Testing and Characterizing Commercial 18650 Lithium-Ion Batteries

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Testing and Characterizing Commercial 18650 Lithium-Ion Batteries

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Advances in Energy Storage Materials/Devices and Solid-State Batteries

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14 May 2024

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21 May 2024

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Abstract

Reduced-order electrothermal models play a key role in the design and control of lithium- ion cell stacks, calling for accurate model parameter calibration. This paper presents a complete electrical and thermal experimental characterization procedure for coupled modeling of cylindrical lithium-ion cells in order to implement them in a prototype Formula SAE hybrid racing car. The main 4goal of the tests is to determine cell capacity variations with temperatures and discharge currents, to predict the open circuit voltage of the cell and its entropic component. A simple approach for the characterization of the battery equivalent electrical circuit and a two-steps thermal characterization method are also shown. The investigations are carried out on four commercial 18650 NMC lithium cells. The model demonstrated to predict the battery voltage at a RMS error lower than 20mV and the temperature to a RMS error equal to 0.5 ◦C. The authors hope that this manuscript can contribute to the development of standardized characterization techniques for such cells, while offering experimental data and validated models that can be used by researchers and BMS designers in different applications.

Keywords:

Subject: Engineering - Electrical and Electronic Engineering

1. Introduction

Thanks to the high energy density and specific energy [1], lithium-ion batteries have gone through a dizzying diffusion in recent years, both in the automotive sector (passing from a market share of 0.2 in 2013 to 13% in 2022 [2]) and for portable electronic devices (15 billion of mobile phones in the world in 2021 [3]). Cells are typically assembled in modules, or packs, to achieve the desired battery rating. In modules, cells are connected both in series and in parallel to attain the desired voltage and energy capacity. For instance, many electric cars operate in the range 400-800 volts, while individual cells generally have voltages ranging from 3-4 volts. The proper and safe module operation is ensured by the Battery Management System (BMS), whose effective design calls for an accurate and physically consistent electrical and thermal model of the Li-ion pack [4]. This applies to several BMS features, such as: State of Charge (SoC) measurements, State of Health (SoH) estimation (also in extreme conditions), circuit balancing and thermal runaway detection and suppression to preclude fire hazards.

As regards the last issue, the acceptable operational temperature for Li-ion cells spans from -20 to 60 °C, with optimal performance occurring between 15 °C and 35 °C. Nevertheless, heat generation within a Li-ion battery pack is inevitable due to various losses and entropic effects, resulting in a uneven temperature distribution with gradients among module cells. Uncontrolled heat generation can lead not only to thermal runaway but also to capacity loss and cell instability, so that the temperature differences among cells should be limited to 6 °C to ensure optimal operation and preserve the battery SoH.

Developing a BMS is a complex task that entails creating reduced battery models, estimators, and functionalities to guarantee the battery optimal performance in all operating conditions and throughout its entire lifespan. All of them must operate with limited computational resources on a cost-effective microcontroller. This calls for significant expertise and technical know-how, which may lack in a framework of a rapidly developing technology, a condition particularly evident in the battery industry with emerging chemistries, each presenting its own challenges, requirement and features. To address this, an accurate characterization of the cells is vital.

This paper describes some electrical and thermal experimental characterization procedures conceived for producing with high accuracy all the cell physical parameters needed in a reliable electrical and thermal lumped models. Four commercial 18650 Li-ion cells of different manufacturers have been considered: Molicel^® P28A, P28B and P30B and Sony Murata VTC5D. The following parameters have been obtained: the cell capacity at different temperatures and discharge currents (C-rates), the Open Circuit Voltage (OCV) at varying State of Charge (SoC), the entropic coefficient and electrical and thermal lumped parameters.

This work is part of a collaborative research between three groups within the Department of Industrial Engineering (DII) of the University of Padua (Padova, Italy): Electrochemical Energy Storage and Conversion Lab (EESCOLab), Modelling, Analysis and Research in Turbomachinery and Energy Systems (MARTES), RaceUp Formula SAE Students Team, togheter with the company FIAMM Energy Technology S.p.A. The target of this work is to analyse different lithium-ion cells in order to implement them in a prototype Formula SAE hybrid racing car. Formula SAE is a student design competition program organized by SAE International (previously known as the Society of Automotive Engineers). Few articles in the literature report accurate descriptions of measurement techniques, experimental results and their use in suitably validated models. For the sake of comparison, different techniques published in the literature are also detailed. The obtained models demonstrated to successfully predict the battery voltage at a 8 RMS error lower than 20 mV and the temperature to a RMS error equal to 0.5 °C. The authors hope that this this manuscript can be useful for the development of standardized characterization techniques of such cells, while also providing experimental data and validated models that researchers and BMS designers can utilize across various applications.

Section 2 describes the reduced-order modeling of 18650 cells, both thermal and electrical. Section 3 describes the methods for the electrical and thermal characterization of the four type of cells. The former concern the determination of the cell capacity at different C-rate currents and temperatures, the dependence of the OCV with the SoC, the impulsive current charge/discharge tests to identified the Equivalent Circuit Model (ECM) parameters and the determination of the entropic contribution. The thermal characterization deals with the methods for determining the main thermal parameters involved in thermal modeling, i.e. the cell thermal capacity, the conduction thermal resistance between cell bulk and surface and the convection thermal resistance between the cell surface and environment. In Section 4 the validation of the battery models for four different load profiles is presented, demonstrating their good accuracy. The significance of this work is finally outlined in the conclusion in Section 5.

2. Reduced-Order Coupled Modeling of 18650 Cells

Several approaches are presented in the literature to develop reduced-order models capable of predicting the battery voltage and temperature for short dynamic current cycle [5,6], spanning from electrochemical-based to circuit-based types, as well as empirical and data-driven models for voltage prediction coupled with thermal models. Due to ease of characterization and implementation in Simulink [7], an Electrical Circuit Model (ECM) approach was chosen to model the cell electrical behaviour, coupled with an array-based thermal circuit model simulating the battery temperatures.

