608 ieee transactions on automation science and

608 IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 14, NO. 2, APRIL 2017

Power Management for Hybrid Energy StorageSystem of Electric Vehicles Considering

Inaccurate Terrain InformationQiao Zhang,Student Member, IEEE,FengJu,Member, IEEE, Sumin Zhang,Member, IEEE,

Weiwen Deng,Member, IEEE,JianWu,Member, IEEE,and Chao Gao,Student Member, IEEE

Abstract— Terrain information can significantly impact loadpower demand, and in turn, on battery life and system efficiencyof a hybrid energy storage system (ESS) with battery andsupercapacitor. Taking terrain information ahead into consid-eration for proactive power management is one of the mostimportant ways to improve battery life and overall system effi-ciency. However, since terrain information is typically availablefrom commercial geographic information systems database, itis by nature inaccurate with uncertainties with respect to therequirements of power management. This is often worseningwhen combining with commercially low-quality global positioningsystems. This paper proposes a novel power management strategyto cope with the inaccuracy and uncertainties of the terraininformation with the aim to improve battery life, while main-taining overall system performance. First, the impact of terraininaccuracy on battery life and system efficiency is analyzedbased on two different hybrid ESSs with semiactive topologies.Then, a power management control strategy is developed thatactively distributes the power between battery and supercapacitorwith adaptation to terrain inaccuracy and uncertainties. Theobjective of the proposed power management control strategyis to minimize the total cost of the system, including the cost forbattery life and energy. Finally, simulation is conducted that hasverified the effectiveness of the proposed control strategy.

Note to Practitioners—Recently, advanced technologies ingeographic information systems and global positioning systemshave supplied more opportunities for the prediction of futuredriving conditions, which will help more reasonable use of thesystem power demand by extending the planning horizon. How-

Manuscript received October 21, 2016; accepted December 23, 2016. Dateof publication January 20, 2017; date of current version April 5, 2017.This paper was recommended for publication by Associate Editor H. Huand Editor S. Grammatico upon evaluation of the reviewers’ comments.This work was supported in part by NSFC under Grant U1564211, in partby NSF under Grant CNS-1638213, in partby the National Key Researchand Development Program under Grant 2016YFB0100904, and in part byFoundation of State Key Laboratory of Automotive Simulation and Control.(Corresponding authors: Jian Wu; Qiao Zhang.)Q. Zhang is with the School of Automobile and Traffic Engineering,Wuhan University of Science and Technology, Wuhan 430081, China, andalso with the State Key Laboratory of Automotive Simulation and Control,Jilin University, Changchun 130025, China (e-mail: [email protected]).F. Ju is with the School of Computing, Informatics, and DecisionSystems Engineering, Arizona State University, Tempe, AZ 85281 USA(e-mail: [email protected]).S. Zhang, W. Deng, J. Wu, and C. Gao are with the State Key Laboratoryof Automotive Simulation and Control, Jilin University, Changchun 130025,China (e-mail: [email protected]).Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TASE.2016.2645780

ever, the inaccuracy and uncertainties of prediction informationcould have an important effect on the HESS with battery andsupercapacitor. This paper contributes to a better understandingof the details of the impacts of the inaccuracy and uncertainties ofthe terrain information on battery life and system efficiency basedon two different hybrid energy storage systems with semiactivetopologies, and furthermore, a novel power management strategyis developed to deal with inaccuracy and uncertainties. Theresults of this paper will be useful for a practical implementof an HESS for battery life and system efficiency improvement.

Index Terms— Battery life, hybrid energy storagesystem (ESS), power management strategy, system efficiency,terrain inaccuracy.

I. INTRODUCTION

ELECTRIC vehicles are considered to be one of mostpromising transportation tools in addressing issues faced

