PHEV Charging Strategies for Maximized Energy Saving · Maximized Energy Saving Ernesto Inoa,...

2978 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 7, SEPTEMBER 2011

PHEV Charging Strategies forMaximized Energy Saving

Ernesto Inoa, Student Member, IEEE, and Jin Wang, Member, IEEE

Abstract—This paper studies the charging strategies of anLi-ion battery with a focus on the battery’s power loss model. Itis found that when the temperature is assumed constant, constantcurrent/constant voltage (CC/CV) is near optimal for energy lossminimization. However, when the temperature is considered as astate variable, an optimal profile different from CC/CV is found.This new profile can be used to warm-up batteries during colddays, hence reducing the need for existing battery heating systems.As a result of the elevated battery temperature, significant energysavings can be achieved if the vehicle is used soon after thecharging process ends. In this paper, the form of the optimizationproblem resembles a classic form, with the peculiarity of beinghighly nonlinear and time varying. The charging strategies result-ing from this study will have significant impact on how plug-inhybrid electric vehicles (PHEVs) are charged and utilized.

Index Terms—Battery chargers, lithium-ion battery, optimalcontrol, plug-in hybrid electric vehicles (PHEVs).

I. INTRODUCTION

THE NUMBER of plug-in hybrid electric vehicles(PHEVs) on the market is expected to increase in the

coming years. From the grid side perspective, a PHEV can besimply considered as a load. However, when the number ofPHEVs rises, these vehicles could have a significant impact onthe electrical power grid [1]. Therefore, the efficiency of bothcharging and discharging (driving) processes deserves carefulconsideration. Proper charging strategies need to be derived toeither minimize the energy loss during the charging process orutilize the energy loss to regulate the battery temperature toachieve better overall energy savings.

So far, based on criteria, such as short charging time andextended energy capacity, many charging strategies have beenproposed. Some of these strategies involve modern techniques,such as fuzzy control, neural networks, genetic algorithms, antalgorithms, grey prediction, task scheduling algorithms, andpower management policies [2]–[8]. However, the implemen-tation of these intelligent techniques remains relatively compli-cated and expensive [9]. This is one of the reasons why constantcurrent/constant voltage (CC/CV) is still one of the most widely

Manuscript received September 23, 2010; revised January 24, 2011 andApril 17, 2011; accepted June 24, 2011. Date of publication July 14, 2011;date of current version September 19, 2011. This work was supported in partby Smart@CAR, an industry consortium for plug-in hybrid electric vehicles.The review of this paper was coordinated by Prof. M. E. Benbouzid.

The authors are with the Department of Electrical and ComputerEngineering, The Ohio State University, Columbus, OH 43210 USA (e-mail:[email protected]; [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/TVT.2011.2162085

Fig. 1. CC/CV charging.

used methods. As described in Fig. 1, CC/CV consists of afirst stage in which the charging current is maintained constant,and when the maximum acceptable voltage across the batteryterminals is reached, the charging voltage is held constant untilthe battery is considered as fully charged.

Furthermore, all the aforementioned charging strategies havenot considered the minimization or utilization of energy lossduring the charging procedure.

In this paper, the battery charging strategy is posed as an op-timization problem, which is done by modeling the energy lossincurred in the battery during the charging process. Two charg-ing strategies are proposed. For normal temperature operations,the charging strategy is optimized to minimize the energyloss. With this charging strategy, the charging efficiency couldbe maximized, thus minimizing the impact to the electricalpower grid.

In addition to the charging efficiency, the final battery’s tem-perature is another important criterion that should be addressedin the charging operation. Since the battery’s capacity has beenfound to decrease with ambient temperature, several externalheating methods have been proposed to warm up batteriesduring cold weather, such as thermal jackets and space heater[10]–[13]. These external heating methods require significantamount of time and energy to warm the battery because theexternal heat must penetrate the large thermal mass of the bat-tery pack. Therefore, it could be more beneficial to heat thebattery from within the battery pack. Common ways of doingthis are to embed resistive heating elements within the batteriesor to apply high ac currents that provide heat via the internalresistive losses [14]. These methods require either additionalhardware or additional current just for the purpose of heating.

