Performance analysis framework for structural battery composites in electric vehicles

Performance analysis framework for structural battery composites in electric vehicles

Journal Pre-proof Performance analysis framework for structural battery composites in electric vehicles David Carlstedt, Leif E. Asp PII: S1359-8368(...

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Journal Pre-proof Performance analysis framework for structural battery composites in electric vehicles David Carlstedt, Leif E. Asp PII:

S1359-8368(19)35150-9

DOI:

https://doi.org/10.1016/j.compositesb.2020.107822

Reference:

JCOMB 107822

To appear in:

Composites Part B

Received Date: 1 October 2019 Revised Date:

12 December 2019

Accepted Date: 26 January 2020

Please cite this article as: Carlstedt D, Asp LE, Performance analysis framework for structural battery composites in electric vehicles, Composites Part B (2020), doi: https://doi.org/10.1016/ j.compositesb.2020.107822. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

12 Dec. 2019

Leif E. Asp Professor in Lightweight Composite Materials and Structures Dept of Applied Mechanics Chalmers University of Technology 412 96 Gothenburg, Sweden

Author statement This work has been performed in close collaboration between the two authors. Mr Carlstedt conducted most of the programming work and performed the computational work. The authors jointly planned the work and wrote the paper.

Yours sincerely,

Leif Asp

DEPARTMENT OF INDUSTRIAL AND MATERIALS SCIENCE Chalmers University of Technology SE 412 96 Gothenburg, Sweden Visiting address: Hörsalsvägen 7b Phone: +46 (0)31-722 15 43 E-mail: [email protected] Web: www.chalmers.se Chalmers tekniska högskola AB Reg.No: 556479-5598 VAT No: SE556479559801

Performance analysis framework for structural battery composites in electric vehicles David Carlstedt1, Leif E. Asp1* 1

Department of Industrial and Materials Science, Chalmers University of Technology, SE-

412 96 Gothenburg, Sweden ∗ Corresponding author. E-mail: [email protected] Abstract: In this paper, a novel modelling framework to estimate system level performance of electric vehicles utilizing a structural battery composite material is presented. Electrical and mechanical properties are derived from material data of the constituents, device design and connection / layup schemes. Knowledge of the multifunctional, i.e. electrical and mechanical, performance of the structural battery composite allows for estimation of the electric vehicle drive range for any known drive cycle. The framework is used to evaluate effect on drive range from the introduction of structural batteries into existing electric vehicles. Comparative studies performed for Tesla model S and BMW i3 demonstrate a compelling vehicle weight saving potential with maintained drive range performance. Alternatively, if vehicle weight is to be maintained from the introduction of structural batteries the resulting drive range for lightweight EVs will be increased by 70%. Keywords: A. Carbon fibre; A. Smart materials; C. Computational modelling; Energy storage 1. Introduction In recent years the demand for electric vehicles (EVs) has increased with amplified restrictions on CO2 emissions. Battery electric vehicles (BEVs) and plug-in hybrid electric vehicles (PHEVs) are today considered to be vital pathways to meet future requirements on

1

environmental impact. In order for these technologies to be competitive alternatives to conventional cars (powered by internal combustion engines) for long distance transportation the EV drive range needs to increase [1,2]. This can be achieved by an increase in the total energy storage (size of the battery pack) or by reduced vehicle weight. An alternative design approach is to use multifunctional materials or structures with ability to combine two or more functions [3–9]. One such solution is integrated structural energy storage. This type of material/structure has the ability to store electrical energy in the load path of a structural system. Hence, this material/structure enables the option of increasing the total energy storage with constant or even significantly reduced vehicle weight. Furthermore, this material/structure offers substantial volume savings on a system level as well as the possibility to distribute the energy storage, which reduces the need for cables [10]. Due to its multifunctionality, integrated structural energy storage is often referred to as “massless” energy storage and has the potential to revolutionize future design of electric vehicles. There are in general two types of integrated structural energy storage solutions: (i) structural power

materials

(multifunctional

material)

and

(ii)

structural

power

structures

(multifunctional structure). The difference between multifunctional materials and multifunctional structures is that in the former all constituents perform multiple functions, which means that the material itself is multifunctional, while in a multifunctional structure monofunctional subcomponents are combined [10]. An example of the latter solution is embedding thin-film batteries within composites laminates [11–15]. In this work we focus on the application of structural power materials, in particular structural battery composites (SBCs) [10,16–18], in electrical vehicle design. The structural battery composite is a composite material made from carbon fibre reinforced polymer (CFRP) with the ability to store electrical energy (i.e. work as a battery) while providing mechanical integrity in a structural system. Carbon fibres are used due to their high specific mechanical 2

