The heating triangle: A quantitative review of self-heating methods for lithium-ion batteries at low temperatures

Journal of Power Sources 581 (2023) 233484 Available online 22 August 2023 0378-7753/© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Review article The heating triangle: A quantitative review of self-heating methods for lithium-ion batteries at low temperatures Haijun Ruan a , b , * , 1 , Jorge Varela Barreras c , d , 1 , Marco Steinhardt e , 1 , Andreas Jossen e , Gregory J. Offer f , g , Billy Wu b , g , ** a Institute for Clean Growth and Future Mobility, Coventry University, Coventry, CV1 5FB, UK b Dyson School of Design Engineering, Imperial College London, London, UK c Department of Electronic Engineering, Technical University of Catalonia, Vilanova i la Geltru, Spain d Department of Civil and Environmental Engineering, Imperial College London, London, UK e Technical University of Munich (TUM), TUM School of Engineering and Design, Institute for Electrical Energy Storage Technology (EES), Arcisstrasse 21, 80333, Munich, Germany f Department of Mechanical Engineering, Imperial College London, London, UK g The Faraday Institution, Didcot, UK HIGHLIGHTS GRAPHICAL ABSTRACT •Self-heating methods are not just reviewed but also quantitatively evaluated/compared. •Heating triangle introduced as a universal quantitative indicator for heating comparison. •Heating triangle metrics are calculated and discussed for each self-heating approach. •Same self-heating method shows very similar metrics irrespective of study case. •Critical insights gained lead to new research directions towards advanced self-heating. ARTICLE INFO Keywords: lithium-ion battery Low temperature Preheating Self-heating ABSTRACT Lithium-ion batteries at low temperatures have slow recharge times alongside reduced available power and energy. Battery heating is a viable way to address this issue, and self-heating techniques are appealing due to acceptable efficiency and speed. However, there are a lack of studies quantitatively comparing self-heating methods rather than qualitatively, because of the existence of many different batteries with varied heating parameters. In this work, we review the current state-of-the-art self-heating methods and propose the heating * Corresponding author. Institute for Clean Growth and Future Mobility, Coventry University, Coventry, CV1 5FB, UK. ** Corresponding author. Dyson School of Design Engineering, Imperial College London, London, UK. E-mail addresses: [email protected] (H. Ruan), [email protected] (B. Wu). 1 These authors contributed equally to this work. Contents lists available at ScienceDirect Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour https://doi.org/10.1016/j.jpowsour.2023.233484 Received 16 June 2023; Received in revised form 24 July 2023; Accepted 3 August 2023 Journal of Power Sources 581 (2023) 233484 2 Thermal management Metrics triangle as a new quantitative indicator for comparing self-heating methods, towards identifying/developing effective heating approaches. We define the heating triangle which considers three fundamental metrics: the specific heating rate (◦C⋅g⋅J −1 ), coefficient of performance (COP) (−), and specific temperature difference (◦C⋅hr), enabling a quantitative assessment of self-heating methods using data reported in the literature. Our analysis demonstrates that very similar metrics are observed for the same type of self-heating method, irrespective of the study case, supporting the universality of the proposed indicator. With the comparison insights, we identify research gaps and new avenues for developing advanced self-heating methods. This work demonstrates the value of the proposed heating triangle as a standardised approach to compare heating methods and drive innovation. 1. Introduction Lithium-ion batteries have relatively high energy and power densities, as well as reasonable lifetimes, leading to their mainstream adoption in electric vehicles (EV) [1,2]. However, they suffer from poor performance at low temperatures due to sluggish kinetics and mass transport issues [3–5]. The available energy and power are dramatically decreased at sub-zero temperatures, with charging rates particularly limited due to the high risk of lithium plating [5–7]. Improving electrode materials and the electrolyte is one way to resolve this challenge [8,9], but commercialization of material innovations can take significant time [4,7,10,11]. Since the kinetic and transport processes are highly temperature dependent, the performance of the batteries can be restored after being warmed up [12,13]. Therefore, preheating the battery is a viable approach to enhance battery performance; enabling higher EV adoption in cold regions. Indeed, considerable research efforts have been dedicated to formulating battery heating methods, with these generally classified as external or internal heating methods [14–17]. For external heating methods, the battery is warmed up using the heat transferred from external sources (e.g. heaters), where the state-of-charge (SOC) is kept unchanged [18–20]. This method is useful, however, the relatively low though-plane thermal conductivity of batteries (ranging from 0.40 to 1.03 W m −1 K −1 [21]) limits the heat transfer rate [22], leading to long heating times and large temperature gradients. Moreover, the lengthy heat transfer pathway generally exists in external heating applications, which causes appreciable heat dissipation to the surroundings [22–25], resulting in higher energy consumption; prolonging the heating duration. Conversely, for internal heating, where batteries are warmed up using self-generated heat, and there is no impact by the long heat transfer pathways, nor the limited thermal conductivity of batteries [26–29]. Therefore, the heating efficiency and speed is usually high with good temperature uniformity. Provided that the heating energy comes from the battery, the internal heating method is termed internal self-heating, which is independent of external power sources [10,12,30, 31]. Recently, a new hybrid self-heating (HSH) method, integrating internal and external heating without additional external power [22,32], has been developed to further shorten the heating