# Determination of Internal Temperature Differences for Various Cylindrical Lithium-Ion Batteries Using a Pulse Resistance Approach

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experiment

#### 2.1. Investigated Cells

_{2}O

_{4}(LMO) chemistry [34,35] was chosen to investigate if the relation of the ${R}_{\mathrm{DC}}$ and temperature is altered by different chemistry. To verify the cell chemistries, the open-circuit voltages (OCVs) of the cells were analyzed using differential voltage analysis (DVA). The results are briefly presented in Appendix A. For each cell format, a batch of five sample cells was initially cycled for ten cycles according to the manufacturer’s standard charge and discharge procedure.

#### 2.2. Experimental Setup

#### 2.3. Test Procedures

#### 2.3.1. Isothermal ${R}_{\mathrm{DC}}$ Characterization

- (P.1)
- Our previous analysis in [27] revealed that the optimal evaluation time $\Delta t$ for the ${R}_{DC}$ for temperature estimation is in the region of 10 $\mathrm{m}$$\mathrm{s}$ to approximately 100 $\mathrm{m}$$\mathrm{s}$. To cover this range with margin, the pulse duration (${t}_{\mathrm{pulse}}$) was set to 150 $\mathrm{m}$$\mathrm{s}$. However, the exact evaluation time ($\Delta t$) is determined in Section 4.1 with the results listed in Table 4.
- (P.2)
- The continuous pulses may affect each other since LIBs are time-variant systems. The pause between the charging and discharging pulses (${t}_{\mathrm{break}}$) was set to 5 $\mathrm{s}$, which proved to be long enough to avoid the preceding pulse to affect the following one (see Section 4.1).
- (P.3)
- To analyze the transient temperature behavior (see Section 2.3.2), the cell temperature is changed by externally heating the cell and simultaneously applying current pulses. Internal temperature changes due to heating of the cells through ohmic losses [37] caused by the continuous application of the pulses had to be avoided. Therefore, the pulse current and duration had to be small. The pulse duration with 150 $\mathrm{m}$$\mathrm{s}$ selected in (P.1) is already relatively short. Nevertheless, the current had to be large enough to induce a voltage response with a sufficient signal-to-noise ratio (SNR) to avoid inaccurate measurements. The trade-off resulted in a pulse current ${I}_{\mathrm{p}}$ of $\pm 0.1\mathrm{C}$. Taking the resistance values for ${\overline{R}}_{\mathsf{\Omega}}$ from Table 2 into account, the resulting heat generation of the applied pulses is less than $5.329$ $\mathrm{m}$$\mathrm{W}$ for each cell.

#### 2.3.2. Transient Temperature ${R}_{\mathrm{DC}}$ Characterization

## 3. 2D Thermal Model

## 4. Results & Discussion

#### 4.1. Isothermal ${R}_{\mathrm{DC}}$ Characterization

- (E.1)
- Ohmic losses, due to limiting electronic/ionic conductivity of the current collectors, the electrolyte, the active materials of the electrodes, and additives, such as carbon black.
- (E.2)
- Contact losses, attributed to contact resistance between one of the electrodes and the current collector, as well as from particle-to-particle contacts.
- (E.3)
- Interface losses, related to the charge transfer at the electrodes, as well as the contribution of the solid electrolyte interface (SEI).

#### 4.2. Transient Temperature ${R}_{\mathrm{DC}}$ Characterization

#### 4.3. Internal Temperature: Model versus ${T}_{\mathrm{R}}$

- (R.1)
- Although the simulation parameters are for the same pristine cell type, they were not determined for exactly the same cell and thus might slightly differ between the cells used in [31] to parameterize the 2D thermal model and the ones used in this study. Also, the SOC points in the study by Steinhardt et al. [31] do not exactly match the SOC points investigated in this study. Since the thermal conductivity of a LIB is dependent on the SOC [47], the parameter deviation in thermal conductivity might partly cause the deviation between the simulation and $\Delta {T}_{\mathrm{R}}$.
- (R.2)
- The 2D thermal model does not consider thermal conductivity changes related to mechanical changes. The jelly roll expands when the cell is charged [48] and the contact area and pressure between the layers in the jelly roll and between the jelly roll and the metal casing of the cell increases. Several studies [49,50] showed that increased compression reduces the thermal contact resistance, leading to improved thermal conductivity and therefore reducing the difference between surface and core temperature.

