-
Applied Energy 135 (2014) 212224
Contents lists available at ScienceDirect
Applied Energy
journal homepage: www.elsevier .com/ locate/apenergy
Multi-objective optimization of a semi-active
battery/supercapacitorenergy storage system for electric
vehicles
http://dx.doi.org/10.1016/j.apenergy.2014.06.0870306-2619/ 2014
Elsevier Ltd. All rights reserved.
Corresponding author. Tel.: +86 10 62792797; fax: +86 10
62789699.E-mail addresses: [email protected] (Z. Song),
[email protected] (J. Li),
[email protected] (X. Han), [email protected] (L.
Xu), [email protected] (L. Lu), [email protected] (M.
Ouyang), [email protected] (H. Hofmann).
Ziyou Song a, Jianqiu Li a, Xuebing Han a, Liangfei Xu a,
Languang Lu a, Minggao Ouyang a,,Heath Hofmann b
a State Key Laboratory of Automotive Safety and Energy, Tsinghua
University, Beijing 100084, PR Chinab Department of Electric
Engineering and Computer Science, The University of Michigan, Ann
Arbor, MI 48109, USA
h i g h l i g h t s
A new battery/supercapacitor energy storage system is proposed
in this paper. A novel dynamic battery capacity fade model is
employed in system optimization. The system cost and the battery
capacity loss are simultaneously minimized. The battery degradation
is reduced rapidly with the initial increase in SC usage.
Candidates appear in the inflection area can be regarded as the
optimal solutions.
a r t i c l e i n f o
Article history:Received 7 January 2014Received in revised form
7 May 2014Accepted 3 June 2014Available online 16 September
2014
Keywords:Electric city busHybrid energy storage system
(HESS)LiFePO4 battery degradationMulti-objective optimization
a b s t r a c t
This paper proposes a semi-active battery/supercapacitor (SC)
hybrid energy storage system (HESS) foruse in electric drive
vehicles. A much smaller unidirectional dc/dc converter is adopted
in the proposedHESS to integrate the SC and battery, thereby
increasing the HESS efficiency and reducing the system cost.We have
also included a quantitative battery capacity fade model, in
addition to the theoretical HESSmodel proposed in this paper. For
the proposed HESS, we have examined the sizing optimization ofthe
HESS parameters for an electric city bus, including the parallel
and series number of the battery celland the SC module. Considering
the constraint of requirement on minimal mileage, the optimization
goalis to simultaneously minimize (i) the total cost of the HESS
and (ii) the capacity loss of a LiFePO4 batteryover a typical China
Bus Driving Cycle. The simulation result shows that these two
objectives are conflict-ing, and trades them off using a
non-dominated sorting genetic algorithm II. Finally, the Pareto
frontincluding optimal HESS parameter groups has been obtained,
which indicates that the battery capacityloss can be reduced
rapidly when the SC cost increases within the range from 10 to 40
thousand RMB.
2014 Elsevier Ltd. All rights reserved.
1. Introduction
Energy storage systems (ESSs) form an integral part of
hybridelectric vehicles (HEVs), plug-in hybrid electric vehicles
(PHEVs),and all-electric vehicles (EVs) [13]. Till date, batteries
are one ofthe most widely used ESS. However, the current
state-of-the-artbattery-based ESS has several drawbacks, including
low powerdensity, battery life, and high cost. These limitations
have providedan impetus to develop alternative strategies [14]. In
principle, the
power density of battery needs to be high enough to meet the
peakpower demand, the mere increase of which leads to an
undesirableincrease in the battery size because it increases the
overall cost ofthe ESS. In addition, it becomes highly difficult to
balance the indi-vidual cell voltage within a battery pack,
especially when the num-ber of battery cells in a pack is very high
[5]. In addition, batteriesused in electric vehicles often
encounter instantaneous powerdemand. Under such instantaneously
varying power input and out-put conditions, batteries perform
frequent charge and dischargeoperations, which tend to have adverse
effect on battery life[68]. To circumvent the aforementioned
problems, researchershave proposed hybrid energy storage systems
(HESSs), which com-bine the functionalities of supercapacitor (SC)
and battery. So far,several studies have been performed on this
technology, with anaim to realize improved performance [916]. This
technology
http://crossmark.crossref.org/dialog/?doi=10.1016/j.apenergy.2014.06.087&domain=pdfhttp://dx.doi.org/10.1016/j.apenergy.2014.06.087mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.apenergy.2014.06.087http://www.sciencedirect.com/science/journal/03062619http://www.elsevier.com/locate/apenergy
-
MInverterBattery Supercapacitor
DC Bus
+
-
Fig. 1. Passive parallel configuration.
Z. Song et al. / Applied Energy 135 (2014) 212224 213
utilizes the unique advantages of SCs that offer relatively
highpower density, yet low energy density, when compared to thoseof
conventional batteries. Therefore, this combination (of SCs
andbatteries) in HESSs inherently offers better performance
incomparison to the use of either of them alone [4].
HESSs can be classified into three major types, namely,
passive,semi-active, and fully active. In passive HESSs, the
battery and SCpacks are connected in parallel and directly coupled
to the dcbus [911]. The passive HESS is the most simple and
low-costtopology. Nevertheless, the performance is often
compromised,as SCs cannot be used effectively in this topology, and
there is nodegree of freedom (DOF) in the control algorithm. On the
otherhand, a fully active HESS achieves the best control effect, as
itinvolves the use of two dc/dc converters and an additional
controlcircuit [1214]. Nonetheless, this topology demands
compromisein terms of cost, weight volume, efficiency, and
simplicity. Thesemi-active HESS, which consists of one dc/dc
converter, is a goodtradeoff between performance and system cost.
Given theseadvantages, semi-active HESS is favored to be the most
intensivelyused topology [4,15,16]. In this study, we have proposed
a novelsemi-active HESS, which uses a converter with the lowest
ratingamong the semi-active HESS. The effectiveness of the
proposedHESS has been verified by the simulation results.
The main purpose of using a HESS is to protect the batteryunder
conditions of frequent and peak power demand. However,to the best
of our knowledge, there are no quantitative studiesreported on the
use of HESS to optimize the battery capacity loss.Therefore, in
this study, we have designed a dynamic batterycapacity fade model
on the basis of the Arrhenius degradationmodel. In addition, the
key factors influencing the battery capacityloss, namely, working
temperature, charge/discharge rate, and Ah-throughput, have been
calibrated in this model via experimentaldata by using the least
squares method. On the basis of the batterycapacity fade model,
this paper presents an optimal sizing methodfor a LiFePO4 battery
and SC-powered electric city bus equippedwith the proposed HESS.
The optimization was performed fromthe viewpoints of two
conflicting objectives, namely (i) minimizingthe cost of the HESS
and (ii) minimizing the battery capacity lossover a typical China
City Bus Driving Cycle (CBDC). In this study,we have proposed four
sizing parameters for the HESS, e.g., theparallel and series
numbers of battery cells and SC modules. More-over, the requirement
of minimal mileage with constant vehicularspeed was considered as
the constraint for the optimizationprocess. To this end, we used
the non-dominated sorting geneticalgorithm II (NSGA-II) developed
by Deb et al., to optimize theseconflicting objectives [17]. The
optimal Pareto front, which offersa reasonable tradeoff between the
two objectives, and severaloptimal sizing rules have been obtained
and discussed.