time and enhance the Nomenclature ΔT Temperature rise/increase (◦C) μ I Specific heating rate (◦C⋅g⋅J −1 ) ΔT STD Specific temperature difference (◦C⋅hr) E ρ Energy density (Wh⋅kg −1 ) c p Specific heat capacity (J⋅◦C −1 ⋅g −1 ) Q bat Battery nominal capacity (Ah) k bat Battery thermal conductivity (W⋅m −1 ⋅K −1 ) L bat Characteristic length of heat transfer (m) h Convective heat transfer coefficient (W⋅m −2 ⋅K) T amb Ambient temperature (◦C) T tgt Target temperature (◦C) I heat Heating current (A) U bat Battery voltage (V) R ext External heating resistance (Ω) f AC AC frequency (Hz) q gen Heat generation rate (W) R b Battery lumped resistance/impedance (Ω) U ocv Open circuit voltage (V) m Battery mass (g) T Battery temperature (◦C) q loss Heat loss/dissipation rate (W) A The area that heat convection occurs (m 2 ) ˙ T Temperature rise rate (◦C⋅min −1 ) IC−rate Heating C-rate (h −1 or hr −1 ) E H Total energy used for heating (Wh) E bat Maximum available energy (Wh) e h Energy consumption (%) DOD SOC loss/capacity consumption (%)  Vsoc Average OCV during heating (V) Q loss Capacity consumption (Ah) V Battery nominal voltage (V) ΔT b Maximum temperature difference (◦C) SOC 0 Initial SOC of heating (%) t h Heating duration (s)  Up Equivalent polarization voltage (V)  Rb Equivalent heating resistance (Ω) Abbreviations AC Alternating current CC Constant current COP Coefficient of performance CV Constant voltage DC Direct current EV Electric vehicles HSH Hybrid self-heating LCO LiCoO 2 LFP LiFePO 4 LMO LiMn 2 O 4 NMC111 LiNi 1/3 Mn 1/3 Co 1/3 O 2 NMC532 LiNi 0.5 Mn 0.3 Co 0.2 O 2 NMC622 LiNi 0.6 Mn 0.2 Co 0.2 O 2 OCV Open circuit voltage PC Pulse current SAC Sinusoidal AC SOC State of charge SOH State of health H. Ruan et al. Journal of Power Sources 581 (2023) 233484 3 heating efficiency. Whilst many heating methods have been developed, their validation has been generally done on different battery types [15–17]. The existence of many different batteries with varied heating parameters, thus, makes it complicated to perform a fair quantitative comparison. For example, the energy consumption during heating highly depends on a range of factors such as specific heat capacity, and energy density (Fig. 1a, Eq. (S3) in Supplementary Note S1). Xu et al. [32], for instance, reported that 4% of the battery capacity was used for a 20 ◦C temperature rise for their cell with an energy density of 191 Wh⋅kg −1 , while Jiang et al. [33] reported a 6.6% capacity utilisation for a temperature rise of 23 ◦C for a cell with an energy density of 128 Wh⋅kg −1 . Thus, energy (capacity) consumption during battery heating is not a fair metric to assess heating methods. Moreover, the target heating temperature is often varied, and heat generation is generally different at different temperatures due to the diverse activation energies of the various electrochemical processes [3,14–16,19]. In addition, some heating parameters, such as heating current, differ broadly between studies. For example, sometimes parameters are selected conservatively, such as the heating C-rate of 1.3 C in Ref. [32], and sometimes aggressively, such as the heating C-rate of above 8 C in Ref. [34]. The issue is obviously that heating time is shorter with higher heating current [14,33,35,36], due to higher heat generation (Supplementary Fig. S1). Therefore, only using the temperature-rise rate or heating time is not sufficient to fairly evaluate different heating methods. For example, the rate of temperature increase was 3.39 ◦C⋅min −1 at 1.9 C in Ref. [37] while it reached 8.6 ◦C⋅min −1 at 4 C in Ref. [38]. Thus, the varied use of different battery types and different heating parameters makes it challenging to establish a fair quantitative comparison between different heating methods (Fig. 1b), and explains why almost all the comparative studies in the literature so far focus on qualitative rather than quantitative indicators. For example, Hu et al. [15], Wu et al. [16] and Wang et al. [17], reviewed different heating methods using qualitative ratings and displayed the results in the form of a 1–5 star scale [15], plus-minus signs [16] or a radar chart without values on axes [17], respectively. To bridge this gap, this review paper defines a new universal indicator: the heating triangle, to achieve a fair quantitative comparison between self-heating methods. We highlight the advantages and shortcomings of the self-heating methods using quantitative metrics, and provide underpinning insights, toward the identification of new pathways to develop advanced self-heating methods. The remaining part of this paper is organized as follows. The selfheating methods are classified and briefly described in Section 2, with a discussion of key factors influencing heating performance. Section 3 defines the heating triangle and subsequently Section 4 quantitatively compares self-heating methods. Section 5 discusses the rationality of defined triangle metrics and identifies the research gaps and directions, followed by conclusions in Section 6. 2. Self-heating methods 2.1. Classification of self-heating methods The term battery self-heating refers to the fact that it is heated by its own energy. Self-heating methods thus include internal self-heating methods, where the heat is only generated from the battery, and hybrid self-heating methods, where the heat comes from the heaters inside/outside the battery without an additional power supply [15,16, 22]. Internal self-heating methods can be classified based on the heating current waveforms, which include direct-current (DC), and alternating current (AC) plus DC (AC +DC) heating methods, as shown in Fig. 2a. The DC heating method is commonly used in the discharge direction (Fig. 2b), i.e. DC self-heating [39], as there is a high risk of lithium plating during charging at low temperatures [5,40,41]. Constant current (CC) and constant voltage (CV) modes are the two types of DC heating approaches [15–17]. The pure AC, including pure sinusoidal AC (SAC) and pure pulse current (PC), can effectively warm up the battery but an external power source is required [42–44], thus the pure AC heating method is not considered as a self-heating method [15,45]. When there is the DC component