and electrical performance, which makes them ideal for multifunctional application [19,20]. The fibres are embedded in a multifunctional matrix specifically designed for structural battery application [21,22]. Given the fact that this material is lightweight, has good mechanical properties and work as energy storage, this material offers a highly efficient material for future EVs. Benefits from using this multifunctional material in an EV are found on the systems level. Scholz et al. [23,24] has performed a feasibility study and comparative assessment of structural power technologies in electric aircraft. In these studies, Scholz et al. indicate potentials for significant gain in endurance for aircraft utilizing structural power materials. Furthermore, Adam et al. [6] showed that substantial range extension for electric aircraft can be achieved by introducing multifunctional energy storage composites. Moreover, several studies have been performed to study the benefits of this type of material for simple geometries (such as a rectangular plate or similar) [25,26] and how the mechanical properties are affected by electrochemical cycling [27–31]. In the work by Johannisson et al. [26] the potential mass savings for replacement of monofunctional components (e.g. a steel roof of a car or an interior panel of an aircraft) with structural battery composites was investigated. To date, no study exists to determine the potential benefits of such mass savings on the system level performance (e.g. drive range) for application of SBC in EV design. Furthermore, a modelling framework for such evaluation is currently lacking. In this work a modelling framework is developed to estimate the system level performance of EVs utilizing SBC. The framework is set up in two steps. First the material properties (electrical and mechanical) are estimated based on its constituent materials data, proposed design and connection/layup schemes. This provides the electrical performance (energy, internal resistance and power) and mechanical performance (elastic properties) of the material. In a second step the vehicle drive range is estimated based on the material design 3

and assumed battery mass allocation. In this study the developed framework is used to evaluate the effect on vehicle drive range when introducing SBC in existing EVs. Comparative studies are performed for Tesla model S and BMW i3 to assess potential benefits acquired introducing this novel energy storage solution in EVs, entirely or partially replacing the monofunctional battery pack and structural system. Furthermore, the framework is used to identify critical design parameters for the electrical performance and to study the mechanical performance of this material. By modifying the framework and input data, the proposed framework can be used to study the system level benefits of using embedded pouch cells (multifunctional structures) in electric cars or to study other electric vehicles e.g. busses or motorcycles. 2. Materials and geometry Two types of SBC designs have been proposed, the laminated and the 3D (or Micro) battery [10]. In this work we focus on the laminated structural battery as this design is assumed most suitable for EV application due to the limited sample sizes of the 3D battery [32]. The laminated structural battery design was first proposed by Wetzel [33] and later demonstrated by Ekstedt et al. [34] and Carlson [35]. Johannisson et al. [17] studied the multifunctional performance of laminated structural battery negative half-cells and demonstrated high multifunctional performance for this type of material. In this design the individual laminae work as different components in the battery cell (i.e. electrode, separator, collector, etc.). These laminae are stacked into a battery composite laminate as schematically illustrated in Figure 1. In Figure 1 the upper lamina corresponds to the negative electrode, which consists of carbon fibres (CF) embedded in a structural battery electrolyte (SBE) matrix [21,22]. The SBE is a polymer electrolyte which has the ability to transfer mechanical load and transport ions (i.e. function as electrolyte), simultaneously. The lower lamina corresponds to the positive 4

electrode and consists of carbon fibres coated with lithium-metal-oxide doped coating embedded in the same SBE [36]. The carbon fibres in the negative electrode and the electrode material (e.g. LiFePO4 or NMC particles) in the coating in the positive electrode are the active electrode materials in the battery cell. Due to the fact that the electrode laminae contain SBE (which function as electrolyte in the battery cell), the laminae contain both electrode materials and electrolyte matrix. 2.1 Material design and layup In earlier work by the authors [37] a conceptual design for a laminated structural battery component was proposed. The material design and layup for the individual battery cell in [37] is illustrated in Figure 2. The design is used in this study as the baseline design configuration. In this design the battery cell consists of one negative electrode lamina sandwiched between two positive electrode laminae. Between each lamina a thin separator layer is added to ensure that the electrodes do not come in contact. This layup is selected in order to minimize internal resistance (minimize distance between electrodes), improve the capacity of the cell (balance the amount of electrode materials) and to ensure that the laminate is balanced and symmetric to avoid unwanted deformation and warpage. Furthermore, the cell is protected against moisture and oxygen by adding insulating layers/laminae of soft pouch cell material (made of PET/Al/PE), surrounding the battery cell. Finally, reinforcement plies made from conventional carbon fibre reinforced polymer are added above and below to protect the structural battery cell and further reinforce the structure. Due to the integrated structure of the material, integrated electronic circuits are needed to connect the cells. This can e.g. be done by using printed electronics for current collector and circuit design [38]. In the developed framework the material properties, thicknesses of layers, volume fractions, etc. are defined as input parameters. Furthermore, these cells are connected in parallel or in 5

series (e.g. by placing them next to each other or stacking them). In this way, increased current and voltage can be delivered by the complete battery pack/structure. The number of cells in series/parallel are defined based on the cell design, voltage required by the engine and the total mass of SBC. The complete set of assumed model parameters is listed in Table 1. 2.2 Effective material properties The effective material properties are derived based on the material composition. In this work the electrical performance is assessed by the specific capacity (i.e. energy stored per weight of material), internal electrical resistance of the battery cell and electrical potential curve during discharge. The mechanical performance is assessed by the in-plane elastic constants (i.e. the material stiffness). 2.2.1 Electrical performance The specific capacity of the material is estimated as ,

