# How long could EV batteries last if their thermal management is optimized?

Mathis Boutrouelle, Remy Panariello, Yvan Reynier, Eric Mayousse, Sebastien Martinet

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Mathis Boutrouelle, Remy Panariello, Yvan Reynier, Eric Mayousse, Sebastien Martinet. How long could EV batteries last if their thermal management is optimized?. Journal of Energy Storage, 2025, 149, pp.120262. 10.1016/j.est.2025.120262. cea-05513819

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Submitted on 16 Feb 2026

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# How long could EV batteries last if their thermal management is optimized?

Mathis Boutrouelle<sup>a,*</sup>, Remy Panariello<sup>a,**</sup>, Yvan Reynier<sup>a</sup>, Eric Mayousse<sup>a</sup>, Sébastien Martinet<sup>a</sup>

## Highlights

* Electro-thermal and ageing model of 3 cell types in 3 climates with same driving profile

* Calendar degradation accounts for 62% to 83% of total capacity loss

* 1% to 20% lifespan increase with improved thermal contact between fluid and cell

* 18% to 87% lifespan increase by cooling the pack during parking phases

* Up to 29% CO₂ emissions saving by parkcooling with low-carbon electricity

## Keywords

* Battery thermal management

* Heat transfer coefficient

* Driving profile

* Calendar ageing

* Environmental impacts

* Temperature gradients

## Abstract

Electric vehicles are prime for the energy transition, but their lithium-ion batteries are not carbon-neutral. To decrease their environmental impacts, it is essential to increase their lifespan. For this purpose, temperature can play a major role. This paper suggests an approach to assess the potential lifespan and environmental savings of various improvements of battery thermal management. To this end, an electro-thermal model coupled with degradation models of three different battery pack chemistries (NMC/LMO, NMC and LFP), in three different climates, and with real-world driving conditions, was developed. It showed that optimizing the heat transfer pathways in the battery pack could lead to a maximum of 20% lifespan increase. The model also showed that capacity losses in parking phases account for 62% to 83% of total battery degradation. Therefore, solutions tackling calendar losses, for example cooling the pack during parking phases, can lead to 87% lifespan increase in a warm climate. Life Cycle Assessment showed that this solution could decrease greenhouse gases emissions over the life cycle of the vehicle by up to 29%. Therefore, parkcooling of battery packs seems a more relevant solution than improving the thermal contact in order to decrease the environmental impacts of battery packs.

<footnote><sup>a</sup> Univ. Grenoble Alpes, CEA, LITEN, DEHT, 38000 Grenoble, France.</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>** Corresponding author.</footnote>
## Nomenclature

<table><tr><td>EV</td><td>Electric Vehicle</td></tr><tr><td>NMC</td><td>Nickel Manganese Cobalt</td></tr><tr><td>LMO</td><td>Lithium Manganese Oxide</td></tr><tr><td>LFP</td><td>Lithium iron phosphate</td></tr><tr><td>SOC</td><td>State Of Charge</td></tr><tr><td>SOH</td><td>State Of Health</td></tr><tr><td>SEI</td><td>Solid-Electrolyte Interphase</td></tr><tr><td>BTMS</td><td>Battery Thermal Management System</td></tr><tr><td>PCM</td><td>Phase Change Materials</td></tr><tr><td>LCA</td><td>Life Cycle Assessment</td></tr><tr><td>GWP</td><td>Global Warming Potential</td></tr><tr><td>EoL</td><td>End of Life</td></tr></table>

# 1. Introduction

Electric vehicles (EV) represent an increasing share of automotive sales in many countries, which is expected to grow even more in the next decade, in order to meet net-zero CO₂ targets [1]. However, production of lithium-ion batteries is not carbon neutral, representing an estimated 41% of the greenhouse gases (GHG) emissions due to the production of an EV [2]. Solutions to reduce batteries environmental footprint include the recycling and second life in stationary energy storage of used batteries [3,4]. Another solution is increasing batteries lifespan, decreasing the need to produce new ones in the future. Lifespan depends on battery use conditions: current, high or low State of Charge (SOC), mechanical stress, and temperature [5]. Especially, temperature is one of the main degradation factor for lithium-ion batteries [5]. It is generally recommended to keep batteries temperature between 15 °C and 35 °C during cycling [6]. High temperatures accelerate side reactions such as Solid-Electrolyte Interphase (SEI) growth, while low temperatures decrease lithium ions insertion kinetics and can lead to lithium plating and accelerated degradation in charge [5]. To mitigate these problems, commercial EVs integrate a battery thermal management system (BTMS). BTMS of commercial EVs is often composed of a cold plate below or between the cells, in which a liquid flows [7]. These BTMS face a constraint of cost and weight, and are therefore not optimal for cell cooling. To mitigate this issue, many experimental and numerical studies try to improve BTMS efficiency on the pack level [7–9], with technologies like direct liquid cooling [10] or phase change materials (PCM) [11]. There is also room for improvement on cell design level. Due to the intricate structure of li-ion battery cells, internal heat pathways are complex and can be optimized [12,13].

Still, these solutions would increase battery weight, leading to increased electricity consumption and therefore environmental impacts. It is therefore crucial to assess their battery lifespan increase potential. For this, there is a need for a general framework to assess the potential environmental gains of future battery thermal management technologies.

## 1.1. State of the art

In Life Cycle Assessment (LCA) studies, lifetime of the battery is often independent of the battery pack design. For example, Khanna et al. [14] studied the impact of different materials, climates and driving patterns on battery electric vehicles environmental impacts, but they considered lifetime as a sensitivity parameter, and not arising from climate, materials and driving patterns. Conversely, most papers integrating an ageing model of the battery do not include LCA computations. One exception is the work from Lavisse et al. [15] as they integrate an ageing model to link an EV battery pack design to
its lifespan in order to compute the environmental impacts of the pack, but do not focus on thermal aspects.

In most studies assessing the benefits of a thermal management technology, calendar ageing is not taken into account. Yet, personal cars spend over 95% of the time at parking [16]. Also, these studies consider a severe power profile, not representative of actual EV use. Chen et al. [17] compared active air cooling and PCM passive cooling, considering battery degradation, but they only considered cycling ageing, and a discharge current of 4.25C for an electric bus use case, which is around 10 times higher than EVs. Koltsakis et al. [18] compared the degradation of a battery with several thermal management systems, considering non-uniformity inside the pack and the cells. They compared indirect liquid cooling, PCM with fins, and immersion direct cooling. They showed that direct cooling can significantly increase battery lifespan. However, they set the external temperature to 35 °C and applied a 2C charge and discharge rates, which is around 5 times higher than EVs average currents. Wei et al. [19] modelled a battery pack cooled with a cold plate during fast-charging cycles. They modelled the individual ageing of the 124 cells of the pack and showed that, while optimizing the thermal management strategy can increase fast-charging time, it has little effect on battery lifespan. As a reminder, all the studies mentioned above did not consider calendar ageing.

