
is shown
in Figure
24d, From
theproves
figure, the
total
torque of the
engine response
and motor
tracks
thetorque
require
torque
very well,
which
that
theoutput
Simplified-ECMS-based
engine
andapplied
motor tracks
thetime
require
torquecompletely.
very well, which proves that the Simplified-ECMS-based
Strategy
can be
to real
control
Strategy can be applied to real time control completely.

64

105

48

70

32

35

16

00

10

20

30

60

50

40

70

80

a5
3

a4

90 100 110 120 130 140 150 160 170 180 0
Time (s)
(a)
6
Driving mode
m eq (Tm 1 )

2.5

meq (Tm 2 )

5

meq (Tm3 )
m eq (Tm 4 )

Driving mode

2

3

1.5
a2

a3

1

2

0.5

1

0

10

20

30

40

50

60

70

80

90 100 110 120 130 140 150 160 170 180
Time (s)
(b)
Motor torque
Engine torque

0

10

20

30

40

50

60

70

80

90 100 110 120 130 140 150 160 170 180
Time (s)
(c)
Require torque
Engine and motor’s total output torque

0

10

20

30

40

50

60

70

80

90 100 110 120 130 140 150 160 170 180
Time (s)
(d)

0.81 0

10

20

30

40

50

60

70

80

90 100 110 120 130 140 150 160 170 180
Time (s)
(e)

0

Torque (Nm)

150
100

0

50
0

200
Torque (Nm)

4

m eq (Tm 5 )

a1

Velocity (km/h)

Require torque
Velocity

The total equivalent fuel rate (g)

Require torque (Nm)

140

150
100
50
0
-50

SOC

0.825
0.82

0.815

Figure 24. Road test results. (a) Velocity and require torque curve of the road test; (b) the curves of

Figure five
24. candidates’
Road test results.
(a) Velocity
and(c)require
torque
curve
ofdistribution
the road test;
(b) testing;
the curves
total equivalent
fuel rate;
engine and
motor
toque
during
(d) of five
candidates’
total
rate;
(c) engine
andtomotor
toquetorque;
distribution
during
testing;
(d) engine
engine
and equivalent
motor’s totalfuel
output
torque’s
response
the require
(e) variation
of battery
SOC.
and motor’s total output torque’s response to the require torque; (e) variation of battery SOC.

Sustainability 2018, 10, 2060

22 of 24

7. Conclusions
The models of the engine’s fuel rate and battery’s consumption rate are approximately fitted by
the piecewise function, which is made up of two quadratic functions. Then, the total equivalent fuel
rate can also be expressed by piecewise function, which is a convex function actually. According to the
properties of convex functions, the Simplified-ECMS-based strategy is proposed, this strategy only
needs to calculate and compare five candidates’ total equivalent fuel rate to determine the optimal
control for the Plug-in HEV.
CD-CS-based, ECMS-based and Simplified-ECMS-based strategies are simulated under ten
repeated NEDC driving cycles, simulation results show that the Simplified-ECMS-based strategy
can obtain excellent fuel economy, and shorten the calculation time obviously.
An initial function of the equivalent factor is established, then, searching the optimal equivalent
factor converts to searching the optimal correction coefficient. After that, the parameter of the
Simplified-ECMS-based strategy is optimized using the PSO algorithm, and the MAPs of this parameter
under different driving patterns, driving distances and initial SOC are obtained.
Based on above MAPs, the adaptive Simplified-ECMS-based strategy is proposed, and the simulation
is carried out to validate the control effect of this strategy. The simulation results show that the proposed
strategy reduces the fuel consumption by 16.43% under the testing driving cycle, compared to CD-CSbased strategy.
Finally, the Simplified-ECMS-based strategy is validated on a prototype PHEV by a road test.
The test results show that the Simplified-ECMS-based strategy can effectively distribute the engine
torque and motor torque, and can be applied to real time control completely.
Currently, the adaptive Simplified-ECMS-based strategy is only verified through simulations.
The next step is to perform hardware-in-the-loop test or experimental validations.
Author Contributions: Y.Z. wrote the paper and provided algorithms; Y.C. built the simulation model and
completed the simulation for different strategies; G.K. and W.G. analyzed the simulation results; D.Q. provided
suggestions and made revisions to the manuscript.
Funding: This research was funded by the National Natural Science Foundation of China (Grant No. 51665020)
and the state key laboratory of mechanical transmission’s open fund (Grant No. SKLMT-KFKT-201617).
Conflicts of Interest: The authors declare no conflict of interest.

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© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
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