Optimization of Sizing and Battery Cycle Life in ...

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Optimization of Sizing and Battery Cycle Life in Battery/Ultracapacitor Hybrid Energy Storage Systems for Electric Vehicle Applications Junyi Shen, Serkan Dusmez, Student Member, IEEE, and Alireza Khaligh, Senior Member, IEEE Abstract—Electric vehicle (EV) batteries tend to have accelerated degradation due to high peak power and harsh charging/discharging cycles during acceleration and deceleration periods, particularly in urban driving conditions. Oversized energy storage system (ESS) meets the high power demand; however, in tradeoff with increased ESS size, volume and cost. In order to reduce overall ESS size and extend battery cycle life, battery/ultracapacitor (UC) hybrid energy storage system (HESS) has been considered as a solution in which UCs act as a power buffer to charging/discharging peak power. In this manuscript, a multi-objective optimization problem is formulated to minimize the overall ESS size while maximizing the battery cycle life according to the assigned penalty functions. An integrated framework for HESS sizing and battery cycle life optimization applied in a midsize EV, using an Autonomie simulation model, is described and illustrated in this manuscript. This multi-dimensional optimization is realized by a sample-based, global search algorithm, DIRECT algorithm. The optimization results under Urban Dynamometer Driving Schedule (UDDS) are compared with the battery-only ESS results, which demonstrate significant battery cycle life extension of 76% achieved by the optimized HESS with 72 UC cells. Index Terms — Battery cycle life estimation, electric vehicle, hybrid energy storage system, multi-objective optimization, ultra-capacitor.

I.

INTRODUCTION

To provide longer driving range, high energy density batteries are preferred in electric vehicles (EV). In current and upcoming EVs, the batteries are oversized in order to deliver to Manuscript received July 15, 2013; revised Mar. 10, 2014 and May 9, 2014; accepted June 18, 2014. Copyright © 2014 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]. This work is supported partly by the National Science Foundation award number 1307228 and partly by the Genovation Cars Inc, which are gratefully acknowledged. J. Shen and A. Khaligh are with the Power Electronics, Energy Harvesting and Renewable Energies Laboratory (PEHREL), Electrical and Computer Engineering Department, University of Maryland, College Park, MD 20742 USA (e-mail: [email protected]; [email protected]). S. Dusmez was with the Power Electronics, Energy Harvesting and Renewable Energies Laboratory (PEHREL), Electrical and Computer Engineering Department, University of Maryland. He is now with the Electrical and Computer Engineering Department, University of Texas at Dallas, Richardson, TX 75080 USA (e-mail: [email protected]).

high power and avoid unwanted degradation due acceleration and deceleration. Ultracapacitors (UCs) are well known for their extremely high power density, high cycle lifetime and cycling efficiency. The integration of a high energy (HE) density battery pack and an ultracapacitor (UC) pack in the EV powertrain creates a hybrid energy storage system (HESS), which combines the HE density attribute of batteries and the high power (HP) density of UCs. With these complementary features, a HESS can achieve high power capabilities and large energy storage at the same time with smaller size and weight in comparison to the HP battery-only ESS counterpart [1]. Hybridization of UCs with batteries also enhances battery cycle life through peak power shaving, improved dynamic performance and thermal burden relief [1]-[6]. The trade-offs between ESS size/weight, battery cycle life, economic cost, overall vehicle efficiency and driving range have been studied partly in the literature. The design methodologies of ESS sizing have been proposed in [7]-[9], in which the general approach is to determine the load requirements and size the ESS based on the transient power requirements and constraints imposed by the main energy source needs. The relationship between battery size and its cost are studied in [10]-[11]. Furthermore, the influence of battery/UC sizing on HESS efficiency and battery cycle life extension have been discussed in [12]-[14]. This manuscript proposes an integrated framework for HESS sizing and battery cycle life optimization based on a developed battery cycle life degradation model. It distinguishes itself from existing studies, since it (a) optimally sizes the ESS size/weight under the power and energy requirements and battery cycle life constraint; (b) adopts a validated battery cycle life estimation model and extends its usage to scenarios under varying current rates and driving profiles for EV applications. In addition, majority of published work on ESS power management use dynamic programming and control State-of-Charge (SoC) of batteries and UCs as state variables for offline optimization. In these studies, the optimization objectives such as fuel economy, ESS energy efficiency or energy loss are directly controlled by the SoC [15]-[17]. Different from fuel economy or energy loss, the battery cycle life and battery capacity degradation are difficult to be discretized for each SoC, thus dynamic programming based on SoC state is not an appropriate technique for such studies. In this study, the battery cycle life is evaluated based on the