#### 4.4. Internal Temperature: Cell Geometry & State of Charge

## 5. Summary & Conclusions

- The ${R}_{\mathrm{DC}}$ can be utilized to determine the internal cell temperature for different cell chemistries and cylindrical cell formats.
- The comparison with the 2D thermal model shows that ${T}_{\mathrm{R}}$ most likely represents the average jelly roll temperature (${T}_{\mathrm{avg}}$). Thus, ${T}_{\mathrm{R}}$ offers an advantage over conventional temperature sensors, which only determine the surface temperature at one point of the cell.
- An important point regarding the applicability is the temperature range, for which ${R}_{DC}$-based methods are applicable. As shown in Figure 3, the accuracy of the method strongly depends on the slope of the estimation function (Equation (4)), which steadily increases with rising temperatures. For this reason, correspondingly precise measurement hardware for the current and voltage monitoring of the BMS is a prerequisite to avoid large temperature estimation errors in the elevated temperature range.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

BMS | battery management system |

CC | constant current |

CMU | cell measurement unit |

CTS | cell test system |

CV | constant voltage |

DVA | differential voltage analysis |

EIS | electrochemical impedance spectroscopy |

FEM | finite element model |

LIB | lithium-ion battery |

LMO | LiMn${}_{2}$O${}_{4}$ |

NMC | nickel manganese cobalt oxide |

NTC | negative temperature coefficient |

OCV | open-circuit voltage |

${R}^{2}$ | R-Square |

${R}_{\mathrm{adj}}^{2}$ | adjusted R-Square |

${R}_{\mathrm{DC}}$ | direct current resistance |

RMSE | root mean square error |

SEI | solid electrolyte interface |

SNR | signal-to-noise ratio |

SOC | state of charge |

SOH | state of health |

SSE | sum of square error |

SST | total sum of squares |

${T}_{\mathrm{amb}}$ | ambient temperature |

${T}_{\mathrm{avg}}$ | simulated average jelly roll temperature |

${T}_{\mathrm{c}}$ | temperature at the center of the cell |

${T}_{\mathrm{core}}$ | temperature simulated at half of the cell height and at the core of the jelly roll |

${T}_{\mathrm{ctr}}$ | temperature simulated at half of the cell height and at the center of the jelly roll |

$\Delta {T}_{\mathrm{ext}}$ | external change in temperature |

${T}_{\mathrm{n}}$ | temperature at the negative terminal |

${T}_{\mathrm{p}}$ | temperature at the positive terminal |

${T}_{\mathrm{R}}$ | temperature indicated by the ${R}_{\mathrm{DC}}$ |

$\Delta {T}_{\mathrm{R},18650}$ | temperature difference between ${T}_{\mathrm{surf}}$ and the ${T}_{\mathrm{R}}$ for the 18650 cell |

$\Delta {T}_{\mathrm{R},21700}$ | temperature difference between ${T}_{\mathrm{surf}}$ and the ${T}_{\mathrm{R}}$ for the 21700 cell |

$\Delta {T}_{\mathrm{R},26650}$ | temperature difference between ${T}_{\mathrm{surf}}$ and the ${T}_{\mathrm{R}}$ for the 26650 cell |

${T}_{\mathrm{surf}}$ | averaged surface temperature |

## Appendix A. Differential Voltage Analysis

**Figure A1.**Differential voltage analysis with representative peak markers for silicon (Si${}_{x}$), graphite (Gr${}_{x}$), and NMC for the three investigated cell formats: 18650 with NMC | Si/Gr (

**a**), 21700 with NMC | Si/Gr (

**b**), and 26650 with LMO | Gr (

**c**).

## Appendix B. Function Parameters

**Figure A2.**Fitting results for Equation (4) for the parameter ${E}_{\mathrm{A}}$, each investigated cell format, and the four different pulse current types (${P}_{1}$ to ${P}_{4}$) at the SOCs 90% (

**a**), 50% (

**b**), and 10% (

**c**).

**Figure A3.**Fitting results for Equation (4) for the parameter ${R}_{0}$, each investigated cell format, and the four different pulse current types (${P}_{1}$ to ${P}_{4}$) at the SOCs 90% (

**a**), 50% (

**b**), and 10% (

**c**).

**Figure A4.**Fitting results for Equation (4) for the parameter ${R}_{1}$, each investigated cell format, and the four different pulse current types (${P}_{1}$ to ${P}_{4}$) at the SOCs 90% (