in the AC signals, we strictly term the heating method as an AC +DC approach [33,46], although some references [10, 37,38] term this an AC heating method, under the condition of including small DC component. The AC +DC heating method comprises the SAC discharge [10,37], and PC discharge [38,47,48] approaches (Fig. 2a). The hybrid self-heating method is also called the compound self-heating method, where both the internal battery heat and heat from the electrical load are used (Fig. 2b), with both the heating energies coming from the battery [22,32,49,50]. The external heat can be transferred to the battery from heaters either in or outside the battery [22]. An example of internal heating elements includes the work by Wang et al. [51] whereby the battery is heated by internal heat generation and the heat from an embedded Nickel foil, and thus this is classified as a HSH method. In HSH methods, the current waveforms can be DC or AC +DC, with DC often utilized due to its simplicity [22,32,34,51,52]. 2.2. Heating performance areas/indicators When considering suitable low-temperature heating methods, there are six typical performance areas and/or indicators: heating duration, coefficient of performance (COP), energy consumption, battery degradation, temperature gradient, and engineering implementation (Fig. 2c) [15–17,22]. When choosing a heating method, a reduction in heating duration, energy consumption, battery degradation, and temperature gradients along with an increased COP, and easy engineering implementation are desirable, but there are usually conflicting goals. For example, for the Fig. 1. a, The minimum energy consumption of batteries with different energy densities and specific heat capacities for three temperature rise ranges (ΔT). The calculation of minimum energy consumption is described in Supplementary Note S1. b, illustration of challenges for comparing heating methods. H. Ruan et al. Journal of Power Sources 581 (2023) 233484 4 HSH method in Ref. [22], a very short heating duration of 16.8 s from −30 ◦C to 0 ◦C at 100% SOC is accompanied by a high degradation of 7.9% over 500 heating cycles, while a low degradation of 1.2% can be achieved with a relative slow heating duration of 86 s. The heating duration is indicated by the rate of temperature increase, with a high value resulting in a short heating duration. The COP represents the ratio of useful heat supplied (stored energy in the battery) to the electrical energy required, which corresponds to the heating efficiency. The energy consumption is also an indicator to show the efficiency of the heating method, but it is a metric mainly driven by the battery heat capacity, energy density, and temperature increase (ΔT, See Fig. 1a). For that the COP is a more suitable metric, as discussed later. In the literature, several studies suggest a high impact of the heating process on battery degradation, examples being a capacity fade of 7.7% [47] and ~7.2% [51] after 200 and 500 heating cycles, respectively, but usually this is reported as low [28,33,35,38]. For example, after 600 heating cycles, Jiang et al. [33] found the capacity remained relatively constant; Li et al. [38] demonstrated the capacity fade was only 0.5% after 5000 heating cycles. This highly depends on the heating methods and the particular type of cell [1,2,53,54], but also is influenced by the intrinsic complexity of the degradation mechanisms [55–57], Therefore, we consider that it is very challenging to define a universal metric to compare heating methods irrespective of the battery and the heating parameters. Therefore, here we do not propose a metric to evaluate battery degradation. Instead, we are only analysing quantitatively some of the influencing parameters, such as temperature gradient. Temperature gradients within the battery corresponds to the maximum temperature difference, with a high rate of temperature-rise generally leading to non-uniform temperature profiles. Engineering implementation includes many aspects, such as cost, weight increase, safety, and reliability, which are seldom mentioned in the reported heating works and are not easy to compare quantitatively [15–17,58]. The DC discharge heating method is easy to implement, but implementing the HSH method embedded with Nickel foils in the battery [50,51] is more challenging, as the battery structure needs to be modified with uncertainty around safety and reliability. The AC +DC heating method using the motor and its drive circuitry to generate heating current is not as difficult to implement, and the additional weight and volume would be low [38]. On the other hand, considering battery cooling is important for thermal management system design [25, 39,59], therefore, integrating heating and cooling methods is preferable. 2.3. Factors influencing heating performance Qualitatively, links between the heating performance of different methods and internal, external, and methodological aspects are illustrated in Table 1. The internal metrics often refer to battery parameters, such as energy density (E ρ ), specific heat capacity (c p ) and battery states, while the external parameters generally include the heat transfer conditions and ambient temperatures. The methodological parameters depend on the heating method, two examples of which are the heating current and battery voltage. 