3

r b

g Ungh

The power usage for battery-powered electricxamineand veperatin

pression for the optimal operating point in terms of the component and envi-

energy management may have various meanings in different con-texts, all share the common goal of improving the energy efciencyand maximizing the utilization of stored energy in the batteriesequipped on the vehicle.

Xiong et al. andimation methodsterminal

thod for stcharge estimation of the battery pack which accounted for tference among the cells [4]. Besides the in-depth analysestery performance, the study of other key components ofsystem, such as power converters and motors, also abounds inthe literature. Pahlevaninezhad et al. proposed a Control-Lyapu-nov-Function based approach to regulate the input power of theinverter so that higher energy efciencies and larger stability mar-gin could be attained [5]. Faiz et al. designed a direct torque controllaw for induction motors used in EVs with the improved overallefciency and reasonable dynamic response [6]. Although physical

Corresponding author at: University of MichiganShanghai Jiao Tong UniversityJoint Institute, Shanghai Jiao Tong University, Shanghai 200240, China. Tel.: +86 2134207212.

E-mail address: [email protected] (M. Li).

Applied Energy 134 (2014) 332341

Contents lists availab

Applied

lsesubstitute for the conventional ones, have received much moreattention than ever before. However, due to limited energy densityof batteries nowadays, energy management has always been thecentral and critical issue in the control of EVs. Although the term

lithium-based batteries for EV applications [1].Hu et al. proposed adaptive state-of-charge estbased on real-time measurements on the batteryand current [2,3]. Zhong et al. developed a mehttp://dx.doi.org/10.1016/j.apenergy.2014.08.0330306-2619/ 2014 Elsevier Ltd. All rights reserved.voltageate-of-he dif-of bat-the EVBattery poweredEVsOptimal control

ronment parameters can be obtained. Owing to this nding, the derived control strategy is also rendereda simple structure for real-time implementation. Simulation results demonstrate that the proposedstrategy works both adaptively and robustly under different driving scenarios.

2014 Elsevier Ltd. All rights reserved.

1. Introduction

In response to renewed pleadings for energy efciency andenvironment protection, the electric vehicles (EVs), as a promising

In order to achieve the purpose of energy management, exten-sive research work has focused on energy control by analyzingthe component characteristics, especially for battery-poweredEVs. For example, Capasso and Veneri veried the applicability ofKeywords:Energy management

work is that an analytic ex The battery and motor dynamics are e The optimal control strategy is derived An analytic expression of the optimal o

a r t i c l e i n f o

Article history:Received 18 April 2014Received in revised form 17 July 2014Accepted 7 August 2014Available online 29 August 2014al vehicles with in-wheel motors is maximized.d emphasized on the power conversion and utilization.ried by simulations.g point is obtained.

a b s t r a c t

Due to limited energy density of batteries, energy management has always played a critical role inimproving the overall energy efciency of electric vehicles. In this paper, a key issue within the energymanagement problem will be carefully tackled, i.e., maximizing the power usage of batteries for bat-tery-powered electrical vehicles with in-wheel motors. To this end, the battery and motor dynamics willbe thoroughly examined with particular emphasis on the power conversion and power utilization. Theoptimal control strategy will then be derived based on the analysis. One signicant contribution of thish i g h l i g h t sOptimal energy management strategy fovehicles

Jiaqi Xi a, Mian Li a,b,, Min Xu baUniversity of MichiganShanghai Jiao Tong University Joint Institute, Shanghai Jiao TonbNational Engineering Laboratory for the Automotive Electronic Control Technology, Sha

journal homepage: www.eattery powered electric

niversity, Shanghai 200240, Chinaai Jiao Tong University, Shanghai 200240, China

le at ScienceDirect

Energy

vier .com/ locate/apenergy

untouched. The lack of this essential part of contents makes the

simplications, we identify the dependence of the optimal operat-

ergycharacteristics of a specic component were fully explored in allthose work, the analysis was only performed in a somewhat iso-lated manner and the coupling effects between different compo-nents were neglected.

In parallel to component level analysis, much of attention in theenergy-control area has been directed to hybrid energy systemdesign by integrating, for example, ultra-capacitors into the energystorage system of EVs. The dening features of the ultra-capacitorare its high power density and long life cycle [7]. By combining thecomplementary characteristics of the battery and the ultra-capac-itor, a superior dynamic behavior can thus be achieved. Along thisdirection, the research has been carried out in full length. Forexample, Dougal et al. analyzed the performance improvement ofthe hybrid energy system when the ultra-capacitor was connectedin parallel with the battery directly [8]. Lu et al. explored a newtopology to interface the battery and ultra-capacitor, and proposedthe corresponding energy management schemes [9]. Kupermanet al. and Garcia et al. focused on the power ow control of thehybrid energy system. An embedded control topology was pro-posed to guarantee that the extra power during peak time willbe provided by the ultra-capacitor while keeping the battery cur-rent unchanged [10,11]. Lukic et al. compared different topologiesin terms of efciency and stability and showed that an active com-bination of the battery with ultra-capacitor was a promisingapproach [12]. Under this active topology, Laldin et al. designedan optimal power split path in real time based on the predictionof future load demand and the energy loss model for all systemcomponents [13]. The similar problem was approached fromanother perspective in the work done by Wang et al., in whichthe way of hybridization between the battery and the ultra-capac-itor was determined by solving an optimization problem for thetotal fuel economy of the energy system [14]. Besides, there arealso fuzzy approaches proposed in the literature. Wang et al.designed the fuzzy logic based on the power requirement of EVs[15]. Hannan et al. presented a multi-source model and designeda rule-based power sharing strategy according to the energy sourcestates and load conditions [16].