= where

(1)

.

and

are the assumed reversible specific capacity of carbon fibres (subscript f)

and positive electrode particles (subscript p), respectively. These capacities are approximated based on experimental data [17,20,39,47]. The mass of the fibres and particles are denoted and

, respectively and the total mass of the cell is denoted

. Since the capacity depends

on the mass of the individual constituents and their ratios, the thickness of the different layers, volume fractions of materials, etc. affect the electrical performance of the SBC. Furthermore, the internal resistance of the individual cell is estimated as =∑



+

,

(2)

where ! ∗ is the effective length of the conductive path (in the direction of the current flow inside the cell), " is the conductivity and # is the cross-sectional area of the ith layer/component of the material through which the current flows. Moreover, 6

is the

added resistance from connecting leads per cell. Any additional resistance due to external connectors are neglected. The i layers correspond to the components in which current flows inside the battery cell (i.e. electrodes, separator and current collectors). These resistances are estimated as done in [28] and depend the geometry of the cell and conductivities of conducting phases in the material (e.g. electrical conductivity of the fibres, ion conductivity of the SBE, etc.). The lengths and areas for the different phases are approximated as !∗ #

$

= !∗

= /!

= %, , ! ∗ &' = &' 0

,#

()*

+

, !∗

= /!

,

=

,0

∗ , !,& = !,& ,

(3)

&'

(4)

-.

%

,#

=#

,

= #,& = /1.

In Eq. (3)–(4) 1 is the length of the cell, / is the width of the cell, !

negative electrode lamina, !

,

&'

is the thickness of the

is the thickness of the positive electrode lamina and !,& is the

thickness of the separator (see Figure 2). The effective lengths ! ∗

and ! ∗

refer to the

assumed average length of the current flow in the current collector (fibres) in the negative and positive electrode, respectively. Moreover, the volume fraction of fibres in the negative and positive electrodes are denoted 0

and 0 , respectively. The assumed properties are

listed in Table 1. It should be noted that the conductivities of the collectors are assumed equal to the electric conductivity of the carbon fibres [20] and the conductivity of the electrode laminae and separator are assumed equal to the ion conductivity of the SBE [21,22]. The open circuit voltage during discharge is defined as (based on a simple linear regression model) 3 = 3 4 − 676,

(5)

where 3 4 is the cell potential at full charge (DoD = 0) and DoD is the depth of discharge

defined as 676 =

,

In Eq. (6)

.

(6) ,

refers to the consumed capacity at time t and

is the capacity when the

battery is fully charged. This means that DoD varies from 0 to 1 and 3 varies from 3 4 to 7

(3 4 − 1) V going from fully charged to discharged state. The cell potential at full charge 3 4 is 3.8 V for the SBC and 4.2 V for the conventional battery cell. This corresponds to a nominal voltage (which refers to the average voltage during discharge) of 3.3 V for the SBC which is slightly lower compared with a conventional battery cell using NMC or similar positive electrode material [39]. The assumed reduction in nominal voltage is linked to the reduced conductivities of the constituents in the SBC compared to conventional batteries. It should be noted that the voltage curve during discharge for this type of material is typically non-linear but due to lack of experimental data a linear approximation is used (conservative estimate). The error induced due to the assumed approximation (cf. Eq. (5)) is considered negligible for the studied cases. Furthermore, to ensure that the current extracted during operation is not unrealistically high a maximum current is defined. This value depends on several factors and is approximated based on values for a comparable conventional Li-ion battery cell [41]. In addition to the battery cell design, additional design freedoms are available related to the internal arrangement of the battery cells, as illustrated in Figure 3. The number of cells connected in series determines the output voltage of the battery pack. Moreover, the number of cells connected in parallel determines the total capacity of the battery pack and the maximum current that the battery pack can deliver. The total capacity, resistance, voltage and current for the battery pack are estimated as 9 9 9 9

39 ?9

9 9

=:

;<

,

(7)

,

(8)

= :,&< 3 ,

(9)

=

=:

.)=

>=

;< ?

,

where :,&< and :

(10) ;<

are the number of battery cells connected in series and parallel,

respectively.

8

2.2.2 Mechanical performance The mechanical performance is assessed estimating the in-plane elastic properties of the composite laminate using Classical Laminate Theory (CLT). It is assumed that the laminate is symmetric and balanced (i.e. no coupling between extension and bending). Due to volume changes of constituents associated with electrochemical cycling it is important to assure that the composite laminate is symmetric and balanced to avoid unwanted deformation and warpage during operation. Hence, the in-plane engineering constants for the laminate can be estimated as [37] ̅ = 1/[email protected] . [email protected] = 1/[email protected] , [email protected] = 1/[email protected]%% , EAD

(11)

where [email protected] = !J; H#IK ,

(12)

# L = ∑N M ∗L OℎN − ℎNK Q . N

In Eq. (11)-(13) !J;

