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EVS26Los Angeles, California, May 6 - 9, 2012

Optimal Lightweighting in Battery Electric Vehicles

Johannes Hofer1, Erik Wilhelm2, Warren Schenler1

1Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland; E-mail: [email protected] Institute of Technology, Cambridge, MA 0213 9-4307, USA

Abstract

This paper presents an analytic solution to find the optimal amount of lightweighting in a battery electricvehicle (BEV). The additional cost of lightweighting is traded off against the cost savings due to thesmaller battery and motor required at constant performance and range. Current technology cost estimatesindicate that for a medium sized BEV, optimal glider mass reduction is on the order of 450 kg in 2012leading to estimated manufacturing cost reductions of 4.9%. Declining powertrain costs are expected toreduce the importance of lightweighting in minimizing BEV cost in the future, and rising electricity coststo increase the gap between the optimal solutions based on minimizing manufacturing versus total costs.The results are strongly dependent on the future development of lightweighting, battery, and electricitycosts. The sensitivity of the optimal mass reduction to these critical parameters has been evaluated, andis shown to increase over time.

Keywords: BEV (battery electric vehicle), cost, optimization, light weighting

1 Introduction

Over the last decades rising fuel prices andtighter regulation have stimulated technical de-velopments to improve fuel economy and re-duce emissions. Relative to conventional inter-nal combustion engine vehicles (ICEVs), bat-tery electric vehicles (BEVs) constitute a dra-matic improvement in vehicle energy efficiencydue to the high efficiency of the electric motor.However, their relatively high cost and low rangecontinue to be the great challenges in commer-cialization. Reducing the energy consumptionof electric vehicles is therefore of utmost impor-tance in order to increase range and reduce costs.Besides reduction of vehicle resistances and im-provement of powertrain efficiency, a very im-portant option to reduce energy consumption of aBEV is by replacing conventional by lightweightmaterials. Several studies have evaluated a rangeof current and emerging technologies in terms oftheir vehicle energy consumption reduction po-tential and associated costs [1, 2, 3, 4, 5]. How-ever, technical and economic aspects are usu-ally treated separately, making it difficult to un-derstand how to best implement new technolo-gies. In a recent analysis we have developed

a methodology to find the optimum combina-tion of vehicle mass reduction and powertrain ef-ficiency improvement to minimize vehicle life-time costs [6]. This paper develops an origi-nal optimization framework specifically suited toanalyze the implementation of lightweighting inBEVs. Lightweighting is beneficial in designingBEVs as it allows a higher range for the samecost, or similarly, a smaller battery and motorat constant range and performance. In the lattercase, the driveline costs for smaller and cheaperdrivetrain components can be traded off againstthe higher costs of producing a lighter vehicleglider based on lightweight materials [7, 8]. Inthis paper we solve for the optimal weight reduc-tion at constant range and performance minimiz-ing either manufacturing or total costs over vehi-cle lifetime. The approach is fully parameterized,so an optimum is found as a function of vehicletechnical characteristics, driving conditions, andtechnology costs.The remainder of this paper is organized intofive sections. Section 2.1 reviews currentlightweighting trends and costs, section 2.2 dis-cusses the influence of vehicle mass on the en-ergy consumption of BEVs, section 2.3 assessesthe BEV cost structure today and in the future,

EVS26 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium 1

World Electric Vehicle Journal Vol. 5 - ISSN 2032-6653 - © 2012 WEVA Page 0751

section 2.4 analyses powertrain resizing effectsat constant range and performance, and section2.5 presents the optimization results for the ref-erence sceanrio and their sensitivity with respectto the main cost factors. Section 3 presents theconclusions.