Recently, several studies have addressed the system
configura-tion and component sizing of HESSs. For instance, Donghwa
et al.[18] presented a battery-SC hybrid system that employs a
con-stant-current regulator to improve the delivered energy
density.It uses a design space exploration algorithm based on
thecharacteristics of the proposed architecture. Similarly,
Henson[19] performed a comparative study between different depths
ofdischarge, with an aim to reduce the lifetime cost of the
bat-tery/SC energy storage system. Meanwhile, Bashash et al.
[20]used NSGA-II to optimize the charge pattern of a battery/SC
HESSused in PHEVs, to simultaneously minimize (i) the total cost
offuel and electricity and (ii) the total battery health
degradation.In addition, some studies have focused on the sizing
and optimi-zation of other types of HESSs, such as the fuel
cell-battery HESS[21]. However, to the best of our knowledge, there
are no pub-lished papers that focus on the size of the battery/SC
HESS forminimizing both the system cost and the battery
degradationquantitatively.
This paper is organized as follows: In Section 2, we
introducethe theoretical models of LiFePO4 batteries and SCs.
Section 3presents a detailed description of the proposed HESS, and
analyzesthe comparative results between different HESSs. In Section
4, wepropose the optimal sizing method for the proposed HESS to
simul-taneously minimize the system cost and battery degradation,
andobtain the optimal Pareto front that trades off the two
objectives.The conclusions derived in this study are presented in
Section 5.
2. The proposed HESS
In general, batteries have a relatively high energy density
of30200 Wh/kg, whereas SCs are characterized by relatively
lowerenergy density and significantly higher power density. On
theother hand, the lifespan of SCs is over one million cycles,
whichis about hundreds times higher than that of batteries.
Moreover,SCs exhibit superior low-temperature performance compared
tobatteries. Given the advantages of the SC and battery
combination,several studies were performed on the design and
control of HESSsin different configurations [4,916]. In this
section, we have pro-vided a brief summary of the most widely used
HESS topologies.
2.1. Passive parallel topology
The passive parallel topology shown in Fig. 1 is the
simplestmethod of combining batteries and SCs, as it does not
involve theuse of any additional electronic converters/inverters
[911]. Hencethis topology offers the advantages of high efficiency
and relativelylow cost. However, the two sources in this topology
are alwaysparalleled, which limits the effective utilization of the
SC storedenergy. As illustrated in Eqs. (1)(3), SCs essentially
work as alow-pass filter, whose performance is related to the
resistancesof battery/SC and the SC capacity.
IBatjx ILoadjx HSCjx 1
HSCjx 1 jxCSCrSC
1 jxCSCrSC rBat2
ISCjx ILoadjx IBatjx 3
where ILoad is the load current, IBat is the battery pack
current, ISC isthe SC pack current, and Hsc is the transfer
function from ILoad to IBat.In principle, HSC(jx) is a leadlag
filter. Nevertheless, it exhibitslow-pass characteristics, as the
battery pack resistance rBat is muchhigher than the SC pack
resistance rSC. In this topology, increasingthe SC capacity is the
direct method for improving the filter perfor-mance, so as to
protect the battery in a better manner. However,this will increase
the usage of SCs, which in turn will increase theassociated
cost.
2.2. Fully active topology
The fully active topology, as shown in Fig. 2,
ultimatelydecouples the battery and SC with dc bus by employing
two
-
MInverterBattery
Supercapacitor
DC Bus
+
-
Bidirectional DC/DC
Converter
Bidirectional DC/DC
Converter
Fig. 2. Fully active configuration.
MInverterBattery
Supercapacitor
DC Bus
+
-
Bidirectional DC/DC
Converter
Fig. 4. Battery/SC configuration.
MInverter
BatterySupercapacitor
DC Bus+
-
Bidirectional DC/DC
Converter
Fig. 5. A semi-active configuration incorporated with a
diode.
214 Z. Song et al. / Applied Energy 135 (2014) 212224
dc/dc converters [1214]. Voltages of both the battery and SC
canbe independently maintained lower than the dc bus
voltage,thereby providing an opportunity to fully utilize the
functionalitiesof SC. However, the control algorithm associated
with this topologyis rather complex. In addition, this topology
involves the use of twofull-sized converters, which might lead to a
decrease in systemefficiency, as well as an increase in the
cost.
2.3. SC/battery topology
The SC/battery topology shown in Fig. 3 uses a bidirectional
dc/dc converter to interface the SC, thereby allowing the
deploymentof a wide range of the SC voltage [15]. Although it is
one of themost widely studied configurations, the bidirectional
dc/dcconverter should be of large size to handle the SC power flow.
Inaddition, the SC should operate frequently under
high-pulsedcharging/discharging power conditions, which in turn
tends todecrease the overall efficiency of the system.
2.4. Battery/SC topology
The battery/SC topology can be achieved by interchanging
thepositions of the battery and SC in the SC/battery configuration,
asshown in Fig. 4 [4]. In this topology, the SC is directly
connectedto the dc bus working as a low-pass filter, while the
battery isindependently controlled via a dc/dc converter. One of
the majorproblems associated with this topology is the requirement
of a fullsize converter. In addition, the voltage of the dc bus
varies in awide range. This is not desirable in some applications,
taking intoconsideration the requirements of motors and their
controllers.
2.5. Semi-active topology incorporated with a diode
Cao et al. first proposed the semi-active HESS that is
equippedwith a small dc/dc converter and a diode, as shown in Fig.
5 [16].In this topology, the dc/dc converter works as a controlled
energypump, thereby maintaining the SC voltage at a value higher
thanthe battery voltage. The primary role of the battery is to
provide
MInverterBattery
Supercapacitor
DC Bus
+
-
Bidirectional DC/DC
Converter
Fig. 3. SC/battery configuration.
power when the SC voltage drops below the battery
voltage,thereby creating a relatively constant load profile for the
battery.
2.6. Novel semi-active topology proposed in this study
To further reduce the size of the dc/dc converter as well as
tosimplify the control algorithm of the semi-active topology
pro-posed by Cao et al., we have proposed a modified semi-active
HESS,as shown in Fig. 6. Most advantages of the topology proposed
byCao et al. have been reserved in the proposed topology.
Moreover,the dc/dc converter is unidirectional, the essential
function ofwhich is to store the regenerative braking energy into
the battery,under the condition that the SC is fully charged. Thus,
the dc/dcconverter can be much smaller when compared to the ones
usedin the other topologies. Additionally, the HESS efficiency can
beincreased further, as the converter operates sporadically
undermost city driving conditions.
The operation of the proposed HESS can be separated into
fourmodes according to its status and vehicle operation
conditions.When the vehicle is in driving mode, two operation modes
areincluded, depending on whether the SC voltage USC is higher
thanthe battery voltage UBat. Under the condition that UBat is less
thanUSC, the SC supplies the entire demanded power, while the
batteryis neither absorbing nor providing power to the electric
motorbecause the diode is reversely biased as shown in Fig. 7(a).