The ECM, represented in Figure 1, consists of a voltage source

U_{O C}

giving the cell OCV, a resistor

R_{s}

and the series of two

R C

loops, each consisting of a resistor

R_{i}

and a capacitor

C_{i}

. Similar models using only resistors and capacitors as passive elements are largely presented in the literature ([8,9,10]). To account for the effects of the physical conditions on the cell performance, the ECM elements were assumed to be driven as follows:

U_{o c}

is driven by the SoC, while

R_{s}

R_{i}

and

C_{i}

are driven by the SoC, operating temperature and current sign. Consistently with the targeted model accuracy, minor dependencies such as current magnitude and aging, were neglected [10,11].

The electrical model is coupled with the thermal model through the heat generation equation [12]:

Q = I (V_{t} - U_{O C}) + I T_{a v g} \frac{d U}{d T}

(1)

where

T_{a v g}

[

K

] is the battery average temperature and

d U

d T

[

V

K

] is the entropic coefficient, i.e. the temperature derivative of the OCV, that depends on the SoC [13].

The lumped thermal model is shown in Figure 2. As commonly done in literature [12,14], the battery surface temperature was assumed homogeneous and the battery thermal behaviour perfectly axis-symmetric, so that heat exchanges at the top and bottom cell caps were neglected. The room temperature was assumed homogeneous and constant. The battery casing thermal capacity was neglected, because it was considered orders of magnitude smaller than the cell one [15].

The equations of the thermal model are reported in Equation 2:

\{\begin{matrix} C_{c} \frac{d T_{c}}{d t} = \frac{T_{s} - T_{c}}{R_{c}} + Q \\ 0 = \frac{T_{a i r} - T_{s}}{R_{u}} + \frac{T_{c} - T_{s}}{R_{c}} \end{matrix}

(2)

where

T_{c}

is the cell bulk temperature,

T_{s}

is the cell surface temperature,

C_{c}

is the cell thermal capacity,

R_{c}

is the conduction thermal resistance between cell bulk and surface and

R_{u}

is the convection thermal resistance between the cell surface and the room, while Q is the heat rate, generated by the cell losses.

3. Testing and Characterization

3.1. Materials and Experimental Set-Up

Four commericial 18650 Li-ion cells of different manufacturers underwent the testing procedure: Molicel^® P28A, P28B and P30B and Sony Murata VTC5D (Figure 3.) In Table 1, the cells characteristics and performance are reported as from the manufacturers data-sheet.

The tests were mostly conducted in the laboratories of FIAMM Energy Technology using the following major equipment:

Thermal chamber Binder Mk115, to maintain constant operating temperature in each experiment and to allow testing at different temperatures.
Four-terminal sensing cell holder: a BioLogic CBH-4 was used for electrical tests,.
In-house polymeric cell holder for thermal tests.
Thermocouples array, to detect the battery surface temperature and the room temperature in side the thermal chamber, connected to a Hioki LR8450 data logger.
Cell cycler, consisting of a Rohde&Schwarz^® HMP4040 charger and a) a Rigol DLC3031 load, to measure the entropic contribution and the pseudo- $U_{O C}$ experiment, and b) a Digatron Systems UBT150-020 for other tests.

The experimental set-up was controlled by a PC and data were post-processed in MatLab and Simulink environments. Figure 4 shows a scheme of the experimental set-up.

3.2. Electrical Characterization Tests

3.2.1. Capacity Determination

The battery capacity at the Beginning of Life (BoL) is an important Key Performance Indicator (KPI) for applications where the long cycle life is not a driving design parameters, as in the case of the target application of this work, i.e. a FSAE racing car [16,17,18].

In order to evaluate the dependence of cell capacity on the temperature and discharge current, as in [19,20,21,22], the following testing procedure was implemented:

Fully charge the cell to $S o C = 100 %$ with a) 1 C Constant Current (CC) till the voltage reaches the upper cut-off ( $4.2$ $V$ ) and b) Constant Voltage (CV) till the current reduces to the rate C/20, at reference temperature $T_{r e f}$ = 25 °C.
Put the thermal chamber at the temperature $T_{i}$ and wait 1 h to allow cell temperature and voltage relaxation.
Discharge the cell at CC with a rate $C_{r, i}$ till the voltage reduces to the lower cut-off voltage $2.5$ $V$ .
Bring the thermal chamber to the reference temperature $T_{r e f}$ and wait 1 h to allow cell temperature and voltage relaxation.
Repeat step 1-4 five times.

The testing procedure was run at

T_{i}

= 5 °C, 25 °C, and 40 °C and at discharge currents with C-rate

C_{r, i}

0.5

C, 1 C, 3 C, and 5 C. The cell charge capacity [mAh] for each test was computed as the time integral of the current during the CC discharge. To quantify the spread of performance among different cells of the same type [23], three samples for each model were tested and each of them underwent five discharges. The capacity of the cell model was then obtained as the average of such 15 tests. In addition, the standard deviations of these tests are are shown in Table 2.

3.2.2. OCV Measurements

Determining the dependence of

U_{o c}

on SoC is crucial to accurately predict the battery voltage

V_{t}

. The main experimental techniques for a priori OCV vs SoC measurements are the "pseudo-

U_{o c}

test", also referred to as "low current continuous OCV measurement", and the "intermittent current pulse test" [24,25]. Measurement data can be collected in look-up table or used to fit mathematical functions [26]. In the present work, the OCV vs SoC curve was obtained applying the pseudo-

U_{o c}

test for all the cells, conisting in the following procedure:

Fully charge the cell to $S o C = 100 %$ with a) 1 C Constant Current (CC) till the voltage reaches the upper cut-off ( $4.2$ $V$ ) and b) a Constant Voltage (CV) till the current reduce to a rate C/20, at reference temperature $T_{r e f}$ = 25 °C.
Relax the cell voltage for 1 h.
Discharge the cell with CC at a rate C/20 till the voltage reduces to the lower cut-off $2.5$ $V$ .
Charge the cell with CC at a rate C/20 till the voltage reaches the upper cut-off $4.2$ $V$ .