2 Lightweighting of Battery Elec-tric Vehicles

2.1 Lightweighting trends and costs

Reduction of vehicle mass can be achieved byshifting sales from larger and heavier vehiclesto smaller and lighter vehicle categories, vehi-cle redesign, or material substitution [9, 10].Lightweighting usually refers to reduction of ve-hicle weight by substituting advanced materialswith a higher strength and/or stiffness per weightthan traditional materials. This can be realizedby replacing, for example, heavier iron or steelparts with high strength steel (HSS), aluminum,magnesium, and/or composite materials such asglass- and carbon-fiber-reinforced polymers. Inrecent years many low carbon steel parts of ve-hicle powertrains and body structures have in-crementally been replaced by HSS. In fact, HSScontent doubled in the last two decades to makeup approximately 13% in 2007 [11]. Similarly,aluminum alloys continue to replace low car-bon steel, mainly in the engine, transmission,and wheels, but more advanced concepts for allaluminum bodies are implemented. The use ofaluminum increased from approximately 5% in1980 to 9% in 2010 [11]. In addition, there isalso an increasing trend towards the use of mag-nesium, plastics and polymer composites, whichaccount for approximately 0.2% and 8% of theweight of the average US car, respectively [11].Several major research projects have examinedthe mass-reduction potential for future vehicles[12, 13, 14, 15]. It is possible to reduce vehi-cle mass relative to today by approximately 20%with intensive use of HSS, an additional 20% re-duction with extensive use of aluminum, magne-sium, plastics and polymer composites, and up to60% with extensive use of carbon fiber compos-ites. Even though some studies indicate that thehigher costs of lightweight materials do not in-crease vehicle costs, actual manufacturing costsare very much dependent on the particular mate-rials used and the associated changes in toolingand assembly. Ultimately, manufacturing costsare expected to increase with the application ofadvanced materials. Figure 1 shows the esti-mated additional manufacturer cost per kg re-duced as a function of glider mass reduction froma collection of cost analysis [1, 5, 16]. An ex-change rate of 0.8 Euro to 1 USD has been usedto compare reports prepared in different curren-cies. All prices are inflation adjusted to 2011according to the US consumer price index. Anexponential cost function has been used to pre-dict for increasing marginal costs for increasingweight reduction

Figure 1: Lightweighting cost estimates [1, 5, 16] andexponential marginal cost function.

MClw = CRFlw · a · eb·∆mlw (1)

A fit to the data points shown in Figure 1 with anexponential cost function of the form of Eq.(1)yields a = 3 and b = 2.9. Although many in-dividual lightweighting options are mutually ex-clusive, these studies represent the gross aggre-gation of many options that lead to the choiceof this smoothly continous cost model. To ex-press marginal costs as a function of kg glidermass reduction instead of % reduction, the coeffi-cient b has to be expressed relative to the baselineglider mass. The baseline vehicle configurationsdescribed in the following sections form the ba-sis for the application of lightweight materials. Itis assumed that the selected glider material com-position and lightweighting marginal cost curveis representative for the reference midsize BEV.If a different reference material composition isassumed, the lightweighting cost curve needs tobe adjusted accordingly. A cost reduction fac-tor CRFlw is introduced to describe future costreductions due to learning effects and mass pro-duction. It is used in section 2.5 for scenario andsensitivity analysis. Lightweighting costs Clw asa function of weight reduction are found by inte-grating the marginal cost function

Clw =

∫MClw · d(∆mlw) (2)

=a

b· CRFlw ·

(eb·∆mlw − 1

)(3)

2.2 Energy consumption and influenceof vehicle mass

This section explains the approach used to cal-culate the energy consumption of the baselineBEV configuration as shown in Table 1, as well



as how to determine its sensitivity to mass reduc-tion. The chracteristics in Table 1 are assumed tobe representative for a midsize BEV in 2012. Thevalues for vehicle mass, motor power, battery ca-pacity, and retail price are based on BEVs in themedium passenger car segment (e.g. the NissanLeaf, Renault Fluence Z.E., etc.) from a reviewof electric vehicles currently on the market or indevelopment. Estimates for vehicle frontal areaAf , aerodynamic drag cd, and tyre rolling resis-tance cr are based on typical values found forthese vehicles and comparison with other sources[20]. In terms of materials, current BEV modelsare mostly based on previous ICEV model. Ex-ceptions include the BMW i3 (CFRP body, alu-minium chassis), the VW e-Up (HSS), or TeslaS (aluminum body). As such it is reasonable toassume that ...

Table 1: Baseline vehicle characteristics for the 2012medium segment BEV.

