# Capacity Recovery Effect in Lithium Sulfur Batteries for Electric Vehicles

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Capacity Recovery Effect

## 3. Experimental Capacity Recovery Study

#### 3.1. Recovery Time Constant

#### 3.2. Recovery Cycle

#### 3.3. Parameter Variation

#### 3.4. Basic Recovery Model

## 4. Results

#### 4.1. Constant Current Condition

#### 4.2. Drive Cycle Condition

#### 4.3. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Urbonaite, S.; Poux, T.; Novák, P. Progress Towards Commercially Viable Li-S Battery Cells. Adv. Energy Mater.
**2015**, 5, 1500118. [Google Scholar] [CrossRef] - VDI. Available online: https://www.vdi.de/ (accessed on 24 June 2017).
- Barghamadi, M.; Kapoor, A.; Wen, C. A Review on Li-S Batteries as a High Efficiency Rechargeable Lithium Battery. J. Electrochem. Soc.
**2013**, 160, 1256–1263. [Google Scholar] [CrossRef] - Busche, M.R.; Adelhelm, P.; Sommer, H.; Schneider, H.; Leitner, K.; Janek, J. Systematical electrochemical study on the parasitic shuttle-effect in lithium-sulfur-cells at different temperatures and different rates. J. Power Sources
**2014**, 259, 289–299. [Google Scholar] [CrossRef] - Kolosnitsyn, V.S.; Kuzmina, E.V.; Karaseva, E.V. On the reasons for low sulfur utilization in the lithium-sulfur batteries. J. Power Sources
**2015**, 274, 203–210. [Google Scholar] [CrossRef] - Mikhaylik, Y.V.; Akridge, J.R. Polysulfide Shuttle Study in the Li/S Battery System. J. Electrochem. Soc.
**2004**, 151, 1969–1976. [Google Scholar] [CrossRef] - Waluś, S.; Barchasz, C.; Bouchet, R.; Leprêtre, J.C.; Colin, J.F.; Martin, J.F.; Elkaïm, E.; Baehtz, C.; Alloin, F. Lithium/sulfur Batteries Upon Cycling: Structural Modifications and Species Quantification by In Situ and Operando X-ray Diffraction Spectroscopy. Adv. Energy Mater.
**2015**, 27, 5203–5209. [Google Scholar] [CrossRef] - Jongerden, M.R.; Haverkort, B.R. Battery Modeling; Technical Report TR-CTIT-08-01; Centre for Telematics and Information Technology, University of Twente: Enschede, The Netherlands, 2008. [Google Scholar]
- Zhang, T.; Marinescu, M.; Walus, S.; Offer, G.J. Modelling transport-limited discharge capacity of lithium-sulfur cells. Electrochim. Acta
**2016**, 219, 502–508. [Google Scholar] [CrossRef] [Green Version] - Parfitt, C. Characterisation, Modelling and Management of Lithium-Sulphur Batteries for Spacecraft Applications. Ph.D. Thesis, University of Warwick, Coventry, UK, 2012. [Google Scholar]
- Knap, V.; Stroe, D.I.; Teodorescu, R.; Swierczynski, M.; Stanciu, T. Electrical circuit models for performance modeling of Lithium-Sulfur batteries. In Proceedings of the Energy Conversion Congress and Exposition (ECCE), Montreal, QC, Canada, 20–24 September 2015. [Google Scholar]
- Kumaresan, K.; Mikhaylik, Y.; White, R.E. A Mathematical Model for a Lithium-Sulfur Cell. J. Electrochem. Soc.
**2008**, 155, A576–A582. [Google Scholar] [CrossRef] - Marinescu, M.; Zhang, T.; Offer, G.J. A zero dimensional model of lithium-sulfur batteries during charge and discharge. Phys. Chem. Chem. Phys.
**2015**, 18, 584–593. [Google Scholar] [CrossRef] [PubMed] - Zhang, S.S. Liquid electrolyte lithium/sulfur battery: Fundamental chemistry, problems, and solutions. J. Power Sources
**2013**, 231, 153–162. [Google Scholar] [CrossRef] - Hancock, K.; Hagen, M.; Fanz, P.; Joos, M.; Müller, D.; Abert, M.; Tübke, J. Electrolyte decomposition in Li-S cells. In Proceedings of the Li-SM3 Conference, London, UK, 26–27 April 2017. [Google Scholar]
- Howell, D. Update on US DOE Electric Drive Vehicle R&D and Deployment Activities. In Proceedings of the 6th US-China Electric Vehicle and Battery Technology Workshop, Boston, MA, USA, 22–24 August 2012. [Google Scholar]
- Keil, P.; Jossen, A. Aging of Lithium-Ion Batteries in Electric Vehicles: Impact of Regenerative Braking. In Proceedings of the 28th EVS, Goyang, Korea, 3–6 May 2015. [Google Scholar]

