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Thermal management of batteries
CHAPTER
Thermal management of batteries
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6.1 Introduction Thermal transport and thermal management in batteries are important issues with direct impact on the performance and safety as well as on the reliability of the energy conversion and storage behavior. Basically the heat generated during charging or discharging due to ohmic (Joule heating) and non-ohmic mechanisms (internal electrochemical processes) has to be transported by conduction through the various materials and material interfaces within the cell before it is removed from the outer cell surface by convection and/or radiation to the ambient. The generation of heat and the internal conduction of it have to be analyzed by considering the interaction with the electrochemical and charge transport processes. However, the thermal processes in battery cells take place over multiple length scales all the way from atomistic scales via the electrode material scales to the macroscales of the complete energy storage devices. This means that depending on the problem or phenomena being of interest, different modeling and simulations approaches have to be applied. This will be discussed later in this chapter. If batteries are not kept with the optimum operational limits, the performance will decay. For most batteries, the temperature should be kept within 5e30 C. Also it is preferable if the temperature variation between the cells in a pack is kept within 5 C. It is also known that the battery life is curtailed if its temperature is above 40 C, even if this is caused by the ambient temperature rather than by the loading. Similarly, extremely cold climates (below freezing point) may limit the amount of the current that can be drawn from the battery. In the past, the largest battery packs did not always need any special cooling as the physical size of the packs was sufficient and the flow of the current was not large compared to the overall capacity of the battery pack. However, as faster battery charging rates are demanded with recharge power above 200 kW to deliver times of 30 min or less, the higher performance electric vehicles with a requirement for consistent performance and adequate durability has implied that special thermal management methods for the battery packs are required.
Hydrogen, Batteries and Fuel Cells. https://doi.org/10.1016/B978-0-12-816950-6.00006-3 Copyright © 2019 Elsevier Inc. All rights reserved.
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6.1.1 State functions (SOF) The factors affecting the capacity, energy and power output of a battery, are correlated and depend on the particular technology being used. To operate an electric vehicle, the battery management system (BMS) should be able to inform about the power and energy status of the battery. So-called state functions are used and the most common ones are the state of function (SOF), state of charge (SOC) and state of health (SOH). Such functions operate on different time scales. SOF represents the power capability and operates on second or millisecond basis while SOC is on minute scale and SOH is on monthly or yearly basis. The SOF refers to the capability to fulfill the demand, e.g., the power requirement, at a specific time. The SOF can be estimated in some different ways and is strongly dependent on the SOC and SOH as well as the temperature. The accuracy of measurements of voltage, current and temperature is important for the SOF prediction.
6.1.2 State of charge (SOC) The state of charge is defined as the ratio of the available capacity Q(t) and the maximum possible charge that can be stored in a battery, i.e., the nominal capacity Qn. SOCðtÞ ¼
QðtÞ Qn
(6.1)
A fully charged battery has SOC 1 or 100% while a fully discharged battery has an SOC of 0 or 0%. The rated capacity or the capacity at the beginning of life (BOL) is commonly used as the reference value. SOC is the key parameter to properly control the electrical vehicle and to secure the power responses due to changes in operating conditions. The factors affecting the SOC significantly on a short time basis are temperature and the C-rate. The underlying fundamental subjects of the SOC are thermodynamics, electrochemistry and material constraints of the considered battery technology and involved chemistry. However, no simple method is available to accurately estimate the SOC. The SOC level is related to the properties of the active electrode materials and different active materials behave differently. For a Li-ion cell, 100% SOC means a state where all cyclable lithium ions are inserted in the negative electrode material, and at 0% SOC all cyclable lithium is found in the positive electrode. For cells based on lithium-cobalt oxide, the amount of cyclable lithium is less than the total amount of lithium in the active materials due to stability issues of the lithium poor structure. Sometimes the depth of discharge (DOD) is used to describe how deeply the battery has been discharged. In most cases it is related to SOC by DOD ¼ 100 SOC(%).
6.2 Thermal runaway
In real vehicle applications, it is very hard to accurately measure the lithium content in an electrode but instead the SOC has to be estimated based on voltage, current and temperature measurements in real time.
6.1.3 State of health (SOH) The state of health is an indicator of the remaining battery capacity compared to the capacity at BOL. The aging processes, which lower the SOH, start as soon as the cells are assembled. As the battery ages, the SOC will decrease until the battery can no longer fulfill the requested performance and the end of life (EOL) has been reached. SOH is not a physical quantity but it depends on parameters like number of charge-discharge cycles, capacity and power fade, and internal resistance. The aging process of a battery is complex and depends on the involved mechanisms. The aging depends on the vehicle usage, battery and cell design. Temperature, SOC range, energy and power conditions and time are essential parameters. For further reading about state functions Ref. [1] is recommended.
6.2 Thermal runaway The generation of heat in batteries deteriorates the performance and life time of the batteries but can also lead to the phenomenon of thermal runaway. This phenomenon is caused by an over-charging or an over-discharging rate which produces more internal heat than the battery can dissipate. The generated heat which cannot be dissipated causes the cell temperature to rise. This temperature rise makes the chemical reactions within the cell to take place at a faster rate. Accordingly, the increased rate of the chemical reactions generates even more heat that cannot be dissipated. If this phenomenon occurs, failure and destruction (by explosion and fire) of the battery may happen. Failure of a single cell can lead to failure of the whole battery pack, in particular if the cells are connected in series. Thermal runaway and the destruction it causes might be dangerous as the chemicals being released are toxic and in extreme cases the thermal runaway can cause fires and make the battery to explode. Batteries connected to a charger must be temperature controlled and the charging voltage and current must be limited. Once thermal runaway has begun, it cannot stop itself. The battery will be heated up and accordingly its internal resistance to the charging current will be reduced. Then it permits more current which creates additional heat and due to this, the notation runaway is used. The only way to stop this is to remove the battery from the facility, install a new battery and then dispose the faulty battery properly. Establishment of regular preventative maintenance is important to identify problematic cells before failure occurs and then adjust the charging voltage and
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FIG. 6.1 Thermal runaway.
current to ensure that the battery is not overcharged. The ambient air temperature must also be properly maintained. It is also recommended to provide adequate ventilation and forced convective cooling. Fig. 6.1 illustrates the processes in thermal runaway. There are several mechanisms or processes that can trigger the event of thermal runaway, namely over-charge, over-discharge, external short-circuit, over-heating, internal short-circuit caused by crash or dendrite formation or impurities caused by the manufacturing. Additional information about thermal runaway can be found in Refs. [2e4].