2.3.1. Internal parameters Reversible entropic heat generation is generally negligible under AC excitation and is relatively low under the high DC currents [14,22,33, 35]. Thus, the battery heat generation is dominated by the irreversible heat generation (q gen ), expressed as: qgen =Iheat ⋅(UOCV −Ubat) ≈ I2 heat⋅Rb(1) where I heat , U OCV , U bat , and R b represent the heating current (I heat > 0 denotes a discharge process), the open circuit voltage (OCV), battery terminal voltage, and battery lumped resistance (impedance), respectively. Battery SOC and state-of-health (SOH) have an effect on the heat generation (q gen ) of different self-heating methods and thus the heating duration, as battery impedance (R b ) changes with the SOC and SOH [33, 60–62]. The impedance of batteries with different energy densities (E ρ ) generally varies [63]. In general, higher power density requires the reduction of cell resistance, e.g. based on thinner electrodes and separators, thicker tabs and current collectors, reduced particle sizes for the active materials or higher loadings of conductive materials in the cathode [64–66]. Thus, the E ρ is considered to have an influence on the Fig. 2. a, Classification of self-heating methods (See collected methods in Supplementary Table S1); b, equivalent circuit of three self-heating methods; c, heating performance areas/indicators. In Fig. 2b, the battery is simply represented by the open circuit voltage (OCV) and its resistance (R b ), while the loading and heating controllers are represented by their equivalent resistances, R eq and R ext , respectively. (See representative experimental set-up of the three self-heating methods in Supplementary Fig. S2). H. Ruan et al. Journal of Power Sources 581 (2023) 233484 5 heat generation and heating duration. For the same battery materials, a battery with a high capacity (Q bat ) generally has a low resistance and the capacity (Q bat ) impacts the heating duration. The specific heat capacity (c p ) affects the rate of temperature rise (Eq. (2)) and thus the heating duration. mcp dT dt =qgen −qloss (2) qloss =h⋅A⋅(T−Tamb)(3) where m, c p , T, T amb , A, and h represent the mass, specific heat capacity, and temperature of the battery, the ambient temperature, the area that heat convection occurs, and the convective heat transfer coefficient, respectively. The thermal conductivity (k bat ) and characteristic length of heat transfer (L bat ) within the battery have almost no effect on the rate of temperature rise of the internal self-heating methods. This is because the heat transfer processes are quite slow in the battery under the good heat insulation between the battery and surroundings, and relatively uniform battery internal heat generation [22,67,68]. However, they essentially influence the heat propagation for the HSH methods due to the heat transferred from external heaters [69–71], and thus impact the heating duration, energy consumption, COP, and temperature gradient. Heating at an extremely low or high SOC is often not permitted for the self-heating methods as it may accelerate battery degradation [17, 72,73]. For example, AC +DC loads can make the battery voltage at high SOC go over the upper voltage limit, while the three self-heating methods can render the voltage of batteries at low SOC go below the lower voltage. Heating at a high SOC/OCV for the HSH methods likely leads to a high temperature gradient, such as ~30 ◦C [34,50], which causes local overheating and may influence battery degradation [74, 75]. This can be explained by the high heat generation from the external heaters due to the high heating current at the high SOC/OCV. 2.3.2. External parameters The external parameters, h, T amb , affect the heat dissipation (q loss ) [14,22,76,77], as shown in Eq. (3), and thus influences the heating duration, energy consumption, COP, and temperature gradients for the three self-heating methods. 2.3.3. Methodological parameters The target temperature (T tgt ) of heating is often different, such as 0 ◦C in Refs. [22,51], 5.6 ◦C in Ref. [35], 10 ◦C in Ref. [41], 29.1 ◦C in Ref. [38], 60 ◦C in Ref. [4], which is generally determined by the expected battery performance [7,13,18]. This greatly impacts the heating duration and energy consumption, and also influences the COP, temperature gradients, and degradation of batteries [18,78]. The applied heating current and battery voltage likely impact the heat generation and degradation of batteries [3,22,35,79,80]. For the HSH methods, the heat generation relies, in part, on the external heating resistance (R ext ) [22,32,34,51,52]. Furthermore, R ext also affects the heating current and battery voltage [22,51] and thus influences battery degradation. For the AC +DC heating methods, the heat generation depends on the AC frequency (f AC ) [3,14,33,35,81] and special heating equipment is generally needed to generate AC +DC signals, which influence the COP. 3. The heating triangle To enable a quantitative assessment, we introduce the heating triangle as a new universal indicator (Fig. 3). The heating triangle Table 1 Internal, external and methodological parameters that significantly affect the heating duration, energy consumption, COP, temperature gradient and battery degradation for self-heating methods. H. Ruan et al. Journal of Power Sources 581 (2023) 233484 6 considers three fundamental quantitative metrics: the specific heating rate (◦C⋅g⋅J −1 ), the coefficient of performance (COP) (−), and the specific temperature difference (◦C⋅hr). During heating, it is ideal to minimise heat loss from the battery to its surroundings as much as possible, with different insulation materials used [3,14–16,22,33–35,51,52]. For example, insulation such as polyfoam, insulation cotton, and others have been used to wrap the batteries, where convective heat transfer coefficients between ~0 and 9.6 W m −2 ⋅K [33,34,38,48,51,52] have been achieved. Thus, these values are generally consistent with each other, and the variation in external heating parameters on heating performance is limited and can be ignored, allowing for the focus to be on internal and methodological parameters. As we discussed in Section 2.3.1, battery resistance generally shows a positive correlation with energy density. While it often has a negative relationship with battery capacity, a simple example of which several cells connected in parallel decrease resistance but increase capacity. Thus, the energy density and capacity that usually vary with batteries, pose a great influence on battery heat generation and heating speed. Furthermore, the heat generation and heating speed increase with the heating current (Eq. (1)). Therefore, accounting for the dominant internal and methodological influencing parameters on heating speed, we define the specific heating rate ( μ I, ◦C⋅g⋅J −1 ) as the temperature-rise rate (˙ T) and battery capacity (Q bat ) per heating current (Iheat, A) and energy density (E ρ , Wh⋅kg −1 ), expressed as: μ I= ˙ T⋅Qbat Iheat⋅E ρ (4) We consider the heating current (Iheat), rather than the square of heating current (I2 heat) in Eq. (4), as