(13)

is the total thickness of the laminate and OℎN − ℎNK Q represents the

thickness of the kth layer. Moreover, M ∗L

N

is the ijth component of the stiffness matrix of the

kth layer which can be derived using standard micro-mechanics models such as Rule-ofMixture, Halpin-Tsai or similar [27]. Details for how the elastic properties of the SBC are estimated are provided in Appendix A. 3. Electric vehicle drive range algorithm The EV drive range is assessed as the travelled distance for a given vehicle with a total electrical capacity (energy storage). This distance depends on several factors such as vehicle mass and shape, available energy (cell capacity and allocated mass), internal resistance, etc. The flowchart of the modelling framework implemented in MATLAB to estimate the vehicle drive range is schematically illustrated in Figure 4. This model is based on the work from [42] but with extensions related to limiting the extracted current and defining the material performance for structural battery composites based on the material and geometrical 9

properties, connection scheme, etc. By altering the material design (cf. Section 2) the vehicle drive range is directly affected. This means that the material design plays a vital role for the system level performance. Hence, the developed framework can be used to identify critical material design parameters with respect to the vehicle performance at system level. 3.1 Drive cycles The vehicle drive range is estimated based on the drive characteristics of the New European Drive Cycle (NEDC) [43]. This drive cycle provides a series of velocities for different time steps and is designed to simulate typical drive conditions in European cities. Hence, the velocity R and acceleration C are defined based on the given drive conditions. The distance travelled in one cycle is approximately 10 km with a duration of 1180 seconds. This cycle is repeated until the energy storage is depleted or until the battery pack is unable to provide the required power to accelerate the vehicle. The NEDC velocity profile is presented in Figure 5. 3.2 Tractive effort The total tractive effort for a vehicle with mass

, driving at a velocity R, on level ground

can be expressed as [42] S9& = % T; < #U

VR

%

+ WXX Y + 1.05 C.

(14)

In Eq. (14), T; < is the density of the surrounding air, #U is the frontal area,

V

is the drag

coefficient, WXX is the coefficient of rolling resistance, Y is the acceleration due to gravity and C is the acceleration. The last term in Eq. (14) is related to the acceleration force where the mass is increased by 5%. This is done as an approximation in order to ignore the force needed to provide the angular acceleration at the wheels [42]. The total traction effort is the sum of the forces the vehicle must overcome to propel forward. These forces are related to aerodynamic drag, rolling resistance, acceleration, etc. The energy required each second is equal to the power defined as 10

\9& = S9& R.

(15)

Due to energy losses within the system during operation the total power required to accelerate the vehicle and to power the auxiliary system (e.g. radio, lights, etc.) is defined as \<&] =

^_)

`* `a

+ \; .

(16)

where \; is the power required to run the auxiliary systems, b' is the transmission efficiency and b is the electric motor efficiency defined as b = cdeN

cd

g j f c eNh deNi d ek)l

.

(17)

In Eq. (17) m is the copper losses coefficient, m is the iron losses coefficient, mn is the windage loss coefficient, o is the angular velocity of the motor and p&J is the constant losses that apply at any speed. Furthermore, q is the torque which is defined as q=`

^_)



*E

r

,

(18)

where E ∗ is the relative gear ratio defined as the gear ratio of the system connecting the motor to the axle over the radius of the tyre (E ∗ = E/s). 3.3 Battery model The battery performance is predicted using an equivalent circuit model (ECM) illustrated in Figure 6. To describe the dynamic behaviour of battery cells using this type of models, the circuit network is usually defined by resistors and capacitors arranged in series and parallel. In this framework the equivalent circuit is approximate using a single equivalent resistor for the internal resistance of the battery cell. With such estimation, a small error is inflicted but is considered acceptable for the studied cases as the velocity changes from the drive cycle are slow in comparison with the dynamic behaviour of the electrochemical processes. Hence, the dynamic behaviour of the battery only has minor influence on the complete vehicle drive range for the studied drive cycle. Equivalent circuit models are often used to characterize behaviour of batteries for system analysis purposes, e.g. to estimate the state of charge in 11

battery management systems (BMS) [44]. Using the proposed ECM the power delivered by the battery pack can be approximated as \9

= 39 9 ?9 9 − ?9% 9

9

9 9.

(19)

For a fully electric vehicle the power delivered by the battery pack must be equal to the power needed to propel the vehicle and run the auxiliary system which can be expressed as \9

= \<&] .

9

(20)

This means that the current the battery pack must deliver at a given time instance can be approximated as ?9

9

=

g K+v t_-_ Kut_-_ _-_ ^=)w

%v_-_

(21)

.

The current in Eq. (21) is derived as the lower root of the quadratic equation for the battery power (cf. Eq. (19)). It should be noted that the upper root corresponds to the case when the current is large enough such that the internal resistance causes the voltage to drop to a low value. This is an extremely inefficient way of providing the power and is therefore excluded [42]. Furthermore, if \<&] > 39% 9 /4

9 9

the power required by the motor is assumed larger

than what the battery pack can deliver. This corresponds to the case when the discriminant of Eq. (19) is negative. For a sum of time steps z{ (in seconds) the energy consumed at time tn is estimated as 9 9,

=∑

|} ?N ~G44 9 9,

(22)

,

where k is the Peukert coefficient [40] which accounts for the reduced capacity of the batteries with increased current. To describe the reduction in capacity of the battery pack with increased current, the capacity at full charge is redefined as the Peukert capacity defined as 9 9

=•

_-_

c

N

€ q.

