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IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 32, NO. 3, MARCH 2013 325

Large-Scale Energy Storage System Design andOptimization for Emerging Electric-Drive Vehicles

Jie Wu, Student Member, IEEE, Jia Wang, Member, IEEE, Kun Li, Student Member, IEEE,

Hai Zhou, Member, IEEE, Qin Lv, Li Shang, Member, IEEE, and Yihe Sun, Member, IEEE

AbstractEnergy consumption and the associated environ-mental impact are a pressing challenge faced by the transporta-tion sector. Emerging electric-drive vehicles have shown promisesfor substantial reductions in petroleum use and vehicle emissions.Their success, however, has been hindered by the limitationsof energy storage technologies. Existing in-vehicle lithium-ionbattery systems are bulky, expensive, and unreliable. Energystorage system (ESS) design and optimization is essential foremerging transportation electrification. This paper presents anintegrated ESS modeling, design, and optimization frameworktargeting emerging electric-drive vehicles. A large-scale ESS mod-eling solution is first presented, which considers major runtimeand long-term battery effects, and uses fast frequency-domainanalysis techniques for efficient and accurate characterization oflarge-scale ESS. The proposed design framework unifies design-time optimization and runtime control. This conducts statisticaloptimization for ESS cost and lifetime, which jointly considersthe variances of ESS due to manufacture tolerance and hetero-geneous driver-specific runtime usage. This optimizes ESS designby incorporating complementary energy storage technologies,e.g., lithium-ion batteries and ultracapacitors. Using physicalmeasurements of battery manufacture variation and real-worlduser driving profiles, our experimental study has demonstratedthat the proposed framework effectively explores the statisticaldesign space and produces cost-efficient ESS solutions withstatistical system lifetime guarantees.

Index TermsBattery systems, design optimization, embeddedsystems, hybrid vehicles.

I. Introduction

TRANSPORTATION electrification has drawn significantattention over the past decade, mainly driven by theManuscript received November 15, 2011; revised August 19, 2012; accepted

October 6, 2012. Date of current version February 14, 2013. This work wassupported in part by the National Nature Science Foundation of China underGrant 61006021. Part of the material in this paper was presented at theInternational Symposium on Low Power Electronics and Design, Austin, TX,in 2010. This paper was recommended by Associate Editor N. Chang.

J. Wu and Y. Sun are with the Institute of Microelectronics, Tsinghua

University, Beijing 100084, China (e-mail: [email protected];[email protected]).J. Wang is with the Department of Electrical and Computer Engineer-

ing, Illinois Institute of Technology, Chicago, IL 60208 USA (e-mail:[email protected]).

K. Li, Q. Lv, and L. Shang are with the Department of Electrical andComputer Engineering, University of Colorado, Boulder, CO 80305 USA(e-mail: [email protected]; [email protected]; [email protected]).

H. Zhou is with the Department of Electrical Engineering and Com-puter Science, Northwestern University, Evanston, IL 60208 USA (e-mail:[email protected]).

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

Digital Object Identifier 10.1109/TCAD.2012.2228268

pressing energy and environmental challenges. Indeed, the

transportation sector currently accounts for 70% of petroleum

consumption and over one-third of greenhouse gas emissions.

Electric-drive technologies show great promises to address

these challenges [1]. Hybrid electric vehicles (HEVs) have

been fast adopted and widely deployed over the past decade.

Currently, plug-in hybrid electric vehicles (PHEVs), which

allow the vehicle to be directly charged by the electric power

grid, are under active development and will become market

ready in the coming few years. These electric-drive vehiclesare usually featured with an internal combustion engine pow-

ered by fuel and an electric motor powered by energy storage

system (ESS). With the assistance of the electric-drive system,

(P)HEV fuel use can be significantly reduced by operating

the vehicle in an electric mode without using the combustion

engine, or allowing the combustion engine to operate more

efficiently.

The success of electric-drive technologies, however, has

been seriously hindered by shortcomings of electric ESS.

Indeed, for decades, energy storage technology has been the

key bottleneck in electric-drive vehicle design [2]. This is

mainly due to the fact that the advances of battery technology,

the primary energy storage solution, have not kept pace with

the fast-growing energy demands. Among (P)HEV technical

challenges, ESS has been singled out as a potential show

stopper due to its high cost, limited energy capacity, safety

issues, and limited long-term cycle life [3]. Therefore, the

technology and the system innovation of energy storage are

timely and important.

A. Related Work

Several works have focused on the optimization of ESS for

embedded systems with small size, such as mobile devices.

They have worked on the maximization of battery short-term

lifetime with single battery cell. Because of the high-power

density of the ultracapacitor, recent studies have started to

consider hybrid energy storage technology, named battery-

ultracapacitor integration [4]. For example, Shin et al. [5]

proposed a battery-ultracapacitor hybrid architecture to max-

imize the deliverable energy density for portable electronics.

Mirhoseini and Koushanfar [6] developed a hybrid battery-

ultracapacitor power supply optimization to improve the life-

time of portable systems.

Although the aforementioned methods for embedded

system offer optimal solutions for single battery cell, they are

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326 IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 32, NO. 3, MARCH 2013

Fig. 1. ESS for electric-drive vehicles.

challenging, if not impossible, to extend to the (P)HEV

application. The (P)HEV consists of a large number of units

(even more than 1000) connected in parallel and serial. Direct

extensions of existing methods used for single battery cell

to (P)HEV are therefore computationally prohibitive and also

fail to characterize the interaction effect among the energy

storage units (e.g., capacity variation and heterogeneous

thermal effects).

From the perspective of (P)HEV application, the energy

storage technology and hybrid ESS design have drawn signifi-

cant attention in recent years. Dumitrescu and Gausemeier [7]proposed hybrid integration of NiMH battery and double-

layer capacitor technologies. Cooper et al. [8] developed a

hybrid lead-acid battery-ultracapacitor ESS to enhance the

runtime power demand and lifetime. Garcia et al. [9] proposed

the charge allocation strategy for battery-ultracapacitor to

coordinate the (P)HEV power demand.

This paper distinguishes itself from existing studies, not

only because it minimizes the ESS cost, instead of the runtime

energy consumption, by optimizing the ESS configurations,

such as the number of storage units and the type and size for

each storage unit, but also because it models several effects

that are important to the ESS cost and lifetime. For instance,

it considers the ESS long-term aging effects, their impacts on

ESS long-term cycle life, and interaction effects, such as the

variances of manufacture tolerance and the heterogeneous en-

vironment. Compared with existing studies, our work provides

an in-depth study, from a different perspective, for large-scale

ESS design and optimization of (P)HEV applications.

B. Our Contributions

In contrast to existing engineering and development efforts,

the goal of this paper is to, for the first time, provide an

integrated modeling, design, and optimization framework to

enable rigorous (P)HEV large-scale ESS analysis, design, and

optimization. The proposed framework uses fast frequency-domain analysis techniques for efficient and accurate charac-

terization of large-scale ESS runtime cycle efficiency and long-

term cycle life. It optimizes the ESS design by incorporating

complementary energy storage technologies and conducts sta-

tistical optimization for ESS cost and lifetime. Specifically,

our work makes the following contributions.

1) A modeling solution for accurate large-scale ESS

analysis via comprehensive consideration of major

runtime and long-term effects, e.g., temperature-

dependent aging effects. Our large-scale ESS model

supports the heterogeneous energy storage technologies,

e.g., Li-ion battery and ultracapacitor. Manufacture

variation and runtime heterogeneous aging effects are

carefully modeled. The proposed modeling and analysis

solution is then used to drive the proposed large-scale

ESS design and optimization flow.

2) A design and optimization solution of ESS considers

variances due to battery system manufacture tolerance

and the user-specific driving behavior, and presents

statistical optimization techniques to optimize ESS

cost, yet providing statistical lifetime guarantee.