WhenUSC drops to the same level as UBat, the battery and SC
becomedirectly paralleled through the diode, thereby supplying
thedemanded power simultaneously, as shown in Fig. 7(b).
MInverter
BatterySupercapacitor
DC Bus+
-
Undirectional DC/DC
Converter
Fig. 6. The semi-active topology proposed in this study.
-
MInverter
BatterySupercapacitor
DC Bus+
-
Undirectional DC/DC
Converter
No operation
(a) Traction operation energy flow when USC > UBat
MInverter
BatterySupercapacitor
DC Bus+
-
Undirectional DC/DC
Converter
No operation
(b) Traction operation energy flow when USC UBat
MInverter
BatterySupercapacitor
DC Bus+
-
Undirectional DC/DC
Converter
No operation
(c) Regenerative braking operation energy flow when SC is not
fully charged
MInverter
BatterySupercapacitor
DC Bus+
-
Undirectional DC/DC
Converter
Buck operation
(d) Regenerative braking operation energy flow when SC is fully
charged
Fig. 7. Operation modes of the HESS.
5V
SC pack voltage (V)
1
-1
USC_max
Fig. 8. Hysteresis control of regenerative braking energy
flow.
Table 1Basic parameters of the SC module.
Parameter Value
Maximal voltage (V) 27CM, Capacity (F) 140CostSC_M, Cost of the
SC module (RMB) 950Stored energy (kJ) 5103
Z. Song et al. / Applied Energy 135 (2014) 212224 215
When the vehicle is in braking mode, there are again two
oper-ation modes, depending on whether or not the SC is fully
charged.If the SC is not fully charged, then all the regenerative
brakingenergy will be stored in the SC, as shown in Fig. 7(c). On
the con-trary, if the SC is fully charged, all the regenerative
braking energywill be stored in the battery, as shown in Fig.
7(d).
Furthermore, hysteresis control schemes were applied to con-trol
USC, to avoid the frequent start/stop of the dc/dc converter
inregenerative braking state. The control scheme is shown in Fig.
8,wherein the status 1 indicates the operational mode of
dc/dcconverter, while the status 1 implies that the dc/dc
converteris idle. The core philosophy of the charging strategy is
that the bat-tery only receive the regenerative energy when the SC
is fully
charged. This strategy allows a more efficient use of the SC,
andreduces the battery stress in practical applications.
3. Theoretical model
3.1. SC model
Compared to LiFePO4 batteries, SCs have a higher
charge/discharge efficiency, longer cycle life, and wider operating
temper-ature range. However, the energy density of a SC is much
lowerthan that of the LiFePO4 battery. In this study, the capacity
fadeof SCs has been neglected, with the primary focus of
themulti-objective optimization process being the cost of the
SC.The SC module used in this paper consists of 40 (4 parallel
con-nected and 10 series connected) SC cells (2.7 V, 350 F). This
SCmodule is the minimum unit in the optimization process,
theparameters of which are listed in Table 1. The relationship
betweendischarge resistance RSC_M,ch, charge resistance RSC_M,ch,
anddischarge and charge currents were experimentally determined,as
shown in Fig. 9.
Assume that the SC pack is composed of the aforementioned
SCmodules that are grouped via NSC series and MSC parallel
connec-tions. Accordingly, the following equations can be
deduced:
CSC MSCCM=NSCRSC;ch NSCRSC M;ch=MSCRSC;disch NSCRSC
M;disch=MSCVSC VSC MNSC
8>>>>>:
; 4
where CSC is the capacity of the SC pack, RSC,ch is the charge
resis-tance of the SC pack, RSC,disch is the discharge resistance
of the SCpack, VSC_M is the open circuit voltage (OCV) of the SC
module,and VSC is the OCV of the SC pack. The state of charge (SOC)
of theSC is linearly proportional to VSC as follows:
SOCSC VSCVn2 0;1 5
Erel 0:5CSCV2n1 SOC20 6
where Vn is the SC voltage under fully charged condition, Erel
is thereleased energy of the SC when its SOC drops to SOC0.
Generally, theSOC working range of the SC is 0.51 because 75% of
the energy
-
Fig. 9. Resistance of the SC module.
Table 2Basic parameters of the battery cell.
Parameter Value
VBat_cell, Nominal voltage (V) 3.3CBat_cell, Capacity (Ah)
60Stored energy (kJ) 831.6Mass (kg) 2.5Operation temperature range
(C) 20 to 45
Fig. 11. Charge and discharge resistances of the LiFePO4
cell.
216 Z. Song et al. / Applied Energy 135 (2014) 212224
stored in SC is released when its SOC is 0.5. Therefore, from
the effi-ciency standpoint, the SOC of SC is typically controlled
above 0.5.
This paper focuses on the HESS performance over a prolongedtime
range, namely, a CBDC. Therefore, there is no stringentrequirement
for the transient response accuracy of the HESS.Accordingly, the
Rint-Capacity model shown in Fig. 10(a) wasadopted to represent the
behavior of SCs, primarily due to its sim-plicity and sufficient
accuracy.
3.2. Battery model
Compared to the other types of batteries utilized in EVs, such
asnickelmetal hydride, nickelcadmium, and leadacid batteries,the
LiFePO4 battery is preferred owing to its high voltage,exceptional
specific capacity, and long cycling life. However, itdoes not
exhibit desirable performance at low temperatures [21].The
parameters of the LiFePO4 cell used in this study are shownin Table
2.
The Rint model shown in Fig. 10(b) was adopted to representthe
battery behavior. The charge resistance RBat_cell,ch and
dischargeresistance RBat_cell,disch of the cell are measured under
differenttemperatures and SOCs. Accordingly, two maps can be
generatedon the basis of the experimental results shown in Fig. 11,
andinserted in the battery model.
Assuming that the battery pack in the HESS is grouped bybattery
cells via NBat series and MBat parallel connections,
CBat MBatNBatCBat cellRBat;ch NBatRBat cell;ch=MBatRBat;disch
NBatRBat cell;disch=MBatVBat VBat cellNBat
8>>>>>:
: 7
CSC
RSC
VSC
ISC
(a) RC model of the SC
V
Fig. 10. Simplified circuit mod
3.2.1. Battery degradation modelThe basic motivation of using a
HESS is to prolong the lifespan
of the battery under frequent charge/discharge operations.
How-ever, there are no published articles that provide a
quantitativecomparison of battery capacity loss between different
HESS topol-ogies. Over the past years, there have been substantial
efforts todevelop models for predicting capacity fade in lithium
ion batteries[2225]. These models have been developed from
different scenar-ios, such as parasitic side reactions [22],
solid-electrolyte interfaceformation [23], and resistance increase
[24], which contribute tocapacity fade in batteries. However, these
models need sufficientexperimental data to study the aging process
of a battery systemand validate the capacity fading mechanism.