by automotive industry worldwide on energy and environ-ment [1]. On-board energy storage system (ESS) is undoubt-edly one of the critical systems that mostly influence theenergy efficiency. Although there are various types of ESSsused for electric vehicles, batteries are so far the most widelyadopted energy unit in electric vehicles [2]. However, bat-teries alone as energy sources still face many challenges inmeeting the power requirements for electric vehicles, suchas higher efficiency, smaller voltage drops, larger vehicleacceleration, higher energy recovery rate during braking, betteruphill climbing performance, and so on. Although high-powerbatteries can be made available, they are often very bulky yetcost prohibitive.Supercapacitors, as emerging ESSs, have much higherpower density compared with batteries. They perform wellunder a wider range of low temperature, while batteriestypically claim a smaller operating range and often losetremendous amount of energy at low temperature. In addi-tion, supercapacitors have much lower internal resistance anddeliver over 95% efficiency in general and more than a millionlife cycles by storing energy in an electrostatic field, muchmore than batteries, since batteries rely on chemical reactionto dissipate stored energy and have life of hundreds to lowthousands of cycles. In addition, the cost of supercapacitorshas fallen much more than the cost of batteries. This disparityis likely to continue, since the market is adopting supercapac-itors in greater numbers and the cost of related raw materialsis falling [3], [4].

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ZHANGet al.: POWER MANAGEMENT FOR HYBRID ESS 609

Weighing with factors, such as cost, power, andperformance, it is thus compelling and very advantageousto pair a supercapacitor with a battery to form a hybridizedESS (HESS) with combined power density and energy densityto meet various driving demands on both performance andtravel range, for greener and more sustainable future energystorage products. As a result of the hybridized energy storage,it allows a downsized battery for reduced weight, and allowsbattery to operate without large current spike for extended life.

A. Literature Review

The HESS topology structures can be categorized into threetypes: passive, semiactive, and fully active structures [5]–[8].In passive structure, power distribution between battery andsupercapacitor is inherently realized by the internal resistancesof individual power source without using a bidirectional dc/dcconverter. Therefore, the supercapacitor in this topology can-not be effectively used. In semiactive structure, a bidirec-tional dc/dc converter is used to interface the battery withthe supercapacitor/dc bus, or to interface the supercapacitorwith the battery/dc bus. The fully active structure adopts twobidirectional dc/dc converters such that both sources can becontrolled individually. By comparing the three structures,it can be found that the passive hybrid system is simple instructure and more cost effective, but the fully active hybridsystem offers the best performance. Therefore, a semiactivehybrid system is often a good tradeoff among them in termsof the performance, the structure complexity, and the cost.The HESS control strategies can be broadly classified

into rule-based and optimization-based strategies. Rule-basedstrategies rely only on instantaneous power demand and stateof the HESS for power distribution between battery andsupercapacitor. Optimization-based strategies consider pastand, if possible, future driving condition to determine dis-tribution ratio for the HESS, thus have shown better perfor-mance compared with rule-based strategies [9]–[20]. However,their performance strongly depends on the upcoming drivingcondition.Recently, advanced technologies in geographic information

systems (GISs) and global positioning systems (GPSs) makefuture driving conditions become available. Study on the use ofterrain information to improve fuel economy and system effi-ciency has been done over the past few years. Reference [21]studies a scenario-based drive mission for a heavy dieseltruck. Look-ahead terrain information is used for optimizingthe velocity trajectory with respect to a criterion formulationthat weighs trip time and fuel consumption. Experimentalresults have shown that a fuel consumption reduction ofabout 3.5% on the 120-km route without an increase in triptime. Reference [22] quantifies the potentials of 3-D roadterrain maps to improve the fuel economy of a parallel hybridvehicle. Simulation results have shown that an average fueleconomy improvement of 1%–4% is possible with terrainpreview. A model predictive control (MPC) strategy utilizingthe terrain data is developed to obtain a time-varying powersplit between the combustion engine and the electrical machinein [23]. Simulation results have shown that the MPC strategy

utilizing terrain data gives an improvement of up to 2.2%in fuel economy with respect to the same controller withoutterrain information, on the same route. Reference [24] presentsa power management strategy based on fuzzy logic takinginto consideration information on the slope of a terrain forbattery and supercapacitor hybrid system. Both simulationand experiment results have shown that power managementstrategy can reduce power impulses drawn from the batteryby taking into consideration information on the slope of aterrain.

