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1880 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 9, NO. 4, OCTOBER 2018

An Energy Management Strategy of Hybrid EnergyStorage Systems for Electric Vehicle Applications

Chunhua Zheng , Member, IEEE, Weimin Li, Member, IEEE, and Quan Liang

Abstract—In order to mitigate the power density shortage of cur-rent energy storage systems (ESSs) in pure electric vehicles (PEVsor EVs), a hybrid ESS (HESS), which consists of a battery and asupercapacitor, is considered in this research. Due to the use of thetwo ESSs, an energy management should be carried out for theHESS. An optimal energy management strategy is proposed basedon the Pontryagin’s minimum principle in this research, whichinstantaneously distributes the required propulsion power to thetwo ESSs during the vehicle’s propulsion and also instantaneouslyallocates the regenerative braking energy to the two ESSs duringthe vehicle’s braking. The objective of the proposed energy man-agement strategy is to minimize the electricity usage of the EV andmeanwhile to maximize the battery lifetime. A simulation study isconducted for the proposed energy management strategy and alsofor a rule-based energy management strategy. The simulation re-sults show that the proposed strategy saves electricity compared tothe rule-based strategy and the single ESS case for the three typi-cal driving cycles studied in this research. Meantime, the proposedstrategy has the effect of prolonging the battery lifetime comparedto the other two cases.

Index Terms—Battery lifetime, energy management strategy,electric vehicle, electricity usage, hybrid energy storage system,Pontryagin’s minimum principle.

I. INTRODUCTION

CURRENTLY, pure electric vehicles (PEVs or EVs) usu-ally have a single energy storage system (ESS), i.e., a

battery. Batteries, however, have a limited power density be-cause of their inherent chemical characteristics, and this willdefinitely influence the performance of EVs. In order to re-spond to the frequent power transient requirements and meetthe peak power demands of the vehicle, a secondary ESS shouldbe considered for EVs, which can recover the disadvantage ofthe battery. Super-capacitors can be the ideal solution for thesecondary ESS, which present a much better power density,a higher charge/discharge efficiency, and a longer cycle life

Manuscript received June 5, 2016; revised January 22, 2017, April 27, 2017,and August 1, 2017; accepted September 29, 2017. Date of publication March22, 2018; date of current version September 18, 2018. This work was sup-ported in part by the National Natural Science Foundation of China underGrants 51305437 and 61573337 and in part by Shenzhen Science and Technol-ogy Innovation Commission under Grant JSGG20141020103523742. Paper no.TSTE-00419-2016. (Corresponding author: Chunhua Zheng.)

C. Zheng and W. Li are with Shenzhen Institutes of Advanced Technology,Shenzhen 518055, China (e-mail:,[email protected]; [email protected]).

Q. Liang is with Sinopoly New Energy System Co., Ltd., Shenzhen 518055,China (e-mail:,[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TSTE.2018.2818259

compared to batteries [1], [2]. Although the super-capacitors aredifficult to provide a good performance on the energy density,a hybrid ESS (HESS), which consists of a battery and a super-capacitor, shows an improved performance considering boththe power density and the energy density compared to the singlebattery.