the heat generation depends on the heating current (Iheat) in some cases, such as the HSH methods [22,32,34, 51,52], where it equals Iheat ∗Uocv. We define the heating C-rate (IC−rate) as Iheat/Qbat with the unit of h −1 or hr −1 , and the specific heating rate ( μ I, ◦C⋅g⋅J −1 ) is describe by the temperature-rise rate ( ˙ T) per heating C-rate (IC−rate, h −1 or hr −1 ) and energy density (E ρ , Wh⋅kg −1 ), expressed as: μ I= ˙ T IC−rate⋅E ρ (5) The specific heating rate ( μ I) describes the temperature (◦C) increase per unit mass (g) when 1 J heat is absorbed, which is proportional to the inverse of the specific heat capacity ((J⋅◦C −1 ⋅g −1 ) −1 ). Thus, it allows for the fair comparison between self-heating speeds. More relevant discussion will be performed later. The COP is commonly used in heating/cooling systems, which indicates the ratio of useful heating to the energy input, with a higher COP equating to higher efficiency and lower specific energy consumption. For battery self-heating, the COP can be described by: COP =m⋅cp⋅ΔT EH ⋅1[Wh] 3600 [J]=m⋅cp⋅ΔT 3600⋅eh⋅Ebat =cp⋅ΔT 3600⋅eh⋅E ρ (6) where E H , E bat , and ΔT stand for the total energy (Wh) used in the heating system, the maximum available energy (Wh) in the battery, and temperature difference (◦C) between the initial and target heating temperatures, respectively. e h is the energy consumption (%) during heating, which equals the per cent relative to the maximum available energy in the battery, but it is rarely reported in the heating papers. Alternatively, the capacity consumption, i.e. DOD (depth-of-discharge) during heating, is often presented [32,33,38,51,52,82], which represents the per cent relative to the maximum available capacity in the battery. We thus need to convert the capacity consumption (DOD) to energy consumption, expressed as: EH≈Qloss⋅ Vsoc ≈DOD⋅Qbat⋅ Vsoc (7) where  Vsoc, Qloss and Qbat are the average OCV and capacity consumption (Ah) during heating, and the nominal capacity (Ah) of batteries, respectively. Therefore, the conversion coefficient, which is the ratio of energy consumption (e h , %) and DOD, can be expressed as: eh DOD =EH/Ebat DOD ≈Qbat⋅ Vsoc Ebat ≈ Vsoc V(8) where V is the nominal voltage of batteries. Consequently, when given the capacity consumption (DOD), the COP can be approximately calculated as: Fig. 3. The heating triangle: three fundamental quantitative evaluation metrics. The specific heating rate relates to the heating speed and heating duration. The COP reflects the energy consumption and indicates the heating efficiency. The specific temperature difference links with the temperature gradient, and thus local overheating risk and the uneven degradation of batteries. H. Ruan et al. Journal of Power Sources 581 (2023) 233484 7 COP ≈cp⋅ΔT DOD⋅E ρ ⋅V  Vsoc (9) To our knowledge, there is no existing preheating paper that uses the COP for assessing the efficiency of battery self-heating methods [15–17, 83]. The commonly used energy/capacity consumption highly depends on battery types (i.e. E ρ , c p ), while the COP considers the dominant internal and methodological influencing parameters, which facilitates the fair comparison of heating efficiency for self-heating methods. The heating C-rate has a significant impact on the battery temperature gradient during heating, with a higher heating C-rate generally leading to a larger temperature gradient [22,52]. Given the relatively low effect of other influencing parameters on the temperature gradient of batteries, we define the specific temperature difference (ΔT STD , ◦C⋅hr) as the measured (calculated) maximum temperature difference (ΔT b , ◦C) of both through plane and in plane per heating C-rate (I C-rate , hr −1 or h −1 ), described as: ΔTSTD =ΔTb IC−rate (10) 4. Quantitative comparison of self-heating methods In this section, the three presented metrics are calculated for 23 heating study cases, with the mean and uncertainty of each self-heating method estimated. The quantitative comparison of three types of selfheating method was then performed. Although there are 30 papers on self-heating presenting more than 30 heating cases (Supplementary Table S1), certain key parameters are missing in several papers, and thus 23 heating cases are reviewed quantitatively and systematically. 4.1. DC heating method Nine DC heating cases were analysed as representative methods, where the heating parameters are different (Table 2). In CC discharge modes, the battery voltage decreases first, and then increases as battery temperature increases [85], and analogously, in CV modes the heating current decreases first, and then increases. Both the CC and CV modes can achieve a high temperature-rise rate, especially with a high heating current or a low heating voltage (Fig. 4a). For different DC heating methods, the temperature-rise rate ( ˙ T) was between 1.89 and 18.83 ◦C⋅min −1 , where the maximum is nearly ten times the minimum, indicating a large difference. The specific heating rate ( μ I) is calculated with Eq. (4), and its values range from 0.14 to 0.45 ◦C g J −1 with an average value of 0.32 ◦C g J −1 . The μ I narrowed the difference between the various DC heating methods, but the increasing trend of the μ I with the heating current still exists. This is because the heat generation of I heat ⋅(U ocv -U bat ) highly depends on battery terminal voltage (U bat ), and the U bat correlates with the DC heating current (I heat ); with a low U bat at a high discharge I heat . As only the capacity consumption (DOD) is given in references [86, 88] (Supplementary Table S2), we approximately calculate the COP with Eq. (9) by estimating the conversion coefficient (e h /DOD) during heating with the use of the OCV-SOC data. The e h /DOD approximates the average OCV during heating divided by the nominal voltage of batteries (Eq. (8)), and Fig. 4b and c illustrate the values of LiNi x Mn y Co 1-x-y O 2 (NMC) and LiFePO 4 (LFP) batteries when heating with different DOD (capacity consumption) from the various starting SOC (SOC 0 ). The e h /DOD increases with the SOC 0 due to the increased average OCV, but decreases with the DOD, which is attributed to the reduced average OCV during heating. It is higher than 1 at the high SOC 