energies
Article
Optimization of Battery Capacity Decay for
Semi-Active Hybrid Energy Storage System
Equipped on Electric City Bus
Xiaogang Wu 1,2, * and Tianze Wang 1
1
2
*
College of Electrical and Electronics Engineering, Harbin University of Science and Technology,
Harbin 150000, China; [email protected]
State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China
Correspondence: [email protected]
Academic Editor: Rui Xiong
Received: 9 May 2017; Accepted: 6 June 2017; Published: 9 June 2017
Abstract: In view of severe changes in temperature during different seasons in cold areas of northern
China, the decay of battery capacity of electric vehicles poses a problem. This paper uses an electric
bus power system with semi-active hybrid energy storage system (HESS) as the research object
and proposes a convex power distribution strategy to optimize the battery current that represents
degradation of battery capacity based on the analysis of semi-empirical LiFePO4 battery life decline
model. Simulation results show that, at a room temperature of 25 ◦ C, during a daily trip organized
by the Harbin City Driving Cycle including four cycle lines and four charging phases, the percentage
of battery degradation was 9.6 × 10−3 %. According to the average temperature of different months
in Harbin, the percentage of battery degradation of the power distribution strategy proposed in this
paper is 3.15% in one year; the electric bus can operate for 6.4 years until its capacity reduces to 80% of
its initial value, and it can operate for 0.51 year more than the rule-based power distribution strategy.
Keywords: electric bus; hybrid energy storage system; energy management; convex optimization;
LiFePO4 battery degradation
1. Introduction
As the sole power source in a traditional electric vehicle, a battery needs to satisfy the power and
energy demands of a bus under different operating conditions. When the battery is repeatedly
over-charged and over-discharged in the long-term operating, the battery degradation will be
accelerated. Furthermore, when the battery is operated at low temperature, its capacity degradation
is more significant. The hybrid energy storage system (HESS) is composed of a battery and super
capacity (SC); the battery provides the required energy and the SC satisfies the instantaneous power
requirements, can effectively inhibit the battery charge and discharge current changes, and optimizes
the working conditions of the energy system [1].
Currently, experts and scholars in the field of electric vehicle hybrid energy storage research
are focused on the modeling and performance of the system components, system parameters
matching, power distribution, etc. In terms of system component modeling and experimentation,
Luo et al. [2] derived and verified a driving cycle life prediction model for LiFePO4 battery based
on the experimental verification of the existing capacity decay model for LiFePO4 under a constant
current charge/discharge condition. Abeywardana et al. [3] proposed a new type of inverter combined
with boost circuits used in HESS, which eliminates the high current injected into the drive motor as
compared to conventional controllers that eliminate the equivalent series resistance of the inverter.
Henson et al. [4] conducted a comparative study of the battery/SC with different depths of discharge
Energies 2017, 10, 792; doi:10.3390/en10060792
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Energies 2017, 10, 792
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(DODs) for minimizing the cost of the HESS. Xiong et al. [5,6] used different algorithms to estimate
the relationship of the voltage to the state-of-charge (SOC) and capacity of lithium ion battery, and
they also validated the accuracy of the method through hardware-in-the-loop experiments. In terms of
system parameter matching and power distribution, Mid-Eum et al. [7] used the convex optimization
method to optimize the power loss and battery power fluctuations considering the real-time dynamic
load to propose a method for calculating the SC reference voltage. Song et al. [8,9] proposed a new
semi-active topology; the operation cost of the HESS, including the battery degradation cost and
electricity cost, is minimized by using the dynamic programming (DP) approach. Further, they studied
four topologies and proposed a rule-based power distribution strategy with four kinds of topologies
based on the optimization results. Hu et al. [10] conducted energy efficiency analysis and component
selection of the plug-in hybrid power system using convex optimization.
In summary, there have been studies related to the parameter matching and system control of
HESS facing battery degradation. However, to the best of our knowledge, there are no published papers
that combine the climatic conditions in northern China and the corresponding urban driving cycle
operating conditions to optimize the functioning of the HESS. In order to attain the full potential of the
HESS to enhance the battery life of electric buses under local conditions, in this study, we considered
the electric bus operating in Harbin, China as an example, and proposed a method to optimize
charge/discharge current of battery through convex optimization considering the average monthly
temperature change in one year.
This paper is organized as follows. In Section 2, we analyze the configuration and working modes
of the HESS. In Section 3, we introduce the models of LiFePO4 batteries, SCs, and vehicle. Section 4
presents a convex optimization power distribution strategy based on the semi-empirical model of
battery degradation. In Section 5, the simulation results and operating years were analyzed and the
results are compared with those of the rule-based strategy.
2. Analysis of Configuration and Working Modes of Hybrid Energy Storage System
As the main energy source of electric vehicles, energy-based batteries have the disadvantages of
low power density and high capacity degradation [11]. In order to satisfy the peak power demand,
the power density of batteries should be sufficiently high; further, considering a battery that is the
only power source of a traditional electric car, in principle, the only way to increase the power density
of the batteries is to increase the number of batteries. Thus, it will result in high cost and high
battery degradation. However, the SCs have characteristics of high power density and low capacity
degradation. A combination of the battery and SC satisfies power and energy requirements, as well as
the different performance requirements of the vehicles.
According to the different connections between the battery, SC, and DC/DC converter, the HESS
can be classified into three major types, namely, fully active, passive, and semi-active, as shown in
Figure 1. In the fully active HESSs, both the battery and SC are connected to the DC bus via a DC/DC
converter; two DC/DC converters can simultaneously control the output power of the battery and the
SC. Further, it has good control margins. However, a fully active HESS has low system efficiency and a
complicated system structure owing to the existence of the two converters; it also increases the system
cost owing to the additional cost of the DC/DC converter. Therefore, the fully active topology can
achieve a good control effect, but at the expense of system efficiency, complexity, and cost [12]. In the
passive topology, the battery and SC are directly connected to the DC bus and the system structure
is simple. Owing to the absence of a converter, the system efficiency of the passive topology is the
highest, whereas it is uncontrollable of the energy flowing [13]. In the semi-active topology, either
the battery or the SC is connected to the DC/DC converter through a unique converter to control the
distribution of the output power of the two energy sources. Since the DC bus is connected to one of
the battery and SC directly, a fast DC/DC converter is required to maintain DC voltage when the load
is changed. However, compared to the fully active and passive topologies, the semi-active topology
solved the problems of low efficiency, high cost, uncontrollability, etc. [14].
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33 of
of 20
20
(a)
(a)
(b)
(b)
(c)
(c)
(d)
(d)
Figure
Figure
1.
The
topology
ofofthe
the
electric
vehicle
HESS:
(a)
fully
active
topology;
(b)
passive
parallel
Figure1.
1.The
Thetopology
topologyof
theelectric
electricvehicle
vehicleHESS:
HESS:(a)
(a)fully
fullyactive
activetopology;
topology;(b)
(b)passive
passiveparallel
parallel
topology;
(c)
semi-active
topology
1;
and
(d)
semi-active
topology
2.
topology;
topology;(c)
(c)semi-active
semi-activetopology
topology1;1;and
and(d)
(d)semi-active
semi-activetopology
topology 2.
2.
The
topology adopted
in this
study is
shown in
Figure 1d.
Semi-active topology
2 employs aa
The
The topology
topologyadopted
adoptedin
in this
this study
study isis shown
shown in
in Figure
Figure 1d.
1d. Semi-active
Semi-activetopology
topology22 employs
employs a
DC/DC
converter
to
decouple
the
SC
from
the
battery/DC
bus.
Furthermore,
the
DC
bus
voltage
is
DC/DC
converter
to
decouple
the
SC
from
the
battery/DC
bus.
Furthermore,
the
DC
bus
DC/DC converter to decouple the SC from the battery/DC bus. Furthermore, the DC busvoltage
voltageisis
equal
to
the
battery
voltage
as
they
are
directly
connected.
Compared
to
the
other
three
topologies,
equal
equalto
tothe
thebattery
batteryvoltage
voltageas
asthey
theyare
aredirectly
directlyconnected.
connected.Compared
Comparedtotothe
theother
otherthree
threetopologies,
topologies,
the
use
of
SC
is
more
flexible
[15],
and
its
working
mode
is
shown
in
Figure
2.
In
the
driving mode,
the
use
of
SC
is
more
flexible
[15],
and
its
working
mode
is
shown
in
Figure
2.
In
the
the use of SC is more flexible [15], and its working mode is shown in Figure 2. In thedriving
drivingmode,
mode,
both
the
battery
and
SC
provide
power
to
the
motor,
and
the
SC
satisfies
the
instantaneous
high
both
the
battery
and
SC
provide
power
to
the
motor,
and
the
SC
satisfies
the
instantaneous
high
both the battery and SC provide power to the motor, and the SC satisfies the instantaneous high power
power
requirements.
In
the
braking
mode,
the
energy
charging
for
the
SC
first
through
the
converter,
power
requirements.
In
the
braking
mode,
the
energy
charging
for
the
SC
first
through
the
converter,
requirements. In the braking mode, the energy charging for the SC first through the converter, then the
then
the
braking
energy
charging
for
battery
when the
SC is
full.
the
conversion
then
the energy
braking
energy for
charging
for the
the
battery
full. For
For
the power
power
conversion
braking
charging
the battery
when
the SCwhen
is full.the
ForSC
theispower
conversion
between
SC and
between
SC
and
DC
bus,
a
fast
three-leg
bidirectional
DC/DC
converter
is
used.
It
can
be
operated
in
between
andthree-leg
DC bus,bidirectional
a fast three-leg
bidirectional
DC/DC
converter
is operated
used. It can
be operated
in
DC bus, SC
a fast
DC/DC
converter
is used.
It can be
in the
interleaved
the
interleaved
manner
and
has
the
merit
of
being
commercially
available
[16,17].
The
degradation
the
interleaved
manner
and
has
the
merit
of
being
commercially
available
[16,17].
The
degradation
manner and has the merit of being commercially available [16,17]. The degradation of the SC is very
of
the
is very
small
its
life
accommodate
millions
cycles.
The
of
the SC
SC
very
small and
and
its working
working
life can
canmillions
accommodate
millions of
of charge/discharge
charge/discharge
cycles.
The
small
andisits
working
life can
accommodate
of charge/discharge
cycles. The power
demand
power
demand
from
the
vehicle
will
be
volatile
during
rapid
acceleration
and
braking;
hence,
the
SC
power
demand
from
the
vehicle
will
be
volatile
during
rapid
acceleration
and
braking;
hence,
the
SC
from the vehicle will be volatile during rapid acceleration and braking; hence, the SC plays the role
plays
the
role
of
power
and
energy
buffer
when
it
is
connected
between
the
battery
and
driving
motor
plays
the
role
of
power
and
energy
buffer
when
it
is
connected
between
the
battery
and
driving
motor
of power and energy buffer when it is connected between the battery and driving motor through the
through
the DC/DC
through
DC/DC converter.
converter.
DC/DCthe
converter.
(a)
(a)
(b)
(b)
Figure
Figure 2.
2. The
The different
different modes
modes of
of operation
operation of
of semi-active
semi-active topology:
topology: (a)
(a) power
power flow
flow based
based on
on driving
driving
Figure 2. The different modes of operation of semi-active topology: (a) power flow based on driving
mode;
and
(b)
power
flow
based
on
braking
mode.
mode;
mode;and
and(b)
(b) power
power flow
flow based
based on
on braking
braking mode.
mode.
3.
3. Power
Power System
System Modeling
Modeling Based
Based on
on HESS
HESS
3. Power System Modeling Based on HESS
3.1.
Battery Model
3.1.
3.1.Battery
BatteryModel
Model
Compared
to the
Nickel Metal
Hydride (Ni-MH)
power battery,
lead-acid power
battery, and
Compared
Comparedto
tothe
theNickel
NickelMetal
MetalHydride
Hydride(Ni-MH)
(Ni-MH)power
powerbattery,
battery,lead-acid
lead-acidpower
powerbattery,
battery,and
and
the
other
driving
batteries
utilized
in
electric
vehicles,
the
LiFePO
4 battery has the characteristic of
the
theother
other driving
driving batteries
batteriesutilized
utilizedin
in electric
electric vehicles,
vehicles, the
the LiFePO
LiFePO44battery
batteryhas
hasthe
thecharacteristic
characteristicof
of
good
battery
service
life
and
high
energy
density.
However,
its
low
temperature
performance
is
not
good
battery
service
life
and
high
energy
density.
However,
its
low
temperature
performance
is
not
good battery service life and high energy density. However, its low temperature performance is not
outstanding
[18]. The
parameters of
the LiFePO
