A self-discharge model of Lithium-Sulfur batteries based on direct shuttle current measurement
Summary (4 min read)
1. 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.
- A mechanistic model of the polysulfide shuttle causing the self-discharge of the Li-S battery cells was presented in [8].
- The self-discharge current was identified to be proportional to the square root of the idling time.
- Furthermore, a methodology for direct shuttle current measurement was proposed in [12], where its results were analyzed and validated using the one-dimensional phenomenological model, which is based on Nernst and species concentrations equations.
2. Methodology
- The work flow followed in this paper is summarized and presented in Fig.
- 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.
- Later on, there were considered three fitting cases.
- Each of these fitting cases parameterize the selfdischarge model and its accuracy is later validated in Section 3.2 by an use of the validation measurements (Section 2.2) and the SOC estimation model for the validation (Section 2.3) with the consideration of the total capacity concept (Section 2.4).
- Ah long life chemistry Li-S pouch cell manufactured by OXIS Energy.
2.1 Direct Shuttle Current Measurement
- The applied test procedure for the direct shuttle current measurement is based on the methodology presented in [12] and illustrated in Fig.
- The second cycle was used for the cell’s capacity check and its calculation for the further procedure steps.
- In practice, due to the noise in the voltage signal, the reliable value of the OCV was determined when the battery voltage dropped from the maximum point by 0.6 mV (three times the value of the battery test station accuracy which was equal to 0.2 mV) as it is presented in Fig.
- The voltage and current signals during the direct shuttle current measurement procedure are shown in Fig. 3 for DOD equal to 10 % at 35 °C.
2.3 Matlab/Simulink Model for Validation
- The self-discharge Li-S model is going to be integrated into a Matlab/Simulink model, which allows for SOC estimation based on the coulomb counting method.
- The used SOC definition in this work follows the definition described in [13].
- So the SOC represents the relation between the actual useable battery capacity (Ca) and the total capacity (Ct) available to be discharged after the battery being fully charged.
- Using only coulomb counting method, without accounting for the fast self-discharge of the Li-S batteries will lead inevitably to a growing error due to not capturing the self-discharge current.
2.4 Concept of the total capacity of the Li-S batteries
- The standard practice to determine the capacity of Li-S battery cells is to continuously discharge before-hand fully charged battery by a specific current at a specific temperature.
- The obtained discharged capacity is considered as the capacity of the cell at those conditions.
- As the polysulfide shuttle is present during the Li-S cell discharging, it causes self-discharge, which consequently reduces the measured capacity.
- Csd is obtained from the simulation of the cell’s continuous discharge with Ccdch replacing Ct in (1).
- Moreover, the Ish is excluded from the coulomb counting in (1) and it is integrated and recorded separately.
3. 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.
- 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 current ranges.
- For the demonstration purposes of the model, in this paper, it is considered sufficient to take an average of the last ten minutes of the current profile during constant voltage charging step as the value for the shuttle current.
- The measured shuttle current values for pre-determined DOD points.
3.1.1 Fitting Case 1
- The first fitting step, referred as Fitting Case 1 (FC1), was performed by fitting the experimentally determined direct shuttle current values against the DOD points (see Fig. 6).
- For the last DOD level, when during the battery cell relaxation period of 12 hours a peak voltage value was not detected (as described in the methodology in the previous section), a shuttle current value equal to zero was considered for fitting purposes.
- The considered DOD levels are shown in Table I for FC1 and 35 °C.
- These predetermined DOD points might not accurately correspond to the actual DOD levels of the cell as the influence of the shuttle current was not considered during the measurement procedure.
3.1.2 Fitting Case 2
- Therefore, for the Fitting Case 2 (FC2), it was assumed that the self-discharge was ongoing already during the discharging steps, during the relaxation periods before the constant voltage charging step, and during the constant voltage charging step in the characterization experiment, as it is illustrated in Fig.
- The time values of discharging and relaxation were computed and multiplied by the measured shuttle current value for the first DOD point (i.e. 2 %), which provided an estimate of the ampere-hours lost due to self-discharge during that period.