Mass (kg) 1500Power (kW) 87Battery capacity (kWh) 25Retail Price ($2011) 43000Af (m2) 2.2cd (drag coefficient) 0.28cr (rolling resistance coefficient) 0.008Battery type Li-IonMotor type PMSMTransmission Single-speed

To model the energy consumption of the baselineBEV and to assess its sensitivity to mass, weemploy a backward facing vehicle simulation[21, 18] implemented in MATLAB/Simulinkin combination with a parametric analysis ofenergy demand. The backward simulation startsby calculating the tractive power required at thewheel over a predefined driving cycle. In the fol-lowing we use the New European Driving Cycle(NEDC), the standard test cycle for emissioncertification of light-duty vehicles in Europe.It consists of four repeated urban sectionsfollowed by an extra-urban part. Though thereare concerns about the appropriateness of theNEDC in assessing real-world emission levels ofICEVs [19], we assume that it captures the basickinematic properties of BEV driving and thata scaling factor can be introduced if necessaryor the results adjusted to another driving cycle.The model structure is illustrated in Figure 2,including the three main powertrain componentsof a BEV generating losses, i.e. transmission,motor/inverter, and battery. Based on currentBEV designs we consider a single-gear trans-mission, permanent magnet synchronous electricmotor, and a Li-ion battery [17, 22, 23, 24, 25].To model the efficiency of the motor and inverterwe use ORNL measurement data of the 2004Toyota Prius combined permanent magnetmotor/inverter efficiency map [27]. The Priusmotor can deliver a peak power output of 50 kWfrom 1200 to 1540 rpm. In order to match this

peak power to the requirement listed in Table 1,we linearly scale the motor torque and assumethe efficiency remains unaffected. Using thisapproach we find an average cycle efficiency ofmotor/inverter on the NEDC of 79%. In addition,we assume mechanical drivetrain losses of 3%[28], and an average accessory load of 1.5 kW[25, 26]. Note however that accessory loads canbe much higher in extreme weather conditions.Batteries are the most expensive and techni-cally most challenging component of a BEV.Therefore consideration of battery lifetime andcycle efficiency is essential in optimizing thetechno-economic performance. Two commonforms of models employed [29] are the electricalequivalent circuit [30] and models based on thefirst principles of electrochemistry [31]. Moststudies conclude that efficiency and lifetimedepend, among other things, on cell temperature,charge/discharge rate, state of charge, anddepth of discharge. It is out of the scope ofthis analysis to model these effects, insteadwe use appropriate results from the literature.Similar to [32, 28, 33, 35] we assume an averagedischarge/charge efficiency of 98% for Li-ionbatteries used in BEVs on the NEDC. Targets setby car and battery manufacturers for calendarand deep-cycle life are typically about 10 yearsand 5000 cycles, respectively. However, it isnot yet clear whether current batteries can meetthese targets, especially at more severe ambienttemperatures [22]. In this analysis we assumea calendar life of ten years for average use atmoderate temperature.

Motor/Inverter

Trans-mission

Vehicle dynamics

Battery

Accessory

ChargerReal

SimulationPower flow:

Figure 2: Schematic of the BEV model structure inbackward simulation.

In order to estimate the dependence of energyconsumption on mass, and hence the influenceof weight reduction on energy use, we quicklyreview the basic equations of motion governinglongitudinal vehicle dynamics. On a flat road,the mechanical power at the wheel Pw is givenby

Pw = Pa + Pr + Pm (4)

where Pa is the power necessary to overcomeaerodynamic drag, Pr rolling resistance, and Pmthe power necessary for acceleration or poweravailable from deceleration. The individual con-tributions of Pa, Pr, and Pm to the mechanical



power at the wheel Pw acting on the baseline ve-hicle driving the NEDC are shown in Figure 3.

Figure 3: Power at the wheel of the baseline vehicleon the NEDC.

In the case of conventional vehicles without recu-peration, the energy consumption Econv can becalculated by integrating the power demand atthe wheel in traction phases, devided by the cycleaverage vehicle efficiency ηveh

Econv =1

ηveh·∫

t∈trac

(Pa + Pr + Pm) dt (5)

as described in [18]. Traction and braking phasesare characterized by positive and negative Pw, re-spectively. Electric vehicles offer the possibil-ity to recuperate parts of the kinetic energy usedfor acceleration by reconverting negative powerat the wheel through the powertrain into electricenergy in the battery. If ηpt and ηrec are the cy-cle average battery-to-wheel (BtW) and wheel-to-battery (WtB) efficiency, respectively, the en-ergy consumption for an electric vehicle Eev isgiven by

Eev =1

ηpt·∫

t∈trac

(Pa + Pr + Pm) dt (6)

+ ηrec ·∫

t∈brake

(Pa + Pr + Pm) dt

Note that the sum in the second integral is nega-tive, i.e. reduces the net energy consumption. ηpt

and ηrec include the efficiencies of the compo-nents transmission, motor/inverter, and battery,in traction and braking phases

ηpt = ηtranstr · ηmot/invtr· ηbatdis (7)

ηrec = ηtransbr · ηmot/invbr· ηbatch (8)

In general, the efficiency of energy conversionof the electric motor is different in motor andgenerator mode for the same speed and oppositetorque demand/supply [18]. However, sinceno information on the efficiency of the motorconsidered was available in generator mode,we assume it to be the same as in motor mode.We also assume the same efficiency for batterycharging and discharging [32, 28, 33]. Withthese assumptions the recuperation efficiencyηrec is equivalent to the battery-to-wheel effi-ciency ηpt.