Thus, the second charging strategy proposed in this paperutilizes the charging current itself to generate energy loss insidethe battery to regulate the battery temperature when the ambient

0018-9545/$26.00 © 2011 IEEE

INOA AND WANG: PHEV CHARGING STRATEGIES FOR MAXIMIZED ENERGY SAVING 2979

Fig. 2. Equivalent circuit of a battery cell.

temperature is low. Although the charging efficiency may notbe optimized, due to better battery temperature regulation,the overall energy saving for a charging and drive cycle isimproved.

This paper is divided into five sections. By utilizing thebattery cell model and the parameters obtained by Hu et al.[15]–[18], Section II develops the power loss model of thebattery. Then, based on the power loss model, an optimalcurrent profile (OCP) for energy loss minimization is derived inSection III. Section IV presents the temperature-control-basedcharging strategy, whereas Section V concludes this paper andmakes final remarks.

II. BATTERY POWER LOSS MODEL

A. Nonlinear and Dynamic Battery Parameters

Fig. 2 presents an equivalent circuit model for an Li-ion bat-tery cell. This circuit is the same as the standard Randle equiv-alent circuit, which is composed of an ideal voltage source, aninternal resistance R0, and two parallel RC elements. R0 rep-resents the dc impedance, whereas the two RC elements repre-sent the short- and long-time constants for transient responses.Voc, which is a dependant voltage source, represents the amountof energy available in the battery cell. Its voltage level is afunction of the state of charge (SoC), which is the percentageof charge currently available in the battery cell. The parametersof this model were found using genetic algorithm techniques ona commercially available PHEV Lithium-ion battery cell [15]–[18]. Although this model is not very sophisticated, generally,it can approximate the battery behavior very well.

As shown in Table I, the values of the electrical elements inthe circuit model are highly dependent on temperature, SoC,and direction of current, i.e., whether the battery cell is beingcharged or discharged. As a way to illustrate the sensitivity ofthe parameters to the status of the battery, the change of the timeconstants of the RC networks as a function of SoC is shown inFig. 3. From Fig. 3 and the last column of Table I, it is safe tosay that the parameters of the system under study possess a highdegree of nonlinearity.

B. State-Space Modeling for Battery Power Loss

Based on the equivalent circuit shown in Fig. 2, a mathemat-ical model of the battery power loss in state-space format isderived in this section. The goal is to use this power loss modeltogether with optimization algorithms to find OCPs that will

TABLE IRANGE OF BATTERY CELL MODEL PARAMETERS

Fig. 3. Time constant for RC networks in the equivalent circuit of a batterycell.

TABLE IIBATTERY CELL MODEL DEFINITIONS

minimize the battery energy losses and, as a consequence, max-imize the efficiency of the charging process. The terminologiesthat are used hereafter are summarized in Table II.

A paralleled RC circuit can be described with the followingequation:

dvc

dt= − 1

RCvc +

1C

i (1)


where i is the current entering the network, vc is the voltageacross the network, and R and C are the values of resistanceand capacitance, respectively.

Therefore, by referring to Fig. 2 and considering the currenti as the control input, the state variables of the circuit can bechosen as

�x = [SoC vc1 vc2]T (2)

where vc1 and vc2 are the capacitor voltages. Thus, the systemequations in state-space form become

x1 =1

3600 · C(Tbattf)i

x2 =−1

R1(x1, Tbattf) · C1(x1, Tbattf)x2 +

1C1(x1, Tbattf)

i

x3 =−1

R2(x1, Tbattf) · C2(x1, Tbattf)x3 +

1C2(x1, Tbattf)

i

(3)

where Tbattf is the battery’s temperature, and C(Tbattf) is thebattery’s capacity in ampere-hours.

The power consumed by R0 is PR0 = i2R0, whereas thepower consumptions at R1 and R2 are

Pr1 =v2

c1

R1and Pr2 =

v2c2

R2. (4)

Hence, the power loss Ploss in the resistive elements (R0, R1,and R2) becomes

Ploss = �xT Q�x + R0(x1, Tbattf)i2 (5)

with

Q =

⎡⎣

0 0 00 1

R1(x1,Tbattf) 00 0 1

R2(x1,Tbattf)

⎤⎦ .