0 , which means the energy consumption (e h , %) is higher than the capacity consumption (DOD). At the SOC 0 of 100% and 90%, the e h /DOD is calculated as 1.12 and 1.01 for DC V and DC IX methods, respectively. Similarly, there is an increasing trend of COP with the heating current, mainly attributed to the decreasing U bat (Supplementary Eq. (S12)), which leads to reduced Table 2 Heating parameters and conditions, battery parameters, and maximum temperature difference for the typical DC heating methods. Other parameters, such as heating current and DOD are listed in Supplementary Table S2. References Heating parameters Heating conditions Battery parameters ΔT b (◦C) SOC 0 (%) t h (s) T amb (◦C) T tgt (◦C) Thermal condition Battery types c p (J⋅K −1 ⋅g −1 ) E ρ (Wh⋅kg −1 ) DC I , Ji et al. [85] 2C CC 64 416 −20 15 Adiabatic condition 2.2 Ah fresh 18650 NMC111/Gr 0.823 180 – DC II , Ji et al. [85] 3C CC 240 20 - DC III , Ji et al. [85] 4C CC 137 - DC IV , Ji et al. [85] 2.2V CV 127 - DC V , Ruan et al. [86] 2.43V CV 100 103 −30 2.1 In the climate chamber 8 Ah fresh pouch NMC111/Gr 1.127 96 ~3 DC VI , Ji et al. [85] 2.5V CV 64 196 −20 20 Adiabatic condition 2.2 Ah fresh 18650 NMC111/Gr 0.823 180 – DC VII , Ji et al. [85] 2.8V CV 356 - DC VIII , Oehl et al. [87] Nearly 1.86C CC ~82 (4.0V) 194 −12 4.5 Thermal insulation condition 3.5 Ah fresh 18650 NCA/Gr 0.979 260 – DC IX , Du et al. [88] optimal discharge currents 90 476 −10 5 h: 25.45 W m −2 K −1 5 Ah fresh 32650 LFP/Gr 1.13 110 – NMC111: LiNi 1/3 Mn 1/3 Co 1/3 O 2 ; Gr: Graphite; SOC 0 : Initial SOC of heating; t h : Heating duration; LFP: LiFePO 4 ; NCA: LiNi x Co y Al 1-x-y O 2 ; ΔT =T tgt -T amb ; In the CV modes, the average current is used for calculating the μ I. H. Ruan et al. Journal of Power Sources 581 (2023) 233484 8 discharge energy lost in the load controller. The COP ranges from 0.14 to 0.44, with an average of 0.29, showing a low heating efficiency. As shown in Table 2, there is only one study providing experimental data on the temperature gradient for DC methods. For that case the gradient is low as generally expected for DC methods, given that the heat generation is uniformly distributed within the battery volume [84] and generally good heat insulation with surroundings. 4.2. AC +DC heating We collect seven typical AC +DC heating methods and find the temperature-rise rate ( ˙ T) varies with different heating parameters (Table 3), with its values between 2.29 and 9.48 ◦C⋅min −1 (Fig. 5). Similarly, the specific heating rate ( μ I) shows a narrow difference, and it is almost the same with values from 0.14 to 0.20 ◦C g J −1 , except for the AC +DC II method. The μ I of AC +DC heating methods appears to be not correlated with the AC frequency, which likely results from the difference in the proportion of AC and DC components. This may be explained by the similar voltage limits for different batteries which are taken as the constraints during selecting the heating current [33,46], and the resultant similar current for heating. The COP for the typical AC +DC heating methods varies from 0.27 to 0.86 (Fig. 5b), with an average value of 0.59. Since the energy dense batteries are utilized in the AC +DC VI method [38], the energy consumption percent per temperature rise (e h /ΔT) is quite low (Fig. 5b), which can be explained by Fig. 1a, and Supplementary Note S1, but the COP is comparable to other AC +DC methods (AC +DC II and AC +DC IV [33,92]). This implies the proposed new metric, COP, provides a fair comparison between approaches, by removing the major influencing factors. The COP of AC +DC V [93] is the lowest (Fig. 5b), as only the pulse discharge current is used without the current in the charging direction and the DC component is high (Supplementary Eq. (S14)). Although the pulse heating current can be considered as AC +DC current, only discharge current is applied to the battery, and thus like the DC discharge case, the COP is low due to the energy lost in the load controller (Supplementary Eq. (S12)). The maximum temperature difference (ΔT b ), below 1.6 ◦C (Table 3), is low with AC +DC internal self-heating methods, which is generally expected because the heat generation is uniformly distributed within the battery and good heat insulation measures are usually taken. 4.3. Hybrid self-heating The seven typical HSH methods are compared in Table 4 and Fig. 6. We show that the temperature-rise rate ( ˙ T) is largely different, with the maximum of 96.0 ◦C⋅min −1 and the minimum of 0.35 ◦C⋅min −1 . However, the specific heating rate ( μ I) calculated by removing the varied battery and methodological influence is almost the same, with values between 0.49 and 1.15 ◦C g J −1 . This highlights the advantage of the proposed metric to find the common characterization of the same type of heating method, which contributes to fairly comparing different heating methods. The COP of different HSH methods ranges from 0.63 to 1.12, with the average value of 0.82. The COP that is above 1 is likely attributed to the uncertainty of the used specific heat capacity during the COP calculation (More explanation described in Discussion section). Due to the less heat dissipation to the surroundings with the heaters embedded in the battery, the COP of HSH methods using the inserted Nickel foils (HSH V , HSH VI and HSH VII [34,51,99]) generally exhibits a high COP (>0.78). The e h /ΔT in the HSH IV method [98] is rather high owing to the low energy density (96 Wh⋅kg −1 ) of the battery but the COP is not so low (0.80). This again indicates energy consumption highly depends on Fig. 4. a, Quantitative comparison of typical DC heating methods from the specific heating rate ( μ I), the temperature-rise rate ( ˙ T), and COP during heating. There is missing data on COP for the CC modes because the reference did not report the energy/capacity consumption. The conversion coefficient, i.e. ratio of energy consumption (e h , %) and capacity consumption (DOD) of b, NMC battery at 0 ◦C and c, LFP battery at −10 ◦C with different DOD under different starting SOC of heating (SOC 0 ). The OCV data refers to Refs. [89,90]. The metrics in Fig. 4a are calculated based on the data in Table 2, Fig. 4b, c, and Supplementary Table S2. H. Ruan et al. Journal of Power Sources 581 (2023) 233484 9 battery parameters and the COP offers a fair metric for heating comparison. The specific temperature difference (ΔT STD ) varies from 0.57 to 4.75 ◦C⋅hr. Despite the low temperature gradient in the HSH I method due to the low heating current [96], its ΔT STD is pretty high, due to the only one external heater used. For HSH IV and HSH VI methods [98,99], two heaters are used, with the ΔT STD obviously decreased, and the HSH VII [34], with three heaters features the lowest ΔT STD . With the greater number of heaters, both the short heat transfer pathway and low heat generation of each heater are achieved, which facilitates uniform temperature distribution during heating. 