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‘

ln (Q)+Ea/RT

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Crate = 0.5 Experiment of battery capacity loss Crate = 2 and fitting result at different Crate Crate = 6 Crate = 10

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simulation results of battery depth-of-discharge (DoD), temperature and current rate from a midsize EV model developed with Argonne National Laboratory (ANL)'s Autonomie software. A sample-based and derivative-free DIRECT algorithm is implemented to globally search the optimal design variables of HESS under given drive cycles. This manuscript is organized as follows. Section II provides detailed information of the battery cycle life estimation model. The EV model and sizing constraints are discussed in Section III, along with the HESS power management strategy. DIRECT algorithm and the proposed optimization framework are explained in Section IV. In addition, optimization results and comparison of ESS and HESS battery cycle life extension are presented in Section IV. Finally, the conclusions of this work are provided in Section V. II. BATTERY CYCLE LIFE ESTIMATION MODEL U.S. Advanced Battery Consortium (USABC) has defined battery cycle life as the number of discharge-charge cycles it can experience before the battery capacity degrades to 80% of its nominal capacity. The accelerated battery cycle life is strongly affected by battery DoD, temperature and current rate. A. Battery Cycle Life Estimation Model There are many literatures that focused on the development of battery cycle life models to predict capacity loss in Li-ion batteries [18]-[20]. Different models have been developed to account for various incidents responsible for capacity loss such as the parasitic side reactions [18], SEI (solid electrolyte interface) formation [19], and resistance increase [20]. However, experimental data are essential for the study and validation of battery cycle life models. Not many groups have developed a battery cycle life prediction model based on large experimental data set. Bloom et al. presented the testing results and developed a battery cycle life prediction model using large experimental data set [21]. This developed model is later adopted as a starting point by Wang et. al [22] to predict the battery cycle life for LiFePO4 batteries. This developed model, as shown in Eq. (1), also achieves quantitative agreement with the experimental data in [22].  (1) Q  B exp( Ea / RT ) Ah

where Q represents the battery capacity loss, B the pre-exponential factor, Ea the activation energy from Arrhenius law, T the absolute temperature and R the gas constant of 8.314 Jmol-1K-1. The parameters in the battery capacity loss estimation model, B, Ea and ρ, are obtained based on the empirical fitting of a large experimental data set. The Ah-throughput, Ah, as described in Eq. (2), is the product of cycle number N, battery DoD and battery capacity C, which represents the amount of charge delivered by the battery during cycling [22]. (2) Ah  N  DoD  C This equation can be linearized by taking the natural logarithm of both sides, which yields to E 1 (3) ln(Q) = ln B - a × + r ln(Ah ) R T The slope of the linear model, ρ≈0.5, is the power law factor. This power law factor represents a square-root of time dependence, which indicates that the battery capacity loss due to SEI growth, is often controlled by a diffusion controlled process and governed by parabolic kinetics [21]-[22]. B. Current Effect on Battery Cycle life Although it is still a subject of research that how peak current impacts on battery degradation and cycle life, there are established models that account for the effect of current rate on battery cycle life, which is incorporated in the battery cycle life estimation model. It is reported that the activation energy is decreased with increasing current rate. The activation energy magnitude under different current rates is adjusted as E'a=Ea-bCrate to account for this inverse relationship between activation energy and current rates. Here, b is a constant with the value of 370.3 [22]. The value of the pre-exponent parameter B also decreases with increasing current rates. However, the relationship between the pre-exponent parameter B and the current rate is not fully quantitatively described [22]. Fig. 1 presents the experimental data of battery capacity losses at current rates of 1/2C, 2C, 6C, and 10C based on the test results in [22]. In this work, a linear fit function, shown in red, is derived based on Eq. (4). E 1 (4) ln(Q)  a   ln B   ln( A ) R T

h

The inverse relationship between the activation energy and current rate, Crate, is described in Eq. (5). E'a=31500-370.3∙Crate

(5)

Thus, the value of lnB can be calculated for the current rates

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of 1/2C, 2C, 6C, and 10C as shown in Fig. 2 in blue dots. In order to extend this battery cycle life estimation model to other scenarios with current rates below 10C, a curve fitting is employed to derive the relationship between the value of lnB and intermediate current rates. Fig. 2 shows the curve fitting result for lnB, which generalizes the value of pre-exponent parameter at different current rates. The curve fitting is based on Eq. (6), with the fit parameter values given in Eq. (7). (  Crate )

ln B  a  e d a  1.226;   0.2797; d  9.263.