The first term of (5) is a vector–matrix multiplication represent-ing the power loss at R1 and R2.

After these derivations, the cost function that would eventu-ally lead to minimized energy loss can be written as

J = (x1(tf ) − SoC∗)2 +

tf∫0

Ploss dτ (6)

where SoC∗ is the targeted SoC. Thus, the first term in thecost function imposes a penalty if the final SoC deviates fromthe desired value SoC∗. By including this term, the trivialsolution of i(t) ≡ 0 is excluded. The integral term in the costfunction represents the energy loss in the resistive components.This optimization problem is also subject to the followingconstraints:

0 ≤ i(t) ≤ imax for all t : 0 ≤ t ≤ tf

Vbatt < VMax for all t : 0 ≤ t ≤ tf . (7)

It is clearly shown in (3) that the state-space presentationof the battery power loss is quite nonlinear since R1, R2, C1,

Fig. 4. Current profile comparison for a single cell.

and C2 are all dependent on SoC and the battery temperature.Thus, it is much easier to find numerical solutions for optimizedbattery charging profiles than to find analytical solutions.

III. CHARGING STRATEGY FOR LEVEL I CHARGING

WITH CONSTANT TEMPERATURE

A. System Description

In this section, an OCP that minimizes energy loss is pre-sented. Due to the nonlinearity of the model, a numerical solveris used.

The nominal capacity of the battery cell described inSection II is 2.3 Ah, and its nominal operational voltage is3.3 V. A hypothetical 5-kWh battery pack similar to that usedin hybrid vehicle conversion systems [19] was emulated byconstructing a matrix of ten strings of 65 cells in series. Theoptimization is subject to the following constraints.

1) 0 ≤ i(t) ≤ 0.7 A for all t : 0 ≤ t ≤ tf (maximum charg-ing current per battery cell).

2) Vbatt < 3.33 V for all t : 0 ≤ t ≤ tf (maximum batterycell terminal voltage).

3) tf : 0 ≤ tf ≤ 3.0 hr (maximum charging time).4) SoC∗ = 85% (upper SoC limit).The current limit is selected based on Level I charging (110 V

ac, maximum 1.5 kW). With a small charging current (< 0.7 A),it is safe to assume that the battery temperature almost remainsconstant during the charging process.

B. Optimization Results

The set of equations (3) and (5)–(7) were programmed intothe MATLAB-based general pseudospectral optimal controlsoftware (GPOPS) to find OCPs [20]–[27]. One of the resultingOCPs is plotted in Fig. 4 along with a CC/CV profile that isrequired to charge the battery to 85% of SoC with the same timerestriction. A test current profile is also plotted as a reference.More OCPs for different charging times are shown in Fig. 5.The energy loss for each current profile has also been calculatedbased on the integration of the power loss model over time. Thecalculation results are shown in Table III.

The test current profile, which is shown in Fig. 4, averagesmost oscillations that appear in the optimal current profile. Thisprofile, which can be seen as a variation from the solution found


Fig. 5. Optimal current profiles (OCP) for different charging times (values ofcurrent are for a single cell.).

TABLE IIIENERGY LOSS COMPARISONS

by GPOPS, was created as a way to test whether the OCPindeed results in minimized energy loss. As seen in Table III,the OCP does produce less energy loss than both the testingcurrent profile and the traditional CC/CV profile. Figs. 4 and 5also show that the OCP switches to constant voltage at the exactsame time as the CC/CV method. Considering the minor energyloss difference shown in Table III and the similarity betweenthe OCP and CC/CV profiles, the CC/CV can be seen as nearoptimal for energy loss minimization.

For all the charging OCPs shown in Fig. 5, the battery had aninitial SoC of 20%, reaching an SoC of 85% after the chargingprocess. From Fig. 5, it is clearly seen that all OCPs have thesame amount of “peaks” and “valleys,” which oscillate aroundan average current. In addition, at the end of the chargingprofiles, the current will exponentially decay, which indicatesconstant voltage charging.