6.3 Importance of temperature Batteries are affected by the environment they are operating in, i.e., temperature and humidity. The temperature affects the operation of the electrochemical system, round-trip efficiency, charge acceptance, power and energy capability, reliability, life and lifecycle cost. If a battery is too hot or too cold, the battery will behave quite differently than at the normal and designed operating specifications. This is a consequence of using the battery in an environment it was not designed to be used in. If a battery is exposed to extreme weather conditions, negative effects can occur. For instance, it may stop working, bulge, bubble, melt, damage the device it is used in, generate smoke, create sparks or flames, expand or contract and during severe circumstances it may blow up. An uneven temperature distribution in the battery pack will lead to a localized detoriation. Accordingly, temperature uniformity within a single cell and from cell to cell, is important to achieve maximum lifecycles of the cells, packs and battery systems. Between the two electrodes in a battery, an electric current runs due to the voltage differential between the anode and cathode. At the same time an electrochemical reaction takes place inside the battery to replenish the electrons. When
6.3 Importance of temperature
FIG. 6.2 Battery capacity drop at various temperatures.
FIG. 6.3 Influence of operating temperature.
the ambient temperature is changing, the electrons within the battery are affected. An increase in temperature excites the electrons while a decrease in temperature inhibits electrons. Fig. 6.2 shows the influence of temperature on the voltage versus time characteristics. It is evident that as the temperature is reduced the battery capacity drops rapidly. Fig. 6.3 shows the power limit during discharge is affected by the operating temperature. The optimal or recommend temperature range is between 15 and 35 C. Above 35 C the degradation processes start and the aging is accelerated. Below 15 C the electrochemistry becomes sluggish and for Li-ion batteries lithium plating and dendrite formation may occur. For further information, see also Refs. [5e7].
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6.4 Examples of thermal management systems There are a number of ways in which cooing of a battery pack can be done. The system for this is generally called the battery thermal management system (BTMS). The tasks of the BTMS are to maintain the operating temperature within 5e30 C, maintain the temperature difference between any cells in the pack to be less than 5 C, prevent thermal runaway, maximize the useful energy from cells and pack, and use a small amount of energy for operation. The types of BTMS are classified as active or passive systems. In a passive cooling system, the heat is dissipated through natural convection and thermal radiation. These have no moving parts and are sufficient if a large space is available or if low performance (i.e., low charge and discharge rates) is required. The thermal inertia of the system is important and sometimes this is increased by adding more thermal mass. Active cooling systems rely on a cooling fluid, which is forced through the battery by a fan (air cooling) or pump (liquid cooling). For electric vehicles on the market currently, both air cooling and liquid cooling are used. There is also a development trend to use phase change materials (PCMs). Higher performance electric cars seem to apply liquid cooling as the high heat capacity of a liquid allows for better control of the heat dissipation. Some caution is, however, needed as using a conducting liquid through an electric environment is very hazardous and then isolation should be applied. The head wind created as the vehicle moves can be used for aiding the cooling but is not sufficient by its own. Generally, also the battery packs are shielded in layers of protective casing. Accordingly, the head wind cooling is limited. General descriptions of thermal management of batteries are presented in, e.g., Refs. [8e10].
6.4.1 Air cooling For applications of batteries where extreme performance or heavy duties are not required, air cooling can be employed. BTMS0 based on air cooling are generally low cost alternatives and less complicated than liquid cooling systems. However, with an air cooled system it is hard to maintain an even temperature distribution across the battery pack. In the simplest form of an air cooling system, the air is forced by a fan over the batteries being lumped together. The air is not confined to channels within the battery pack but is directed over different parts of the battery pack through baffles. A disadvantage of this simple system is that the heat dissipation can only be controlled by the air speed or the fan capacity. However, in advanced air cooling systems the air flow is directed to various regions of the battery pack by employing different channels. The channels increase the overall needed space and accordingly the volume of the battery pack is increased. Fig. 6.4 illustrates air cooling systems.
6.4 Examples of thermal management systems
FIG. 6.4 Illustration of air cooling of a battery pack.
6.4.2 Liquid cooling BTMS0 based on liquid cooling are classified as: cooling fins, cooling matrix and cooling plates. The liquid might be water, glycol, oil, acetone or refrigerants. Cooling fins dissipate heat from the wide face of a cell. A single fin is placed between two adjacent cells. Fig. 6.5 illustrates the principle. The cooling fin has a series of channels running through it. This cooling method is suitable for both pouch cells and rectangular prismatic cells. It occupies a small space and provides direct cooling to at least one face of a cell. Among the disadvantages are the high design cost and that leakage between the interfaces may occur if the sealing is not adequately designed.
FIG. 6.5 Liquid cooling with a cooling fin.
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The method of a cooling matrix is commonly employed for cylindrical cells. A hollow cooling shell is manufactured with holes to contain the cells. The cooling liquid enters at one end of the jacket and exits at the diagonal end. Generally, the cooling matrix is robust and helps to maintain the temperature limits by surrounding the cell with large thermal mass. The cooling jackets are welded leaving only spigots at the end where sealing must be considered. The disadvantage with the cooling matrix method is that it is space consuming and reduces the battery pack energy density. The weight is also increased by the metal jacket and the cooling liquid. Fig. 6.6 illustrates the cooling matrix method. In a so-called cooling plate, a cold liquid is flowing in serpentine or concentric channels and by convection the cell generated heat is dissipated. Cooling plates
FIG. 6.6 Illustration of (A) a cooling matrix for cylindrical cells, (B) cooling matrix for rectangular cells.
6.4 Examples of thermal management systems
FIG. 6.7 Illustration of liquid cooling by a cooling plate.
present a cost effective solution for liquid cooling. One drawback of cooling plates is added weight to the pack. Another is that the cooling plates are commonly deployed underneath the cells. This is not the most effective means to dissipate the heat as the cell is hotter close to the tabs at the top because of the higher current density there. Fig. 6.7 illustrates the cooling plate layout. Evaluation of liquid versus air cooling has been presented in Ref. [11].