**a**), 50% (

**b**), and 10% (

**c**).

## Appendix C. Fitting Quality & Error

- -
- the sum of square error (SSE) in Equation (A1) describes the total deviation of the response values of the fit ${\widehat{y}}_{i}$ from the measured response values ${y}_{i}$,$$SSE=\sum _{i=1}^{n}{({y}_{i}-{\widehat{y}}_{i})}^{2}$$
- -
- the total sum of squares (SST) in Equation (A2) describes the total deviation of the mean $\overline{y}$ from the measured response values ${y}_{i}$,$$SST=\sum _{i=1}^{n}{({y}_{i}-\overline{y})}^{2}$$
- -
- the general ${R}^{2}$ in Equation (A3) determines how successful the fit is in explaining the variation of the data,$${R}^{2}=1-\frac{SSE}{SST}$$
- -
- and the adjusted R-Square statistic in Equation (A4) considers the number of fitted model variables m in addition to the number of response values n.$${R}_{\mathrm{adj}}^{2}=1-(1-{R}^{2})\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\frac{n-1}{n-m}=1-\frac{SSE}{SST}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\frac{n-1}{n-m}$$

**Figure A5.**${R}_{adj}^{2}$ results for fitting Equation (4) for each investigated cell format and the four different pulse current types (${P}_{1}$ to ${P}_{4}$) at the SOCs 90% (

**a**), 50% (

**b**), and 10% (

**c**).

**Figure A6.**RMSE results for fitting Equation (4) for each investigated cell format and the four different pulse current types (${P}_{1}$ to ${P}_{4}$) at the SOCs 90% (