B. Main Contribution

Prior research work has demonstrated that terrain playsan important role in improving fuel economy and systemefficiency based on the assumption that the attainable terraininformation is accurate. However, it is practically impossi-ble, particularly for on-board application, since complicatedvehicle environment can have significant effect on predictionaccuracy. The main purpose of this paper is to reveal the influ-ence details of the inaccuracy and uncertainties of the terraininformation on the HESS, then propose a power managementstrategy by taking into consideration terrain inaccuracy toimprove system efficiency. The objective of the proposedpower management strategy is to minimize the total cost ofthe system, including the cost for battery life and energy.The main contributions that are fundamentally different fromprior research are summarizedas follows. First, this papercontributes to a better understanding of the details of theimpacts of the inaccuracy anduncertainties of the terraininformation on battery life and system efficiency of the HESS.Second, a novel power management strategy is developed todeal with inaccuracy and uncertainties. The results of thispaper will be useful for a practical implement of the HESSfor battery life and system efficiency improvement.

C. Paper Organization

The remainder of this paper is organized as follows. A semi-active hybrid ESS and its life model are first establishedin Section II. In Section III, the influence of terrain infor-mation inaccuracy is analyzed, in particular, on battery life.A power management control strategy is then developedin Section IV, with effectiveness of the proposed strategyevaluated in Section V. Finally, some conclusive remarks areincluded in Section VI.

II. SEMIACTIVEHESS MODELING

A. Semiactive HESS Topologies

Two typical semiactive HESSs are described in this paper.The first semiactive HESS is shown in Fig. 1, in which adc/dc converter is used to interface the supercapacitor withthe battery/dc bus. The supercapacitor in this topology iseffectively used, because its voltage is decoupled from thebattery. However, the supercapacitor should operate frequentlyunder pulsed and peak power conditions, so that it willdecrease the system efficiency.


Fig. 1. Battery controlled semiactive topological hybrid system.

Fig. 2. Supercapacitor controlled semiactive topological hybrid system.

The second semiactive HESS is shown in Fig. 2, in whichthe dc/dc converter is used to interface the battery with thesupercapacitor/dc bus. The power level of the dc/dc converterin this topology can be reduced compared with the firsttopology. However, the major problem associated with thistopology is that the dc bus voltage varies in a wide range,which will limit its application range.

B. HESS Modeling

Electrochemical models thatare developed to capture allkey behaviors at the battery cell level can achieve highaccuracy. They are suitable for understanding the distributedelectrochemistry reactions in the electrodes and electrolyte.However, these models are usually complicated and significantrequirement for memory and computation. Therefore, they arenot desirable for actual electric vehicle application. Equiv-alent circuit battery models have been developed especiallyfor the purpose of vehicle energy management and batterymanagement system research. Compared with electrochemicalbattery models, equivalent circuit battery models are relativelysimple with a few number of model parameters. At the sametime, they can provide enough accuracy for the investigation ofelectric vehicle energy management. Consequently, equivalentcircuit battery model is adopted for simulating battery.

TABLE I

ELECTRICALPARAMETERS OFBATTERY

Fig. 3. Battery Rint equivalent circuit schematic.

Fig. 4. SupercapacitorRCequivalent circuit schematic.

The basic parameters of the battery used in this paper arelisted in Table I. This paper focuses on the battery life modeland energy model. Therefore, the Rint battery model shownin Fig. 3 is used to represent the battery characteristics dueto its simplicity and sufficient accuracy. The mathematicaldescription can be written by

⎧⎨

⎩

UL=Uoc−Ibat·Rbat

Ibat=Uoc− U2oc−4RPL

2R.

(1)

The load power can be calculated using the multiplicationof current and voltage as follows:

PL=UL·Ibat. (2)

State of charge (SOC) is traditionally used to indicate theresidual electricity of the battery, and its definition is usuallygiven by

SOC=SOC0−kchkdis· ε·Ibatdt/Cbat (3)

where SOC0represents the initial value of SOC, andkchandkdisrepresent the impact coefficients on the current integra-tion from charging current (IL<0) to discharging current(IL>0), respectively.Cbatrepresents the nominal capacityof the battery, whileεis the coulomb efficiency (includingcharging efficiencyεchand charging efficiencyεdis).The supercapacitor is modeled by a first-orderRCequivalentcircuit, as shown in Fig. 4.ISCis the supercapacitor currents(positive for discharging and negative for charging). The main


TABLE II

ELECTRICALPARAMETERS OFSUPERCAPACITOR

TABLE III

PARAMETERS OFBATTERYDEGRADATIONMODEL

parameters are listed in Table II. The mathematic modeldescription can be written by