4 cell used in this study are shown in Table 1.
outstanding
outstanding[18].
[18].The
Theparameters
parametersof
ofthe
theLiFePO
LiFePO44cell
cellused
usedininthis
thisstudy
studyare
areshown
shownin
inTable
Table 1.
1.
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Table 1. Basic parameters of the LiFePO4 battery cell.
Table 1. Basic parameters of the LiFePO4 battery cell.
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Item
Value
Item
Value
V
bat_norm
,
nominal
voltage
(V)
3.2
Vbat_norm , nominal voltage (V)
3.2
Qbat
, capacity
180
Qbat
, capacity
(A(A
180
h ) h)
mbat_cell
, cell
(kg)
5.6
mbat_cell
, cellmass
mass
(kg)
5.6
Ibat_max,min
540
Ibat_max,min,,max
maxdis/charge
dis/chargecurrent
current(A)
(A) ±±540
4 of 20
Table 1. Basic parameters of the LiFePO4 battery cell.
Value
Rint
model
shown
Figure3 3was
wasItem
adopted to
to represent
represent
the
Ubat
is
TheThe
Rint
model
shown
ininFigure
adopted
the battery
batterybehavior,
behavior,where
where
Ubat
Vbat_norm, nominal voltage (V)
3.2
thebattery
batteryterminal
terminal voltage
voltage and
isisthe
of of
thethe
battery.
Since
the the
voltage
andand
SOCSOC
are
is the
and RRbat
theresistance
resistance
battery.
Since
voltage
batQ
bat, capacity (Ah)
180
and
in
order
to
adopt
the
subsequent
power
distribution
are strongly
strongly correlated
correlated [19]
[19] in
in Equation
Equationm(1),
(1),
and
in
order
to
adopt
the
subsequent
power
distribution
bat_cell, cell mass (kg)
5.6
strategy,
the one-time
curve
fitting
is
used
to the
findfunctional
the functional
between
the battery
Ibat_max,min
, max
current
(A) relationship
±540 relationship
strategy,
the one-time
curve
fitting
is used
todis/charge
find
between
the battery
open
open
circuit
voltage
V
bat and its SOC, as shown in Figure 4.
circuit voltage V and its SOC, as shown in Figure 4.
Thebat
Rint model shown in Figure 3 was adopted to represent the battery behavior, where Ubat is
Vbatbat is=the
(Vbat1
− Vbat 0 of
)SOC
(1)
the battery terminal voltage and R
resistance
the battery.
the voltage and SOC are
bat + VbatSince
0
Vsubsequent
(1)
bat = (V
bat1
bat0 )SOC
bat +
bat0
strongly correlated [19] in V
Equation
(1),
and−inVorder
to adopt
the
power distribution
where strategy,
Vbat1 is the
open
circuit
voltage
corresponding
to
SOC
bat
=
100%
and
V
bat0
is
the
open
circuit
the one-time curve fitting is used to find the functional relationship between the battery
open
voltage
bat and
its SOC,corresponding
as shown
in Figure
voltage
when
bat =
0.VThe
storage
energy
Ebat
of the
can and
be calculated
as open circuit
where
Vbat1
is circuit
theSOC
open
circuit
voltage
to4.battery
SOCbatpack
= 100%
Vbat0 is the
voltage when SOCbat = 0. The storage V
energy
E − Vbatof0 )SOC
the bat
battery
+ Vbat 0 pack can be calculated as
(1)
bat = (V1
bat1 bat
n bat Q bat (Vbat 2 − Vbat 0 2 )
2
where Vbat1 is the open circuit voltage corresponding to SOCbat = 100% and Vbat0 is the open circuit
E bat =
(2)
1
2
2
) be calculated as
(2)
− Vpack
nbatEQbatbat
Vbat
Ebat =energy
voltage when SOCbat = 0. The storage
of (the
battery
bat0 can
where nbat is the number of battery
cells2 and
Qbat is the
cell capacity.
The battery pack output power
Pbat can be calculated by Equation (3).E = 1 n bat Q bat (Vbat 2 − Vbat 0 2 )
(2)
where nbat is the number of battery cells bat
and2Qbat is the cell capacity. The battery pack output
power
dE
Pbat can bewhere
calculated
by
Equation
(3).
bat
nbat is the number of battery cells and Q
bat is the cell capacity. The battery pack output power
Pbat
=−
(3)
dt
Pbat can be calculated by Equation (3).
dEbat
dE
(3)
Pbat = −resistance
The power consumption on battery internal
Pbat_loss can be calculated by the
Pbat = − bat
(3) following
dt
dt
equation, where Ibat is the current flowing through the battery cell. The charge resistance and
The power consumption on battery internal resistance Pbat_loss can be calculated by the following
can be calculated
bytemperature
the following of 25 °C,
The power consumption
on battery
internal
resistance
Pbat_loss SOCs
discharge resistance
of the cell are
measured
under
different
at a room
equation, where
Ibatwhere
is theIbatcurrent
flowing
through
the battery
cell.cell.
TheThe
charge
resistance
equation,
is the current
flowing
through
the battery
charge
resistance and
and discharge
as shown
in Figure
5.
resistance
of the cellunder
are measured
under
different
at temperature
a room temperature
resistance discharge
of the cell
are measured
different
SOCs
at aSOCs
room
of 25of◦25
C,°C,
as shown in
2
as
shown
in
Figure
5.
P
=
n
I
R
(4)
bat _ loss
bat bat
bat
Figure 5.
2
2
Pbat _ loss== n
n bat
R batRbat
Pbat_loss
Ibat
(4)
(4)
bat I bat
R
I bat
Rbatbat I bat
UUbat
bat
VbatVbat
Figure
3. Rint
model of
the
LiFePO
4 battery.
Figure
3. 3.
Rint
model
the
LiFePO
Figure
Rint
modelofof
the
LiFePO
battery.
4 4battery.
3.55
OCV of battery
OCV
of fitting
OCV
of battery
3.55
3.50
OCV of fitting
OCV of battery (V)
OCV of battery (V)
3.50
3.45
3.453.40
3.403.35
3.30
3.35
3.25
3.30
3.20
0
3.25
10
20
30
40
50
60
70
80
90
100
SOC of battery (%)
3.20
Figure
4. The relationship between Vbat and SOC.
0
10
20
30
40
50
60
70
80
90
100
SOC of battery (%)
Figure
4. The
relationship
betweenVVbatand
andSOC.
SOC.
Figure
4. The
relationship
between
bat
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discharge resistance
charge resistance
discharge resistance
charge resistance
7.0
discharge resistance (mΩ)
discharge resistance (mΩ)
7.0
6.5
6.5
6.0
6.0
5.5
5.5
5.0
5.0
4.5
4.5
0
0
10
10
20
20
30
30
40
50
60
SOC
of50battery
(%)
40
60
70
70
80
80
90
90
100
100
SOC of battery (%)
◦
Figure
ofof
the
LiFePO
atatroom
4 cell
Figure5.5.Charge
Chargeand
anddischarge
dischargeresistances
resistances
the
LiFePO
4 cell
roomtemperature
temperatureofof2525C.
°C.
Figure 5. Charge and discharge resistances of the LiFePO4 cell at room temperature of 25 °C.
3.2.
3.2.Super
SuperCapacitor
CapacitorModel
Model
3.2. Super Capacitor Model
The
purpose
of using
the SCthe
is toSC
protect
batterythe
more
effectively;
the characteristics
Themain
main
purpose
of using
is tothe
protect
battery
moreit has
effectively;
it has the
Thecharge
main and
purpose
of using
SC
is efficiency,
to protect
the service
batterylow
more
it has the
ofcharacteristics
high
discharge
efficiency,
long
service
life,long
and
better
temperature
performance.
of
high
charge
and the
discharge
life,
andeffectively;
better low
temperature
characteristics
of
high
andiscircuit
discharge
long
service
and
better
temperature
The
SC equivalent
circuit
model
shown
in efficiency,
Figure
6, where
Rcap 6,
is life,
the equivalent
series
resistance,
performance.
The
SC charge
equivalent
model
is shown
in Figure
where
Rcap
is thelow
equivalent
series
The
SC
equivalent
circuit
model
is
shown
in
Figure
6,
where
R
cap
is
the
equivalent
series
Iperformance.
is
the
current
flowing
through
the
SC
cell,
C
is
the
capacitance
of
the
SC
cell,
and
V
iscap
resistance,
I
cap
is
the
current
flowing
through
the
SC
cell,
C
cap
is
the
capacitance
of
the
SC
cell,
and
cap
cap
cap V
®®
resistance,
I
cap
is
the
current
flowing
through
the
SC
cell,
C
cap
is
the
capacitance
of
the
SC
cell,
and
V
cap
the
Open
Circuit
Voltage
(OCV)
of the
SC SC
cell.
In In
this
study,
wewe
use
The
is the
Open
Circuit
Voltage
(OCV)
of the
cell.
this
study,
use
TheMaxwell
MaxwellTechnologies
Technologies
®
iscompany’s
the Opensuper
Circuit
Voltageand
(OCV)
ofparameters
the SC cell.
this
we
use in
The
Maxwell
Technologies
company’s
ofofIn
the
SC
cell
listed
2.2.Since
the
supercapacity
capacity
andthe
theparameters
the
SCstudy,
cellare
are
listed
inTable
Table
Since
theSC
SCcan
can
company’s
superofcapacity
and the parameters
ofarticle
the SC
cell are
listed
in Table
2. Sinceof
the
SC
can
achieve
cycles,
ignores
the
capacity
degradation
SC
inin
achievemillions
millions
ofcharge/discharge
charge/discharge
cycles,this
this
article
ignores
the
capacity
degradation
ofthe
the
SC
achieve
millions
of
charge/discharge
cycles,
thismethod
article
ignores
the
of
the
SC its
in
the
process
[20].
The
open
circuit
voltage
is
used
to
express
thedegradation
relationship
between
theentire
entire
process
[20].
The
open
circuit
voltage
method
is used
tocapacity
express
the relationship
between
the
process
[20].
The
open
open
circuit
voltage
Vcap
and
SOCcircuit
itsentire
open
circuit
voltage
V
cap
and
SOC
cap . cap.voltage method is used to express the relationship between
its open circuit voltage Vcap and SOCcap.
V = Vcap1SOC cap
(5)
Vcap cap
= Vcap1 SOCcap
(5)
Vcap = Vcap1SOC cap
(5)
where Vcap1 is the open circuit voltage corresponding to SOCcap = 100%. As shown in Equation (6), Ecap
where
Vcap1
theopen
opencircuit
circuitvoltage
voltagecorresponding
corresponding
SOC
in Equation
cap = 100%. As shown
cap1isisthe
where
toto
SOC
cap = 100%. As shown
Equation
(6), E(6),
cap
is theV
energy
released
when the
SC is discharged from
the fully-charged
state toin
SOC
cap.
E
the energy
released
theisSC
is discharged
the fully-charged
to SOC
cap .
iscap
theisenergy
released
whenwhen
the SC
discharged
fromfrom
the fully-charged
statestate
to SOC
cap.
1
E cap = n cap C cap Vcap12 (1 − SOC cap )
(6)
1 12
22 (1 − SOC
EcapE=
n
C
V
)
(6)
cap
cap
cap
=
n
C
V
(1
−
SOC
)
cap1
(6)
cap
cap
2 2 cap cap cap1
where ncap is the number of SC cells. The output power of the SCs Pcap is the first derivative of its
where ncap is the number of SC cells. The output power of the SCs Pcap is the first derivative of its
is the
numberinof
SC cells.(7).
The output power of the SCs Pcap is the first derivative of its
where
ncap
release
time,
as shown
Equation
release time, as shown in Equation (7).
release time, as shown in Equation (7).
dE cap
Pcap = −dEcap
(7)
dE
dt
cap
Pcap
(7)
Pcap== −
− dt
(7)
dt
canbe
becalculated
calculatedby
byEquation
Equation(8),
(8),
Thepower
powerconsumption
consumptionononSCs
SCsinternal
internalresistance
resistance
Pcap_loss can
The
Pcap_loss
TheIcap
power
consumption
on through
SCs internal
resistance
Pcap_loss can be calculated by Equation (8),
where
thecurrent
currentflowing
flowing
theSC
SC
cell.
where
Icap isisthe
through the
cell.
where Icap is the current flowing through the SC cell.
(8)
Pcap_ loss = n cap I cap 2 R cap
2
2
Pcap_loss
Icap Rcap
(8)
(8)
Pcap_ loss== nncap
cap I cap R cap
Ccap
Ccap
Rcap I cap
Rcap I cap
Vcap
Vcap
Figure 6. Equivalent circuit modelof the SC.
Figure 6. Equivalent circuit modelof the SC.
Energies 2017, 10, 792
6 of 20
Table 2. Basic parameters of the SC cell.
Item
Value
Vcap_norm , nominal voltage (V)
Ccap , capacity (F)
Rcap , resistance (Ω)
mcap_cell , cell mass (kg)
Icap_max,min, max dis/charge current (A)
2.7
2 × 103
3.5 × 10−4
0.36
±1.6 × 103
3.3. Battery Degradation Model
The high cost of lithium-ion battery is one of the main factors restricting the development of
electric vehicles. The conversion cost of electric vehicles can be reduced by extending the lifespan
of lithium-ion battery. In recent years, researchers have made significant efforts to calculate and
predict the degradation of the battery [21–23]. In Ref. [21], the authors conducted a series of
charge/discharge experiments through constant current-constant voltage (CC-CV) and used a scanning
electron microscope (SEM) to characterize the structure of cathode, anode, and separator in Li-ion
batteries. The results have shown that the capacity fading of batteries can be attributed primarily to
the loss of active Li+ and the losses of cathode and anode active materials. In Ref. [22], a large number
of charge and discharge experiments were carried out on LiFePO4 batteries, and the semi-empirical
formula of battery decay percentage and ambient temperature, charge/discharge rate, and cycling
time were obtained. In Ref. [23], the effect of parameters such as the end of charge voltage, DOD,
film resistance, exchange current density, and over voltage of the parasitic reaction on the capacity
fading and battery performance were studied. However, in summary, it is very difficult to calibrate
and parameterize the degree of battery degradation in an electric vehicle during actual operation.
Therefore, we considered many factors that affect battery degradation and adopted the semi-empirical
model used in Ref. [24]. The semi-empirical formula is as shown in Equation (9).
Qloss = B · e−(
E+a·n )
RT
( Ah ) x
(9)
where Qloss is the percentage of battery degradation, E is the activation energy, R is the gas constant,
T is the absolute temperature, Ah is the Ah -throughput, and B, a, and x are constants. The percentage
of discrete battery degradation at different temperatures can be calculated using Equation (10).
Qloss_k+1 − Qloss_k = 9.78 × 10−4 e
−1516·n
−( 0.849R15162
)
(|285.75−T|+265)
· ∆Ah · Qloss_k −0.1779
(10)
where Qloss_k and Qloss_k+1 are the percentages of battery capacity decay degradation for the steps k
and k + 1, respectively. ∆Ah is the Ah -throughput from tk to tk+1 , and it satisfies Equation (11), where
∆t is the sampling time.
∆Ah =
1
· |I | · ∆t
3600 bat
(11)
3.4. Vehicle Model
The vehicle power system model can be used to obtain the power demand of the vehicle at
different times during the operation. The power demand of a vehicle should be the output power of
the driving wheel for an electric bus with semi-active HESS. The output power of the driving wheel is
the product of the demand torque and the required angular velocity, as shown in Equation (12).
Pdem = Tdem ωdem ηT −k
(12)
where ηT is transmission system efficiency; and k is the power factor: k = 1 when the bus is in the
driving state and k = −1 when the bus is in the braking state. Tdem and ωdem are the demand torque and
Energies 2017, 10, 792
7 of 20
the demand angular velocity, respectively, which can be calculated as shown in Equation (13). The basic
parameters involved in Equation (13) are listed in Table 3. In Table 3, aω is angular acceleration, and
the total mass mbus is equal to the sum of the body quality, passenger quality, batteries, and SCs mass
(15% additional mass).
i
h