Whether it be control methods for the individual componentsor power split mechanisms for hybrid systems, it can be noted thatmost of the work above were targeted at minimizing the powerloss in power sharing for a given power demand. This demand isusually either obtained priori or estimated in real time. On the con-trary, another point of view in this area has been concerned withthe maximization of the travel distance for a given amount ofstored energy [17]. Instead of determining the power sharing pro-le at each instant, it aimed to nd an optimal velocity prole thatwould maximize the travel distance. As a rst step, this work builta simplied yet complete EV model. Based on the terrain informa-tion and the operating efciency of the in-wheel motors, the opti-mal velocity prole can be found using the dynamic programmingor other optimization algorithms. The originality of this work liesin that it offers a new perspective to treating the energy manage-ment problem.

However, the approach in Ref. [17] is plagued by two majorissues that can undermine the optimality of its solution. First, thebattery and motor are statically viewed as the energy storageand energy consumption components, and the dynamic behaviorsassociated with those two components are totally ignored, not tomention the energy ow associated with those dynamic behaviors.Because of this intrinsic model discrepancy, the optimal velocityprole obtained may not produce the corresponding optimalpower ow prole as expected in a real-world test. To make thingsworse, the optimal velocity prole itself might not even be repro-

J. Xi et al. / Applied Enducible due to the coupling effects and dynamic constraints.Relevant to the rst issue, the second one is that since everythingis viewed statically, the technical details of control implementa-ing point on the component and environment parameters in ananalytic form. This not only provides a guideline on the drivingmode in different road conditions, but also offers insights to thephysical mechanism behind the optimality for further theoreticalinvestigation. Owing to this nding, the derived energy manage-ment strategy is also rendered a simple and compact structure thatfacilitates the real-time implementation. Simulation results fortwo case studies will be demonstrated and analyzed. It can beshown that the proposed strategy works both adaptively androbustly under different driving scenarios.

The rest of the paper is organized as follows. A brief introduc-tion to the vehicle architecture considered in our study is providedin Section 2. In Section 3, the component model for the battery andthe motor are derived step by step. Based on this model, the con-trol strategy is developed accordingly. The simulation is demon-strated in Section 4, including the initial condition settings,simulation results, and post analysis. Finally the conclusion ofthe proposed work and possible future improvement are summa-rized in Section 5.

2. Background

In this paper, the energy management strategy will be devel-oped for an electric vehicle driven by two rear in-wheel motors.The vehicle topology is shown in Fig. 1. The battery power is deliv-ered to the motors through the DCDC converter, which is con-trolled by an energy management unit (EMU) on the vehicle.

Notice that in this work the ultra-capacitor is not included as apart of the power source system like other hybrid systems.Undoubtedly adding ultra-capacitors can improve the transientdynamics of the vehicle at acceleration and can take care of theenergy recovery at regenerative braking much better. However,in the authors opinion, the study of power transportation andpower usage is of more fundamental importance from the energymanagement point of view. In this regard we restrict our focus tothese key aspects and temporarily set aside the discussion of theancillary function of the ultra-capacitor, which will be an extensionof this work and addressed in our future work.

3. Proposed energy management methodproposed strategy incomplete or inconvincible to some extent.In this paper, amore systematic and renedapproach is proposed

for energy management of EVs with in-wheel motors and a singlepower source, i.e., batteries. Two major issues mentioned above inprevious work will be carefully tackled. The discussion will beginwith the component analysis by examining the battery and motordynamics respectively. The vehicle dynamics will also be accountedfor in our work and special attention will be paid to the power andtorque couplings between motor and vehicle dynamics. The energymanagement problemwill then be reformulated as an optimal con-trol problem with input constraints. With the help of justied sim-plications, we can nally nd an analytic solution to this energymanagement problem, which can serve as an important guidelineto energy control of battery-powered EVs. After that we will moveon to the control implementation of the proposed energy manage-ment strategy. Specically, we will provide the details of the PI con-troller design for the DCDC converter in this work which accountsfor both the dynamic response and noise rejection.

One signicant contribution of this work is that, with justiabletion, especially the control of the DCDC converter, remain

134 (2014) 332341 333The ultimate goal of energy management is to maximize thepower usage of the battery on the vehicle. To this end, two aspects

B C o

rgyof the matter need to be considered concurrently. The rst issue isto minimize the power loss during the energy transportation onthe vehicle. Another issue, of course closely coupled with the rstone, is to extend the driving range as much as possible for a givenamount of energy. These two issues occur at two ends of the sameproblem and are associated with two key components of the vehi-cle: the battery and motor. In the following discussion, we willstart with the component-level analysis.