Moreover, it is a chal-lenging task to implement these three models
in practical EVs dueto their complex calculation and calibration
processes. Wang et al.
CBat
RBat
Bat
IBat
DC
(b) Rint model of the battery
el of SC and battery packs.
-
:
Fig. 12. Verification of the battery degradation model.
Z. Song et al. / Applied Energy 135 (2014) 212224 217
proposed a semi-empirical life model, considering the effects
offour parameterstime, temperature, depth of charge, and dis-charge
rate [25]. As shown in Eq. (8), this semi-empirical model,which is
based on the Arrhenius degradation model, can reliablydescribe the
factors affecting the battery life.
Q loss Ae EaBC RateRTBat
Ah z; 8
where Qloss is the battery capacity loss (the initial capacity
of thebattery is normalized to 1), A is the pre-exponential factor,
Ea isthe activation energy (J), R is the gas constant (J/(mol K)),
T is theabsolute temperature (K), Ah is the Ah-throughput, C_Rate
is thedischarge rate, and B is the compensation factor of C-rate.
To usethis model in dynamic processes, such as in CBDC, an
assumptioncan be made according to the cumulative damage theory
[26].
Assumption the capacity fade model of LiFePO4 battery shown
inEq. (8) can also be used for predicting the battery
dynamicdegradation.
Throughout the experiments, the battery was charged at0.3C-rate,
and discharged at 1.5C-rate. Thus, in the followinganalysis, the
C_Rate is considered constant for simplicity. TheEq. (8) can be
transformed to
Ah Q losseEaBC Rate
RT =A 1
z: 9
And its derivative can be deduced as
_Q loss zAe EaBC RateRTBat
Ahz1: 10
By incorporating with Eqs. (9) and (10), we get
Q loss;p1 Q loss;p DAhzA1ze EaBC RatezRTBat
Q
z1z
loss;p; 11
where Qloss,p and Qloss,p+1 are the accumulated battery capacity
lossat instants t and t + 1; DAh is the Ah-throughput during tp to
tp+1defined as
DAh 1
3600
Z tp1tpjIBatjdt: 12
Furthermore, we performed the battery degradation experi-ments
on the LiFePO4 cell, to calibrate the parameters in thebattery
capacity fade model as well as to verify its accuracy. Inthe
experiment, the cell was discharged from 100% SOC to 0%SOC at
1.5C-rate. Subsequently, after a standing period of 20 min,the cell
was charged to 100% SOC at 0.3C-rate, once again followedby a
standing time of 20 min. The experiment cycle repeats as
illus-trated above. After every 30 cycles, the battery cell
capacity isachieved by averaging three measurements and the Hybrid
PulsePower Characterization (HPPC) test is done. To consider the
effectof working temperature on battery degradation, during the
exper-iment, the temperature of the thermotank was changed between5
C and 45 C after every 90 cycles. The initial capacity of the
cellis 61.82 Ah, and the initial capacity loss is zero. The
theoreticalcapacity loss after 30 experimental cycles can be
deduced fromEq. (13) given below:
Q 0lossQ loss;0X30i1
CBatzA1z e Ea1:5BzRTBat
Q
z1z
loss;2i1CBatzA1z e Ea0:3BzRTBat
Q
z1z
loss;2i
!
13
Based on the Eq. (11) and the experimental data, the
variousparameters, including A, B, Ea, and z, are calibrated using
leastsquare fit method.
Q loss 0:0032e 151621516C RateRTBat
Ah0:824: 14
The verification result of the battery capacity fade model
shownin Fig. 12 reveals that the prediction accuracy of the
proposedmodel is satisfactory under different C-rates and
temperatures.Therefore, the battery degradation model can be
considered suit-able for calculating battery capacity loss in
dynamic processes,and can be used in this study to provide an
important index forassessing the HESS performance.
3.2.2. Battery thermal modelAs mentioned above, temperature is
the key factor that influ-
ences the battery degradation rate. Therefore, it is important
togain a comprehensive understanding of the temperature
changescaused in the battery as a result of heat generation during
thecharging/discharging process, to accurately predict the
batterycapacity loss. To this end, the thermal-electrochemical
model hasbeen proposed and verified by C. Forgez et al., in which
the internalheat generation during regular charge/discharge can be
simplifiedas Eq. (15) [27] given below:
_QBat IBatVBat UavgBat IBatTBat@UavgBat@TBat
; 15
where _QBat is the heat generation rate (positive for heat
generationand negative for heat absorption), IBat is the battery
operating cur-rent (positive for discharging and negative for
charging), UBat isthe battery terminal voltage (the value with
superscript avg denotesan average concentration in a certain
volume), VBat is the batteryOCV, and TBat is the battery
temperature. The first part of the equa-tion on the right side
denotes the resistive joule heat, while the sec-ond part denotes
the reversible entropic heat, or the reaction heatthat indicates
entropic change during the charge/discharge process.
The joule heat can be calculated by using the
charge/dischargeresistance shown in Fig. 11, while the reaction
heat is determinedby the battery operating current and the
effective entropic poten-tial (@UavgBat =@TBat; in which T is the
absolute temperature). Theentropic potential is strongly influenced
by the SOC of the battery,but the influence of temperature on the
entropic potential is stillnot clear. In this study, we performed
the entropic potentialcalibration of the LiFePO4 cell, and the
corresponding results areshown in Fig. 13. The accuracy of the
results was verified by con-ducting an experiment in which the UBat
is measured during eachtemperature test cycle at different SOCs.
The results of the verifica-tion experiment shown in Fig. 14
indicate that the measured effec-tive entropic potential is
accurate to be used in the battery thermalmodel.
Considering the heat dissipation, the complete battery
thermalmodel can be described as
Cpack@TBat@t hBatTBat Tenv _QBat; 16
-
Fig. 13. dU/dT under different SOCs.
Fig. 14. dU/dT verification results.
Fig. 15. Typical CBDC.
Table 3Basic parameters of the city bus.
Parameter Value
m, Vehicle mass (kg) 14,000Vehicle length (m) 12R, Wheel radius
(m) 0.5g, Gravity acceleration (m s2) 9.8CD, Air drag coefficient
0.7A, Front area (m2) 7.5q, Air density (kg m3) 1.29gT,
Transmission efficiency (%) 90gmd, Motor efficiency (%) 85gHess,
HESS Efficiency (%) 95Paux, Auxiliary power (kW) 8DC bus voltage
(V) 300600
218 Z. Song et al. / Applied Energy 135 (2014) 212224
Cpack MBatNBatCcell; 17
where Ccell is the thermal capacity of the battery cell, Cpack
is thethermal capacity of the battery pack, hBat is the heat
transfer coeffi-cient, and Tenv is the environmental temperature.
By performing theadiabatic test, the fitting result of Ccell was
obtained to be 2299 J/C,and hBat is assumed as 15 W/C.
3.3. Comparative analysis and simulation results
The configured city bus is simulated in Matlab/Simulink byusing
the third-order BogackiShampine formula (the ode3 solver).To verify
the effectiveness of the HESS topology proposed in thisstudy, we
compared its performance with that of battery-only con-figuration
and passive parallel configuration under the CBDC, asshown in Fig.
