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Rinnakkaistallenteet Luonnontieteiden ja metsätieteiden tiedekunta
2019
Cylindrical Li-Ion Battery State of
Health Evaluation by Differential Heat Analysis During Calendar Ageing
Murashko, K A
Electrochemical Society
Tieteelliset aikakauslehtiartikkelit
© The Electrochemical Society All rights reserved
http://dx.doi.org/10.1149/2.0711913jes
https://erepo.uef.fi/handle/123456789/25484
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Cylindrical Li-Ion Battery State of Health Evaluation by Differential Heat Analysis During Calendar Ageing
K.A. Murashkoz,1, A.V. Mityakov2, V.Y. Mityakov3, S.Z. Sapozhnikov3, J. Pyrhönen2 and J.
Jokiniemi1
1 University of Eastern Finland, Kuopio Campus, P.O. Box 1627, FI-70211 Kuopio, Finland
2 Lappeenranta University of Technology LUT, Yliopistonkatu 34, 53850 Lappeenranta, Finland
3 Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya, 29, 195251 Saint-Petersburg, Russia
zCorresponding Author E-mail Address [kirill.murashko@uef.fi]
Abstract
A novel method for the state of health (SoH) estimation and determination of the degradation mechanisms of cylindrical Li-ion cells after long storage time is presented. The proposed method is based on differential curves obtained with the help of temperature and heat flux measurements on the surface of a cylindrical lithium iron phosphate (LFP) cell. The applicability and advantages of the proposed differential curves for the SoH estimation and determination of degradation mechanisms are discussed and verified based on a comparison with currently existing in-situ diagnostic methods such as differential voltage (DV) analysis method. The results of the comparison show that the proposed differential curve can provide information about capacity fading and prevailing degradation mechanism at higher than 1 C- rate discharging current while the application of the DV curve may not be possible. Moreover, the presented method allows identification of the changes in the entropic heat generation, which may improve the SoH estimation and the determination of the degradation mechanisms in a cylindrical Li-ion cell after a storage period.
Keywords: Li-ion batteries; In-situ diagnostic methods; SoH estimation; Degradation mechanisms; Heat flux measurements; Thermal model.
1. Introduction.
Li-ion technology is a fast growing and the most promising battery technology nowadays
1. Rechargeable Li-ion batteries are widely used in portable devices because of their high volumetric and gravimetric energy density, high cycle life and low self-discharge rate. In addition, the Li-ion batteries are considered as the most suitable technology for the creation of energy storage systems in electric vehicles (EVs), hybrid electric vehicles (HEVs) and hybrid mobile off-road machines. Despite the advantages of the Li-ion batteries, there are major technical and financial challenges remaining that limit their application. The Li-ion battery is a non-linear and a time-variable system, whose internal electrochemical processes are almost impossible to be observed directly 2. The complicated electrochemical processes occurring in the battery lead to a battery degradation and decreasing of its performance. A battery degradation may happen not only during operation but also during storage. Especially, in such applications as EVs and HEVs, where most of the battery life time takes place in so called parking mode 3, the degradation of the battery during storage should be taken into account, as it may lead to loss of device performance or even more serious consequences such as fire, a failure of an expensive equipment and even in the worstcase casualties. Unfortunately, the non- observability of the electrochemical processes in the battery does not allow direct measurements of the battery lifetime and only estimation of this parameter is possible.
Nowadays, the estimation of the battery lifetime is performed by considering such characteristic as the SoH. Many different methods have been suggested to estimate the SoH.