Due to the use of the two ESSs, an energy management shouldbe carried out for the HESS. Previously, some researchers haveconsidered the HESS INSTEAD of the single ESS in EVs or inhybrid electric vehicles (HEVs) and have presented the energymanagement strategies [3]–[9]. In the research [3], an HEVcomposed of an internal combustion engine (ICE) and an HESSwas studied. The equivalent consumption minimization strategy(ECMS) was adopted between the ICE and the HESS, and a cou-ple of novel energy management strategies, which take into ac-count the battery lifetime, were proposed for the HESS betweenthe battery and the super-capacitor, including a model predictivecontrol (MPC) algorithm and a dynamic programming (DP) al-gorithm. In the research [4], the same HEV configuration withthe research [3] was discussed. A fuzzy controller was used forthe energy management between the ICE and the HESS, and aDP algorithm was proposed for the energy management of theHESS, which maximizes the battery life. Previous research [5]dealt with a fuel cell hybrid vehicle (FCHV) which is composedof a fuel cell system (FCS) and an HESS. A multi-dimensionalDP code was studied for the energy management among theFCS, the battery, and the super-capacitor to reduce the hydro-gen consumption. Previous research [6] applied the Pontryagin’sMinimum Principle (PMP) to the energy management amongthe ICE, the battery, and the super-capacitor for an HEV in or-der to achieve the optimal fuel economy and battery lifetime.The above studies were conducted for HEVs or FCHVs. Al-though, the energy management between the battery and thesuper-capacitor can be the reference for the HESS of EVs, butthe energy management among the ICE or the FCS, the battery,and the super-capacitor is not suitable to be the reference. Thereare few previous studies with regard to the energy managementof the HESS aimed at EVs. In the research [7], a rule-basedenergy management strategy was proposed for the HESS to im-prove the range and the performance of the EV. In the research[8], authors compared several energy management strategiesof the HESS for EVs including the rule-based controller, thefiltration-based controller, the model predictive controller, andthe fuzzy logic controller, and in their later research [9], a DPapproach was presented for the HESS to reduce the battery lossin EVs.

1949-3029 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

https://orcid.org/0000-0002-6973-1827

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ZHENG et al.: ENERGY MANAGEMENT STRATEGY OF HYBRID ENERGY STORAGE SYSTEMS FOR ELECTRIC VEHICLE APPLICATIONS 1881

Fig. 1. Configuration of the EV with the HESS.

Summing up the previous research, there are mainly twotypes of energy management strategies for the HESS: one is theheuristic concept-based strategy such as the rule-based strategyand the fuzzy logic-based strategy; the other is the optimal con-trol theory-based strategy such as the DP approach. The formerstrategy is explicit and much easier to be implemented on board,but it is still difficult to achieve the theoretically optimal resultsby applying control rules or fuzzy logics, although there aresome studies showed near-optimal results by extracting rulesfrom the DP approach [10], [11]. The latter strategy guaranteesthe theoretically optimal control results, however it can onlybe the benchmark of other control strategies, as it cannot beimplemented in reality due to the backward calculation processand the long calculation time. Being confronted with such abackground, this research proposes a PMP-based energy man-agement strategy of the HESS for EVs, which instantaneouslycalculates the optimal solutions for the battery and the super-capacitor during driving. This strategy recovers disadvantagesof the two types of strategies above, as it is based on the opti-mal control theory and the optimal solutions can be calculatedwithin a short time. The control objective is to minimize theelectricity usage of the EV and to maximize the battery lifetimeat the same time. The proposed strategy cannot be consideredas a subset of the one proposed in [6], as the two-power source-optimization and the three-power source-optimization problemsare theoretically different.

The outline of this paper is organized as follows: inSection II, the EV model used in this research is introduced;Section III presents the formulation of the HESS control prob-lem for EVs and proposes the PMP-based energy managementstrategy for the control problem; in Section IV, the PMP-basedenergy management strategy is implemented to the EV in a com-puter simulation environment and the simulation results regard-ing the electricity usage and the battery lifetime are comparedto those of a rule-based strategy and the single ESS case; at theend, conclusions are drawn from this research in Section V.

II. THE EV MODELING

Fig. 1 shows the configuration of the EV studied in this re-search. The battery is the primary ESS which undertakes thesmooth loads, while the super-capacitor is the secondary ESSwhich covers the frequent transient loads. Both the battery andthe super-capacitor can recover the vehicle mechanical energythrough the regenerative braking. Similarly, the battery and thesuper-capacitor are responsible for the smooth charging and thefrequent charging respectively. The super-capacitor can also becharged by the battery in some cases such as when the super-capacitor state of charge (SOC) is too low. Parameters regarding

TABLE IPARAMETERS REGARDING VEHICLE DYNAMICS

Parameter Value

Vehicle total mass (kg) 1550Tire radius (m) 0.31Aerodynamic drag coefficient 0.275Vehicle frontal area (m2) 2.688Air density (kgm−3) 1.23Rolling resistance coefficient 0.014

Fig. 2. Equivalent circuit diagram of the battery internal resistance model.

the vehicle dynamics of the EV are described in Table I, whichare sourced from the available literature [7]. The final drivegear efficiency is considered to be 95%, and the converters areassumed to be ideal converters with the efficiency of 95% here.