In the analysis of battery dynamics, we will thoroughly investi-gate the impact of the current intensity on the power loss duringthe energy transportation. The analysis will be based on a well-known battery model which is generally used to characterize prop-erties of different types of batteries. In this regard, our objective forthe battery analysis is to nd a discharge prole to minimize thepower loss during the energy transportation.

In the analysis of motor dynamics, we will study the couplingrelationship between the electrical and mechanical behavior ofin-wheel motors to clearly demonstrate their dynamic characteris-tics (which were usually neglected in the previous work). Since in-wheel motors are applied in this work, the mechanical coupling

atter y

nv erter

Motor

EMU

Fig. 1. Vehicle topology used in our analysis.Motor

334 J. Xi et al. / Applied Enebetween motor and vehicle dynamics, which depends on the wayof connection between the wheel and the vehicle, will also beinvestigated and claried. Given that, our objective of study onmotor dynamics is to nd an optimal operating point which mini-mizes the total energy usage for a given driving range.

The study of these two components goes in parallel to eachother and gets merged under the system-level analysis by combin-ing results from them together. The overall control hierarchy willbe proposed based on results from the component-level analysis;and then we will discuss the real time implementation of our con-trol strategy on the DCDC converter. At the end of this section,several practical considerations of the control strategy will be pro-vided including the choice of lter parameters and controlfrequency.

3.1. Component analysis: battery

A generic battery model proper for dynamic characterizationhas been proposed by Tremblay et al. [18], who assume that thebattery state-of-charge (SOC) is the only state variable and othercharacteristics of the battery can be derived from it. In their work,the battery is modeled as a controlled voltage source in series con-nection with a resistance. The expression for the voltage source isgiven byvb E0 k QcQc QQ AeBQ k Qc

Qc Qib 1

where Qc is the battery capacity and Q is the actual battery chargewhich is a value related to the current ib dened by:

_Q ib 2Here the battery constant voltage E0 and polarization voltage k, aswell as the exponential zone coefcients A and B, can be identiedusing the experimental data. The detailed discussion on this modelcan be found in the literature [18]. Our interest is to analyze theimpact of the current intensity on the total power loss both undercharging and discharging conditions. The instant power of the bat-tery can be calculated as: p = vb ib, where vb is the no-load voltageof the battery. By integrating the instant power over a period oftime, we can obtain the corresponding energy ow of the batteryas below:

W Z tft0

E0 k QcQc QQ AeBQ

dQ

Z tft0

kQc

Qc Qi2bdt

W1 W2 3Two terms can be recognized from Eq. (3):W1 andW2. SinceW1 is afunction solely depending on Q, its value is independent of any spe-cic power ow path. In other words, W1 is a state function. W2, onthe contrary, is a process function. In view of this particular energyfeature, we only need to focus on the term W2 when analyzing thepower loss since W1 will not be affected by any specic power owpath. A closer look at Eq. (3) reveals that the term Qc/(Qc Q) isstrictly positive, which means the entire integrand of W2 is strictlynegative contributing to the energy loss during the irreversible pro-cess. The question following is whether there exist such a currentprole (power ow path) that can minimize this energy loss, thatis, to minimizeW2. Reformulating this problemmathematically willgive us a minimization problem by changing the variable Q:

minZ tft0

kQc

Qc Q_Q2 dt; withQt0 Q0 and Qtf Qf 4

where Q0 and Qf correspond to the initial and nal battery chargerespectively. Both of them can be easily obtained by on-line SOCestimation of the battery. The charging and discharging processcan be differentiated by the relative magnitude of Q0 and Qf. Letus denote the integrand in Eq. (4) as L. By invoking the EulerLagrangian condition [19], the following condition has to be satis-ed for an extremal:

LQ ddt L _Q 5

where LQ and L _Q denote the partial derivative with respect to Q and_Q . Expressing the Eq. (5) explicitly yields

_Q2 2 Q QcQ 6which is a second order nonlinear differential equation and the fea-sible solution to it takes the form as:

Q Q2c b

2

4Q0 Qc t2 bQc t Q0; where

b 2 1tf

1Qf QcQ0 Qc

s ! Q0

Qc 1

7

Notice that the term b in Eq. (7) will be positive in the dischargingprocess (Q0 < Qf) and negative in the charging process. The currentintensity can then be readily calculated as

134 (2014) 332341ib Q2c b

2

2Q0 Qc t bQc 8

When the time span tf is long enough, b2 will be relatively smallcompared to b. So the optimal current intensity ib will stay on a con-stant value b for a long charging or discharging duration.

