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IFAC-PapersOnLine 48-15 (2015) 086–092

Available online at www.sciencedirect.com

2405-8963 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.Peer review under responsibility of International Federation of Automatic Control.10.1016/j.ifacol.2015.10.013

© 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Keywords : Battery Electric Vehicles, Energy Management System, Battery Health, DynamicProgramming.

INTRODUCTION

Global warming, limited fossil fuel resources, and theincreasing price of oil have encouraged people to find a clean,safe and efficient solution for their mobility, and it seems thatthe electrified transportation is the right way to go. HybridElectric Vehicles (HEVs) were introduced in the last decade,and gained a lot of attention from research communities andcar manufactures. They take advantage of an IC engine alongwith an electric motor/generator, and also a battery as theirstorage unit. This hybridization of the vehicle powertrainmakes the engine smaller and more efficient. The HEVs ’

potentials in the efficiency enhancement, energy saving andemission reductions have resulted in many successfulcommercial products. Later, Plug-in Hybrid Electric Vehicles

(PHEVs) were introduced to the car market as a bridge fromHEVs to the full-electric transportation. They use larger

batteries than conventional HEVs that can be fully charged before starting off, which results in a better fuel economy(Taghavipour, Vajedi et al. 2012). Although HEVs andPHEVs have been successful, they are only an interim solutionto reduce our ecological footprints. Due to the use of ICEs inHEV/PHEVs, they are not entirely green and zero-emissionlevel. On the other hand, full electric vehicles use on-boardelectrical energy storages and electric motors for the energygeneration. BEVs are fully green because the battery is used asthe only energy source of the vehicle, and also, they are veryefficient due to the use of electric motors instead of ICEs.

However, in comparison with ICEVs and HEVs, BEVs have a

short operating range, and also, their expensive battery has alimited service life, which restricts BEVs’ wide market

presence at the end. The development of an effective EnergyManagement System (EMS) for BEVs is critical to address theabove-mentioned issues.

Many EMSs have been developed for HEVs, and they havecaused a significant effect on reducing the ve hicle’s ene rgyconsumption and emissions (Sciarretta and Guzzella 2007,Wirasingha and Emadi 2011). EMSs for HEVs can becategorized into rule-based and model-based controlstrategies. The rule-based strategies try to operate each vehicle

powertrain’s subsystem (ICE or electric motor) at its highestefficiency points. In (Banvait, Anwar et al. 2009, Liu, Du et al.2012), a deterministic rule-based EMS was developed for

PHEVs. This strategy does not require future knowledge of thevehicle ’s path, and it works based on a set of the rules that have been set up before the actual operation. Fuzzy logic controllersare another kind of rule-based EMSs with less computational

burden, but they are only optimum for special predefineddriving cycles. In (Xia and Langlois 2011, Denis, Dubois et al.2015), an adaptive fuzzy logic controller was introduced,which adapts to different driving cycles but increases thecomputational load. The rule-based controllers find the nearoptimum working condition for each component of thevehicle ’s powertrain, but not the global optimal point in thegeneral case. However, the model-based control strategies canfind a global optimal solution to the power distribution

problem for every driving condition. (Piccolo, Ippolito et al.

Abstract: Environmental pollution and high fuel costs have increased demands for an alternativeenergy source for transportation. Battery Electric Vehicles (BEVs) are attracting the attention ofresearchers of automotive engineering field to address these concerns because of their reputation forbeing fully green as well as more efficient than Internal Combustion Engine Vehicles (ICEVs).However, two major problems with BEVs are their short driving range and the limited service lifeof their costly batteries. Enhancing BEVs’ driving range and their batteries’ lifetime are possiblethrough developing more effective energy management systems (EMSs) for them. This study

proposes an optimal EMS for a BEV, the Toyota RAV4 EV, by considering the power flow betweenthe energy consumers inside the vehicle. Dynamic programming (DP) is used to find an optimalpower distribution between the vehicle drivetrain and the heating system for a standard drivingcycle. A high-fidelity model of the vehicle in Autonomie is also employed to demonstrate theeffectiveness of the devised EMS. The results show that the proposed strategy can improve thebattery health of the considered BEV.

An Optimal Energy Management System for Battery Electric Vehicles

B. Sakhdari*. N. L. Azad**

*Systems Design Engineering Department, University of Waterloo,Waterloo, ON, Canada (Tel: 226-929-3333; e-mail: [email protected]).