The internal resistance model is used for the battery, the equiv-alent circuit of which is illustrated in Fig. 2. This model has beenwidely adopted when evaluating the energy management strate-gies of EVs or HEVs. In this model, the open circuit voltage(OCV) and the internal resistance are dependent on the batterySOC, and the battery parameters are related to each other asfollows:

•SOCb = −Ib

Q

Ib =Vb (SOCb) −

√Vb(SOCb)

2 − 4Rb (SOCb) · Pb

2Rb (SOCb)(1)

Here, SOCb represents the battery SOC, Ib represents the bat-tery current, Q represents the battery capacity, Vb is the batteryOCV, Rb is the battery internal resistance, and Pb is the bat-tery output power. A 93 Ah battery is used in this research, andthe dependency diagrams are given in Fig. 3. Fig. 4 illustratesthe battery current limits for both the discharging and chargingcases. The output power range of this battery is from −150 kWto 105 kW, and the battery SOC usage ranges from 0.4 to 0.8here.

There are several super-capacitor models have been used tovehicular applications [1]–[3], [5], [8], [9], [12], [13]. Amongthem, the simple internal resistance model, in which a seriesresistance is connected to the capacitor, is widely adopted whendeveloping energy management strategies of EVs or HEVs dueto its simplicity and sufficient accuracy [2], [3], [8], [9], [12],


Fig. 3. (a) Battery OCV versus battery SOC. (b) Battery internal resistanceversus battery SOC.

Fig. 4. Battery current limits for both discharging and charging cases.

[13]. In this research, a parallel resistance Rp is also consideredother than the series resistance Rs , in order to take into accountthe overall leakage in addition to the resistance against chargingand discharging. The equivalent circuit of the super-capacitormodel used in this research is illustrated in Fig. 5, which isalso widely used previously [1], [3], [5]. In Fig. 5, Ic is thecapacitance current, Ip is the leakage current, and It is thesuper-capacitor output current, which are related to each otheras follows:

It = Ic − Ip Discharging

It = Ic + Ip Charging (2)

Fig. 5. Equivalent circuit diagram of the super-capacitor model.

TABLE IISUPER-CAPACITOR PARAMETERS

Parameter Value

C (F) 28Rs (Ohm) 0.01Rp (Ohm) 10000Vs,m ax (V) 305

In Fig. 5, the super-capacitor parameters are related to eachother as follows:

•SOCs = − 1

C·((

12Rs

± 1Rp

)· SOCs

− 12Rs

√SOCs

2 − 4Rs

Vs,max2 · Ps

)(3)

Here, SOCs is the super-capacitor SOC, C is the capaci-tance of the super-capacitor, Vs,max is the maximum capacitancevoltage, and Ps represents the super-capacitor output power.The positive sign corresponds to the discharging case, whereasthe negative sign corresponds to the charging case. The super-capacitor data used in this research are described in Table II,which are sourced from the literature [5], [7].

A 50 kW electric motor is used for the EV in this research. Themotor is modeled using an efficiency map illustrated in Fig. 6,where quadrants I and IV correspond to the vehicle propulsionmode and the regenerative braking mode, respectively.

III. A PMP-BASED ENERGY MANAGEMENT

STRATEGY OF THE HESS

PMP stems from the optimal control theory, which instanta-neously provides the necessary optimality conditions to controlproblems [14]. Such characteristics make the PMP one of themost promising candidates of the energy management for vehic-ular applications. Previously, some researchers have adopted thePMP to the energy management of HEVs or FCHVs [15]–[18].However, there are few studies dealing with the PMP aimedat the energy management between the battery and the super-capacitor for EVs. Here, the HESS control problem formulationis introduced and the PMP is applied to the control problem.


Fig. 6. Electric motor efficiency map.