3.2. Component analysis: motor

The motor dynamics can be fully characterized in terms of its

di

dt Jvb

dhdt

x 20

where h is the traversed angle of the wheel. Dene the state vectorx = (im,x,h) and the control variable u = vm, we can rewrite Eqs.(18)(20) in a compact form:

_x f x;u; t 21The control objective is to drive the state h from h0 to hf with theminimal total electrical energy. So the cost functional is

Crr Cd

J. Xi et al. / Applied EnergyMVelectrical and mechanical behaviors [20]. The governing equationsof these two behaviors are derived from Kirchhoffs Voltage Lawand Newtons Second Law, respectively, as below:

Lmdimdt

vm kb x Rm im 9

Jmdxdt

kb im Cf x sL 10

In these two equations, vm and im are the input voltage and currentto the motor, and x is the angular velocity of the motor. Rm and Lmrepresent the resistance and inductance of the rotor loop, while Jmand Cf are the moment of inertia of the rotor and coefcient of vis-cous friction, respectively. The electrical and mechanical parts arelinked with each other through the electromagnetic conversion fac-tor kb, which measures how the electrical energy is transformedinto the mechanical one. In Eq. (10), sL represents the external loadon the motor, which depends on the way of the connection betweenthe motor and the vehicle system as well as on the vehicle dynam-ics. In order to link these two aspects together, here we consider asimplied vehicle dynamics model shown in Fig. 2, with road fric-tion, rolling resistance, and drag coefcients indicated as l, Crr,and Cd, respectively.

The vehicle here is powered by two rear in-wheel motors.Before the analysis two basic assumptions are made: (1) the masscenter of the vehicle body is low, so the lifting effect can beneglected and only the forces in the horizontal direction are con-sidered; (2) the variation of the vehicle speed is within a certainrange and thus the air resistance can be considered proportionalto the vehicle velocity v [21]. The free body diagram of the entiresystem including the front wheels, the rear wheels and the mainbody is shown in Fig. 3. The wheels are pin-connected with thevehicle body.

Applying the force and torque balance to the system gives:

4Jwdxdt

2sL 2f 1 rw 2f 2 rw Crr Mvg 11

Mvdvdt

2f 1 2f 2 qaCdAF rwx 12

where x is the angular velocity of the wheel (which is the same asthat of the motor), rw is the wheel radius, and v is the correspondinglinear velocity (v =x rw). f1 and f2 represent the static road fric-tions on the front and rear wheels respectively. The air resistancehas been written out as a multiplication of the air density qa, thedrag coefcient Cd, the cross-sectional area AF, and the velocity v.sL is driving torque provided by the in-wheel motor. It is assumedthat the vehicle mass Mv is evenly distributed among the fourwheels and no slip occurs. Multiplying Eq. (12) with rw and adding

Fig. 2. Schematic of an electric vehicle on the road.Lmm

dt vm kb x Rm im 16

Jvdxdt

2kb im Cv x sv 17

3.2.1. Solving for the optimal operating pointWith the augmented motor model discussed above, the next

goal is to nd an optimal operating prole for the motor in thesense that the energy consumption for a given driving range isminimized. In view of its complicated nature, we will break downthe analysis into two stages. Namely we will rst study an uncon-strained case, i.e., there is no constraint on the system states andcontrol variable. Then we will come to tackle with the constrainedone. It will become clear later that the approach we take in solvingthe unconstrained case will shed meaningful lights on the deriva-tion of controller for the constrained one. Both of these cases willbe studied in the optimal control context. As a preliminary step,let us specify the control objective mathematically. The controlsystem under consideration takes the form as:

dimdt

1Lm

vm kb x Rm im 18dx 1 2k im Cv x sv 19to Eq. (11), we can ultimately obtain the relationship between sLand the external load to the vehicle.

2sL Mvr2 4Jw dxdt

qaCdAF rwx CrrMv 13

Substituting the expression for sL into Eq. (10) will give us

Mvr2w 4Jw 2Jm dx

dt 2kb im 2Cf qaCdAFrw x CrrMvg

14Since in general Mv rw2 is much larger than Jw and Jm, and Cd ismuch larger than Cf, Eq. (14) can be simplied as Eq. (15) with onlydominant terms reserved

Jvdxdt

2kb im Cv x sv 15

where Jv =Mv rw2, Cv = qaCdAF rw and sv = CrrMvg. Then the aug-mented motor model can be written as

Jw JwMV

Crr Cd

f1 f2 L

Fig. 3. Free body diagram of the vehicle.

134 (2014) 332341 335P Z tft0

vm imdt; where vm 2 U 22

rgywhere U is the feasible control set, which will be discussed in detailsin Section 3.2.3. Overall Eq. (22) is a free time xed endpoint prob-lem. The Hamiltonian associated with the system is

Hx;p;u; t pT f x;u; t vs im 23and the corresponding co-state p is given by

dp1dt

RmLm

p1 2kbJv

p2 v s 24dp2dt

kbLm

p1 CvJv

p2 p3 25dp3dt

0 26

By invoking the Pontryagins Minimum Principle [19], we have thefollowing two conditions:

Hx;p;u; t 6 Hx;p;u; t; for all u 2 U 27Hx;p;u; t 0 28Eq. (28) follows the fact that H does not explicitly depend on time t.Given the discussion above, now we can discuss the unconstrainedand constrained cases separately one by one.