6.4.3 Cooling by phase change material (PCM) PCM has been used for many years in building thermal systems, spacecraft thermal systems, medical supply shipping, chemical reaction exotherm smoothing and to some extent in HVAC (heating, ventilation and air conditioning) for vehicles. PCMs often rely on solid-liquid transition or vice versa in a small temperature range but the selection of material will depend on the application. The PCM absorbs or releases a large amount of energy compared to conduction heat transfer. As it absorbs heat it is converted into liquid state and vice versa as heat is rejected. The ability to store thermal energy, generated in the battery, at an almost constant temperature (the melting temperature of the PCM), is the key advantage for BTMS. Different phase changing materials with different characteristics are available on the market. Paraffin wax is such a substance which in its normal state is a semiviscous solid. Paraffin-epoxy mixtures are also used. Various salts are also used as phase change materials. PCMs have in general a low thermal conductivity and thus it is important to find methods to increase the thermal conductivity of PCM. PCM pouches and plastic packs are available on the market and such can be placed next to the battery surface for cooling. PCM can also be used for heating in extremely cold climates.
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FIG. 6.8 Characteristics of a PCM material.
PCM improves the battery cost, efficiency and weight compared to active systems. The PCM material has high fusion heat which stores and releases the amount of heat during melting and solidification at a certain temperature. Fig. 6.8 illustrates that when the temperature is below the melting point, the PCM is in solid state and heat is absorbed as sensible heat as the temperature rises. As the melting point is reached, heat is absorbed and stored as latent heat until the latent heat reaches the maximum without a temperature change. After that the PCM is in the liquid state. Heat is then absorbed as sensible heat and the temperature rises. The melting point of the PCM depends on the particular material. The function temperature of the PCM should be higher than the ambient temperature but it must be lower than the operating temperature of the battery. Fig. 6.9 shows a specific case where active air cooling is compared with PCM passive cooling. The battery temperature is displayed for two air flow rates (given by Reynolds numbers) and it is obvious that none of the air cooling cases can keep the battery temperature below 55 C, which on the other hand is possible with the PCM. This shows the strength of PCM cooling. Additional information on PCM for thermal management can be found in Refs. [12,13]. A comparison between air cooling and PCM cooling was presented in Ref. [14].
6.4.3.1 Heat pipes with phase change Heat pipes are known to be very efficient to passively transport heat. Phase change (vapor-liquid) is used to remove the heat from the source. A heat pipe is a closed
6.5 Mathematical modeling and experimental approaches
FIG. 6.9 Comparison of air cooling and PCM cooling. Based on Sabbah et al. [14].
loop pipe with two major segments, namely the evaporator and the condenser. The heat generation part is attached with the evaporator while the condenser removes the heat to the surroundings. An overview of the heat pipe technology is available in Ref. [15].
6.4.4 Drawbacks of thermal management systems The BTMS has also some drawbacks. It increases the complexity of the system, consumes energy for the operation, reduces the reliability of the system and also add up to the weight and total cost.
6.5 Mathematical modeling and experimental approaches Mathematical modeling is a way to estimate battery performance. Battery modeling or mathematical description of batteries is nowadays more accessible to battery developers as general purpose computational tools are available. The approach can be applied in estimation of the battery performance and in battery design as well as in developing and evaluation of thermal management methods. For a complete modeling of a battery, heat and mass transport, charge transport, the electrode kinetics and the processes at the electrode-electrolyte interfaces need to be considered. However, sometimes it is possible to use simplified models. So for instance the modeling tools can be classified as (a) first-order or lumped capacitance thermal and fluid models, (b) 1-D and 2-D thermal and fluid performance models, (c) 1-D vehicle integrated thermal and fluid flow models, (d) 3-D electro-thermal models, (e) 3-D electrochemical-thermal model. The detailed modeling approaches require: solution of the electron current via, e.g., the Butler - Volmer equation (see Chapter 2), conservation of charge (electrons and ions) and energy conservation. The experimental tools to design and evaluate battery thermal management systems are exemplified by (a) isothermal calorimeters and battery testers, (b) infrared
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thermal imaging, (c) thermal conductivity meters, (d) heat transfer characterization setup and (e) battery thermal testing loops. For an existing battery, the problem is to estimate how the battery will perform and specific conditions demanded by the user. At the stage of designing a battery, it is of interest to estimate how the design impacts the performance. The various physical mechanisms including battery chemistry etc. need to be considered. Examples of studies considering the general energy balance and heat generation of batteries are refs. [16e20].
6.5.1 Simple energy balance of a battery Fig. 6.10 show a sketch of common battery. Energy is entering and leaving the battery poles. Inside the battery, energy or heat is generated and on the surfaces exposed to the surrounding environment, energy losses occur by convection and radiation. Mathematically the energy balance reads: dE ¼ E_ generated E_ losses þ E_ in E_ out (6.2) dt If the battery is assumed to have a uniform temperature Ts, the energy accumulation rate can be written as dE dTs ¼ mcp (6.3) dt dt The energy loss from the surface is composed of convective and radiative heat transfer as given below Eloss ¼ hAðTs Ta Þ þ εFA T4s T4a (6.4) where h is the convective heat transfer coefficient, A is the surface area, Ta the ambient temperature, ε the surface emissivity and F the view factor between the battery surface and the surroundings. The generated heat or energy in the battery consists of contributions from the electrochemical reactions, phase changes, mixing effects and joule heating (ohmic losses). Expressions will be given in a later section. Fig. 6.11 illustrates the temperature-time history of a certain simple battery. The influence of the discharge rate is evident.
FIG. 6.10 Energy flow in a simple battery.
6.5 Mathematical modeling and experimental approaches
FIG. 6.11 Temperature versus time for various discharge rates. Based on Ref. [21].
6.5.2 Energy balance of a non-isothermal battery The energy balance in Section 6.5.1 can be extended to include heat conduction inside the battery and then the temperature is not uniform. The heat balance reads vT ¼ V$kVT þ Q_ generated (6.5) vt where k is the thermal conductivity of the battery material and Q_ generated is the generated heat per unit volume. The boundary condition at the battery surface is now written as rcp
vT ¼ hðTs Ta Þ þ εF T4s T4a vn where kn is the thermal conductivity in the surface normal direction. kn
(6.6)
6.5.3 Governing equations for convective cooling of a battery pack For analysis of air or liquid cooling of batteries also the fluid flow and convective energy transport need to be taken into account and the flow channels need separate treatment. Appropriate boundary conditions need to be formulated. Then the mass conservation equation, the Navier-Stokes equation and the heat transport equation have to be numerically solved, [22]. These equations are here given for a steady state flow field but the energy exchange is time dependent. The case of a turbulent flow is included by incorporating a turbulent viscosity and a turbulent diffusivity.