The proposed optimization framework allows hybridsystem integration by considering two complementary

energy storage technologies, i.e., Li-ion battery and

ultracapacitor, for ESS cost optimization under runtime

performance and long-term cycle life constraints.

3) The proposed solution is evaluated using physical

measurements of battery manufacture variation and

real-world user driving profiles. The results demonstrate

that the proposed design and optimization framework

effectively explore the statistical ESS design space,

minimize ESS cost, and provide statistical system

lifetime guarantee.

II. Motivation and Rationale

This section overviews the energy storage technologies for

(P)HEV and summarizes the design challenges.

A. ESS Overview and Design Metrics

Fig. 1 shows a block diagram of an ESS connected to

electric-drive propulsion components. Regardless of the chem-

istry specifics, a single battery units voltage, current, and

energy storage capacity are relatively low. Therefore, a large-

scale ESS usually consists of a large number of energy storage

units (even more than 1000) connected in parallel and series,

controlled by a distributed battery management system (BMS).

The BMS monitors the runtime current, temperature, as well

as unit voltage to assess battery state of charge (SOC) and stateof health (SOH), which are then communicated to a vehicle

system controller. The following design metrics are commonly

considered during ESS design [10].

1) Energy capacity: It determines the maximal available

energy within an ESS charge cycle. Compared with other

electrochemical energy storage technologies, e.g., NiMH and

ultracapacitor, Li-ion battery offers superb energy storage

density, hence higher total energy capacity under the same

weight and form factor.

2) Peak power: This determines the maximal instantaneous

power that can be delivered by the ESS to the vehicle. Note

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Fig. 2. Aging impacts of (a) and (b) manufacture tolerance and (c) heterogeneous runtime user driving behavior. (a) Manufacture tolerance for 15 cells.(b) Manufacture tolerance for 30 cells. (c) Heterogeneous runtime user driving behavior.

that energy capacity and the peak power are two distinct design

metrics. Compared with Li-ion battery, ultracapacitor provides

higher power density, hence higher peak power support [2].

3) Cost: As the primary hurdle for transportation electrifica-

tion, ESS cost is mainly contributed by energy storage units.

Minimizing ESS cost is a primary objective of this paper.

4) Lifetime: ESS lifetime is characterized as long-term cycle

life, i.e., the total number of chargedischarge cycles be-

fore the system capacity permanently degrades below certain

threshold. (P)HEVs impose stringent lifetime constraints onESS. For instance, automotive vendors typically target a 10

20-year ESS lifetime guarantee with 20%30% maximal ca-

pacity degradation [11]. Aging effects are the primary lifetime

concern of Li-ion battery, which is strongly affected by tem-

perature. In contrast, ultracapacitor demonstrates excellent life

span [12].

B. ESS Design Challenges

The ESS design and optimization need to jointly consider

system cost, runtime performance, and long-term cycle life.

More specifically,

1) Since Li-ion battery is the primary energy storage technol-

ogy, ESS system lifetime is mainly affected by Li-ion runtime

aging effects. The dominant aging effects are strong functions

(typically exponential) of temperature, which is mainly due to

the battery runtime chargedischarge-induced battery heating.

Therefore, to improve ESS lifetime, constraining the battery

runtime current becomes essential. A more effective approach

is to consider hybrid ESS integration [4]. For instance, ul-

tracapacitor has unlimited cycle life [12], leveraging ultra-

capacitor to offload runtime current demand can effectively

improve the ESS lifetime. However, ultracapacitor has lower

energy capacity density, hence higher per energy capacity cost

(approximately 30 over Li-ion). Hybrid ESS integration is

challenging.2) The ESS performance, e.g., energy capacity and

cycle life are constrained by the weakest unit. Due to the lim-

ited capabilities of monitoring unit and system SOC and SOH

over high-voltage boundaries, existing BMS offers limited

control over individual units. As a result, mismatches among

units (due to manufacturing tolerance, temperature gradients

across the pack, and mismatched degradation over cycle and

calendar life) can lead to overcharge and excessive discharge

of individual units, resulting in overall system performance

degradation and severe cycle life limits. This problem becomes

increasingly worse with the increase of the number of battery

units. Fig. 2(a) and (b) show the capacity degradation mea-

surement results we conducted on 30 Li-ion battery modules

in a (P)HEV. It shows that over 40% capacity variation is

observed among these modules due to manufacture variation-

dependent aging. Therefore, manufacture variation must be

carefully considered during ESS design and optimization.

3) Furthermore, (P)HEV operation, hence ESS use and aging,

are heavily affected by users runtime driving behaviors. User-

specific driving patterns are dynamic and differ substantially

among drivers, so do ESS runtime performance and long-term cycle life. Aggressive driving patterns, e.g., frequent

speeding up and slowing down, result in high runtime charge

discharge current. Such intensive use causes significant bat-

tery self-heating, accelerating temperature-dependent aging

effects, hence battery long-term capacity degradation. Using

the proposed the model of large-scale system-level ESS (see

Section III), Fig. 2(c) shows the estimated long-term capacity

degradation of ESS based on ten users daily commute driving

profiles. It shows that user driving behavior has significant

impact on ESS lifetime. Targeting the worst-case driving

scenario would dramatically increase the ESS cost.

III. ESS Modeling and Analysis

This section presents a large-scale ESS modeling and

analysis framework to facilitate the proposed ESS design

and optimization. Specifically, this section is organized as

follows: Section III-A introduces the ESS unit major effects

and the challenges of large-scale system-level ESS modeling.

Section III-B overviews the framework of large-scale system-

level ESS modeling. Section III-C proposes the thermal model

of large-scale system-level ESS to characterize the thermal

effect of ESS. Meanwhile, the Section III-C develops a uni-

fied frequency-domain thermal analysis method (multinode

moment matching method) to enable fast and accurate ESS

analysis. Section III-D proposes the runtime aging and chargecapacity model of large-scale system-level ESS to depict the

system-level ESS capacity fading and variation with a primary

focus on the temperature effect; it also illustrates the runtime

performance of ESS by using the proposed frequency-domain

electric analysis method. Section III-E presents the validation

of the accuracy for our proposed ESS high-level modeling.

A. ESS Unit Major Effects and Challenges

This section overviews the major effects of ESS unit and

summarizes the large-scale ESS modeling challenges.

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1) ESS Unit Major Effects: Considering the complex

electrochemical characteristics of Li-ion batteries and ultraca-

pacitors, the primary electrochemical properties of ESS units

[13] include runtime recovery effect, rate capacity effect, self-

discharge effect, and aging effect, as described as follows.

Runtime recovery effect: The ESS provides energy to meet

demands of the runtime usage of different driving users. In

the ESS, runtime charging or discharging current is burst; that

is, the ESS is charged or discharged for short time intervals,followed by idle periods. According to the previous studies, the

Li-ion battery cell of ESS unit partially recovers the capacity

lost during the runtime idle periods [14]. This phenomenon,

named recovery effect, is caused by the reactants inside the

Li-ion battery. This effect is a function of the battery discharge

profile, battery construction, and idle time duration [14].

In this paper, due to the characteristics of ultracapacitor [12],

we ignores the recovery effect in ultracapacitor. From the

perspective of Li-ion battery, we model the runtime recovery

effect of Li-ion battery cell as

Voci (t+tidle) =Voci (t) (1 +tidleeSOCi(t)) (1)

where tidle is the duration of the battery idle period; is

an experimentally determined positive constant; Voci is open-

circuit voltage of battery cell i; SOCi is state of charge

SOC of unit i. As shown in (1), the recovery effect is

linearly proportional to the idle time duration and has negative

exponential dependency on battery SOC.

Runtime rate capacity effect: Based on the literature [15],

the lifetime of a battery depends on the active reaction sites

in the cathode. During the discharge procedure, if the current

discharge profile (i.e., rate of discharge) is high, the reduction

occurs only at the outer surface of the cathode. Thus, the

cathode surface is coated with an insoluble compound, which

prevents access to many active internal reaction sites [16].