3.2.2. Optimum of the unconstrained caseIn the unconstrained case, the condition in Eq. (27) will indicate

that u* is a stationery point of H.

Hux; p;u; t juu 0 29By solving it we will have the relationship between im and p1 as:

1Lm

p1 im 0 30

This equation is supposed to hold for all time, and so does its timederivative. Substituting p1 with im in Eq. (24) and collecting the rel-ative terms, we will obtain

dimdt

1Lm

Rm im 2kbJv p2 vm

31

By comparing Eq. (31) with Eq. (18), we will have

2Rm im 2kbJv p2 kb x 0 32

Substituting p2 with im and x, and repeating the same procedure asfor p1 will give us

dimdt

CvJv

im kbCvRmJvx kb

RmJv

sv2

p3

33

Finally we have a set of equations that im and x need to satisfy:

dimdt

CvJv

im kbCvRmJvx kb

RmJv

sv2

p3

34dxdt

2kbJv

im CvJvx 1

Jv sv 35

and a quick calculation can show that the eigenvalues of this linearsystem are:

k1;2 C2vJ2v

k2bCvJ2vRm

vuut 36Since there is a positive eigenvalue, for a given initial condition, thestate variable im and x will eventually increase exponentially. Byexamining Eq. (18), this implies that the control variable vm will

336 J. Xi et al. / Applied Eneincrease exponentially, which is impractical for a real controller.So we need to nd a stationery solution with appropriate boundaryconditions that satisfy Eqs. (28) and (29). By a stationary solution,we mean that all the dynamics of the state variables tend to zero,which means two derivatives in Eqs. (34) and (35) become zero.Thus we have:

CvJv

im kbCvRmJvx kb

RmJv

sv2

p3

0 372kbJv

im CvJvx 1

Jv sv 0 38

Combining them with the condition in Eq. (28), we can nd aunique solution which is:

vm Rm svkb

11 2k

2b

Rm Cv

s0@

1A 39

Since in general Pontryagins Minimum Principle (PMP) is a neces-sary condition of the optimality, it is still necessary to verify thesolution to be a local minimum. Notice that our goal is to minimizethe cost function G. In the stationery case where im and x are allconstants, the expression for G can be written as:

P Z tft0

vm im dt vm im hx g h 40

Here the physical meaning of the term g can be interpreted as theenergy consumption per unit distance. If im and x are the corre-sponding optimal states, then g should attain its minimum value.In order to verify this point, we need to nd out the minimum valueof g. By expressing im and x in terms of vm, the term g can berewritten as

g Cvvm kbsv2kbvm Rmsv vm 41

Taking derivatives with respect to vm and setting the equation to bezero gives us:

2kbCv v2m 2RmCvsv vm Rmkbs2v 0 42After solving it we have

vm Rm svkb

11 2k

2b

Rm Cv

s0@

1A 43

which coincides with the one obtained by solving the PMP condi-tion. A further check of the second derivative of g at the value vm*

shows:

d2gdv2m

> 0 44

So it is indeed the local minimum. Since g is a convex function of vm,the local minimum is also a global one and any deviation from vm*

will result in an increase of g. Next we will discuss the constrainedcase.

3.2.3. Optimum of the constrained caseIn the constrained case, we will study how the optimal point

may shift in accordance with the constraints on the system statesand control variable. For the current control system, the constraintmainly arises from safety considerations. In order to avoid slip, themaximum angular acceleration of the wheel needs to be carefullyspecied, which is closely related to the road friction coefcient l.

Jw dxdt6 lMv

445

Since it is usually not easy to deal with state constraints in the opti-

134 (2014) 332341mal control problem, we try to translate the constraint on dx/dtinto the restriction on vm. This can be done by examining the trans-fer function of dx/dt with respect to vm,

Hs _xsvms 46

If we further assume the control variable vm to be of some particularforms, e.g., piecewise constant functions, the inverse Laplace Trans-form of H(s) vm(s) can then be written out explicitly and the limiton the magnitude of vm(t) can be calculated accordingly,

zero too. After solving the set of equations explicitly, we then need

will be maintained at the optimal value. In this regard, we will rstanalyze the entire power system in terms of the power circuit,including the battery, the booster, and the motor connected in cas-cade as shown in Fig. 5.