Thermal management strategies to reduce ageing during the cycling phases are widely studied. Zhang et al. [20] optimize the operation strategy of plug-in hybrid electric buses. They stress the importance of considering calendar ageing in the optimization process due to its significant contribution to capacity loss. Han et al. [21] study the preheating of a plug-in hybrid electric vehicle battery pack in a cold climate, considering ageing costs. They show that using the battery energy to preheat the cells increases ageing, compared to using grid energy. Chen et al. [22] optimize the power management of a plug-in hybrid electric vehicle. They do so because a too high current will increase battery temperature and therefore accelerate ageing. Similarly, Schimpe et al. [23] studied the current derating impact on temperature and ageing for a stationary storage battery. All the studies mentioned above compute calendar ageing. To go further, Smith et al. [24] mentioned cooling the battery pack during the parking phases to reduce calendar ageing, without studying the benefits of this strategy. These studies focus on strategy rather than thermal management technology, and they do not model battery electric vehicles.

Other studies evaluate battery lifespan of electric vehicles in real-world conditions. De Gennaro et al. [25] used four different ageing models to predict battery lifespan in various operating conditions, but they set the temperature to a fixed value during cycling. Bamdezh et al. [26] developed a detailed model of an electric vehicle containing a battery pack cooled with a cold plate, including an ageing model, but without studying the influence of the thermal management parameters on the lifespan.

The benefits of including a thermal management system on battery lifespan has been investigated. Yuksel et al. [27] compared an air-cooling system with no cooling for a plug-in hybrid electric vehicle. They showed that the air-cooling system can double battery lifespan compared with no cooling. They also showed that the benefits highly depend on the climate. Jafari et al. [28] compared an active thermal management system with a passive one for a battery electric vehicle. They showed that the active system can reduce ageing by up to 30% in a hot climate. Teichert et al. [29] assessed the economic benefits of installing a cooling or heating system in a stationary storage battery, considering ageing. They showed that installing active cooling is not cost-effective for this use case. The studies mentioned above compare a BTMS with no BTMS. However, they do not study how much battery lifespan can be increased with an optimized thermal management system, direct cooling for example, compared to current EVs state-of-the-art BTMS like cold plates [30]. Also, they do not consider thermal gradients inside the battery pack and cells, which can lead to a degradation increase [31,32].
Patil et al. [33] developed a computing time-efficient electro-thermo-ageing model of a plug-in hybrid electric vehicle in order to find the most important parameters for lifespan calculation. They found that battery lifespan is almost insensitive to the thermal model parameters, because the vehicle is in use for a small part of the time. However, they considered only passive cooling. Additionally, fast charging was not included, a strategy that will gain importance in modern EVs and may worsen thermal-induced degradation.

All of the studies mentioned above, except [25], draw conclusions using only one battery degradation model. The models they use are semi-empirical, that is, based on cycling and calendar test data. Now, these models are highly dependent on the cell used and fitting parameters [34]. It is then interesting, for sensitivity analysis, to use three of these models in the same study.

From this review, several key research gaps emerge in the field of thermal management for extending battery lifespan. While many studies incorporate ageing models, they often exclude LCA computations or focus exclusively on cycling degradation, neglecting calendar ageing—despite vehicles spending over 95% of their time parked. Additionally, many studies use simplified power profiles or fixed temperatures, failing to capture real-world operating conditions. There is also a lack of comparative studies between optimized thermal management strategies (e.g., direct cooling) and conventional systems (e.g., cold plates), as well as insufficient analysis of thermal gradients within battery packs, particularly during fast charging. Furthermore, most research relies on a single degradation model, limiting sensitivity analysis. Addressing these gaps is essential for developing thermal management systems that are truly optimized to maximize battery lifespan while minimizing environmental impacts.

## 1.2. Contributions

To go beyond this state of the art, the present work builds up on Lavisse et al. [15] model to integrate several cell chemistries, ageing and thermal models, in order to assess the benefits of various improvements of thermal management system on battery lifespan and environmental impacts. The model includes thermal management strategies during the parking phases, fast charging, as well as thermal gradients inside the cells. In particular, the main contributions of this work are:

1. **Comparative analysis of thermal management systems.** We evaluated the advantages of advanced thermal management systems relative to conventional indirect liquid cooling with cold plates. This assessment was conducted using three distinct thermo-electro-ageing models, three climatic conditions, and an EV-representative driving profile.

2. **Parking phase thermal management strategies.** We analyzed strategies for thermal management during parking phases to mitigate calendar ageing. Life Cycle Assessment (LCA) was employed to assess the trade-off between extended battery lifespan and increased electricity consumption.

3. **Impact of temperature gradients on battery lifespan.** We investigated the effects of temperature gradients within individual cells on the overall lifespan of EV batteries. This was achieved by discretizing the cell model and comparing it with a homogeneous cell of identical properties.

The remainder of this paper is organized as follows. In Section 2, the modelling of the electric vehicle, pack, and cell electro-thermal and ageing aspects are described, with the definitions of several real-world scenarios. Among the scenarios are improvements to thermal interfaces and the use of thermal management strategies during pause phases. In Section 3, the results of the scenarios are presented, giving battery lifespan increase, along with life cycle assessment (LCA) calculations. These results are compared with the ones obtained for the reference battery pack. In Section 4, the assumption of
homogeneous battery pack is challenged through a discretization of battery cells. Conclusions are drawn in Section 5.

## 2. Methods

The model described in this section is based on a python code by Lavisse and coworkers, partly detailed in [15].

### 2.1. Cells, pack and EV sizing

We consider an electric vehicle with a 45 kWh battery pack. This capacity was deemed a good compromise between representability of current EV batteries (2023 world sales average is 55 kWh [1]) and sufficiently low capacity to enhance cyclic ageing and temperature effects in real-world driving profiles. The battery pack was inspired by Tesla model 3, released in September 2023, tore-down and characterized by Rosenberger and coworkers [30]. Three different lithium-ion cells were considered:

- A NMC+LMO/graphite prismatic cell, largely commercialized in EV packs, characterized in previous internal projects. It is named further on **NMC-p**.

- LG INR18650 HG2 NMC811/graphite+SiO cylindrical cell, with gravimetric energy density 231 Wh/kg [35], named **NMC-c**.

- Sony/Murata US26650FTC1 LFP/graphite cylindrical cell, with gravimetric energy density 114 Wh/kg [36], named **LFP-c**.

These cells were chosen because their chemistries are representative of past and current commercialized EV batteries [37], and most of the data concerning these cells is available in literature.

Given cell gravimetric energy density, $e_{cell}$, we can calculate the total mass of cells needed

$$m_{cells} = \frac{45 \text{ kWh}}{e_{cells}} \qquad (1)$$

Then, we consider a constant integration factor $m_{cells}/m_{pack}$. This integration factor is equal to 0.71 for Tesla model 3 battery pack [30]. Thus the pack mass is chosen as

$$m_{pack} = \frac{m_{cells}}{0.71} \qquad (2)$$

The values of battery pack masses for NMC-p, NMC-c and LFP-c are respectively 496 kg, 274 kg and 554 kg. Nicoletti et al. defined the spiral factor to calculate how the mass reduction, or increase, of an EV component impacts the total EV mass [38]. We use their formula here to calculate the EV mass

$$m_{EV} = 1.5 \cdot (m_{pack} - m_{pack}^{model3}) + m_{EV}^{model3} \qquad (3)$$

The values of EV masses for NMC-p, NMC-c and LFP-c are respectively 1909 kg, 1577 kg and 1997 kg.