The diagnostic methods are considered as the most suitable methods nowadays for the realtime SoH observation. These methods do not require utilisation of the battery models, which should be adjusted by using sufficient data from prior tests. The following methods can be attributed to the currently existing diagnostic methods: electrochemical impedance spectroscopy (EIS), differential voltage analysis, incremental capacity (IC) analysis and differential thermal voltammetry (DTV). The EIS method allows measuring of the battery impedance and creation of an equivalent electrical circuit model (EECM), based on the measured data fitting. The SoH can be estimated by considering the variation of the EECM parameters. The EIS method was used for the SoH estimation in 4–8. The disadvantage of the EIS method is the implementation complexity in a battery management system (BMS). The IC and DV analysis methods allow to estimate SoH by analysis of the differential curves such as IC curves vs. operation voltage (dQ/dU vs. U) and DV curves vs. capacity (dU/dQ vs. Q). The use of IC and DV analysis methods for the online SoH estimation in a BMS was shown in 9–12. Moreover, these methods can be used for an indication of the prevailing degradation mechanism as it was shown in 13–16 and in 17–25 for DV and IC analysis methods, correspondingly. However, despite the attractiveness of the IC and DV analysis methods, they have disadvantages, which may limit the application of these methods in a BMS. The methods require a constant battery temperature during measurements 26. The DV and IC curves must be obtained by a slow rate non-stop discharge or/and charge current, for which a 1/25 C-rate current is usually used 1. Moreover, DV and IC curves are created based on the terminal voltage of the Li-ion battery, which is the difference between potentials of the positive and negative electrode. However, in the majority of Li-ion battery chemistries, the LFP is an exception, the terminal voltage is mostly determined by the positive electrode potential, and therefore changes of the negative electrode potential with its degradation are difficult to discern 26. It may lead to impossibility to take into account some degradation mechanisms in the Li-ion battery and incorrect SoH estimation results. The DTV method, which is capable of monitoring the SoH by using voltage and temperature measurements in galvanostatic operating modes, was suggested by Wu et al. 26. This method allows taking into account the entropy change (ΔS) profile variation with the aging of the Li-ion battery, which can be used as an indication of the degradation mechanisms occurring in the specific electrode and for the determination of the SoH 27,28. However, in spite of the advantages of the DTV method, the requirement that the Li-ion battery should be thermally isolated before measurements 29 is considered as the main disadvantage of this method. Such requirement limits possible applications of the method in a BMS for the real- time SoH estimation as without a proper cooling system there is a high probability of the battery overheating, which strongly decreases its lifetime and may be a reason of a thermal runaway and even fire.
It seems that in spite of the availability of a big number of different techniques for the estimation of the SoH, all techniques have limitations for their implementation in a BMS.
Therefore, the development of a new method for the SoH estimation, which does not have disadvantages of the currently existing diagnostic methods and can be used as a separate method or together with existing methods, is still necessary. This paper aims to investigate the possibility to consider heat, generated during the Li-ion battery operation after storage, as an indication of the SoH. A cylindrical LFP cell is selected for the analysis. The estimation of the heat generation during the aging of a cylindrical LFP cell is based on the thermal model of the cylindrical cell and information obtained from the heat flux and temperature measurements.
The results obtained by the proposed method are compared with results obtained from one of the most promising currently existing in-situ diagnostic method such as DV analyses method.
2. Materials and methods 2.1 Aging test
The cylindrical 2.5 Ah A123 Systems LFP cell (ANR26650M1B) was selected for the analysis. The cell was activated by five 1 C-rate charging/discharging cycles at room temperature and then it was fully charged according to manufacturer’s recommendations 30. A Potentiostat/Galvanostat Gamry Reference 3000 was used for the charging and discharging of the cell in all tests. For the calendar aging test, the LFP cell was sent to an oven storage controlled to 60 °C. The storage temperature of the cell was selected with purpose to speed up the capacity loss in the cell and, because of this, to decrease the storage time needed similarly as it was done e.g. by Li et al. 31. The storage period of the LFP cell was divided in five intervals.
The storage time and capacity loss of the cell under study during calendar ageing test are shown in Table 1. In the beginning of the calendar ageing test and between the intervals selected, the DV curves, electormotive force (EMF) and heat generation were measured. The total storage time was 10 months.
2.2 DV curves and EMF measurements
The DV (𝜕U/𝜕Q) curves were obtained by a commonly used method from the terminal voltage (U) and the storage capacity (Q) measured data. The required data were measured during discharging of the fully charged LFP cell by various constant currents (0.25, 0.75, 1.5 and 3.0 A) until a cut-off voltage. 1.6 V was selected as the cut-off voltage for the considered LFP cell. Different values of constant discharging current (CC) were used with purpose to analyse its influence on the shape of the DV curve. In the end of the discharging process the cell was fully charged according to the manufacturer’s recommendations 30. The relaxation time between CC charging and discharging of the LFP cell was 5 hours.