(6) (7)

The pre-exponent parameter under different battery current profiles and current rates can be estimated dynamically based on Eq. (6). Thus, the battery cycle life estimation model can be used under various current profiles. C. Battery Cycle Life Estimation Under Non-uniform profiles In order to estimate the cycle life of EV batteries under realistic driving profile, a statistical method is used to analyze the battery current rate distribution under a non-uniform profile. To illustrate this method, an Urban Dynamometer Driving Schedule (UDDS) drive cycle is used to generate a battery cell current profile. The histogram in Fig. 3, is used to represent the statistical distribution of battery current rate. In the histogram, at a current rate value of Crate(k), the battery DoD under this current rate can be calculated as DoD(k). For charging current, the absolute value of its current rate is used. Thus, Ah(k) can be expressed as (8) Ah (k )  N  DoD(k )  C The capacity loss under Crate(k) can be estimated as,  E bCrate ( k )   a 

(9) Q(k )  B(Crate (k )) e  RT  Ah (k )  The total capacity loss Qloss of battery during drive cycle is the sum of all capacity losses of each contributing current rate. (10) Q   Q( k ) loss

k

D. Validation of Battery Cycle Life Estimation Model The cycle life estimation model for LiFePO4 battery is constructed based on the available experimental results. In order to extend this model for use in other scenarios, it is compared with several other experimental results to examine its mathematical consistency with the empirical data

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under different cycling profiles. Two commercially available 1.1Ah 18650 and 2.4Ah 26650 LiFePO4 battery cells from A123 Systems are investigated [23]-[24]. Their cycle life performances under different temperatures and different current rates are predicted using the battery cycle life model as shown in Fig. 4(a) and Fig. 4(b). In Fig. 4(a), the 1.1Ah LiFePO4 battery is cycled under current rate of 1C with 100% DoD at room temperature. For the current rate of 1C, the pre-exponent parameter of lnB equals to 10.19 according to Eq. (6). The capacity retention after 1700 cycles is estimated as 95% of its nominal capacity. According to the experimental data in the datasheet, the capacity loss is reported to be around 5% [23]. Thus, the estimation is consistent with the experimental data. In Fig. 4(b), three different cycling profiles are simulated with various discharging/charging current rates under different temperatures. The estimated battery capacity retention after 600 cycles are 97.9%, 92.8%, and 90.1% for the three cycling profiles shown in Fig. 4(b), which are consistent with the experimental data presented in [24] with the capacity retention of around 99%, 95%, and 91%. To investigate the cycling degradation of an automotive EV LiFePO4 battery, a 16.4Ah LiFePO4 cell with deep cycling of 50% DoD is studied in [25]. It is reported that the capacity loss after 600 cycles is 14.6% at 45˚C with a current rate of 3C. Based on the battery cycle life estimation model, the pre-exponent of lnB is 9.79 under a current rate of 3C. The estimated capacity retention after 600 cycles is 87.2% as shown in Fig. 5, which is close to the experimental result of

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TABLE I. Characteristics of midsize EV model.

Parameter

Value

Vehicle mass [kg] Motor Continuous Power [kW] Motor Peak Power [kW] Frontal Area [m2] Aerodynamic drag coefficient Wheel Radius [m]

~1500 80 105 2.35 0.3 0.30

TABLE II. HE/HP battery and UC cell characteristics.