Jaω
1
2 ) · Rw

+
ρAc
v
T
=
m
gc
cos
(
θ
)
+
m
a
+
m
g
sin
(
θ
))
+
(
(

r
d
dem
bus
bus
bus
R
2
gfinal

w


v·gfinal

 ωdem = Rw
(13)
Among :




mbus = mveh + mp + 1.15(nbat mbat_cell + ncap mcap_cell )



a
a = dv
dt ; aω = Rw
In the optimization process, the minimal mileage L of more than 50 km should be considered,
obtained at a constant cruising speed v0 (50 km/h) on a flat road [25]. Accordingly, we can deduce the
following inequality constraints.
nbat ≥
1
L
2
ρAcd v0 + mbus gcr
2
Vbat_norm Qbat ηT
(14)
We assume that the maximum required power in the drive mode and brake mode is provided by
the SCs (SCs output power in driving mode, and SCs absorb power in braking mode). The following
inequality constraints should be satisfied when selecting the number of SCs.
max{|Pdem |}
ncap ≥ Icap_max Vcap_norm
(15)
Table 3. Basic parameters of the vehicle.
Item
Value
mveh , body quality
mp , passenger quality (F)
cr , rolling resistance coefficient
ρ, air density (kg/m3 )
J, total inertia (kgm2 )
A, frontal area (m2 )
cd , aerodynamic drag coefficient
Rw , wheel radius (m)
gfinal ,final gear ratio
ηDC , DC/DC converter efficiency
ηT , powertrain efficiency
1.3 × 104
3 × 103
0.007
1.18
143.41
7.83
0.75
0.51
6.2
0.9
0.9
4. Convex Optimal Control Strategy Based on the Battery Degradation
Through the driving cycle, we can calculate the power demand of the bus at every step. In the
driving mode, the required power Pdem should be the output power of the drive motor on its output
shaft. The electrical power output on the DC bus is equal to the motor output power plus the motor
power loss, which is obtained by the fitting. The electrical power output on the DC bus at this time
is the total power to be satisfied by the batteries and the SCs (considering the efficiency of DC/DC
converter).
Assuming that the SCs are in the same energy storage state at the beginning and end of the driving
cycle, the degradation percentage Qloss_sum of the battery is calculated using the following equation.
N
Qloss_sum =
∑ Qloss (k)
k=1
(16)
Energies 2017, 10, 792
8 of 20
Energies 2017, 10, 792
8 of 20
N
Qloss _ sum =  Qloss (k)
(16)
In order to reduce the computation time ink =the
convex optimization, as shown in Figure 7,
1
the relationship between the battery current Ibat and the battery degradation percentage Qloss is
In order to reduce the computation time in the convex optimization, as shown in Figure 7, the
determined at room temperature 25 ◦ C based on Equation (9). Irrespective of the braking or driving
relationship between the battery current Ibat and the battery degradation percentage Qloss is
modes, Qloss always increases as the charge or discharge current Ibat increases. Hence, the optimization
determined
at room temperature 25 °C based on Equation (9). Irrespective of the braking or driving
of the entire driving cycle of battery degradation can be equivalent to optimizing the entire driving
modes, Qloss always increases as the charge or discharge current Ibat increases. Hence, the optimization
cycle of the battery current in the absolute value. There is the following relationship:
of the entire driving cycle of battery degradation can be equivalent to optimizing the entire driving
(
(
)
cycle of the battery current in the absolute
value.)There is the following
relationship:
N
N
Qloss (k) ⇔ Minimize ∑ |Ibat (k)|
∑
1



Minimizek=
I 1 (k) 
  Q (k)  ⇔ Minimize  k=




Minimize
N
(17)
(17)
N
loss
bat
k =1
k =1
Therefore, as shown in Equation (18), the equivalent optimization target for the purpose of
Therefore,
as shown
in Equation
(18),
the equivalent
optimization
target for
purpose of
optimizing
the battery
degradation
could
be obtained.
According
to the constraints
of the
the optimization
optimizing
theconvex
batteryoptimization
degradation[26],
could
be obtained.
According
to the constraints
the
target in the
Equation
(18) satisfies
the requirement
that the of
convex
optimization
target
in
the
convex
optimization
[26],
Equation
(18)
satisfies
the
requirement
that
the
optimization must be a convex function or an affine function for the objective function.
convex optimization must be a convex function or an affine function for the objective function.
(
)
N
N
∑

J=
Ibat
J =Minimize
Minimize 
I|bat
(k)(k)|
k
=
1
 k =1

Qloss of braking
Qloss of driving
Qloss of braking (×10-7%)
3.5
8
7
3.0
6
2.5
5
2.0
4
1.5
3
1.0
2
0.5
1
0.0
-300
-200
-100
0
100
200
300
400
Qloss of driving (×10-6%)
4.0
(18)
(18)
0
500
Current of battery (A)
Figure
Figure7.7. The
Therelationship
relationshipbetween
between battery
battery charge/discharge
charge/dischargecurrent
currentIbat
Ibatand
andbattery
batterydegradation
degradation
loss.
percentage
Q
percentage Q .
loss
The implementation process of the convex optimization strategy used in this study is shown in
The implementation process of the convex optimization strategy used in this study is shown
Figure 8. In order to satisfy the constraints on the number of battery cells and SC cells in Equations
in Figure 8. In order to satisfy the constraints on the number of battery cells and SC cells in
(14) and (15), the number of selected battery and SC cells is nbat = 120 and ncap = 240, respectively. The
Equations (14) and (15), the number of selected battery and SC cells is n = 120 and ncap = 240,
battery pack and SC pack in the HESS are all grouped by n series and one bat
parallel connection, and
respectively. The battery pack and SC pack in the HESS are all grouped by n series and one parallel
the unbalance between the cells is ignored [27]. As the energy source of the vehicle, the LiFePO4
connection, and the unbalance between the cells is ignored [27]. As the energy source of the vehicle, the
battery pack is not only for the drive motor to provide energy, but also for the super capacitor when
LiFePO battery pack is not only for the drive motor to provide energy, but also for the super capacitor
SOCcap is4 low. The SC pack is between the LiFePO4 battery pack and the drive motor, acting as an
when SOCcap is low. The SC pack is between the LiFePO4 battery pack and the drive motor, acting as
energy and power buffer, and absorbing the braking energy from the drive motor during braking.
an energy and power buffer, and absorbing the braking energy from the drive motor during braking.
According to the output voltage changes of the battery and the SC cell, we can constrain the
According to the output voltage changes of the battery and the SC cell, we can constrain the
output energy range of the battery pack and capacitor group,
output energy range of the battery pack and capacitor group,
n Q

(
(k) ∈ bat bat ([ Vbat _ min22 , Vbat _ max 2 ] 2− Vbat 0 2 ) 2
 E
Ebat
(kbat) ∈ nbat2Qbat
2 ([Vbat_min , Vbat_max ] − Vbat0 )
(19)

(19)
n cap
C
ncap
Ccap
2
2
22
2
2
 E(cap
Ecap
k)(k)
∈ ∈ 2 cap([V
, Vcap_max
]−V
)
([V
cap_min
cap_ min , Vcap_
max ] − Vcap0 )cap0