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Mass conservation: vui ¼0 vxi
(6.7)
Navier-Stokes equation:
( " )# vui vp v vui vuj ¼ þ þ ðm þ mturb Þ ruj vxi vxj vxj vxj vxi
Convective-diffusive unsteady heat transport: vT vT v mturb vT ¼ þ Q_ generated lþ rcp þ rcp uj vt vxj vxj Prturb vxj
(6.8)
(6.9)
Eq. (6.9) is written in the way of a conjugate formulation so it can also be applied inside the cells as well but then the thermophysical properties are for the battery pack and the generated heat is inside the cells. The treatment of turbulence is here illustrated by given the equations for the socalled k-ε model including the formula for the turbulent viscosity. Further details can be found in Ref. [23]. Turbulent kinetic energy k: " #2 " # vk v mturb vk mturb vui vuj ruj þ ¼ þ rε (6.10) mþ vxj vxj sk vxj 2 vxj vxi Turbulent kinetic energy dissipation ε: " #2 " # vε v mturb vε ε mturb vui vuj ε2 þ C1 ruj ¼ þ C2 r mþ vxj vxj k 2 vxj vxi sε vxj k
(6.11)
The turbulent viscosity mturb is calculated as: ε2 (6.12) k The common constants in the equations above and the appropriate boundary conditions can be found in, e.g., Ref. [23]. mturb ¼ rCm
6.5.4 Heat generation The heat generation in electrochemical devices is a complex phenomenon involving the operating voltage, current, cell size and materials of the components etc. The generated heat by the battery cells depends on the temperature of the cells, the discharge rate and the state of charge (SOC). In single cells of a battery or a fuel cell, the heat sources are comprised of reversible and irreversible processes and, governed by one term representing the reversible entropic heat generation and a second
6.5 Mathematical modeling and experimental approaches
term representing the irreversible heat by ohmic heating (Joule heating) and losses incurred to facilitate the reactions in the activation region. See also Chapters 2 and 9. Here the heat generation equation developed by Bernardi et al. [17] is commonly adopted. I dEoc Q_ generated ¼ Eoc E T (6.13) Vtotal dT where I is the total current of the battery, Vtotal is the total volume of the core region, Eoc the open circuit voltage, E the operating voltage and T the temperature. The limitation of this equation is that the voltage or potential terms must be obtained and the effect of temperature on the electrochemical behavior cannot be evaluated. However, a more rigorous electrochemical model to theoretically predict the heat generation rate can be established and then phase change and mixing in the cell are considered, see Refs. [7,17]. However, for large batteries resistance heating in the current collectors might be significant relative to the electrochemical heat generation rate even for well designed batteries. Additional terms then appear in Eq. (6.13).
6.5.5 Multi-scale multi-dimensional modeling Depending on what level of details being of interest, different mathematical approaches are necessary. This is because the various phenomenological processes occur at quite different scales. At the smallest scales, i.e., in the particle domain, the kinetics of the charge transfer and for a lithium-ion battery, the Li transport in active particles is analyzed. In the electrode domain, charge balance in solid composite electrode matrices as well as charge balance in the liquid pore channels have to be investigated. In the electrolyte, the Li transport needs consideration. At the cell domain scale, energy conservation needs consideration and in the current collectors, the charge conservation should be analyzed. Then at module and system scale more overall conditions like thermal management, safety and control strategies are considered. Fig. 6.12 summarizes the multi-physics and multi-scale phenomena for lithiumion battery systems at different length scales. The methods of modeling and simulations are depending on the time and length scales involved. From the smallest (atomic scale) to the largest (continuum formulation), the methods might be classified as: quantum chemistry, molecular dynamics, kinetic Monte Carlo approaches, meso-scale methods (e.g., lattice Boltzmann approaches) and finally continuum methods based on computational fluid and solid dynamics. In general, molecular dynamics (MDs) based approaches have been used for atomistic modeling of thermal transport in materials and interfaces of engineering applications but for thermal transport in electrochemical materials and interfaces, works are lacking. However, atomistic modeling methods can only handle a small number of molecules and accordingly reducedeorder models based on MD, like coarse-grained MD, need to be developed, [24,25].
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FIG. 6.12 Multi-physics and multi-scale phenomena in lithium-ion batteries.
For length scales of single cells and battery packs, the thermal transport is governed by the well-established continuum formulated energy conservation equations, see Section 6.5.3. In some cases, analytical solutions can be found but more commonly numerical solutions methods (like CFD) are more suitable. Nevertheless, due to the large scale and complexity of cells and battery packs, detailed thermal modeling is not always possible and also some reduced-order models and parameterized models are needed to find a compromise between computational efforts and accuracy. Lithium ion electrodes constitute heterogeneous mixtures of multiple materials including the active material, binders etc. The thermal transport through these materials is not well known. Analytical models for predicting the thermal conductivity of such heterogeneous materials are requested. Theoretical models are needed to understand how interfacial thermal transport is affected by the electrochemical ambient, nature of surfaces and the presence of intermediary molecules. Similar but more detailed descriptions for analysis of fuel cells will be presented in Chapter 10.
6.6 Available softwares Most battery modeling and simulation are carried out using general-purpose tools like MATLAB, ANSYS and COMSOL. Nevertheless, the growing importance of battery modeling has resulted in development of customized computational software. The most comprehensive software for battery design, modeling and simulation is the Battery Design Studio. The Battery Design Studio is mainly a user interface to access battery models and it provides a user friendly environment for battery design and simulation as well as
References
analysis of battery data. The software includes routines for sizing various cell geometries (stacks or spirally wound), models for simulation of battery behavior, a database and tools for visualization and analyzing battery data. Links to the softwares are given by Refs. [26e28].
6.7 Summary The temperature of a battery is important as it affects the life, performance, reliability and cost of the batteries for, e.g., electric vehicles. The battery life and performance are very sensitive to temperature exposure. Generally thermal management by some method is needed. At high temperature the primary considerations are on life, safety and non-uniform aging due to thermal gradients. Typically cooling is required in hot environments, during moderate to large current demands during operation and during fast charging. At low temperature the primary considerations concern the performance and damage due too fast charging. Typically heating is required in cold environments during charging and discharging. To reduce the over-sizing of batteries at BOL, thermal control might be a good option, particularly in hot and cold climates. Due to the wide range of scales of the multi-physics phenomena and processes in lithium-ion batteries, different computational approaches are needed.