### 2.2. Driving profile and EV model

The studied EV drives a total of 29000 km per year, on highways, rural roads and urban sections. Every weekend, this EV performs a highway trip of 200 km and stops at a fast charge station. This driving profile is realistic and voluntarily severe in order to highlight thermal aspects. The driving profile is presented in Figure 1. Urban, Road and Highway cycles are based on European project ARTEMIS driving cycles [39]. They give speed and acceleration of the vehicle at a time step of 1 second.
<figure><img src="image_2.png" /><figcaption>Figure 1: Driving profile</figcaption></figure>

Given vehicle speed $v$ and acceleration $a$, the power drawn from the battery required to drive the vehicle $P_{drive}$ can be calculated using equation (4), adapted from Peterson et al. [40] with no road inclination. Negative $P_{drive}$ corresponds to regenerative braking.

$$P_{drive} = \begin{cases} \frac{(m_{EV}a + \frac{1}{2}\rho_{air}v^2C_dA + C_{rr}m_{EV}g)v}{\eta_{pt}}, & \text{if } P_{drive} > 0 \\ (m_{EV}a + \frac{1}{2}\rho_{air}v^2C_dA + C_{rr}m_{EV}g)v \cdot \eta_{pt}, & \text{if } P_{drive} < 0 \end{cases} \quad (4)$$

Where air density $\rho_{air} = 1.23 \text{ kg.m}^{-3}$, vehicle drag coefficient $C_d = 0.22$ [41], vehicle area $A = 2.66 \text{ m}^2$ [42], rolling resistance coefficient $C_{rr} = 0.01$ [40], acceleration of gravity $g = 9.81 \text{ m.s}^{-2}$, and powertrain efficiency $\eta_{pt} = 0.85$ [43]. To get the full power drawn from the battery $P_{bat}$, we add the auxiliary power need (navigation, lights, radio), $P_{aux}$, the power consumed by the BTMS, $P_{BTMS}$, and the power needed to heat/cool the cabin for passenger comfort, $P_{cabin}$ (Eq. (5)).

$$P_{bat} = P_{drive} + P_{aux} + P_{BTMS} + P_{cabin} \quad (5)$$

Where $P_{aux} = 160 \text{ W}$ [43], $P_{BTMS}$ is defined in Section 2.4, and $P_{cabin}$ is a function of external temperature $T_{ext}$. This function is taken from Mansour et al. [44]. For $T_{ext}$, three different climates are considered: cold (Trondheim, Norway), mild (Lyon, France) and warm (New Delhi, India). Day-averaged temperatures for the year 2019 are taken. Table 1 gives average, min and max daily temperature for these three cities.

Charge is done at constant power and stopped when the State of Charge (SOC) reaches 90%, in slow charge, and 80%, in fast charge. This threshold is enforced to avoid degradation occurring at high SOC. The profile is discretized in driving phase, charge phase, fast charge phase and rest phase with time step 1 s, 10 s, 1 s, and 1 h, respectively.
<table><caption>Table 1: Average, min and max day-averaged temperature in Lyon, Trondheim and Delhi for the year 2019</caption><thead><tr><th>Climate</th><th>City</th><th>Average temperature (°C)</th><th>Minimum temperature (°C)</th><th>Maximum temperature (°C)</th><th>Source</th></tr></thead><tbody><tr><td>Cold</td><td>Trondheim (Norway)</td><td>7.1</td><td>-6.8</td><td>24.8</td><td>[45]</td></tr><tr><td>Mild</td><td>Lyon (France)</td><td>14.2</td><td>-1.8</td><td>31.4</td><td>[45]</td></tr><tr><td>Warm</td><td>New Delhi (India)</td><td>25.6</td><td>6.9</td><td>39.2</td><td>[46]</td></tr></tbody></table>

## 2.3. Electrical model

Each modelled battery pack is composed of a number of cells $n_{cells}$, assembled in series and parallel. The pack is first considered homogeneous, therefore only one cell is modelled. This assumption will be challenged in section 4. With $V_{cell}$ the cell voltage, the current $I$ drawn from the cell is

$$I = \frac{P_{bat}}{n_{cell}V_{cell}} \qquad (6)$$

The electrical behavior of the cell can be modeled using an equivalent circuit model (ECM) [47] (Figure 2 (a)). Cell voltage can be calculated with equation 7.

$$V_{cell} = OCV - R_{0}I - \sum_{1 \le k \le 4} R_{k}i_{k} \qquad (7)$$

Where OCV, $R_0$, $R_k$ are function of State of Health (SOH), SOC and $T_{cell}$. SOH is defined here as the ratio of current cell capacity to its nominal capacity. OCV, $R_0$, $R_k$ are determined experimentally for several breakpoints using current pulses. Typically, resistances increase when SOH decreases, because of phenomena such as SEI growth, and they decrease when temperature increases, because of faster kinetics. Currents $i_j$ are determined by solving equation (8) with an implicit scheme.

$$\forall k \in [1,4], \quad C_k \frac{dV_k}{dt} + \frac{1}{R_k} V_k = I \qquad (8)$$

<figure><img src="image_3.png" /><figcaption>Figure 2: (a) Equivalent Circuit Model (ECM) of a battery cell (b) Lumped thermal model of battery pack</figcaption></figure>

For the three cells under study, the sources of the data are:

* **NMC-p**: electrical characterization of this cell was performed during previous internal projects, it is the same used in [15].
* **NMC-c**: electrical model for this cell is built from data by Luh *et Blank* [48], using linear regression of the voltage response from current pulse tests.

* **LFP-c**: full data for this cell are not available in the literature. We only find one measurement of $R_{30s}$, and its evolution with SOH in [49]. As a replacement for the missing data, we used the model of another commercial automotive LFP cell, characterized in previous internal projects, and completed it with $R_{30s}$ and SOH dependency of actual US26650FTC1 cell from [49].

Irreversible heat generation of one cell is calculated using equation (9).

$$Q_{gen} = R_0 I^2 + \sum_{1 \le k \le 4} R_k i_k^2 \qquad (9)$$

Reversible heating due to entropy changes is neglected due to its relatively small contribution to total heating, as mentioned in [50,51].