2
Energies 2017, 10, 792
9 of 20
where Vbat_min , Vbat_max, Vcap_min , and Vcap_max are the maximum and minimum voltages
corresponding to the battery and the SOC of the SC, given by Equation (20).
(
Energies 2017, 10, 792
Vbat_min,max = SOCbat_min,max (Vbat1 − Vbat0 ) + Vbat0
Vcap_min,max = SOCSC_min,max VSC1
9 of 20
(20)
, Vbat_max,
Vcap_min
, and V
the maximum
minimum
corresponding
Thewhere
rangeVbat_min
of the
output
power
ofcap_max
the are
battery
and SCand
pack
can bevoltages
limited
according to the
to the battery and the SOC of the SC, given by Equation (20).
maximum charge/discharge current of the battery and SC cell.
(Vbat _ min,max = SOCbat _ min,max (Vbat1 − Vbat 0 ) + Vbat 0

SOCSC ,_ min,max
VSC1 ]nbat Vbat
Pcap_
∈ [I=bat_min
Ibat_max
 V
batmin,max
Pcap ∈ [Icap_min , Icap_max ]ncap Vcap
(20)
(21)
The range of the output power of the battery and SC pack can be limited according to the
maximum charge/discharge current of the battery and SC cell.
The power consumed on the battery pack and the SC pack internal resistance can be calculated
 Pbat ∈ [I bat _ min , I bat _ max ]n bat Vbat
from Equation (22).
( 
(21)
2 V
Pcap ∈ [I cap_
I cap_I max ]n
Pbat_loss
=minn,bat
bat Rcapbatcap
(22)
2
Pcap_loss
ncap
Rcap internal resistance can be calculated
The power consumed on the battery
pack=and
theIcap
SC pack
from Equation (22).
where Ibat and Icap are the currents flowing through the battery and the SC cell, respectively. Both Ibat
2
and Icap have the following constraints. Pbat _ loss = n bat I bat R bat
(

2
 Pcap_ loss = n cap I cap R cap
(22)
Ibat ∈ [Ibat_min , Ibat_max ]
where Ibat and Icap are the currents flowing through the battery and the SC cell, respectively. Both Ibat
Icap ∈ [Icap_min , Icap_max ]
and Icap have the following constraints.
(23)
∈ [I bat _ min , I batto
]
_ max
For the battery pack and the SC pack, itIisbat necessary
satisfy
the total power demand in different
(23)

I
∈
[I
,
I
]

cap
cap_
min
cap_
max
cases, by satisfying the following equation constraints.
( pack and the SC pack, it is necessary to satisfy the total power demand in
For the battery
Pcapopen
ηDCequation
= Pemloss
+ Pdem /ηT Pdem ≥ 0
batopen +the
different cases, byPsatisfying
following
constraints.
Pbatopen +PPcapopen
/η η =
Pemloss + PdemPηT ≥ 0Pdem < 0
 batopen + PcapopenDC
DC = Pemloss + Pdem / ηT
dem

Pbatopen + Pcapopen / ηDC = Pemloss + PdemηT
Pdem < 0
(24)
(24)
where Pbatopen and Pcapopen are the output powers of the battery pack and SC pack, respectively. Pemloss
where
Pbatopenloss
and P
capopen
arebe
theinterpolated
output powersby
ofthe
the motor
battery pack
andloss
SC pack,
respectively. Pemloss
is the motor
power
and
can
power
curve.
is
the
motor
power
loss
and
can
be
interpolated
by
the
motor
power
loss
curve.
In this study, we use Equation (18) as an optimization target, and the battery pack energy Eb , SC
In this study, we use Equation (18) as an optimization target, and the battery pack energy Eb, SC
pack energy Ecap , battery pack port output power Pbatopen , and SC pack port output power Pcapopen
pack energy Ecap, battery pack port output power Pbatopen, and SC pack port output power Pcapopen as
as the convex
optimization
variables.
powerPbat
Pbat
, SC
pack
power
cap , battery
the convex
optimization
variables.The
Thebattery
battery pack
pack power
, SC
pack
power
Pcap, P
battery
pack pack
power loss
P
,
and
SC
pack
power
loss
P
are
used
as
the
equation
constraints
of
the convex
bat_loss
power
loss Pbat_loss, and SC pack power loss cap_loss
Pcap_loss are used as the equation constraints of the convex
optimization.
The overall
optimization
function
in Table
Table4.4.
optimization.
The overall
optimization
functionisisgiven
given in
The implementation
processof
of the
the convex
strategy.
FigureFigure
8. The8.implementation
process
convexoptimization
optimization
strategy.
Energies 2017, 10, 792
10 of 20
Table 4. Convex optimization function of hybrid energy storage system
Table 4. Convex optimization function of hybrid energy storage system
Variables Ebat (N+ 1), Ecap (N+ 1), Pbatopen (N), Pcapopen (N)
Ebat (NN + 1), Ecap (N + 1), Pbatopen (N), Pcapopen (N)
Variables
I bat (k)
Minimize
N k =1
Minimize
∑ |Ibat (k)|

k=1  P
(k) + P
(k)η =P
(k) + P
(k) / η
P
(k) ≥ 0
capopen
DC
emloss
dem
T
dem
 batopen
η(TkP)/η
≥ 0(k) ≥ 0
(k)(k/ )ηηDC
(k) (+kP
(k)++PP
=emloss
Pemloss
) dem
+ P(k)
Pdem
capopen
dem
DC=P
batopen (k)
capopen
demT(k)
PPbatopen
2 ) /η
2 (k)η P
P
(
k
)
+
P
(
k
=
P
(
k
)
+
P
capopen
emloss
dem
DC
T dem (k) ≥ 0
Pbatbatopen
_ loss (k) = n bat I bat 0 (k) R bat ; Pcap_ loss = n cap I cap0 (k) R cap
2
(k)2 R ; P
Pbat_loss
(
k
)
=
n
I
=
n
I
(
k
)
R
Pbat (k) = −ΔEbat
−ΔE cap (k) cap cap0
cap
bat0 Pcap (k)
bat = cap_loss
bat (k);
2 − ∆E
Pbat
=∈
−([
∆E
(k);2P, V
k) Q / 2
cap (k) =
cap2()n
]
−
E (batk)(k)
Vbat
V
bat _ min
bat _ max
bat 0
bat bat
Subject to Ebat (k) ∈ ([Vbat_min 2 ,2Vbat_max 22] − Vbat0 22)nbat Qbat /2
Subject to
E cap (k) ∈ ([ Vcap_ min2 , Vcap_ max 2] − Vcap0 2)n cap C cap / 2
Ecap (k) ∈ ([Vcap_min , Vcap_max ] − Vcap0 )ncap Ccap /2
P (k) ∈[ I bat _ min , I bat _max ]n bat Vbat (k)
Pbatbat
(k) ∈ [I
,I
]n Vbat (k)
P (k) ∈[bat_min
I cap_ min ,bat_max
I cap_max ]nbat
Vcap (k)
Pcapcap
(k) ∈ [Icap_min
, Icap_max
]ncap
cap Vcap (k)
∈
I
[I
,
I
];
I
∈
[I
bat _ max]; I cap∈ [I cap_ min ,, II cap_ max ]]
bat _ min
Ibatbat∈ [Ibat_min
, Ibat_max
cap
cap_min cap_max
∀k ∀
∈k{∈
0, {. 0,...,
. . , NΝ}}
According to
the description
description of
the convex
convex optimization
optimization problem
problem in
Ref. [26],
[26], the
the constraint
constraint
According
to the
of the
in Ref.
conditions
in
Table
4
are
convex
or
affine
functions;
the
entire
convex
optimization
problem
conditions in Table 4 are convex or affine functions; the entire convex optimization problem satisfies
satisfies
the
convex
optimization
requirement,
and
the
convex
optimization
implementation
flow
is
shown
in
the convex optimization requirement, and the convex optimization implementation flow is shown in
Figure
9.
Figure 9.
Optimize variables：Ebat (N + 1), Ecap (N + 1),
Pbatopen (N), Pcapopen (N)
Equality constraints：Pbat , Pcap ,
Pbat _ loss , Pcap_ loss，
Pbatopen (k) + Pcapopen (k)ηDC ,
Pbatopen (k) + Pcapopen (k) / ηDC ,
N