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Thermal management of batteries
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6.1 Introduction Thermal transport and thermal management in batteries are important issues with direct impact on the performance and safety as well as on the reliability of the energy conversion and storage behavior. Basically the heat generated during charging or discharging due to ohmic (Joule heating) and non-ohmic mechanisms (internal electrochemical processes) has to be transported by conduction through the various materials and material interfaces within the cell before it is removed from the outer cell surface by convection and/or radiation to the ambient. The generation of heat and the internal conduction of it have to be analyzed by considering the interaction with the electrochemical and charge transport processes. However, the thermal processes in battery cells take place over multiple length scales all the way from atomistic scales via the electrode material scales to the macroscales of the complete energy storage devices. This means that depending on the problem or phenomena being of interest, different modeling and simulations approaches have to be applied. This will be discussed later in this chapter. If batteries are not kept with the optimum operational limits, the performance will decay. For most batteries, the temperature should be kept within 5e30 C. Also it is preferable if the temperature variation between the cells in a pack is kept within 5 C. It is also known that the battery life is curtailed if its temperature is above 40 C, even if this is caused by the ambient temperature rather than by the loading. Similarly, extremely cold climates (below freezing point) may limit the amount of the current that can be drawn from the battery. In the past, the largest battery packs did not always need any special cooling as the physical size of the packs was sufficient and the flow of the current was not large compared to the overall capacity of the battery pack. However, as faster battery charging rates are demanded with recharge power above 200 kW to deliver times of 30 min or less, the higher performance electric vehicles with a requirement for consistent performance and adequate durability has implied that special thermal management methods for the battery packs are required.
Hydrogen, Batteries and Fuel Cells. https://doi.org/10.1016/B978-0-12-816950-6.00006-3 Copyright © 2019 Elsevier Inc. All rights reserved.
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6.1.1 State functions (SOF) The factors affecting the capacity, energy and power output of a battery, are correlated and depend on the particular technology being used. To operate an electric vehicle, the battery management system (BMS) should be able to inform about the power and energy status of the battery. So-called state functions are used and the most common ones are the state of function (SOF), state of charge (SOC) and state of health (SOH). Such functions operate on different time scales. SOF represents the power capability and operates on second or millisecond basis while SOC is on minute scale and SOH is on monthly or yearly basis. The SOF refers to the capability to fulfill the demand, e.g., the power requirement, at a specific time. The SOF can be estimated in some different ways and is strongly dependent on the SOC and SOH as well as the temperature. The accuracy of measurements of voltage, current and temperature is important for the SOF prediction.
6.1.2 State of charge (SOC) The state of charge is defined as the ratio of the available capacity Q(t) and the maximum possible charge that can be stored in a battery, i.e., the nominal capacity Qn. SOCðtÞ ¼
QðtÞ Qn
(6.1)
A fully charged battery has SOC 1 or 100% while a fully discharged battery has an SOC of 0 or 0%. The rated capacity or the capacity at the beginning of life (BOL) is commonly used as the reference value. SOC is the key parameter to properly control the electrical vehicle and to secure the power responses due to changes in operating conditions. The factors affecting the SOC significantly on a short time basis are temperature and the C-rate. The underlying fundamental subjects of the SOC are thermodynamics, electrochemistry and material constraints of the considered battery technology and involved chemistry. However, no simple method is available to accurately estimate the SOC. The SOC level is related to the properties of the active electrode materials and different active materials behave differently. For a Li-ion cell, 100% SOC means a state where all cyclable lithium ions are inserted in the negative electrode material, and at 0% SOC all cyclable lithium is found in the positive electrode. For cells based on lithium-cobalt oxide, the amount of cyclable lithium is less than the total amount of lithium in the active materials due to stability issues of the lithium poor structure. Sometimes the depth of discharge (DOD) is used to describe how deeply the battery has been discharged. In most cases it is related to SOC by DOD ¼ 100 SOC(%).
6.2 Thermal runaway
In real vehicle applications, it is very hard to accurately measure the lithium content in an electrode but instead the SOC has to be estimated based on voltage, current and temperature measurements in real time.
6.1.3 State of health (SOH) The state of health is an indicator of the remaining battery capacity compared to the capacity at BOL. The aging processes, which lower the SOH, start as soon as the cells are assembled. As the battery ages, the SOC will decrease until the battery can no longer fulfill the requested performance and the end of life (EOL) has been reached. SOH is not a physical quantity but it depends on parameters like number of charge-discharge cycles, capacity and power fade, and internal resistance. The aging process of a battery is complex and depends on the involved mechanisms. The aging depends on the vehicle usage, battery and cell design. Temperature, SOC range, energy and power conditions and time are essential parameters. For further reading about state functions Ref. [1] is recommended.
6.2 Thermal runaway The generation of heat in batteries deteriorates the performance and life time of the batteries but can also lead to the phenomenon of thermal runaway. This phenomenon is caused by an over-charging or an over-discharging rate which produces more internal heat than the battery can dissipate. The generated heat which cannot be dissipated causes the cell temperature to rise. This temperature rise makes the chemical reactions within the cell to take place at a faster rate. Accordingly, the increased rate of the chemical reactions generates even more heat that cannot be dissipated. If this phenomenon occurs, failure and destruction (by explosion and fire) of the battery may happen. Failure of a single cell can lead to failure of the whole battery pack, in particular if the cells are connected in series. Thermal runaway and the destruction it causes might be dangerous as the chemicals being released are toxic and in extreme cases the thermal runaway can cause fires and make the battery to explode. Batteries connected to a charger must be temperature controlled and the charging voltage and current must be limited. Once thermal runaway has begun, it cannot stop itself. The battery will be heated up and accordingly its internal resistance to the charging current will be reduced. Then it permits more current which creates additional heat and due to this, the notation runaway is used. The only way to stop this is to remove the battery from the facility, install a new battery and then dispose the faulty battery properly. Establishment of regular preventative maintenance is important to identify problematic cells before failure occurs and then adjust the charging voltage and
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FIG. 6.1 Thermal runaway.
current to ensure that the battery is not overcharged. The ambient air temperature must also be properly maintained. It is also recommended to provide adequate ventilation and forced convective cooling. Fig. 6.1 illustrates the processes in thermal runaway. There are several mechanisms or processes that can trigger the event of thermal runaway, namely over-charge, over-discharge, external short-circuit, over-heating, internal short-circuit caused by crash or dendrite formation or impurities caused by the manufacturing. Additional information about thermal runaway can be found in Refs. [2e4].