Based on the analysis result of the battery, the battery modelhas been simplied as an equivalent voltage source in series con-nection with a resistance as shown in Fig. 5. ib represents the out-ow current from the battery. The motor model, as discussed

DC

Lev

J. Xi et al. / Applied Energy 134 (2014) 332341 337to check the inequality condition of the PMP. It turns out that theinequality always holds for any vm* > umax(l). This also conrmswith the conclusion made previously in the unconstrained case.To sum up, we are ended with the following result for the optimalcontrol problem.

vm Rm svkb

11 2k2bRm Cv

q umaxl

8 umax(l). Motivated by the fact vm* is a globalminimum of the convex function g, we expect the optimum tooccur at the value of umax(l) in the constrained case. In order toverify this case, we follow the same line of reasoning in the uncon-strained case. Again, we need to nd a stationery solution in thesense that the dynamics of the state variables along with the co-state variables tend to become zero. A slight modication for thecurrent case is that, in addition to the requirements on im and x,we also require that the time derivatives of p1 and p2 should beRoad Friction

Fig. 4. The overall cobefore, is represented as an inductance in series connection witha resistance together with a back EMF. im and vm represent theinput current and voltage to the motor, respectively. The boostermodel is composed of two switches and a low pass lter. Herethe control variable in the converter is q(t), the on/off state of theswitch. The choice of L and C should meet the specications givenby:

C Pib1 d T

Dvb; LP

vm1 d TDim

49

In these inequalities, T is the switching period and d is the dutyratio, which is related to q(t) in the following way.

d Z tTt

qs ds 50

Dvb andDim are the ripple components of the voltage and current atthe steady state, and they are specied based on design require-ments. The state space representation of the circuit model is shownbelow, in which ib, vm, im and xm are the corresponding systemstates.

dibdt

1Lvb Rbib q vb vm 1 q 51

dvmdt

1Cim q ib im 1 q 52

dimdt

1Lm

vm Rm im kb x 53

dxdt

1Jv2kb im Cv x sv 54

Intrinsically this is a nonlinear time-varying system with the con-trol in the switched state. In dealing with the systemwhich involvesswitching, a common approach is to perform the state-space averag-ing [22]. Instead of focusing on the full dynamics of the waveform,we pay special attention to the low frequency averaged component,which is of greater importance from the control perspective. Theaveraging operator is dened as

Xt 1T

Z ttT

xs ds 55

When acting on both sides of Eqs. (51) and (52), we will have

dibdt

1Lvb Rbib d vm 1 d 56

dvmdt

1Cim ib 1 d 57

C/DController DC/DC Motor

PWMelntrol hierarchy.

tion in a city. All the road information as well as the trafc situa-tion is incorporated into the speed of the vehicle moving ahead.In contrast to the previous scenario, for the most cases in the sec-ond scenario, there tends to be a continuous change in the speed.So it sets a higher demand on the controllers adaptability. Apartfrom those external variations, in both scenarios some randomnoises have been purposely introduced into the model parameters,which in some sense accounts for a discrepancy between themodel and the actual system. We would like to test whether thecontroller can work robustly in the uncertain environment, i.e., inthe presence of the process noise. In the following part, quantita-tive descriptions of the road conditions will be given for each sce-nario together with the initial conditions of the EV system. Thenthe simulation results will be shown followed by a discussionfocusing on the vehicle behavior and controller performance. Asan illustration of the controllers optimality, vehicle behavior at anon-optimal operating point will also be shown and comparedwith that of the optimal solution. It can be noted that any variationin the optimal vehicle speed will ultimately contribute to a totalincrease in the energy dissipation. The vehicle parameters usedin both of the simulations are listed in Table 1.

rgy 134 (2014) 332341It can be noted that in Eqs. (56) and (57), all the state variables havebeen replaced with their averaged ones over the period T, and q(t)automatically becomes d. As long as the switching period T is muchsmaller than the time constant at the system input side given by L/Rb and time constant at the system output side given by RmC, thesimplied model will sufce to capture the averaged behavior ofthe system. Since it is a regulatory problem, we further linearizethe system about its operating point Xss, which yields

~

Fig. 5. Power circuit for electric vehicle.

Compensator Booster

d

vreff

verr

vm

Fig. 6. DCDC level control.Em

ib

q(t) vm

Rb

vb

L

C

Lm

Rm

im

338 J. Xi et al. / Applied Enedibdt

1LRb d ~ib 1 d ~vm vb Rbib ~d 58

d~vmdt

1C1 d ~ib ~im ib ~d 59

d~imdt

1Lm

~vm Rm ~im kb ~x 60

d ~xdt

1Jv2kb ~im Cv ~x 61

After applying the Laplace Transform and obtaining the transferfunction for the duty ratio d and output voltage vm, we can thenanalyze its pole location and design the feedback PI compensator.The block diagram of the closed-loop control system is shown inFig. 6. Detailed numerical simulations and corresponding resultswill be given in the next section.

4. Simulation and case studies

In this section, the proposed controller performance will betested with respect to its adaptability and robustness under twodifferent scenarios using simulations. The rst scenario is drivingon a country road with variations in road conditions includingthe road friction and air resistance at some particular locationsalong the way, assuming no vehicle ahead of the test EV. This sce-nario is designed to test the controllers adaptability to discreteabrupt changes from the external environment. The second sce-nario is driving behind another vehicle which has a varying speed.This scenario is specically designed to simulate the driving situa-Table 1Vehicle parameters used in the simulations.

Battery pack No-load voltage vb 48 VInternal resistance Rb 0.15 ohm

Motor Resistance of the rotor loop Rm 0.6 ohmInductance of the rotor loop Lm 12 mHConversion factor kb 0.25 V/rad

Vehicle dynamics Vehicle mass Mv 250 kgWheel radius rw 0.3 mCross-sectional area AF 2 m2

Table 2Road conditions and initial settings of the EV, Scenario I.