In Table III, the first column shows the energy loss ofthe charging profiles shown in Fig. 4, whereas the next fourcolumns show the different energy losses of the profiles that areshown in Fig. 5. Although the differences are small, the OCPsresult in lower energy losses than CC/CV if the charging timeand the change of SoC are the same.

Because of the nonlinear nature of the battery model, it ismathematically intractable to prove that the presented OCP

provides absolute minimum energy loss. However, in principle,numerical algorithms like GPOPS use searching heuristics tofind a minimum for the cost function. One such heuristicprocedure explores the solution space given an initial value anddefined delta step; therefore, the minimum reported by GPOPSwill in fact be a local minimum since all the neighboringsolutions would result in a higher value of the cost function.Interested readers are referred to [20]–[27].

Nevertheless, since the percentages of the energy gains fromthe OCPs are relatively small, as seen in Table III, the workpresented here could also be interpreted as a mathematicalargument supporting the rationality of CC/CV, not only for itsease of implementation but for its near minimization of energyloss as well.

The work presented in this section was based on the assump-tions that a Level I charger is utilized and the temperature of thebattery remained almost constant during the charging period.In the next section, the battery temperature change during thecharging procedure is studied and utilized.

IV. CHARGING STRATEGY WITH TEMPERATURE AS A

STATE VARIABLE: TEMPERATURE CONTROL

A. Motivation

It is generally known that the batteries’ power and energydensity decrease with temperature [14]. This could easily beexplained with the battery impedance change versus tempera-ture. Fig. 6 shows the estimated values of the dc impedance(R0 in Fig. 2) of a commercially available Li-ion battery cellat different SoCs [15]–[18]. As seen from Fig. 6, the batteryimpedance increases as the temperature decreases. Thus, theratio of the battery’s dc impedance at cold temperature to thatat a higher temperature can be defined as k = zC/zH . If acurrent IH at a relatively high temperature generates the sameheat (power loss) as a current Ic generates at a relatively lowertemperature, then based on

PLoss = I2C · zC = I2

H · zH (8)

the ratio between these two currents can be defined asIH/IC =

√k.

With this current ratio, the ratio of the voltages at the bat-tery’s terminals for different temperatures can be defined as

VBattH

VBattC

=Voc − k− 3

2 · zC · IC

Voc − zC · IC.

Hence, the ratio of the battery’s output power at a highertemperature over the battery’s output power at a relativelycolder temperature can be found as

PH

PC=

VBattH

VBattC

· IH

IC=

√k · Voc − k−1 · zC · IC

Voc − zC · IC(9)

where PH and PC are the battery’s output power at twodifferent temperatures, and Voc is the open circuit voltage, asshown in Fig. 2.

One of the main physical constraints of a battery is its capa-bility to dissipate the heat generated by its internal power loss


Fig. 6. DC battery cell impedance (discharging mode) versus temperature fordifferent values of SoC.

Fig. 7. Power ratio versus impedance ratio.

PLoss. From (8) and (9), it can be seen that it is possible to makePH > PC while maintaining the same PLoss. This means thata higher output power can be obtained at higher temperaturewithout putting more power loss (stress) to the battery.

Plots of PH/PC versus impedance ratio k are shown inFig. 7. From Fig. 6, it can be seen that for the battery that hasbeen studied in this paper, k is almost equal to 4 when the coldertemperature is 0 ◦C and the hotter temperature is 25 ◦C. Thus,based on Fig. 7, the battery could deliver more than two timesof power at 25 ◦C than at 0 ◦C, whereas the power loss in thebattery is the same for both cases.

Not only the power density of Li-ion batteries decreases withtemperature, the energy density is adversely affected with lowtemperatures as well. This can be seen from Fig. 8, in whichthe capacity as a function of temperature is plotted. Fig. 8shows that the battery capacity drops by 11% when the batterypack under study is used at 0 ◦C, as opposed to when it is usedat 30 ◦C.