In other words, if the current discharge profile is greater

than the electrochemical rated threshold, the temperature of

the battery increases dramatically; then, the potential energy

delivering capability is deteriorated, and the battery lifetime

decreases. This effect, named rate capacity effect, represents

the dependency between the actual capacity of battery and the

magnitude of the current discharge profile [17].

In this paper, we assume the delivered energy efficiency

of Li-ion battery is (0 < 1), which follows anexperimentally determined demand. The current i or I in

the following sections refers to Idemand/. Moreover, the rate

capacity effect is ignored in ultracapacitors because of thecharacteristics of ultracapacitor [12].

Aging effect: Different from the ultracapacitor with unlim-

ited cycle lifetime [12], aging effect is a primary lifetime

concern of Li-ion battery. The long-term cycle lifetime of Li-

ion battery is affected by aging effects, such as electrolyte

decomposition and cell oxidation [15]. Among these, the cell

oxidation is the most significant effect. It leads to a film (called

solid-electrolyte interphase) grown on the electrode, increasing

battery internal resistance, and reducing battery long-term

capacity. The thickness of the passive film increases over time

and reduces the effective surface between the electrode and

electrolyte. And finally, cell oxidation effect leads to worse

electrolyte conductivity.

In this paper, considering battery aging effects, a Li-ion

energy-storage unit is output voltage is given by [3]

Vouti (t) = Voci (t) (sai sci )

(ohmai ohmci ) (diffai diffci ) (2)

where Voci is unit is open-circuit voltage; sa

i (sc

i ), ohma

i

(ohmci ), and diffai (diffci ), are the surface overpotential, ohm

overpotential, and concentration overpotential of unit is anode

(cathode), respectively. Surface overpotential is due to elec-

trochemical reaction between the electrodes surface and the

electrolyte. Ohm overpotential and concentration overpotential

are due to ion migration and diffusion in the electrolyte. The

above equation can be further simplified as follows:

Vouti (t) =Voci (t) ii(t) ri(t) +iln(1 i(t)i(t)i(t)) (3)

where ri(t) is the battery cell internal resistance; i is an

experimentally determined constant; i(t) and i(t) denote the

temperature dependence of the diffusion coefficient of theactive material. i(t) models run-term aging, as follows:

i(t) =

1

i(t)

1 exp(

ii(t) ri(t) (Voci (t) Vci )

i

1i (t)

(4)

whereVci is the cutoff voltage for unit i;i(t) andi(t) are the

temperature dependence factor, which can be obtained using

the Arrhenius temperature dependence equation [18].

Li-ion battery aging effect, in particular, cell oxidation, is

affected by various parameters (e.g., chargedischarge current,

depth of discharge, and temperature), among which, tempera-

ture dependency is a primary effect. More specifically, both r i

and Voci are strongly correlated with temperature. ri and Vocican be described as follows:

dri(t)

dt=kncexp(

Eactive

Ti(t) +) (5)

where Ti(t) is the runtime battery temperature profile. k and

nc are constant values. Eactive is the activation energy. equalsEactive

Tref, and Tref is the reference temperature. Voci is also a

function of temperature. Following the Nernst equation [18],

we have:

dVoci(t)

dt=

RcTi(t)

neFcln Qi(t) (6)

whereneis the number of electrons transferred, Fcis Faradaysconstant,Rc is a constant, and Qi(t) represents the electrolyte

equilibrium concentration, which is a function of the depth

of discharge based on our previous study [19]. Overall, the

aging-induced capacity fading of Li-ion unit has exponential

temperature dependency.

2) Large-Scale ESS Modeling Challenges: The previous

studies on ESS modeling have focused on the single unit, due

to its small size used in mobile devices. Generally, because of

the computational complexity, estimating single unit electro-

chemical properties takes a long time [3]. Meanwhile, limited

work has considered the large-scale ESS modeling. Recent

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Fig. 3. Large-scale system-level ESS modeling infrastructure.

studies by National Renewable Energy Laboratory [20] and

Argonne National Laboratory [21] discussed ESS modeling

using the equivalent circuit method to capture the ESS run-

time chargedischarge cycle behavior. However, they ignore

interunit capacity variation, heterogeneous manufacture varia-

tion, and heterogeneous thermal effects.

As discussed above, the primary challenges of large-scale

integrated ESS modeling are summarized as follows.

1) A large-scale integrated ESS modeling is influenced

by accurately capturing the characteristics of energy

storage unit. For instance, the long-term cycle life of

lithium-ion battery system is affected by various agingeffects, which in turn are affected by runtime thermal

effects and depth of discharge; the ultracapacitor has fast

response to runtime peak energy demand, since the low

resistance of ultracapacitor enables high load currents.

Meanwhile, the ultracapacitor can be cycled millions

of time without aging effect concerned [12]. Therefore,

all these features must be carefully considered during

integrated ESS modeling and analysis.

2) Computational complexity is a primary challenge for

large-scale ESS modeling. Since lithium-ion battery cell

and ultracapacitor are paralleled as the energy storage

unit, it is essential to accurately model the runtime

behavior of individual energy storage unit. The ESSruntime usage changes from second to second, and the

long-term battery aging effects vary from months to

years. Accurate and fast modeling of ESS consisting of

a large number of cells over such a large time span

is challenging. Meanwhile, ESS modeling is further

complicated by the thermal analysis, which is known

to have high computational complexity [22].

B. Large-Scale System-Level ESS Modeling Framework

Overview

As illustrated in Fig. 1, the ESS for (P)HEV application con-

sists of a large-number energy storage units N(e.g., a lithium-ion battery cell connected in parallel with a ultracapacitor)

which is connected in parallel and serial to provide output

voltage and current to vehicles. Each energy storage units

are individually controlled by distributed ESS management

system. As shown in Section II, the manufacturing tolerance

and the heterogeneous runtime usage and environment, in

particular, thermal effects, lead to significant degradation and

variations among energy-storage units. Accurate system-level

ESS modeling is thus essential. Considering the interunit

connection and interaction, we propose the system-level ESS

model to characterize the overall ESS runtime performance

and long-term cycle life. The large-scale system-level ESS

modeling framework is shown in Fig. 3.

Section III-C operates in synchrony to characterize the

system-level ESS thermal profile, which is fed back to the

Section III-D to characterize the system-level ESS runtime

charge capacity and aging-induced capacity degradation. By

continuing the above analysis process over the targeted life-

time span, the ESS long-term cycle life is then obtained.

C. Large-Scale ESS runtime Thermal Modeling

The large-scale ESS thermal analysis is the process of

characterizing the 3-D thermal profile of the ESS. A large-scale ESS thermal profile is a complex function of its design,

configuration, power consumption, and ambient environment.

The thermal analysis requires accurately modeling of heat

transport across different energy-storage units.

Given the runtime current chargedischarge profile and the

configuration of the ESS, we propose the ESS runtime thermal

model as follows:

Cheat[NN]dT[N1](t)

dt=G[NN] T[N1](t) + P[N1]U(t) (7)

where matrix Cheat[NN] models the heat capacity of the N

units. MatrixG[NN

]models the thermal conductance between

adjacent units.P[N1] models the runtime power dissipation of

individual units. For a Li-ion battery unit, its runtime power

is contributed by the battery cell(s) runtime chargedischarge

current profile (derived by user-specific driving profile) and

its internal resistance. For an ultracapacitor unit, the power

is mainly contributed by its runtime chargedischarge current

profile, which obtained by user-specific driving profile. U(t)

is a step function.