Road conditions Rolling resistance coefcient Crr 0.01Air density qa 1.2 kg/m3

Drag coefcient Cd 0.200 t150s

Initial settings Battery current Ib 132.6 AInput voltage to the rotor motor vm 66.4 V4.1. Scenario I

The road conditions for the rst scenario and the initial settingsof the EV system are specied in Table 2, and the correspondingresults are shown in Fig. 7.

In this scenario, the vehicle is supposed to be initially cruising atthe optimal speed of 105 rad/s on the country road when a suddenincrease in the drag coefcient occurs at t = 150 s. With this varia-tion in the drag coefcient, the optimal operating point shiftsaccordingly. The energy efciency diagrams for the change of envi-ronmental conditions are shown in Fig. 7(I), where the efciency isdened as x/(vm im), a measure of the energy consumption perunit angle. It can be noted that as the drag coefcient Cd increasesfrom 0.20 to 0.28, the optimal voltage level shifts from 66.35 V to62.45 V and at same time the overall energy efciency drops from0.0197 to 0.0160 (from the black curve to the grey curve). This ulti-mate decline indicates that more energy has to be used for over-coming the air resistance.Input current to the rotor motor Im 80.2 AAngular velocity of the wheel x 105 rad/s

ergy 134 (2014) 332341 339J. Xi et al. / Applied EnIn order to adapt to this change in the environment, the inputvoltage to the motor has to be altered accordingly. Under the pro-posed control strategy, it can be seen in Fig. 7(II) that the motorvoltage (black line) experiences a smooth transition to the newoptimal level within a few seconds. In accordance with this varia-tion, the angular velocity of the wheel in Fig. 7(III) also transitionsto a new value, even though it takes a relatively longer time. This ismainly because of a longer response time of the mechanical sys-tem. As the voltage and angular velocity transition to their corre-sponding new values, the energy efciency rst increases andthen declines rapidly and converges to the new level (as shownin Fig. 7(IV)). The initial increase is mainly attributed to the differ-ence in response time between the mechanical and electrical sys-tem, as mentioned before.

The motor voltage in the comparison group (grey line) is main-tained at 50 V all the time and the corresponding angular velocityprole is shown in Fig. 7(III). As the drag coefcient increases, theangular velocity drops accordingly. It can be noted that the energyefciency in the comparison group always lies below that of thecontrolled one, which conrms the observation in Fig. 7(I). In bothconditions, the voltage level 50 V is well below the optimal one.

4.2. Scenario II

The road conditions for the second scenario and the initial set-tings of the EV system are specied in Table 3, and the correspond-ing results are shown in Fig. 8.

Fig. 7. (I) The efciency map under two conditions, (II) the response of the motor voltagenergy efciency.In this scenario there is no change in the road conditions butthere is a vehicle ahead with varying speeds as indicated inFig. 8(I) by the black dashed line. As long as its speed is greateror equal to the optimal cruising speed (105 rad/s in this case),the controlled system will just stay on the optimal one. Howeverwhen the speed of the vehicle ahead falls below, the optimal oper-ating point cannot be attained anymore and we have to follow thatspeed. It can be noted in Fig. 8(I) that the tracking performance ofthe angular velocity (black solid line) is still quite good, except for aminor undershoot around the corner point at t = 650 s. After a shortperiod of the transient stage, the angular velocity nally convergesto 85 rad/s, the same value we chose for the angular velocity in thecomparison group. The motor voltage which produces this velocityprole is shown in Fig. 8(II). The corresponding energy efciencyassociated with this process is shown in Fig. 8(III). As the angularvelocity deviates from the optimal value, the energy efciencynally converges to a value below the optimal one.

e, (III) the angular velocity of the wheel, and (IV) the corresponding instantaneous

Table 3Road conditions and initial settings of the EV, Scenario II.

Road conditions Rolling resistance coefcient Crr 0.01Air density qa 1.2 kg/m3

Drag coefcient Cd 0.200

Initial settings Battery current Ib 132.6 AInput voltage to the rotor motor vm 66.4 VInput current to the rotor motor Im 80.2 AAngular velocity of the wheel x 105 rad/s

rgy340 J. Xi et al. / Applied Ene5. Conclusion

In this paper the energy management for battery powered elec-tric vehicles has been approached from a comprehensive and sys-tematic perspective. By examining the battery and motor dynamicsrespectively, we have acquired an analytic expression that relatesthe optimal operating point of components to the vehicle and envi-ronmental parameters. Based on this analysis, we have proposed acontroller hierarchy suitable for real-time implementation. Fromthe simulation results it can be seen that the controller can adaptto different road conditions and work robustly under uncertainty.To achieve the performance of the proposed integrated approach,the dynamics and couplings of the battery and motor have beenfocused in this work with other minor effects being neglected forthe time being, so that the focus of this work will not be diluted.Those minor effects will be considered in our future work, forexample, as uncertain factors or additional estimated terms inthe models. Another natural extension of the current work wouldbe to integrate the ultra-capacitor into the power source system.