6.3 Importance of temperature Batteries are affected by the environment they are operating in, i.e., temperature and humidity. The temperature affects the operation of the electrochemical system, round-trip efficiency, charge acceptance, power and energy capability, reliability, life and lifecycle cost. If a battery is too hot or too cold, the battery will behave quite differently than at the normal and designed operating specifications. This is a consequence of using the battery in an environment it was not designed to be used in. If a battery is exposed to extreme weather conditions, negative effects can occur. For instance, it may stop working, bulge, bubble, melt, damage the device it is used in, generate smoke, create sparks or flames, expand or contract and during severe circumstances it may blow up. An uneven temperature distribution in the battery pack will lead to a localized detoriation. Accordingly, temperature uniformity within a single cell and from cell to cell, is important to achieve maximum lifecycles of the cells, packs and battery systems. Between the two electrodes in a battery, an electric current runs due to the voltage differential between the anode and cathode. At the same time an electrochemical reaction takes place inside the battery to replenish the electrons. When
6.3 Importance of temperature
FIG. 6.2 Battery capacity drop at various temperatures.
FIG. 6.3 Influence of operating temperature.
the ambient temperature is changing, the electrons within the battery are affected. An increase in temperature excites the electrons while a decrease in temperature inhibits electrons. Fig. 6.2 shows the influence of temperature on the voltage versus time characteristics. It is evident that as the temperature is reduced the battery capacity drops rapidly. Fig. 6.3 shows the power limit during discharge is affected by the operating temperature. The optimal or recommend temperature range is between 15 and 35 C. Above 35 C the degradation processes start and the aging is accelerated. Below 15 C the electrochemistry becomes sluggish and for Li-ion batteries lithium plating and dendrite formation may occur. For further information, see also Refs. [5e7].
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6.4 Examples of thermal management systems There are a number of ways in which cooing of a battery pack can be done. The system for this is generally called the battery thermal management system (BTMS). The tasks of the BTMS are to maintain the operating temperature within 5e30 C, maintain the temperature difference between any cells in the pack to be less than 5 C, prevent thermal runaway, maximize the useful energy from cells and pack, and use a small amount of energy for operation. The types of BTMS are classified as active or passive systems. In a passive cooling system, the heat is dissipated through natural convection and thermal radiation. These have no moving parts and are sufficient if a large space is available or if low performance (i.e., low charge and discharge rates) is required. The thermal inertia of the system is important and sometimes this is increased by adding more thermal mass. Active cooling systems rely on a cooling fluid, which is forced through the battery by a fan (air cooling) or pump (liquid cooling). For electric vehicles on the market currently, both air cooling and liquid cooling are used. There is also a development trend to use phase change materials (PCMs). Higher performance electric cars seem to apply liquid cooling as the high heat capacity of a liquid allows for better control of the heat dissipation. Some caution is, however, needed as using a conducting liquid through an electric environment is very hazardous and then isolation should be applied. The head wind created as the vehicle moves can be used for aiding the cooling but is not sufficient by its own. Generally, also the battery packs are shielded in layers of protective casing. Accordingly, the head wind cooling is limited. General descriptions of thermal management of batteries are presented in, e.g., Refs. [8e10].
6.4.1 Air cooling For applications of batteries where extreme performance or heavy duties are not required, air cooling can be employed. BTMS0 based on air cooling are generally low cost alternatives and less complicated than liquid cooling systems. However, with an air cooled system it is hard to maintain an even temperature distribution across the battery pack. In the simplest form of an air cooling system, the air is forced by a fan over the batteries being lumped together. The air is not confined to channels within the battery pack but is directed over different parts of the battery pack through baffles. A disadvantage of this simple system is that the heat dissipation can only be controlled by the air speed or the fan capacity. However, in advanced air cooling systems the air flow is directed to various regions of the battery pack by employing different channels. The channels increase the overall needed space and accordingly the volume of the battery pack is increased. Fig. 6.4 illustrates air cooling systems.
6.4 Examples of thermal management systems
FIG. 6.4 Illustration of air cooling of a battery pack.
6.4.2 Liquid cooling BTMS0 based on liquid cooling are classified as: cooling fins, cooling matrix and cooling plates. The liquid might be water, glycol, oil, acetone or refrigerants. Cooling fins dissipate heat from the wide face of a cell. A single fin is placed between two adjacent cells. Fig. 6.5 illustrates the principle. The cooling fin has a series of channels running through it. This cooling method is suitable for both pouch cells and rectangular prismatic cells. It occupies a small space and provides direct cooling to at least one face of a cell. Among the disadvantages are the high design cost and that leakage between the interfaces may occur if the sealing is not adequately designed.
FIG. 6.5 Liquid cooling with a cooling fin.
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The method of a cooling matrix is commonly employed for cylindrical cells. A hollow cooling shell is manufactured with holes to contain the cells. The cooling liquid enters at one end of the jacket and exits at the diagonal end. Generally, the cooling matrix is robust and helps to maintain the temperature limits by surrounding the cell with large thermal mass. The cooling jackets are welded leaving only spigots at the end where sealing must be considered. The disadvantage with the cooling matrix method is that it is space consuming and reduces the battery pack energy density. The weight is also increased by the metal jacket and the cooling liquid. Fig. 6.6 illustrates the cooling matrix method. In a so-called cooling plate, a cold liquid is flowing in serpentine or concentric channels and by convection the cell generated heat is dissipated. Cooling plates
FIG. 6.6 Illustration of (A) a cooling matrix for cylindrical cells, (B) cooling matrix for rectangular cells.
6.4 Examples of thermal management systems
FIG. 6.7 Illustration of liquid cooling by a cooling plate.
present a cost effective solution for liquid cooling. One drawback of cooling plates is added weight to the pack. Another is that the cooling plates are commonly deployed underneath the cells. This is not the most effective means to dissipate the heat as the cell is hotter close to the tabs at the top because of the higher current density there. Fig. 6.7 illustrates the cooling plate layout. Evaluation of liquid versus air cooling has been presented in Ref. [11].