(23)

where q is the discharge rate at which the capacity is measured.

12

4. Case studies: Tesla model S and BMW i3 4.1 Battery design To study the potential benefits acquired by introducing SBCs in EVs a series of case studies are performed on two existing EVs. For the given material design the energy density is estimated to be 146 Wh/kg at 10 h discharge (i.e. C-rate 1/10) based on the assumed battery characteristics (Table 1). It should be noted that the assumed specific capacity of the NMC is comparable with the typical value in commercial cells stated in [47]. Moreover, the specific capacity for the carbon fibres is comparable to experimental data for SBC half-cells measured by Johannisson et al. [17]. In addition, in the work by Johannisson et al. [26] the energy density for the target design was estimated to be 110 Wh/kg using LiFePO4. In this work we assume that NMC can replace the LiFePO4. Hence, the electrical performance estimated in this work is similar to earlier estimates. To compare with the conventional cells for which the capacity is often rated at C-rate 1/5, the estimated capacity is reduced by 20% linked to the assumed reduction in capacity of the fibres [20]. Due to the fact that the energy is distributed over a larger area (reduced risk for thermal runaway), the mechanical robustness of the material, less volatiles, etc. it is assumed that no additional packaging structure is needed in addition to the reinforcement plies already accounted for. Nevertheless, an additional knockdown of 10% is added to account for an assumed weight penalty from added wiring and safety control circuitry. This gives a final energy density of approximately 105 Wh/kg on battery pack level at a C-rate of 1/5. This effective energy density is similar to numbers presented for multifunctional structures utilizing embedded Li-ion batteries [14]. The cells are assumed to be 10 by 10 cm and 0.065 cm thick and the estimated capacity per cell is 0.373 Ah. Moreover, the internal resistance is estimated to be 0.95 Ohm which is linked to the assumed thicknesses, cell dimensions and conductivities. This is approximately one order of magnitude larger compared with a conventional Li-ion battery cell. Moreover, it is 13

assumed that the added resistance due to connecting leads and the external circuit is similar for both cases using conventional batteries and SBC. Hence, it is assumed that highly conductive printed electronic circuits are used to connect the cells [38]. The mass of the battery cell is 11.7 g and the maximum safe discharge current is set as 4 A which corresponds to a C-rate of approximately 10. The used material properties of the SBC are listed in Table 1 and the details for how the electrical properties of the material are estimated are presented in supplementary data in Appendix A. 4.2 Electric vehicles studied In this work two EVs are studied: the Tesla Model S and BMW i3. These vehicles have rated ranges of 500 km (85 kWh battery pack) and 300 km (33 kWh battery pack) for the NEDC velocity cycle, respectively [45,46]. In Figure 7 estimated breakdowns of the vehicle weights for the two EVs are listed. The components highlighted with bold text correspond to parts that potentially can be replaced with SBCs. It should be noted that additional vehicle weight reduction can be achieved by downsizing the drivetrain and electrical wiring etc. with reduction in total vehicle weight. This is not considered in the current study. 4.3 Case studies Three scenarios for the two vehicles are outlined to study the potential benefits of using SBC in the vehicle design (Table 2). The listed three cases for the Tesla Model S correspond to equivalent cases for the BMW i3. The main differences between the studied EVs are their rated vehicle drive range and total weight. In the first case (Case 1) the existing batteries are removed and replaced by 270/170 kg of SBC in the structural system. This corresponds to approximately 70% (with respect to mass) of the interior and exterior panels being made from SBC. Hence, this is considered a highly feasible design option. In Case 2 the battery is assumed to be removed and 70% of the interior and exterior panels are made from SBC (as in

14

Case 1). In addition, SBCs are introduced in the space frame and the life module of the Tesla and BMW, respectively. The total mass of SBC in Case 2 is 490/260 kg. This corresponds to approximately replacing 60% of the space frame/life module in the Tesla and BMW i3 with SBCs, respectively, in addition to 70% of the interior and exterior panels. Finally, Case 3 corresponds to Case 2 but where the mass of the SBC is doubled, and the additional mass is added to the total weight of the vehicle. This can e.g. be done by doubling the thicknesses of the components made of SBC. 4.4 Connection scheme To power electric engines in the EVs a required nominal voltage during discharge of 350 V [45] is assumed. Based on the assumed battery characteristics 106 cells are required to be connected in series. The number of cells connected in parallel is determined based on the assumed cell design (cell capacity) and total available mass of SBC. The cells are assumed to be placed in accordance with previous presented design concept for an A4 sized demonstrator proposed by the authors [37]. In this design concept the cells are assumed to be placed adjacent to each other with minor gaps between each cell. The battery cells (Figure 2) are also assumed to be stacked on top of each other and the complete stack is assumed to be balanced and symmetric. Moreover, the electrical losses associated with the connections between the cells are assumed to be accounted for in the added resistance from connecting leads (