The cell OCV curve was obtained as the average between voltages in charge and discharge (Figure 5).

This is a simple and reliable method, which has proven to be successful in the present application. Future developments may involve the use of more complex post-processing data algorithms, aimed at identifying voltage hysteresis in OCV measurements [27], correcting partial relaxations effects during pulse tests [28], or implementing filtering techniques (e.g., Kalman filters) as in [29].

3.2.3. GITT characterization tests

Impulsive current charge/discharge tests are commonly presented in literature to determine the ECM parameters of lithium-ion batteries [10,12,30]. Such impulsive test take different names, e.g. Galvanostatic Intermittent Titration Technique (GITT) test. Considering the ECM decribed above, the test was oriented to identify the circuit parameters in charge and discharge at different operating temperatures. The testing procedure used for GITT characterization was as follows:

Fully charge the cell ( $S o C = 100 %$ ) with a) 1 C Constant Current (CC) till the voltage reacheas the upper cut-off ( $4.2$ $V$ ) and b) Constant Voltage (CV) till the current reduced to a rate C/20, at reference temperature $T_{r e f}$ = 25 °C.
Relaxe the cell voltage for 1 h.
Impose a discharge 2 C current impulse lasting for $τ_{i m p}$ , then relax the battery voltage for 1 h.
Repeat 3 till the voltage reachers the lower cut-off $2.5$ $V$ , then relax the battery voltage for 1 h.
Repeat 3 with charge current impulse till the voltages reachers the upper cut-off $4.2$ $V$ .
Repeat the impulsive test at 5 and 40 °C.

The duration of the load impulse

τ_{i m p}

varied between 180

s

when

25 % \leq S o C \leq 75 %

, and 72

s

otherwise.

Data-post processing consisted in an optimization procedure, with the goal of minimizing the error between the cell voltage measured during experiments and that computed with ECM-based simulations. The output of the GITT characterization was a set of look-up tables defined for different temperatures and SoCs, in charge and discharge. The optimization problem was developed in the Matlab Optimization Toolbox making use of the lsqnonlin solver. A finite difference approximation approach was used to implement ECM behaviour. The differentiation time step corresponded to the sampling frequency of cell voltage during experiments. To reduce the computational cost, instead of performing a single optimization through the entire GITT test, independent optimizations were run for each GITT cycle (pulse and relaxation), corresponding to given SoC, temperature, and current sign. The output parameters calculated for a given cycle were then used as guess values for the subsequent one, which resulted in a layered approach [8]. Figure 6 shows the experimental and modelled GITT test voltages , while the ECM parameters tables for the four tested cell models are reported in Appendix.

3.3. Entropic Contribution Measurement

Entropic contribution of lithium-ion cells is traditionally determined from potentiometric and calorimetric measurements [31]. The former consists in measuring the cell OCV at different temperatures and SoCs [32]. A thermal cycle needs to be applied after complete relaxation of the cell voltage. In addition, at each temperature of the cycle the thermal equilibrium condition requires some time to be reached and the larger the thermal capacity of the cell, the larger the system thermal time constant [33]. Instead, the calorimetric method is based on the cell heat flux measurement during charge/discharge operations: the entropic contribution is determined after separating the irreversible and the reversible heat contributions in the overall measured heat flux [33]. This method can be considered superior to the potentiometric one, allowing for a quasi-continuous measurement of the cell entropic profile. On the other hand, it presents some disadvantages: many cell electrical parameters [34,35] have to be previously determined and advanced cell-specific experimental equipment is needed, as an isothermal or accelerating-rate calorimeters.

To overcome the limitations of the potentiometric and calorimetric methods, a novel

\partial U / \partial T

determination technique via Electrothermal Impedance Spectroscopy (ETIS) has been developed by Schmidt et al. in [36]: a thermal transfer function is obtained to relate the surface temperature to the heat flux, then the reversible heat flux is split from the irreversible term by Fourier analysis. Such technique, used also by Geng et al. in [33], presents some drawbacks regarding the precise determination of a thermal transfer function and the spectroscopy data analysis [31].

Recently, different improved approaches have been proposed to reduce the testing time required by the potentiometric method, mainly in the form of correction of the voltage baseline drift, as in [37] and [31]. Furthermore, in [38] Lin et al. proposed an improved potentiometric method based on current Positive Adjustment Method (PAM). In the present work, the Common Potentiometric Method (CPM) was modified to reach the desired SoC, i.e. after a long charge (or discharge) phase an opposite current was applied for a short time. Such PAM was expected to accelerate the depolarization and reduce the voltage relaxation time (from 10 - 20 h of the CPM to

\sim 10

min of the PAM). The approach was validated by comparing the measured entropy profile of 18650 lithium ion cylindrical cells with those obtained from CPM: results showed good agreement between the two, thus confirming the advantage of saving test time.

A similar approach to the PAM was used in this paper. Considering that all cells are based on similar NMC chemistry and have similar forms, sizes and capacities, only the P30B model was tested. The testing procedure consisted of:

Fully charge the cell to $S o C = 100 %$ at the reference temperature $T_{r e f}$ = 25 °C.
Relax the cell voltage for 20 h.
Apply a controlled thermal cycle ( 1 h at 20 °C, 1 h at 10 °C, 1 h at 30 °C, 1 h at 40 °C, 1 h at 25 °C).
Discharge the cell for $τ_{e n t r}$ at 1 C rate and then charge at $0.1$ C rate for $2 \times τ_{e n t r}$ .
Relax the cell voltage for 1 h.
Repeat step 3-5 till the voltage reaches the lower cut-off $2.5$ $V$ .