The state equation here is the super-capacitor dynamic eq.(3), which can be simplified as follows:

•SOCs = f (Ps, SOCs) (4)

Considering that the vehicle driving cycle is provided in ad-vance, the totally required power Preq is accordingly given,which is expressed as follows:

Preq = Pb + Ps (5)

Then, the state equation can be transformed using anotherfunction as follows:

•SOCs = F (Pb, SOCs) (6)

In this control problem, the state variable is the super-capacitor SOC SOCs , and the control variable is the batteryoutput power Pb . The control objective is to find the optimalPb trajectory along the driving cycle to make the system (6)follow the optimal SOCs , so that the whole electricity usageof the EV is minimized and the battery lifetime is also maxi-mized. The battery usage can be represented by the root meansquare (RMS) of the battery current, which can be replaced withthe integrated square of the battery current along the drivingcycle [6]. Thus, the performance measure to be minimized canbe expressed as follows:

J =∫ tf

t0

k · I2b (Pb, SOCb) dt (7)

Here, the battery current Ib can be found in (1), and k is atuning parameter. t0 and tf represent the starting time and theending time of the vehicle driving cycle respectively. There is noextra term for the battery lifetime extension in (7), as reducingthe battery usage is also beneficial to prolong the battery lifetime.

According to the PMP, when a Hamiltonian is defined as

H = k · I2b (Pb, SOCb) + p · F (Pb, SOCs) (8)

Fig. 7. A visual example of the optimal control variable determination at amoment during vehicle’s propulsion.

the necessary conditions of the above optimal control problemare as follows:

•SOCs

∗ =∂H

∂p(SOCs

∗, P ∗b , p∗)

•p∗ = − ∂H

∂SOCs(SOCs

∗, P ∗b , p∗)

H (SOCs∗, P ∗

b , p∗) ≤ H (SOCs∗, Pb , p

∗) (9)

Here, p represents the co-state variable of the PMP. The firstnecessary condition is the state eq. (6), which indicates that theoptimal solution should first satisfy the system constraint. Thesecond one provides the optimal co-state variable determinationcondition. The third necessary condition implies that the optimalcontrol variable P ∗

b is the one which minimizes the Hamiltonianamong all admissible control variable candidates. The three nec-essary conditions should be satisfied all the time during driving,so that the optimal solution trajectories can be obtained for theentire driving. Based on the characteristics of the control prob-lem formulation in this research, the co-state variable p shouldbe negative during vehicle’s propulsion and positive during re-generative braking. Two points should be emphasized here: theoptimal solution can be found only if the future driving cy-cle information is provided in advance; three conditions in (9)are necessary conditions, thus the optimal solution is under theassumption of its uniqueness.

Fig. 7 illustrates a visual example of the optimal control vari-able determination at a moment during vehicle’s propulsion.Parameters related to this moment are described in Table III.The first and the second subplots represent the first term andthe second term without p of the Hamiltonian, respectively. The


TABLE IIIPARAMETERS RELATED TO FIG. 7

Parameter Value

SOCs 0.224p −1.95Preq (kW) 20.166Available Pb range (kW) −97–105

Fig. 8. Another visual example of the optimal control variable determinationat a moment during vehicle’s regenerative braking.

range of the battery power in Fig. 7 indicates the control variablecandidates at this moment, which is determined based on the to-tally required power at this moment and the super-capacitorpower range. At this moment, the available battery power rangeis from −97 kW to 105 kW. It can be observed that the co-statevariable should be a negative value, so that the optimal controlvariable which minimizes the Hamiltonian can be a positivevalue, namely the battery provides power to propel the vehicle.Finally, it can be found that the optimal battery power is 20 kWat this moment.

Fig. 8 shows another visual example of the optimal con-trol variable determination at a moment during vehicle’s re-generative braking. Parameters related to this moment are de-scribed in Table IV. For this moment, the available battery powerranges from −61 kW to 105 kW. It can be observed that theco-state variable should be a positive value here, so that theoptimal control variable can be a negative value, namely thebattery is charged through the regenerative braking. Finally, itcan be found that the optimal battery power is −7 kW at thismoment.

TABLE IVPARAMETERS RELATED TO FIG. 8

Parameter Value

SOCs 0.147p 0.4Preq (kW) −10.622Available Pb range (kW) −61–105

IV. SIMULATION RESULTS ANALYSIS OF THE PROPOSED

ENERGY MANAGEMENT STRATEGY

In this section, the proposed energy management strategyis applied to the EV introduced in Section II in a computersimulation environment. Regarding the electricity usage and thebattery lifetime, the simulation results of the proposed energymanagement strategy are compared to those of a rule-basedstrategy and the single battery case.