15. The initial capacity loss of the battery is 10%and the ambient
temperature is 15 C. Prior to the comparison,the following two
assumptions were made, so as to ensure a fairlyjustifiable
comparison.
(1) Battery pack with the same storage-size and
configuration(100 series and 6 parallel) is applied to the three
HESSs,the initial SOCs of which in the three configurations are
0.9.
(2) Similarly, SC pack with same storage size and
configuration(14 series and 3 parallel) is applied to the proposed
and pas-sive parallel HESSs. Furthermore, the initial voltage of
thesetwo HESSs is equal to the initial voltage of the battery
pack.
The parameters of the prototype electric bus modeled in
thisstudy are listed in Table 3.
As evidenced from the simulation results shown in Fig. 16,
thebattery in the battery only configuration experiences the most
fluc-tuating power profile. Further, it needs to provide the
largest peakpower especially under regenerative braking conditions.
On theother hand, in the passive parallel configuration, the
battery cur-rent profile is filtered by the SC, which can be
visualized fromthe less fluctuating current profile when compared
to the batterycurrent profile of the battery only configuration.
However, the cur-rent profile of the battery in the passive
parallel configuration istoo fluctuating, when compared to that of
the HESS topology pro-posed in this study. This reveals that the
filter performance of theSC in the proposed HESS is much better,
although the same SC packsize has been adopted in the two
configurations. As shown inFigs. 16(b) and (c), the SC in the
proposed topology is used in awider range when compared to the
passive parallel topology. Asa result, the battery in the proposed
HESS is protected more effec-tively than the other topologies.
Further, as shown in Figs. 16(d)and (e), the temperature increase
and the capacity loss of the bat-tery in the proposed HESS is about
40% less than those of the othertopologies. Moreover, the battery
charge frequency and amplitudein the proposed HESS are the lowest,
indicating that the dc/dc con-verter can be downsized to reduce the
system cost.
4. Optimal sizing methodology
4.1. Optimization formulation and procedure
This paper pursues two objectives in terms of the optimizationof
the proposed HESS. One objective is to minimize the cost of the
-
(a) Comparison of the battery pack current profile
(b) Comparison of the SC current profile
(c) Comparison of the SC voltage profile
(d) Comparison of the increase in battery temperature
(e) Comparison of battery capacity fade
Fig. 16. Comparison results between the proposed HESS,
battery-only configuration, and passive parallel HESSs.
Z. Song et al. / Applied Energy 135 (2014) 212224 219
HESS, and the other objective is to reduce the capacity loss of
thebattery for the city bus over a given CBDC. The first objective
isequivalent to reducing the amount of SCs because the cost
ofbattery is definite in this study (600 LiFePO4 cells are adopted,
asdiscussed in the next section). The NSGA-II developed by Debet
al. is used in this paper to deal with this multi-objective
optimization problem. The entire Pareto front of the optimal
con-figuration parameters can be obtained by using the NSGA-II.
Thisis beneficial from the standpoint of picturing and
understandingthe tradeoffs between HESS cost and battery
degradation. Theoptimal sizing problem can be mathematically
expressed asfollows:
-
220 Z. Song et al. / Applied Energy 135 (2014) 212224
Minimize ff 1x1 costSCx1&f 2x1; x2 Q loss Batx1; x2g;
where x1 MSC;NSC; x2 MBat;NBat;
subject toMBat NBat 600
300 6 3:3NBat 6 600USC max > UBat max
8>: 18
where costSC is the cost of the SC pack, Qloss_Bat represents
thecapacity loss of the battery pack over a CBDC, and USC_max
andUBat_max denote the fully charged voltages of the SC and the
battery,respectively. Accordingly, in the optimization problem we
considerthe following variables: MSC, NSC, MBat, and NBat, which
are not com-pletely independent. The schematic of the size
optimization of SCusing the proposed HESS (optimal sizing process)
is shown inFig. 17.
4.2. Boundary conditions of the optimization
The requirement of minimal mileage is considered as aconstraint
in the optimal sizing problem, based on the vehicledynamic model
(traction mode) given as
mgfv cos a 0:5CDAqv3 mvdvdtmgv sin a PmgTgmd; 19
where m is the EV mass, g is the gravitational acceleration, f
is therolling resistance coefficient, v is the vehicle velocity, a
is the climb-ing angle, CD is the air drag coefficient, A is the
front area, q is the airdensity, Pm is the input electric power of
the dc/ac power inverterrequired by the electric motor, gT is the
transmission efficiency,and gmd is the efficiency of the motor.
Furthermore, the equationdescribing the power balance in an EV
powertrain under tractionmode is shown as
Pm PBat PSCgHess; 20
where PBat is the output power of the battery pack, PSC is the
outputpower of the SC, and gHess is the average efficiency of
HESS.
The optimization process considers the minimal mileage L ofmore
than 100 km, obtained at a constant cruising speed v0(50 km/h) on a
flat road. Accordingly, we can deduce the followingequation:
CDAqv202
mgf
LgTgmdgHess
6 EHess: 21
In terms of the HESS, the energy stored in the SC is much
lessthan the energy stored in the battery pack. Therefore, the
energyin the SC could be neglected in calculating the number of
batterycells required to fulfill the minimal mileage
requirement.
HESSs
The proposed HESS Electrica
Multi-objectiveoptimizer
Optimization variables
System cost&
Battery degradation
Power demand
Poweroutput
Fig. 17. Schematic of the optimal sizing
CDAqv202
mgf
LgTgmdgHess
13600CBat cellVBat cell
6 NBatMBat 22
According to Eq. (22), the number of the battery cell should
bemore than 605. Considering the arrangement of the battery
pack,600 battery cells would be appropriate for grouping. Thus,
thenumber of battery cells is fixed at 600 in the following
analysis,while NBat and MBat change simultaneously in the
optimizationprocess. Several boundary conditions of the
optimization problemare given below:
(1) To fairly evaluate every member (a definite group of MSC,
NSC,MBat, and NBat), the battery capacity loss value is the
averagevalue of the results when the initial SOC of the battery
packare 30%, 40%, 50%, 60%, 70%, 80%, and 90%. This implies
thatseven simulations are necessary to evaluate one configura-tion
candidate.
(2) The initial SOC of the SC pack is 1.1 times more than that
ofthe battery pack. This is considered reasonable because theSC
will be charged during the last period of every drivingcycle due to
the braking process. Thus, at the beginning ofeach new cycle, the
voltage of the SC pack will be slightlyhigher than that of the
battery pack.
(3) To ensure the validity of the optimized result under
differenttemperatures, the optimization problem is performed at
twotemperature conditions, namely, 15 C and 40 C.
(4) Considering the requirement of dc bus voltage (e.g.,300600
V), the following three different grouping patternsare included in
this paper:
l bus m
proces
Battery group 1 : x2 MBat;NBat 6;100;Battery group 2 : x2
MBat;NBat 5;120;Battery group 3 : x2 MBat;NBat 4;150:
23
(5) Focusing on each battery pack, 66 different SC packs
aretaken into consideration. Assume that NSC0 is the least
seriesnumber of SC module to ensure USC_max > UBat_max.