**a**), 50% (

**b**), and 10% (

**c**).

## References

- Ma, S.; Jiang, M.; Tao, P.; Song, C.; Wu, J.; Wang, J.; Deng, T.; Shang, W. Temperature effect and thermal impact in lithium-ion batteries: A review. Prog. Nat. Sci. Mater. Int.
**2018**, 28, 653–666. [Google Scholar] [CrossRef] - Morello, R.; Di Rienzo, R.; Roncella, R.; Saletti, R.; Schwarz, R.; Lorentz, V.; Hoedemaekers, E.; Rosca, B.; Baronti, F. Advances in Li-Ion Battery Management for Electric Vehicles. In Proceedings of the IECON 2018-44th Annual Conference of the IEEE Industrial Electronics Society, Washington, DC, USA, 21–23 October 2018; IEEE: Piscataway, NJ, USA, 2018; pp. 4949–4955. [Google Scholar] [CrossRef][Green Version]
- Alipour, M.; Ziebert, C.; Conte, F.V.; Kizilel, R. A Review on Temperature-Dependent Electrochemical Properties, Aging, and Performance of Lithium-Ion Cells. Batteries
**2020**, 6, 35. [Google Scholar] [CrossRef] - Raijmakers, L.; Danilov, D.L.; Eichel, R.A.; Notten, P. A review on various temperature-indication methods for Li-ion batteries. Appl. Energy
**2019**, 240, 918–945. [Google Scholar] [CrossRef] - Beelen, H.; Mundaragi Shivakumar, K.; Raijmakers, L.; Donkers, M.; Bergveld, H.J. Towards impedance–based temperature estimation for Li–ion battery packs. Int. J. Energy Res.
**2020**, 44, 2889–2908. [Google Scholar] [CrossRef] - Richardson, R.R.; Zhao, S.; Howey, D.A. On-board monitoring of 2-D spatially-resolved temperatures in cylindrical lithium-ion batteries: Part II. State estimation via impedance-based temperature sensing. J. Power Sources
**2016**, 327, 726–735. [Google Scholar] [CrossRef][Green Version] - Liu, X.; Ai, W.; Naylor Marlow, M.; Patel, Y.; Wu, B. The effect of cell-to-cell variations and thermal gradients on the performance and degradation of lithium-ion battery packs. Appl. Energy
**2019**, 248, 489–499. [Google Scholar] [CrossRef] - Srinivasan, R. Monitoring dynamic thermal behavior of the carbon anode in a lithium-ion cell using a four-probe technique. J. Power Sources
**2012**, 198, 351–358. [Google Scholar] [CrossRef] - Carkhuff, B.G.; Demirev, P.A.; Srinivasan, R. Impedance-Based Battery Management System for Safety Monitoring of Lithium-Ion Batteries. IEEE Trans. Ind. Electron.
**2018**, 65, 6497–6504. [Google Scholar] [CrossRef] - Srinivasan, R.; Carkhuff, B.G.; Butler, M.H.; Baisden, A.C. Instantaneous measurement of the internal temperature in lithium-ion rechargeable cells. Electrochim. Acta
**2011**, 56, 6198–6204. [Google Scholar] [CrossRef] - Schmidt, J.P.; Arnold, S.; Loges, A.; Werner, D.; Wetzel, T.; Ivers-Tiffée, E. Measurement of the internal cell temperature via impedance: Evaluation and application of a new method. J. Power Sources
**2013**, 243, 110–117. [Google Scholar] [CrossRef] - Raijmakers, L.; Danilov, D.L.; van Lammeren, J.; Lammers, M.; Notten, P. Sensorless battery temperature measurements based on electrochemical impedance spectroscopy. J. Power Sources
**2014**, 247, 539–544. [Google Scholar] [CrossRef] - Beelen, H.; Raijmakers, L.; Donkers, M.; Notten, P.; Bergveld, H.J. An Improved Impedance-Based Temperature Estimation Method for Li-ion. IFAC-PapersOnLine
**2015**, 48, 383–388. [Google Scholar] [CrossRef] - Spinner, N.S.; Love, C.T.; Rose-Pehrsson, S.L.; Tuttle, S.G. Expanding the Operational Limits of the Single-Point Impedance Diagnostic for Internal Temperature Monitoring of Lithium-ion Batteries. Electrochim. Acta
**2015**, 174, 488–493. [Google Scholar] [CrossRef] - Sun, J.; Wei, G.; Pei, L.; Lu, R.; Song, K.; Wu, C.; Zhu, C. Online Internal Temperature Estimation for Lithium-Ion Batteries Based on Kalman Filter. Energies
**2015**, 8, 4400–4415. [Google Scholar] [CrossRef][Green Version] - Zhu, J.G.; Sun, Z.C.; Wei, X.Z.; Dai, H.F. A new lithium-ion battery internal temperature on-line estimate method based on electrochemical impedance spectroscopy measurement. J. Power Sources
**2015**, 274, 990–1004. [Google Scholar] [CrossRef] - Zhu, J.; Sun, Z.; Wei, X.; Dai, H. Battery Internal Temperature Estimation for LiFePO4 Battery Based on Impedance Phase Shift under Operating Conditions. Energies
**2017**, 10, 60. [Google Scholar] [CrossRef][Green Version] - Srinivasan, R.; Demirev, P.A.; Carkhuff, B.G. Rapid monitoring of impedance phase shifts in lithium-ion batteries for hazard prevention. J. Power Sources
**2018**, 405, 30–36. [Google Scholar] [CrossRef] - Wang, L.; Lu, D.; Song, M.; Zhao, X.; Li, G. Instantaneous estimation of internal temperature in lithium–ion battery by impedance measurement. Int. J. Energy Res.
**2020**, 44, 3082–3097. [Google Scholar] [CrossRef] - Raijmakers, L.H.J.; Danilov, D.L.; van Lammeren, J.P.M.; Lammers, T.J.G.; Bergveld, H.J.; Notten, P.H.L. Non-Zero Intercept Frequency: An Accurate Method to Determine the Integral Temperature of Li-Ion Batteries. IEEE Trans. Ind. Electron.
**2016**, 63, 3168–3178. [Google Scholar] [CrossRef][Green Version] - Haussmann, P.; Melbert, J. Internal Cell Temperature Measurement and Thermal Modeling of Lithium Ion Cells for Automotive Applications by Means of Electrochemical Impedance Spectroscopy. SAE Int. J. Altern. Powertrains
**2017**, 6, 261–270. [Google Scholar] [CrossRef] - Wang, X.; Wei, X.; Chen, Q.; Zhu, J.; Dai, H. Lithium-ion battery temperature on-line estimation based on fast impedance calculation. J. Energy Storage
**2019**, 26, 100952. [Google Scholar] [CrossRef] - Richardson, R.R.; Ireland, P.T.; Howey, D.A. Battery internal temperature estimation by combined impedance and surface temperature measurement. J. Power Sources
**2014**, 265, 254–261. [Google Scholar] [CrossRef] - Richardson, R.R.; Howey, D.A. Sensorless Battery Internal Temperature Estimation Using a Kalman Filter With Impedance Measurement. IEEE Trans. Sustain. Energy
**2015**, 6, 1190–1199. [Google Scholar] [CrossRef][Green Version] - Xie, Y.; Li, W.; Hu, X.; Lin, X.; Zhang, Y.; Dan, D.; Feng, F.; Liu, B.; Li, K. An Enhanced Online Temperature Estimation for Lithium-Ion Batteries. IEEE Trans. Transp. Electrif.