Due to the complicated large-scale ESS thermal model [see

(7)], the computational complexity is the primary challenge

for system-level ESS modeling. Since the existing traditional

thermal analysis, e.g., the Boltzmann transport equation, is

extremely time consuming, even for a single unit, we de-velop a unified frequency-domain thermal analysis method,

which builds upon the multinode moment matching method

(MMM) [23], to enable fast whole large-scale ESS thermal

analysis with accuracy. Compared with conventional single-

point moment matching techniques, such as the asymptotic

waveform evaluation method, the multinode MMM requires

fewer number of moments under the same accuracy constraint

and hence has higher computation efficiency and better nu-

merical stability.

Since the power profile does not vary with time in short-

time period, we transform the (7) to the frequency domain as

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follows:

sCheat T(s) G T(s) =P/s+ Cheat T(0). (8)

The multinode MMM is then applied to calculate the poles

and residues. After that we transform the (8) back to the time

domain. The runtime temperature of each energy storage unit

i is then estimated as follows:

Ti(t) =

qt1l=0

Xti,l eptl t( P

i(t)ptl

+ Q) (9)

whereQ is the coefficient vector, which is a function ofCheat T(0);ptl is thelth-order pole for the system; qtdetermines the

order hence the accuracy of the model; Xti,l is the residue for

node (i, l) of interest.

D. Large-Scale ESS runtime Charge Capacity and Aging

Modeling

Given an ESS consisting of N energy-storage units (Li-

ion and ultracapacitor), the system-level ESS runtime charge

capacityCe(t) is given as follows:

Ce(t) =

Ni=1

Cei (t)

Cei (t) =

tt0

1

i Vouti ()ii() d+ Cei (t0) i(t) (10)

where Cei (t0) is the fully charged capacity of energy storage

unit i at t0; ii(), Vouti (), and i are, respectively, runtime

current, output voltage, and corresponding dcdc converter

efficiency for uniti. Note that the output voltage Vouti (t) is the

function of open circuit voltage Voci (t). i(t) models run-term

aging or capacity fading, which is explained in Section III-A.

Based on the (10), we define the large-scale system level of

ESS runtime state of charge (SOC(t)), which is the percentage

of runtime charge capacity Ce(t) of ESS over the rated capacity

Ce(t0), as follows:

SOC(t) = Ce(t)

Ce(t0) =

Ni=1

Cei (t)/

Ni=1

Cei (t0). (11)

Taken account for ESS unit runtime effects (see Sec-

tion III-A), the system-level ESS runtime charge capacity

characterizes the ESS runtime charge efficiency. Due to the

large-scale ESS has complex connectivity interrelations, we

modify the (10) and develop a matrix differential equation of

runtime charge capacity, as follows:

dCe[NN](t)

dt= K[NN] V[NN] I U(t)

+ Ce[NN](t0) d[NN](t)

dt(12)

where matrix Ce[NN](t) is a diagonal matrix that models the

runtime charge capacities of the N energy-storage units. Ma-

trix K[NN] models the ESS topology and the corresponding

current distribution I among the N units. Diagonal matrix

V[NN] represents the output voltage of ESS among the N

units. U(t) is a step function. Diagonal matrix [NN] models

the runtime aging of individual units, which is a function of

Fig. 5. ESS long-term aging effect validation.

Ce[NN](t). Note that the variable [NN] is a matrix form of

aging factor [see (4)], as follows:

(t) =1

(1 e

(t) ) 1

, where (13)

(t) = K R I (Voc(t) Vc)

whereR, Voc, Vc , , and are the matrix form of resistance

r, open-circuit voltage Voc, cutoff voltage Vc , , and ,

specifically. Based on the our previous study [19] and (1),

the open-circuit voltage Voc(t) is the function of Ce(t).

Considering the large-scale ESS runtime charge capacity

model [see (12)], the computational complexity is the primary

challenge for system-level ESS modeling. More specifically,for the (12), given a (P)HEV ESS containing a large number

of energy storage units (e.g., more than 1000), the runtime

behavior of individual units must be accurately modeled.

However, the ESS runtime usage changes from second to

second, and the long-term aging effects vary from month to

year. Accurate and fast modeling of a large-scale ESS over

such a large time scale range is challenging. Therefore, we

also utilize the MMM frequency-domain analysis method (see

Section III-C) to transform the (12) to the frequency domain.

In the short-term quasi-static model, Ce(t) and Voc(t) vary

significantly over time, and other long-term time-dependent

terms can be assumed to be time-invariant during short runtime

intervals. The frequency-domain equation of charge capacity

is shown as follows:

sCe(s) Ce(0) =J I/s Z + Y Ce(s) (14)

where Z, J, and Y are coefficient vectors.

And then, we apply the poles and residues form multinode

MMM and transform the equation back to the time domain.

The runtime charge capacity of each energy storage unit i is

estimated as follows:

Cei(t) =

qe1l=0

Xei,l epel t(

J

pelI(t) Z +Ce(0)) (15)

where pel is the lth-order pole for the system; qe determines

the order hence the accuracy of the model; Xei,l is the residue

for node (i, l) of interest.

E. ESS Modeling Validation

This section presents the validation of the accuracy for our

proposed ESS high-level modeling using physical measure-

ments and real-world user driving studies [24].

1)Real-time energy usage validation:To validate the proposed

ESS runtime charge cycle model, we randomly pick six

users driving traces with its real-time voltage and temperature

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Fig. 4. ESS runtime charge-cycle model validation.

information to simulate the SOC at each time point and

compare the simulated SOC values to the physically measured

values. In this paper, the (P)HEV ESS consists of over 1000

2.6-Ah Lithium-ion battery cells with a total energy capacity

of 5.1 kWh. Fig. 4 shows that the ESS runtime charge-cycle

analysis accurately matches the measurement results of six

users driving profiles using converted Toyota PHEVs [24].2) Long-term aging effect validation: We use the generalized

Sony 18 650 battery cell with 1.8 Ah capacity to evaluate the

long-term aging effect. Fig. 5 demonstrates the high accuracy

of the lithium-ion battery long-term aging modeling, com-

pared to physical measurements under different temperature

conditions [25] (the results for 45 deg C also match well).

Fig. 5 shows that different temperatures have similar impact

on battery aging during the initial cycles. As the number of

cycles increases, higher battery temperature has more impact

on battery capacity degradation.

3) Efficiency of modeling: By leveraging the proposed unified

frequency-domain electric and thermal analysis approach, we

accurately model large-scale battery system with high effi-ciency. Table I shows the computation time needed in 15-

year battery system lifetime simulation using ten daily driving

traces with diverse duration, i.e., the same trace is repeated

daily for 15 years. As shown in the table, the proposed ESS

model can simulate 15-year battery system lifetime in less than

2 min, and it scales well as trace duration increase.

4) ESS long-term performance analysis: By leveraging the

proposed ESS modeling framework and collected data from

real-world user study [24], we evaluate the (P)HEV ESS

long-term performance and quantify some of the key chal-

lenges, as discussed in Section II-B. Fig. 6(a) characterizes

the 15-year ESS long-term capacity reduction distribution for

the six different drivers with initial battery system capacity

5.1 kWh. It also illustrates that the battery system aging

varies significantly among the six drivers, ranging from 14.9%

to 74.3%. This phenomenon reflects the strong correlation

between ESS capacity and user-specific driving patterns. For

example, the third driver drives most aggresively; therefore, the

corresponding ESS capacity degrades most. The same trend

is demonstrated in Fig. 6(b). For each driver, the thermal

effects are heterogeneous in the large-scale ESS. Among dif-

ferent drivers, different driving patterns cause different long-

term thermal distribution. For instance, the third driver has

TABLE I

Efficiency of 15-Year System Lifetime Simulation

Trace 1 2 3 4 5

Daily trip duration (s) 211 516 1202 1470 1598

Computation time (s) 8.6 15.5 37.5 45.3 50.0

Trace 6 7 8 9 10

Daily trip duration (s) 1717 2140 2571 2894 3536Computation time (s) 53.5 67.5 81.7 92.0 112.4

significantly higher thermal distribution variation than others,

which exacerbate his aging effects, resulting more capacity

loss, as shown in Fig. 6(a) and (b). The system capacity

reduction variation, as shown in Fig. 6(c), is contributed by the

capacity loss of individual battery cells. The aging effect varies

significantly due to the heterogeneous thermal distribution. As

shown in Fig. 6(c), for the third driver, the highest thermal

distribution variation leads to most significant cell capacity

distribution variation. Other users show similar results.