ULSC=USC−RSCISC. (4)

A semiempirical battery capacity degradation model isadopted in this paper [25]. Themodel includes four parame-ters: time, temperature, depth of charge, and discharge rate.Its formula description is given by

Qloss=B·e−Ea+A·CrateR·Tbat (Ah)

z (5)

whereQlossis the battery capacity loss, which ranges from0to1.Bis the preexponential factor.Eais the activationenergy (J mol−1).Ris the gas constant [J (mol−1k)−1].Tisthe battery absolute temperature (K).Ahis the Ah-throughput,whichisexpressedasAh,zis the power law factor,Crateisthe battery discharge rate, andAis the compensation factorofCrate. Corresponding parameters used in this formula arelisted in Table III. The Ah-throughput is defined as

Ah=1

3600

tf

t0

|Ibat|dt (6)

wheret0andtfare the initial time and final time of a drivingcycle, respectively.

III. INFLUENCE OFTERRAININACCURACY ONHESS

A. Assumption

In this section, the influence law of terrain inaccuracy onthe cost of battery degradation and system energy for twosemiactive HESSs is studied. For the terrain inaccuracy, theerror needs to be modeled as a certain distribution. However,it is impossible to create an exact distribution to describeall situations. Three typical distributions, normal distribution,Laplace distribution, P-distribution, have been studied fordescribing error distribution [26]. In this paper, the error ismodeled as normal distribution. Its mean value is assumed tochange from−0.1 to 0.1 rad. The described range is not anabsolute limit for its maximum value, but it can be scaled toany range for specific applications.

The cost of the battery system is assumed to beU.S. $1600 per kWh [27]. Here, we assume that the super-capacitor has no degradation during the life of the battery, butthe battery has degradation process and its capacity range isconsidered from 100% to 80%. The electricity cost is assumedto be U.S. $0.1 per kWh according to the report of the U.S.Energy Information Administration.

B. Cost Model for Battery Degradation

The cost of battery degradation and energy can bedescribed by

Costbat_ degr(t)=Qbat·Ubat·p·Ah

1000·0.2

×exp−31700−370.3Crate

8.314Tbat(7)

Costenergy(t)=0.1

3600

T

0[PSC(t)+Pbat(t)+Ploss] (8)

where Qbatrepresents battery normal capacity (Ah).Ubatrepresents battery normal voltage (V),andpis the unit energycost for battery U.S. ($/kWh).Plossrepresents the power lossof the HESS, including battery resistance loss, supercapacitorresistance loss, and dc/dc efficiency loss, which is written asthe following:

Ploss=Pbat,loss+PSC,loss+PDC,loss (9)

Pbat,loss=tf

t0

I2bat(t)·Rbat·Ubat(t)dt (10)

PSC,loss=tf

t0

I2SC(t)·RSC·USC(t)dt (11)

PDC,loss=(1−ηDC)·PDC. (12)

Finally, the unit cost ($/km) for battery degradation andenergy can be expressed as

Costbat_ degr=

tft0Costbat_ degr(t)

Ld(13)

Costenergy=

tft0Costenergy(t)

Ld(14)

whereLdrepresents the driving range of an electric vehicle.

C. Terrain Information Error

Vehicle state and altitude data are collected based on a highaccuracy GPS system (the positioning accuracy radius is lessthan 0.01 m), which logs velocity and position informationat 10-Hz frequency. The collected altitude profile is shownin Fig. 5, and the same altitude profile is duplicated multipletimes to form a new profile, which is shown in Fig. 6 withsix duplications. Since a GPS receiver provides a 3-D position(latitude, longitude, and altitude) together with a signal indi-cating the number of satellites used for the position fix. Thevehicle velocity and the road slope are used to calculate thetime derivative of the altitude and thus provide a link betweenthe GPS and the vehicle model [28]. The road slope can thusbe estimated using this relationship and shown in Fig. 7.


Fig. 5. Elevation profile.

Fig. 6. Duplication of six identical elevation profiles from Fig. 5.

Fig. 7. Road slope grade.

When the terrain inaccuracy is considered, the slope gradecan be written by

α(t)=α(t)+ε(t) (15)

where the error ε(t) follows normal distribution, namely,ε(t)∼N(μ,σ2).