**2020**, 6, 375–390. [Google Scholar] [CrossRef] - Forgez, C.; Vinh Do, D.; Friedrich, G.; Morcrette, M.; Delacourt, C. Thermal modeling of a cylindrical LiFePO4/graphite lithium-ion battery. J. Power Sources
**2010**, 195, 2961–2968. [Google Scholar] [CrossRef] - Ludwig, S.; Zilberman, I.; Horsche, M.F.; Wohlers, T.; Jossen, A. Pulse resistance based online temperature estimation for lithium-ion cells. J. Power Sources
**2021**, 490, 229523. [Google Scholar] [CrossRef] - Ludwig, S.; Zilberman, I.; Oberbauer, A.; Rogge, M.; Fischer, M.; Rehm, M.; Jossen, A. Adaptive method for sensorless temperature estimation over the lifetime of lithium-ion batteries. J. Power Sources
**2022**, 521, 230864. [Google Scholar] [CrossRef] - Tranter, T.G.; Timms, R.; Shearing, P.R.; Brett, D.J.L. Communication—Prediction of Thermal Issues for Larger Format 4680 Cylindrical Cells and Their Mitigation with Enhanced Current Collection. J. Electrochem. Soc.
**2020**, 167, 160544. [Google Scholar] [CrossRef] - Tomaszewska, A.; Chu, Z.; Feng, X.; O’Kane, S.; Liu, X.; Chen, J.; Ji, C.; Endler, E.; Li, R.; Liu, L.; et al. Lithium-ion battery fast charging: A review. eTransportation
**2019**, 1, 100011. [Google Scholar] [CrossRef] - Steinhardt, M.; Gillich, E.I.; Rheinfeld, A.; Kraft, L.; Spielbauer, M.; Bohlen, O.; Jossen, A. Low-effort determination of heat capacity and thermal conductivity for cylindrical 18650 and 21700 lithium-ion cells. J. Energy Storage
**2021**, 42, 103065. [Google Scholar] [CrossRef] - Shenzhen Fest Technology Co., Ltd. Efest IMR 26650 5000mAh 40A Flat Top Battery. Available online: https://www.efestpower.com/index.php?ac=article&at=read&did=448. (accessed on 18 January 2022).
- Popp, H.; Zhang, N.; Jahn, M.; Arrinda, M.; Ritz, S.; Faber, M.; Sauer, D.U.; Azais, P.; Cendoya, I. Ante-mortem analysis, electrical, thermal, and ageing testing of state-of-the-art cylindrical lithium-ion cells. e & i Elektrotechnik und Informationstechnik
**2020**, 137, 169–176. [Google Scholar] [CrossRef] - Wei, Y.; Agelin-Chaab, M. Experimental investigation of a novel hybrid cooling method for lithium-ion batteries. Appl. Therm. Eng.
**2018**, 136, 375–387. [Google Scholar] [CrossRef] - Wei, Y.; Agelin-Chaab, M. Development and experimental analysis of a hybrid cooling concept for electric vehicle battery packs. J. Energy Storage
**2019**, 25, 100906. [Google Scholar] [CrossRef] - Gantenbein, S.; Weiss, M.; Ivers-Tiffée, E. Impedance based time-domain modeling of lithium-ion batteries: Part I. J. Power Sources
**2018**, 379, 317–327. [Google Scholar] [CrossRef] - Bernardi, D. A General Energy Balance for Battery Systems. J. Electrochem. Soc.
**1985**, 132, 5. [Google Scholar] [CrossRef][Green Version] - Illig, J.; Ender, M.; Chrobak, T.; Schmidt, J.P.; Klotz, D.; Ivers-Tiffée, E. Separation of Charge Transfer and Contact Resistance in LiFePO 4 -Cathodes by Impedance Modeling. J. Electrochem. Soc.
**2012**, 159, A952–A960. [Google Scholar] [CrossRef] - Zhou, X.; Huang, J.; Pan, Z.; Ouyang, M. Impedance characterization of lithium-ion batteries aging under high-temperature cycling: Importance of electrolyte-phase diffusion. J. Power Sources
**2019**, 426, 216–222. [Google Scholar] [CrossRef] - Barai, A.; Uddin, K.; Widanage, W.D.; McGordon, A.; Jennings, P. A study of the influence of measurement timescale on internal resistance characterisation methodologies for lithium-ion cells. Sci. Rep.
**2018**, 8, 21. [Google Scholar] [CrossRef] - Song, J.Y.; Wang, Y.Y.; Wan, C.C. Conductivity Study of Porous Plasticized Polymer Electrolytes Based on Poly(vinylidene fluoride) A Comparison with Polypropylene Separators. J. Electrochem. Soc.
**2000**, 147, 3219. [Google Scholar] [CrossRef] - Suresh, P.; Shukla, A.K.; Munichandraiah, N. Temperature dependence studies of a.c. impedance of lithium-ion cells. J. Appl. Electrochem.
**2002**, 32, 267–273. [Google Scholar] [CrossRef] - Muto, S.; Tatsumi, K.; Kojima, Y.; Oka, H.; Kondo, H.; Horibuchi, K.; Ukyo, Y. Effect of Mg-doping on the degradation of LiNiO2-based cathode materials by combined spectroscopic methods. J. Power Sources
**2012**, 205, 449–455. [Google Scholar] [CrossRef] - Schranzhofer, H.; Bugajski, J.; Santner, H.J.; Korepp, C.; Möller, K.C.; Besenhard, J.O.; Winter, M.; Sitte, W. Electrochemical impedance spectroscopy study of the SEI formation on graphite and metal electrodes. J. Power Sources
**2006**, 153, 391–395. [Google Scholar] [CrossRef] - Raju, N.S.; Bilgic, R.; Edwards, J.E.; Fleer, P.F. Methodology Review: Estimation of Population Validity and Cross-Validity, and the Use of Equal Weights in Prediction. Appl. Psychol. Meas.
**1997**, 21, 291–305. [Google Scholar] [CrossRef] - Fuller, T.F. Relaxation Phenomena in Lithium-Ion-Insertion Cells. J. Electrochem. Soc.
**1994**, 141, 982. [Google Scholar] [CrossRef][Green Version] - Maleki, H.; Hallaj, S.A.; Selman, J.R.; Dinwiddie, R.B.; Wang, H. Thermal Properties of Lithium–Ion Battery and Components. J. Electrochem. Soc.
**1999**, 146, 947–954. [Google Scholar] [CrossRef] - Willenberg, L.; Dechent, P.; Fuchs, G.; Teuber, M.; Eckert, M.; Graff, M.; Kürten, N.; Sauer, D.U.; Figgemeier, E. The Development of Jelly Roll Deformation in 18650 Lithium-Ion Batteries at Low State of Charge. J. Electrochem. Soc.
**2020**, 167, 120502. [Google Scholar] [CrossRef] - Maleki, H.; Selman, J.; Dinwiddie, R.; Wang, H. High thermal conductivity negative electrode material for lithium-ion batteries. J. Power Sources
**2001**, 94, 26–35. [Google Scholar] [CrossRef] - Richter, F.; Kjelstrup, S.; Vie, P.J.; Burheim, O.S. Thermal conductivity and internal temperature profiles of Li-ion secondary batteries. J. Power Sources
**2017**, 359, 592–600. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Study overview. (