As outlined in [18] the phases of traction, coast-ing, and braking can be separated by calculatingthe coasting velocity. Based on this approach thecontributions of Pa, Pr, and Pm to the mechan-ical energy demand and hence energy consump-tion can be evaluated as a function of vehicle anddriving cycle dependent coefficients

Eev =1

ηpt· (A cd Af + B cr m + C m) (9)

+ ηrec · (A′ cd Af + B′ cr m + C′m)

where m is the vehicle mass including the rota-tional inertia of the wheels and motor rotor, andA, B, C, A′, B′, and C′ are driving cycle param-eters. Table 2 lists the coefficients calculated forNEDC, the urban FTP-75, the highway HWFET,and the Artemis 130 driving cycles.

Table 2: Mechanical energy demand parametrizationcoefficients for the NEDC, the FTP-75, the HWFET,and the Artemis 130 driving cycles.

NEDC FTP-75 HWFET Artemis 130

A 19100 12600 29200 36200

B 840 730 900 780

C 11.2 15.9 4.4 14.0

A’ 2890 2870 2100 5450

B’ 140 250 90 200

C’ -11.2 -15.9 -4.4 -14.0

Figure 4 shows the contributions of the aerody-namic drag, rolling resistance, and kinetic energyto the mechanical energy demand at the wheel ofthe baseline vehicle specified in Table 1 on thefour considered cycles. Obviously the aerody-namic drag is more important in the highway cy-cle HWFET part due to higher speeds whereasthe kinetic energy fraction is higher in the urbanFTP-75 cycle due to more acceleration phases.The recuperable part of the total energy demandis higher in urban than highway driving due toa higher fraction of kinetic to total energy and ahigher relative fraction of recuperable kinetic en-ergy.



Figure 4: Mechanical energy demand of the baselineBEV on the NEDC, FTP-75, HWFET, and Artemis130.

The battery-to-wheel energy consumption Ebtwis calculated by taking into consideration the en-ergy demand of accessory loads Pacc

Ebtw = Eev +

∫Pacc dt

ηbat(10)

For the calculation of the electricity cost to theconsumer additional energy losses of the bat-tery charger are taken into account. At modestcharging levels (3 kW) an AC/DC battery chargeroperates with an efficiency ηch of about 92%[32, 33, 35]. With this the plug-to-wheel energyconsumption Eptw is

Eptw =Ebtw

ηch(11)

Based on Eq.(9-11) the sensitivity of energy con-sumption to mass (keeping other vehicle charac-teristics unchanged) can be assessed by calculat-ing the partial derivatives

∂Ebtw

∂m=

1

ηpt· (B cr + C) + ηrec · (B′ cr + C′)

(12)∂Eptw

∂m=∂Ebtw

∂m/ηch (13)

The calculated BtW and PtW energy consump-tion for the baseline vehicle on the NEDC, aswell as the partial derivatives with respect tomass, are summarized in Table 3. Note that theenergy consumption can be significantly higherat extreme weather conditions and/or aggressivedriving.

2.3 Baseline vehicle cost structure todayand in 2030

In this section we estimate the manufacturingcosts of BEVs in 2012, 2020, and 2030 for the

Table 3: Simulation results of energy consumptionand mass sensitivity for the baseline BEV on theNEDC.

