effi

Applied Energy 135 (2014) 212224

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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
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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


DC Bus+

-

Undirectional DC/DC

Converter

Fig. 6. The semi-active topology proposed in this study.

MInverter


DC Bus+

-

Undirectional DC/DC

Converter

No operation

(a) Traction operation energy flow when USC > UBat

MInverter


DC Bus+

-

Undirectional DC/DC

Converter

No operation

(b) Traction operation energy flow when USC UBat

MInverter


DC Bus+

-

Undirectional DC/DC

Converter

No operation

(c) Regenerative braking operation energy flow when SC is not fully charged

MInverter


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


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.


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.


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


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.


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:


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.


Fig. 19. Optimal Pareto front obtained using NSGA-II.


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.


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


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.

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system optimization

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battery capacity loss

battery celland

battery capacityloss

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electric drive vehicles