In summary, the power and energy density of a Li-ion batterydecrease with temperature; hence, a charging current profilethat warms-up the battery on cold winter days can significantlybe useful.

B. Battery Pack Thermal Model Estimation

This section derives the thermal model of the battery pack instate-space format (see Fig. 9). The thermal model is necessary

Fig. 8. Battery capacity versus temperature. Energy density increases withtemperature.

Fig. 9. Thermal model of a battery pack.

for the calculation of the temperature-based charging profile.Following common practice, a simple parallel RC network isadopted as a battery’s thermal model, with the current repre-senting power loss and the voltage drop representing tempera-ture difference. Thus, the equation of the thermal model can bewritten as

ΔT = − 1RT CT

ΔT +1

CTPloss ⇔ x = Acx + Bcu (10)

where ΔT is the temperature difference between the batteryand the ambient temperature, CT and RT are the thermalcapacitance and thermal resistance, respectively, and Ploss is thepower loss within the battery.

To discretize the system, the following transformations,based on Taylor series, are utilized:

Ad = I + AcT + A2c

T 2

2+ . . .

Bd = BcT + AcBcT 2

2+ . . . .

In the foregoing transformations, T is the sampling period,and the “d” and “c” subscripts mean discrete and continuous,respectively. Assuming a high enough sampling rate, the pre-ceding expressions can be reduced to

Ad ≈ I + AcT Bd ≈ BcT.

Then, (10) becomes

ΔT [k + 1] =(

1 − T

RT CT

)ΔT [k] +

T

CTPloss[k].


Fig. 10. Comparison between measured and estimated battery voltage.

Posing the foregoing problem as a system in which RT andCT need to be found, and using the estimation techniquespresented in [28], the following equation can be written:⎛⎝ ΔT [2]

...ΔT [N ]

⎞⎠=

⎛⎝ ΔT [1] Ploss[1]

......

ΔT [N−1] Ploss[N−1]

⎞⎠(

1− TRT CTT

CT

)(11)

where N is the total number of samples, and T is the samplingperiod of the recorded data. With (11) and drive cycle data, thevalues of RT and CT are obtained and used in the battery modelto estimate the battery temperature change and the resultingbattery terminal voltage.

A comparison between estimated voltage and measured drivecycle data is shown in Fig. 10. The plots show a high degreeof agreement between estimated and measured voltages, hencevalidating the found parameters RT and CT .

C. State-Space Modeling Including Temperature

This section covers the derivation of the mathematical modelof the battery power loss when the battery’s temperature isincluded as a state variable. With temperature being a statevariable, (2) is expanded to

�x = [SoC vc1 vc2 ΔT ]T (12)

where ΔT is the temperature difference between the hottestpoint in the battery and the ambient temperature. Then, the totalsystem becomes

x1 =1

3600 · C(x4 + Tamb)i

x2 =−1

R1(x1, x4 + Tamb) · C1(x1, x4 + Tamb)x2

+1

C1(x1, x4 + Tamb)i

x3 =−1

R2(x1, x4 + Tamb) · C2(x1, x4 + Tamb)x3

+1

C2(x1, x4 + Tamb)i

x4 =−1

RT · CTx4 +

1CT

Ploss (13)

Fig. 11. Optimal charging current for battery pack. The current is positivewhen going into the battery.

where Tamb is the ambient temperature, and RT and CT

account for the battery’s thermal model parameters found inthe previous section. Thus, the power loss Ploss in the batterybecomes

Ploss = �xT Q�x + R0(x1, x4 + Tamb)i2 (14)

where

Q =

⎡⎢⎢⎣

0 0 0 00 1

R1(x1,x4+Tamb) 0 00 0 1

R2(x1,x4+Tamb) 00 0 0 0

⎤⎥⎥⎦ .

Thus, the cost function for charging profile optimization canbe written as

J = (x1(tf ) − SoC∗) + (x4(tf ) + Tamb − T ∗)

+

tf∫0

�xT Q�x + R0(x1, x4)i2 dτ. (15)

The first and second terms in the cost function imposepenalties if the final SoC or battery temperature deviates fromthe desired values. With the second term and the third terms inthis equation, the battery temperature could be controlled withminimum energy loss.