Specifications Nominal voltage (V) Nominal capacity (Ah) Rated capacitance (F) Internal resistance (mΩ) Energy storage (Wh) Weight (kg) Max. continuous discharge current (A) Max. pulse discharge current (A)

HE 3.3 44 N/A 3.6 140 0.9 50 100

HP 3.2 2.6 N/A 9 8.32 0.0825 42 150

UC 2.7 N/A 2000 0.35 2.03 0.36 120 1600

85.4% with the remaining battery capacity estimation error of 1.8%. The accelerated battery degradation under a cell-scaled power profile based on UDDS driving schedule is also studied in [25]. It is reported that the electric-only range is reduced due to a battery capacity loss of 23.2% for 600 cycles at 25˚C. For this non-uniform current profile with varying current rates, the battery cycle life estimation model is applied at various discretized current rates. The estimated battery capacity retention is 78.3% as shown in Fig. 6. In comparison to the experimental data of 76.8%, the remaining battery capacity estimation error is 1.5%. Through comparison with the cycle life experimental data from [23]-[25], the battery cycle life estimation model that is incorporated in the optimization problem, is validated to achieve mathematical consistency. Despite the simple formula of this battery cycle life estimation model, it provides satisfactory prediction for LiFePO4 battery under various cycling profiles. III. SIZING ANALYSIS AND HESS POWER CONTROL STRATEGY A midsize EV powertrain model is constructed in Autonomie software with the run-time parameters of the midsize EV model listed in Table I. It is assumed that a daily commute for this midsize EV model consists of a 6 consecutive UDDS drive cycles, which sums up to 45 miles per day. One daily commute is called one cycle for the battery cycle life estimation. To provide a 10-year life EV, the battery capacity loss should be at least less than 20% after 3650 cycles.

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Fig. 7. (a) HE battery-only ESS sizing; (b) HP battery-only ESS sizing.

A. Battery/UC Characteristics This work uses a Saft VL45E LiFePO4 battery as HE battery [26] and K2 Energy LFP26650P as the HP battery. A BCAP 2000 UC from Maxwell Technology [27] is also considered. The battery and UC characteristics are listed in TABLE II. Here, the maximum storable energy in battery cell and UC cell is denoted as Eb,cell and Euc,cell. The maximum discharge power is estimated as Pb,cell and Puc,cell. Generally, the charging capability of HE battery is far less than its discharging capability. The recommended max continuous charging current for this Saft HE battery is at a current rate of C/7, which is about 6.28A [26]. On the other hand, UC has both strong charging and discharging capabilities. Hence, UC is more suitable to receive the regenerative braking power, especially during the urban driving cycles in which the regeneration percentage can be more than 87% of the EV kinetic energy [12],[28]. B. Battery-only ESS Sizing Analysis In a battery-only ESS, the battery pack is directly connected to the dc/ac EV inverter with the input voltage range from Vdc,min to Vdc,max. This voltage range constrains the battery pack terminal voltage that is dependent on the number of series-connected battery cells Nb,ser, in Eq. (11) and Eq. (12). The battery is assumed to operate with SoC from 0.3 to 0.9, with initial SoC of 0.9. (11) Nbat , serVbat  Vdc ,min Nbat , serVbat  Vdc ,max

(12)

In this work, the EV inverter voltage range is set to 130V to 520V according to the operation requirement of a BRUSA DMC524 dc/ac inverter [29]. Thus, Nb,ser for both HE and HP batteries can be estimated. Besides, the battery cell number Nbat is also determined by the energy needs imposed by the EV range requirements and the max transient power demand from the load as shown in Eq. (13) and Eq. (14). The energy needs is evaluated according to the driving range under UDDS cycle

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Inverter

Motor

Fig. 8. The system diagram of the UC/battery configuration for HESS.

and the max power demand of the load is set as 80kW.