Fig. 8. Energy management diagram based on a frequency approach.

TABLE IV

MAINPARAMETERS OFTESTEDELECTRICVEHICLE

Central limit theorem is employed to produce the randomdiscrete points that follow normal distribution, and the detailedsteps can be described as the following.1) First,Ndiscrete points,γ1,γ2,...,γN, are producedrandomly.

2) Then, these random points are calculated according to

x=

N

i=1

γi−N

2

N

12. (16)

3) Finally, random points that follow distributionε(t)∼N(μ,σ2)can be obtained by

y=σ·x+μ. (17)

D. Power Sharing Algorithm

In the proposed HESS, a power management strategy isimplemented, so that the power demand is assigned to twodifferent power sources: battery and supercapacitor. Sincesupercapacitor has fast dynamic characteristics compared withbattery, namely, the energy stored in supercapacitor can bedischarged quickly than battery. Therefore, the high-frequencycomponents of power demand are assigned to the supercapac-itor and remaining low-frequency components are assigned tothe battery. Two filters (characterized by two cutoff frequenciesf0andf1)are used to obtain the power mission for eachpower source, which is shown in Fig. 8. In order to studythe influence law of error on the HESS cost, these two cutofffrequencies are first optimized so that the current distributedto the battery could be controlled within 0.5 °C range foreach cell.

E. Result Analysis

In this section, simulations are performed based on twosemiactive HESSs and three constant velocities: 10, 15and 20 m/s. The power demand is calculated by the longi-tudinal dynamic model and the vehicle main parameters arelisted in Table IV.


Fig. 9. Battery degradation cost.

Fig. 10. Energy cost of two topologies.

The battery degradation cost of the HESS is shown in Fig. 9.Since the amount of power distributed to the battery is thesame, there is no significant difference between two semi-active topologies. When the error is close to−0.02 rad, thebattery degradation cost approaches to minimum value. Then,it increases as the absolute value of error increases. This isbecause power demand is influenced by error directly and thusthe battery needs to supply more power.The energy cost of two semiactive HESSs is shown

in Fig. 10. It can be found that there is a similar trendwhen comparing the results of all the battery degradationcost. However, they are slightly different due to the differentlocations of the dc/dc converter in two semiactive HESSs.The energy cost of the supercapacitor controlled topology isa little higher than that of thebattery controlled topology.This is because the dc/dc converter in the supercapacitorcontrolled topology is operated frequently under pulsed andpeak power conditions so that more energy is dissipated.Compared with Fig. 9, the energy cost is much less than thebattery degradation cost over the two semiactive topologies,because the battery price is high.Therefore, the operation costof the HESS is mainly determined by the battery degradationcost. To some degree, the energy cost can be neglected.

Fig. 11. Comparison of battery degradation cost for different velocities.

Fig. 12. Energy cost comparison of battery controlled topology for differentvelocities.

Fig. 13. Energy cost comparison of supercapacitor controlled topology fordifferent velocities.

The influence of the error with different velocities on batterydegradation and energy cost is given in Figs. 11–13. The costis higher for 20 m/s, which is the highest velocity. In otherwords, the higher the velocity is, the higher the cost is.


IV. POWERMANAGEMENTCONTROLSTRATEGY

As discussed above, the cost of the HESS is influenced byboth the velocity and terrain information error significantly.Specifically, it is intuitive that the faster the speed is, themore cost the degradation process will induce. However, thereis a similar trend for the degradation cost for all differentspeeds with respect to the terrain information error. In orderto investigate the influence of the error variation, we focus ona constant-velocity cruise situation. Consequently, velocity isnot given in the following formula derivation. In general, theelectric power consumption of auxiliary electric devices in theEV is about 2 kW. It is typically treated as a fixed constantvalue and solely provided by the battery. Therefore, the powerconsumption of auxiliary devices does not affect the powermanagement strategy for the HESS, and also is irrelevant tothe terrain information error, which is the main focus of thispaper. Therefore, we ignore theimpact of auxiliary electronicdevice.The total cost can be written as the function of load power

demand

Cost=T

oCost(PL(t))dt. (18)

In this paper, the load power can be expressed as the sum ofbattery and supercapacitor power