** (e-mail:[email protected])

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2001, Delprat, Lauber et al. 2004) used offline optimizationmethods to solve the energy distribution problem in a givenvehicle. Their proposed EMS can be useful for offline tuningsof the energy flow in the design process, but cannot beemployed in real-time applications. Stochastic dynamic

programming (SDP) can be used to determine the optimalenergy flow for a more general case in real-world driving

scenarios. (Moura, Stein et al. 2013) used SDP to investigatetrade-offs between the battery health and energy consumptionof a given vehicle. Model predictive controllers (MPC) arealso very popular for the real-time energy management ofHEVs (Borhan, Vahidi et al. 2012). (Taghavipour, Vajedi etal. 2012) utilized the MPC theory for the optimal EMS designof a PHEV with four different cases of the knowledge of futuretrip information.

Compared with the extensive literature on the EMS design forHEV/PHEVs, there are only a few studies on the energymanagement of pure EVs, which could be because of theirsimpler powertrain architectures and limited degrees of

freedom for the energy distribution. Many studies haveinvestigated an optimum power distribution between ultra-capacitors and batteries for EVs hybridized with ultra-capacitors, which will increase the vehicle’s driving range andthe lifecycle of its energy storage system (Romaus, Gathmannet al. 2010, Trovao, Santos et al. 2013). There are morelimitations in terms of the EMS enhancement in BEVs becausethey have only batteries as their energy sources. In (Kachroudi,Grossard et al. 2012), the authors used the particle swarmoptimization (PSO) method to optimally control the energyflow between the powertrain and the other vehicle ’s auxiliariesfor a given BEV. They tried to decrease the vehicle’s energyconsumption, and at the same time maintain the comfort of the

passengers, by providing some suggestions to the driver.(Masjosthusmann, Kohler et al. 2012) took advantage of theheating system’s power control, and (Roscher, Leidholdt et al.2012) used the cooling system ’s power control to reduce theoverall energy consumption and increase the battery health ofBEVs. They developed a rule-based method that turned off thevehicle’s HVAC system in high drivetrain power demands,and turned it on again in the low driving power demands so theresulting battery current peaks diminished. These methodscannot guarantee finding optimum power distributions indifferent conditions to maintain the comfort and increase thefuel economy. Also, they cannot be adjusted by the driver tochoose different operating modes, such as the comfort or fuel

economy.In this study, the authors develop an optimal EMS for a BEV,the Toyota RAV EV, to increase the battery ’s service life. Thedrivetrain and heating system as the two major energyconsumers are considered, and then, DP is applied to find anoptimal power distribution between them. The optimal powerdistribution means smoother current demands from the batterywith reduced current peaks. This will result in less sudden heatgenerations and temperature gradients inside the battery whichcause shortening the battery life (Savoye, Venet et al. 2012).The proposed strategy is simulated using an Autonomie-basedmodel of the vehicle in the FTP driving cycle.

In what follows, first, the modeling of the vehicle ’slongitudinal dynamics and the cabin ’s thermal model are

introduced. Then, the proposed EMS and the applied DPmethod will be mentioned. After implementing the proposedstrategy on the vehicle ’s model, the results of the simulationswill be presented, along with some discussions and concludingremarks.

BEV SYSTEM MODEL

The Autonomie software was used to create a high-fidelitymodel of the considered BEV. Autonomie is an automotivemodeling and simulation package developed by the Argonne

National Lab. In this study, we employed a modified versionof the Autonom ie’s default BEV model by incorporatingknown parameters of the baseline RAV4 EV. Figure 1 showsthe considered high-fidelity model in the Simulinkenvironment. The mechanical part of the model includes thelongitudinal dynamics of the vehicle and the drivetrain system.The electrical portion of the model consists of high-voltageand low-voltage batteries, a DC/DC converter, and also, anelectrical heater unit.

Figure 1. Autonomie-based BEV model

The longitudinal dynamics model is based on the external

forces applied to the vehicle, as shown in Figure 2:

= 1∗ ( − − − ) (1)

where is the vehicle ’s acceleration, is the vehicle ’sequivalent mass, is the propulsion force form both vehicle ’sdriving wheels, is the aerodynamic resistance force, isthe friction force due to the rolling resistance of the wheels,and is the gravity force due to the road slope:

Figure 2. Vehicle’s longitudinal dynamics model

= + − (2)

= 12 . . . .

(3)

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88 B. Sakhdari et al. / IFAC-PapersOnLine 48-15 (2015) 086–092

= . . . . (4)

= . . (5)

where , are the right and left wheel ’s drivingtorques and braking torque, respectively, is the wheelradius, is the air density, is the vehicle ’s frontal area, is the aerodynamic coefficient, is the vehicle ’s velocity,

is the rolling resistance coefficient, and is the road slope.