4.4. Summary of quantitative comparison With the three proposed universal metrics, we find the same type of heating methods show very similar performance (Fig. 7), and thus we can quantitatively compare the three types of typical self-heating methods, regardless of the different methodological parameters and battery types. The specific heating rate ( μ I) is the lowest for AC +DC heating methods (Fig. 7a), primarily due to the lower AC resistance. As multiple dynamic processes, such as charge-transfer, double layer charging and diffusion, are involved during DC excitation [3,14,33,35, 54], the DC resistance is often higher than the AC resistance of batteries, and the μ I is thus higher for DC heating methods. The μ I for HSH methods is the highest. Including the external heating can be equivalently taken as the increase of battery heating resistance [22,32], thus resulting in the high μ I in HSH methods. The average μ I of DC heating methods is 2.2 times the AC +DC methods, while that of HSH methods is 2.6 times the DC methods. The COP of DC heating methods is the lowest (Fig. 7b), because the energy of the battery discharged to the load controller is not used. With the utilization of the discharge energy in HSH methods, the COP is significantly increased and we find HSH methods show the highest average COP (above 0.82), increasing by 181% compared to DC heating. The COP of AC +DC heating methods is relatively high (0.59), because the relatively low DC component compared with the applied heating current leads to less energy consumption (Supplementary Eq. (S14)). The HSH methods exhibit a 38% higher COP than the AC +DC heating methods, which is likely attributed to the recycling of the discharge energy and the low heat dissipation to the surroundings due to the fast heating speed. The temperature gradient within the battery is high for the HSH methods (Fig. 7c), due to integrating external heating. Since the thermal conductivity of batteries is limited with the through-plane values ranging from 0.40 to 1.03 W m −1 K −1 [21,101,102], there is a large temperature difference within the battery. The specific temperature difference (ΔT STD ) within the battery reaches 2.68 ◦C⋅hr for the HSH methods. While for the other self-heating methods, the ΔT STD is low and below 0.41 ◦C⋅hr, due to just including the internal self-heating. It should be mentioned that the temperatures, capacity consumption (DOD), starting SOC (SOC 0 ) for heating, and current, which are measured in various ways (including varied sensors) in different references, would pose uncertainty to the calculated triangular metrics. This would be one reason for the variance of each calculated indicator in Fig. 7a, b and c. To make a consistent comparison, it is suggested to calibrate the sensing precision for measuring temperature, current and capacity in each heating paper. 5. Discussion 5.1. Rationality analysis on triangle metrics We investigate the physical meaning of the defined metric, μ I. If the heat dissipation is neglected, deduced from Eq. (2) (See Supplementary Note S2), the specific heating rate, μ I, equals the ratio of the (equivalent) Table 3 Heating parameters and conditions, battery parameters, and maximum temperature difference for the typical AC +DC heating methods. Other parameters are listed in Supplementary Table S2. References Heating parameters Heating conditions Battery parameters ΔT b (◦C) SOC 0 (%) t h (s) T amb (◦C) T tgt (◦C) Thermal condition Battery types c p (J⋅K −1 ⋅g −1 ) E ρ (Wh⋅kg −1 ) AC +DC I , Mohan et al. [91] 10Hz pulse current 60 274 −20 10.8 h: 5 W⋅m −2 ⋅K −1 2.3 Ah fresh 26650 LFP/Gr 1.109 105 – AC +DC II , Jiang et al. [33] 754Hz SAC 100 600 −20.8 2.1 h: 2.04 W⋅m −2 ⋅K −1 35 Ah fresh pouch NMC/Gr 1.177 128.2 1.6 AC +DC III , Shang et al. [37] 833Hz SAC – 354 −20 0 In the climate chamber 2.5 Ah 18650 NMC/Gr – ~200 - AC +DC IV , Shang et al. [92] 22 kHz SAC 162 AC +DC V , Qu et al. [93] 0.5s pulse current 100 175 −10 10 h: 5.32 W⋅m −2 ⋅K −1 2.0 Ah 18650 LCO/Gr 1.05 164 – AC +DC VI , Li et al. [38] 1.6s Pulse (4C/4C) 50 300 −7 29.1 h: 9.6 W⋅m −2 ⋅K −1 50 Ah fresh prismatic NMC532/Gr 1.126 262 - AC þDC VII , Zhang et al. [94] 10 kHz SAC 100 132 −20 0 In the climate chamber 2.5 Ah 18650 NMC/Gr – 200 0.3 NMC532: LiNi 0.5 Mn 0.3 Co 0.2 O 2 ; LCO: LiCoO 2 . H. Ruan et al. Journal of Power Sources 581 (2023) 233484 16 [81] Xiaogang Wu, Zhihao Cui, Ersong Chen, Jiuyu Du, Capacity degradation minimization oriented optimization for the pulse preheating of lithium-ion batteries under low temperature, J. Energy Storage 31 (2020), 101746. [82] Ryan S. Longchamps, Xiao-Guang Yang, Shanhai Ge, Teng Liu, Chao-Yang Wang, "Transforming rate capability through self-heating of energy-dense and nextgeneration batteries.", J. Power Sources 510 (2021), 230416. [83] Nan Piao, Xuning Gao, Huicong Yang, Zhenqiang Guo, Guangjian Hu, HuiMing Cheng, Feng Li, Challenges and development of lithium-ion batteries for low temperature environments, eTransportation 11 (2022), 100145. [84] Yudi Qin, Zhoucheng Xu, Yueqiang Wu, Languang Lu, Xuebing Han, Jiuyu Du, Minggao Ouyang, Temperature distribution of lithium ion battery module with inconsistent cells under pulsed heating method, Appl. Therm. Eng. 212 (2022), 118529. [85] Yan Ji, Chao Yang Wang, Heating strategies for Li-ion batteries operated from subzero temperatures, Electrochim. Acta 107 (2013) 664–674. [86] Haijun Ruan, Jiuchun Jiang, Bingxiang Sun, Xiaojia Su, Xitian He, Kejie Zhao, An optimal internal-heating