PL(t)=Pbat(αroad(t))+PSC(αroad(t)). (19)

Consequently, the total cost can be rewritten by

Cost=T

oCost(Pbat(αroad(t)),PSC(α(t)))dt. (20)

The error is modeled with normal distribution, namely,ε(t)∼N(μ,σ2)with its mean valueμand varianceσknown,but the duration time of error is unknown. Therefore, the spe-cific power demand at each instant is still unknown. Besides,in order to describe the problem clearly, the varianceσis setas a fixed constant value. As a result, the error can be featuredby mean valueμonly. The mean valueμcan be described asfollows:

μ(t)=

⎧⎪⎨

⎪⎩

μ1,t∈(0,t1)

μ2,t∈(t1,t2)

0, otherwise

(21)

wheret1represents the duration time ofμ1andt2representsthe duration time ofμ2. In this paper, botht1andt2are knownrandom variables and modeled as a certain distribution.Therefore, the total cost is the sum of cost during twoduration times of error, which can be expressed as

Cost=t1

0Cost(Pbat(αroad(t)),PSC(αroad(t)))dt

+t2

0Cost(Pbat(αroad(t)),PSC(αroad(t)))dt.(22)

In order to describe the stochastic behavior, the durationtime of each error mean value is weighted by the probabilityof its occurrence. The probability density functions oft1andt2

are defined asϕ(t1)andh(t2), respectively. Then, the total costcan be rewritten by

Cost

=T1

0ϕ(t1)

t1

0Cost(Pbat(αroad(t)),PSC(αroad(t)))dt dt1

+T2

0h(t2)

t2

0(Pbat(αroad(t)),PSC(αroad(t)))dt dt2

(23)

whereT1andT2are the possible maximum values of durationtimest1andt2. By adjusting the amount of power distributedto battery and supercapacitor, the total cost can be minimizedadapting to the variations of error under the condition of acertain probability. The minimum cost thus can be described as

Cost∗min=arg min

Pbat,Psc

×T10 ϕ(t1)

t10Cost(Pbat(αroad(t)),PSC(αroad(t)))dtdt1

+T20 h(t2)

t20Cost(Pbat(αroad(t)),PSC(αroad(t)))dtdt2

=arg minPbat,Psc

T1

0ϕ(t1)

×t1

0Cost(Pbat(tαroad(t)),PSC(αroad(t)))dt dt1

+arg minPbat,Psc

T2

0h(t2)

×t2


=Cost∗t1,min+Cost∗t2,min

(24)

where

Cost∗t1,min

=arg minPbat,Psc

T1

0ϕ(t1)

×t1


(25)

Cost∗t2,min

=arg minPbat,Psc

T2

0h(t2)

×t2

0Cost(Pbat(αroad(t)),PSC(αroad(t)))dt dt2.

(26)

Since probability density functionsϕ(t1)does not dependon timet, thus the left integral of (25) can be obtained as

T1

0ϕ(t1)

t1

0Cost(Pbat(t),PSC(t))dt dt1

=T1

0

t1

0ϕ(t1)·Cost(Pbat(t),PSC(t))dt dt1. (27)

According to the Fubini theorem, the integration order of theequation can be changed. The original time ranget1∈[0,T1]


andt∈[0,t1] can be transformed to:t∈[0,T1], t1∈[t,T1].Then, (27) can be written by

T1

0ϕ(t1)

t1


=T1

0

T1

tϕ(t1)·Cost(Pbat(αroad(t)),PSC(αroad(t)))dt1dt

=T1


×T1

0ϕ(t1)dt1−

t

0ϕ(t1)dt1 . (28)

Based on the probability density functions ϕ(t1),thecumulative density function (CDF) oft1 can be readilyobtained as

ψ(t)=t

−∞ϕ(t1)dt1

=0

−∞ϕ(t1)dt1+

t

0ϕ(t1)dt1

=t

0ϕ(t1)dt1. (29)

For the possible maximum valueT1of duration timet1,CDF has its final value 1, namely

ψ(T1)=T1

0ϕ(t1)dt1=1. (30)

Therefore, (28) can be written by

T1

0ϕ(t1)

t1


=T1

0

T1

tϕ(t1)·Cost(Pbat(αroad(t)),PSC(αroad(t)))dt1dt

=T1


×T1

0ϕ(t1)dt1−

t

0ϕ(t1)dt1

=T1

0(1−ψ(t))·Cost(Pbat(αroad(t)),PSC(αroad(t)))dt.