MSC 1;2; . . . ;6NSC NSC0;NSC0 1; . . . ;NSC0 10
: 24
4.3. Optimization results
The analysis of the optimization results is rather
complexbecause of the very large initial population of
approximately 198members at each temperature. The system cost is
linearly propor-tional to the amount of SC modules used in the
configuration.However, the relationship between battery capacity
loss and opti-mal variables is highly non-linear. Accordingly, the
simulation
odel China bus drive cycleSpeed demand
s using the proposed HESS.
-
Fig. 18. Battery capacity loss at 15 C with various HESS
parameters.
Z. Song et al. / Applied Energy 135 (2014) 212224 221
-
Fig. 19. Optimal Pareto front obtained using NSGA-II.
222 Z. Song et al. / Applied Energy 135 (2014) 212224
results indicating the effect of various optimal variables
(e.g., MSC,NSC, MBat, and NBat) on battery capacity loss is shown
firstly inFig. 16. With increase in MSC, the battery capacity loss
tends toreduce. This could be attributed to the fact that the
increase ofSC capacity brings a better filter performance, as
proven by Eq.(2). For MSC less than five, the battery capacity loss
decreases withan increase in NSC. This is because the operation
range of the SCpack becomes wider with increase in
(USC_maxUBat_max). The bat-tery will be better protected when the
SC works in a wider range.On the other hand, for MSC value of six,
the battery capacity lossfalls initially, followed by an increase
with increase in NSC. Thistrend exhibits an inflection point. The
reason is that all the regen-erative braking energy can be absorbed
by SCs for large MSC andNSC. Furthermore, the SC operation range is
wider enough to pro-tect the battery. Further increase in NSC has
no significant effecton the battery capacity loss because of the
decrease in the capacityof the SC pack and increase in the average
resistance of the SC pack.This tends to impair the filter
performance as shown in Eq. (2). Insummary, the battery pack
exhibits better performance for largeMSC and NSC; however, it
increases the cost of the HESS.
Focusing on different battery grouping patterns, the overall
bat-tery capacity loss declines with scaling up of NBat as a result
of theincrease in the average resistance of the battery pack, as
illustratedin Eq. (25). Notably, when the power demand of the
battery is con-stant, the system efficiency will not change because
the battery cellamount is definite, as presented in Eq. (25).
gBat 1PBat
NBatUBat cell
2 NBatRBat cellMBat
1 P
2BatRBat cell
MBatNBatU2Bat cell
;
25
where PBat is the battery power, UBat_cell is the voltage of the
batterycell, RBat_cell is the resistance of the battery cell, and
gBat is the effi-ciency of the battery pack.
To sum up, the two objectives in the optimal sizing problem
areconflicting, according to the simulation results shown in Fig.
18. Thus,the NSGA-II used in this paper provides the optimal Pareto
front, aswell as trades off the two independent optimization
objectives.
The optimization results at 15 C and 40 C are shown inFigs.
19(a) and (b), respectively. There are 198 members at
eachtemperature. After 100 generations, we obtained two Pareto
frontsthat show similar law. In order to compare the performance of
dif-ferent members, all members results are shown in the figure.
Focus-ing on the optimization result at 15 C (Fig. 18(a)), the
batterycapacity loss in the Pareto front ranges from 1.74 104%
to3.12 104%, while the SC cost ranges from 10 to 180 thousandRMB.
It could be realized that the battery capacity loss can bereduced
rapidly when the SC cost is increased in the range of 1040 thousand
RMB. However, the effect of increasing the SC usageon reducing the
battery capacity loss is not obvious for the SC cost-ing more than
40 thousand RMB. As shown in Fig. 19(b) the batterycapacity loss
increases overall under 40 C, because of the rise in theworking
temperature of the battery. However, the underlying law issame as
that at 15 C. Furthermore, they have the same optimalsolutions that
form their Pareto fronts, indicating that the optimiza-tion results
are meaningful for a wide range of working temperature.
There are 36 optimal solutions in each Pareto front with
aninflection point in each front, which can be regarded as the
nearoptimal solution. In fact, any solution in the Pareto front can
beconsidered the optimal solution from different standpoints. All
inall, a group of design references are provided in the Pareto
front.
4.4. Sample optimal solutions of the proposed HESS
In this section, we have presented three optimal solutions of
theproposed HESS selected from the Pareto front, and compared
at
15 C. These solutions include the HESS associated with least
SCcost, namely, Sol. #1, and least battery capacity loss; Sol.
#138,as well as the inflection solution; Sol. #115, which reflects
the dif-ferent trade off relationships between the two optimization
objec-tives. The three selected solutions are listed in Table 4
according tothe order of the associated SC cost. In the comparison,
the initialSOC of the battery pack is considered as 80%. The
results are shownin Fig. 20, from which the following conclusions
can be derived:
(1) Sol. #1 involves the use of least amount of SC modules,
andhence incurs the lowest cost among all the members. How-ever,
the battery operates in the adverse condition, and theSC operates
in a narrow range. The SC is not used effectively,thus the battery
will be damaged by the undulate powerdemand. Therefore, this
configuration is expected toincrease the all life circle cost of
the HESS.
(2) Sol. #138 corresponds to the configuration that results in
theleast battery capacity loss. The fluctuations in the
batterypower profile are well suppressed due to the effective
usageof SC modules. There is no charging process in battery
powerprofile because USC_max is much higher than UBat_max. The
-
Table 4Sample optimal solutions in the Pareto front.
Solution MBat NBat MSC NSC Supercapacitorcost (thousand RMB)
Battery capacity lossunder 15 C (104%)
Battery capacity lossunder 40 C (104%)
#1 6 100 1 13 13 2.97 5.21#115 5 120 1 25 25 1.92 3.36#138 4 150
6 21 126 1.73 3.03
(a) Battery power
(b) SC power
(c) SC voltage
(d) Battery temperature rise
Fig. 20. Selected solutions in the Pareto front.
Z. Song et al. / Applied Energy 135 (2014) 212224 223
battery pack in this member is well protected, and the
leastbattery capacity loss is achieved. However, the cost of
SCmodules is up to 130 thousand RMB.
(3) Sol. #115 is the inflection optimal solution in the
Paretofront shown in Fig. 19(a), which trades off the HESS costand
battery capacity loss with a reasonable balance on thetwo
objectives. As shown in Fig. 20, the battery power profileis almost
similar to that of Sol. #138; however, it hasobvious difference
with Sol. #1. This implies that Sol. #115is much effective in
protecting the battery. As shown inFig. 20(c), the SC operates in a
wider range when comparedwith Sol. #138, which means that the SC in
Sol. #115 ismuch more efficient. Moreover, it uses much less
numberof SCs when compared to Sol. #138. Given these
considerations, this configuration can be considered
moresuitable for practical applications.
A quantitative analysis of battery life extension is addressed
inthis paper. Assuming that the battery cannot be used when
itscapacity reduces to 80% of its initial value. Furthermore, the
drivingdistance of one CBDC is 5.84 km. Thus the equivalent driving
dis-tance that the battery can support can be determined from Eq.