## 2.4. Thermal model

Cooling and heating of the battery pack is performed by a thermal management system inspired by Tesla model 3, equipped with LFP cells, dismantled by Rosenberger and coworkers [30] (Figure 2 (b)). An aluminum cold plate is located under the prismatic cells, in which glycolated water flows in 24 parallel channels. An epoxy resin performs the electrical insulation and thermal conduction between the cells and the cold plate. As for the electrical model, the battery cells and pack are assumed homogeneous. This assumption will be discussed and validated in section 4. The thermal equation for the cells is

$$m_{cells} c_{p}^{cell} \frac{dT_{cell}}{dt} = Q_{gen} + h_{ext} A_{ext} (T_{ext} - T_{cell}) + h_{cond} A_{bot} (T_{plate} - T_{cell}) \quad (10)$$

Where $m_{cells}$ is the total cells mass, cells heat capacity $c_{p}^{cell} = 1371 J kg^{-1}K^{-1}$ [52], heat transfer coefficient with outside air $h_{ext} = 10 W K^{-1}m^{-2}$, calculated from [30]. An explanation of the calculation can be found in the supplementary materials. $A_{ext}$ is the area of the pack in contact with the outside and $A_{bot}$ is the area of the cold plate. The values of all the geometrical parameters are cell-dependent and are listed in the supplementary materials. The equivalent heat transfer coefficient between the cells and the plate is calculated with equation below

$$h_{cond} = \left( \frac{L_{z}^{cell}}{2} + \frac{t_{pad}}{\lambda_{pad}} + \frac{t_{plate}}{\lambda_{plate}} \right)^{-1} \qquad (11)$$

Where $L_{z}^{cell}$ is cells height. Equivalent thermal conductivity of cells $\lambda_{cell} = 16 W m^{-1}K^{-1}$ is derived from [52,53]. Detailed explanation for this value can be found in the supplementary materials. The electrically-insulating pad is assumed to be thermal epoxy with thickness $t_{pad} = 0.5 mm$ [30] and thermal conductivity $\lambda_{pad} = 0.8 W m^{-1}K^{-1}$ [54]. Aluminum cold plate thickness $t_{plate} = 3 mm$ [30] and thermal conductivity $\lambda_{plate} = 237 W m^{-1}K^{-1}$ [55]. The thermal equation for the plate is

$$m_{plate} c_{p}^{plate} \frac{dT_{plate}}{dt} = h_{cond} A_{bot} (T_{cell} - T_{plate}) + h_{conv} A_{tubes} (T_{fluid} - T_{plate}) \quad (12)$$

Where $m_{plate}$ is cold plate mass and depends on pack dimensions, aluminum heat capacity $c_{p}^{plate} = 890 J.K^{-1}kg^{-1}$ [55]. $A_{tubes}$ is the area of the 24 channels. Heat transfer coefficient between plate and fluid $h_{conv}$ is calculated using the laminar flow in tube formula from Bejan [55]. The thermal equation for the fluid is
$$m_{fluid} c_{p}^{fluid} \frac{dT_{fluid}}{dt} = h_{conv} A_{tubes} (T_{plate} - T_{fluid}) + 2c_{p}^{fluid} \dot{m}_{fluid} (T_{inlet} - T_{fluid}) \quad (13)$$

Where $m_{fluid}$ is fluid mass and depends on pack dimensions, fluid heat capacity $c_{p}^{fluid} = 4128 \text{ JK}^{-1}\text{kg}^{-1}$ [55] and fluid mass flow rate $\dot{m}_{fluid}$ is set to $10 \text{ kg min}^{-1}$ [56]. Parameters values that are not listed above can be found in the supplementary materials. Equations 10, 12, 13 are discretized and solved using an implicit scheme. The electrical power consumption of BTMS is

$$P_{BTMS} = \frac{|2c_{p}^{fluid} \dot{m}_{fluid} (T_{inlet} - T_{fluid})|}{COP} \quad (14)$$

Where BTMS coefficient of performance COP = 3 [57]. To reflect actual systems, and to avoid high currents, $P_{BTMS}$ is limited to $P_{BTMS}^{max} = 10 \text{ kW}$. Cell temperature $T_{cell}$ is monitored by adjusting fluid inlet temperature $T_{inlet}$. The control law for $T_{inlet}$ is given in Section 2.6.

## 2.5. Degradation model

The battery ageing model estimates battery capacity loss. Battery cell degradation arises from its use-conditions, namely State of Charge (SOC), temperature $T_{cell}$ and $C_{rate}$, defined as the ratio between cell current $I$, in A, and its capacity, in Ah. In this paper, we use semi-empirical models. These models are built by fitting capacity loss functions on experimental data. They distinguish cycling capacity loss $Q_{loss}^{cycling}$, when a current is flowing through the cell, and calendar capacity loss $Q_{loss}^{calendar}$, at all time. The model postulate additivity between calendar capacity loss and cycling capacity loss, with no interaction between them, as done previously by various authors [58,59]. These models are widely used to study the influence of the use conditions of EVs on their lifespan, primarily because of their computing efficiency [24,25,27,33,60]. Time resolved capacity loss equation is given below, where $\frac{dQ_{loss}^{cycling}}{dt}$ and $\frac{dQ_{loss}^{calendar}}{dt}$ are fitted from experimental data.

$$Q_{cell}(t + dt) = Q_{cell}(t) - dt \left( \frac{dQ_{loss}^{cycling}}{dt}(SOH, SOC, T_{cell}, C_{rate}) + \frac{dQ_{loss}^{calendar}}{dt}(SOH, SOC, T_{cell}) \right) \quad (15)$$

For the three cells presented above, we defined an ageing model:

* **NMC-p:** this ageing model was built during previous internal projects, with a similar approach as Montaru et al. [61]. The model takes the form of a dataset of $dQ_{loss}^{cycling}/dt$ and $dQ_{loss}^{calendar}/dt$ for several SOH, SOC, $T_{cell}$ and $C_{rate}$ breakpoints. The domain of validity of this model is -4C to 4C (convention for this paper: current is negative during charge and positive during discharge), and -10 °C to 60 °C. Linear interpolation is performed between data points.

* **NMC-c:** Luh et Blank [48] gathered data from 228 cells and 76 parameter sets for the LG HG2 cell. These parameter sets comprise SOH down to 80%, C-rate ranging from -5/3C to 1C, and temperature from 0 °C to 40 °C. Capacity loss results were used to build an ageing cartography in the same form as NMC-p, and linear interpolation was performed between data points. The detailed explanation for the construction of this model and its validation can be found in the supplementary materials.

* **LFP-c:** Schimpe et al. [58] built an analytical ageing model from 97 parameter sets for Sony/Murata US26650FTC1 battery cell. They validated this model with SOH down to 80%, C-rates ranging from -1.7C to 1.7C and temperatures between 0 °C and 55 °C.

Figure 3 shows cycling and calendar capacity loss rate, as a function of C-rate and temperature, for the three models under study. We observe a peak at low temperature charge for all three models. This is
probably due to lithium plating. For NMC-p, the profile is symmetrical vs. C-rate and this peak is also present in discharge. Our tests did not allow distinguishing between charge and discharge, so this peak in discharge may not be present in reality. Nevertheless, this has little effect on overall results, as shown in Sections 3 and 4. We observe an increase in cycling ageing during discharge and calendar ageing at high temperatures. This is attributed to the enhanced kinetics of solid electrolyte interface (SEI) growth.

<figure><img src="image_4.png" /><figcaption>Figure 3: Capacity loss rate (SOC=70%; SOH=90%); (a)-(c) cycling, respectively for NMC-p, NMC-c and LFP-c cells, versus C-rate and temperature (negative C-rate in charge, positive in discharge); (d) calendar, for NMC-p, NMC-c and LFP-c cells, versus temperature.</figcaption></figure>

End of Life (EoL) condition is defined as $SOH < 80\%$. There are three reasons for this. First, this criterion is widely used in the literature [25,62]. Second, some “knee effects” often occur around this 80% threshold [63,64]. Third, two out of three ageing models under study may not be valid under this value.