Ebtw ( kWh100km ) 15.4

Eptw ( kWh100km ) 16.7

∂Ebtw

∂m ( Whkg·100km ) 5.2

∂Eptw

∂m ( Whkg·100km ) 5.7

baseline configuration, i.e. without the applica-tion of lightweight materials. This is done by as-sessing the costs of components that are commonwith conventional vehicles, plus the costs for ad-ditional key components needed in a BEV, simi-lar to the approach followed in [36, 37, 7, 38, 39,34].Total manufacturing costs of the glider compo-nents, i.e. body-in-white, closures, chassis, sus-pension, single gear transmission, interior, andlow-voltage electrical equippment are taken fora medium size conventional vehicle from [1, 36,25]. No future cost reductions are assumed forthese mature components. Additional compo-nents considered for the BEV are a Li-ion batterypack, permanent magnet motor, inverter, con-troller, high voltage wiring, a DC/DC converterfor supply of accessory loads, and a 3kW charger.The largest fraction of the battery costs increaseslinearly with battery capacity (for the consideredbattery capacity of the baseline BEV approxi-mately 97%), and similarly costs of the motorand inverter scale linearly with motor power out-put. In this sense, additional BEV componentsare divided into variable costs which scale lin-early with capacity and power, and fixed coststhat are independent of battery energy contentand motor power. Fixed components includehigh-voltage wiring, DC/DC converter, charger,and some battery and motor safety and controlparts.Due to technology improvements and the effectsof increased production volume of electric vehi-cles, the weight and cost of BEV componentsis expected to decrease in the future. This ef-fect is anticipated to be particularly pronouncedfor Li-ion batteries due to new electrode andelectrolyte materials of next-generation batter-ies [43, 44, 45], and strong expected growth ofglobal electric vehicle production [46]. Figure 5shows projections for Li-ion battery pack costsfrom some recent studies [22, 40, 41, 42]. Allassume cost reductions due to a combination oftechnical advances and mass production effectsbased on rising sales volume of electric vehiclesand Li-ion batteries. If a range of values was in-dicated it is shown here as an arithmetic mean.Battery and motor component costs used in thissection are based on [22]. Table 4 summarizesthe assumed specific mass SMb, SMp, and spe-cific cost SCb, SCp of variable battery and mo-tor components, i.e. parts of the battery and mo-tor/inverter that scale linearly with battery energycontent and motor power, respectively. Note that



Figure 5: Projections of Li-ion battery costs [22, 40,41, 42].

these costs are expected to be the high volume,unsubsidised costs to the vehicle manufacturer.

Table 4: Assumed specific mass and cost for batteryand motor/inverter components [22].

2012 2020 2030

SMb ( kgkWh ) 9.5 6.9 4.2

SMp ( kgkW ) 0.91 0.81 0.70

SCb ( $kWh ) 775 413 238

SCp ( $kW ) 22.5 18.0 14.4

Due to the expected improvements in batteryenergy and motor power density, the specificmass of both components decreases. This anal-ysis aims to compare future BEVs having thesame performance and range as assumed for thebaseline vehicle described for 2012 in Table 1.Due to the reduction in specific mass, the futureBEV with same range and performance will belighter and as a consequence will consume lessenergy. The weight reduction at constant rangeR and performance due to reduction of specificmasses of battery and motor in the future canbe estimated as described in Eq.(14-16). Rangeis defined here as the maximum range that canbe reached at full battery discharge, and per-formance as the initial power to mass ratio P0

m0,

which is approximately inverse proportional tothe acceleration time. In Eq.(14) the total newmass m of the vehicle is expressed as the sumof the new battery mb, motor mp, and glidermass mgl (including the mass of fixed batteryand powertrain parts). In Eq.(16), the new en-ergy consumption Ebtw is expressed as the orig-inal consumption Ebtw0 minus the reduction dueto weight reduction. Note that in this analysis noadditional future energy consumption reductionsdue to, e.g., powertrain efficiency improvements

are assumed.

m = mb + mp + mgl (14)

= R · Ebtw · SMb +P0

m0· m · SMp + mgl (15)

= R ·(Ebtw0 − ∂Ebtw

∂m· (m0 − m)

)· SMb

+P0

m0· m · SMp + mgl (16)

Solving for the new vehicle mass yields

m =R · SMb · (Ebtw0 − ∂Ebtw

∂m· m0) + mgl

1 − P0m0

· SMp − ∂Ebtw∂m

· R · SMb

(17)

Based on Eq.(17), the mass and energy consump-tion of the baseline BEV configuration in the year2020 and 2030 are adjusted relative to the BEVin 2012 to account for the lower specific mass ofbattery and motor/inverter in 2020 and 2030 ac-cording to Table 4. The baseline BEV character-istics, and the cost and weight structure for 2012,2020, and 2030 are summarized in Table 5. Notethat range, performance, and the values of Af , cd,and cd are held constant. The ratio of 1.3 of thepurchase price of the BEV in 2012 (Table 1) andtotal manufacturing costs as given in Table 5 isin good agreement with a review of retail priceequivalent markup factors in [1].