Minimize  I bat (k) 
 k =1

Inequality constraints：
Pbat , Pcap , E bat , E cap
Figure 9.
9. Convex
Convex optimization
optimization implementation
implementation flow.
flow.
Figure
5. Simulation and Results Analysis
In order
thethe
effectiveness
of the
optimization
proposed
in this study,
westudy,
compared
ordertotoverify
verify
effectiveness
ofHESS
the HESS
optimization
proposed
in this
we
its
performance
with
that
of
the
rule-based
power
distribution
strategy
under
the
Harbin
city
driving
compared its performance with that of the rule-based power distribution strategy under the Harbin
cycle
[28]. The
Harbin
cycledriving
and thecycle
power
is shown
in Figure
10.inThe
convex
city driving
cycle
[28]. city
The driving
Harbin city
anddemand
the power
demand
is shown
Figure
10.
The convex optimization result is shown in Figure 11. It can be observed that the battery only
Energies 2017, 10, 792
11 of 20
optimization result is shown in Figure 11. It can be observed that the battery only provides a small range
of demand for power fluctuations, whereas the SC satisfies instantaneous high power requirements.
Energies
2017,
10,10,
792
11 11
of of
20together
When the
required
power
is greater than a certain threshold, the SC and the battery pack
Energies
2017,
792
20
provide the power required. However, owing to the presence of DC/DC converter efficiency and
provides
a small
range
ofof
demand
forfor
power
fluctuations,
whereas
the
SCSC
satisfies
instantaneous
high
provides
a small
range
demand
power
fluctuations,
whereas
the
satisfies
instantaneous
high
powertrain
efficiency,
the When
sum of
the
powerpower
of theisbattery
packa and
thethreshold,
SC pack the
is much
greater
than
power
requirements.
the
required
greater
than
SCSC
and
the
power
requirements.
When
the
required
power is
greater
than certain
a certain
threshold, the
and
the
the power
demand.
Furthermore,
the
same
asrequired.
the
result
of two owing
efficiency
effects,
in the
braking
battery
pack
the
power
However,
ofofDC/DC
battery
packtogether
togetherprovide
provide
the
power
required.
However,
owingtotothe
thepresence
presence
DC/DC mode,
efficiency
and
powertrain
efficiency,
the
sum
of
the
power
of
the
battery
pack
and
the
SCSC only
the SC converter
cannot
recover
all
the
braking
energy.
In
addition,
as
shown
in
Figure
11b,
the
converter efficiency and powertrain efficiency, the sum of the power of the battery pack and battery
the
pack
is
much
greater
than
the
power
demand.
Furthermore,
the
same
as
the
result
of
two
efficiency
pack
is
much
greater
than
the
power
demand.
Furthermore,
the
same
as
the
result
of
two
efficiency
provides a small demand for power and the SC satisfies instantaneous high power requirements;
inin
the
braking
the
SCSC
cannot
recover
allall
the
braking
energy.
InIn
addition,
asas
shown
inin
effects,
the
braking
mode,
the
cannot
recover
the
braking
energy.
addition,
shown
this caneffects,
be reflected
in themode,
relationship
between
power
demand
and SC
power.
When
the
power
Figure
11b,
the
battery
only
provides
a small
demand
forfor
power
and
the
SCSC
satisfies
instantaneous
Figure
11b,
the
battery
only
provides
a small
demand
power
and
the
satisfies
instantaneous
demand fluctuates in the range of 0 kW to 20 kW, the SC does not output power. This part of the
high
power
requirements;
this
can
bebe
reflected
inin
the
relationship
between
power
demand
and
SCSC
high
power
requirements;
this
can
reflected
the
relationship
between
power
demand
and
power power.
ispower.
borne
by the
the
battery
and fluctuates
when
the
power
demand
fluctuates
inSCSC
the
range
of
20 kW to
When
power
demand
inin
the
range
ofof
0 kW
to
2020
kW,
the
does
not
output
When
the
power
demand
fluctuates
the
range
0 kW
to
kW,
the
does
not
output
the highest
power
demand,
the
SC
satisfies
the
power
demand.
Owing
to
the
efficiency
of
DC/DC
power.
This
part
of
the
power
is
borne
by
the
battery
and
when
the
power
demand
fluctuates
in
the
power. This part of the power is borne by the battery and when the power demand fluctuates in the
range
of
20
kW
to
the
highest
power
demand,
the
SC
satisfies
the
power
demand.
Owing
to
the
converter
and
the
efficiency
of
the
powertrain,
the
slope
of
the
fitted
line
k
is
slightly
greater
range of 20 kW to the highest power demand, the SC satisfies the power demand. Owing to the than 1
efficiency
ofof
DC/DC
converter
and
the
efficiency
ofof
the
powertrain,
the
slope
of
the
fitted
line
kk
isnegative
DC/DC
and
the
efficiency
the
powertrain,
the
slope
of
the
fitted
line
is
when theefficiency
demand
power
isconverter
greater
than
20
kW. When
the
power demand
fluctuates
in
the
slightly
greater
than
1 when
the
demand
power
is is
greater
than
2020
kW.
When
the
power
demand
slightly
greater
than
1
when
the
demand
power
greater
than
kW.
When
the
power
demand
range, the SC absorbs the braking energy, and the slope of the fitting line k is less than 1 owing to
fluctuates
inin
the
negative
range,
the
SCSC
absorbs
the
braking
energy,
and
the
slope
ofof
the
fitting
line
kk
fluctuates
the
negative
range,
the
absorbs
the
braking
energy,
and
the
slope
the
fitting
line
the DC/DC
converter
efficiency
andconverter
the efficiency
of and
the the
powertrain.
The
entire convex
optimization
is is
less
than
1 owing
toto
the
DC/DC
efficiency
efficiency
ofof
the
powertrain.
The
entire
less
than
1 owing
the
DC/DC
converter
efficiency
and
the
efficiency
the
powertrain.
The
entire
7 J, i.e., approximately 3.70
processconvex
consumes
1.33 × 10
Since
the optimization
target
isthe
absolute
7 J,
7 kWh.
process
3.70
Since
convexoptimization
optimization
processconsumes
consumes1.33
1.33× ×1010
J,i.e.,
i.e.,approximately
approximately
3.70kWh.
kWh.
Sincethe
value ofoptimization
the
battery
current,
while
the
terminal
voltage
drop
of
the
battery
pack
is
very
small
target
is
absolute
value
of
the
battery
current,
while
the
terminal
voltage
drop
of
the
optimization target is absolute value of the battery current, while the terminal voltage drop of the in one
battery
pack
is is
very
small
one
driving
cycle.
optimization
goal
also
has
a significant
driving cycle.
Therefore,
the in
optimization
goalTherefore,
also
hasthe
athe
significant
role
inalso
optimizing
the battery
battery
pack
very
small
in
one
driving
cycle.
Therefore,
optimization
goal
has
a significant
role
in
optimizing
the
battery
energy
consumption.
role in optimizing the battery energy consumption.
energy consumption.
6 6
50 50
5 5
40 40
4 4
30 30
3 3
20 20
2 2
10 10
1 1
Speed (km/h)
Speed (km/h)
Distance (km)
Distance (km)
60 60
0 0
0 0
200200
400400
600600
800800
1000
1000
1200
1200
0 0
1400
1400
200200
100100
100100
Pdem (kW)
Pdem (kW)
200200
0 0
0 0
-100
-100
-100
-100
-200
-200
0 0
200200
400400
600600
800800
1000
1000
1200
1200
-200
-200
1400
1400
Time
(s)(s)
Time
Figure
10.10.
Harbin
city
driving
cycle
and
the
power
demand.
Figure
Harbin
city
driving
cycle
and
thethe
power
demand.
Figure
10.
Harbin
city
driving
cycle
and
power
demand.
175175
150150
Power
of battery
Power
of battery
Power
of SC
Power
of SC
Power
demand
Power demand
Power (kW)
Power (kW)
125125
100100
75 75
50 50
25 25
0 0
-25-25
-50-50
-75-75
-100
-100
-125
-125
-150
-150
0 0
200200
400400
600600
800800 1000
1000 1200
1200 1400
1400
Time
(s)(s)
Time
(a)(a)
Figure 11. Cont.
Energies 2017, 10, 792
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12 of 20
Energies 2017, 10, 792
12 of 20
150
150
100
Pcap (kW)
Pcap (kW)
100 50
k ∈ (1,1 + δ)
20kW
50 0
k ∈ (1,1 + δ)
20kW
0 -50
k ∈ (1 − δ,1)
-50-100
k ∈ (1 − δ,1)
-100-150
-150
-100
-50
0
50
100
150
200
100
150
200
Pdem (kW)
-150
-150
-100
(b)
-50
0
50
Pdemdistribution
(kW)
Figure 11. Convex optimization results: (a) power
results based on convex optimization;
Figure 11. Convex optimization results: (a) power(b)
distribution results based on convex optimization;
and (b) the relationship between power demand and SC power.
and (b) the relationship between power demand and SC power.
Figure 11. Convex optimization results: (a) power distribution results based on convex optimization;
Figure 12 shows the battery current and battery degradation percent at a room temperature of
and (b) the relationship between power demand and SC power.
Ibat (A)
25 °C based on convex optimization. In the latter part of the driving cycle, the
Figure
12 shows the battery current and battery degradation percent at a room temperature of
acceleration/deceleration of the vehicle is violent; hence, the battery current undergoes greater
◦
Figure
12 shows
the battery current
and battery
at aacceleration/deceleration
room temperature of
25 C based
on convex
optimization.
In the latter
part ofdegradation
the driving percent
cycle, the
fluctuations. However, the maximum value of the battery current does not exceed 200 A. The battery
25
°C
based
on
convex
optimization.
In
the
latter
part
of
the
driving cycle,However,
the
of the vehicle
is violent;
hence,
the battery
undergoes
fluctuations.
runs within
1C discharge
magnification
ratecurrent
altogether.
In addition,greater
according
to the relationship
acceleration/deceleration
of
the vehicle
is violent;
hence, the 200
battery
undergoes
the maximum
of thecharge/discharge
battery
current
doesIbatnot
A. current
The battery
runsQgreater
within
1C
betweenvalue
the battery
current
andexceed
the battery degradation
percentage
loss in
fluctuations.
However,
the
maximum
value
of
the
battery
current
does
not
exceed
200
A.
The
battery
7, it can berate
observed
that theIn
battery
current
has approximately
an exponential
relationship
dischargeFigure
magnification
altogether.
addition,
according
to the relationship
between
the battery
runswith
within
1C discharge
magnification
rate
altogether.
In addition,
to the relationship
the battery
degradation
percentage
Qloss when
the battery
current isaccording
greater
Therefore,
charge/discharge
current
Ibat and
the battery
degradation
percentage
Qlossthan
in zero.
Figure
7, it can be
between
the battery
charge/discharge
current
bat and
thecurrent
batteryfluctuation.
degradation
percentage
Qloss in
Qloss obtained
in Figure
12 is more intense
thanIthe
battery
At room
temperature
observed
that itthe
battery
current
approximately
anapproximately
exponential relationship
with the battery
Figure
can
be observed
thathas
the
battery
has
of 257,°C,
the battery
degradation
percent
in current
one driving
cycle is 2.16 × 10−4an
%. exponential relationship
degradation
Qloss when
the battery
greatercurrent
than zero.
Therefore,
Qloss
obtained in
with thepercentage
battery degradation
percentage
Qloss current
when theisbattery
is greater
than zero.
Therefore,
◦ C, the battery
200
FigureQ12
is
more
intense
than
the
battery
current
fluctuation.
At
room
temperature
of
25
loss obtained in Figure 12 is more intense than the battery current fluctuation. At room temperature
degradation
in one
driving
cycle isin
2.16
10−4 %.
of 25 °C,percent
the battery
degradation
percent
one×driving
cycle is 2.16 × 10−4%.
150
200100
100
50
0
0
200
400
600
800
1000
1200
1000
1200
1000
1200
1400
50 2.0
Qloss (×10-6%)
Ibat (A)
150
0
1.5
0
200
1.0
400
600
800
1400
Qloss (×10-6%)
2.0
0.5
1.5
0.0
0
1.0
200
400
600
800
1400
Time (s)
0.5
Figure 12. Battery current and battery degradation percentage at room temperature of 25 °C based on
0.0
convex optimization.
0
200
400
600
800
1000
1200
1400
Time (s)
In order to verify the effectiveness of the proposed optimization method in this paper for the
electric
equipped
withand
semi-active
HESS, it ispercentage
comparedatwith
the rule-basedofstrategy
in Harbin
Figure bus
12. Battery
current
battery degradation
on
◦ C based
Figure
12. Battery
current
and battery
degradation percentage
atroom
roomtemperature
temperature 25
of °C
25 based
on
driving
The rule-based strategy is shown in Figure 13 [9,29]. When the power demand Pdem ≥