References

[1] Capasso C, Veneri O. Experimental analysis on the performance of lithiumbased batteries for road full electric and hybrid vehicles. Appl Energy 2014.

[2] Xiong R, Sun F, Gong X, Gao C. A data-driven based adaptive state of chargeestimator of lithium-ion polymer battery used in electric vehicles. Appl Energy2014;113:142133.

Fig. 8. (I) The angular velocity of the wheel, (II) the response of the motor134 (2014) 332341[3] Hu C, Youn BD, Chung J. A multiscale framework with extended kalman lterfor lithium-ion battery soc and capacity estimation. Appl Energy2012;92:694704.

[4] Zhong L, Zhang C, He Y, Chen Z. A method for the estimation of the battery packstate of charge based on in-pack cells uniformity analysis. Appl Energy2014;113:55864.

[5] Pahlevaninezhad M, Das P, Drobnik J, Moschopoulos G, Jain PK, Bakhshai A. Anonlinear optimal control approach based on the control-lyapunov functionfor an ac/dc converter used in electric vehicles. IEEE Trans Ind Inform2012;8(3):596614.

[6] Faiz J, Sharian MBB, Keyhani A, Proca AB. Sensorless direct torque control ofinduction motors used in electric vehicle. IEEE Trans Energy Convers2003;18(1):110.

[7] Faggioli E, Rena P, Danel V, Andrieu X, Mallant R, Kahlen H. Supercapacitors forthe energy management of electric vehicles. J Power Sources1999;84(2):2619.

[8] Dougal RA, Liu S, White RE. Power and life extension of battery-ultracapacitorhybrids. IEEE Trans Compon Pack Technol 2002;25(1):12031.

[9] Lu S, Corzine KA, Ferdowsi M. A new battery/ultracapacitor energy storagesystem design and its motor drive integration for hybrid electric vehicles. IEEETrans Veh Technol 2007;56(4):151623.

[10] Kuperman A, Aharon I, Malki S, Kara A. Design of a semiactive battery-ultracapacitor hybrid energy source. IEEE Trans Power Electron2013;28(2):80615.

[11] Garcia F, Ferreira A, Pomilio J. Control strategy for battery-ultracapacitorhybrid energy storage system. In: Proc applied power electronics conferenceand exposition, twenty-fourth annual IEEE. IEEE; 2009. p. 82632.

[12] Lukic SM, Wirasingha SG, Rodriguez F, Cao J, Emadi A. Power management ofan ultracapacitor/battery hybrid energy storage system in an hev. In: Procvehicle power and propulsion conference, IEEE. IEEE; 2006. p. 16.

[13] Laldin O, Moshirvaziri M, Trescases O. Predictive algorithm for optimizingpower ow in hybrid ultracapacitor/battery storage systems for light electricvehicles. IEEE Trans Power Electron 2013;28(8):388295.

voltage; and (III) the corresponding instantaneous energy efciency.

[14] Wang L, Collins Jr EG, Li H. Optimal design and real-time control for energymanagement in electric vehicles. IEEE Trans Veh Technol 2011;60(4):141929.

[15] Wang G, Yang P, Zhang J. Fuzzy optimal control and simulation of battery-ultracapacitor dual-energy source storage system for pure electric vehicle. In:Proc intelligent control and information processing international conferenceon, IEEE; 2010. p. 55560.

[16] Hannan M, Azidin F, Mohamed A. Multi-sources model and control algorithmof an energy management system for light electric vehicles. Energy ConversManage 2012;62:12330.

[17] Li X, Chen Y, Wang J. In-wheel motor electric ground vehicle energymanagement strategy for maximizing the travel distance. In: Proc americancontrol conference, IEEE; 2012. p. 49938.

[18] Tremblay O, Dessaint L-A, Dekkiche A-I. A generic battery model for thedynamic simulation of hybrid electric vehicles. In: Proc vehicle power andpropulsion conference, IEEE. IEEE; 2007. p. 2849.

[19] Liberzon D. Calculus of variations and optimal control theory: a conciseintroduction. Princeton University Press; 2011.

[20] Chiasson J. Modeling and high performance control of electricmachines. Wiley-IEEE Press; 2005.

[21] Gillespie TD. Fundamentals of vehicle dynamics. Society of AutomotiveEngineers; 1992.

[22] Kassakian JG, Schlecht MF, Verghese GC. Principles of powerelectronics. Prentice Hall; 1991.

J. Xi et al. / Applied Energy 134 (2014) 332341 341

Optimal energy management strategy for battery powered electric vehicles1 Introduction2 Background3 Proposed energy management method3.1 Component analysis: battery3.2 Component analysis: motor3.2.1 Solving for the optimal operating point3.2.2 Optimum of the unconstrained case3.2.3 Optimum of the constrained case

3.3 Proposed control strategy

4 Simulation and case studies4.1 Scenario I4.2 Scenario II

5 ConclusionReferences