). Moreover, it is assumed that the elastic properties are not significantly affected

by the gaps between the cells. 5. Results 5.1 Vehicle drive range Figure 8 shows the relative vehicle drive range for the three cases for the Tesla Model S normalized with respect to the range with conventional battery cells estimated using the

15

developed performance analysis framework. It should be noted that the estimated drive range of the vehicle with conventional cells using the developed framework is 481 km, which is very close to the vehicle drive range of 500 km reported in [45]. It should be noted that this prediction is based on a series of assumptions. For example, the complete DoD window (from 0 to 1) is used. Moreover, the vehicle parameters presented in Table 1 are not the actual data for the given EVs. Due to the fact that the parameters related to the vehicle dynamics are not significantly affected by the introduction of SBCs and that only the relative improvement in drive range is studied these assumptions are assumed acceptable for the current studies. For Case 1 the vehicle drive range is reduced but the results still illustrate that with minor modifications in the design, reasonable drive range for certain applications can be achieved. In Case 2 approximately 64% of the original drive range for the Tesla is predicted. This indicates that a 25% weight reduction can be achieved with only a moderate reduction in drive range. Finally, in Case 3 a 20% increase in drive range is predicted. In Figure 8 the relative vehicle drive range for the three cases for the BMW i3, normalized with respect to the range with conventional battery cells, is also presented. The results for the studied cases for the BMW i3 are similar to those for the Tesla Model S but with two conspicuous differences. Firstly, the relative vehicle drive range is longer for all cases even though the relative mass fraction of SBC (mass of SBC/vehicle mass) is lower (Figure 8). This is due to the lower total weight of the vehicle. This means that significant range enhancement can be achieved using this type of material in lightweight vehicles. For example, for Case 3 for the BMW i3 the vehicle drive range is increased by approximately 70% with maintained vehicle weight. The predicted range extension in Case 3 is in close agreement with the predicted range extension for electric aircraft for the case of complete structural integration and comparable battery mass fraction from [6]. This illustrates that for a feasible design solution significant increase in vehicle range can be achieved at maintained vehicle weight. Secondly, 16

for Case 1 the DoD during the simulation reaches only 0.6 for the BMW. This means that the vehicle stops before the battery is empty. Hence, the vehicle stops when the battery pack is unable to provide enough power to accelerate the vehicle and not when the energy is depleted. This is due to the high internal resistance of the SBC compared to conventional battery cells (linked to the assumed cell geometry and conductivities), connection scheme, current collector design and the total available mass of the SBC. This must be considered in the final design when using this type of material. Another option (not studied in the current cases) is to keep the original battery pack and replace some of the components with SBC (e.g. 70% of the interior and exterior panels as in Case 1). This will allow for increased drive range or facilitate a downsize of the original battery pack with maintained drive range. As described above, 106 cells are connected in series to provide the required 350 V for all cases. In contrast, the number of cells connected in parallel is different for the different vehicles and cases as the number of cells needed depends on the assumed cell design (cell capacity) and total available mass of SBC. Given the small cell dimensions for the studied SBC cells (10 by 10 cm and 0.065 cm thick) many cells connected in parallel are required. For Case 3, 786 and 417 parallel packs of 106 cells connected in series were required for the Tesla and BMW, respectively. Consequently, in total 83,316 SBC cells were required to power the Tesla Model S for Case 3. This can be compared to the total number of 7,104 conventional Li-ion battery cells used in the Tesla Model S (85 kWh) today. It should be noted that the number of cells is directly linked to the assumed dimensions of the cell. Hence, increased cell dimensions will result in reduced number of cells. This will also result in increased internal resistance unless additional extraction points for the current are added (this would reduce ! ∗

and ! ∗

which would lead to reduced internal resistance

). This means

that the cell dimensions, the current collector design and the connection scheme (cf. Eq. (2)) are important design parameters for SBC components. 17

5.2 Effects of separator thickness The complete set of input parameters used in the above analysis is listed in Table 1. Some of these data are easily modified. As an example, constituent volume fractions and layer thicknesses can be changed with little effort. As discussed above, the internal resistance of the SBC is a critical design parameter. For example, increased separator thickness leads to increased internal resistance and slight reduction in elastic properties and energy density of the cell. Effects of change in separator thickness on relative vehicle drive range are illustrated in Figure 9. In the figure, increased internal losses (IR-losses) caused by an increase in separator thickness, and hence ion transport, is shown to significantly reduce the vehicle drive range. This is due to the relatively low ion conductivity of the separator (assumed equal to the conductivity of SBE [21,22]). Hence, the increased thickness results in a larger penalty on the final range compared to what it would for conventional battery cells (using liquid electrolyte). For this reason, both separator thickness (i.e. distance between electrodes) and constituent conductivities are critical design factors for the electrical performance of the structural battery composite material. For Case 2 in Figure 9 the relationship between relative vehicle drive range and separator thickness is not linear. The change in slope for Case 2 (at around 150 um separator thickness) is inherent to the configuration for which the vehicle drive range becomes limited by the power supply rather than the available energy (i.e. vehicle stops before DoD =1). Obviously, other alterations in dimensions and designs are expected to have similar effect on SBC performance and subsequent vehicle drive range. For example, if multiple cells were stacked on top of each other between one set of reinforcement plies or if the pouch bag material was replaced with a very thin moisture barrier, the weight penalty from these materials will decrease. This in turn will increase the energy density of the structural battery composite and positively influence drive range of the vehicle for the given mass of SBC. 18