Nbat Pb,cell  Pdmd ,max

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(14) Nbat Eb,cell  Edmd Based on the terminal voltage constraints, power and energy demand constraints as given in Eq. (11)-Eq. (14), the optimal sizes for HE and HP battery-only ESS are plotted for different driving ranges in Fig. 7. As shown in Fig. 7, to meet the same driving range criteria, it requires a much larger number of HP batteries (and consequently heavier) in comparison to HE batteries due to their different energy densities. It is also shown that for a HP battery-only ESS, the energy needs imposed by the EV range requirement is the dominant factor in battery sizing as shown in Fig. 7(b). However, for HE battery-only ESS, the power demand becomes the dominant factor for EV driving range within 140 miles. For an EV with range requirements of 100 miles, the energy needs can be satisfied with 150 HE battery cells. However, this amount of battery cells cannot satisfy the power demand. Thus, the HE battery is oversized in order to satisfy the power demand and the high discharge/charge current requirement of load. In this case, HESS can help to reduce the battery size by hybridizing them with UCs and reduce the load power stress on batteries. C. HESS Model and Sizing Analysis The system diagram of HESS configuration is shown in Fig. 8. The battery pack is directly connected to the dc bus, and a bidirectional dc/dc converter is used to interface the UC to the dc bus [30]. With this configuration, the voltage of UC can swing in a wider range; thus, the utilization factor of UC can be increased. The input voltage range of the bidirectional dc/dc converter constrains the battery/UC terminal voltage as noted in Eq. (15) Eq. (18). Here, Vh,min and Vh,max represent the high side voltage bounds and Vl,min and Vl,max represent the low side bounds. In this work, a Brusa BDC546 dc/dc converter is considered with the high side voltage range of [150V,750V] and the low side [50V,430V] [31]. The UC SoC range is constrained by SoCuc,min and SoCuc,max with value from 0.3 to 1 during the operation with the initial SoCuc,ini of 0.7 which permits near balanced room for both charge and discharge energy. Nbat ,serVbat  Vh ,min

(15)

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The energy and power constraints on HESS sizing are described in Eq. (19) and Eq. (20). Nbat Pb,cell  Nuc Puc,cell  Pdmd ,max (19)

Nbat Eb,cell  Nuc Euc ,cell  Edmd

(20)

Thus, the HESS sizing constraints are formulated as Eq. (15) Eq. (20). D. HESS Power Control Strategy In HESS, UC pack is used to provide high peak power and receive regenerative braking power. The power control strategy is formulated to make the best advantage of their different features. To split the transient demand power for batteries and UCs, the power control strategy also provides insight on how to size the battery/UC in order to satisfy their energy and power requirements. A rule-based strategy for HESS power control, shown in Fig.9, is used as Control Strategy-I. This rule-based control strategy controls the HESS power based on a defined reference power value Pmin. The UC power is determined based on the following rules.  Pdmd  0 : UC receives all regenerative braking power.  Pdmd  Pmin :UC delivers (Pdmd -Pmin) or its max discharging power at that state;  0  Pdmd  Pmin : battery supplies the discharging power. Following this power control strategy, the UC energy Euc can be estimated based on Eq. (21). (21) Euc (t  t )  Euc (t )  Puc (t )  t Assuming that the discharging power is positive and the charging power is negative, the UC energy reaches the lowest value when it discharges most during the driving cycle. The difference between the initial UC energy and the lowest energy value is defined as ∆Euc,max to indicate the max discharge energy from UC. Similarly, the difference between the initial UC energy and the highest energy value in UC is

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defined as ∆Euc,min to indicate the max charging energy into UC. By choosing different reference power value Pmin, the UC energy variation bounds of ∆Euc,max and ∆Euc,min are different. When Pmin value is small, UC tends to discharges more power; while a greater value of Pmin leads to lower UC discharge. For a UDDS drive cycle, the value of ∆Euc,max and ∆Euc,min at different Pmin are shown in Fig. 10. Large difference between ∆Euc,max (blue line) and ∆Euc,min (green line) indicates large energy variation in UC. With the UC SoC constraints, the max discharged/charged energy bounds value can be used to estimate the UC number as shown in Eq. (22). The estimated UC number is denoted as Nuc,est. 

 Euc ,max ( Pmin ) Euc ,min ( Pmin ) ,  2 2 2 2 E  ( SoC  SoC ) E  ( SoC  SoC ) uc ,ini uc ,min uc , cell uc ,ini uc ,max   uc,cell

Nuc ,est  max 

(22)

This equation shows the interdependence between the reference power value Pmin and the UC sizing requirement. As shown in Fig.10, the smallest difference between ∆Euc,max and ∆Euc,min is attained when Pmin=13 kW. Based on Eq. (22), it is estimated that at least 223 UC cells are required in this case with weight of 80kg, which is heavy. To address this problem, the proposed strategy provides a way to limit the UCs energy variation bounds by combining the rule-based strategy with a UC SoC control algorithm, which maps the UC SoC to a power map. Thus, the UC power is the sum of the power generated by the rule-based control and the power provided by the SoC to power map. The proposed control strategy is shown in Fig.11. Given the SoC index values, the power map is generated as using Eq. (23). SoC _ idx  [0,0.1,0.25,0.5,0.75,0.9,1]