**a**) Experimental setup: climatic chamber for temperature control, temperature sensor placement on investigated cells (temperature at the positive terminal (${T}_{\mathrm{p}}$), temperature at the center of the cell (T

_{c}), and temperature at the negative terminal (T

_{n})), ambient temperature (T

_{amb}), and measurement equipment as follows: Potentiostat (VMP3) from BioLogic, cell test system (CTS) and cell measurement unit (CMU) from BaSyTec. (

**b**) RDC characterization (flowchart from top to bottom): investigated cell formats, SOCs, and temperature range followed by the pulse pattern used for the characterization of the investigated cells, the equation for the R

_{DC}calculation (Equation (1)), and an exemplary result for the temperature estimation function. (

**c**) Internal temperature characterization: flowchart for the investigation of the relation between the internal temperature calculated by the 2D thermal model and the temperature calculated from R

_{DC}values during an external change in temperature (ΔT

_{ext}) by increasing the ambient temperature (T

_{amb}) from 10 °C to 40 °C.

**Figure 2.**Exemplary fitting results of Equation (4) for $\Delta t=100\mathrm{m}\mathrm{s}$ for different cell formats and current changes ${P}_{1}$ to ${P}_{4}$ (see pulse pattern in Figure 1b) at the investigated SOCs (

**a**) 90%, (

**b**) 50%, and (

**c**) 10%. The marker type represents the averaged value from the repeated pulse pattern (360 values) at each temperature point. The close-ups in (

**a**,

**b**) visualize the minimal difference between current changes ${P}_{1/3}$ and ${P}_{2/4}$.

**Figure 3.**Exemplary temperature estimation results for the investigated cell formats 18650 (

**a**), 21700 (

**b**), and 26650 (

**c**) at a SOC of 50% evaluated with Equation (4) and the setting according to Table 4. ${T}_{\mathrm{R},\mathrm{org}}$ shows the originally calculated values and ${T}_{\mathrm{R},\mathrm{fltr}}$ shows the values filtered with a moving average filter. The different and increased noise can be related to the individual slopes of the estimation functions in (