The same types of constrains as described in (7) also standtrue for (15) but with Level II charging parameters.

D. Optimal Current Profiles

Again, the MATLAB-based GPOPS optimal control soft-ware is used to find numerical solutions for the optimizedcharging profile. Based on Level II charging, the maximumcharging current is set as of 5.0 A per string.

Fig. 11 shows the result obtained with GPOPS. This resultagrees with the intuitive idea of increasing the current up toimax at the end of the charging operation to take advantage ofthe recently generated heat, thereby ensuring that the final tem-perature of the battery reaches the desired value. It is importantto point out that the total charging time is a parameter neededfor the charging algorithm. In practical implementations, thePHEV will be used soon after the charging is completed totake advantage of the batteries’ elevated temperature. Fig. 12shows the zoomed-in picture of the SoC and ΔT versus time.


Fig. 12. SoC and temperature difference between hottest point in battery andenvironment. Only the last hour of charging is shown.

Fig. 13. PHEV battery current during a sample trip (discharging).

The initial SoC is 15%, and the final SoC achieved is 85%. ΔTrepresents the temperature difference between the battery andthe environment. It is shown, in agreement with Fig. 11, that thetemperature increases mainly at the end of the charging opera-tion; hence, power loss during most of the charging operation isreduced, but the battery is warmed up right before the vehiclewill be driven. This result would be impossible to be obtainedif the traditional CC/CV charging method was used. In CC/CV-based charging, the current and the associated produced heatare reduced during the last charging stage CV.

E. Energy Savings

This section demonstrates that when the PHEV’s batterysystem is current controlled, the power (and by default energy)delivered by the battery will be higher if the battery’s initialtemperature is higher rather than lower. This will happen evenif the PHEV’s main controller is not aware of the higher powerdensity. As explained in Section IV-A, the reason behind thehigher power capability is that the battery’s internal impedanceis lower when the battery is warm. Hence, for the series circuitformed by the battery’s impedance and the load, the battery’sinternal impedance will have a lower voltage drop for the samecurrent. Thus, more energy will be transferred from the batteryto the load, which can be translated as fuel savings. Differentcombinations of drive cycles, vehicles, and powertrain controlstrategies will result in different energy savings.

Data from a short-range PHEV city drive cycle were usedfor a case study. The current delivered by the battery, as plottedin Fig. 13, is the main input to the battery model described by(12)–(14). The battery current does not go to negative (charging

Fig. 14. Time window of power supplied by battery when starting fromdifferent initial temperatures.

Fig. 15. Energy supplied by battery when starting from different initialtemperatures.

Fig. 16. Zoom-in of last 5 min of energy supplied by battery when startingfrom different initial temperatures.

mode) because it is extracted from an add-on battery in a PHEVconversion kit. Hence, the battery will be charged only whenit is plugged-in. Although this indeed is different from futureproduction PHEVs, it does not introduce any error in validatingtemperature regulation-based energy saving. This model holdstrue for both charging and discharging modes. The impedancedifference between charging and discharging modes is alsoincluded in the case study. The zoomed view of power deliveredby the battery with different initial temperatures, i.e., 0 ◦C and12 ◦C, is shown in Fig. 14. It can be seen that the battery couldprovide more power when the initial temperature is higher.

Thus, as shown in Figs. 15 and 16, the energy provided bythe battery is also higher when the battery initial temperature ishigher.


TABLE IVENERGY SAVINGS FOR A DRIVE CYCLE AT DIFFERENT BATTERY’S INITIAL TEMPERATURES

Table IV summarizes the case study. The second column ofthe table shows the initial battery capacity, which is largelydecided by the battery’s initial temperature. The ampere-hournumbers for the two different temperatures, i.e., 0 ◦C and 12 ◦C,are directly taken from Fig. 8.

The third column shows the overall energy supplied to thePHEV from the battery. This result was obtained by calculatingthe areas under the curves of Fig. 15; as shown in Table IV, thewarmer the battery, the higher the energy supplied to the PHEV,which means that less energy is taken from the gasoline engine.