## 2.6. Temperature control strategy

In commercial EVs, battery temperature is generally kept between 15 and 35 °C for it to work optimally [6]. In fast charge, to avoid lithium plating and to decrease cell resistance, some BTMS can heat the battery between 40 and 50 °C [30]. In this paper, we chose to control the temperature in order to minimize cell degradation. For this, we define three operating points, corresponding to the phases of the use profile: discharge at C/2, slow charge at C/4, and fast charge at 5/3C (because of lack of data at higher C-rates). The calculation of the optimal temperature in order to minimize degradation, for the three ageing models under study, is done using python library `scipy. This optimization was performed with bounds on temperature corresponding to the domain of validity of each model. Obtained optimal temperatures are presented below:
* NMC-p:

* In discharge, slow charge and fast charge, the optimal temperature to minimize degradation is the same: 16 °C.

* NMC-c:

* In discharge and slow charge, the optimal temperature to minimize degradation was found to be 25 °C.

* In fast charge, the function is monotonic, the degradation decreases when temperature increases. This would lead to an optimal temperature of 40 °C, considering the domain of validity of our model. Because the temperature limit for the other models is higher, and Tesla model 3 BTMS heats the cells up to 50 °C [30], we decided to linearly extrapolate the ageing model up to 50 °C, and set the optimal temperature for NMC-c in fast charge to 50 °C.

* LFP-c:

* In discharge and slow charge, the optimization algorithm returns the lower bound of the optimization range, i.e. 0 °C. However, this optimization did not take into account the increase of internal resistance at low temperature, and therefore power losses. To find a compromise between high resistance and degradation, and to match NMC-p, we chose an optimal temperature in discharge and slow charge of 16 °C.

* In fast charge, the optimization algorithm returns the upper bound of the optimization range, i.e. 50 °C. This seems a sensible compromise between slow degradation and safety.

The temperature of the cells, assumed uniform, is controlled by the BTMS. For this, inlet temperature of the cooling fluid $T_{inlet}$ is adjusted dependent on cell temperature $T_{cell}$, and maximum BTMS power $P_{BTMS}^{max}$. This is done in three steps:

1) Compute the desired inlet fluid temperature $T_{inlet}^{target}$:

$$ T_{inlet}^{target} = \begin{cases} 50 \,^{\circ}\text{C}, & \text{if } T_{cell} < T_{opt} \\ T_{fluid}, & \text{if } T_{opt} \le T_{cell} \le T_{opt} + 1 \,^{\circ}\text{C} \\ 0 \,^{\circ}\text{C}, & \text{if } T_{cell} > T_{opt} + 1 \,^{\circ}\text{C} \end{cases} \quad (16) $$

2) Using equation 14, compute the BTMS power needed to reach the target inlet temperature:

$$ P_{BTMS}^{target} = \frac{|2c_{p}^{fluid} \dot{m}_{fluid} (T_{inlet}^{target} - T_{fluid})|}{COP} \quad (17) $$

3) If the required BTMS power $P_{BTMS}^{target}$ is inferior to the maximum allowable BTMS power $P_{BTMS}^{max}$, the inlet temperature is set equal to the target. Otherwise, the inlet temperature is adjusted so that $P_{BTMS}^{max}$ is equal to $P_{BTMS}^{target}$:

$$ T_{inlet} = \begin{cases} T_{inlet}^{target}, & \text{if } P_{BTMS}^{target} \le P_{BTMS}^{max} \\ T_{fluid} + \frac{COP \cdot P_{BTMS}^{max}}{2c_{p}^{fluid} \dot{m}_{fluid}}, & \text{if } P_{BTMS}^{target} > P_{BTMS}^{max} \text{ and } T_{inlet}^{target} \ge T_{fluid} \\ T_{fluid} - \frac{COP \cdot P_{BTMS}^{max}}{2c_{p}^{fluid} \dot{m}_{fluid}}, & \text{if } P_{BTMS}^{target} > P_{BTMS}^{max} \text{ and } T_{inlet}^{target} < T_{fluid} \end{cases} \quad (18) $$

In the highway section before fast charge, the BTMS is deactivated: the battery heats by itself in order to start fast charge at high temperature, as Tesla model 3 BTMS does [30], in order to avoid high degradation at low-temperature fast charge.
Table 2 summarizes the main properties of the cells and ageing models under study.

<table><caption>Table 2: Summary of the main properties of cells and models used</caption><thead><tr><th></th><th>NMC-p</th><th>NMC-c</th><th>LFP-c</th></tr></thead><tbody><tr><td>Chemistry</td><td>NMC + LMO / Graphite</td><td>NMC811 / Graphite + SiO</td><td>LFP / Graphite</td></tr><tr><td>Format</td><td>Prismatic</td><td>Cylindrical</td><td>Cylindrical</td></tr><tr><td>Energy density [Wh·kg<sup>-1</sup>]</td><td>128</td><td>231 ([35])</td><td>114 ([36])</td></tr><tr><td>Ageing model: Valid temperature range [°C]</td><td>-10 to 60</td><td>0 to 50 ([48])</td><td>0 to 55 ([58])</td></tr><tr><td>Optimal temperature for ageing: discharge &amp; slow charge [°C]</td><td>16</td><td>25</td><td>16</td></tr><tr><td>Optimal temperature for ageing: fast charge [°C]</td><td>16</td><td>50</td><td>50</td></tr></tbody></table>

## 2.7. Scenarios

In this paper, we define several scenarios in order to answer the research question “how long could EV batteries last if their thermal management is optimized?”.

### 2.7.1. Hardware scenarios

First, we investigate purely passive, or hardware, scenarios, where we improve or deteriorate the thermal contact between the cooling fluid and the cell, without changing the thermal management strategy.

1. **Degraded contact:** we divide the heat transfer coefficient between the aluminum plate and the center of the cell by a factor of 2. $h_{cond} = h_{cond}^{ref}/2$. This scenario approaches the case of a soft case pouch cell, cooled by its edge [56].

2. **Ideal contact:** we set the heat transfer coefficient between the plate and the center of the cell to a very high value. $h_{cond} = +\infty \Rightarrow T_{cell} = T_{plate}$. This scenario simulates an optimization of the internal heat paths of the cell and an optimization of the interface material (here epoxy) between the bottom of the cell and the cold plate.

3. **Ideal BTMS:** we set both heat transfer coefficients between the center of the cell and the plate, and between the plate and the fluid, to a very high value. ($h_{cond}, h_{conv}) = (+\infty, +\infty$) ⇒ $T_{cell} = T_{plate} = T_{fluid}$. This scenario approaches direct cooling by a dielectric fluid.

### 2.7.2. Active strategies

Second, we investigate active, or software, scenarios, where we change the thermal management strategy while keeping the same thermal contact coefficient as the reference scenario. We define three strategies for which we assume that the vehicle is plugged to the grid at any time during the rest phases.

* **Precondition:** before every cycling phase (charge or discharge), the BTMS preheats or precools the cells, using grid energy, to optimal temperature.