2.4 Powertrain resizingIn the following the resizing effects of a smallerrequired battery and motor when lightweight-ing the glider at constant range and peformanceare examined. Glider lightweighting reduces theBtW energy consumption as described in section2.2. The reduced energy consumption results ina lighter powertrain due to a smaller necessarybattery and motor at constant range and perfor-mance. This first order effect in turn reduces en-ergy consumption further and higher order sec-ondary mass reductions are achieved. This recur-sive sequence is described by Eq.(18,19), where∆mgl is the glider mass reduction due to the ap-plication of lightweight materials

m[0] = m0 (18)

m[n + 1] = m0 − ∆mgl − mb ·(1 − Ebtw

Ebtw0

)−mp ·

(1 − m[n]

m0

)(19)

which converges to

m = m0 −mb + ∆mgl − Ebtw

Ebtw0· mb

1 − mp

m0

(20)



Table 5: Baseline BEV characteristics, weight and cost structure in 2012, 2020, and 2030 keeping range andperformance constant.

2012 2020 2030

ECbtwNEDC ( kWh100km ) 15.4 15.0 14.6

Battery capacity (kWh) 25 24.3 23.6Range (km) 162 162 162Power (kW) 87 82 87.5Power/mass ( W

kg ) 58 58 58Mass (kg) Cost ($) Mass (kg) Cost ($) Mass (kg) Cost ($)

Glider (+ stable parts) 1183 11500 1183 11500 1183 11500Variable partsBattery 238 19375 168 10023 98.4 5610Motor, Inverter 87 1958 82 1479 77.5 1114Total manufacturing 1500 32832 1417 23002 1336 18222

From this the total vehicle mass reduction rela-tive to primary glider mass reduction ∆m

∆mglfol-

lows

∆m

∆mgl=

m − m0

∆mgl

=mb + ∆mgl − Ebtw

Ebtw0· mb

mgl · (1 − mp

m0)

(21)

Eq.(20,21) depend on the new energy consump-tion Ebtw of the lightweighted vehicle which isa priori not known. Ebtw can be either calcu-lated iteratively for each level of lightweightingapplied, or by solving a second recursive equa-tion which results in a solution for ∆m

∆mglas a

function of mgl applied. To do so, the new en-ergy consumption is expressed as a function of∆mgl and ∂Ebtw

∂m

Ebtw = Ebtw0− ∂Ebtw

∂mgl· ∆mgl

= Ebtw0 −∂Ebtw

∂m· ∆m

∆mgl· ∆mgl (22)

Substituting Eq.(21) in (22) we find the recursivefunction for Ebtw

Ebtw[0] = Ebtw0(23)

Ebtw[n + 1] = Ebtw0− ∂Ebtw

∂m

·(mb + ∆mgl − Ebtw[n]

Ebtw0· mb)

(1 − mp

m0)

(24)

which converges to

Ebtw = Ebtw0

−∂Ebtw

∂m · m0 · ∆mgl

(m0 − mp) − ∂Ebtw

∂m · m0·mb

Ebtw0

(25)

Substituting Eq.(25) in (21) yields

∆m

∆mgl=

1

1 − mp

m0− ∂Ebtw

∂m · mb

Ebtw0

(26)

This factor indicates the change of total vehiclemass to primary glider weight reduction. It in-cludes the achieved powertrain mass reduction∆mpt = ∆mb + ∆mm of battery and motor thatcan be achieved at constant range and power tomass ratio. It is a function of the initial vehicle,battery and motor mass, initial energy consump-tion, and the partial derivative of energy con-sumption with respect to mass (which was deter-mined in section 2.2). Accordingly the total pow-ertrain mass reduction due to resizing the batteryand motor (keeping range and performance con-stant) relative to the applied glider mass reduc-tion is

∆mpt

∆mgl=

∆m − ∆mgl

∆mgl

=1

1 − mp

m0− ∂Ebtw

∂m · mb

Ebtw0

− 1 (27)

In the preceeding equations the initial batterymass can be equally expressed as a function ofthe range R and the specific battery mass SMb:mb = R ·Ebtw0 ·SMb, and the initial motor massas mp = P · SMp. Substituting in Eq.(27) yields



∆mpt

∆mgl=

1

(1 − ∂Ebtw

∂m · R · SMb − Pm · SMp)

− 1

(28)

which is a simple, analytical expression for theestimation of battery and motor mass reductionthat can be achieved with lightweighting theglider at a given range and performance. Notethat battery and motor sizing effects investigatedin this section also define achievable powertraincost reductions as cost an mass are linearly re-lated. The cost implications are outlined in thenext section.