convex cycle.
optimization.
convex
optimization.
0, the battery only provides the threshold power Pthr, and when Pdem > Pthr, the battery will provide
the
of power
demand
exceed according
toproposed
the SOCcap.optimization
When the power
demand
Pdem paper
< 0, it isfor
also
In part
order
to verify
the effectiveness
of the
method
in this
the
need
to
charge
for
SC
according
to
the
charge
of
state
of
the
SC,
when
the
SC
pack
is
fully
charged
In
orderbus
to equipped
verify thewith
effectiveness
the proposed
optimization
methodstrategy
in this paper
for the
electric
semi-active of
HESS,
it is compared
with the rule-based
in Harbin
driving
cycle. The with
rule-based
strategyHESS,
is shown
Figure 13 [9,29].
the powerstrategy
demand in
Pdem
≥
electric
bus equipped
semi-active
it isincompared
with When
the rule-based
Harbin
0,
the
battery
only
provides
the
threshold
power
P
thr
,
and
when
P
dem
>
P
thr
,
the
battery
will
provide
driving cycle. The rule-based strategy is shown in Figure 13 [9,29]. When the power demand Pdem ≥ 0,
the part
of power
demand
exceed according
the, and
SOCcap
. When
the >
power
Pdemwill
< 0, itprovide
is also the
the battery
only
provides
the threshold
powerto
Pthr
when
Pdem
Pthr , demand
the battery
need to charge for SC according to the charge of state of the SC, when the SC pack is fully charged
part of power demand exceed according to the SOCcap . When the power demand Pdem < 0, it is also
need to charge for SC according to the charge of state of the SC, when the SC pack is fully charged and
Energies 2017, 10, 792
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Energies
2017,
10, 792
Energies
2017,
10, 792
13 of
1320
of 20
then
to
thetobattery
packpack
for energy
braking.
According
to to
the
characteristics
ofofthe
SC
power
and the
andand
then
battery
forfor
energy
braking.
According
the
characteristics
the
SCSC
power
and
then the
to the
battery
pack
energy
braking.
According
to the
characteristics
of the
power
and
power
demand
relationship
obtained
from
the
convex
optimization,
the
threshold
power
P
in the
thr
thethe
power
demand
relationship
obtained
from
the
convex
optimization,
the
threshold
power
P
thr
in
power demand relationship obtained from the convex optimization, the threshold power Pthr in
rule-based
strategy
is setisto
and
the
same
power
system
model
and
initial
parameters
are
thethe
rule-based
strategy
set
tokW,
20
kW,
and
the
same
power
system
model
and
initial
parameters
areused
rule-based
strategy
is20
set
to 20
kW,
and
the
same
power
system
model
and
initial
parameters
are
toused
calculate
the
power
distribution
based
on
the
rules
strategy,
as
shown
in
Figure
14.
to calculate
thethe
power
distribution
based
on on
thethe
rules
strategy,
as shown
in Figure
14.14.
used
to calculate
power
distribution
based
rules
strategy,
as shown
in Figure
Pdem P
(k)
≥0
dem (k) ≥ 0
PdemP(k)
≤ P≤ Pthr
dem (k) thr
SOCSOC
≥ 50%
cap (k)
cap (k) ≥ 50%
Pbat (k)
Pbat =
(k)Pdem
= P(k)
dem (k)
Pcap P
(k)
=0
cap (k) = 0
Pbat (k)
Pbat =
(k)Pthr= Pthr
=
P
− P − Pthr
Pcap P
(k)
=
P(k)
(k)
dem
cap
dem (k)thr
Pbat (k)
Pbat =
(k)Pdem
= P(k)
dem (k)
Pcap P
(k)
=0
cap (k) = 0
Pbat (k)
Pbat =
(k)0 = 0
Pcap P
(k)
=0
cap (k) = 0
SOCSOC
≥ 90%
cap (k)
cap (k) ≥ 90%
Pbat (k)
Pbat =
(k)0 = 0
Pcap P
(k)
=
−
P
(k)
=dem
− P(k)
cap
dem (k)
Figure
13. 13.
TheThe
implementation
process
of rule-based
strategy.
Figure
implementation
process
ofrule-based
rule-based
strategy.
Figure
13. The
implementation
process
of
strategy.
200 200
175 175
150 150
Power
of battery
Power
of battery
Power
of SC
Power
of SC
Power
demand
Power
demand
125 125
100 100
Power (%)
Power (%)
75 75
50 50
25 25
0 0
-25 -25
-50 -50
-75 -75
-100-100
-125-125
-150-150
0 0
200 200 400 400 600 600 800 800 1000
1000 12001200 1400
1400
Time
(s) (s)
Time
Figure
14.14.
Power
distribution
results
based
rule-based
strategy.
Figure
14.
Power
distribution
results
based
onon
thethe
rule-based
strategy.
Figure
Power
distribution
results
based
on
the
rule-based
strategy.
Figure
15 shows
shows
thethe
battery
current
and
battery
degradation
percent
at 25
°C °C
on on
the
rule
◦based
Figure
15
shows
battery
current
and
battery
degradation
percent
at 25
rule
Figure
15
the
battery
current
and
battery
degradation
percent
at
25
C based
based
onthe
the
rule
strategy.
In
the
latter
part
of
the
driving
cycle,
it
can
be
seen
that
the
SC
obtained
the
energy
from
strategy.
In the
latter
part
drivingcycle,
cycle,ititcan
canbe
beseen
seen that
that the
the SC
SC obtained
obtained the
strategy.
In the
latter
part
of of
thethe
driving
theenergy
energyfrom
from
braking
cannot
satisfy
the power
demand;
thisthis
part
of the
power
demand
difference
can only
be borne
braking
cannot
satisfy
power
demand;
part
the
power
demand
difference
braking
cannot
satisfy
thethe
power
demand;
this part
ofofthe
power
demand
difference can
canonly
onlybe
beborne
borne
Energies 2017, 10, 792
Energies 2017, 10, 792
14 of 20
14 of 20
by
Therefore,
the the
battery
experiences
a large
outputoutput
power power
fluctuation.
The battery
bythe
thebattery.
battery.
Therefore,
battery
experiences
a large
fluctuation.
The current
battery
and
battery
decay
percentages
have
several
significant
peaks
in
the
later
stages
based
on
the
current and battery decay percentages have several significant peaks in the later stages based onrule
the
strategy.
However,
in contrast,
the SCthe
satisfies
the instantaneous
high power
the battery
rule strategy.
However,
in contrast,
SC satisfies
the instantaneous
high ripple
powerand
ripple
and the
outputs
smaller apower
fluctuation
in the convex
According toAccording
the energy to
management
battery aoutputs
smaller
power fluctuation
in optimization.
the convex optimization.
the energy
strategy
evaluation
method
in
Ref.
[30],
the
standard
deviation
of
the
battery
current
in
two
management strategy evaluation method in Ref. [30], the standard deviation of the battery strategies
current in
has
calculated,
as shown
in Equation
(25),
the(25),
Ib_avg
is thethe
average
battery
current,
s is
twobeen
strategies
has been
calculated,
as shown
in where
Equation
where
Ib_avg isofthe
average
of battery
the
standard
deviation
of battery
current.
current,
s is the
standard
deviation
of battery current.
v N
u N
u  (I b (k) − I b _ avg ) 2 2
u ∑ (Ib (k) − Ib_avg )
(25)
st
= k =1
s = k=1
(25)
N
N
The standard deviation of the battery current based on the convex optimization strategy and
The standard deviation of the battery current based on the convex optimization strategy and
rule-based strategy is 31.03 and 43.99, respectively, the battery current fluctuation based on the
rule-based strategy is 31.03 and 43.99, respectively, the battery current fluctuation based on the
convex optimization strategy is smaller than rule-based strategy. Figure 16 shows the battery capacity
convex optimization strategy is smaller than rule-based strategy. Figure 16 shows the battery capacity
degradation curve based on convex optimization and rule-based strategy. At approximately t = 1050
degradation curve based on convex optimization and rule-based strategy. At approximately t = 1050 s,
s, t = 1320 s, and t = 1360 s, the battery degradation percent based on the rule strategy has three
t = 1320 s, and t = 1360 s, the battery degradation percent based on the rule strategy has three significant
significant rising intervals, which correspond to three battery current pulses based on the rules
rising intervals, which correspond to three battery current pulses based on the rules strategy; further,
strategy; further, it can be reflected from the battery current and battery degradation percentage
it can be reflected from the battery current and battery degradation percentage result of the rule-based
result of the rule-based strategy shown in Figure 15. In contrast, the battery power fluctuation is
strategy shown in Figure 15. In contrast, the battery power fluctuation is smoother when based
smoother when based on the convex optimization strategy, thus protecting the battery better. The
on the convex optimization strategy, thus
protecting the battery better. The rule-based strategy
rule-based strategy7 consumes 1.35 × 107 J in one driving cycle, i.e., approximately 3.75 kWh, and the
consumes 1.35 × 10 J in one driving cycle, i.e.,−4approximately 3.75 kWh, and the percentage of battery
percentage of battery degradation is 2.31 × 10 %.
degradation is 2.31 × 10−4 %.
500
Ibat (A)
400
300
200
100
0
0
200
400
600
800
1000
1200
1400
0
200
400
600
800
1000
1200
1400
Qloss (×10-6%)
16
12
8
4
0
Time (s)
Figure 15. Battery current and battery degradation percentage at room temperature of 25 ◦ C based on
Figure 15. Battery current and battery degradation percentage at room temperature of 25 °C based on
the rule strategy.
the rule strategy.
In
Inorder
orderto
tofurther
furtherreflect
reflectthe
thereal
realsituation
situationof
ofaabus
busrunning
runningon
onHarbin
Harbincity
city roads
roads in
in aaday,
day,and
and
quantitatively
quantitatively analyze
analyze the
the potential
potential of
of convex
convex optimization
optimization relative
relative to
to the
the rule-based
rule-based strategy
strategy to
to
improve
battery
life,
we
use
nine
Harbin
city
driving
cycles
(total
50.4
km)
to
simulate
a
cycle
line:
improve battery life, we use
driving cycles (total 50.4 km) to simulate a cycle line: a
abus
busfrom
fromthe
thebus
busterminal,
terminal, followed
followed by a cycle line, and subsequently
subsequently back
backto
tothe
thebus
busterminal.
terminal.When
When
the
terminal
again,
thethe
CC-CV
is used
to recharge
the battery.
WhenWhen
the battery
pack
thebus
busarrives
arrivesatatthe
the
terminal
again,
CC-CV
is used
to recharge
the battery.
the battery
ispack
recharged,
the
SOC
returns
to
0.9.
Table
5
shows
the
indicators
of
the
battery
pack
when
the
is recharged, thebatSOCbat returns to 0.9. Table 5 shows the indicators of the battery pack whenbus
the
drives
in one
line based
on the
bus drives
incycle
one cycle
line based
ontwo
thestrategies.
two strategies.
Energies
Energies 2017,
10,2017,
792 10, 792
15 of
1520of 20
Energies 2017, 10, 792
15 of 20
2.5
convex optimization strategy
rule-based strategy
2.3
2.16
2.5
2.04
convex optimization strategy
rule-based strategy
Qloss (×10-4%)
Qloss (×10-4%)
2.3
2.16
1.71
2.04
1.71
1.24
1
1.24
1
0.0
0
200
400
600
800
1000
1200
1400
Time (s)
0.0
0
200
400
600
800
1000
1200
1400
Figure
16. The
percentage
of battery
degradation
strategies.
Figure
16. The
percentage
of battery
degradationunder
under two
two strategies.
Time (s)
5. The
indicators
of two
strategiesunder
underone
one cycle
cycle line.
TableTable
5. The
indicators
of two
strategies
line.
Figure 16. The percentage of battery degradation under two strategies.
Strategy
Total Length Initial SOC Final SOC ΔSOC Recharge Time
Strategy
Total Length
Initial SOC
Final SOC
∆SOC
Recharge Time
Based on convex
0.4223
Table 5.50.4
Thekm
indicators of 0.9
two strategies
under one0.4777
cycle line. 1561 s
Based
onon rules
Based
50.4 km
0.4112
0.4888
1598
50.4
km
0.9 0.9SOC 0.4223
1561 ss Time
Strategy
Total
Length Initial
Final SOC 0.4777
ΔSOC Recharge
convex
Based
onon
rules
50.4 50.4
km
0.9cells
0.4112
1598
Based
convex
km
0.9in series
0.4223
0.4777 the SOC
1561
s battery
For the
LiFePO
4 battery
pack
with 120
and
one in0.4888
parallel,
ofsthe
on rules
50.4batkm
0.9 one cycle0.4112
1598 s and the
variesBased
from SOC
bat = 0.9 to SOC
= 0.4223 through
line under 0.4888
convex optimization,
SOC
of
the
battery
varies
from
SOC
bat = 0.9 to SOCbat = 0.4112 through one cycle line under rule-based
For the LiFePO4 battery pack with 120 cells in series and one in parallel, the SOC of the battery
For theInLiFePO
4 battery
pack
with 120
cells the
in series
andmagnification
one in parallel,
theto
SOC
theentire
battery
strategy.
the process