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pwr  [ Puc,chg ,0.1Puc,chg ,0.025Puc,chg ,0,0.025Puc,dis ,0.1Puc,dis , Puc,dis ] For an UC pack, the Puc,chg power and Puc,dis power are generated based on the max UC charging and discharging currents. This power map sets the UC SoC equilibrium to 0.5,

32 24 26 30 28 Pmin (kW) at different reference power Pmin using proposed 22

which is a relatively deep discharged state in order to take as much regenerative braking power as possible. The constant coefficients in the power map are the proportional gain constants, which are tuned in simulation to give robust response while keep the UC stable. The UC SoC to power map for 80 UC cells is shown in Fig. 12. The proposed HESS power control strategy reduces the energy fluctuation bounds ∆Euc,max and ∆Euc,min of UC. With this proposed HESS power control strategy, the energy variation bounds of ∆Euc,max and ∆Euc,min are shown in Fig. 13. The UC energy variation bounds are greatly reduced in comparison to the result shown in Fig. 10. Based on Eq. (22), it is estimated that up to 135 UC cells should be sufficient for the proposed control strategy under various reference powers as shown in Fig. 13. IV. MULTI-OBJECTIVE OPTIMIZATION PROBLEM In this work, the multi-objective optimization problem is to find an optimal combination of the design variables (Nbat, Nuc, Pmin). The motivation of this multi-objective optimization problem is to both minimize the weight and cost of the HESS and also prevent the battery degradation due to overstress. A. Design Variables Based on the HESS sizing constraints, the design range of battery cell number is [150, 175]. The UC cell number is [60, 160]. The reference power is tested within the range of 15kW to 30kW with a 100W increment. B. Trade-Off Analysis It is obvious that larger amount of UC cells combined with a lower reference power Pmin can lead to excellent battery current shaving effect. However, with an increasing number of battery and UC cells, the benefit of battery cycle life extension is in tradeoff with the HESS weight. To quantify the trade-off between HESS sizing and battery cycle life, two penalty functions are defined as shown in Eq. (24) and Eq. (25). The penalty function J1 is the HESS sizing, which equals to the sum of battery and UC pack mass. Here, mbat, muc represent the battery/UC cell mass. The penalty function J2 is the battery capacity loss percentage number. J1 ( Nbat , Nuc )  Nbat mbat  Nuc muc

(24)

J 2 (Nbat , Nuc , Pmin )  Qloss

(25)

The multi-objective function is designed as J1+ γJ2 with the weight factor of γ. Different weight factor, γ, leads to different

Battery Capacity Loss(%)

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J2: Battery Capacity Loss (%)

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Fig. 15. Trade-off Analysis between J1 and J2 at Pmin=18kW.

optimization result. A larger value of the weight factor, γ, may results in lower battery capacity loss in tradeoff with larger HESS size. The HESS sizing penalty function is only dependent on Nbat, Nuc, and it is easy to calculate. On the other hand, the battery capacity loss depends on all-three design variables and is estimated based on the EV simulation results. With a reference power value Pmin at 18kW, the battery capacity loss of J2(Nbat, Nuc, Pmin) is shown in Fig. 14. The reference power value is fixed in this case for simple illustration. It can be observed that the battery capacity loss decreases faster along the axis of Nuc in comparison to the axis of Nbat. This is because increasing number of UC cells can achieve stronger effect in battery power shaving. It is also noticed that there is less variation in battery capacity loss when Nuc is above 120. In this case, this is due to the power reference value that limits the room to improve the battery power shaving. Based on the design variables of (Nbat, Nuc) with a fixed reference power at 18kW, the relationship between the two penalty functions is quantitatively investigated. The trade-off between HESS sizing and the battery capacity loss is presented in the objective function space as shown in Fig. 15. It is observed that the penalty function value is noisy. With all-three design variables of (Nbat, Nuc, Pmin) considered, the multi-objective function value is expected to be noiser and may involve local minima. Thus, a sample-based optimization algorithm is required for solving this problem. C. DIRECT Algorithm The multi-objective function of J1+ γJ2 is defined in a multi-dimensional space that is discontinuous and may involve

Generate HESS simulation output

Update design variables for next iteration

Postprocess and evaluate objective function

DiRect Algorithm Stopped?