The drivetrain of the vehicle is modeled by mapping anefficiency factor relating the mechanical power and theelectrical power from the energy supply of the vehicle:

ℎ = , ∗ (6)

ℎ = (7)

where and are the torque and angular velocity of thevehicle ’s wheel. are the batter y’s charging anddischarging voltage and current. Because of the mechanicalfrictions and also limitations in the regenerative braking, theefficiency in the regenerative mode is different from theelectrical to mechanical power efficiency amount defined

previously for the propulsion mode:

= , ∗ ℎ (8)

A battery model similar to (Dib, Chasse et al. 2012) has beenemployed, in which the batter y’s open circuit voltage and theresistance are related to the state of charge or SOC.Due to the internal resistance of the battery, the final voltageof the battery will be less than the open circuit voltage, andalso, a higher battery current will cause a lower final voltage.

Figure 3 shows a simple circuit-based model of the vehicle ’s battery. The battery current can be calculated from the total power, as follows:

= − √ − 4 2 (9)

where depend on the battery ’s SOC.

Figure 4. Battery ’s equivalent circuit model

is the total system ’s power, and two most importantconsumers of it are the drivetrain and the vehicle’s accessories:

= + (10)

is the summation of power demand from the drivetrain andthe generated power by regenerative braking with consideringefficiencies. The drivetrain ’s power is a function of thevehicle ’s speed and the motor torque. The speed and torquetrajectories of the vehicle can be predicted using the datareceived from GPS, GIS and ITS technologies for a given

route. is the power of low-voltage energy consumers whichreceive their power through the DC/DC converter. The DC/DCconverter was modeled with a constant efficiency:

= / . ℎ (11)

The most important low-voltage consumer is the HVACsystem. In this work, we are considering the cabin ’s heater asthe only low-voltage consumer. ℎ is the required power forheating the vehicle ’s cabin. It mostly depends on the ambienttemperature, available sunlight, number of the passengers, andtheir desired cabin ’s temperature. The cabin`s air temperaturediffers with respect to the amount of heat transferred from andto the vehicle ’s cabin, as given below:

= (12)

where is the total heat flow into and from the vehicle ’scabin. This quantity consists of the heat conduction, radiation,

passenger s’ heat dissipation, and the HVAC system ’s power.

is the air density, is the volume of the cabin ’s air, and is the specific heat capacity of air. The passenger specifies thedesired temperature, and the HVAC unit tries to maintain thetemperature in a region near the desired value:

= + + + ℎ (13)

= . ∆ (14)

= 100. (15)

The conduction trough the vehicle ’s body is related to thedifference between the cabin and ambient temperature with aconduction constant . is the heat dissipation by each

passenger, which is known to be around 100 W for each person. The radiation can be neglected for low temperaturesituations.

The driver tries to follow the predefined speed trajectory, andapplies the required driving or braking torques to the wheels:

∗= ( ∗ − )∗ (16)

where is the driver ’s model, ∗ is the desired speed, isthe vehicl e’s actual speed, and ∗ is the driver`s desired torquein frequency domain.

Figure 3 . Proposed architecture of BEV’s EMS

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PROPOSED EMS CONCEPT

The goal of the vehicle’s EMS is to decrease the energyconsumption and increase the battery life through an optimaldistribution of the power. Figure 4 illustrates the proposedarchitecture of the EMS unit.

The devised EMS determines an optimal energy flow for the

electrical components to achieve the reference speed, byconsidering the driver’ s demand and the vehicleenvironmen t’s information. The EMS outputs can besuggested to the driver on a monitor, or it can be implementedto operate automatically as part of a supervisory control unit.In this study, we are just considering the power distribution tothe electrical heater for a preliminary investigation of the

proposed concept.