- During the previous one hour and fifty minutes, the shuttle current is only partially compensated as the external current is lower.
- Therefore, the amount of the self-discharged ampere-hours can be obtained by integration of the area above the current curve in a rectangle from the beginning of the constant voltage charging up to one hour and fifty minutes time coordinates.
- The same procedure was repeated for the remaining DOD points, considering also the correction from the previous DOD point.
3.1.3 Fitting Case 3
- For the further improvement of the model, the Fitting Case 3 (FC3) was applied to obtain the total capacity.
- The Simulink model, including the self-discharge model obtained at the end of FC2, was fed by the current profile obtained from the direct current shuttle procedure.
- Thus, the DOD points, corresponding to the shuttle current values, were extracted and are presented in Table I for 35 °C.
- The parameters c, d, e and f of the shuttle current model for all the fitting cases are presented in Table II.
- The presented fitting procedure with all three fitting cases and their steps are visualized in Fig. 7.
3.2 Validation of the self-discharge model
- For the validation of the self-discharge model, four validation measurements were performed according to the procedure described in Section 2.2.
- The validation cases consider various temperature conditions, idling times and initial DOD levels.
- A comparison of the accuracy values of the developed self-discharge model for the different used fitting cases is shown in Table III.
- The relative errors are noticeably reduced by moving from FC1 to FC2, except the Validation Case 1, where only a minor increase is observed.
- The error reduction implies the correctness of the assumptions used for FC2 and that the self-discharge due to the polysulfide shuttle is still present, no matter if the Li-S battery is in charging, relaxation or discharging stage.
4.1 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.
- In [15], for practical reasons, the mixed pulse discharge was used to determine Ccdch.
- Therefore, the DOD of the performance model has to be converted into DOD of the self-discharge model at its input.
4.2 Open-circuit voltage based self-discharge model
- Alternatively, the DOD dependence of the self-discharge model can be replaced by the open-circuit voltage (OCV) dependence.
- By following this approach, the shuttle current values related to the OCV are presented in Fig. 8, where it is important to note that this relation is valid only for OCV values at the side of the high voltage plateau.
- The OCV values in the practical use can be obtained for example by online parameter identification techniques [16].
- Based on the curve fitting of the shuttle current dependency on DOD and temperature, a simple mathematical model for the self-discharge estimation of Li-S batteries was obtained.
- The developed model was successfully validated by the experiments considering various conditions with a relative error smaller than 7 %.
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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Cites methods from "A self-discharge model of Lithium-S..."
...…and Chen, 2014c) Martin Rolf Busche 2014 Cell Shuttle-effect at different temperatures and different rates (Busche et al., 2014) Vaclav Knap 2016 Battery A self-discharge model based on direct shuttle current measurement (Vaclav Knap et al., 2016) Peng Tan 2017 Battery Mass…...
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...Even though, as explained above, the shuttle effect has several undesired consequences on LiS batteries, Vaclav Knap et al. make use of this effect to introduce a new type of passive dissipative balancing method, based on electrochemistry, which allows to take better advantage of the total capacity....
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...Abdollahi et al., 2017) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 Abbas Fotouhi 2017 Cell Equivalent Circuit Network Model Parameterization and Sensitivity Analysis (Fotouhi et al., 2017b) Vaclav Knap 2017 Battery Model to study the selfbalancing feature (Knap et al., 2017) Daniel-Ioan Stroe 2017 Battery Modelling the discharge phase (Stroe et al., 2017) Abbas Fotouhi 2017 Battery SOC observability Analysis and Estimation (Fotouhi et al., 2017c) S. E. A. Yousif 2018 Battery Self-Discharge Effects in Lithium- Sulphur Equivalent Circuit Networks (Yousif et al., 2018) Table 2: Li-S models classifieds by the type of model Due to the computational limitations of the microprocessors on board EVs and that they execute many tasks besides those related to the battery; battery models implemented on EV should demand low computational resources....