We observed in Figure 3 (d) that the lower the temperature, the lower the degradation when the car is parked. Therefore, the two following strategies aim to decrease the car temperature when it is parked.
* **Valve**: we suppose that the battery pack is equipped with a valve that, when opened, lets external air flow in the battery pack. This leads to an increased exchange surface between the cells and outside. The valve opens when external temperature is inferior to cell temperature.

$$A_{ext} = \begin{cases} L_x^{pack} L_y^{pack}, & T_{cell} \le T_{ext} \\ 2L_x^{pack} L_y^{pack} + 2n_y^{cells} L_x^{pack} L_z^{pack}, & T_{cell} > T_{ext} \end{cases} \quad (19)$$

* **Parkcooling**: at the start of each parking phase, the BTMS cools the pack to 10 °C, using grid power, and actively keeps it at this temperature if the ambient temperature is above 10 °C. In this scenario, the parking phases are treated like the driving and charging phases: BTMS is activated, with target temperature $T_{opt} = 10$ °C. This leads to a non-zero BTMS power $P_{BTMS}$ during the rest phases and therefore additional electricity consumption.

From these 3 active strategies, we define 3 software scenarios: **precondition**, **precondition & valve**, and **precondition & parkcooling**.

## 2.8. Environmental evaluation of scenarios

For every scenario, in every climate, the algorithm returns battery lifespan $d_{EoL}$, the total distance driven by the vehicle until its battery capacity reaches 80% of its nominal capacity, in km, and electricity consumption, in Wh/km. Electricity consumption includes all the electricity consumed by the vehicle, even when the car is not in movement. It is calculated using equation 20.

$$E_{conso} = \frac{\int_{0}^{t_{EoL}} P_{bat}(t) dt}{d_{EoL}} \quad (20)$$

Where $t_{EoL}$ is the time when the battery has reached its end of life, $P_{bat}$ is the power flowing through the battery at any instant, and $d_{EoL}$ is the total distance driven by the vehicle until its battery's end of life.

Active scenarios will inevitably lead to an increase in electricity consumption. In order to find a tradeoff between lifespan increase and electricity consumption increase, we performed a Life Cycle Assessment (LCA) calculation. Python library brightway2 was used for LCA calculations, with background database ecoinvent version 3.9.1, and impact calculation methods were taken from EF3.1 no LT.

### Production phase:

For the production of the vehicle without battery pack, the activity "market for passenger car, electric, without battery (GLO)" was used. For the battery pack, the impacts are not the same for every chemistry, so different activities were used:

* **NMC-p**: "market for battery, Li-ion, NMC111, rechargeable, prismatic (GLO)"

* **NMC-c**: "market for battery, Li-ion, NMC811, rechargeable, prismatic (GLO)"

* **LFP-c**: "market for battery, Li-ion, LFP, rechargeable, prismatic (GLO)"

These activities represent the consumption mix of batteries in the Global geography. Note that ecoinvent 3.9.1 only includes prismatic cell format. Nonetheless, most of the environmental impacts come from active material production [65], so the difference between cylindrical and prismatic is small.

### Use phase:

If the electricity mix of the country where the vehicle is used is low-carbon, as in France or Norway, the tradeoff between lifespan and electricity consumption will not be the same as in high-carbon electricity mixes, like in India. In order to do a detailed comparison, we chose, for each climate, a
country where the electricity mix is low-carbon, and one where it is not. These countries are listed in Table 3.

<table><caption>Table 3: Choice of country for high and low carbon electricity mixes and each climate.</caption><thead><tr><th>Carbon intensity /Climate</th><th>Warm</th><th>Mild</th><th>Cold</th></tr></thead><tbody><tr><th>Low</th><td>Panama</td><td>France</td><td>Norway</td></tr><tr><th>High</th><td>India</td><td>China</td><td>Russia</td></tr></tbody></table>

Functional unit:

When *I* is an environmental impact, we compare *I*<sub>FU</sub> calculated with equation (21). This paper presents only the results for greenhouse gases emissions. Results for other impact categories can be found in the supplementary materials.

$$I_{FU} = \frac{I_{production} + I_{use}}{d_{EOL}} \qquad (21)$$

# 3. Results and discussion

## 3.1. Model validation

The electro-thermal model was validated with the data collected by Rosenberger and coworkers for a Tesla model 3 (58 kWh) [30]. They submitted the vehicle to repeated standardized highway driving cycles on a single-axis chassis dynamometer. The external temperature was set to 15 °C and the cabin heating and ventilation were deactivated. They measured the battery current, voltage, SOC, cells temperature and cooling fluid temperature. For this validation, the mass of the vehicle was set equal to the actual mass of Tesla model 3, namely 1825 kg [30]. The same was done for the battery mass and energy, respectively 458 kg and 58 kWh [30]. The temperature of the cooling fluid in the computation is set equal to the measured temperature for this test. Figure 4 shows a comparison between the measured and simulated SOC and temperature for the 3 cells under study. The same 20-minutes speed profile was applied 8 times.

<figure><img src="image_5.png" /><figcaption>Figure 4: Validation of the electrothermal model. Measured data is taken from [30]. Results are shown for the three cell models, namely NMC-p, NMC-c and LFP-c. (a) State of Charge of the battery as a function of time. (b) Cooling fluid temperature and cells temperature as a function of time.</figcaption></figure>

Figure 4 (a) illustrates a slight underestimation of battery SOC attributable to an overestimation of vehicle electrical energy consumption. Nevertheless, the simulated results demonstrate good
agreement with experimental measurements. Figure 4 (b) presents the cooling fluid temperature and the average cell temperatures for both measurements and simulations. The three simulated cells temperatures follow the same trend as the measured one. Discrepancies between simulations and measurements can be ascribed to variations in individual cell properties. The cells under investigation differ from those in the Tesla Model 3, resulting in disparities in internal resistance and, consequently, variations in heating behavior. Notably, the internal resistance of NMC-c cells increases significantly at low SOC, leading to a more pronounced temperature rise compared to measurements and other simulated cells. Despite these individual variations, simulated and measured temperature curves align closely during the initial 30 minutes of testing. Within this period, the cooling fluid temperature exceeds cells temperature, as the BTMS heats the cells to the desired temperature. Thus, cell temperature evolution during the first 30 minutes is predominantly governed by the BTMS rather than cell self-heating. This observation corroborates the validity of our BTMS model.

## 3.2. Reference scenario

### 3.2.1. Lifespan and electricity consumption

Table 2 gives the lifespan and electricity consumption for the reference scenario of each cell and climate. NMC-c has a low lifespan compared to the others because of its high calendar capacity loss rate. The reference consumptions obtained are close to the consumptions observed by Rosenberger and coworkers [30] for the Tesla model 3 on highway, namely 207 Wh.km⁻¹.