As mentioned before, a higher amount of the battery currentmay result in a higher voltage drop, which, in turn, requiresmore current for a specific power demand. The higher batterycurrent amount means more power loss, producing more heat

inside the battery, which also requires more power for coolingit down again; therefore, high peaks in the battery currentshould be avoided. The battery current fluctuates due to thechanges of power demands of the vehicle ’s drivetrain andelectrical components during a specific trip. If we assume thatthe current fluctuates with a sinusoidal form, then:

sin( ) (17)

where is the mean current value, and is the amplitude of thesinusoidal current fluctuations. With this formulation of thecurrent, the total consumed battery energy and the total

produced heat inside the battery for a fluctuation periodwill be:

∫ . ∫. . ( ). (18)

∫ . . . 12 . (19)

where , , and are the battery`s voltage, current, andinternal resistance, respectively. The energy loss inside the

battery is related to the square of mean current and currentfluctuations. By reducing the fluctuations of the batterycurrent, the energy loss decreases for the same final powerdemand. The vehicle’s EMS can smoothen the battery currentand reduce the current peaks by distributing the demanded

power wisely to the vehicle ’s components. During theacceleration or when the vehicle is moving on a high sloperoad, EMS will put the heater in a low power mode. When thedrivetrain ’s power demand decreases, EMS returns the heaterto a high power mode. In this way, EMS acts as a virtualcapacitor that uses the thermal capacity of the vehicle ’s cabinto achieve a smoother power demand profile.

OPTIMUM EMS DESIGN PROCESS

A typical heating system in BEVs increases the temperature tothe drive r’s demanded value, and then tries to maintain thetemperature in a region close to it. So, when the temperaturereaches the higher limit, the heater will be turned off or

brought to a lower power mode, and when the temperaturereaches the lower limit, the heater will be turned on again. In

this study, we want to change this simple strategy withconsidering the vehicle’s future power demands for thedrivetrain component, and also, find an optimal trajectory forthe electrical heater ’s power . This can be formulated as anoptimal control problem which will be solved to obtain theoptimum heater ’s power trajectory, as shown later.

The objectives of the optimal control problem are to minimizefailures in maintaining the cabin ’s temperature close to thedesired value as well as the fluctuations in the battery currentwith a minimum of the total consumed energy. A cost functionis defined with the three above-mentioned goals, as follows:

1-The temperature needs to be maintained close to the desiredvalue so the following term should be minimized:

∗∑( − )=

(20)

where is a weighting coefficient.

2- The main objective is to achieve a smoother battery current,which, in turn, means a smoother overall power demand

profile. Minimizing the term below gives us a smoother powerdemand sequence:

∗∑( − )=

(21)

where is a weighting coefficient, and is the expectedmean power demand for a given trip. is calculated byaveraging the expected powers of the drivetrain and aconventional heating system for a given driving cycle andambient temperature.

3- The last objective is to minimize the total consumed energy:

∗∑=

= (22)

is the summation of the drivetrain and heating system’s powers. The required drivetrain ’s power is known for aspecified speed trajectory based on the vehicle ’s model. Theheating power is the system’s input, and the temperature is thestate of the system. The relation between the heating powerand the cabin ’s temperature provides the plant model. Thisresults in the optimization problem below:

min (, ) (23)

ℎ

+ ℎ ∗∆ 0≤ℎ≤4000 [ ]

0≤ ≤ 30 [℃]

DP was used to solve the optimal control problem through

considering the heating power ℎ as a discretized input from 0to 4000 W, and the cabin ’s temperature was discretized from

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0 to be 30 ° . This algorithm tries to find an optimal trajectoryfor ℎ by minimizing ( , ) and using the state equation todetermine the cabin ’s temperature resulting from different ℎ sequences.

SIMULATION RESULTS

We chose the FTP-75 driving cycle to evaluate the performance of the proposed EMS. The vehicle ’s high-fidelitymodel was simulated with the knowledge of FTP-75 speedtrajectory. Considering the efficiencies of the drivetrain,converter and actuators, the total driving power demand of thevehicle was calculated from a forward simulation. This powerdemand was then used as a known input for the defined DP

problem. Figure 5 shows the speed trajectory, and the driving power demand resulting from the vehicle’s model simulation.

Figure 5. FTP-75 driving cycle and the resulting powerdemand

Figure 6. Cabin’s temperature and the required heating powerfor the optimum and non-optimum strategies

The maximum driving power demand is about 60 kW, and the

total driving energy demand for the whole cycle is about 4.79kWh with considering the regenerative braking. With this

power demand profile, an optimal heating power trajectory tominimize the defined cost function was found. Figure 6illustrates the resulting optimal trajectory for the heater’s

power and the cabin’s tempera ture variations during the FTPdriving cycle. The driver’s desired temperature was assumedto be 22 ° , and the ambient temperature was fixed at −10 ℃ .

Also, the passenger compartment’s initial temperature was 0℃ and the maximum heating power was set at 4000 W.

