Lifetime Models for Lithium-ion Batteries used in Virtual Power Plant Applications

Daniel Stroe

Lifetime Models for Lithium-ion Batteries used in Virtual Power Plant Applications

Daniel Stroe

2014

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Abstract

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Figures (383)

Figure 1.1: Change in the installed power capacity paradigm between year 2000 (blue), 2009 (green), and 2013 (red) in European Union

Figure 1.2: Cumulative installed wind power capacity (blue) and annual installed wind power capacity (red) in European Union

schematic representation of the VPP concept is illustrated in Fig. 1.3. By integrating ESSs within WPPs, the output power of the new system, further referee: as virtual power plant (VPP), will become mote dispatchable, predictable, and less var able [5]. Consequently, the VPP will behave similar to today's CGUs, seen from the tran: mission system operator's perspective, and will be able to meet future more stringent eri codes, which will ask for more flexibility from the WPPs side [22], [23]. Moreover, th VPP will be able to provide ancillary services such as inertia [20], primary frequenc regulation [24], and will be able to reduce the wind power forecast error [25], [26]. Th schematic representation of the VPP concept is illustrated in Fig. 1.3.

Figure 1.4: The used methodology for developing the lifetime model service, as illustrated in Fig. 1.4 (see Part IID). into a VPP, while it was delivering the targeted grid service in the Danish energy market

Table 2.1: Main requirements imposed by the considered VPP applications

Figure 2.2: Classification of the rechargeable lithium battery family based on anode structure and electrolyte type

Figure 2.3: Schematic representation of a common Li-ion battery cell. During the battery discharging, this process is reversed.

Table 2.4: Comparison of Li-ion battery chemistries from various perspectives (legend: "++" denotes very good p a4 perp S DS performance, "+" denotes good performance, "-" denotes acceptable performance, "--" denotes low performance) [33], I87].

As Table 2.4 shows, none of the Li-ion battery chemistries is superior to the other chemistries on all the six considered dimensions. In most of the cases, optimizing a _i-ion battery chemistry for one dimensions means compromising other dimension (or limensions); for example Li-ion batteries based on NCA chemistry have very good spe- ‘ific energy and specific power characteristics but present safety issues, while on contrary _i-ion batteries based on LiyTisOj2 are having lower specific energy and power charac- eristics but they are very safe and characterized by long lifetime. Thus, the selection of

Figure 3.1: Typical Nyquist curve of a Li-ion battery cell

Figure 3.2: Typical EEC used for curve fitting the impedance spectrum of Li-ion battery cells out at vatious conditions, have to be considered.

Figure 3.3: Test sequence for characterization of the LFP/C battery cells at BOL.

figure 3.4: Capacity of the LFP/C battery cell mea- Figu ured during the preconditioning test durin

Figure 3.5: Change in the LFP/C battery cell capacity, during five consecutive charge/discharge cycles

Table 3.2: Voltage of the LFP/C battery cell measured at 50% SOC after various relaxation time periods Based on the results summarized in Table 3.2, it was concluded that OCV value, neasuted at 50% SOC, is only slightly influenced by a relaxation time, which varies be- ween 15 minutes and 24 hours. Similar results were obtained for the other two SOC evels at which the relaxation tests were performed, as presented in Appendix C.2 (see [able C.4 and Table C.5 for 20% and 80% SOC, respectively). Therefore, a relaxation deriod of one hour was considered enough for the LFP/C battery cell to stabilize and consequently to allow for accurate measurements of the desired parameters. This relax- ition period was used for the measurement of the battery cell's capacity and OCV vs various relaxation time periods together with their corresponding error.

Figure 3.9: Open-circuit voltage error depending on the relaxation time (discharging case, SOC=50%) Figure 3.8: Open-circuit voltage error depending on the relaxation time (charging case, SOC=50%)

Fig. 3.11, for the charging and discharging cases, respectively.

Figure 3.13: Pulse profile applied to the LFP/C battery cell for measuring the internal resistance.

Figure 3.14: Li-ion battery cell's theoretical voltage response due to a discharging current pulse. resistance is of interest and will be calculated. The internal resistance of the LFP/C battery cell was computed based on the Ohm's

Figure 3.20: Charging PPC of the LFP/C battery Fi cell measured for the entire SOC range at various tem- ce peratures (measurements performed with nominal current, tu 2.5 A). A PPC values were calculated for a battery current value equivalent to 1C-rate (i.e. 2.54) As a consequence of the flat charge and discharge voltage curves [84], [95], the mea-

Figure 3.23: Dependence of the impedance spectra on the SOC (measured at T = 25°C). Figure 3.22: Impedance spectrum of the tested LFP/C battery cell, measured at BOL, 25°C, and 50% SOC

Figure 3.24: Dependence of the impedance spectra on the temperature (measured at SOC = 50%).

Figure 3.25: The basic configuration of the EIS-based electrical battery cell model .

Table 3.4: Comparison between the curve fitting results obtained for the tvo considered EEC configurations As shown in Table 3.4, the EEC based on ZARC elements is able to fit better dower NRMSE) the impedance spectra of the tested LFP/C than the EEC configuration based on RC networks. The better fitting accuracy is mainly due to the use of ZARC ele- ments, which are able to fit better the depressed semi-circles, which are characteristics for Nyquist curves measured on Li-ion batteries [99], [112]. Consequently, the EEC con- figuration based on ZARC elements was used to fit all the measured impedance spectra (at different conditions) and to model the performance behaviour of the tested LFP/C battery cell.

Figure 3.27: EEC based on ZARC elements. Figure 3.26: EEC based on RC parallel networks.

Figure 3.29: Measured and fitted impedance spectrum using the EEC configuration based on ZARC elements (see Fig. 3.27). Figure 3.28: Measured and fitted impedance spectrum using the EEC configuration based on RC parallel net- works (see Fig. 3.26).