N

Y Return Optimal Design Variables

Fig. 17. Flowchart of the HESS optimization algorithm.

local minima. Without derivative information, gradient-based algorithms cannot be used to find the local or global minima. DIRECT is a sampling algorithm, which requires no knowledge of the objective function gradient. Instead, the algorithm samples points in the domain, and uses the information it has obtained to decide where to search next. DIRECT, as a global search algorithm, can be very effective when the objective function is a "black box" function, which is suitable for this problem since it highly depends on EV Model in MATLAB/Simulink for simulation. DIRECT algorithm begins its optimization process by transforming the design variables space of (Nbat, Nuc, Pmin) into a unit hyper-cube as, (26) S  xi  R n , 0  xi  1



Fig. 16 is used to illustrate the optimization process of DIRECT algorithm. The objective function value at center of this normalized space, f (c1), is first evaluated. The functions f (c1ei), where i=1,2,3...n, are evaluated at the next step. Here,  is one-third of the side-length of the c1 hypercube and ei is the ith unit vector of the current hypercube. If f(c1+ek)=min{f(c1ei)}, c1+ek becomes the center of the new hyper-cube that will be

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8

4

Battery Current (A)

UC Power (W)

Battery Power (W)

HESS Power (W)

5 x 10 3 1 -1 -3 1200 800 0 400 4 Time (s) x 104 5 5 x 10 3 3 1 1 -1 -1 -3 -3 1200 0 0 400 800 800 1200 400 Time (s) Time (s) Fig. 18. HESS power distribution between battery/UC for UDDS drive cycle. 120 100 80 60 40 20 0 -20 -40 -60 -80 0

Peak discharge current reduction: 67%

Peak charge current reduction: 74% 200

400

(a)

600 800 Time (s)

1000

1200

1400

Optimized HESS Battery-only ESS

95 90

Battery Cycle Life Extended for 76%

85 NEOL=5732

80 75

NEOL=3244 0

percentage can be evaluated based on the battery cycle life estimation model as described in Section II-C. The estimated battery cycle life is shown in Fig. 19(b), which shows that a 76% extension of the battery cycle life is achieved by the optimized HESS in comparison to the battery-only ESS. E. Validation of the Optimization Results

100

Capacity Retention(%)

Optimized HESS Battery-only ESS

Fig. 20. Simulation data and estimated Pareto frontier.

1000

2000

(b)

3000 4000 Cycles

5000

6000

For this multi-objective optimization problem, there is no unique optimal point that dominates both penalty functions. With different values of the weight factor, different optimization results can be achieved. To validate the optimization result and analyze the trade-off between HESS sizing and battery cycle life, a large set of simulation data is used to generate the Pareto frontier as shown in Fig. 20. The estimated Pareto frontier is shown in red. It is verified that the optimization result generated by DIRECT algorithm lies on the Pareto frontier of this multi-objective optimization problem, which validates its optimality.

7000

Fig. 19. (a) Battery current comparison; (b) Estimated battery cycle life.

divided again, which starts the loop of identifying the potential optimal hyper-cubes, dividing them appropriately and sampling at their centers [32]. D. HESS Optimization Result DIRECT algorithm evaluates function value in this multi-dimensional space and returns the optimal design parameters after iterations following the flowchart shown in Fig. 17. Given the weight factor γ as 2, the optimization result indicates that the optimal design variables are Nbat of 152, Nuc of 72 with Pmin of 16.6kW. The optimized weight of the battery/UC pack is 162.7kg. Considering the dc-dc converter and a packaging factor of 1.25, the optimized HESS is less than 230kg. Using the battery cycle life estimation model, it is estimated that the battery capacity loss reaches 15.9% under the daily commute assumptions for 3650 cycles. The optimized HESS splits the load power between battery and UC as shown in Fig. 18. UCs are frequently charged and discharged with high peak power while battery power has reduced peak power, particularly during regenerative braking. In the optimized HESS, the peak battery discharging and charging currents have been reduced by 67% and 74% in comparison to the battery-only ESS. With the battery current profiles shown in Fig. 19(a), the battery capacity loss