6.4.3 Cooling by phase change material (PCM) PCM has been used for many years in building thermal systems, spacecraft thermal systems, medical supply shipping, chemical reaction exotherm smoothing and to some extent in HVAC (heating, ventilation and air conditioning) for vehicles. PCMs often rely on solid-liquid transition or vice versa in a small temperature range but the selection of material will depend on the application. The PCM absorbs or releases a large amount of energy compared to conduction heat transfer. As it absorbs heat it is converted into liquid state and vice versa as heat is rejected. The ability to store thermal energy, generated in the battery, at an almost constant temperature (the melting temperature of the PCM), is the key advantage for BTMS. Different phase changing materials with different characteristics are available on the market. Paraffin wax is such a substance which in its normal state is a semiviscous solid. Paraffin-epoxy mixtures are also used. Various salts are also used as phase change materials. PCMs have in general a low thermal conductivity and thus it is important to find methods to increase the thermal conductivity of PCM. PCM pouches and plastic packs are available on the market and such can be placed next to the battery surface for cooling. PCM can also be used for heating in extremely cold climates.
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FIG. 6.8 Characteristics of a PCM material.
PCM improves the battery cost, efficiency and weight compared to active systems. The PCM material has high fusion heat which stores and releases the amount of heat during melting and solidification at a certain temperature. Fig. 6.8 illustrates that when the temperature is below the melting point, the PCM is in solid state and heat is absorbed as sensible heat as the temperature rises. As the melting point is reached, heat is absorbed and stored as latent heat until the latent heat reaches the maximum without a temperature change. After that the PCM is in the liquid state. Heat is then absorbed as sensible heat and the temperature rises. The melting point of the PCM depends on the particular material. The function temperature of the PCM should be higher than the ambient temperature but it must be lower than the operating temperature of the battery. Fig. 6.9 shows a specific case where active air cooling is compared with PCM passive cooling. The battery temperature is displayed for two air flow rates (given by Reynolds numbers) and it is obvious that none of the air cooling cases can keep the battery temperature below 55 C, which on the other hand is possible with the PCM. This shows the strength of PCM cooling. Additional information on PCM for thermal management can be found in Refs. [12,13]. A comparison between air cooling and PCM cooling was presented in Ref. [14].
6.4.3.1 Heat pipes with phase change Heat pipes are known to be very efficient to passively transport heat. Phase change (vapor-liquid) is used to remove the heat from the source. A heat pipe is a closed
6.5 Mathematical modeling and experimental approaches
FIG. 6.9 Comparison of air cooling and PCM cooling. Based on Sabbah et al. [14].
loop pipe with two major segments, namely the evaporator and the condenser. The heat generation part is attached with the evaporator while the condenser removes the heat to the surroundings. An overview of the heat pipe technology is available in Ref. [15].
6.4.4 Drawbacks of thermal management systems The BTMS has also some drawbacks. It increases the complexity of the system, consumes energy for the operation, reduces the reliability of the system and also add up to the weight and total cost.
6.5 Mathematical modeling and experimental approaches Mathematical modeling is a way to estimate battery performance. Battery modeling or mathematical description of batteries is nowadays more accessible to battery developers as general purpose computational tools are available. The approach can be applied in estimation of the battery performance and in battery design as well as in developing and evaluation of thermal management methods. For a complete modeling of a battery, heat and mass transport, charge transport, the electrode kinetics and the processes at the electrode-electrolyte interfaces need to be considered. However, sometimes it is possible to use simplified models. So for instance the modeling tools can be classified as (a) first-order or lumped capacitance thermal and fluid models, (b) 1-D and 2-D thermal and fluid performance models, (c) 1-D vehicle integrated thermal and fluid flow models, (d) 3-D electro-thermal models, (e) 3-D electrochemical-thermal model. The detailed modeling approaches require: solution of the electron current via, e.g., the Butler - Volmer equation (see Chapter 2), conservation of charge (electrons and ions) and energy conservation. The experimental tools to design and evaluate battery thermal management systems are exemplified by (a) isothermal calorimeters and battery testers, (b) infrared
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thermal imaging, (c) thermal conductivity meters, (d) heat transfer characterization setup and (e) battery thermal testing loops. For an existing battery, the problem is to estimate how the battery will perform and specific conditions demanded by the user. At the stage of designing a battery, it is of interest to estimate how the design impacts the performance. The various physical mechanisms including battery chemistry etc. need to be considered. Examples of studies considering the general energy balance and heat generation of batteries are refs. [16e20].
6.5.1 Simple energy balance of a battery Fig. 6.10 show a sketch of common battery. Energy is entering and leaving the battery poles. Inside the battery, energy or heat is generated and on the surfaces exposed to the surrounding environment, energy losses occur by convection and radiation. Mathematically the energy balance reads: dE ¼ E_ generated E_ losses þ E_ in E_ out (6.2) dt If the battery is assumed to have a uniform temperature Ts, the energy accumulation rate can be written as dE dTs ¼ mcp (6.3) dt dt The energy loss from the surface is composed of convective and radiative heat transfer as given below Eloss ¼ hAðTs Ta Þ þ εFA T4s T4a (6.4) where h is the convective heat transfer coefficient, A is the surface area, Ta the ambient temperature, ε the surface emissivity and F the view factor between the battery surface and the surroundings. The generated heat or energy in the battery consists of contributions from the electrochemical reactions, phase changes, mixing effects and joule heating (ohmic losses). Expressions will be given in a later section. Fig. 6.11 illustrates the temperature-time history of a certain simple battery. The influence of the discharge rate is evident.
FIG. 6.10 Energy flow in a simple battery.
6.5 Mathematical modeling and experimental approaches
FIG. 6.11 Temperature versus time for various discharge rates. Based on Ref. [21].
6.5.2 Energy balance of a non-isothermal battery The energy balance in Section 6.5.1 can be extended to include heat conduction inside the battery and then the temperature is not uniform. The heat balance reads vT ¼ V$kVT þ Q_ generated (6.5) vt where k is the thermal conductivity of the battery material and Q_ generated is the generated heat per unit volume. The boundary condition at the battery surface is now written as rcp
vT ¼ hðTs Ta Þ þ εF T4s T4a vn where kn is the thermal conductivity in the surface normal direction. kn
(6.6)
6.5.3 Governing equations for convective cooling of a battery pack For analysis of air or liquid cooling of batteries also the fluid flow and convective energy transport need to be taken into account and the flow channels need separate treatment. Appropriate boundary conditions need to be formulated. Then the mass conservation equation, the Navier-Stokes equation and the heat transport equation have to be numerically solved, [22]. These equations are here given for a steady state flow field but the energy exchange is time dependent. The case of a turbulent flow is included by incorporating a turbulent viscosity and a turbulent diffusivity.