A. Simulation Results of the Proposed EnergyManagement Strategy

Three typical driving cycles, i.e., the FTP72 urban drivingcycle, the NEDC 2000, and the Japan 1015 driving cycle arestudied in this research. Fig. 9 illustrates the power allocationresults on the three driving cycles. Here, different powers aredistinguished more clearly for a part of the driving cycle. Itcan be observed that the battery power trajectories are smoothcompared to the super-capacitor power and the total power tra-jectories, which will result that the absolute value of the batterycurrent is also low for the entire driving. This is beneficial tominimize the whole electricity usage and maximize the batterylifetime for the EV.

B. A Rule-Based Energy Management Strategy and ItsSimulation Results

A rule-based energy management strategy is also adoptedin this research in order to evaluate the effectiveness of theproposed strategy, the control rules of which are as follows:

Ps (t) = Preq (t) acc (t) ≥ x or acc (t) ≤ y

Pb (t) = Preq (t) other (10)

Here, Preq is the power totally required to the vehicle, and accis the vehicle acceleration. The control rules are sourced from theheuristic concept that the super-capacitor covers the quick loadtransients and the battery undertakes the other loads. The controlrules are determined by x and y, which are dependent on thedriving cycle. Fig. 10 shows the power distribution results of therule-based strategy. Here, different powers are also distinguishedmore clearly for a part of the driving cycle.

C. Electricity Usage Comparison

Fig. 11 illustrates the battery SOC trajectory comparison forthe proposed energy management strategy, the rule-based strat-egy, and the single ESS case. The trajectories of the proposedand the rule-based strategies here correspond to the simulation


Fig. 9. Power allocation results of the proposed energy management strategyon (a) FTP72 urban driving cycle, (b) NEDC 2000, and (c) Japan 1015 drivingcycle.

results in 4.1 and 4.2. For a fair comparison, the final super-capacitor SOC of the two strategies is set to be similar, which isillustrated in Fig. 12. This can be achieved by tuning x and y inrule-based strategy and the co-state variable in the PMP-basedstrategy. In the single ESS case, the battery introduced in Sec-tion II is the only ESS. Table V describes the final battery SOCon the three typical driving cycles for the three cases. It canbe observed that the final battery SOC of the proposed energymanagement strategy is the highest one, which proves the elec-tricity saving effect of the proposed strategy. According to thefinal battery SOC values, the electricity is saved around 6.5%and 12.2% for the FTP72 urban driving cycle, around 6.5% and14.0% for the NEDC 2000, and around 10.0% and 67.9% for theJapan 1015 driving cycle by the proposed strategy compared tothe rule-based strategy and the single battery case respectively.Obviously, the electricity saving effect of the proposed energymanagement strategy is different for each driving cycle. It alsodepends on the co-state variable of the proposed energy manage-ment strategy and the control rules of the rule-based strategy.

Fig. 10. Power distribution results of the rule-based energy management strat-egy on (a) FTP72 urban driving cycle, (b) NEDC 2000, and (c) Japan 1015driving cycle.

D. Battery Lifetime Comparison

The battery lifetime is one of the key factors for EVs totake the place of conventional vehicles. Previously, the batterylifetime model was studied by some researchers [3], [4], [19]–[22], and among them, the general model [20] for all batteryC-rates is adopted in this research. According to the generalmodel, the battery life capacity is dependent on the batterycurrent. The dependency relationship is illustrated in Fig. 13for the battery used in this research, which is sourced from theprevious research [4]. This figure reveals that higher batterycurrent will result in shorter battery lifetime and they have anonlinear relationship. Generally, the battery charging wearsthe battery more than the battery discharging [23], [24], thus a5% tuning is adopted for the charging case in this research.