(31)

Similar deduction can be applied to the left integral of (26).Then, we have equality as follows:

T2

0h(t2)

t2


=T2

0(1−H(t))·Cost(Pbat(αroad(t)),PSC(αroad(t)))dt

(32)

where

H(t)=t

−∞h(t2)dt2

=0

−∞h(t2)dt2+

t

0h(t1)dt2

=t

0h(t1)dt2. (33)

Fig. 14. Energy management diagram based on a frequency approachconsidering terrain inaccuracy.

Consequently, (24) can be rewritten as follows:

Cost∗min=arg minPbat,Psc

T1

0(1−ψ(t))

·Cost(Pbat(αroad(t)),PSC(αroad(t)))dt

+arg minPbat,Psc

T2

0(1−H(t))

·Cost(Pbat(αroad(t)),PSC(αroad(t)))dt (34)

As described above, the expected total cost can be mini-mized by adjusting the amount of power distributed to batteryand supercapacitor under known CDFs of error. Therefore,power management control strategy can be developed byadjusting separation frequency according to CDFs. The spe-cific diagram is shown in Fig. 14. For each terrain error, sincethe duration time is unknown, the load power distribution isexecuted from maximum separation frequency to minimumseparation frequency, because the variations of CDFs are fromminimum to maximum. In order to prevent the violation ofthe maximum SOC bound, the maximum separation frequencyneeds to be limited to a reasonable value.

V. CASESTUDY

To illustrate the applicability of our proposed method,a case study is conducted using simulation. The distributionsof duration timest1andt2are set to be the same, andfollow normal distribution, namely,t1∼N(μ1,σ

21)andt2∼N

(μ2,σ22),whereμ1 = μ2 = 20 s andσ1 = σ2 = 5.

A load power demand can be obtained according to vehiclelongitudinal dynamic equation and the parameters of vehicleand terrain, which is shown in Fig. 15. The segment number ofthe duration time is 100 for positive terrain error and 100 fornegative terrain error. The histogram of duration time and thecorresponding CDF is shown in Figs. 16 and 17, respectively.Combining the accurate load power demand and the estimatederror, the stochastic power demand can be obtained in Fig. 18.The simulation is carried out in MATLAB environment, andthe comparison results between the proposed control approach(frequency approach with error consideration) and the con-ventional control approach (frequency approach without errorconsideration) are shown in Figs. 19–21. A comparison of thebattery cell current is shown in Fig. 19. It can be observed


Fig. 15. Load power demand based on accurate terrain information.

Fig. 16. Distribution of duration time error.

Fig. 17. CDF of error duration time.

clearly that the proposed control approach can better suppressthe charging/discharging current of the battery within a smallervariation range compared withconventional control approach,which would be very helpful to increase battery life.

Fig. 18. Load power demand with stochastic normal distribution error.

Fig. 19. Battery cell current comparison.

Fig. 20. Battery cell voltage comparison.

A comparison of the battery cell voltage is shown in Fig. 20.It can be seen that the proposed control approach can maintainthe cell voltage within the range from 3.79 to 3.95 V, whichis roughly estimated to be a maximum 0.16 V voltage drop


Fig. 21. Battery SOC comparison.

TABLE V

COMPARISONSBETWEENPROPOSED ANDCONVENTIONALAPPROACHES

compared with a maximum 0.5 V voltage drop for the con-ventional control approach. Therefore, it is obvious that thebattery system is operated in much smaller voltage range andthe potential battery cell balancing problem can be avoided toprevent individual cell voltages from a big drifting apart overtime, which leads to rapid decreases of the total pack capacity.From Fig. 21, since the power demand caused by the error

is distributed to the supercapacitor actively, the battery outputis smoothed, and its SOC consumption is decreased by 1.5%compared with conventional control approach, which couldpotentially extend the driving range of electric vehicles.The costs are compared and listed in Table V. It is observed

that the proposed approach is able to achieve reduction indegradation and energy costs for the HESS. This is becausethat error power is actively distributed to supercapacitor, andtherefore, battery degradation and system energy costs ofbattery controlled semicontrolled HESS are decreased. On thecontrary, the system energy costs of supercapacitor controlledsemicontrolled HESS is increased.

