Elsevier

Journal of Power Sources

Volume 336, 30 December 2016, Pages 325-331
Journal of Power Sources

A self-discharge model of Lithium-Sulfur batteries based on direct shuttle current measurement

https://doi.org/10.1016/j.jpowsour.2016.10.087Get rights and content

Highlights

  • Concept of total capacity with respect to Li-S battery self-discharge is proposed.

  • Shuttle current is identified for various temperatures and states-of-charge.

  • Self-discharge model for Li-S batteries is proposed, parametrized and validated.

  • Practical integration of the self-discharge model into other models is discussed.

Abstract

In the group of post Lithium-ion batteries, Lithium-Sulfur (Li-S) batteries attract a high interest due to their high theoretical limits of the specific capacity of 1672 Ah kg−1 and specific energy of around 2600 Wh kg−1. However, they suffer from polysulfide shuttle, a specific phenomenon of this chemistry, which causes fast capacity fade, low coulombic efficiency, and high self-discharge. The high self-discharge of Li-S batteries is observed in the range of minutes to hours, especially at a high state of charge levels, and makes their use in practical applications and testing a challenging process. A simple but comprehensive mathematical model of the Li-S battery cell self-discharge based on the shuttle current was developed and is presented. The shuttle current values for the model parameterization were obtained from the direct shuttle current measurements. Furthermore, the battery cell depth-of-discharge values were recomputed in order to account for the influence of the self-discharge and provide a higher accuracy of the model. Finally, the derived model was successfully validated against laboratory experiments at various conditions.

Introduction

Lithium-Sulfur (Li-S) batteries represent a promising alternative to the Lithium-ion battery chemistry, due to their high theoretical limits in terms of specific capacity (i.e. 1672 Ah kg−1) and specific energy (i.e. 2600 Wh kg−1). Furthermore, they are expected to become a cheaper and more environmentally friendly solution, mainly due to the use of sulfur, which is an abundant and benign element. However, besides other chemistry related phenomena, Li-S batteries suffer from polysulfide shuttle, which results in several commonly known drawbacks: fast capacity fade, low coulombic efficiency, and high self-discharge [1], [2].

For the practical use of the Li-S batteries, there is a need not only to characterize the self-discharge behavior as it was done in Ref. [3], but also to provide a proper simulation tool (a model), relevant for industrial applications and laboratory experiments as well; otherwise, biased results can be acquired (e.g. not corresponding depth-of-discharge (DOD) levels assigned). The main cause of self-discharge for Li-S cells was identified to be the polysulfide shuttle and afterwards the corrosion of the current collectors [4], [5], [6], [7]. Because the polysulfide shuttle is present not only during the cell idling, but also during charging and discharging, the self-discharge appears as well during these conditions. A mechanistic model of the polysulfide shuttle causing the self-discharge of the Li-S battery cells was presented in Ref. [8]. However, the purpose of the model was to provide insights into the key battery mechanisms, rather than to be used from an end-application perspective. The mathematical model presented in Ref. [9] and a zero dimensional model for the Li-S batteries introduced in Ref. [10] are using the relations for the polysulfide shuttle derived from Ref. [4]. However, these relations are based on determining experimentally a shuttle constant kS, which is a time-consuming procedure; moreover, it might not always provide sufficiently accurate results for the self-discharge estimation, as it was indicated in Ref. [3]. Another simple approach was used in Ref. [11], where the self-discharge current was related to the charge lost during idling at 100% state-of-charge (SOC). The self-discharge current was identified to be proportional to the square root of the idling time. However, the model characterization tests for the 100% SOC condition took more than nine days and it was assumed that self-discharge current is dependent on the used power profile. Furthermore, a methodology for direct shuttle current measurement was proposed in Ref. [12], where its results were analyzed and validated using the one-dimensional phenomenological model, which is based on Nernst and species concentrations equations. This methodology allows for a simple and time-effective measurement of the shuttle current at different SOC levels; it is based on the premise that the shuttle current can be observed as the steady-state current flows through the cell, while its voltage is kept constant during constant voltage operation to prevent the voltage decay.

In this paper, the direct shuttle current measurement method is used to identify the shuttle current of a 3.4 Ah Li-S pouch cell at different depth-of-discharge levels and temperatures. Furthermore, the obtained results are used to derive a simple and easy-to-use mathematical model of the self-discharge in the Li-S battery cell that is related to the polysulfide shuttle phenomenon. This model is validated against several self-discharge experiments at various conditions and it is suitable to predict the self-discharge during idling and operation of the battery.

Section snippets

Methodology

The work flow followed in this paper is summarized and presented in Fig. 1. At first, the measurements were performed and they are described in Section 2.1 for direct shuttle current measurements and in Section 2.2 for the self-discharge model validation measurements. The current shuttle measurement results are presented in Section 3 and later on in Section 3.1 it is also shown how the mathematical expression for the self-discharge model dependent on DOD and temperature is derived. Later on,

Measurement results and modelling

The current profiles obtained from the constant voltage charging steps during the direct shuttle current measurements, at 35 °C, are presented in Fig. 5. At least 2 h of constant voltage charging are necessary to reach a state close to steady-state. Due to the accuracy of the test station, extra noise is appearing at the current values lower than 0.06 A. In order to get a higher accuracy of the measured shuttle current values, the measurement can be repeated using equipment dedicated for lower

SOC reference frame & cell history effect

The challenging part of the integration of the presented self-discharge model into any other model is that the battery performance model has to have the same DOD/SOC reference frame in order that the dependency states to be matched. Due to the ‘rate capacity effect’ [14], the available battery capacity varies according the applied current. Therefore, Ccdch term is also current dependent. Usually, to obtain this Ccdch, continuous discharge tests are used. However, alternative approaches can be

Conclusions

The direct shuttle current measurement methodology was applied to a 3.4 Ah Li-S pouch cell, which allows for the shuttle current quantification at various battery cell DODs and temperatures. In this study, the shuttle current is considered as the only source of the self-discharge and therefore, the high voltage plateau was in focus. The pre-determined DOD steps from the measurement were recomputed in order to take into account the shuttle current and thus obtain the actual corresponding DOD

Acknowledgments

This work has been part of the ACEMU-project. The authors gratefully acknowledge the Danish Council for Strategic Research (1313-00004B) and EUDP (1440-0007) for providing financial support and would like to thank OXIS Energy for supplying the Lithium-Sulfur battery cells.

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