<table><caption>Table 2: Table of lifespan and electricity consumption for the reference scenario.</caption><thead><tr><th rowspan="2"></th><th colspan="3">Reference lifespan d<sub>EoL</sub> (× 1000 km)</th><th colspan="3">Reference consumption E<sub>conso</sub> (Wh/km)</th></tr><tr><th>Warm</th><th>Mild</th><th>Cold</th><th>Warm</th><th>Mild</th><th>Cold</th></tr></thead><tbody><tr><th>NMC-p</th><td>324</td><td>388</td><td>379</td><td>214</td><td>205</td><td>213</td></tr><tr><th>NMC-c</th><td>88</td><td>134</td><td>141</td><td>194</td><td>194</td><td>201</td></tr><tr><th>LFP-c</th><td>272</td><td>326</td><td>352</td><td>224</td><td>216</td><td>226</td></tr></tbody></table>

### 3.2.2. Main degradation modes

Figure 5 shows the share of total capacity loss of parking, fast charge, slow charge and driving phases. We observe a predominance of capacity loss during parking phases: 62% to 83% of overall capacity loss. Note that, in this study, time spent in parking phase accounts for 89% of total time spent. The European Joint Research Center assessed that parking time accounts for more than 92% of the total time spent for European cars [66]. Thus, even though the use profile chosen in this study is severe (29 000 km per year; highway and fast charge every weekend), calendar ageing is still predominant.
<figure><img src="image_6.png" /><figcaption>Figure 5: Share of total capacity loss during each phase, for the reference scenario of each cell and climate.</figcaption></figure>

We observe accentuated degradation for LFP-c in fast charge, especially in a cold climate. This is consistent with Figure 3. Most of the degradation occurs at the beginning of fast charge, when temperature is still between 16 and 30 °C. In addition, we observe a relatively high degradation for NMC-p during discharge, especially in cold climate. It happens at the beginning of discharge while the pack is cold and might be an artefact of the symmetrical ageing parametrization test plan.

### 3.3. Impact of hardware scenarios

Figure 6 (a) shows an example of the evolution of LFP-c fluid inlet and cell temperatures. The main difference between scenarios is the time necessary to reach the optimal cell temperature.

<figure><img src="image_7.png" /><figcaption>Figure 6: Simulation results for hardware scenarios; (a) LFP-c cell and fluid inlet temperatures as a function of time for a highway-fast charge-highway profile. Reference and 3 hardware scenarios; (b) Battery lifespan increase due to hardware scenarios, for all 3 cells and climates, compared to reference.</figcaption></figure>

In the figure, at the beginning of the first driving phase, for ideal BTMS, ideal contact, reference, and degraded contact scenarios, this time is respectively 5 min, 8 min, 11 min, and 14 min before reaching the optimal temperature of 16 °C. Thus, an ideal BTMS leads to a twice-lower time needed to reach the optimal temperature, compared to the reference. In the fast charge phase, the reference BTMS
reaches 37 °C, while the ideal BTMS reaches the optimal temperature of 50 °C. Note that, for the ideal BTMS scenario, inlet temperature does not reach 50 °C or 0 °C instantly because of the upper bound set on the thermal power of the BTMS. The time the cells spend at non-optimal temperature leads to higher degradation. Therefore, increasing the heat transfer coefficient between cooling fluid and cell leads to higher lifespan, as shown in Figure 6 (b).

Figure 6 (b) shows the relative lifespan increase, compared to reference, for the hardware scenarios. Degraded contact leads to a decrease in lifespan of 0% to 7%, ideal contact leads to an increase in lifespan of 1% to 8%, and ideal BTMS leads to an increase in lifespan of 2% to 20%. For all cells, we observe higher gains in cold climate than warm climate. There are three reasons for this. First, for NMC-p and NMC-c, discharge at low temperature leads to higher degradation than discharge at high temperature. Second, regenerative braking recharges the battery and, when it occurs at low temperature, this can lead to high degradation for all three cells. Third, for NMC-c and LFP-c, the BTMS lets the battery heat by itself before fast charging. In a cold climate, this self-heating leads to a lower temperature than in a warm climate, because the starting temperature is lower. Therefore, in cold climate, the temperature at beginning of fast charge is lower than in warm climate. This leads to higher degradation and therefore higher gains when the BTMS is improved. LFP-c cell is particularly sensitive to fast charge at low and medium temperatures; this explains the high lifespan increase of ideal BTMS in a cold climate. The high degradation at the beginning of fast charge could be avoided by actively preheating the pack on the highway section before fast charge, as it is done in Tesla model 3 for example [30].

The change in electricity consumption for all scenarios, compared to the reference consumption, is at a maximum of 1.4%. The reduction of Global Warming Potential (GWP) thanks to hardware scenarios is maximum 14% for LFP-c ideal BTMS in a cold climate. For all other cells, climates, and scenarios, maximum GWP reduction is 6%. Full results can be found in the supplementary materials.

Overall, the lifespan and GWP gains achieved by improving the hardware of the BTMS are low. In addition, improving the heat transfer coefficient would lead to additional weight, so the gain in GWP would be further limited. Moreover, the driving profile chosen is quite severe, and gains would be even lower when using a profile with fewer highway and fast charge phases. Still, thermal contact may become necessary to optimize in case of ultrafast charging, simply to be able to evacuate the heat generated by the cells.

### 3.4. Impact of active strategies

Figure 7 (a) shows an example of the evolution of NMC-c cell temperature for active scenarios and reference.
<figure><img src="image_8.png" /><figcaption>Figure 7: Simulation results for software, or active, scenarios; (a) NMC-c cell and fluid inlet temperatures as a function of time for a urban+road-pause-urban+road-pause-charge profile. Reference and 3 software scenarios; (b) Battery lifespan increase due to software scenarios, for all 3 cells and climates, compared to reference; (c) Battery electricity consumption increase due to software scenarios, for all 3 cells and climates, compared to reference.</figcaption></figure>

The effect of preconditioning can be seen at the beginning of driving and charging phases. Cell temperature is optimal directly at the beginning of cycling, instead of 11 min after the beginning, for the reference scenario. In this regard, the precondition scenario is an improvement of the ideal BTMS scenario. During the pauses, when the valve is active, cell temperature decreases faster than for the reference scenario, and reaches the outside temperature sooner. In the parkcooling scenario, cell temperature decreases to 10 °C just after the car is stopped. With the precondition strategy, the cell is always at optimal temperature during cycling. With valve and parkcooling strategies, calendar ageing is expected to be reduced.

Figure 7 (b) shows the relative lifespan increase, compared to reference, for the software scenarios. As expected, gains for precondition scenario are of the same order of magnitude, and higher, as ideal BTMS. They range from 2% to 27% lifespan increase, and are higher in cold climate. The valve scenario leads to 3% to 44% lifespan increase. This increase is higher in cold climate, because this strategy is efficient when cell temperature is higher than external temperature. Gains in cold climate range between 15% and 44%. The parkcooling scenario leads to 16% to 87% lifespan increase. Lifespan increase is particularly high in warm climates, 31% for NMC-p, 63% for LFP-c, and 87% for NMC-p. Overall, active strategies seem the most efficient way to improve battery lifespan.

However, for these strategies to work, the vehicle has to be plugged to a charger at any time, and its electricity consumption is expected to increase, especially for the parkcooling strategy. Figure 7 (c) shows the relative electricity consumption increase, compared to reference, for the software scenarios. The precondition & parkcooling scenario leads to an increase of electricity consumption of
7% to 23%. Electricity consumption is higher in warm climate, where the external temperature is well above 10 °C, respectively 13%, 20% and 23% increase for NMC-p, NMC-c and LFP-c cells. To reduce electricity consumption, we investigated a 4th active scenario: precondition & parkcooling with a thermally insulated battery pack. The pack is insulated with 2 cm insulating material (glass wool, λ = 0.037 W m⁻¹K⁻¹ [55]). Lifespan increase is the same as if the pack was not insulated, but electricity consumption increases only up to 11%, compared to reference.