The value of

τ_{e n t r}

varied in order to collect more data points at high and at low

S o C

. Figure 7 shows the current profile imposed and the voltage measured at the cell terminals, with a zoom on the temperature profile for

U_{O C}

3.832

V

During the PAM test, the battery Open Circuit Voltage (OCV) was measured at various temperatures and SoCs (Figure 8).

3.4. Thermal Characterization Tests

The thermal parameters involved in thermal modeling of lithium ion cell can be identified in different ways. A common approach is to used calorimetric measurements to determine the battery heat capacity and the anisotropic thermal conductivity: Vertiz et al. [40] used Accelerating Rate Calorimeter (ARC) technique to determine heat capacity and thermal conductivity of a lithium-ion pouch cell, coupling an electrical circuit model to a thermal circuit model. Sheng et al. [41] imposed controlled heat flux to investigate thermal parameters of a prismatic lithium-ion cell, whereas Cao et al. studied the heat generation characteristics through heat flux measurements of commercial 18650 cells [42]. Calorimetric measurements, though precise, require expensive equipment: this is one of the reason why many papers on thermal modelling of Li-ion cells cited above adopted the volume-fraction method to determine the battery thermal parameters from the materials properties. This is the case of [43,44] or [45], where cylindrical cells are studied coupling a electrochemical model with a 2-D thermal model.

Other works present thermal characterization procedures based on cell surface temperature measurements and obtain the internal thermal parameters through numerical optimization studies. Al-Zareer et al. [46] determined the heat capacity and the radial and axial cell thermal conductivities by measuring the cell surface temperature and implementing an optimization routine on a COMSOL Multiphysics^® 3-D model for a cylindrical 18650 cell. A similar approach to identify the heat transfer coefficient and the thermal parameters for a prismatic lithium-ion cell was adopted by Samad et al. [47] using MATLAB software and considering an array of surface temperature probes, coupling the thermal model with a two RC-loops ECM. Different online parameterization algorithms have also been proposed, in particular for BMS application for battery stacks, as that described by Lin et al. [48], which implemented a simple equivalent circuit-based thermal model, or that described in [49].

Bryden et al. [50] proposed a new method based on a non-invasive cell surface temperature measurements in two experimental heat transfer conditions: natural convection and forced convection. Such method, used also by Akbarzadeh et al. [9] on prismatic cells, allows a fast and easy thermal characterization and it is particularly suitable for equivalent thermal circuit models and for these reasons it was chosen in this work.

The experimental procedure applied to the cell model consisted of:

Fully charge the cell and then discharge to $S o C \approx 50 %$ at reference temperature $T_{r e f}$ = 25 °C.
Relax the cell voltage and temperature for 1 h.
Apply a square alternating wave load current with period of 120 $s$ , a peak-to-peak amplitude corresponding to a rate of 6 C till reaching a steady-state thermal equilibrium on the cell surface. In this way, the entropic heat contribution could be neglected (see Equation 1).
Repeat step 1-3 in two heat exchange condition:

$C o n d 1$ ) low-convective heat transfer condition (the cell is placed in the $C e l l H o l d 1$ and exchanges heat by natural convection with the air inside the thermal chamber),

$C o n d 2$ ) high-convective heat transfer condition (the cell is placed in $C e l l H o l d 1$ and a pair of fans cools it down, so that heat exchange is mainly driven by forced convection).

In Equation 2,

T_{c}

in the first equation can be replaced giving:

C_{c} (1 + \frac{R_{c}}{R_{u}}) \frac{d T_{s}}{d t} = \frac{T_{a i r} - T_{s}}{R_{u}} + Q

(3)

By measuring

V_{t}

the time dependent heat rate Q was calculated: once reached the thermal quasi-stationary equilibrium condition (

T_{s, inf}

), we can estimate a first-try value for

R_{u, 0}

as:

R_{u, 0} = \frac{T_{s, \infty} - T_{a i r}}{Q}

(4)

Considering the two different heat transfer conditions

C o n d 1

and

C o n d 2

and defining:

C_{p}^{'} = C_{c} (\frac{R_{c}}{R_{u}} + 1)

(5)

we can write Equation 3 as:

\{\begin{matrix} C_{p, 1}^{'} = C_{c} (\frac{R_{c}}{R_{u, 1}} + 1) \\ C_{p, 2}^{'} = C_{c} (\frac{R_{c}}{R_{u, 2}} + 1) \end{matrix}

(6)

A Levenberg-Marquardt optimization algorithm was run using the MATLAB routine lsqcurvefit: the value of

R_{u, 1}

and

R_{u, 2}

obtained from Equation 4 were considered as first tries, and the final values of

C_{p, 1}^{'}

R_{u, 1}

and

C_{p, 2}^{'}

R_{u, 2}

were calculated by minimizing the residuals between the modelled and the experimental temperature

T_{s}

in the two conditions. Eventually, the algebraic solution of Equation 6 system yielded

C_{c}

and

R_{c}

. Figure 9 shows the thermal characterization

C o n d 1

and

C o n d 2

test profiles of the P28A cell, revealing a good agreement between the experimental and simulated

T_{s}

profiles, obtained using the optimized thermal parameters.

The thermal model parameters obtained from the thermal characterization tests for four tested cell are listed in Table 3.

4. Model Validation

To validate the battery model, four different load profiles have been considered.