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...Karthikeyan Kumaresan 2008 Cell Physical reasons for the two- stage discharge profile (Kumares an et al., 2008) Mahmoudrez a Ghaznavi, P. Chen 2013 Cell Applied discharge current and cathode conductivity (Ghaznavi and Chen, 2014a) Mahmoudrez a Ghaznavi, P. Chen 2013 Cell Precipitation reaction kinetics and Sulphur content (Ghaznavi and Chen, 2014b) Mahmoudrez a Ghaznavi, P. Chen 2014 Cell Variation of the exchange current densities, diffusion coefficients, and cathode thickness over a wide range (Ghaznavi and Chen, 2014c) Martin Rolf Busche 2014 Cell Shuttle-effect at different temperatures and different rates (Busche et al., 2014) Vaclav Knap 2016 Battery A self-discharge model based on direct shuttle current measurement (Vaclav Knap et al., 2016) Peng Tan 2017 Battery Mass transport and electrochemical reaction processes is first developed (Tan et al., 2017) Zhaofeng Deng 2013 Battery Modelling and Analysis of Capacity Fading (Deng et al., 2013) Andreas F. Hofmann 2014 Battery Shuttle and capacity loss (Hofmann et al., 2014) Teng Zhang 2015 Cell Modelling the voltage loss mechanisms (Zhang et al., 2015) Y.X. Ren 2016 Battery Discharge behaviour incorporating the effect of Li2S precipitation (Ren et al., 2016) Monica Marinescu 2016 Battery Dimensional model during charge and discharge (Marinesc u et al., 2015) Mahsa Ebadi 2017 Battery Modelling the Interfacial Chemistry of the LiNO3 Additive (Ebadi et al., 2017) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 Nisa Erisen 2018 Battery Predict the effect of critical cathode design parameters (Erisen et al., 2018) Vaclav Knap 2018 Battery Test Methodology for Degradation Assessment (Knap et al., 2018) Monica Marinescu 2018 Battery Irreversible vs Reversible Capacity Fade during Cycling: The Effects of Precipitation and Shuttle (Marinesc u et al., 2018) Saul Perez Beltran 2018 Battery New understanding of graphene effects on S reduction behaviour (PerezBel tran and Balbuena, 2018) Chen 2006 Battery prediction of the remaining battery capacity of Lithium-ion batteries (Chen et al., 2006) O. Erdinc 2009 Battery Effects of temperature and capacity fading (Erdinc et al., 2009) Natalia A. Cañas 2012 Battery Equivalent circuit model using electrochemical impedance spectroscopy (Cañas et al. 2013) Suguna Thanagasund ram 2012 Cell Cell model for battery simulation (Thanaga sundram et al., 2012) Vaclav Knap 2015 Battery Parametrization Techniques for an Electrical Circuit Model (Knap et al., 2015b) Vaclav Knap 2015 Battery Performance Modelling (Knap et al., 2015a) Abbas Fotouhi 2015 Battery Electric Vehicle Battery Model Identification and State of Charge Estimation in Real World Driving Cycles (Fotouhi et al., 2015) Abbas Fotouhi 2016 Battery Prediction-Error Minimization (PEM) algorithm applied to experimental data (Fotouhi et al., 2016c) Abbas Fotouhi 2016 Cell Graphical User Interface for Battery Design and Simulation; From Cell Test Data to RealWorld Automotive Simulation (Fotouhi et al., 2016d) Abbas Fotouhi 2016 Battery Model in real-time applications where accuracy is important (Fotouhi et al., 2016a) Karsten Propp 2016 Battery Non-linear state-of-charge dependent ECN model (Propp et al., 2016) Ali Abdollahi 2017 Battery Optimal charging for general equivalent electrical battery model, and battery life management....
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...Moreover, Li-S batteries have 8-15% self-discharge rate per month (Kolosnitsyn and Karaseva, 2008)(V. Knap et al., 2016) due to polysulfide shuttle (Mikhaylik and Akridge, 2004) and collector corrosion (Song et al., 2013), (Vaclav Knap et al., 2016), (Marinescu et al., 2015), which is between 10 and 15 times higher than the selfdischarge of Li-ion batteries (Table 1)....
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