IV. System Design and Statistical Optimization

In this section, we formulate the ESS design optimization as

a statistical optimization problem for minimizing the total cost

under the energy/power capacity and the lifespan constraint,

considering both the ESS manufacture process variation and

runtime heterogeneous user-specific driving profiles. Contrary

to a worst case optimization problem which may incur unreal-

istic cost for the majority users, a statistical optimization can

substantially reduce the system cost with only a very low in-

crease on the ESS lifetime loss. The problem is formulated and

solved within a risk-aversion two-stage stochastic optimization

framework. The system optimization procedure is shown in

Fig. 7, as a flowchart. The flowchart explains the completeprocedure for the system design and statistical optimization.

A. Problem Formulation

Targeting the proposed ESS architecture, the design-time

optimization is to quantitatively determine the ESS configu-

ration, including the number of storage units, as well as the

type and size of each unit, to minimize the system cost while

ensuring the target lifetime for most (P)HEV vehicle drivers.

As shown in Fig. 1, the ESS is composed of N = m nunits organized in an m n regular array, meaning that there

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Fig. 6. Long-term performance 15-year analysis. (a) ESS capacity reduction. (b) ESS thermal effects. (c) Cell capacity reduction variation.

Fig. 7. Flowchart for ESS system statistical optimization procedure.

are m modules connected in series and n units connected

in parallel for each module. Each of the units can be any

type of battery cell or ultracapacitor. The design-time opti-

mization needs to decide the numbers m, n, the unit type

qi,j Q, the unit size si,j for each i, j, such that the costis minimized while satisfying the usage demand for a target

lifetime.

Denoting the ESS cost function for unit type qi,j with size

s as ci,j(s), the total cost of ESS is given as follows:

cost(s)=

mi=1

nj=1

ci,j(si,j) (16)

where s is the vector of all unit sizes. Normally, ci,j(s) is a

linear function ofs with constant offset, representing the setup

cost of a unit no matter how small it is. Let Sbe the set of all

feasible assignments of unit sizes, which normally contains

lower- and upper bounds for each size. Two probabilistic

spaces Wand Pare introduced to model user-specific runtime

driving patterns and manufacture tolerance induced process

variation. Assume some runtime control policy is enforced.

At the end of the desired ESS lifespan, the aging of each

unit, measured as the percentage difference of the remaining

capacity and the initial capacity, is modeled by a function

Ai,j : S P W [0, 1]. Let the initial power and

energy capacity per unit size for type j be Pj and Ej,respectively. Since the capacity of ESS is determined by

the weakest module, the remaining capacity at the end of

the lifespan can be derived after introducing the remaining

power and energy capacities, respectively, for each module i as

follows:

PMi (s, w , p) =

nj=1

si,j(1 Ai,j(s, w , p))Pj (17)

EMi (s, w , p)=

nj=1

si,j(1 Ai,j(s, w , p))Ej. (18)

The power and energy capacities at the end of the lifespan are

PESS(s, w , p)=m min

1imPMi (s, w , p) (19)

EESS(s, w , p)=m min

1imEMi (s, w , p) (20)

respectively.

For a particular user w, there are a set of conditions that

need to be satisfied in order to work correctly for the user-

specific power usage demand kw(t) for the during t [0, T].

1) The ESS power capacityPESS(s, w , p) must be at least

the maximal power demand Pd(w)= maxtkw(t).

2) The ESS energy capacityE ESS(s, w , p) must be at least

the maximal energy demand Ed(w) =T

0 kw(t)dt.

3) For each unit to be efficiently used, an upper-bound (0, 1) should be enforced on the percentage-wise aging.

Based on the above discussion, the following hybrid ESS

design optimization (HEDO) problem can be formulated in-

tuitively to determine the sizes of the ESS units to meet a

statistical lifetime guarantee at a minimum cost.

Problem 1 (Hybrid ESS Design Optimization): Let the

battery unit types, prices, and aging models, as well as

the user driving profiles and the process variations of the

units. Let [0, 1] be the statistical lifetime guarantee.

At a lifetime guarantee of 100%, it is equivalent to thedeterministic optimization that targets at the worst-case

scenarios of both the ESS manufacture process variations

and the driving patterns (i.e., ESS runtime use) to meet

a particular remaining capacity requirement. The HEDO

problem is formulated as follows:

min. cost(s) (21)

s.t. Pr[PESS(s, w , p) Pd(w)

EESS(s, w , p) Ed(w)

AESS(s, w , p) ] , s S

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where AESS(s, w , p)

= max1im,1jn Ai,j(s, w , p) is the

worst aging among all ESS units, and the probability is taken

over all w W and p P.

B. Risk-Aversion HEDO

To solve the HEDO problem as formulated in the previous

section is challenging. First, because the problem is not

necessarily convex even when there are guarantees of theconvexity of the individual terms, a local optimal solution

is not necessarily a global optimal solution. Second, there

is no guarantee that HEDO does have a feasible solution.

Moreover, since any ESS failed during the designated ESS

lifespan should be serviced at the cost of the manufacturers,

it is preferable to optimize also for the failures. The above

issues can be addressed by introducing a risk-aversion coherent

measure [26]. Based on this measure, the HEDO problem

can be reformulated as a two-stage stochastic programming

problem with fixed recourse [27]. Details follow.

Instead of explicitly computing the system lifetime at the

end of the ESS lifespan, we introduce a random variable on

the joint probabilistic space of driving patterns and processvariations to represent the violations of the ESS constraints,

such that the tail beyond 0 is the risk of failures within the ESS

lifespan. Formally, this random variable takes the following

quantity VESS(s, w , p) for a specific corner (w, p) within the

joint probabilistic space:

VESS(s, w , p)

= max

P

Pd(w) PESS(s, w , p)

E

Ed(w) EESS(s, w , p)

A

AESS(s, w , p)

. (22)

Here P, E, and A are positive weights to set preferences

over individual constraints. To simplify the presentation, we

assume P =E = A = 1 hereafter.

Equation (22) is actually the so-called fixed recourse within

the second stage of the two-stage stochastic programming

optimization framework. The optimal s sizing depends not

only on the decision made at design time, but also on the

uncertainty of process variations at manufacture-time and of

driving patterns at runtime. To determine the bests is therefore

separated into two stages as suggested by the name of the

optimization framework. In the first stage, a decision of s is

made and will incur an initial cost (not necessarily the ESS

cost, and will be 0 in our problem formulation). In the second

stage, the uncertainty (w, p) is realized and a second stage

cost relevant to the risk is determined from both sand (w, p)through the known deterministic relation (22). Note that since

the output of the second stage is random, a measure that maps

the distribution of the second stage output to a real value must

be chosen so that a decision in the first stage can be made to

minimize the total cost of the two stages.

Rockafellar [26] proposed to use coherent measures to

obtain preferred properties for optimization, i.e., convexity, for

the whole problem, from that of the second stage determin-

istic relation, and showed that a risk-aversion measure called

conditional value-at-risk is actually coherent, which is defined

as follows. Let X be a random variable. For a risk aversion

level , the value-at-risk VaR[X] is first defined as the value

satisfying that P(X VaR[X]) = , or in other words thevalue to achieve the lifetime guarantee . The conditional

value-at-risk CVaR[X] is defined as the average of the 1

tail, i.e. CVaR[X] = E

X|X >VaR[X]

. One proves that

CVaR[X] = VaR[X]+ 1

1 E

max(XVaR[X], 0)

(23)

which can be utilized to evaluate the measure in practice.