For the two cases shown in Table IV, the initial SoCs are thesame, i.e., 85%, but the final SoC is higher if the initial batterytemperature is higher.

Therefore, as shown in the last column of Table IV, moreenergy remains in the battery. The residual energy in the batteryis calculated as the product of the final battery capacity, finalSoC, and final battery voltage.

In summary, the numbers in Table IV mean that with an ele-vated initial battery temperature, 1) there will be fuel economyimprovement because more energy is extracted from the battery,and 2) the battery is less stressed in terms of SoC change.

V. CONCLUSION

This paper has first presented a state-space model of thepower loss incurred in a Li-ion battery cell. The model is thenused together with an optimization tool to identify OCPs. Byadjusting the weight of the terms in the cost functions, theproposed method can be used to identify charging profiles withdifferent main focuses, such as final temperature, final SoC, andtotal energy loss.

For Level I charging, the proposed optimized current profilemainly provides minimized energy loss. Through the study, it isalso proved that the traditional CC/CV charging strategy is nearoptimal in terms of energy consumption, although the powerloss of a battery cell is quite nonlinear.

For Level 2 charging, where high charging currents canbe provided, the battery temperature needs to be built intothe power loss model as a state variable. Then, the chargingprofile is designed to realize battery temperature control withminimum energy loss. A simple thermal model of the batteryis also derived from drive cycle data to estimate instantaneousbattery temperature for case studies. The case study resultsshow that with higher initial temperature, the battery’s energyand power density are increased, which can be translated intofuel savings and battery stress reduction.

Implementation of the proposed new charging profiles shouldnot present any practical complications as long as the optimalcurrent profiles for different charging times and initial SoCshave been found offline and prestored in the memory of mi-

crocontrollers. Since the bandwidth of the charging current isrelatively low, inexpensive metal–oxide–semiconductor field-effect transistors and mature power electronics topologies canbe used for its implementation.

Although the exact charging profiles will only fit one partic-ular battery, the methodologies presented in this paper could beadopted for different types of batteries and even different typesof hybrid energy storage systems.

The charging strategies that result from this study could havea significant impact on how PHEVs are charged and utilized.

ACKNOWLEDGMENT

The authors are indebted to the people at the Center forAutomotive Research, The Ohio State University, for their helpin providing the test data of the battery cells.

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Ernesto Inoa (S’10) was born in the DominicanRepublic. He received the B.S. degree (magna cumlaude) in electronics engineering from PontificiaUniversidad Católica Madre y Maestra, Santiago delos Caballeros, Dominican Republic, in 2000 and theM.S. degree in electrical and computer engineeringfrom University of Central Florida, Orlando, in 2005.He is currently working toward the Ph.D. degree withThe Ohio State University, Columbus.

From 2000 to 2002, he was an Automation En-gineer with CND, a Dominican brewing company,

where he helped to automate several bottling lines with the use of pro-grammable logic controllers. His major research interests are related to theapplication of novel control techniques to power electronics, motor drives, andenergy conversion systems.

Jin Wang (S’02–M’05) was born in Qinghai, China,in 1976. He received the B.S. degree in electricalengineering from Xi’an Jiaotong University, Xi’an,China, in 1998, the M.S. degree in electrical engi-neering from Wuhan University, Wuhan, China, in2001, and the Ph.D. degree in electrical engineer-ing from Michigan State University, East Lansing,in 2005.

From 2005 to 2007, he was a Core Power Elec-tronics Engineer with the Hybrid Electric VehicleGroup, Ford Motor Company. He is currently an

Assistant Professor with the The Ohio State University, Columbus, which iscosponsored by the American Electric Power, Duke Energy, and First Energy.His main research direction is high-power and high-voltage power electroniccircuits and their applications.

Dr. Wang received the National Science Foundation’s CAREER Award in2011 for his work on very-large-scale photovoltaic systems. He currentlyserves an Associate Editor for the IEEE TRANSACTIONS ON INDUSTRY

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