**d**–

**f**).

**Figure 4.**Temperature development during the external temperature change from 10${}^{\xb0}\mathrm{C}$–40${}^{\xb0}\mathrm{C}$ for the different cell formats 18650 (

**a**), 21700 (

**b**), and 26650 (

**c**) at the investigated SOC of 10%, 50%, and 90%.

**Figure 5.**Temperature differences $\Delta {T}_{R,18650}$ (

**a**–

**c**), $\Delta {T}_{R,21700}$ (

**d**–

**f**), and $\Delta {T}_{R,26650}$ (

**g**–

**i**) between the averaged surface temperature (${T}_{\mathrm{surf}}$) and the temperature indicated by the ${R}_{\mathrm{DC}}$ (${T}_{\mathrm{R}}$) at each SOC point and for each cell format. Additional temperature differences $\Delta {T}_{\mathrm{core}}$, $\Delta {T}_{\mathrm{ctr}}$, and $\Delta {T}_{\mathrm{avg}}$ in (

**a**–

**f**) for the three simulated temperature locations of the jelly roll in (

**j**) according to the 2D thermal model simulation results for the 18650 and 21700 format. The differences are again related to the averaged surface temperature. ${T}_{\mathrm{core}}$ and ${T}_{\mathrm{ctr}}$ are simulated at half of the cell height ($h/2$) and at the core (${x}_{\mathrm{core}}$), respectively at the center (${x}_{\mathrm{ctr}}$) of the jelly roll. ${T}_{\mathrm{avg}}$ represents the average simulated jelly roll temperature.

**Figure 6.**Relation between the maximum of the ${R}_{\mathrm{DC}}$-based temperature difference ($\Delta {T}_{\mathrm{max}}$) from Figure 5 and cell diameter d (

**a**), respectively SOC (

**b**).

# | Reference | Temperature | Cell | System | ||||
---|---|---|---|---|---|---|---|---|

Internal Core | Internal Distribution | Average Integral | Capacity | Format | Chemistry Cathode|Anode | |||

1 | [8] | A | 53 Ah | prismatic | LCO|Gr | cell | ||

2 | [9] | C | $5.3$ Ah | 18650 | ? | 1s2p | ||

A | ||||||||

3 | [2] | x | 34 Ah | prismatic | NMC|? | cell | ||

4 | [5] | x | $23.3$ Ah | prismatic | NMC|? | 2s1p | ||

5 | [10] | x | 53 Ah | prismatic | LCO|Gr | cell | ||

$2.3$ Ah | 26650 | LFG|Gr | cell | |||||

$4.4$ Ah | 18650 | ? | 1s2p | |||||

6 | [11] | x | 2 Ah | pouch | LCO+NCA|Gr | cell | ||

7 | [12] | x | $2.3$ Ah | 26650 | LFP|Gr | cell | ||

$7.5$ Ah | cylindrical | NCA|Gr | cell | |||||

8 | [13] | x | 90 Ah | ? | LFP|? | cell | ||

9 | [14] | x | $2.6$ Ah | 18650 | LCO|? | cell | ||

10 | [15] | x | 40 Ah | pouch | LFP|Gr | cell | ||

11 | [16] | x | 8 Ah | prismatic | ? | cell | ||

12 | [17] | x | 30 Ah | pouch | LFP|Gr | cell | ||

13 | [18] | x | 50 Ah | prismatic | LCO|Gr | cell | ||

$5.3$ Ah | 18650 | ? | 1s2p | |||||

3 Ah | 18650 | NMC|? | cell | |||||

14 | [19] | x | $1.3$ Ah | 18650 | LFP|? | cell | ||

15 | [20] | x | 90 Ah | prismatic | LFP|? | 3s1p | ||

16 | [22] | x | 8 Ah | prismatic | LFP|? | cell | ||

40 Ah | pouch | LFP|? | cell | |||||

17 | [23] | (x) | x | $2.3$ Ah | 26650 | LFP|Gr | cell | |

18 | [24] | (x) | x | $2.3$ Ah | 26650 | LFP|Gr | cell | |

19 | [6] | x | x | 20 Ah | prismatic | LMO/NMC|? | cell | |

20 | [25] | x | $3.2$ Ah | 18650 | ? | cell |

**Table 2.**General information and parameters of the investigated cells, including the nominal capacity (${C}_{\mathrm{nom}}$), the average capacity ($\overline{C}$) and resistance (${\overline{R}}_{\mathsf{\Omega}}$) as well as the corresponding relative standard deviations ${\mathsf{\sigma}}_{\mathrm{C},\mathrm{rel}}$ and ${\mathsf{\sigma}}_{\mathrm{R},\mathrm{rel}}$ of the five cell batches used for the cell selection.