We reformulate the HEDO problem into the risk-aversion

hybrid ESS design optimization (RA-HEDO) problem leverag-

ing the two-stage stochastic programming optimization frame-

work with fixed-recourse and the conditional value-at-risk

measure as follows.

Problem 2 (Risk-Aversion Hybrid ESS Design Optimization):

Let the battery unit types, prices, and aging models, as well

as the user driving profiles and the process variations of the

units. Let be the risk-aversion level and C be the ESS

cost upper bound. The RA-HEDO problem is formulated as

follows:

min CVaR[VESS(s, w , p)] (24)

s.t. cost(s) C, s S.

Roughly speaking, the constraint for statistical lifetime guar-

antee and the ESS cost are exchanged in the HEDO problem

to formulate the RA-HEDO problem. The risk-aversion level

plays a similar role as the statistical lifetime guarantee . To

minimize CVaR[VESS] would be of high fidelity to improve

the statistical lifetime guarantee. In addition, while the HEDO

problem could be infeasible, the RA-HEDO problem is always

feasible and one sweeps the upper bound C to obtain the curve

to tradeoff the statistical lifetime guarantee with the cost.

C. Solving the RA-HEDO Problem

We show in this section that under mild assumptions, the

RA-HEDO problem is convex and can be solved efficiently

using convex programming techniques.

Since normally cost(s) is an affine function of s, and S

contains lower- and upper bounds for each size, we have the

proposition concerning the convexity of the feasible region.

Proposition 1: The feasible region of the RA-HEDO prob-

lem is convex.

Moreover, the aging of the units in ESS satisfies that,

Proposition 2: For any given driving pattern w, process

variation p, and i, j, both Ai,j(s, w , p) and si,jAi,j(s, w , p) are

convex functions ofs.Intuitively, Proposition 2 holds due to the diminishing

marginal returns of the increasing unit sizes to the reduction

in aging. When the sizes of the ESS units increase, the ESS

internal power consumption decreases because the effective

ESS internal resistance decreases. Therefore, the temperature

across the whole ESS decreases and so does the aging of

each unit. However, the reduction in aging diminishes as

the sizes increases further more, and both Ai,j(s, w , p) and

si,jAi,j(s, w , p) are convex functions ofs.

Based on Proposition 2, we first show that VESS(s, w , p) is

a convex function of s for any given driving pattern w and

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process variation p. We may choose to omit the symbols wand p for the conciseness of the presentation whenever there

is no confusion.

According to (22) and the definitions for PESS, EESS, and

AESS, theVESS can be obtained by computing the maximum of

the violations in ESS constraints. By introducing a Lagrange

multiplier for each constraint, we can expressVESS as follows:

VESS(s, w , p) = maxhL

mi=1

hPi

Pd(w) PMi (s, w , p)

+

mi=1

hEi

Ed(w) EMi (s, w , p)

+

mi=1

nj=1

hAi,j

Ai,j(s, w , p)

. (25)

Hereh is the vector of all the multipliers hPi ,hEi , and h

Ai,j, and

L is the set of all feasible multipliers, that is

L

= {h: hPi 0, hEi 0, h

Ai,j0i, j,

m

i=1 (h

P

i +h

E

i +

n

j=1 h

A

i,j) = 1}

. (26)

Assume that for a particular s, the maximum in (25) is

achieved when h = g for some g L. Therefore, for anys, we have (omitting w and p)

VESS(s)

mi=1

gPi

Pd PMi (s)

+

mi=1

gEi

Ed EMi (s)

+

mi=1

nj=1

gAi,j

Ai,j(s)

. (27)

In addition, let Psubi (s, w , p), Esubi (s, w , p), and A

subi,j(s, w , p)

be the subgradients of PMi (s, w , p), EMi (s, w , p), and

Ai,j(s, w , p) with respect to s respectively. According to

Proposition 2, we have (omitting w and p)

PMi (s) PMi (s

) (s s)Psubi (s)

EMi (s) EMi (s

) (s s)Esubi (s)

Ai,j(s) Ai,j(s) (s

s)Asubi,j(s).

With (25) and (27), they imply that

VESS(s, w , p) VESS(s, w , p) (s s)Vsub(s, w , p),

where

Vsub(s, w , p)

=

mi=1

nj=1

Asubi,j(s, w , p)

Psubi (s, w , p) Esubi (s, w , p)

. (28)

In other words, the following lemma holds.

Lemma 1: VESS(s, w , p) is a convex function ofs with the

subgradientsVsub(s, w , p).

The objective function of the RA-HEDO problem

CVaR[VESS(s, w , p)] is also convex based on Lemma 1.

Given a risk aversion level , let I(s, w , p) b e 1 i f

VESS(s, w , p) VaR[VESS(s, w , p)] and 0 otherwise. So

CVaR[VESS(s, w , p)] CVaR[V

ESS(s, w , p)]

E

VESS(s, w , p) VESS(s, w , p)

I(s, w , p)

1

1

1 E

I(s, w , p)(s s)Vsub(s, w , p)

= (s s)1

E

I(s, w , p)Vsub(s, w , p)

.

Note that the last expectation operation is applied to each

element of the product of the scalar I(s, w , p) and the sub-

gradients vectorVsub(s, w , p). Therefore, the following lemma

and theorem hold

Lemma 2: CVaR[VESS(s, w , p)] is a convex function ofs

with the subgradients 11

E

I(s, w , p)Vsub(s, w , p)

.

Theorem 1: When Proposition 1 and 2 hold, the RA-HEDO

problem is a convex programming problem.

Since the subgradients of the objective function are known

according to Lemma 2, we can solve the RA-HEDO prob-

lem using Kelleys cutting-plane method [28]. In practice,since PMi (s, w , p), EMi (s, w , p), and Ai,j(s, w , p) are ob-

tained by simulations, we can compute the subgradients

of CVaR[VESS(s, w , p)] by approximating them with the

finite differences. We rely on the statistical aging analy-

sis technique introduced in the next section to compute

CVaR[VESS(s, w , p)] efficiently for each s by obtaining the

distribution of VESS(s, w , p).

D. Statistical Aging Analysis With the Generalized Stochastic

Collection Method

With fabrication process variations and driving behavior

variations, the ESS aging is a random variable dependent

on the basic random variables. We use to represent thebasic independent random variables (i.e. (w, p)) with arbitrary

distributions. Given a sample point composed of a specific

value for each basic random variable, the aging effect of

the system can be calculated through our model presented

in Section III. To compute the aging distribution is more

complicated. The Monte Carlo simulation can be used but

incurs a huge computation time. We employed the generalized

stochastic collection method with a sparse grid technique [29]

to improve the efficiency of the statistical aging analysis.

The statistical aging distribution is first approximated by

generalized polynomial chaos as follows:

V() V(

)

=

M

i1++iN=0

vi1 ,... ,iNH

i1,... ,iN

N () (29)

where V is the exact distribution (i.e. VESS(s)) while V is the

approximated one,Nis the number of basic random variables,

M is the highest order of the polynomial, Hi1,...,iNN () repre-

sents the N-dimensional polynomial chaos, and (i1+ + iN)is its order. The coefficients vi1,... ,iN will be estimated by

equating distribution V and the polynomial chaos (29) at a

set of collocation points in the measure space.

Given the basic random variable distributions and the aging

model, we can find the unknown coefficients vi1,... ,iN in (29)

by the following steps to get the statistical aging distribution.

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Step 1: Select a set of collocation points in the measure

space as {k|k = 1, 2, . . . , P }, where P is the number ofcollocation points.

Step 2: Compute the aging effect V(k) at each collocationpoint k with the aging model in Section III.