(26).
Lcycle 5:84 20Q loss CBDC
; 26
where Qloss_CBDC is the battery capacity loss during one
CBDC.Finally, the comparison results of the battery only
configuration,the solution #1, the solution #115, and the solution
#138 at 15 C
-
Table 5Comparison results of the whole distance that the battery
can support.
Solution The distance that the batterycan support Lcycle (105
km)
Battery only 3.65#1 3.93#115 6.08#138 6.75
224 Z. Song et al. / Applied Energy 135 (2014) 212224
are listed in Table 5. It turns out that the solution #115,
which canbe considered as the best solution, can significantly
extend Lcycle upto 67% when compared to the battery only
configuration. The effec-tiveness of adopting the SC in the ESS is
therefore proved.
5. Conclusion
HESSs used in EVs, HEVs, and PHEVs are extremely importantdue to
the limitations on the cost and relatively short lifetime ofthe
LiFePO4 battery. This study proposes a modified HESS, whichis
equipped with a diode and a unidirectional dc/dc converter, withan
aim to reduce the system cost, as well as increase the
systemefficiency. The effectiveness of the proposed HESS is
verified bythe simulation results, which also reveals that
batteries in the pro-posed HESS can be protected much effectively
when comparedwith the scenario in other topologies.
In addition, the thermal model and the capacity fade model ofthe
LiFePO4 battery are built using Matlab/Simulink and verifiedby
experimental studies.
Based on the aforementioned work, we performed the
sizingoptimization of the proposed HESS under two different
operatingtemperatures, namely, 15 C and 40 C. The requirement of
mini-mal mileage on the proposed HESS is considered in the
optimiza-tion. The optimization goal is to simultaneously minimize
thetotal cost of the HESS as well as the capacity loss of the
LiFePO4battery over a CBDC. Since these two objectives are
inherently con-flicting, we used a non-dominated sorting genetic
algorithm. A Par-eto front of optimal HESS parameter groups was
obtained undereach temperature, wherein two Pareto fronts show
similar laws.The battery capacity loss in the Pareto front ranges
from1.74 104% to 3.12 104% at 15 C, while the SC cost rangesfrom 10
to 180 thousand RMB. The battery capacity loss can bereduced
rapidly when the SC cost increases within the range of1040 thousand
RMB. However, the effect of increase in SC onthe reduction of
battery capacity loss is not obvious for the SC cost-ing more than
40 thousand RMB. In contrast, the battery capacityloss increases
overall under 40 C. However, they have the samesolutions in the
Pareto front, which shows the similar laws. Theseresults indicate
that the optimization results are meaningful for awide working
temperature range of HESS.
Acknowledgements
This research is supported in the part of international
coopera-tion project of new energy vehicle between China and the
USAunder Grant 2012DFA81190, and also supported by NationalNatural
Science Foundation (NSFC) of China under Contract No.61004075. The
first author of this paper is funded by ChinaScholarship
Council.
References
[1] Lukic SM, Cao J, Bansal RC, Rodriguez F, Emadi A. Energy
storage systems forautomotive applications. IEEE Trans Ind Electron
2008;55:225867.
[2] Lukic SM, Wirasingha SG, Rodriguez F, Cao J, Emadi A. Power
management ofan ultracapacitor/battery hybrid energy storage system
in an HEV. U.K.: IEEEVehicle Power Propulsion Conf. Windsor; 2006.
pp. 68.
[3] Baisden AC, Emadi A. An ADVISOR based model of a battery and
an ultra-capacitor energy source for hybrid electric vehicles. IEEE
Trans Veh Technol2004;53:199205.
[4] He HW, Xiong R, Zhao K, Liu ZT. Energy management strategy
research on ahybrid power system by hardware-in-loop experiments.
Appl Energy 2013;112:13117.
[5] Lu L, Han X, Li J, et al. A review on the key issues for
lithium-ion batterymanagement in electric vehicles. J Power Sources
2013;226:27288.
[6] Ichimura M, Shimomura M, Takeno K, Shirota R, Yakami J.
Synergistic effect ofcharge/discharge cycle and storage in
degradation of lithium-ion batteries formobile phones. In: 27th
International conference on telecommunications.Berlin, Germany,
September, 2005.
[7] Jungst RG, Nagasubramanian G, Case HL, Liaw BY, Urbina A,
Paez TL, et al.Accelerated calendar and pulse life analysis of
lithium-ion cells. J PowerSources 2003;119:8703.
[8] Peterson SB, Apt J, Whitacre JF. Lithium-ion battery cell
degradation resultingfrom realistic vehicle and vehicle-to-grid
utilization. J Power Sources 2010;195:238592.
[9] Liu H, Wang Z, Cheng J, Maly D. Improvement on the cold
cranking capacity ofcommercial vehicle by using supercapacitor and
lead-acid battery hybrid. IEEETrans Veh Technol
2009;58:1097105.
[10] Dougal R, Liu S, White R. Power and life extension of
batteryultracapacitorhybrids. IEEE Trans Compon Packag Technol
2002;25:12031.
[11] Zheng J, Jow T, Ding M. Hybrid power sources for pulsed
current applications.IEEE Trans Aerosp Electron Syst
2001;37:28892.
[12] Amjadi Z, Williamson S. Power electronics based solutions
for plug in hybridelectric vehicle energy storage and management
systems. IEEE Trans IndElectron 2010;57:60816.
[13] Trovo JP, Pereirinha PG, Jorge HM, Antunes CH. A
multi-level energymanagement system for multi-source electric
vehiclesan integrated rule-based meta-heuristic approach. Appl
Energy 2013;105:30418.
[14] Ortuzar M, Moreno J, Dixon J. Ultracapacitor-based
auxiliary energy system foran electric vehicle: implementation and
evaluation. IEEE Trans Ind Electron2007;54:214756.
[15] Hung YH, Wu CH. An integrated optimization approach for a
hybrid energysystem in electric vehicles. Appl Energy
2012;98:47990.
[16] Cao J, Emadi A. A new battery/ultracapacitor hybrid energy
storage system forelectric, hybrid, and plug-in hybrid electric
vehicles. IEEE Trans Power Electron2012;27:12232.
[17] Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist
multiobjectivegenetic algorithm: NSGA-II. IEEE Trans Evol Comput
2002;40:18197.
[18] Shin D, Kim Y, Wang Y, Chang N, Pedram M. Constant-current
regulator-basedbattery-supercapacitor hybrid architecture for
high-rate pulsed loadapplications. J Power Sources
2012;205:51624.
[19] Henson W. Optimal battery/ultracapacitor storage
combination. J PowerSources 2008;179:41723.
[20] Bashash S, Moura SJ, Forman JC, Fathy HK. Plug-in hybrid
electric vehiclecharge pattern optimization for energy cost and
battery longevity. J PowerSources 2011;196:5419.