18650 | 21700 | 26650 | ||
---|---|---|---|---|

Identifier | INR18650-MJ1 | INR21700-M50T | IMR26650-V1 | |

Manufacturer | LG Chem | LG Chem | Efest | |

Dimensions | 18.1|65.1 [31] | 21.1|70.2 [31] | 26.5|65.2 [32] | |

($d\phantom{\rule{3.33333pt}{0ex}}|\phantom{\rule{3.33333pt}{0ex}}h$)/$\mathrm{m}$$\mathrm{m}$ | ||||

Chemistry | NMC|Gr/Si ^{(a)} | NMC|Gr/Si ^{(b)} | LMO|Gr ^{(c)} | |

(Cathode|Anode) | ||||

Capacity (${C}_{\mathrm{nom}}$) | $3.35$$\mathrm{Ah}$ | $4.85$$\mathrm{Ah}$ | $5.00$$\mathrm{Ah}$ | |

Batch | ||||

Capacity | $\overline{C}$ | $3.424$$\mathrm{Ah}$ | $4.885$$\mathrm{Ah}$ | $5.511$$\mathrm{Ah}$ |

${\mathsf{\sigma}}_{\mathrm{C},\mathrm{rel}}$ | 0.483% | 0.124% | 0.233% | |

Impedance | ${\overline{R}}_{\mathsf{\Omega}}$ | $31.079$$\mathrm{m}$$\mathsf{\Omega}$ | $22.657$$\mathrm{m}$$\mathsf{\Omega}$ | $16.097$$\mathrm{m}$$\mathsf{\Omega}$ |

${\mathsf{\sigma}}_{\mathrm{R},\mathrm{rel}}$ | 0.379% | 0.868% | 0.618% |

^{(a)}Li(Ni

_{0.84}Co

_{0.11}Mn

_{0.05})O

_{2}|Graphite + 1 wt% Silicon [33];

^{(b)}Li(Ni

_{0.84}Co

_{0.10}Mn0.06)O

_{2}|Graphite + 1 wt% Silicon [33]; (c) LiMn2O4 [34,35]|Graphite (see Appendix A).

Parameter | Value |
---|---|

Pulse Current (${I}_{\mathrm{p}}$) | $\pm 0.1$$\mathrm{C}$ |

Pulse Duration (${t}_{\mathrm{pulse}}$) | 150$\mathrm{m}$ $\mathrm{s}$ |

Break Duration (${t}_{\mathrm{break}}$) | 5 $\mathrm{s}$ |

SOC | Format | RMSE / K | ${\mathit{P}}_{\mathit{x}}$ | $\mathbf{\Delta}\mathit{t}$ / ms |
---|---|---|---|---|

90% | 18650 | 0.223 | 3 | 149 |

21700 | 0.378 | 1 | 130 | |

26650 | 0.162 | 1 | 145 | |

50% | 18650 | 0.248 | 1 | 149 |

21700 | 0.423 | 1 | 90 | |

26650 | 0.158 | 1 | 145 | |

10% | 18650 | 0.208 | 1 | 25 |

21700 | 0.367 | 1 | 25 | |

26650 | 0.106 | 1 | 145 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ludwig, S.; Steinhardt, M.; Jossen, A. Determination of Internal Temperature Differences for Various Cylindrical Lithium-Ion Batteries Using a Pulse Resistance Approach. *Batteries* **2022**, *8*, 60.
https://doi.org/10.3390/batteries8070060

**AMA Style**

Ludwig S, Steinhardt M, Jossen A. Determination of Internal Temperature Differences for Various Cylindrical Lithium-Ion Batteries Using a Pulse Resistance Approach. *Batteries*. 2022; 8(7):60.
https://doi.org/10.3390/batteries8070060

**Chicago/Turabian Style**

Ludwig, Sebastian, Marco Steinhardt, and Andreas Jossen. 2022. "Determination of Internal Temperature Differences for Various Cylindrical Lithium-Ion Batteries Using a Pulse Resistance Approach" *Batteries* 8, no. 7: 60.
https://doi.org/10.3390/batteries8070060