For these active scenarios, it is necessary to find a tradeoff between electricity consumption and
lifespan. If we look at greenhouse gases emissions, this tradeoff will be different if the electricity mix
is low-carbon or high-carbon. In high-carbon electricity mix, increased consumption has a high impact
on climate change, so active scenarios may not be beneficial. Figure 8 shows Global Warming Potential
(GWP) change, compared to reference, for the software scenarios.

<figure><img src="image_9.png" /><figcaption>Figure 8: Change in global warming potential (EF3.1 no LT) for active scenarios and 2 carbon intensity of electricity mix.</figcaption></figure>

It shows that active scenarios generally lead to GWP decrease when the electricity mix is low-carbon, while it is generally not the case when the electricity mix is high-carbon. The higher gains are obtained for precondition & parkcooling with an insulated pack for NMC-c in Panama, with 29% GWP decrease, and precondition & valve or parkcooling for LFP-c in Norway, with 26% GWP decrease. Results with other environmental impacts can be seen in the supplementary materials.

Overall, improving the thermal management system hardware of electric vehicles can achieve some
lifespan and environmental gain. Still, those gains are relatively limited. It appears more beneficial to
precondition the battery pack, when possible. In addition, tackling calendar ageing, in countries where
the electricity is low-carbon, can lead to even higher gains.

4. Impact of temperature gradients

The model used in sections 2 and 3 assumed the cells and the pack to be thermally and electrically homogeneous. This means that the model calculates 1 temperature value, 1 current value, and 1 SOH value for all the cells and all the parts of the cell. In reality, there are some temperature gradients between the cells and inside each cell. This may have an effect on battery pack ageing. In the literature, some teams find an effect of cell temperature gradients on ageing [31,32], while others find no clear
evidence that gradients accelerate ageing, at cell level [67–70], and at module level [71]. In this section, we propose to use our model to investigate this issue on cell level. Because of the cold plate located under the cells, a temperature gradient is expected to arise between the bottom and the top of the cells.

The cell is modelled as two half-cells, one top and one bottom, connected in parallel (Figure 9 (a)-(b)). Current, temperature, *SOC* and *SOH* are computed for each half-cell. Detailed modelling and equations can be found in the supplementary materials. For the reference scenario, we compare the lifespan obtained using the homogeneous model, with the lifespan obtained using the heterogeneous model.

<figure><img src="image_10.png" /><figcaption>Figure 9: Modelling and results of cell gradients. (a) Equivalent Circuit Model (ECM) of a battery cell (b) Lumped thermal model of battery pack (c) NMC-p cell temperatures as a function of time for a highway-fast charge-highway profile. Reference homogeneous and reference heterogeneous scenarios (d) Battery lifespan increase when the cell is discretized with 2 points, for all 3 cells and climates, compared to homogeneous reference.</figcaption></figure>

1 year is computed in approximately 40 minutes on an Intel Core i7-7920HQ CPU (3.10GHz). This is twice longer than for a homogeneous cell. Figure 9 (c) shows an example of the evolution of cell temperature and half-cells temperatures. We observe a temperature gradient during the phases when the BTMS is active, like heating at the beginning of the cycle, and cooling to remove the heat produced during fast charge. The maximal temperature difference between top and bottom for NMC-p, NMC-c and LFP-c cells is respectively 10.8 °C, 7.6 °C and 6.0 °C. NMC-p is two times taller than the other cells, it explains the higher temperature difference. The maximum difference of *SOH* between the two half-cells is observed for NMC-p in a cold climate. It is 1.1%.
Figure 9 (d) shows the relative lifespan difference between the homogeneous and the heterogeneous cell model. This difference is maximal for LFP-c in cold climate, and equals 1.6%. For all other cells and climates, this difference lies between 0.0% and 0.5%. We consider this difference to be negligible. Therefore, temperature gradients seem to have very low effect on EV batteries ageing, even when temperature differences are up to 10 °C. The assumption of homogeneous cell and pack is thus sensible. This assumption simplifies the model and divides computational cost by a factor of 2.

Still, the major assumption of this section is that one cell can be modelled as two cells in parallel, with half capacity. Due to the presence of electrolyte, and mechanical effects arising from SEI growth, this assumption must be challenged. In addition, effects of heterogeneities might become visible with ultrafast charging, when C-rate is superior to 3C.

## 5. Conclusions

This work presented an electro thermal model coupled with degradation for three battery cells chemistries and three climates, under real-world driving profiles. Battery temperature is controlled by a thermal management system in order to minimize capacity loss, improve performance, and reduce safety concerns. Then, different scenarios were investigated. First, several improvements of the heat transfer coefficients between cooling fluid and cell were assessed. Then, active strategies were tried, like preconditioning the pack to optimal temperature before driving and charging, or cooling the pack during parking phases.

One main finding of this study is that capacity losses in parking phases account for 62 to 83% of total capacity loss, the warmer the climate the higher the calendar ageing. Therefore, decreasing degradation in cycling phases can only have a limited effect on lifespan. Improving the thermal contact between the cooling fluid and the center of the cell leads to an average of 3.4% lifespan increase in a warm climate and 11% lifespan increase in a cold climate, with little effect on electricity consumption. Similar gains are achieved when preconditioning the battery pack to optimal temperature before cycling. Instead, tackling calendar capacity losses leads to promising lifespan gains. Maintaining the pack to 10 °C when the car is parked increases its lifespan in a cold climate by 28% in average, at the cost of 9% electricity consumption increase, and increases its lifespan in a warm climate by 61%, at the cost of 19% electricity consumption increase. With thermal insulation, electricity consumption increase can be limited to an average of 5% in a warm climate. This solution leads to an average of 17% decrease of CO₂ emissions when the electricity mix is low-carbon, and only 1.6% when it is high-carbon.

We also used our model to validate the assumption of homogeneous battery cells. This assumption leads to a maximum lifespan deviation of 1.6% compared to a cell discretized with 2 elements, with a temperature difference of up to 10 °C between the elements. Therefore, we find that temperature gradients do not have a visible effect on battery lifespan for electric vehicles.

This paper presented a new overview of the potential gains of thermal management solutions. It was found that improving the heat transfer coefficient between cooling fluid and cell, as direct cooling would do, for example, does not lead to large gains. Instead, manufacturers should tackle calendar ageing, for example by insulating the pack and programming the vehicle to cool the pack while it is parked, providing the electricity used is low-carbon. This promising solution should be further investigated and optimized.

### CRediT authorship contribution statement
**Mathis Boutrouelle:** Conceptualization, Methodology, Software, Investigation, Writing - Original draft.

**Remy Panariello:** Conceptualization, Methodology, Writing - Reviewing and Editing. **Yvan Reynier:** Conceptualization, Writing- Reviewing and Editing.

**Eric Mayousse:** Writing - Reviewing and Editing.

**Sebastien Martinet:** Supervision, Writing - Reviewing and Editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors would like to thank Téo Lavisse for sharing his model and his suggestions of improvements; Fabien Perdu for his critical point of view on the study; Christophe Morel for his help with the thermal model; Samuel Bardy and Mehdi Bey for their help with the cell equivalent circuit parameters.

Data availability

Data will be made available on request, except NMC-p data that is confidential.

Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work the authors used “Le Chat” by Mistral AI in order to improve readability and language. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.

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