[21] Xu L, Ouyang M, Li J, Yang F, Lu L, Hua J. Optimal sizing
of plug-in fuel cellelectric vehicles using models of vehicle
performance and system cost. ApplEnergy 2013;103:47787.
[22] Ramadass P, Haran B, Gomadam PM, White R, Popov BN,
Electrochem J.Development of first principles capacity fade model
for Li-ion cells. JElectrochem Soc 2004;151:A196203.
[23] Spotnitz R. Simulation of capacity fade in lithium-ion
batteries. J PowerSources 2003;113:7280.
[24] Fuller TF, Doyle M, Newman J. Simulation and optimization
of the dual lithiumion insertion cell. J Electrochem Soc
1994;141:110.
[25] Wang J, Liu P, Hicks-Garner J, Sherman E, Soukiazian S,
Verbrugge M, et al.Cycle-life model for graphite-LiFePO4 cells. J
Power Sources 2011;196:39428.
[26] Safari M, Morcrette M, Teyssot A, Delacourt C.
Life-prediction methods forlithium-ion batteries derived from a
fatigue approach. J Electrochem Soc2010;157:A71320.
[27] Forgez C, Vinh Do D, Friedrich G, Morcrette M, Delacourt C.
Thermal modelingof a cylindrical LiFePO4/graphite lithium-ion
battery. J Power Sources 2010;195:29618.
http://refhub.elsevier.com/S0306-2619(14)00896-4/h0005http://refhub.elsevier.com/S0306-2619(14)00896-4/h0005http://refhub.elsevier.com/S0306-2619(14)00896-4/h0010http://refhub.elsevier.com/S0306-2619(14)00896-4/h0010http://refhub.elsevier.com/S0306-2619(14)00896-4/h0010http://refhub.elsevier.com/S0306-2619(14)00896-4/h0015http://refhub.elsevier.com/S0306-2619(14)00896-4/h0015http://refhub.elsevier.com/S0306-2619(14)00896-4/h0015http://refhub.elsevier.com/S0306-2619(14)00896-4/h0020http://refhub.elsevier.com/S0306-2619(14)00896-4/h0020http://refhub.elsevier.com/S0306-2619(14)00896-4/h0020http://refhub.elsevier.com/S0306-2619(14)00896-4/h0025http://refhub.elsevier.com/S0306-2619(14)00896-4/h0025http://refhub.elsevier.com/S0306-2619(14)00896-4/h0035http://refhub.elsevier.com/S0306-2619(14)00896-4/h0035http://refhub.elsevier.com/S0306-2619(14)00896-4/h0035http://refhub.elsevier.com/S0306-2619(14)00896-4/h0040http://refhub.elsevier.com/S0306-2619(14)00896-4/h0040http://refhub.elsevier.com/S0306-2619(14)00896-4/h0040http://refhub.elsevier.com/S0306-2619(14)00896-4/h0045http://refhub.elsevier.com/S0306-2619(14)00896-4/h0045http://refhub.elsevier.com/S0306-2619(14)00896-4/h0045http://refhub.elsevier.com/S0306-2619(14)00896-4/h0050http://refhub.elsevier.com/S0306-2619(14)00896-4/h0050http://refhub.elsevier.com/S0306-2619(14)00896-4/h0055http://refhub.elsevier.com/S0306-2619(14)00896-4/h0055http://refhub.elsevier.com/S0306-2619(14)00896-4/h0060http://refhub.elsevier.com/S0306-2619(14)00896-4/h0060http://refhub.elsevier.com/S0306-2619(14)00896-4/h0060http://refhub.elsevier.com/S0306-2619(14)00896-4/h0065http://refhub.elsevier.com/S0306-2619(14)00896-4/h0065http://refhub.elsevier.com/S0306-2619(14)00896-4/h0065http://refhub.elsevier.com/S0306-2619(14)00896-4/h0070http://refhub.elsevier.com/S0306-2619(14)00896-4/h0070http://refhub.elsevier.com/S0306-2619(14)00896-4/h0070http://refhub.elsevier.com/S0306-2619(14)00896-4/h0075http://refhub.elsevier.com/S0306-2619(14)00896-4/h0075http://refhub.elsevier.com/S0306-2619(14)00896-4/h0080http://refhub.elsevier.com/S0306-2619(14)00896-4/h0080http://refhub.elsevier.com/S0306-2619(14)00896-4/h0080http://refhub.elsevier.com/S0306-2619(14)00896-4/h0085http://refhub.elsevier.com/S0306-2619(14)00896-4/h0085http://refhub.elsevier.com/S0306-2619(14)00896-4/h0090http://refhub.elsevier.com/S0306-2619(14)00896-4/h0090http://refhub.elsevier.com/S0306-2619(14)00896-4/h0090http://refhub.elsevier.com/S0306-2619(14)00896-4/h0095http://refhub.elsevier.com/S0306-2619(14)00896-4/h0095http://refhub.elsevier.com/S0306-2619(14)00896-4/h0100http://refhub.elsevier.com/S0306-2619(14)00896-4/h0100http://refhub.elsevier.com/S0306-2619(14)00896-4/h0100http://refhub.elsevier.com/S0306-2619(14)00896-4/h0105http://refhub.elsevier.com/S0306-2619(14)00896-4/h0105http://refhub.elsevier.com/S0306-2619(14)00896-4/h0105http://refhub.elsevier.com/S0306-2619(14)00896-4/h0110http://refhub.elsevier.com/S0306-2619(14)00896-4/h0110http://refhub.elsevier.com/S0306-2619(14)00896-4/h0110http://refhub.elsevier.com/S0306-2619(14)00896-4/h0115http://refhub.elsevier.com/S0306-2619(14)00896-4/h0115http://refhub.elsevier.com/S0306-2619(14)00896-4/h0120http://refhub.elsevier.com/S0306-2619(14)00896-4/h0120http://refhub.elsevier.com/S0306-2619(14)00896-4/h0125http://refhub.elsevier.com/S0306-2619(14)00896-4/h0125http://refhub.elsevier.com/S0306-2619(14)00896-4/h0130http://refhub.elsevier.com/S0306-2619(14)00896-4/h0130http://refhub.elsevier.com/S0306-2619(14)00896-4/h0130http://refhub.elsevier.com/S0306-2619(14)00896-4/h0140http://refhub.elsevier.com/S0306-2619(14)00896-4/h0140http://refhub.elsevier.com/S0306-2619(14)00896-4/h0140Multi-objective
optimization of a semi-active battery/supercapacitor energy storage
system for electric vehicles1 Introduction2 The proposed HESS2.1
Passive parallel topology2.2 Fully active topology2.3 SC/battery
topology2.4 Battery/SC topology2.5 Semi-active topology
incorporated with a diode2.6 Novel semi-active topology proposed in
this study3 Theoretical model3.1 SC model3.2 Battery model3.2.1
Battery degradation model3.2.2 Battery thermal model3.3 Comparative
analysis and simulation results4 Optimal sizing methodology4.1
Optimization formulation and procedure4.2 Boundary conditions of
the optimization4.3 Optimization results4.4 Sample optimal
solutions of the proposed HESS5
ConclusionAcknowledgementsReferences