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Mass conservation: vui ¼0 vxi
(6.7)
Navier-Stokes equation:
( " )# vui vp v vui vuj ¼ þ þ ðm þ mturb Þ ruj vxi vxj vxj vxj vxi
Convective-diffusive unsteady heat transport: vT vT v mturb vT ¼ þ Q_ generated lþ rcp þ rcp uj vt vxj vxj Prturb vxj
(6.8)
(6.9)
Eq. (6.9) is written in the way of a conjugate formulation so it can also be applied inside the cells as well but then the thermophysical properties are for the battery pack and the generated heat is inside the cells. The treatment of turbulence is here illustrated by given the equations for the socalled k-ε model including the formula for the turbulent viscosity. Further details can be found in Ref. [23]. Turbulent kinetic energy k: " #2 " # vk v mturb vk mturb vui vuj ruj þ ¼ þ rε (6.10) mþ vxj vxj sk vxj 2 vxj vxi Turbulent kinetic energy dissipation ε: " #2 " # vε v mturb vε ε mturb vui vuj ε2 þ C1 ruj ¼ þ C2 r mþ vxj vxj k 2 vxj vxi sε vxj k
(6.11)
The turbulent viscosity mturb is calculated as: ε2 (6.12) k The common constants in the equations above and the appropriate boundary conditions can be found in, e.g., Ref. [23]. mturb ¼ rCm
6.5.4 Heat generation The heat generation in electrochemical devices is a complex phenomenon involving the operating voltage, current, cell size and materials of the components etc. The generated heat by the battery cells depends on the temperature of the cells, the discharge rate and the state of charge (SOC). In single cells of a battery or a fuel cell, the heat sources are comprised of reversible and irreversible processes and, governed by one term representing the reversible entropic heat generation and a second
6.5 Mathematical modeling and experimental approaches
term representing the irreversible heat by ohmic heating (Joule heating) and losses incurred to facilitate the reactions in the activation region. See also Chapters 2 and 9. Here the heat generation equation developed by Bernardi et al. [17] is commonly adopted. I dEoc Q_ generated ¼ Eoc E T (6.13) Vtotal dT where I is the total current of the battery, Vtotal is the total volume of the core region, Eoc the open circuit voltage, E the operating voltage and T the temperature. The limitation of this equation is that the voltage or potential terms must be obtained and the effect of temperature on the electrochemical behavior cannot be evaluated. However, a more rigorous electrochemical model to theoretically predict the heat generation rate can be established and then phase change and mixing in the cell are considered, see Refs. [7,17]. However, for large batteries resistance heating in the current collectors might be significant relative to the electrochemical heat generation rate even for well designed batteries. Additional terms then appear in Eq. (6.13).
6.5.5 Multi-scale multi-dimensional modeling Depending on what level of details being of interest, different mathematical approaches are necessary. This is because the various phenomenological processes occur at quite different scales. At the smallest scales, i.e., in the particle domain, the kinetics of the charge transfer and for a lithium-ion battery, the Li transport in active particles is analyzed. In the electrode domain, charge balance in solid composite electrode matrices as well as charge balance in the liquid pore channels have to be investigated. In the electrolyte, the Li transport needs consideration. At the cell domain scale, energy conservation needs consideration and in the current collectors, the charge conservation should be analyzed. Then at module and system scale more overall conditions like thermal management, safety and control strategies are considered. Fig. 6.12 summarizes the multi-physics and multi-scale phenomena for lithiumion battery systems at different length scales. The methods of modeling and simulations are depending on the time and length scales involved. From the smallest (atomic scale) to the largest (continuum formulation), the methods might be classified as: quantum chemistry, molecular dynamics, kinetic Monte Carlo approaches, meso-scale methods (e.g., lattice Boltzmann approaches) and finally continuum methods based on computational fluid and solid dynamics. In general, molecular dynamics (MDs) based approaches have been used for atomistic modeling of thermal transport in materials and interfaces of engineering applications but for thermal transport in electrochemical materials and interfaces, works are lacking. However, atomistic modeling methods can only handle a small number of molecules and accordingly reducedeorder models based on MD, like coarse-grained MD, need to be developed, [24,25].
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FIG. 6.12 Multi-physics and multi-scale phenomena in lithium-ion batteries.
For length scales of single cells and battery packs, the thermal transport is governed by the well-established continuum formulated energy conservation equations, see Section 6.5.3. In some cases, analytical solutions can be found but more commonly numerical solutions methods (like CFD) are more suitable. Nevertheless, due to the large scale and complexity of cells and battery packs, detailed thermal modeling is not always possible and also some reduced-order models and parameterized models are needed to find a compromise between computational efforts and accuracy. Lithium ion electrodes constitute heterogeneous mixtures of multiple materials including the active material, binders etc. The thermal transport through these materials is not well known. Analytical models for predicting the thermal conductivity of such heterogeneous materials are requested. Theoretical models are needed to understand how interfacial thermal transport is affected by the electrochemical ambient, nature of surfaces and the presence of intermediary molecules. Similar but more detailed descriptions for analysis of fuel cells will be presented in Chapter 10.
6.6 Available softwares Most battery modeling and simulation are carried out using general-purpose tools like MATLAB, ANSYS and COMSOL. Nevertheless, the growing importance of battery modeling has resulted in development of customized computational software. The most comprehensive software for battery design, modeling and simulation is the Battery Design Studio. The Battery Design Studio is mainly a user interface to access battery models and it provides a user friendly environment for battery design and simulation as well as
References
analysis of battery data. The software includes routines for sizing various cell geometries (stacks or spirally wound), models for simulation of battery behavior, a database and tools for visualization and analyzing battery data. Links to the softwares are given by Refs. [26e28].
6.7 Summary The temperature of a battery is important as it affects the life, performance, reliability and cost of the batteries for, e.g., electric vehicles. The battery life and performance are very sensitive to temperature exposure. Generally thermal management by some method is needed. At high temperature the primary considerations are on life, safety and non-uniform aging due to thermal gradients. Typically cooling is required in hot environments, during moderate to large current demands during operation and during fast charging. At low temperature the primary considerations concern the performance and damage due too fast charging. Typically heating is required in cold environments during charging and discharging. To reduce the over-sizing of batteries at BOL, thermal control might be a good option, particularly in hot and cold climates. Due to the wide range of scales of the multi-physics phenomena and processes in lithium-ion batteries, different computational approaches are needed.
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