The first and the second are taken from common autmotive sector oriented testing profiles, respectively the Beijing Dynamic Stress Test (BJDST) and the Federal Urban Driving Schedule (FUDS) [51]. The third profile is named Non-Dynamic Cycle (NDC) and it accounts for non intensive electrical device loads, like smartphones or low usage systems [10]. The fourth is the High Power Load (HPL) profile, characterized by high magnitude discharge current peaks (up to 10 C) [7].

The BJDST, FUDS and NDC profiles were used to validated the model voltage prediction for the batteries considered, while HPL was also targeting the validation of

T_{s}

model prediction.

Experimental data were collected using the testing facility described above, the thermal chamber air temperature equal to 24 °C.

Validation results for BJDST and FUDS profiles are reported in Figure 10 and in Figure 11, while Figure 12 and Figure 13 account for the NDC and the HPL profiles respectively. In Table 4, the Root Mean Square Error (RMSE) for the various profiles tested are reported.

The results show that voltages are predicted with a RMSE lower than 20

m

V

, while

T_{s}

predicition presents a RMSE lower than

0.3

K

. It is worth noting how the ECM could be further improved. In particular, the actual Coulomb counting based SoC estimation could be enhanced by using an optimization routine (e.g., Kalman filter). In this way, the dependence of the battery capacity on the load could be better accounted: in the actual work, a charge/discharge

η

equal to

0.9

was considered. Furthermore, an hysteretic behaviour was noted when measuring the OCV, in particular for the Molicel P30B (that presents the higher errors on voltage prediction): this could be considered adding an hysteresis term in

V_{t}

prediction as in [10].

5. Conclusions

In this work, a group of four different market available 18650 Li-ion cells consisting of Molicel P28A, P28B and P30B and Sony Murata VTC5D was tested and characterized.

The CC discharge performance were measured for all the cells at operating temperature of 5 °C, 25 °C and 40 °C and C-rate of

0.5

C, 1 C, 3 C and 5 C. Performance spreading was accounted giving the standard deviation over a sample of 3 cells per model.

A second order

R C

ECM model was characterized: first the OCV curves were measured through a pseudo-

U_{o c}

technique, then the ECM parameters were extrapolated using a Matlab based algorithm from GITT tests at various temperatures and SoC.

Furthermore, the entropic contribution was measured using a PAM approach. This resulted in shortening the time needed to measure the temperature derivative of the OCV at various

S o C

, without the need for expensive equipment as calorimeters or complex modelling. Results obtained showed a good agreement with literature for NMC based cells.

Moreover, the thermal behaviour of the cells was described using a thermal lumped parameters model, that has been characterized using only temperatures data.

The coupled model was validated over three dynamic and one non-dynamic load profiles. Battery terminals voltages were predicted with an RMSE lower than 20

m

V

, while the battery surface temperature prediction RMSE was lower than

0.3

K

. Further developments of the ECM model can consider the addition of Kalman filter to predict the battery

S o C

over longer simulations and improving the circuit taking into account voltage hysteresis phenomena.

It is worth noting how overall performance of Molicel P28A, P28B and Sony Murata VTC5D are pretty close: in particular, given the same current load profile, overvoltages are similar, thus giving a similar thermal behaviour. On the contrary, the Molicel P30B, considering its higher nominal capacity results in lower overvoltages and in a lower temperature rise considering the same testing profile.

Author Contributions

Conceptualization, N.Z.; methodology, N.Z.; software, N.Z., B.D., E.D., G.C1.; validation, N.Z. and B.D.; formal analysis, A.T. and M.G.; investigation, N.Z.; resources, B.D. and G.C2.; data curation, N.Z. and B.D.; writing original draft preparation, N.Z.; writing, review and editing, A.L., A.T. and M.G.; visualization, N.Z.; supervision, G.C2., A.L. and M.G.; project administration, M.G.; funding acquisition, A.L. and M.G. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author. The data are not publicly available due to confidentiality.

Acknowledgments

This work was supported by FIAMM Energy Technologies, Montecchio Maggiore, Italy.

Conflicts of Interest

The authors declare no conflict of interest.

Sample Availability

Samples of the compounds ... are available from the authors.

Abbreviations

The following abbreviations are used in this manuscript:

ARC	Accelerating Rate Calorimeter
BJDST	Beijing Dynamic Stress Test
BMS	Battery Management System
CC	Constant Current
CPM	Common Potentiometric Method
CV	Constant Voltage
ECM	Equivalent Circuit Model
EIS	Electrothermal Impedance Spectroscopy
FSAE	Formula of the Society of Automotive Engineers
FUDS	Federal Urban Driving Schedule
HPL	High Power Load
NDC	Non Dynamic Cycle
OCV	Open Circuit Voltage
PAM	Positive Adjustment Method
RMSE	Root Mean Square Error
SoC	State Of Charge

Appendix A

Appendix A.1

Here are reported the table containing the ECM parameters for the different cells 386 tested at 5, 25 and 40 °C.

Table A1. The ECM parameters for the P28A cell model.