A moving average (MA) smoothing method was applied on the battery terminal voltage and capacity data obtained after cell discharging and before numerical-derivative method. This method was successfully used to decrease the 𝜕U/𝜕Q curve sensitivity to measurement noise and a trembling by Bloom et al. 14,15,32. In addition, a Gaussian filter was used on the battery voltage and capacity data after the MA smoothing method, as it was suggested by Li et al. 11. The combination of the MA smoothing method and the Gaussian filter allows improving noise removal before numerical-derivative without a significant effect on the shapes of the 𝜕U/𝜕Q curves. The number of the smoothing points and the number of the points in the Gaussian window were selected to be inversely proportional to the values of discharging current and were calculated as:
𝑁 = 𝑎 ∙ 𝑄
∆𝑡 ∙ 𝐼dis (1)
where N is the number of the points, Δt is the time difference between the measurements [h], Q is the storage capacity of the LFP cell [Ah] and Idis is the discharging current [A] and a is the proportional coefficient. The proportional coefficients were selected to be equal to 0.04 and 0.08 for the MA smoothing method and the Gaussian filter, respectively. The selection of the proportional coefficients was done by analysing the impact of the coefficient on the noise removal and on the important features of the curves considered.
In addition to the 𝜕U/𝜕Q curve, the 𝜕UEMF/𝜕Q curve was measured by the same way as it was suggested by Li et al. 31. The consideration of the EMF instead of the terminal voltage in the differential curve allows to neglect the impact of the constant current on the shape of the differential curve. Therefore, the 𝜕UEMF/𝜕Q curve was used as a reference curve in this article during the analysis of the influence of the CC values on the DV curve shape and the changes
in the 𝜕UEMF/𝜕Q curve shape were analysed duting calendar aging of the considered Li-ion cell.
The EMF was measured by an extrapolation method, which has been described by Notten et al. 33–35. In accordance with the extrapolation method, the LFP cell was discharged at various constant currents (0.25, 0.5, 0.75, 1.0, 1.25 and 1.5 A) and the EMF curve was obtained by vertical and horizontal extrapolations of the terminal voltage curves obtained after discharging of the LFP cell as it is shown in Figure 1. The MA smoothing method was applied on the terminal voltage and operation current measured data to improve noise removal before the extrapolation method. The number of smoothing points was calculated by equation (1), where the proportional coefficient was selected to be equal to 0.04.
2.3 Heat generation calculation in the cylindrical LFP cell
The heat generated in the cylindrical cell was measured by a method, which was described in our previous publication 36 and, therefore, in this section only the most important parts of the method are presented. The information about heat generated in the cylindrical LFP cell was obtained after a CC discharging of the cell. 1.5 A and 3.0 A constant currents were applied with purpose to analysis the influence of the CC values on the form of the heat curve. The heat generated during discharging was calculated based on the heat flux and surface temperature data by applying the modified thermal model of an infinitely long cylinder. This is described in detail in 36. A gradient heat flux sensor (GHFS) and a PT100 temperature sensor were used for the heat flux and temperature measurements, correspondingly. The GHFS used was made from bismuth single crystals. The sensitivity of the GHFS is 15.9 mV/W and the dimensions of the GHFS in the plane area are 5×20 mm2, and the thickness is 0.15 mm. More information about GHFS and its calibration can be found e.g. in Refs. 37,38. The GHFS and PT100 sensors were installed on the surface of the cylindrical cell similarly as it was done in 36. In addition, the surface of the cylindrical cell was covered by a 1 mm thick rubber band to change the form of the heat transfer mechanism from convection to conduction,which is the most commonly used heat dissipation mechanism in a big Li-ion battery pack. Moreover, the ends of the cylindrical cell were isolated by a ceramic fibre wool, which allowed considering the cylindrical cell as an infinitely long cylinder, for which the thermal model was presented in 39.