Step 3: Calculate the coefficients vi1,... ,iN in (29). The

generalized stochastic collection method computes the optimal

solution to minimize the error between V() and V() by the

Galerkin approach. It sets

V() V(), Hi1,...,iNN ()= 0 (30)

wherei1+ + iN = 0, 1, . . . , M . Thanks to the orthogonalityof the polynomial chaos, the coefficients can be computed as

vi1,... ,iN =V(), Hi1,... ,iNN (). (31)

Equation ((31)) is a multidimensional integral which can be

solved with numerical quadrature using the value of integrand

taken on the set of collocation points as follows:

vi1,... ,iN =

P

k=1

wkV(k)Hi1,... ,iNN (k) (32)

where wk is the corresponding weight and V(k) is the valueat the collocation point k, computed in Step 2.

We use the sparse grid technique [29] to compute the

multidimensional integral in (31). Compared with the direct

tensor product scheme [30], the sparse grid technique can

significantly reduce the number of collocation points. Further-

more, it is established in [31] that sparse grid is exact for d-

dimensional polynomials of order up to (2k+ 1). The number

of collocation points in the sparse grid method is about 2k

k!dk.

Compared with the direct tensor product scheme having (k+1)d

sample points, the sparse grid technique avoids the exponential

computation cost in terms of the dimensionality [31].

E. Runtime Control Consideration in Design Optimization

The proposed design and optimization flow take the runtime

ESS control policies into consideration and determine the

actual ESS runtime usage. More specifically, to minimize

the overall ESS cost, ESS design only targets the majority

manufacture and runtime usage profiles and ensures statistical

lifetime guarantee. It is the runtime controllers responsibility

to dynamically manage the ESS usage based on individual

users driving profile, provide ESS lifetime guarantee, and

optimize runtime ESS efficiency.

We consider the hybrid Li-ionultracapacitor ESS integra-

tion, in which each ESS row consists of both Li-ion units andultracapacitor units. The design rationale is to leverage ultraca-

pacitors high power density feature and Li-ions high energy

density feature to support, respectively, runtime high peak

power demand and the stringent energy capacity requirement.

In this paper, the runtime power demand is split into low-

frequency and high-frequency components by runtime filtering

conducted by battery manage system. Energy capacity demand

is mainly contributed by the low-frequency components and

is thus distributed to Li-ion battery units. Moreover, the high-

frequency power demand can be handled by the ultracapacitor.

This hybrid design is also essential to minimize Li-ion battery

runtime aging, as the high-frequency components, if handled

by Li-ion units, cause serious battery heating and aging. In the

runtime situation, the cutoff frequency is further dynamically

controlled based on user-specific driving patterns. Our statis-

tical optimization computes the best cutoff frequency, which

entails the minimal lifetime loss.

V. Experimental Evaluation

This section evaluates the proposed ESS design and op-timization framework using physical measurement data of

battery manufacture variations and real-world user driving pro-

files. The proposed solution conducts statistical optimization to

effectively and quickly explore the statistical ESS design space

and generate cost-efficient hybrid ESS solutions with statistical

lifetime guarantee. For instance, targeting 10, 15, and 20 year

lifespan, compared against the worst-case-based Li-ion only

ESS design, the produced hybrid ESS solutions reduce the

system cost on average by 51.4%, 51.3%, and 50.8% with

only 5% lifetime guarantee loss, respectively.

A. Experimental Setup

We first summarize the experimental evaluation settings.

Battery manufacture-induced variation:We conducted mea-

surement on 30 Li-ion battery modules used in a (P)HEV.

The nominal energy capacity of each module is 8.32 Wh.

These battery modules were operated under the same con-

dition. Overall, manufacture variation combined with aging

introduced over 40% capacity variation among these 30 battery

modules. The manufacture variation is extracted using poly-

nomial regression method and integrated with ESS analysis.

User driving profile: We have conducted a set of driving

studies using converted Toyota (P)HEVs. Overall, ten studies

have been conducted and the daily commute driving patterns

along with the ESS runtime chargedischarge current pro-

files were recorded with second-scale time resolution. Ourevaluations also leverage the large-scale Kansas City user

driving studies, which collected user daily commute driving

behavior with second-scale resolution [32]. Using the Kansas

City driving profile as input, we use PSAT (P)HEV vehicle

model [33] to estimate second-scale ESS chargedischarge

profile. Overall, the following studies include 100 user-specific

ESS usage profiles, with 19.95 A current on average and

9.80 A variance, and 0.75 h per day driving duration on average

and 0.56 h variance.

Types and costs of ESS units: Two types of ESS units are

used: Li-ion battery and ultracapacitor. The same type of ESS

units has the same initial size. The cost of Li-ion battery is

$1 per Wh, and the cost of ultracapacitor is $30 per Wh [11].Since the second-order effect on the energy-storage units is not

considered, we applied the size combination for simplicity.

Running time analysis: The following studies were con-

ducted on a workstation with a 1.4 GHz Intel processor and

2 GB of memory. Overall, the proposed optimization with ESS

modeling is efficient, with a running time of 3.4 s on average

and 5.5 s maximum for each design specification.

B. Hybrid ESS Statistical Design Optimization

First, we evaluate the performance of the proposed opti-

mization. For each design specification, the proposed solution

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Fig. 8. ESS system cost under different lifespan and statistical lifetime guarantee constraints. The cost is subject to a maximum $50 000 cost constraint.

statistical lifetime guarantees the following two types of ESS

designs with minimum cost: 1) hybrid ESS design integrating

Li-ion and ultracapacitor, and 2) Li-ion only ESS design. The

ESS design specifications target: 1) three ESS lifespan settings

of 10, 15, and 20 years; 2) five settings of the required ESS

remaining capacity from 70% to 90% with a stepping of 5%;

and 3) five settings of the lifetime guarantee from 80% to

100% with a stepping of 5%. Therefore, a total number of

2 3 5 5 = 150 ESS configurations are considered.We present the aforementioned 150 configurations in subfig-

ures of Fig. 8. Each subfigure on the left shows 50 configura-

tions targeted at the same lifespan, which are organized into 25pairs of bars to facilitate the comparison between Li-ion only

and hybrid ESS. The 25 pairs of bars are further clustered

into 5 groups, one for each of the five remaining capacity

(RC) settings. The 5 pairs of bars within each group are

sorted according to the statistical system lifetime guarantee.

While the height of each bar corresponds to the ESS cost for

subfigures on the left, the cost of a hybrid ESS configuration

is decomposed into the cost of Li-ion battery and the cost of

ultracapacitor, as shown in subfigures on the right.

These studies demonstrate that the ESS cost increases sub-

stantially when the targeted statistical system lifetime guaran-

tee increases. At a lifetime guarantee of 100%, it is equivalent

to the deterministic optimization that targets at the worst-case scenarios of both the ESS manufacture process variations

and the driving patterns (i.e., ESS runtime usage) to meet a

particular remaining capacity requirement. Therefore, the pro-

posed statistical ESS design optimization greatly reduces the

ESS cost with carefully controlled lifetime loss in comparison

to worst-case design optimizations. Quantitatively, for Li-ion

only ESS, average ESS cost reductions of 30.4%, 9.5%, 9.0%,

and 7.5% are observed for every 5% lifetime guarantee loss

from 100% to 80%; for hybrid ESS, the reductions are 33.5%,

12.9%, 10.5%, and 4.4% for every 5% lifetime guarantee loss.

Fig. 9. Impacts of (a) runtime user-specific usage variation and (b) manu-facture process variation.

These studies also demonstrate the advantages of hybrid

energy storage technology integration. Through the incorpora-

tion of Li-ion battery and ultracapacitor, two complementary

energy storage technologies, the overall ESS cost can bereduced substantially. Of all the 75 hybrid design specifications

studied, hybrid ESS design achieves a maximum reduction of

40.0%, a minimum of reduction of 29.6%, and an average

reduction of 37.3% in terms of the ESS cost, compared with

Li-ion only ESS design.