VI. CONCLUSION

In this paper, the inaccuracy ofterrain information is firstinvestigated as how it affects load power demand, and in turn,battery life, and overall system efficiency and performancefor a hybrid ESS in an electric vehicle. To quantify the influ-ence, the operation costs are defined for two hybrid systemswith semiactive topology, including battery degradation costand energy cost. Simulation has been conducted with resultsindicating that error has a significant influence on the costof the HESS. Then, a power management control strategy isdeveloped to minimize the total cost of the HESS by consider-ing terrain inaccuracy. Simulation has been further performed

with results demonstrating theadvantages and effectivenessof the proposed approach compared with conventional controlapproaches.To extend the study, the following topics can be addressed

in the future work.1) Investigate the influence of errors on the HESS withdifferent supercapacitor capacity matches.

2) Optimize topology structures of the HESS with theconsideration of prediction errors.

3) Study the optimal power management strategy for HESSbased on the sensing information with surroundingvehicles.

ACKNOWLEDGMENT

The authors would like to thank the anonymous reviewersfor their valuable comments and suggestions to improve thispaper.

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Qiao Zhang(S’14) was born in Liaoning, China,in 1986. He received the M.S. degree in vehicle engi-neering from the Wuhan University of Science andTechnology, Wuhan, China, in 2012. He is currentlypursuing the Ph.D. degree in vehicle engineeringwith Jilin University, Changchun, China.His current research interests include energymanagement in electric vehicle, modeling, andsimulation.

Feng Ju(M’15) received the B.S. degree from theDepartment of Electrical Engineering, Shanghai JiaoTong University, Shanghai, China, in 2010, and theM.S. degree in electrical and computer engineeringand the Ph.D. degree in industrial and systems engi-neering from the University of Wisconsin–Madison,Madison, WI, USA, in 2011 and 2015, respectively.He is currently an Assistant Professor with theSchool of Computing, Informatics, and DecisionSystems Engineering, Arizona State University,Tempe, AZ, USA. His current research interests

include modeling and control of manufacturing systems, and batterymanagement systems.

Sumin Zhang(M’09) received the Ph.D. degreefrom Jilin University, Changchun, China, in 2011.He is currently an Assistant Professor with theCollege of Automotive Engineering, Jilin Univer-sity. He is the author or co-author of numerouspublications in the areas of vehicle controls andpower management systems, and has been in chargeof several nationally funded government projectson electric vehicles, modeling and simulation tooldevelopment, and power management systems. Hisprimary research interests are in vehicle dynamics

and controls, electric vehicles, and power management systems.

Weiwen Deng (M’09) has been a Staff Researcherwith General Motors Research and DevelopmentCenter, Warren, MI, USA, since 1996 and a Dis-tinguished Professor and the Executive Director ofthe Automotive Research Institute, Jilin University,Changchun, China, since 2010. He holds some 60patents, and is the author or co-author of over100 peer-reviewed papers in international jour-nals and conferences. His current research interestsinclude vehicle controls and intelligence, and mod-eling and simulation technologies.

Dr. Deng was a three-time recipient of the Charles McCuen Award anda twice-recipient of the Boss Kettering Award from GM for his technicalinvention and innovation. He currently serves as an Editor and an EditorialBoard Member of several prestigious international journals, and is the Chairof many international conferences and forums.

Jian Wu(M’09) received the Ph.D. degree fromJilin University, Changchun, China.He is currently an Associate Professor with theCollege of Automotive Engineering, Jilin University.He is the author of over 20 peer-reviewed papers ininternational journals and conferences, and has beenin charge of numerous projects funded by nationalgovernment and institutional organizations on elec-tric vehicles and energy management systems. Hiscurrent research interests include traction controlsystem, electric vehicles, and advanced automotive

electronic control system.

Chao Gao(S’14) was born in Shandong, China,in 1991. He received the B.S. degree in vehicleengineering from Shandong Agricultural University,Taian, China, in 2014. He is currently pursuingthe M.S. degree in vehicle engineering with JilinUniversity, Changchun, China.His current research interests include energymanagement in electric vehicle, modeling, andsimulation.

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