The modification of the thermal model of the cylinder with infinite length (presented in 39) was necessary with purpose to adapt this model to a variable heat flux from the cylindrical cell surface. For this reason, the superposition principle was used. The measured heat flux curve was divided in N equal intervals, where a constant heat flux was assumed. In this case, the heat, generated during CC discharging of the cylindrical cell, at any point in time can be calculated by a numerical differentiation of the following equation:
∫ 𝑄h(𝑡)
𝑡end 𝑡1
d𝑡 =𝑉
𝛼∙ (𝑘 ∙ (𝑇 − 𝑇0) + 𝑟 ∙ 𝛉 × 𝐒) (2) where V is the volume of the cylindrical cell [m3], α is the average thermal diffusivity [m2/s]
inside the cell active mass, k is the average thermal conductivity of the cell active parts [W/(mˑK)], T is the temperature of the cell surface [K], T0 is the initial temperature of the cell surface [K] and r is the radius of the cell [m]. S and Θ are matrices is the matrix, which includes the differences between heat flux data in each of selected intervals and the values of temperature coefficients, correspondidngly. More information about derivation of the equation (2) and calculation of S and Θ matrices can be found in 36.
With purpose to decrease the measured data sensitivity to the measurement noise and trembling, the moving average (MA) smoothing method and the Gaussian filter were applied on the battery surface temperature and heat flux data by a similar way as it was done during
creation of the DV curve. The number of the smoothing points and the number of the points in the Gaussian window were calculated by equation (1), where proportional coefficients were selected to be equal to 0.12 and 0.16 for the MA smoothing method and the Gaussian filter, respectively.
The heat curves obtained after CC discharging of the cylindrical LFP cell by 1.5 A and 3.0 A were presented in form, which is named as differential heat curves, by using similar approach as in the DV curves analysis method. The heat generation curve obtained after cylindrical cell charging was modified by using a simplified form of the battery heat equation presented by Bernardi 40. Its differential is presented as:
−
𝜕 (𝑄̇
𝐼 + 𝑈)
𝜕𝑄 = −𝜕 (𝑈EMF− 𝑇 ∙𝜕𝑈EMF
𝜕𝑇 )
𝜕𝑄 = −𝜕𝑈EMF
𝜕𝑄 +𝜕 (𝑇 ∙𝜕𝑈EMF
𝜕𝑇 )
𝜕𝑄 (3)
where 𝑄̇ is the heat generated in the Li-ion cell (W), I is the current [A], UEMF is the electromotive force [V], and U is the battery voltage [V]. Further, the term (𝑄̇ 𝐼 + 𝑈⁄ ) is denoted as H while 𝜕H/𝜕Q is called the differential heat (DH) curve. Such representation of the heat curves helps to analyse the changes of the curve shape during calendar aging of the cylindrical LFP cell. Moreover, it should decrease the impact of the discharging current on the important futures of the DH curves and allows an identification of the changes in the entropic heat generation, which may improve the SoH estimation and determination of degradation mechanisms in the cylindrical LFP cell.
3. Results and discussion
The DV curves obtained after cell discharging in the beginning of the calendar aging test by different values of CC (0.25, 0.75, 1.5 and 3.0 A) and -𝜕UEMF/𝜕Q curve are shown in Figure 2. The analysis of the -∂U/∂Q curves, obtained by the numerical differentiation of the filtered terminal voltage curves, showed a high dependence of the shape of these curves on the discharging current. Such dependence is similar to the dependence between IC curve shape and the current values, which was previously presented by Ansean et al. 25. As it can be seen, the shapes of the differential curves obtained after CC discharging of the LFP cell by a high C-rate current are significantly deformed. The DV curve obtained after CC discharging by 3.0 A almost does not have any peaks, which are commonly used in the DV curve analysis method for the SoH estimation and determination of battery degradation mechanisms 12. Therefore, an application of this method is only possible if a low C-rate CC can be included in the main operation cycle of the Li-ion battery for its charging or discharging. For example, these methods may be used after a slow overnight charging of EVs. However, in applications where the testing time is limited or in HEVs where Li-ion batteries are used for the power peak compensation and operation cycle cannot be controlled, using the DV analysis method is problematic. Therefore, it is obvious that a method, which does not depend on the battery operation cycle and can be used with high C-rate currents, is necessary for such applications of the Li-ion batteries.