These studies demonstrate the performance of the proposed

ESS design and optimization flow. Overall, compared against

the worst-case-based Li-ion only ESS, the produced hybrid

ESS designs reduce the system cost on average by 51.2% with

only 5% lifetime guarantee loss.

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C. Impacts of Manufacture and Runtime Variance

This section further evaluates the impacts of driving patterns

and manufacture process variations on ESS cost and lifetime,

and demonstrates the importance of statistical optimization.

The following study considers the hybrid ESS configuration

targeting 15-year lifespan, 80% remaining capacity, and 90%

lifetime guarantee. We collect the aging data, i.e., ESS capacity

loss, for each driving trace at the end of the lifespan.

The results are illustrated in Fig. 9. In Fig. 9(a), thehistogram of the average remaining capacity over all possible

process variations for each driving pattern is shown. The upper

bound of the remaining capacity for the driving patterns within

the bin is shown below each bin. For example, 26% of the

driving patterns will result in an average remaining capacity

in the range of 92% to 94% at the end of the 15-year lifespan.

Next, we pick one driving pattern per bin from Fig. 9(a) and

show their remaining capacities with different assumptions on

manufacture process variations in Fig. 9(b). The curve labeled

with nopv" is the remaining capacity without any process

variation and thus is always above the other ones. The curve

labeled with avg" shows the average remaining capacity over

all process variations. In addition, 5 process variation corners

are randomly selected and their impacts on the remaining ca-

pacity are shown in the 5 curves labeled from pv1 to pv5.

This paper demonstrates that the ESS manufacture-time

and runtime usage variations interact with each other and

the joint effect determines the overall ESS lifetime and cost.

Fig. 9(a) shows that, under the same manufacture process

variation, heterogeneous user-specific runtime ESS use leads to

substantially different ESS aging. The resulting ESS capacity

loss varies from a negligible 2% to significant 30%. Fig. 9(b)

further highlights the interaction between manufacture varia-

tions and runtime usage variations. For conservative runtime

use with low ESS aging and capacity loss (i.e., the average98% remaining capacity case), manufacture process variation

has little impact on ESS aging. Similar ESS remaining ca-

pacity is achieved under different process variation settings.

On the other hand, for aggressive runtime usage with high

ESS aging and capacity loss (i.e., the average 70% remaining

capacity case), the change of manufacture process variation

has significant impact on ESS aging. The remaining capacity

varies from 80% to 60% under different process variation

settings. Overall, this paper shows that the manufacture and

runtime variations interact with each other, and such joint

effects become increasingly significant under the worst-case

manufacture and runtime usage. Therefore, statistical opti-

mization is essential for cost-efficient ESS design, and theworst-case-based ESS design is overpessimistic and results in

suboptimal ESS solutions.

VI. Conclusion

In this paper, we presented an integrated design and op-

timization framework for (P)HEV energy storage technol-

ogy and system integration, a foremost design challenge of

emerging transportation electrification. The proposed design

and optimization flow was driven by an accurate and fast

ESS modeling and analysis solution. It targeted hybrid energy

storage technology integration, allowing an optimal integration

of complementary energy storage technologies, i.e., Li-ion bat-

tery and ultracapacitor, during ESS design and optimization.

It conducted statistical optimization to efficiently address the

ESS manufacture and runtime usage variances. The proposed

work was evaluated using physical measurements of battery

manufacture variation and real-world user driving profiles.

Our experimental study showed that the proposed solution can

effectively explore the system design space and produce low-

cost and reliable (P)HEV energy storage solutions.

Acknowledgment

The authors would like to thank the editor and anonymous

reviewers for their thorough reviews and constructive sugges-

tions, which helped to improve the quality of this paper. J. Wu

would like to thank Dr. W. Zeng, Tsinghua University, Beijing,

China, for his useful discussion on the topic of large-scale ESS

modeling and optimization.

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Jie Wu(S08) received the B.S. degree in electronicengineering (Hons.) from the University of Elec-tronic Sciences and Technology of China, Chengdu,China, in 2007. She is currently pursuing the Ph.D.degree with the Institute of Microelectronics, Ts-inghua University, Beijing, China.

Her current research interests include embeddedsystems, renewable energy modeling and optimiza-tion, smart grids, and cyber-physical systems.

Ms. Wu was a recipient of the Best Paper Award

nominations at the International Symposium on LowPower Electronics and Design in 2010 for her work. She was a recipient of theFirst-Class Scholarship Award for Graduate Students at Tsinghua University.

Jia Wang (M08) received the B.S. degree inelectronic engineering from Tsinghua University,Beijing, China, in 2002, and the Ph.D. degree incomputer engineering from Northwestern University,Evanston, IL, in 2008.

He is currently an Assistant Professor of electricaland computer engineering with the Illinois Instituteof Technology, Chicago. His current research in-terests include computer-aided design of very largescale integrated circuits, and algorithm design foremerging computing platforms.

Kun Li(S08) received the B.E. degree from XidianUniversity, Xian, China, in 2006. He is currentlypursuing the Ph.D. degree with the Department ofElectrical and Computer and Energy Engineering,University of Colorado, Boulder.

His current research interests include mobile com-puting, sensing systems, and cyber physical sys-tems.

Mr. Li was a recipient of the nomination for theBest Paper Award at the International Symposiumon Low Power Electronics and Design in 2010 for

his research.

Hai Zhou (M04SM04) received the B.S. andM.S. degrees in computer science and technologyfrom Tsinghua University, Beijing, China, in 1992and 1994, respectively, and the Ph.D. degree incomputer sciences from the University of Texas,Austin, in 1999.

He is currently an Associate Professor of electricalengineering and computer science with Northwest-ern University, Evanston, IL. His current research in-terests include very large scale integration computer-aided design, algorithm design, and formal methods.

Dr. Zhou was a recipient of the CAREER Award from the National ScienceFoundation in 2003.

Qin Lv received the B.E. degree (Hons.) fromTsinghua University, Beijing, China, in 2000, andthe Ph.D. degree in computer science from PrincetonUniversity, Princeton, NJ, in 2006 .

She is currently an Assistant Professor with theDepartment of Computer Science, University of Col-orado, Boulder. She has published more than 40 pa-pers in peer-to-peer networks, large-scale similaritysearches, air quality sensing, PHEV driving studies,and event modeling and recommendation in onlinesocial communities. Her current research interests

include search systems, data mining, mobile systems, social networks, anddata management.

Li Shang (S99M04) received the B.E. degree(Hons.) from Tsinghua University, Beijing, China,and the Ph.D. degree from Princeton University,

Princeton, NJ.He is currently an Associate Professor with the

Department of Electrical, Computer, and EnergyEngineering, University of Colorado, Boulder. Hehas authored or co-authored over 90 publications inembedded systems, design for nanotechnologies, andcomputer systems.

Dr. Shang currently serves as an Associate Editorof the IEEE Transactions onVeryLargeScaleIntegration Systemsand the ACM Journal on Emerging Technologies in Computing Systems . Hewas a recipient of the Best Paper Award in IEEE/ACM DATE 2010 andIASTED PDCS 2002. His work on FPGA power modeling and analysis wasselected as one of the 25 Best Papers from FPGA. His work on temperature-aware on-chip networks was selected for publication in the MICRO TopPicks 2006. His work was a recipient of the Best Paper Award nominationsat ISLPED 2010, ICCAD 2008, DAC 2007, and ASP-DAC 2006. He wasa recipient of the Provosts Faculty Achievement Award in 2010 and his

departments Best Teaching Award in 2006. He was a recipient of the NSFCAREER Award.

Yihe Sun (M00) is currently a Professor withthe Department of Microelectronics and Nanoelec-tronics, Tsinghua University, Beijing, China. Hiscurrent research interests include SoCs testability,design methodology for multimedia very large scaleintegration (VLSI) devices, and Web networks anddata security for VLSI and SoCs based on standardcell technology and digital-signal processing cores.

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