of the
recharge
phase,
recharge
is set
1C. of
The
varies from SOCbat = 0.9 to SOCbat = 0.4223 through one cycle line under convex optimization, and the
recharge
1561
s 0.4223
in convex
optimization
andline
1598
s in rule-based
strategy. After
thethe
varies
fromstate
SOCcontinues
bat = 0.9 tofor
SOC
bat =
through
one cycle
under
convex optimization,
and
SOC of the battery varies from SOCbat = 0.9 to SOCbat = 0.4112 through one cycle line under rule-based
recharge,
the battery
the batconvex
strategy
andone
thecycle
rule-based
strategy
are
SOC
of the battery
variesSOC
fromofSOC
= 0.9 tooptimization
SOCbat = 0.4112
through
line under
rule-based
strategy.
In thefrom
processbatof= 0.4223
the recharge
thetorecharge
magnification
is set to 1C.
The
entire
returned
SOCphase,
bat phase,
= 0.4112
bat = 0.9,magnification
respectively. According
to the
actual
strategy.
In the SOC
process of theand
recharge
theSOC
recharge
is set to 1C.
The
entire
recharge
state
continues
for
1561
s
in
convex
optimization
and
1598
s
in
rule-based
strategy.
After
the
operation,
electric bus
run four
cycles
(approximately
200 km)
one day, strategy.
and the electric
recharge
statethe
continues
for 1561
s in line
convex
optimization
and 1598
s in in
rule-based
After the
recharge,
battery
SOC of
thebattery
convex
optimization
strategy
and
the and
rule-based
strategy
are
busthe
needs
to battery
recharge
the
times.optimization
Assuming
thatstrategy
the battery
is the
fullyrule-based
charged
(SOC
batreturned
= 0.9)are
recharge,
the
SOC
of
thefour
convex
strategy
in the
first
trip
every
day,
the
battery
SOC
change
curve
based
on
the
convex
optimization
strategy
fromreturned
SOC
=
0.4223
and
SOC
=
0.4112
to
SOC
=
0.9,
respectively.
According
to
the
actual
bat from SOCbat = 0.4223bat
and SOCbat = 0.4112 tobatSOCbat = 0.9, respectively. According to the actual
and
rule-based
strategy
can
be
obtained
as
shown
in
Figure
17.
operation,
the electric
bus run
line line
cycles
(approximately
200 200
km)km)
in one
day,day,
and and
the electric
bus
operation,
the electric
bus four
run four
cycles
(approximately
in one
the electric
SOC of battery (%)
SOC of battery (%)
needs
to needs
recharge
the battery
four times.
Assuming
that the
battery
is fully
charged
(SOC
in
bus
to recharge
the 100
battery
four times.
Assuming
that
the battery
is fully
charged
(SOC
= 0.9)
bat =bat0.9)
Battery charging
the first
trip
every
day,
the
battery
SOC
change
curve
based
on
the
convex
optimization
strategy
and
in the first trip every day, the battery
SOC change curve based on the convex optimization strategy
phase (t=1561s)
rule-based
strategy strategy
can be obtained
as shown
in Figure
17.
and rule-based
can90be obtained
as shown
in Figure
17.
10080
Battery charging
phase (t=1561s)
9070
8060
50
70
42.23
Battery discharging phase
60
0
2
4
6
50
8
10
12
14
16
Time (h)
(a)
42.23
Battery discharging phase
0
2
4
6
8
Time (h)
(a)
Figure 17. Cont.
10
12
14
16
Energies 2017, 10, 792
Energies 2017, 10, 792
16 of 20
16 of 20
100
Battery charging
phase (t=1598s)
SOC of battery (%)
90
80
70
60
50
41.12
Battery discharging phase
0
2
4
6
8
10
12
14
16
Time (h)
(b)
Figure 17. The battery SOC change based on different power distribution strategies in one day: (a) the
Figure 17. The battery SOC change based on different power distribution strategies in one day: (a) the
battery SOC based on the optimization strategy described in this paper; and (b) the battery SOC based
battery SOC based on the optimization strategy described in this paper; and (b) the battery SOC based
on the rules of the power distribution strategy.
on the rules of the power distribution strategy.
The battery capacity degradation will occur during the entire charge/discharge process.
The battery
degradation
occur during
the entire
charge/discharge
process.
Therefore,
wecapacity
can obtain
the batterywill
degradation
percentage
curve
of the battery pack
using Therefore,
the semiwe can
obtainmodel
the battery
percentage
curve
of the battery situation.
pack using
semi-empirical
empirical
in onedegradation
day according
to the battery
charge/discharge
Atthe
room
temperature
◦ C,
model
in °C,
oneQday
according
to the battery
charge/discharge
At room
temperature
of 2518.
of 25
loss base
on the convex
optimization
strategy and situation.
the rules strategy
are
shown in Figure
a day
of operation
(four cycle
linesand
andthefour
Qloss
QlossAfter
base on
the convex
optimization
strategy
rulescharging
strategyphases),
are shown
in based
Figureon
18. convex
After a
9.6 ×cycle
10−3%,lines
and and
the battery
pack canphases),
be used Q
forloss
approximately
2.08 ×optimization
103 days whenis
day optimization
of operation is(four
four charging
based on convex
−3 %, and
degradation
attenuated
80%for
ofapproximately
its initial capacity,
Qlosswhen
based
onbattery
rules
9.6 ×the
10battery
the batteryispack
can be to
used
2.08 whereas
× 103 days
the
−3%, and the battery pack can be used for approximately 1.94 × 103 days when the
strategy
is
10.3
×
10
degradation is attenuated to 80% of its initial capacity, whereas Qloss based on rules strategy is
to 80%pack
of itscan
initial
capacity.
10.3 battery
× 10−3 is
%,attenuated
and the battery
be used
for approximately 1.94 × 103 days when the battery is
Notably,
two capacity.
main causes of the greater battery degradation under rule-based strategy:
attenuated
to 80%there
of itsare
initial
(1) The battery current Ibat based on the convex optimization is more stable; hence, this results in a
Notably, there are two main causes of the greater battery degradation under rule-based strategy:
smaller Qloss than the rule-based strategy, and this is reflected in the comparison of battery
(1) The battery current Ibat based on the convex optimization is more stable; hence, this results in a
degradation under the two strategies shown in Figure 16; (2) Since the rule-based strategy consumes
smaller Qloss than the rule-based strategy, and this is reflected in the comparison of battery degradation
more energy in one day, the battery discharges deeper during operation (SOCbat ∈ [0.4223, 0.9]
under the two strategies shown in Figure 16; (2) Since the rule-based strategy consumes more energy
during one cycle line based on convex optimization and SOCbat ∈ [0.4112, 0.9] during one cycle line
in one day, the battery discharges deeper during operation (SOCbat ∈ [0.4223, 0.9] during one cycle
based on rules). Similarly, in order to return the battery back to the initial SOC, the rule-based strategy
line must
basedbeoncharging
convex deeper
optimization
SOCoptimized
0.9] during
onetime
cycle
onon
rules).
bat ∈ [0.4112,
than theand
convex
strategy
(charging
t =line
1561based
s based
the
Similarly,
in
order
to
return
the
battery
back
to
the
initial
SOC,
the
rule-based
strategy
must
be
charging
convex optimization and t = 1598 s based on the rules). Consequently, the rule-based strategy
deeper
than the
optimizedrange
strategy
(charging
1561same
s based
the convex
optimization
increases
theconvex
SOC operating
of the
battery time
used tin= the
roadoncycle
as compared
to the
and strategy
t = 1598 based
s based
on
the
rules).
Consequently,
the
rule-based
strategy
increases
the
SOC
on the convex optimization, which also increases the percentage of batteryoperating
capacity
range
of the battery used in the same road cycle as compared to the strategy based on the convex
degradation.
optimization,
which usage
also increases
the on
percentage
of batteryiscapacity
degradation.
The battery
time based
the two strategies
approximately
15 h in one day, but the
The battery
time based
on theistwo
strategies
approximately
15 h in
oneisday,
but In
theFigure
usage
usage
time ofusage
the rule-based
strategy
slightly
longerisbecause
the charging
time
longer.
Qlossrule-based
slope of the
batteryischarging
phase is
larger than
Qloss at the
time
of traveling
on the
time18,
of the
strategy
slightly longer
because
the charging
time
is longer.
In Figure
18,road;
Qloss
battery
degradation
bythan
charging
battery
charging on
magnification
of 1Cthe
is
slopehence,
of thethe
battery
charging
phasecaused
is larger
Qlossthe
at the
timeatofatraveling
the road; hence,
greater
than that caused
caused by
thebattery
road. at a charging magnification of 1C is greater than
battery
degradation
by running
chargingonthe
that caused by running on the road.
Energies 2017, 10, 792
Energies 2017, 10, 792
17 of 20
17 of 20
0.010
0.0096
Battery charge
phase
Qloss (%)
0.008
0.006
0.004
0.002
0.000
0
2
4
6
8
10
12
14
16
12
14
16
Time (h)
(a)
0.011
0.0103
0.01
Battery charge
phase
Qloss (%)
0.008
0.006
0.004
0.002
0.000
0
2
4
6
8
10
Time (h)
(b)
Figure 18. Qloss based on the two strategies in one day: (a) battery degradation percentage based on
Figure 18. Qloss based on the two strategies in one day: (a) battery degradation percentage based on
convex optimization strategy; and (b) battery degradation percentage based on rules strategy.
convex optimization strategy; and (b) battery degradation percentage based on rules strategy.
In order to obtain further analysis of Qloss for one year in Harbin, we assume that the Harbin city
In will
order
to for
obtain
further
analysis
of Q
for bus
oneoperates
year in Harbin,
we assume
that the
Harbinthe
lossthe
bus
run
cycle
lines in
one day,
and
for 30 days
in a month.
Therefore,
citybus
buswill
willoperate
run forfor
cycle
lines
in
one
day,
and
the
bus
operates
for
30
days
in
a
month.
Therefore,
360 days in a year. According to the average temperature of different months in
theHarbin,
bus willthe
operate
for
360 of
days
infor
a year.
According
to the
average temperature
of different
daily value
Qloss
every
month can
be calculated.
It is assumed
that themonths
vehicle in
in Harbin,
the
daily
value
of
Q
for
every
month
can
be
calculated.
It
is
assumed
that
the vehicle
loss
each month is running at the monthly average temperature value and ignores the self-heating
effect
in each
month
is
running
at
the
monthly
average
temperature
value
and
ignores
the
self-heating
of the battery [31]. The semi-empirical model is also used to calculate the battery degradation. The
effect
of themonthly
battery [31].
The semi-empirical
used
to calculate
battery degradation.
average
temperature
in Harbin ismodel
givenisinalso
Table
6 [32],
i.e., the the
temperature
range of T ∈
The[−18.3
average
monthly
temperature
in
Harbin
is
given
in
Table
6
[32],
i.e.,
the
temperature
range of
°C, 23.0 °C].
T ∈ [−18.3 ◦ C, 23.0 ◦ C].
Table 6. The average temperature of the city in Harbin.
Table 6. The average temperature of the city in Harbin.
Jun
Month
Jan
Feb Mar Apr May
Temp
7.1
14.7
Month
Jan(°C) −18.3
Feb −13.6
Mar −3.4 Apr
May 20.4 Jun
Month
Jul
Aug
Sep
Oct
Nov
◦
Temp ( C)
−18.3
−13.6
−3.4
7.1
14.7 Dec 20.4
Temp (°C) 23.0
21.1
14.5
5.6
−5.3 −14.8
Month
Jul
Aug
Sep
Oct
Nov
Dec
◦
Temp
( C)
23.0
14.5 in different
5.6
−5.3 we−can
14.8calculate the electric
According
to the
different
average21.1
temperatures
months,
bus battery degradation percentage in one day for different months, as shown in Figure 19.
Energies 2017, 10, 792
18 of 20
According to the different average temperatures in different months, we can calculate the electric
Energies 2017, 10, 792
18 of 20
bus battery degradation percentage in one day for different months, as shown in Figure 19.
Qloss base on the convex
Qloss base on the rules
Qloss (%)
0.014
0.014
0.012
0.012
0.010
0.010
0.008
0.008
0.006
0.006
0.004
0.004
0.002
0.002
0.000
0.000
Jan Feb Mar Apr May Jun
Jul Aug Sep Oct Nov Dec
Month
Figure 19. Percentage of battery degradation Qloss in one day for different months.
Figure 19. Percentage of battery degradation Qloss in one day for different months.
As
As evident
evident in
in Figure
Figure 19,
19, Q
Qloss
loss in different months based on the rules strategy is larger than
than that