	T_c $= 5$ °C
	Discharge					Charge
SoC	R_s	R₁	C₁	R₂	C₂	R_s	R₁	C₁	R₂	C₂
	[Ω]	[Ω]	[F]	[Ω]	[F]	[Ω]	[Ω]	[F]	[Ω]	[F]
0.1	0.0271	0.0308	1173	0.0196	21970	0.0266	0.0433	8526	0.0355	24350
0.2	0.0263	0.0219	1412	0.0211	33364	0.0242	0.0662	4058	0.0281	21050
0.3	0.0264	0.0230	1573	0.0225	42927	0.0222	0.0570	512	0.0155	20215
0.4	0.0269	0.0216	1197	0.0154	40665	0.0218	0.0171	886	0.0268	16880
0.5	0.0272	0.0178	819	0.0130	33119	0.0217	0.0132	823	0.0110	20650
0.6	0.0273	0.0152	646	0.0190	23145	0.0208	0.0127	941	0.0092	21596
0.7	0.0283	0.0134	775	0.0325	15821	0.0227	0.0148	1085	0.0135	31539
0.8	0.0305	0.0183	959	0.0397	11399	0.0284	0.0114	1531	0.0140	34055
0.9	0.0313	0.0215	999	0.0180	24522	0.0331	0.0059	2139	0.0096	22909
	T_c $= 25$ °C
	Discharge					Charge
SoC	R_s	R₁	C₁	R₂	C₂	R_s	R₁	C₁	R₂	C₂
	[Ω]	[Ω]	[F]	[Ω]	[F]	[Ω]	[Ω]	[F]	[Ω]	[F]
0.1	0.0191	0.0128	2345	0.0101	21935	0.0166	0.0098	1141	0.0110	38210
0.2	0.0170	0.0083	1844	0.0080	19192	0.0160	0.0092	2314	0.0109	53291
0.3	0.0165	0.0106	2187	0.0101	29387	0.0155	0.0069	1735	0.0099	38424
0.4	0.0170	0.0106	1833	0.0069	36820	0.0152	0.0068	1847	0.0068	34442
0.5	0.0173	0.0077	1408	0.0063	30551	0.0152	0.0093	2521	0.0082	49947
0.6	0.0174	0.0073	1192	0.0121	35108	0.0154	0.0084	2256	0.0075	45617
0.7	0.0173	0.0085	1375	0.0193	24324	0.0155	0.0073	1505	0.0046	36110
0.8	0.0179	0.0106	1953	0.0125	19786	0.0161	0.0110	1623	0.0052	43433
0.9	0.0184	0.0106	1874	0.0056	90703	0.0148	0.0144	2441	0.0116	63415
	T_c $= 40$ °C
	Discharge					Charge
SoC	R_s	R₁	C₁	R₂	C₂	R_s	R₁	C₁	R₂	C₂
	[Ω]	[Ω]	[F]	[Ω]	[F]	[Ω]	[Ω]	[F]	[Ω]	[F]
0.1	0.0141	0.0169	2955	0.0086	162380	0.0121	0.0088	1084	0.0203	40517
0.2	0.0132	0.0094	2871	0.0052	184930	0.0134	0.0076	2574	0.0142	78985
0.3	0.0135	0.0092	3330	0.0045	178230	0.0133	0.0044	1921	0.0121	34480
0.4	0.0137	0.0101	2264	0.0033	133110	0.0132	0.0035	1918	0.0063	21319
0.5	0.0132	0.0082	1705	0.0031	90442	0.0130	0.0046	2800	0.0059	24030
0.6	0.0130	0.0068	1995	0.0054	63078	0.0131	0.0040	2360	0.0050	20253
0.7	0.0130	0.0094	2733	0.0079	48266	0.0132	0.0033	2042	0.0038	17394
0.8	0.0142	0.0085	2367	0.0051	55187	0.0135	0.0046	2425	0.0050	16172
0.9	0.0138	0.0074	1858	0.0044	104600	0.0124	0.0063	2394	0.0096	15963

Table A2. The ECM parameters for the P28B cell model.

	T_c $= 5$ °C
	Discharge					Charge
SoC	R_s	R₁	C₁	R₂	C₂	R_s	R₁	C₁	R₂	C₂
	[Ω]	[Ω]	[F]	[Ω]	[F]	[Ω]	[Ω]	[F]	[Ω]	[F]
0.1	0.0307	0.0269	1037	0.0222	16531	0.0312	0.0194	706	0.0409	16162
0.2	0.0273	0.0220	1333	0.0262	31633	0.0290	0.0168	930	0.0295	15259
0.3	0.0271	0.0227	1208	0.0227	33162	0.0264	0.0139	931	0.0114	19789
0.4	0.0279	0.0197	915	0.0157	25628	0.0235	0.0135	932	0.0114	19789
0.5	0.0276	0.0166	657	0.0136	17738	0.0220	0.0185	921	0.0164	28506
0.6	0.0207	0.0143	581	0.0197	13993	0.0206	0.0212	1121	0.0198	34355
0.7	0.0289	0.0137	744	0.0367	12739	0.0192	0.0175	1338	0.0114	19324
0.8	0.0329	0.0214	911	0.0528	9585	0.0179	0.0190	1303	0.0150	17600
0.9	0.0345	0.0230	817	0.0334	14201	0.0166	0.0185	1206	0.0160	21537
	T_c $= 25$ °C
	Discharge					Charge
SoC	R_s	R₁	C₁	R₂	C₂	R_s	R₁	C₁	R₂	C₂
	[Ω]	[Ω]	[F]	[Ω]	[F]	[Ω]	[Ω]	[F]	[Ω]	[F]
0.1	0.0178	0.0190	2365	0.0105	46810	0.0161	0.0110	1094	0.0203	23947
0.2	0.0161	0.0102	1757	0.0078	27662	0.0155	0.0113	2165	0.0185	44449
0.3	0.0159	0.0106	2445	0.0104	34794	0.0147	0.0071	1525	0.0123	29553
0.4	0.0162	0.0112	1950	0.0071	42074	0.0142	0.0065	1385	0.0077	25390
0.5	0.0163	0.0082	1328	0.0060	37689	0.0139	0.0095	1699	0.0084	37180
0.6	0.0164	0.0083	1039	0.0115	35216	0.0137	0.0099	1510	0.0085	37336
0.7	0.0171	0.0073	1779	0.0202	23936	0.0138	0.0080	1058	0.0052	26508
0.8	0.0177	0.0135	1339	0.0146	16296	0.0138	0.0118	1304	0.0061	33520
0.9	0.0181	0.0114	1615	0.0067	59597	0.0158	0.0130	2103	0.0120	47036
	T_c $= 40$ °C
	Discharge					Charge
SoC	R_s	R₁	C₁	R₂	C₂	R_s	R₁	C₁	R₂	C₂
	[Ω]	[Ω]	[F]	[Ω]	[F]	[Ω]	[Ω]	[F]	[Ω]	[F]
0.1	0.0126	0.0161	2360	0.0084	142620	0.0120	0.0091	1243	0.0143	32013
0.2	0.0111	0.0095	1792	0.0047	104860	0.0116	0.0075	2534	0.0092	75070
0.3	0.0111	0.0086	2315	0.0046	71871	0.0116	0.0055	2529	0.0112	59639
0.4	0.0119	0.0076	2389	0.0048	50264	0.0112	0.0047	2021	0.0060	41868
0.5	0.0125	0.0052	1959	0.0050	43107	0.0106	0.0068	2819	0.0047	53780
0.6	0.125	0.0051	2382	0.0094	43637	0.0100	0.0080	2985	0.0053	78268
0.7	0.0127	0.0083	3214	0.0138	38551	0.0110	0.0062	1864	0.0033	111810
0.8	0.0130	0.0092	2863	0.0091	85219	0.0114	0.0084	2512	0.0046	136800
0.9	0.0132	0.0071	2231	0.0056	93891	0.0116	0.0116	2404	0.0073	74297