5.3 Mechanical performance In this study, secondary structural elements (such as interior and exterior panels) were mainly selected for SBC application. The reason for this is that the mechanical requirements are often less demanding for these components compared with components in the primary load carrying structure. Moreover, these components are often designed based on stiffness requirements. Hence, the elastic properties can be used as reference to determine the mechanical performance when replacing the existing material with SBC. The elastic properties of the studied SBC design are reduced by approximately 50% in the longitudinal direction and 80-90% in transverse and shear compared with an equivalent laminate made of conventional carbon fibre-epoxy unidirectional plies. The large reductions in the transverse and shear stiffness are mainly due to the lower modulus of the SBE (0.5 GPa) compared with conventional epoxy (3 GPa). It should be pointed out that secondary structural elements are rarely made from conventional CFRP material. In Case 3 when the mass of SBC is doubled e.g. by doubling the thicknesses of the components (to fulfill the electric requirements), the added material will partly compensate for the reduction in elastic properties. This means that for any of the cases the loss in mechanical performance can be compensated for by increasing the thickness of the components which will lead to increased drive range. The details for how the elastic properties of the SBC are estimated are presented in the supplied Matlab script in Appendix A. 6. Conclusions A performance analysis framework developed to study system level benefits from using structural battery composites in EVs is presented. The framework is used to evaluate potential benefits from full or partial substitution of conventional Li-ion batteries and automotive structures by structural battery composite structures in contemporary EVs. Based on a series of case studies we demonstrate a significant weight saving potential offered by structural 19

batteries.

Total vehicle weight reductions of 20-30% are possible with only moderate

reductions in vehicle drive range for the two considered EVs. This mass saving potential is in agreement with the work by Johannisson et al. [26] for an EV car roof. Complementary, analyses reveal that the drive range for lightweight vehicles such as the BMW i3 can be increased by 70% with maintained vehicle weight for feasible structural battery designs. Moreover, the elastic properties of the SBC are expected to be reduced by a factor of 0.5-0.9 when compared with the elastic properties of an equivalent laminate made from conventional CFRP unidirectional plies. The loss in mechanical performance can be compensated for by increasing the thickness of the components which will result in increased vehicle drive range. Finally, performance analyses disclose that the separator thicknesses, constituent conductivities and current collector design (related to the internal resistance) are critical design factors for the electrical performance of the structural battery composite material. Acknowledgements This project has been funded by the European Union, Clean Sky Joint Undertaking 2, Horizon 2020 under Grant Agreement Number 738085 and USAF, contract FA9550-17-10338, which are gratefully acknowledged. Rishab Rangarajan and Helena Rivera are acknowledged for their contributions in the initial phase of this work. Appendix A. Supplementary data The following is Supplementary data to this article: References [1]

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[32] Leijonmarck S, Carlson T, Lindbergh G, Asp LE, Maples H, Bismarck A. Solid polymer electrolyte-coated carbon fibres for structural and novel micro batteries. Compos Sci Technol 2013;89:149–157. [33] Wetzel ED. Reducing Weight: Multifunctional Composites Integrated Power, Communications, and Structure. AMPTIAC Q 2004;8(4):91–5. [34] Ekstedt S, Wysocki M, Asp LE. Structural batteries made from fibre reinforced composites. Plast Rubber Compos 2010;39:148–50. [35] Carlson T. Multifunctional composite materials – design, manufacture and experimental characterisation, Doctoral Thesis. Luleå University of Technology, Luleå, Sweden: 2013. [36] Hagberg J, Maples HA, Alvim KSP, Xu J, Johannisson W, Bismarck A, et al. Lithium iron phosphate coated carbon fiber electrodes for structural lithium ion batteries. Compos Sci Technol 2018;162:235–243. [37] Carlstedt D, Johannisson W, Zenkert D, Linde P, Asp LE. Conceptual Design Framework for Laminated Structural Battery Composites. Proc. 18th Eur. Conf. Compos. Mater., Athens, Greece: 2018, p. 24–8. [38] Gu Y, Federici JF. Fabrication of a Flexible Current Collector for Lithium Ion Batteries by Inkjet Printing. Batteries 2018;4:42. [39] Yoshio M, Brodd RJ, Kozawa A. Lithium-Ion Batteries. Springer, 2009. [40] Omar N, Daowd M, van den Bossche P, Hegazy O, Smekens J, Coosemans T, et al. Rechargeable energy storage systems for plug-in hybrid electric vehicles-assessment of electrical characteristics. Energies 2012;5:2952–88. [41] Xu J, Liu B, Wang X, Hu D. Computational model of 18650 lithium-ion battery with coupled strain rate and SOC dependencies. Appl Energy 2016;172:180–9.