that
based
optimization
strategy.
It can
alsoalso
be observed
that, when
the temperature
is within
based on
onthe
theconvex
convex
optimization
strategy.
It can
be observed
that, when
the temperature
is
±
10 ◦ C±10
during
springspring
and autumn,
Qloss isQminimal,
whereas
Qloss isQlarge
in summer
and winter
with
within
°C during
and autumn,
loss is minimal,
whereas
loss is large
in summer
and winter
higher
or lower
Especially
in the winter
December,
January, and
February,
with higher
or temperatures.
lower temperatures.
Especially
in the months
winter of
months
of December,
January,
and
the
two strategies
daily
operation
of the battery
degradation
reached ≥reached
0.01%. ≥This
directly
February,
the two under
strategies
under
daily operation
of the
battery degradation
0.01%.
This
reflects
problem
of large degradation
of LiFePO
battery4 at
low temperatures.
The totalThe
battery
directlythe
reflects
the problem
of large degradation
of4 LiFePO
battery
at low temperatures.
total
degradation
percentage
of
the
year
is
shown
in
Table
7.
battery degradation percentage of the year is shown in Table 7.
Table 7.
Table
7. The total battery degradation
degradation percentage
percentage in
in different
different month
monthof
ofthe
theyear.
year.
Month
Month
Qloss
base
Qloss
baseon
onthe
the
convex/rules(%)
(%)
convex/rules
Month
Month
Qloss
baseon
onthe
the
Qloss
base
convex/rules(%)
(%)
convex/rules
Jan
Jan
Feb
Feb
0.348/0.375
0.348/0.375
0.315/0.342
0.315/0.342
Jul
Jul
Aug
Aug
0.276/0.297
0.276/0.297
0.264/0.288
0.264/0.288
Mar
Mar
Apr
Apr
May
May
JunJun
0.252/0.276 0.195/0.216
0.195/0.216 0.231/0.252
0.231/0.252 0.261/0.282
0.261/0.282
0.252/0.276
Sep
Sep
Oct
Oct
Nov
Nov
DecDec
0.231/0.252
0.231/0.252 0.189/0.207
0.189/0.207 0.264/0.288
0.264/0.288 0.324/0.351
0.324/0.351
In Table
Table7,7,QQloss
loss in one year
year based
based on
on the
theconvex
convexoptimization
optimizationstrategy
strategyisis3.15%,
3.15%,and
andQQ
loss based
based
In
loss
on the
the rules
rules strategy
strategy is
is 3.43%.
3.43%. A quantitative
quantitative analysis of battery life extension
extension is addressed
addressed in
in this
this
on
paper,assuming
assuming that
that the
the battery
battery cannot
cannot be
be used when its capacity reduces to 80% of the initial value.
paper,
Subsequently,the
theyear
yearof
ofusage
usageof
ofthe
thebattery
batterycan
canbe
becalculated
calculatedusing
usingEquation
Equation(26).
(26).
Subsequently,
12
Yope = 20 /12 Qloss _ month (m)
Yope =
20/ ∑m=1Qloss_month (m)
(26)
(26)
m=1
where Yope is the year of usage of battery and Qloss_month is the percentage of Qloss per month. It can be
where Yope is the year of usage of battery and Qloss_month is the percentage of Qloss per month. It can be
calculated that the bus equipped with HESS can operate for 6.35 years based on the convex
calculated that the bus equipped with HESS can operate for 6.35 years based on the convex optimization
optimization strategy. However, the bus equipped with HESS can operate for 5.84 years based on the
strategy. However, the bus equipped with HESS can operate for 5.84 years based on the rules strategy.
rules strategy. The superiority of the convex optimization strategy is reflected, further illustrating the
The superiority of the convex optimization strategy is reflected, further illustrating the effectiveness of
effectiveness of the use of convex optimization.
the use of convex optimization.
6. Conclusions
This paper used the electric bus power system with semi-active HESS as the research object, in
the Harbin city driving cycle and proposed a convex optimization power distribution strategy target
to optimize the battery current that represents battery degradation. According to the average
temperature of different months of the year in the northern city of Harbin, the percentage of battery
Energies 2017, 10, 792
19 of 20
6. Conclusions
This paper used the electric bus power system with semi-active HESS as the research object,
in the Harbin city driving cycle and proposed a convex optimization power distribution strategy
target to optimize the battery current that represents battery degradation. According to the average
temperature of different months of the year in the northern city of Harbin, the percentage of battery
degradation of the electric bus with the HESS is analyzed and calculated. Simulation results show that
using the convex optimization strategy proposed in this paper, at a room temperature of 25 ◦ C, in a
daily trip composed of the Harbin City Driving Cycle—including four cycle lines and four charging
stages—the percentage of the battery degradation is 9.6 × 10−3 %, whereas the battery degradation
is 10.3 × 10−3 % based on the rules under the same conditions. Assuming the daily mileage of an
electric bus is approximately 200 km, and it will operate for 360 days in a year, the percentage of
battery degradation is 3.15% in one year in Harbin. Before the battery capacity reduces to 80% of
the initial value, the electric bus can run for 6.35 years based on the strategy proposed in this paper.
However, the battery degrades 3.43% per year in Harbin using the rule-based strategy, and the bus can
run for 5.84 years. Thus, the convex-based optimization strategy can operate for 0.51 year more than
the rule-based strategy.
Acknowledgments: This work was supported by the State Key Laboratory of Automotive Safety and Energy
under Project No. KF16062 and Science Funds for the Young Innovative Talents of HUST, No. 201503.
Author Contributions: Xiaogang Wu and Tianze Wang conceived and designed the simulations; Xiaogang Wu
analyzed the data; Tianze Wang wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Conte, M.; Genovese, A.; Ortenzi, F.; Vellucci, F. Hybrid battery-supercapacitor storage for an electric forklift:
A life-cycle cost assessment. J. Appl. Electrochem. 2014, 44, 523–532. [CrossRef]
Yutao, L.; Feng, W.; Hao, Y.; Xiutian, L. A Study on the Driving-cycle-based Life Model for LiFePO4 battery.
Automot. Eng. 2015, 37, 881–885.
Abeywardana, D.B.W.; Hredzak, B.; Agelidis, V.G.; Demetriades, G.D. Supercapacitor Sizing Method for
Energy-Controlled Filter-Based Hybrid Energy Storage Systems. IEEE Trans. Power Electron. 2017, 32,
1626–1637. [CrossRef]
Henson, W. Optimal battery/ultracapacitor storage combination. J. Power Sources 2008, 179, 417–423.
[CrossRef]
Xiong, R.; Sun, F.; Chen, Z.; He, H. A data-driven multi-scale extended Kalman filtering based parameter
and state estimation approach of lithium-ion olymer battery in electric vehicles. Appl. Energy 2014, 113,
463–476. [CrossRef]
Zhang, Y.; Xiong, R.; He, H.; Shen, W. Lithium-Ion Battery Pack State of Charge and State of Energy
Estimation Algorithms Using a Hardware-in-the-Loop Validation. IEEE Trans. Power Electron. 2017, 32,
4421–4431. [CrossRef]
Choi, M.; Kim, S.; Seo, S. Energy Management Optimization in a Battery/Supercapacitor Hybrid Energy
Storage System. IEEE Trans. Smart Grid 2012, 3, 463–472. [CrossRef]
Song, Z.; Li, J.; Han, X.; Xu, L.; Lu, L.; Ouyang, M.; Hofmann, H. Multi-objective optimization of a
semi-active battery/supercapacitor energy storage system for electric vehicles. Appl. Energy 2014, 135,
212–224. [CrossRef]
Song, Z.; Hofmann, H.; Li, J.; Han, X.; Zhang, X.; Ouyang, M. A comparison study of different semi-active
hybrid energy storage system topologies for electric vehicles. J. Power Sources 2015, 274, 400–411. [CrossRef]
Hu, X.; Murgovski, N.; Johannesson, L.; Egardt, B. Energy efficiency analysis of a series plug-in hybrid
electric bus with different energy management strategies and battery sizes. Appl. Energy 2013, 111, 1001–1009.
[CrossRef]
Lu, L.; Han, X.; Li, J.; Hua, J.; Ouyang, M. A review on the key issues for lithium-ion battery management in
electric vehicles. J. Power Sources 2013, 226, 272–288. [CrossRef]
Energies 2017, 10, 792
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
20 of 20
Amjadi, Z.; Williamson, S.S. Prototype Design and Controller Implementation for a Battery-Ultracapacitor
Hybrid Electric Vehicle Energy Storage System. IEEE Trans. Smart Grid 2012, 3, 332–340. [CrossRef]
Ma, T.; Yang, H.; Lu, L. Development of hybrid battery-supercapacitor energy storage for remote area
renewable energy systems. Appl. Energy 2015, 153, 56–62. [CrossRef]
Hung, Y.; Wu, C. An integrated optimization approach for a hybrid energy system in electric vehicles.
Appl. Energy 2012, 98, 479–490. [CrossRef]
Vinot, E.; Trigui, R. Optimal energy management of HEVs with hybrid storage system. Energy Convers.
Manag. 2013, 76, 437–452. [CrossRef]
Yoo, H.; Sul, S.; Park, Y.; Jeong, J. System integration and power-flow management for a series hybrid electric
vehicle using supercapacitors and batteries. IEEE Trans. Ind. Appl. 2008, 44, 108–114. [CrossRef]
Li, Y.; Han, Y. A Module-Integrated Distributed Battery Energy Storage and Management System. IEEE Trans.
Power Electron. 2016, 31, 8260–8270. [CrossRef]
Zhao, N.; Li, Y.; Zhao, X.; Zhi, X.; Liang, G. Effect of particle size and purity on the low temperature
electrochemical performance of LiFePO4 /C cathode material. J. Alloys Compd. 2016, 683, 123–132. [CrossRef]
Chen, C.; Xiong, R.; Shen, W. A lithium-ion battery-in-the-loop approach to test and validate multi-scale
dual H infinity filters for state of charge and capacity estimation. IEEE Trans. Power Electron. 2017, PP, 1.
[CrossRef]
Marzougui, H.; Amari, M.; Kadri, A.; Bacha, F.; Ghouili, J. Energy management of fuel
cell/battery/ultracapacitor in electrical hybrid vehicle. Int. J. Hydrogen Energy 2017, 42, 8857–8869. [CrossRef]
Wen-gang, L.; Bo, Z.; Xiao-dan, W.; Jun-kui, G.; Xing-jiang, L. Capacity fading of 18650 Li-ion cells with
cycling. Chin. J. Power Sources 2012, 3, 306–309.
Wang, J.; Liu, P.; Hicks-Garner, J.; Sherman, E.; Soukiazian, S.; Verbrugge, M.; Tataria, H.; Musser, J.;
Finamore, P. Cycle-life model for graphite-LiFePO4 cells. J. Power Sources 2011, 196, 3942–3948. [CrossRef]
Ramadass, P.; Haran, B.; Gomadam, P.M.; White, R.; Popov, B.N. Development of First Principles Capacity
Fade Model for Li-Ion Cells. J. Electrochem. Soc. 2004, 151, A196–A203. [CrossRef]
Song, Z.; Hofmann, H.; Li, J.; Hou, J.; Zhang, X.; Ouyang, M. The optimization of a hybrid energy storage
system at subzero temperatures: Energy management strategy design and battery heating requirement
analysis. Appl. Energy 2015, 159, 576–588. [CrossRef]
New Energy Vehicles Pure Electric Driving Range and Special Inspection Standards, N.E.V.P. Available
online: http://news.xinhuanet.com/auto/2015-05/19/c_127817177.htm (accessed on 6 June 2017).
Boyd, S. Convex Optimization; Cambridge University Press: Cambridge, UK, 2004; pp. 7–13.
Sun, F.; Xiong, R.; He, H. A systematic state-of-charge estimation framework for multi-cell battery pack in
electric vehicles using bias correction technique. Appl. Energy 2016, 162, 1399–1409. [CrossRef]
Hu, C.; Wu, X.; Li, X.; Wang, X. Construction of Harbin City Driving Cycle. J. Harbin Univ. Sci. Technol. 2014,
19, 85–89.
Song, Z.; Hofmann, H.; Li, J.; Han, X.; Ouyang, M. Optimization for a hybrid energy storage system in
electric vehicles using dynamic programing approach. Appl. Energy 2015, 139, 151–162. [CrossRef]
Choi, M.; Lee, J.; Seo, S. Real-Time Optimization for Power Management Systems of a Battery/Supercapacitor
Hybrid Energy Storage System in Electric Vehicles. IEEE Trans. Veh. Technol. 2014, 63, 3600–3611. [CrossRef]
Forgez, C.; Vinh Do, D.; Friedrich, G.; Morcrette, M.; Delacourt, C. Thermal modeling of a cylindrical
LiFePO4 /graphite lithium-ion battery. J. Power Sources 2010, 195, 2961–2968. [CrossRef]
Analysis of Climate Background in Harbin. Available online: http://www.weather.com.cn/cityintro/
101050101.shtml (accessed on 6 June 2017).
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