Table A3. The ECM parameters for the P30B cell model.

	T_c $= 5$ °C
	Discharge					Charge
SoC	R_s	R₁	C₁	R₂	C₂	R_s	R₁	C₁	R₂	C₂
	[Ω]	[Ω]	[F]	[Ω]	[F]	[Ω]	[Ω]	[F]	[Ω]	[F]
0.1	0.0238	0.0311	1356	0.0406	26412	0.0228	0.0795	4076	0.0190	50626
0.2	0.0189	0.0218	1160	0.0231	26096	0.0207	0.0606	4832	0.0319	60550
0.3	0.0176	0.0211	1146	0.0274	24765	0.0174	0.0179	1907	0.0353	57155
0.4	0.0175	0.0211	1011	0.0295	23330	0.0142	0.0116	1858	0.0184	29798
0.5	0.0177	0.0188	824	0.0202	15980	0.0140	0.0134	1026	0.0110	19511
0.6	0.0180	0.0135	652	0.0200	10938	0.0137	0.0158	831	0.0128	28351
0.7	0.0188	0.0147	742	0.0373	10167	0.0135	0.0203	965	0.0170	38968
0.8	0.0213	0.0236	1197	0.0512	16595	0.0137	0.0173	938	0.0089	34889
0.9	0.0224	0.0244	1100	0.0202	27749	0.0145	0.0280	1012	0.0135	47824
	T_c $= 25$ °C
	Discharge					Charge
SoC	R_s	R₁	C₁	R₂	C₂	R_s	R₁	C₁	R₂	C₂
	[Ω]	[Ω]	[F]	[Ω]	[F]	[Ω]	[Ω]	[F]	[Ω]	[F]
0.1	0.0170	0.0394	1760	0.0255	49984	0.0114	0.0345	2178	0.0144	62725
0.2	0.0118	0.0179	1731	0.0115	64108	0.0106	0.0164	1909	0.0338	48519
0.3	0.0110	0.0130	1302	0.0083	43164	0.0096	0.0064	1763	0.0209	23110
0.4	0.0105	0.0110	1239	0.0082	29060	0.0094	0.0041	1100	0.0106	11786
0.5	0.0116	0.0108	1862	0.0090	19562	0.0094	0.0046	1170	0.0078	11054
0.6	0.0119	0.0078	1297	0.0076	16602	0.0093	0.0068	1062	0.0101	16393
0.7	0.0120	0.0086	1273	0.0138	26587	0.0095	0.0060	1109	0.0087	14093
0.8	0.0127	0.0128	2017	0.0168	21666	0.0096	0.0054	1227	0.0075	7982
0.9	0.0127	0.0125	1652	0.0069	95862	0.0103	0.0088	1371	0.0132	10814
	T_c $= 40$ °C
	Discharge					Charge
SoC	R_s	R₁	C₁	R₂	C₂	R_s	R₁	C₁	R₂	C₂
	[Ω]	[Ω]	[F]	[Ω]	[F]	[Ω]	[Ω]	[F]	[Ω]	[F]
0.1	0.0110	0.0274	6336	0.0309	57321	0.0090	0.0160	1332	0.0651	14153
0.2	0.0093	0.0131	3732	0.0141	105080	0.0081	0.0077	1708	0.0662	14516
0.3	0.0087	0.0103	2516	0.0095	124580	0.0076	0.0037	1253	0.0245	26619
0.4	0.0080	0.0083	1943	0.0064	130980	0.0076	0.0045	900	0.0125	39521
0.5	0.0084	0.0095	2198	0.0043	90444	0.0076	0.0061	1006	0.0115	58670
0.6	0.0092	0.0068	2204	0.0066	75590	0.0077	0.0070	1493	0.0081	37061
0.7	0.0093	0.0070	2610	0.0066	78856	0.0078	0.0054	1540	0.0081	37061
0.8	0.0095	0.0102	3046	0.0073	75567	0.0080	0.0045	1549	0.0053	36016
0.9	0.0095	0.0077	2187	0.0054	129950	0.0083	0.0083	2227	0.0081	50669

Table A4. The ECM parameters for the VTC5D cell model.