2.5 Cost minimization and scenarioanalysis

2.5.1 Baseline scenarioAs described in section 2.3 total manufacturingcosts for the baseline BEV configration are thesum of glider, battery, and motor costs. With theapplication of lightweighting, additional costsaccording to Eq.(3) have to be taken into ac-count. In order to find the optimal implementa-tion of lightweighting, total manufacturing costsCman are decomposed into baseline costs Cbl,lightweighting costs Clw, and cost reductions dueto a smaller required battery CRb and motorCRp

Cman = Cbl + Clw − CRb − CRp (29)

CRb and CRp are based on the assumption ofconstant range R and performance P

m and are ex-pressed as a function of lightweighting applied

CRb = CRFb · SCb ·(R · (ECbtw0 − ECbtw)

)(30)

CRp = CRFp · SCp ·(P0 −

P

m· (m0 − ∆m)

)(31)

where ECbtw and ∆m are expressed accordingto Eq.(25, 26) with ∆mgl replaced by ∆mlw.The cost minimum is found by setting the partialderivative ∂Cman

∂∆mlwto zero

∂Cman

∂∆mlw= 0 (32)

The solution for optimal weight reduction∆mlwopt is parameterized as a function of spe-cific battery and powertrain costs, lightweightingmarginal costs, and associated cost reduction fac-tors. A tipping point for marginal lightweightingcost MClwtip

exists up to which the applicationof lightweighting reduces manufacturing costs.Total costs, Ctot are calculated as manufactur-ing costs plus vehicle lifetime electricity costs for

120’000 km of travel, PtW energy consumptionas defined in Eq.(11), and average US retail priceof electricity to ultimate customers in residentialsector according to [50]. The optimal weight re-duction minimizing total costs is equally foundanalytically by setting the partial derivative tozero and solving for ∆mlwopt . Future electricitysavings are not discounted. To solely analyze theimpacts of the trend towards declining technol-ogy and rising electricity costs, no difference inbattery, motor, and lightweighting cost reductionis assumed, i.e. the sames cost reduction factorsare applied in this scenario: CRF = 0.6 in 2020,and 0.4 in 2030.

Table 6: Assumed electricity price according to [50].

2012 2020 2030

SCel ( $centkWh ) 11.7 12.9 15.4

The breakdown of manufacturing and electricitycost as a function of applied glider mass reduc-tion through lightweighting, is shown in Figure 6.The optimization results in this scenario are sum-marized in Table 7. Optimal glider mass reduc-tion is found to be 450 and 490 kg in 2012, reduc-ing manufacturing costs by 4.9% and total costsby 4.6%, respectively. As a result of the assumedreduction of battery and motor costs, higher costsavings with lightweighting can be achieved to-day than in future. The reduction of BEV com-ponent costs and the increase of electricity priceleads to a higher relative share of electricity to to-tal costs in the future, which in turn increases thegap between the optimal solutions based on mini-mizing manfacturing versus total costs. Whetherthe optimum level of weight reduction will de-crease or increase depends on the relative devel-opment of battery vs. lightweighting costs.

Table 7: Optimization results in the baseline scenario.

2012 2020 2030

Manufacturing costs∆mlwopt

(kg) 450 437 423∆Cman(%) 4.9 3.7 2.8

MClwtip( $kg ) 9.1 5.3 3.4

Manufacturing and electricity costs∆mlwopt

(kg) 490 506 540∆Ctot(%) 4.6 3.3 2.2

MClwtip( $kg ) 10.0 6.2 4.5

2.5.2 Sensitivity analysisThe analytic form of the solution allows oneto analyse the dependence of the optimizationresults with respect to all input parameters as



2030

2020

2012 20302020

Cos

t ($)

Glider mass reduction (kg) Glider mass reduction (kg) Glider mass reduction (kg)

2012 2020 2030

Figure 6: Breakdown of OEM manufacturing and electricity cost as a function of primary mass reduction for thebaseline scenario in 2012, 2020, 2030. Red points indicate minimal manufacturing costs, blue points minimal totalcosts.