The battery capacity loss for a driving cycle Qloss,DC can bedefined as follows:

Qloss,DC =∑

(Ib (t) · Δt/3600) /LC (Ib (t))

t = t0 : Δt : tf (11)


Fig. 11. Battery SOC trajectory comparison for the proposed energy manage-ment strategy, the rule-based strategy, and the single ESS case on (a) FTP72urban driving cycle, (b) NEDC 2000, and (c) Japan 1015 driving cycle.

Here, Ib(t) represents the battery current at each time stepduring driving, and LC is the battery life capacity, which can befound from Fig. 13 based on Ib . Considering 8 working hoursin a day and 250 working days in a year, the 10-year batterycapacity loss Qloss,10y can be defined as follows:

Qloss,10y = Qloss,DC/tf × 3600 × 8 × 250 × 10 (12)

Here, if Qloss,10y is less than 1, it means the battery does notneed to be replaced during 10-year working. For the oppositecase, the battery should be replaced and the value of Qloss,10y

indicates the replacing times, i.e., if it is 2.5, it means the batteryshould be changed at least two times during 10-year working.

Table VI provides the simulation results of Qloss,10y for theproposed energy management strategy, the rule-based strategy,and the single ESS case on the three typical driving cycles. Itcan be observed that Qloss,10y becomes less in order of the

Fig. 12. Super-capacitor SOC trajectories for proposed energy managementstrategy and rule-based strategy on (a) FTP72 urban driving cycle, (b) NEDC2000, and (c) Japan 1015 driving cycle.

TABLE VFINAL BATTERY SOC ON THREE TYPICAL DRIVING CYCLES FOR THE

PROPOSED STRATEGY, THE RULE-BASED STRATEGY, AND THE

SINGLE ESS CASE

FTP72 urban NEDC 2000 Japan 1015

Proposed strategy 0.657 0.657 0.691Rule-based strategy 0.654 0.654 0.690Single ESS case 0.651 0.650 0.672

single ESS case, the rule-based strategy, and the proposed strat-egy, which indicates that the battery works longest hours whenadopting the proposed energy management strategy on the threedriving cycles. On the FTP72 urban driving cycle and the NEDC2000, Qloss,10y is greater than 1 for all cases. It conveys that


Fig. 13. Relationship between the battery current and the battery life capacityfor (a) discharging case and (b) charging case.

TABLE VI10-YEAR BATTERY CAPACITY LOSS ON THREE TYPICAL DRIVING CYCLES FOR

THE PROPOSED STRATEGY, THE RULE-BASED STRATEGY, AND THE

SINGLE ESS CASE

FTP72 urban NEDC 2000 Japan 1015

Proposed strategy 1.18 1.38 0.74Rule-based strategy 1.21 1.74 0.80Single ESS case 1.87 2.04 1.18

these two driving cycles are comparatively aggressive, thus thebattery should be changed during 10-year working even thoughthe HESS and the proposed energy management strategy areadopted. Among them, the battery should be changed two timeson the NEDC 2000 for the single ESS case, and one time isenough for the other cases. On the Japan 1015 driving cycle, thebattery should be replaced during 10-year working for the sin-gle ESS case (Qloss,10y > 1), whereas it is safe during 10-yearworking by adopting the HESS and applying the proposed andthe rule-based energy management strategies (Qloss,10y < 1).

V. CONCLUSION

In order to compensate for the shortage of current en-ergy management strategies of HESSs, a PMP-based energymanagement strategy is proposed in this research, which instan-taneously calculates the optimal solutions for the battery and the

super-capacitor during driving. Simulation results show that theproposed energy management strategy presents superiority onboth the electricity usage and the battery lifetime compared tothe rule-based strategy and the single ESS case. Detailed resultsare as follows:

1) The final battery SOC of the proposed strategy is the high-est one and the battery electricity is saved around 6.5% and12.2% for the FTP72 urban driving cycle, around 6.5%and 14.0% for the NEDC 2000, and around 10.0% and67.9% for the Japan 1015 driving cycle compared to therule-based strategy and the single ESS case, respectively.

2) Qloss,10y becomes less in order of the single ESS case,the rule-based strategy, and the proposed strategy for thethree driving cycles studied. It indicates that the batteryworks longest hours when adopting the proposed energymanagement strategy on the three driving cycles, and thusthe superiority of the proposed strategy on the batterylifetime is proved.

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