The LFP cell surface temperature, heat flux from the cell surface and calculated heat curves obtained after discharging of the cell by 1.5 A and 3.0 A constant current at the beginning of the cycle aging tests are shown in Figure 3. As it can be seen in Fig. 3, the shapes of the heat curves obtained after LFP cell discharging by 1.5 A and 3.0 A constant current look similar.
The small difference in the shape of the curves at the end of discharge is probably caused by prevailing of the Joule losses over entropic heat generation. It is well known fact that the impedance of the Li-ion cell is significantly increase at the low SoC. The influence of the Li- ion cell impedance on the total heat generation increases with increasing of the value of
operation current, which may explain the increasing of the difference between heat, generated during CC discharging of the considered LFP cell by 1.5 A and by 3.0 A at the low SoC.
The representation of the heat curves in form of the DH curves (-∂H/∂Q) is shown in Figure 4 (b) together with -∂UEMF/∂Q curve. All curves presented in Fig. 4 were obtained before starting of the calendar aging test. As it can be seen in Fig.4 (b) the DH curve has similarity with the -∂UEMF/∂Q curve and it may indicate two voltage plateaus (① and ⑤, which are shown in Fig.4 (a)) even at high C-rate current. The other voltage plateaus, which can be seen on -∂UEMF/∂Q curve, cannot be noticeable on DH curve. Additional significant distinction of the -∂H/∂Q curve from the -∂UEMF/∂Q curve is the presence of the negative peak. This negative peak is caused by changing of the sign of ∂UEMF/∂T with SoC increasing from negative to positive, which occurs at about 30% SoC as it was measured by Aguirrezabala 41 for the 2.5 Ah A123 Systems LFP cell (ANR26650M1B) and is corresponding to the 1.75 Ah of storage capacity. The analysis of the DH curves obtained after discharging of the LFP cell by different values of the constant current showed small effect of the current on position and intensity of the DH curve picks. This small difference in position and intensity of the peaks may be caused by the neglection of the impact of the phase change and mixing effects on the heat generation.
The difference in position of negative pick is caused by effect of temperature on the entropic heat generation. It can be shown by presenting the (∂UEMF/∂T)/∂Q curves obtained from the heat curves and equation (3). The (∂UEMF/∂T)/∂Q curves are shown in Fig. 4 (c). As it can be seen in Fig. 4 (c), there is similarity between the positions of the negative peak on (∂UEMF/∂T)/∂Q and -∂H/∂Q curves. However, the difference between positions of the negative pick on (∂UEMF/∂T)/∂Q curves, obtained at different current, is much smaller than in the case of -∂H/∂Q curves. This difference is almost negligible, and it is most likely caused by an uncertainty of measurements. Moreover, the dependence of the negative peak intensity on current in the (∂UEMF/∂T)/∂Q curve is opposite to the same dependence, which was previously noticed in the -∂H/∂Q curve. The increasing of the (∂UEMF/∂T)/∂Q curve negative peak intensity as a result of increasing discharging current can be explained by an impact of the phase change and mixing effects on the heat generation. This impact increases with increasing discharging current. Despite the presented small impact of the temperature and current on the shape of the DH curves, the described features of the -∂H/∂Q curve are promising when estimating the Li-ion battery degradation mechanisms and SoH. It can be done by using a similar approach which was suggested for DV curves previously 12,31,42,43.
To confirm the applicability of the -∂H/∂Q curves for degradation mechanism determination and SoH estimation, a calendar aging test of the cylindrical LFP cell was
performed. The measured -∂UEMF/∂Q curves at different SoH are shown in Figure 5. The -∂UEMF/𝜕Q curves at different ageing stages are shifted up for the purpose to improve the
visibility of the curve important features changes upon Li-ion battery ageing. Moreover, all peaks in the -∂UEMF/∂Q curves are aligned with respect to the peak α, which are denoted by a red colour. The analysis of the changes of -∂UEMF/∂Q curve shape during calendar aging gave similar results, which were previously presented by Li et al. 31. The loss of lithium caused by the Solid-Electrolyte-Interphase (SEI) formation is probably a dominant degradation process occurring during calendar aging of the LFP cell. It can be seen from -∂UEMF/∂Q curves by analysing the part of the curve, which is corresponding to the voltage plateaus ① (Fig. 4(a)).