	T_c $= 5$ °C
	Discharge					Charge
SoC	R_s	R₁	C₁	R₂	C₂	R_s	R₁	C₁	R₂	C₂
	[Ω]	[Ω]	[F]	[Ω]	[F]	[Ω]	[Ω]	[F]	[Ω]	[F]
0.1	0.0265	0.0330	1125	0.0271	11198	0.0291	0.0219	658	0.0450	8029
0.2	0.0249	0.0188	1367	0.0154	15964	0.0266	0.0067	768	0.0324	3196
0.3	0.0238	0.0215	1650	0.0197	25405	0.0232	0.0073	804	0.0168	5071
0.4	0.0235	0.0243	1814	0.0218	31775	0.0216	0.0066	1080	0.0144	5541
0.5	0.0238	0.0206	1440	0.0149	30667	0.0216	0.0096	962	0.0211	6901
0.6	0.0243	0.0173	1222	0.0151	30607	0.0218	0.0117	647	0.0214	7393
0.7	0.0254	0.0159	1552	0.0287	26171	0.0227	0.0121	818	0.0128	6113
0.8	0.0273	0.0259	1767	0.0387	20423	0.0264	0.0160	1208	0.0145	8581
0.9	0.0294	0.0259	1251	0.0154	34463	0.0402	0.0245	2300	0.0450	17704
	T_c $= 25$ °C
	Discharge					Charge
SoC	R_s	R₁	C₁	R₂	C₂	R_s	R₁	C₁	R₂	C₂
	[Ω]	[Ω]	[F]	[Ω]	[F]	[Ω]	[Ω]	[F]	[Ω]	[F]
0.1	0.0227	0.0165	2772	0.0123	15823	0.0163	0.0358	2089	0.0175	62603
0.2	0.0176	0.0089	1832	0.0066	19355	0.0154	0.0133	2257	0.0234	51085
0.3	0.0158	0.0105	1741	0.0078	17670	0.0147	0.0106	1727	0.0230	24814
0.4	0.0151	0.0123	1760	0.0092	17286	0.0144	0.0070	1581	0.0118	15220
0.5	0.0156	0.0086	1208	0.0097	13320	0.0144	0.0082	1632	0.0103	16589
0.6	0.0160	0.0079	1198	0.0186	17363	0.0146	0.0084	1337	0.0094	16235
0.7	0.0160	0.0114	1898	0.0259	24139	0.0150	0.0080	1328	0.0057	14737
0.8	0.0167	0.0146	2295	0.0157	18389	0.0158	0.0115	1324	0.0058	21896
0.9	0.0174	0.0127	1965	0.0061	37337	0.0137	0.0197	1617	0.0121	41477
	T_c $= 40$ °C
	Discharge					Charge
SoC	R_s	R₁	C₁	R₂	C₂	R_s	R₁	C₁	R₂	C₂
	[Ω]	[Ω]	[F]	[Ω]	[F]	[Ω]	[Ω]	[F]	[Ω]	[F]
0.1	0.0150	0.0184	2727	0.0086	80205	0.0116	0.0193	1153	0.0372	18047
0.2	0.0138	0.0093	2013	0.0043	44757	0.0117	0.0099	1311	0.0184	40515
0.3	0.0127	0.0083	1614	0.0041	30351	0.0120	0.0078	1806	0.0160	55242
0.4	0.0124	0.0089	1788	0.0060	20576	0.0123	0.0069	1619	0.0083	45626
0.5	0.0133	0.0063	1975	0.0066	16017	0.0122	0.0084	1929	0.0078	38101
0.6	0.0133	0.0057	2361	0.0062	21600	0.0123	0.0068	1826	0.0065	32643
0.7	0.0134	0.0090	3291	0.0090	31691	0.0127	0.0060	1701	0.0040	34223
0.8	0.0137	0.0096	2348	0.0056	21288	0.0131	0.0083	1671	0.0044	39989
0.9	0.0141	0.0058	2081	0.0039	10820	0.0116	0.0142	1904	0.0087	61896

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Figure 1. Equivalent circuit model diagram for a cylindrical Li-ion cell.

Figure 2. Thermal array scheme for a cylindrical Li-ion cell.

Figure 3. The four cells tested: from left to right, Molicel P28A, P28B, P30B, and Sony Murata VTC5D.

Figure 4. The experimental set-up used at FIAMM lab consisting of (left to right): two cell holders, a thermal chamber, two cell cycler sets, a thermocouple array with data logger, a control and data processing pc.

Figure 5. OCV vs SoC curves of the tested cells, obtained as averages in charge and discharge tests performed at C/20 current.

Figure 6. Experimental and fitted fata for of the discharge GITT test for the P28B cell at 25 °C.

Figure 7. Positive Adjustment Method (PAM) applied on P30B cell, in order to measure the profile of the entropic contribution

\partial U / \partial T

: a step shaped current load is applied to the cell to reach the desired

S o C

measurement point. Then, after a relaxation time, a thermal cycle is applied.

Figure 7. Positive Adjustment Method (PAM) applied on P30B cell, in order to measure the profile of the entropic contribution

\partial U / \partial T

: a step shaped current load is applied to the cell to reach the desired

S o C

measurement point. Then, after a relaxation time, a thermal cycle is applied.

Figure 8. Measured OCV at various temperature and SoC

\approx 0.6

: for each SoC, the slope of the interpolation line is the

\partial U / \partial T

term (a); the

\partial U / \partial T

S o C

for the P30B cell is reported in (b), showing good agreement with previous data from literature [38,39] .

Figure 8. Measured OCV at various temperature and SoC

\approx 0.6

: for each SoC, the slope of the interpolation line is the

\partial U / \partial T

term (a); the

\partial U / \partial T

S o C

for the P30B cell is reported in (b), showing good agreement with previous data from literature [38,39] .

Figure 9. P28A cell thermal characterization tests: (a) low convective testing condition; (b) high convective testing condition. The experimental and the modelled cell surface temperatures

T_{s}

are reported.

Figure 9. P28A cell thermal characterization tests: (a) low convective testing condition; (b) high convective testing condition. The experimental and the modelled cell surface temperatures

T_{s}

are reported.

Figure 10. The results of BJDST validation profile: (a) show the current profile, (b) shows the modelled and experimental

V_{t}