Figure 7. Total power demand with and without the proposedEMS

Figure 8 . Battery’s SOC variations and the heat loss inside the

battery during the FTP-75 driving cycle

For the non-optimal heating scenario, the heater starts with themaximum power until the cabin ’s temperature reaches thedesired value, and after that point, the heater is switched to alower power mode that maintains a constant cabin ’s temperature. With the proposed EMS, as shown in Figure 6,the heater tries to increase the cabin ’s temperature to thedesired value, but at the same time prevents high peaks in thetotal power demand. Thus, the initial heating takes longer thanthe non-optimum strategy, and after that, the temperature willfluctuate within a bound near the desired value to avoid high

power demand peaks. Figure 7 depicts the power demand ofthe vehicle with the optimal and non-optimal strategies for a

0 500 1000 1500 20000

20

40

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V e l o c i t y ( m

i l e s / h )

0 500 1000 1500 2000-4

-2

0

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6x 10

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b i n

( C )

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-1

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part of the FTP cycle. The devised EMS algorithm has resultedin smaller peaks in the battery power demand by properlyregulating the heater ’s power. This effect, in turn, improves the

battery service life.

The use of devised EMS causes a smoother power demand,and as a result, a smoother battery current. As discussed

before, a smoother battery current generates less heat loss inthe battery ’s internal resistance. Figure 8 illustrates the totalenergy loss by the battery ’s internal resistance and the

battery ’s state of charge during the simulation.

As it can be seen, the proposed EMS results in a smaller totalenergy loss in the battery ’s resistance, however, it does nothave a significant effect on SOC.

DISCUSSIONS

The proposed EMS uses DP to find an optimal heater ’s powertrajectory for a specific driving cycle. Figure 5 shows the FTP-

75 driving cycle, which is a standard city driving patterndesigned for measuring the fuel consumption of passengercars. The optimized heating causes a fluctuation in the

passenger compartment ’s temperature, as shown in Figure 6.It takes longer to reach the desired temperature with thisstrategy because the driving power demand ’s peaks cause theEMS controller to put the heater in a lower power mode. EMSuses the heating capacity of the passenger compartment as avirtual capacitor to minimize fluctuations in the batterycurrent. As it can be seen in Figure 7, the proposed EMS hasdecreased the power demand peaks of the battery by anoptimal control of the heater. In summary, during the high

propulsion power demand situations, EMS puts the heater in alow power mode, and for the low driving power demands,returns it back to a higher power mode. The weightings in thecost function can be changed to have different driving modes.Increasing will improve the comfort by minimizing thetemperature peaks and overshoots, but it means less emphasison the consumed energy.

The smoother power demand profiles and currents of the battery lead to less heat loss as well as a longer lifetime for it,which is critical for a BEV. Figure 8 shows SOC and the totalenergy loss in the battery ’s resistance. With the devised EMS

controller, the energy loss in the battery has decreased by about13% at the end of the simulated driving cycle. However, thisstrategy does not have a significant effect on the battery ’s finalSOC because, for an efficient low resistance battery, the lossesare generally very small, as compared to the high powerdemands of the vehicle ’s drivetrain for propulsion. Also, the

proposed EMS does not aim at decreasing the mean currentdemand but reducing the fluctuations of the battery current.However, by considering other sources of power loss in thevehicle for the EMS design, such as the DC/DC converter, airconditioner, seat heaters, entertainment systems, andnecessary cooling power for the battery, the final SOC and the

driving range of the vehicle can be improved.

Moreover, the presented results are for using fixed weightingcoefficients in the defined cost function. These weightingcoefficients can be varied for a certain driving mode specified

by the driver to introduce a trade-off between the comfort anddrivability of the vehicle.

CONCLUSIONS

Growing concerns about the global warming and limitedenergy sources have caused global demands to explore moreefficient and green ways of transportation. HEVs wereintroduced in the last decades as a temporary alternative tothese problems, and now, BEVs are finding their way into ourevery day’s transportation. An optimal EMS controller canimprove the both battery life and energy economy of a BEV

by finding the most optimum energy flow within the vehicle.This paper proposed an EMS that controls the powerdistribution between the energy consumers inside a singlesource electric vehicle. A high-fidelity model of BEVs inAutonomie was revised slightly to represent the Toyota RAV4

EV, and also, simulated to calculate the vehicle ’s powerdemand during the FTP driving cycle. The proposed EMSemployed DP to determine an optimum heating power profilewhich resulted in smaller battery current peaks and smoother

power demand sequence for it. In summary, the simulationresults shows that the proposed EMS can decrease the energyloss inside the battery and increase the battery lifetime of theconsidered BEV.

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