This part of the -∂UEMF/∂Q curve is significantly decreased, which may attributed to the immobilization of the lithium ions into SEI layer as it was shown by Li et al. 31. Moreover, a small movement of the β peak to α peak is noticeable, which is shown by a red arrow in Fig.5 and is corresponding to the active material losses of the graphite electrode 31. As it was explained by Li et al. 31, the loss of the active material of the graphite electrode is caused by the iron dissolution from the positive electrode and its deposition onto the negative electrode, making parts of graphite electrode inaccessible for the Li intercalation.
The measured -∂H/∂Q curves at different SoH are shown in Figure 6. Similarly, as it was done at -∂UEMF/∂Q curves analysis, the -∂H/∂Q curves were shifted up and aligned with respect to the β peaks. The curves were obtained after CC discharging of the cell by 1.5 A (Fig. 6 (a)) and by 3.0 A (Fig. 6 (b)). As it can be seen in Fig. 6 the behaviour of the -∂H/∂Q curves during calendar aging of the cylindrical LFP cell has similarities with behaviour of the -∂UEMF/∂Q curves. The comparison of the -∂H/∂Q curves with the -∂UEMF/∂Q curves at different SoH was done by analysing a reduction of the voltage plateau ① on the -∂UEMF/∂Q curves and a reduction of the corresponding to this voltage plateau intervals on the -∂H/∂Q curves denoted as A1 and A2 (Fig 7. (a)). The sub-indices 1 and 2 show that a corresponding -∂H/∂Q curve was obtained after CC discharging of the LFP cell by 1.5 A and 3.0 A, respectively. The reductions of all considered intervals are presented as function of capacity loss of the considered cylindrical LFP cell during calendar aging in Figure 7 (b). The available capacity in the cell was determined from the measured dependence of the EMF on storage capacity during calendar aging test. As it can be seen in Fig.7 (b), the comparison showed a good correlation between the reduction of considered sections on the -∂H/∂Q and -∂UEMF/∂Q curves. In addition, the dependence between reduction of the analysed intervals on -∂H/∂Q and -∂UEMF/∂Q curves on capacity fading in the LFP cell during its calendar aging approximately can be described by linear function, which may be used for the capacity loss prognocis. It was proved by calculating the coefficient of determination (R2) during data fitting by linear function, which for all curves is close to 1. The values of the R2 are shown in Table 2. It is well noticeable that the goodness of the fitting of the dependence between reduction of interval A1 and capacity fading is slightly worse that in case of the fitting of the dependence between reduction of interval A2 and capacity fading. Such a deviation of the obtained data from a linear behaviour may be explained by the impact of ∂(T·(∂UEMF/∂T))/ ∂Q part of the -∂H/∂Q curve, which decreased with increasing of the C-rate constant current due to decreasing of the entropic heat generation effect on the total heat generation in the Li-ion battery. The further analysis showed that utilization of the negative pick of the -∂H/∂Q curve for the SoH estimation at considered degradation mechanism may give better results in the case of a low C-rate currents. The goodness of the fitting of the dependence between reduction of interval B2 and capacity fading is slightly worse that in case of the fitting of the dependence between reduction of interval B1 and capacity fading. Such a result confirms the applicability of the presented DH curves for the SoH estimation and for the determination of degradation mechanisms of the cylindrical LPF cell at calendar aging.
Conclusion
In this article, an analysing of the possibility to consider heat generation in cylindrical LFP cell as an indication of the SoH and cell degradation mechanisms is presented. The analysis was done by considering the heat generation in the cylindrical LFP cell at different SoH after storage. The storage of the LFP cell was done in an oven at 60 °C with purpose to speed up the capacity loss and to reduce the storage time needed in calendar aging tests. The heat generation was calculated based on the suggested thermal model of the cylindrical cell and the information obtained from heat flux and temperature measurements. The values of heat generation, terminal voltage and operation current were used for the creation of the DH curves after CC discharging of the LFP cell. The applicability of the DH curves for the SoH estimation and determination of degradation mechanisms was analyzed.