strategy for lithium-ion batteries at low temperature considering both heating time and lifetime reduction, Appl. Energy 256 (2019), 113797. [87] Joachim Oehl, Andreas Gleiter, Daniel Manka, Fill Alexander, Kai Peter Birke, High frequency alternating current heating method for Li-Ion cells based on boost converter topology, J. Energy Storage 53 (2022), 105169. [88] Jiuyu Du, Zhe Chen, Feiqiang Li, Multi-objective optimization discharge method for heating lithium-ion battery at low temperatures, IEEE Access 6 (2018) 44036–44049. [89] Fangdan Zheng, Yinjiao Xing, Jiuchun Jiang, Bingxiang Sun, Jonghoon Kim, Michael Pecht, Influence of different open circuit voltage tests on state of charge online estimation for lithium-ion batteries, Applied energy 183 (2016) 513–525. [90] Yinjiao Xing, Wei He, Michael Pecht, Kwok Leung Tsui, State of charge estimation of lithium-ion batteries using the open-circuit voltage at various ambient temperatures, Appl. Energy 113 (2014) 106–115. [91] Shankar Mohan, Youngki Kim, G. Anna, Stefanopoulou, Energy-conscious warmup of li-ion cells from subzero temperatures, IEEE Trans. Ind. Electron. 63 (5) (2016) 2954–2964. [92] Yunlong Shang, Kailong Liu, Naxin Cui, Nan Wang, Ke Li, Chenghui Zhang, A compact resonant switched-capacitor heater for lithium-ion battery self-heating at low temperatures, IEEE Trans. Power Electron. 35 (7) (2019) 7134–7144. [93] Z.G. Qu, Z.Y. Jiang, Qiong Wang, Experimental study on pulse self–heating of lithium–ion battery at low temperature, Int. J. Heat Mass Tran. 135 (2019) 696–705. [94] Yuanxi Zhang, Yaning Yang, Yunlong Shang, Naxin Cui, A high frequency AC heater based on switched capacitors for lithium-ion batteries at low temperature, J. Energy Storage 42 (2021), 102977. [95] Xiaoxuan Zhang, Reinhardt Klein, Anantharaman Subbaraman, Sergei Chumakov, Xiaobai Li, Jake Christensen, Christian Linder, Sun Ung Kim, Evaluation of convective heat transfer coefficient and specific heat capacity of a lithium-ion battery using infrared camera and lumped capacitance method, J. Power Sources 412 (2019) 552–558. [96] Chengning Zhang, Xin Jin, Junqiu Li, PTC self-heating experiments and thermal modeling of lithium-ion battery pack in electric vehicles, Energies 10 (4) (2017) 572. [97] Yunlong Shang, Chong Zhu, Yuhong Fu, Chunting Chris Mi, An integrated heater equalizer for lithium-ion batteries of electric vehicles, IEEE Trans. Ind. Electron. 66 (6) (2018) 4398–4405. [98] Haijun Ruan, Bingxiang Sun, Andrew Cruden, Tao Zhu, Jiuchun Jiang, Xitian He, Xiaojia Su, Engy Ghoniem, Optimal external heating resistance enabling rapid compound self-heating for lithium-ion batteries at low temperatures, Appl. Therm. Eng. 200 (2022), 117536. [99] Guangsheng Zhang, Shanhai Ge, Terrence Xu, Xiao-Guang Yang, Hua Tian, ChaoYang Wang, Rapid self-heating and internal temperature sensing of lithium-ion batteries at low temperatures, Electrochim. Acta 218 (2016) 149–155. [100] S.J. Drake, D.A. Wetz, J.K. Ostanek, S.P. Miller, J.M. Heinzel, A. Jain, Measurement of anisotropic thermophysical properties of cylindrical Li-ion cells, J. Power Sources 252 (2014) 298–304. [101] Marco Steinhardt, Elisabeth Irene Gillich, Maximilian Stiegler, Andreas Jossen, Thermal conductivity inside prismatic lithium-ion cells with dependencies on temperature and external compression pressure, J. Energy Storage 32 (2020), 101680. [102] Marco Steinhardt, Elisabeth Irene Gillich, Rheinfeld Alexander, Ludwig Kraft, Markus Spielbauer, Bohlen Oliver, Andreas Jossen, Low-effort determination of heat capacity and thermal conductivity for cylindrical 18650 and 21700 lithiumion cells, J. Energy Storage 42 (2021), 103065. [103] Jiangong Zhu, Zechang Sun, Xuezhe Wei, Haifeng Dai, Weijun Gu, Experimental investigations of an AC pulse heating method for vehicular high power lithiumion batteries at subzero temperatures, J. Power Sources 367 (2017) 145–157. [104] Jiuchun Jiang, Haijun Ruan, Bingxiang Sun, Weige Zhang, Wenzhong Gao, Linjing Zhang, A reduced low-temperature electro-thermal coupled model for lithium-ion batteries, Appl. Energy 177 (2016) 804–816. [105] Sebastian Ludwig, Ilya Zilberman, F. Horsche Max, Tim Wohlers, Andreas Jossen, "Pulse resistance based online temperature estimation for lithium-ion cells.", J. Power Sources 490 (2021), 229523. [106] Sijia Liu, Jiuchun Jiang, Wei Shi, Zeyu Ma, Hongyu Guo, Butler–volmer-equationbased electrical model for high-power lithium titanate batteries used in electric vehicles, IEEE Trans. Ind. Electron. 62 (12) (2015) 7557–7568. [107] Wladislaw Waag, Christian Fleischer, Dirk Uwe Sauer, On-line estimation of lithium-ion battery impedance parameters using a novel varied-parameters approach, J. Power Sources 237 (2013) 260–269. [108] Maan Al-Zareer, Andrew Michalak, Carlos Da Silva, Cristina H. Amon, Predicting specific heat capacity and directional thermal conductivities of cylindrical lithium-ion batteries: a combined experimental and simulation framework, Appl. Therm. Eng. 182 (2021), 116075. [109] Jiacheng He, Rekabra Youssef, Md Sazzad Hosen, Mohsen Akbarzadeh, Joeri Van Mierlo, Maitane Berecibar, A novel methodology to determine the specific heat capacity of lithium-ion batteries, J. Power Sources 520 (2022), 230869. [110] Chong Zhu, Yunlong Shang, Fei Lu, Yan Jiang, Chenwen Cheng, Chris Mi, Core temperature estimation for self-heating automotive lithium-ion batteries in cold climates, IEEE Trans. Ind. Inf. 16 (5) (2019) 3366–3375. [111] Shen Li, Niall Kirkaldy, Cheng Zhang, Krishnakumar Gopalakrishnan, Tazdin Amietszajew, Laura Bravo Diaz, Jorge Varela Barreras, et al., Optimal cell tab design and cooling strategy for cylindrical lithium-ion batteries, J. Power Sources 492 (2021), 229594. [112] Haijun Ruan, Jorge Varela Barreras, Timothy Engstrom, Merla Yu, Robert Millar, Billy Wu, Lithium-ion battery lifetime extension: a review of derating methods, J. Power Sources 563 (2023), 232805. [113] Cheng Zhang, Tazdin Amietszajew, Li Shen, Monica Marinescu, Gregory Offer, Chongming Wang, Yue Guo, Rohit Bhagat, Real-time estimation of negative electrode potential and state of charge of lithium-ion battery based on a half-celllevel equivalent circuit model, J. Energy Storage 51 (2022), 104362. H. Ruan et al.