V. CONCLUSIONS In this work, a multi-objective optimization problem is formulated to optimize the HESS weight and battery cycle life and solved using DIRECT algorithm. A validated battery cycle life estimation model is extended to the automotive usage scenarios with varying current profiles. The interdependence between the power control strategy and HESS sizing design is discussed. The main contribution of this work is to introduce a systematic approach and tool to optimize the HESS sizing and to estimate the battery cycle life. Following this framework, HESS design can be evaluated in terms of its sizing and battery degradation under various drive cycles without a long-term experimental test. To provide accurate evaluation of the HESS system, the MATLAB/Simulink vehicle models developed by ANL is adopted in the proposed framework, which has been verified by Hardware-in-the-Loop (HIL) vehicle testing. In addition, this optimization framework is very flexible and can be easily adapted to different optimization objectives, vehicle models, control strategies and design variables. It is estimated that the optimized HESS under urban driving situations can effectively extend the battery lifetime by 76% with 72 UC cells. REFERENCES [1]

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9 [25] Y. Zhang, C. Wang, X. Tang, "Cycling degradation of an automotive LiFePO4 lithium-ion battery", J. Power Sources, vol. 196, no. 3, pp. 1513-1520, Feb. 2011. [26] Saft Groupe SA, "Technical Datasheet of Rechargeable LiFePO4 lithium-ion battery, Super-Phosphate™ VL 45E Fe," Jun. 2010. [27] Maxwell Technologies Inc., "Technical Datasheet of K2 Series Ultracapacitors", 2013. [28] Y. Gao, L. Chen and M. Ehasni, "Investigation of the effectiveness of regenerative braking for EV and HEV," Society of Automotive Engineers (SAE) Journal, SP-1466, Paper No.01-2901, 1999. [29] BRUSA Elektronik AG, " Motor Controller DMC 524". [30] A. Khaligh and S. Dusmez, “Comprehensive Topological Analysis of Conductive and Inductive Charging Solutions for Plug-In Electric Vehicles,” IEEE Trans. on Veh. Technol., vol. 61, no. 8, pp. 3475-3489, Oct. 2012. [31] BRUSA Elektronik AG, "BDC546 750V DC-DC Converter". [32] D. E. Finkel, "DIRECT Optimization Algorithm User Guide", 2003. Junyi Shen received the B.S degree in electrical engineering from Zhejiang University, Hangzhou, China, in 2011. She is currently working toward the Ph.D. degree at the University of Maryland, College Park. From 2012, she worked as a Graduate Research Assistant in the Power Electronics, Energy Harvesting and Renewable Energies Laboratory (PEHREL) in the Electrical and Computer Engineering Department at the University of Maryland at College Park. Her research interests include energy management strategies for hybrid energy storage systems for electric vehicle applications. Serkan Dusmez (S’11) received the B.S. (Hons) and M.S. degrees in electrical engineering from Yildiz Technical University, Istanbul, Turkey, in 2009 and 2011, respectively. He received the M.S. degree in electrical engineering from Illinois Institute of Technology, Chicago, in 2013. He is currently working toward the Ph.D. degree at the University of Texas at Dallas. From 2012-2013, he worked as a Faculty Research Assistant in the Power Electronics, Energy Harvesting and Renewable Energies Laboratory (PEHREL) in the Electrical and Computer Engineering Department at the University of Maryland at College Park. He is the author/co-author of over 35 journal and conference papers. His research interests include design of power electronic interfaces and energy management strategies for renewable energy sources, integrated power electronic converters for plug-in electric vehicles, and real-time fault diagnosis of power converters. Alireza Khaligh (S’04–M’06–SM’09) is an Assistant Professor at the Electrical and Computer Engineering (ECE) Department and the Institute for Systems Research in the University of Maryland. He is an author/coauthor of over 120 journal and conference papers. Dr. Khaligh is the recipient of various awards and recognitions including the 2013 George Corcoran Memorial Award from the ECE Department of the University of Maryland, 2013 and 2012 Best Vehicular Electronics Awards from the IEEE Vehicular Technology Society (VTS), and 2010 Ralph R. Teetor Educational Award from the Society of Automotive Engineers. He is the Program Chair of the 2015 IEEE Applied Power Electronics Conference and Exposition. He was the General Chair of the 2013 IEEE Transportation Electrification Conference and Exposition, and Program Chair of the 2011 IEEE Vehicle Power and Propulsion Conference. He is an Editor or an Associate Editor for various IEEE Transactions and Journals. He is an IEEE VTS Distinguished Lecturer.