The applicability and advantages of the DH curves were shown based on the comparison of the results obtained by the DH curves analysis at different SoH with results obtained by using another currently existing and proven diagnostic method such as differential voltage analysis method. It was shown that the DH curve proposed in this article gives similar information about predominant degradation mechanism in a Li-ion cell as DV curve.
Moreover, one of the main advantages of the proposed curve is the possibility to use a high C-
rate current during the curve measurements, without loss of the important features on the DH curve, which for example is not possible in case of the DV curve. In addition, the possibility of the DH curve to indicate the changes in the entropic heat generation is considered as an additional advantage of this curve, which may be useful for the improvement of the Li-ion battery SoH estimation and determination of degradation mechanisms.
The analysis of the effect of the C-rate current and temperature of the cylindrical LFP cell on the shape of proposed DH curves showed that such effect is not critical for the proposed curve application. The small dependence of the DH curve shape on discharging current value is most likely caused by the neglection of the impact of the phase change and mixing effects on the heat generation, which was done during creation of the DH curve with simplification point of view. The temperature has a noticeable effect only on the position of the negative peak on the DH curve. The effect of the cell temperature on the position of the other peaks was not noticeable for the cell under study. It was shown that despite the availability of the described dependences of the DH curve on the current and temperature, the DH curves can be successfully used for the capacity loss estimation and prediction by using similar methods which was previously suggested for the DV curves. Therefore, using the proposed DH curves is recommended for the SoH estimation, prediction and determination of the degradation mechanisms of cylindrical LFP Li-ion cells during calendar aging.
Acknowledgements
This research was enabled by the financial support of Academy of Finland (project LIANA).
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Tables
Table 1. capacity loss at calendar ageing test
Parameters Values
Number of the interval 1 2 3 4 5
Storage time, months 2.5 2 2.5 1.5 1.5
Total capacity loss, % 7.2 11.3 16.2 18.2 20.1
Table 2. The coefficient of determination during data fitting by a linear function.
Fitting dependences R2
Dependence between reduction of voltage plateau ① and capacity loss
0.9996 Dependence between reduction of A1 and capacity loss 0.9924 Dependence between reduction of A2 and capacity loss 0.9992 Dependence between reduction of B1 and capacity loss 0.9982 Dependence between reduction of B2 and capacity loss 0.9959 Figure Captions
Fig. 1. Terminal voltage curves (solid lines) obtained at room temperature and constant discharging currents and extrapolated EMF (dotted curve). The insets show examples of the vertical (a) and horizontal (b) extrapolations.
Fig. 2. DV curves obtained after cell discharging by different values of constant current and -𝜕UEMF/𝜕Q curve.
Fig. 3 Surface temperature (a), heat flux (b) and heat (c) at discharging of the cylindrical LFP cell by 1.5 A (0.6C) and 3.0 A (1.2C) constant current.
Fig. 4 EMF of the LFP cell (a), comparison of -∂H/∂Q and -∂UEMF/∂Q curves (b) and
-(∂UEMF/∂T)/∂Q curves at discharging of the LFP cell by 1.5 A and 3.0 A constant current (c).
Fig. 5. -∂UEMF/∂Q curves obtained at different SoH.
Fig. 6 -∂H/∂Q curves obtained after discharging of the LFP cell by 1.5 A constant current (a) and by 3.0 A constant current (b) at different SoH.
Fig. 7 Considered intervals (a) and results of comparison of -∂H/∂Q and -∂UEMF/∂Q curves at different SoH (b) (* points and solid line indicate measured and approximated data of the voltage plateaus ① reduction; o points and dash line indicate measured and approximated data of the A1 reduction; x points and dash dot line indicate measured and approximated data of the A2 reduction).
Figures
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4
Fig.5.
Fig.6.
Fig.7.
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