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Figures

Figure 1: Schematic illustration of the laminated structural battery (CF=carbon fibre, SBE=structural battery electrolyte).

Figure 2: Schematic illustration of the material design and layup proposed for the individual battery cell in [35] which is used in this study as baseline design configuration.

Figure 3: Connection scheme (series vs. parallel).

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Figure 4: Flowchart of the modelling framework implemented in Matlab to estimate the vehicle drive range.

Figure 5: Velocity profile for the NEDC drive cycle.

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Figure 6: Equivalent circuit model (ECM) used to estimate the battery performance.

Figure 7: Estimated breakdowns of the vehicle weights for the studied EVs. The components highlighted with bold text corresponds to parts that potentially can be replaced with SBCs. Images from [45,46].

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Figure 8: Relative vehicle drive range for the three cases for the Tesla Model S and BMW i3, respectively, normalized with respect to the estimated range with conventional battery cells using the developed performance analysis framework. Relative SBC mass fractions (mass of SBC/vehicle mass) for each case are also presented.

Figure 9: The relative vehicle drive range for Case 1-3 for Tesla Model S as a function of separator thickness.

29

Tables Table 1: Assumed model parameters. Parameter

0 0 0 T T m 1 / !< ! • ! &' ! , !,& " ," " &' " , ",& T; < #U V

WXX Y E∗ b' \; m m mn p&J ? ;‚

Value

Unit

Description

Source

240 170 0.6 0.27 0.34 1.8 4.7 1.1 0.1 0.1 50 50 200 100 25 6.9·102 2·10-4 2·10-4 2·10-4 1.25 2.4/2.24 0.24/0.29 0.0048 9.81 37 0.95 250 0.05 0.3 0.01 5·10-6 600 4

[Ah/kg] [Ah/kg] [-] [-] [-] [kg/m3] [kg/m3] [-] [m] [m] [µm] [µm] [µm] [µm] [µm] [S/cm] [S/cm] [S/cm] [S/cm] [kg/m3] [m2] [-] [-] [m/s2] [m-1] [-] [W] [Ω] [m2/s2W] [N] [Ns2/m2] [W] [A]

Specific capacity carbon fibres (10 h discharge) Specific capacity NMC particles (10 h discharge) Volume fraction fibres (negative electrode) Volume fraction fibres (positive electrode) Volume fraction NMC particles Density carbon fibres Density NMC particles Peukert coefficient Length of structural battery cell Width of structural battery cell Thickness of reinforcement ply Thickness of insulating layer Thickness of negative electrode lamina Thickness of positive electrode lamina Thickness of separator Electrical conductivity current collectors Ionic conductivity (negative electrode) Ionic conductivity (positive electrode) Ionic conductivity (separator) Density of air Frontal area (Tesla Model S/BMW i3) Drag coefficient (Tesla Model S/BMW i3) Coefficient of rolling resistance Acceleration due to gravity Relative gear ratio (G/r) Transmission efficiency Power required to run the auxiliary systems Resistance from connecting leads Copper losses coefficient Iron losses coefficient Windage loss coefficient Constant electronics losses Maximum safe discharge current

[20,17] [39,47]

[20] [39] [40]

[20] [21,22] [21,22] [21,22]

[42] [42] [42] [42] [42] [42] [42] [42] [41]

Table 2: Case studies for the two EVs to study the potential benefits of using SBC. Vehicle Tesla Model S Tesla Model S Tesla Model S BMW i3 BMW i3 BMW i3

Case nr. 1 2 3 1 2 3

Mass of SBC (kg) 270 490 980 170 260 520

Total vehicle weight (kg) 1500 1500 1990 1070 1070 1330

SBC mass fraction (-) 0.18 0.33 0.49 0.16 0.24 0.39

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Total energy (kWh) 28 51 103 18 27 55

Description ~70% of interior and exterior Case 1 + ~60% of space frame Case 2 with doubled mass of SBC ~70% of interior and exterior Case 1 + ~60% of life module Case 1 with doubled mass of SBC

12 Dec. 2019

Leif E. Asp Professor in Lightweight Composite Materials and Structures Dept of Applied Mechanics Chalmers University of Technology 412 96 Gothenburg, Sweden

Conflict of interest statement On behalf of the authors I certify that there is no conflict of interest associated with the publication “Performance analysis framework for structural battery composites in electric vehicles”.

Yours sincerely,

Leif Asp

DEPARTMENT OF INDUSTRIAL AND MATERIALS SCIENCE Chalmers University of Technology SE 412 96 Gothenburg, Sweden Visiting address: Hörsalsvägen 7b Phone: +46 (0)31-722 15 43 E-mail: [email protected] Web: www.chalmers.se Chalmers tekniska högskola AB Reg.No: 556479-5598 VAT No: SE556479559801