**Figure 1.**Open circuit voltage of a lithium sulfur cell with reaction products of the multiple reaction stages described in [5]. DOD, depth of discharge.

**Figure 2.**Relative cell capacity influenced by constant discharge current without rest time. The Peukert coefficient of the model is 1.2.

**Figure 3.**Measured and modeled recovered capacity after a 0.8 C constant current discharge at 100% DOD and a recovery break time between zero and 120 min at a constant temperature of 25 ${}^{\circ}$C.

**Figure 4.**Sequence of the recovery cycle, which consists of four single cycles with constant current (CC) discharges and charges. The test parameters are constant within one recovery cycle. These test parameters are ${I}_{test}$ (0.2, 0.4 or 0.8 C), ${\mathrm{DOD}}_{level}$ (20%, 40%, 60% or 80%) and ${t}_{RBT}$ (15 min, 30 min, 60 min or 120 min).

**Figure 5.**Model of the relative recovered cell capacities at 20%, 40%, 60%, 80% DOD level and discharge currents of 0.2 C, 0.4 C, 0.8 C measured at a constant temperature of 25 ${}^{\circ}$C.

**Figure 6.**Measured recovered capacity for 120 min ${t}_{RBT}$ at DOD 60% at 0.2 C, 0.4 C, 0.6 C and 0.8 C and at a constant temperature of 25 ${}^{\circ}$C.

**Figure 7.**Velocity and calculated current profile of the US06 drive cycle. Discharged current is negative.

**Figure 8.**Relative recovered cell capacity by the US06 drive cycle for a maximum discharge current of 0.5 C and 1 C, measured at a constant temperature of 25 ${}^{\circ}$C.

**Table 1.**Discharge current-dependent mean time constant $\overline{\tau}$ of Equation (5) measured at a constant temperature of 25 ${}^{\circ}$C.

${\mathit{I}}_{0.2\phantom{\rule{4.pt}{0ex}}\mathbf{C}}$ | ${\mathit{I}}_{0.4\phantom{\rule{4.pt}{0ex}}\mathbf{C}}$ | ${\mathit{I}}_{0.8\phantom{\rule{4.pt}{0ex}}\mathbf{C}}$ | |
---|---|---|---|

$\overline{\tau}$ | 17.9 | 24.4 | 21.6 |

**Table 2.**Root mean square error between measured and modeled recovered capacity, normalized by the nominal discharge capacity at 0.2 C and measured at a constant temperature of 25 ${}^{\circ}$C.

Discharge Current | 20% DOD | 40% DOD | 60% DOD | 80% DOD |
---|---|---|---|---|

0.2 C | 0.04% | 0.01% | 0.07% | 0.08% |

0.4 C | 0.09% | 0.10% | 0.42% | 0.1% |

0.8 C | 0.08% | 0.35% | 0.48% | 0.28% |

© 2018 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Maurer, C.; Commerell, W.; Hintennach, A.; Jossen, A.
Capacity Recovery Effect in Lithium Sulfur Batteries for Electric Vehicles. *World Electr. Veh. J.* **2018**, *9*, 34.
https://doi.org/10.3390/wevj9020034

**AMA Style**

Maurer C, Commerell W, Hintennach A, Jossen A.
Capacity Recovery Effect in Lithium Sulfur Batteries for Electric Vehicles. *World Electric Vehicle Journal*. 2018; 9(2):34.
https://doi.org/10.3390/wevj9020034

**Chicago/Turabian Style**

Maurer, Christian, Walter Commerell, Andreas Hintennach, and Andreas Jossen.
2018. "Capacity Recovery Effect in Lithium Sulfur Batteries for Electric Vehicles" *World Electric Vehicle Journal* 9, no. 2: 34.
https://doi.org/10.3390/wevj9020034