well as to adjust the solution to a certain sce-nario. This section investigates the sensitivity ofoptimal mass reduction with respect to the as-sumed cost reduction factors for principal com-ponents. As shown in Figure 6, battery and at ahigher degree of mass reduction also lightweight-ing costs are the two main contributors to manu-facturing costs. Figure 7 shows the sensitivityof optimal mass reduction minimizing manufac-turing costs to lightweighting and battery costsfor 2012, 2020, and 2030. Each surface indicatesthe sensitivity of optimal mass reduction withina range of 20% higher to 20% lower lightweight-ing and battery cost reduction as assumed for thisscenario which is represented by a red point forthe respective year. The analysis shows that thesensitivity of optimal weight reduction increasesin the future as a result of the less well definedcost minimum.Figure 8 shows the optimal weight reductionminimizing total costs as a function of the elec-tricity price. Note that if for example the elec-tricity is generated in solar PV plants for whichlevelized cost are approximately a factor of 2.2higher [50], optimal mass reduction is consider-ably higher than for the electricity prices used inthis scenario. At zero electricity cost the solu-tion is equal to optimal mass reduction minimiz-ing manufacturing cost.

3 ConclusionThis paper presents a concise, analytic method-ology to determine the optimal amount oflightweighting for BEVs. This is based on mini-mizing the marginal costs of vehicle lightweight-ing with the cost reductions due to a smallerbattery and motor required to maintain constant

Battery Cost Reduction Factor

Opt

imal

Mas

s R

educ

tion

(kg)

201220302020

Lightweighting Cost Reduction Factor

Figure 7: Optimal weight reduction minimizing man-ufacturing costs. Red points indicate the baseline val-ues and each surface the sensitivity of optimal massreduction within a range of 20% higher to 20% lowerlightweighting and battery cost reduction factors.



Opt

imal

Mas

s R

educ

tion

(kg)

Electricity Cost ($/kWh)

2012

2030

2020

Figure 8: Optimal weight reduction minimizing to-tal manufacturing and electricity costs as a functionof electricity price. Blue points indicate the baselinevalue for the respective year.

range and performance. The powertrain resizingeffect is analytically determined. Current tech-nology costs indicate that for the baseline BEV,optimal glider mass reduction of about 450 kgleads to manufacturing cost reductions of 4.9%.It is shown that declining battery and motor costsreduce the absolute importance of lightweightingin reducing BEV costs over time, and that risingelectricity costs increase the gap between the op-timal solutions, based on minimizing manufac-turing vs. total costs. Whether the optimum levelof weight reduction will decrease or increase de-pends on the relative development of battery vs.lightweighting costs. The sensitivity of the op-timal lightweighting to critical cost parametershas been evaluated, and is shown to increase overtime.In addition to cost and range, other criteria suchas safety and environmental impacts are also im-portant to consumers and the society. Vehiclemanufacturers should consider these aspects intheir decision about the best lightweighting strat-egy. The methodology presented in this pa-per allows the potential economic benefits oflightweighting to be determined early in the ve-hicle development process. It can be easily modi-fied to be applied to other drivetrain types and ve-hicle market segments, and to include other opti-mization objectives.

Acknowledgments

This research was carried out within the projectTechnology-centered Electric Mobility Assess-ment (THELMA), sponsored by the Swiss Com-petence Center for Energy & Mobility, SwissElectric Research, and the Erdoel-Vereinigung.

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AuthorsJohannes Hofer studied Physics atLMU Munich with specializationsin Quantum Optics and IndustrialEngineering. Since 2010 he isworking towards his PhD fromETH Zurich in the Technology As-sessment group at the Paul Scher-rer Institute. His focus is on elec-tric vehicle simulation and fleetmodeling.

Erik Wilhelm is a post-doctoral fel-low in the Field Intelligence Labat MIT. He earned his PhD fromthe ETH Zurich on heuristic vehi-cle design techniques while work-ing in the Technology Assessmentgroup at PSI. His focus is on ad-vanced powertrain simulation andoptimization methods.

Warren Schenler received a BS de-gree in Engineering Physics andPhD in Energy Systems and Policyat MIT. He came to PSI in 2001,and is now in the Technology As-sessment Group within the Labo-ratory for Energy Systems Anal-ysis. He is responsible for theeconomic cost analysis of electricpower systems, including gener-ation technologies, systems inter-actions and multi-attribute, multi-scenario analysis.



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