Figure 3.32: Look-up table implementation of the charging capacity of the LFP/C battery cell.

Figure 3.33: Look-up table implementation of the dis- charging capacity of the LF-P/C battery cell.

Table 3.5: Values of EEC parameters Rept constant for all operating conditions.

Figure 3.35: Look-up table implementation of the OCV of the LFP/C battery cell (discharging case).

Figure 3.37: Look-up table implementation of the re- sistance Ry of the EEC. Figure 3.36: Look-up table implementation of the series resistance Rs of the EEC.

Figure 3.39: Look-up table implementation of the gen- eralized capacitance O, of the EEC.

Figure 3.40: Look-up table implementation of the gen- eralized capacitance Oo of the EEC. Figure 3.38: Look-up table implementation of the re- sistance Ro of the EEC.

Figure 3.41: Look-up table implementation of the voltage correction factors for the T=25,C dimension.

Figure 3.42: Measured and estimated voltage profiles during pulse current charging (Ipa=2.5 A, T=25° ©). Figure 3.43: Distribution of the relative error obtained during the pulse current charging verification. TT As it can be observed ftom Fig. 3.42, the developed model is able to predict with high accuracy the LFP/C battery cell voltage. For the considered pulse charging profile, the model is able to predict the voltage behaviour with a maximum error Eng, of 4.01% and a mean ettot |é| of 7.1 ~I’; by comparing the measured and estimated voltage profiles, a coefficient of determination R? = 0.9637 was obtained. The distribution of the voltage deviations (expressed as the telative error) is presented in Fig. 3.43, showing that the developed model has a slight tendency of under-estimating the behaviour of the voltage of the LFP/C battery cell.

Figure 3.45: Distribution of the relative error obtained during the pulse current discharging verification. Figure 3.44: Measured and estimated voltage profiles | during pulse current discharging (Ipa=2.5 A, T=25°C). ¢ The measured and estimated voltages, which were obtained during the performance model verification using a discharging current pulse profile are presented in Fig. 3.44. The discharging of the LFP/C battery cell was performed with 1C-rate in steps of 10% SOC. The developed performance model is able to estimate very accurately the voltage of the tested battery cell, with a maximum error of 3.66% and a mean error of 6.8 mV. Contrary to the previous case, the distribution of the relative voltage deviations (see Fig. 3.45), is showing that the model has a slight tendency of over-estimating the voltage be- haviour of the LFP/C battery cell. The main contribution to this tendency is represented by the voltage estimation error after the current pulse is cut-off. by the voltage estimation error after the current pulse is cut-off.

Figure 3.46: Measured and estimated voltage profiles obtained by appling a dynamic current pulses profile (T=25°C). 3.3.2 Verification based on PFR profile

Figure 3.47: Distribution of the relative error obtained during the model verification with a dynamic current pulses profile.

Table 3.6: Performance model accuracy for different current profiles. lower than 5% and a mean error below 8.5 mV. The model validation process was cat-

Figure 3.48: Measured and estimated voltage profiles obtained by applying a realistic PFR current profile (T=25°C). CHAPTER 3. PERFORMANCE MODELLING OF LI-ION BATTERY CELLS The slight tendency of the performance model to over-estimate the battery voltage when the PFR current profile was used is visible also on Fig. 3.49, which presents the dis- tribution of the relative voltage errors. Nevertheless, the developed performance model is able to predict accurately the voltage of the LFP/C battery cell, with a mean error of 8.4 mV, a maximum error of 4.54%, and a coefficient of determination of R? = 0.7724.

Table 4.1: Ageing mechanisms of graphite based Li-ion batteries [124], [125]

Figure 4.2: Lifetime modelling approaches of Li-ion batteries which will be briefly discussed in the following sections. 4.2.1 Pure-lifetime models

Figure 4.3: Number of cycles vs. DOD Lifetime curve (values only exemplary). Throughput counting models

Figure 4.4: Ab-Throughput vs. DOD lifetime curve a a ne: eh

Figure 4.5: Schematic representation of EEC configuration for lifetime modelling of Li-ion battery cells considering the dependence of EEC parameters on the operating conditions. is presented. [he second group of performance-degradation models ate the EEC-based lifetime mod- ‘Is. The characteristics, structure, and parametrization approach of an EEC-based model vere presented throughout Chapter 3. The EEC-based lifetime models are obtained by idding the "ageing-dimension" to the EEC-based performance models; thus, in order to epresent the ageing behaviour of the Li-ion battery cell, the values of the parameters of he EEC are updated while the ageing process evolves [39], [133]. In Fig. 4.5, a possible onfiguration of an EEC, which considers the dependence on the parameters on ageing Cc nrecenten

Table 4.2: Comparison of different lifetime modelling approaches for Li-ion battery cells By analysing the properties of the lifetime modelling approaches, which are present n Table 4.2 one can conclude that the EEC-based lifetime models are a trade-off so! ion between the electrochemical and pure-lifetime models. Even though their accura s slightly lower than the one of the electrochemical models, the EEC-based lifetin nodels are easier to parametrize and are able to estimate the lifetime of the Li-ion b erties in terms of capacity fade and power capability decrease. The pure-lifetime mod« ire not of interest for this research since their accuracy is reduced and they offer limit nformation (only RUL) about the ageing behaviour of the tested battery. Consequently, in this thesis an EEC-based lifetime modelling approach was select ‘or developing the lifetime model of the tested LFP/C battery cell. important characteristics of the discussed lifetime modelling approaches.

Figure 5.1: Hypothetical dependence of Li-ion battery cell degradation on the applied stress levels and extrapolation to the normal operating conditions.

Figure 5.3: Reduced test matrix for determining the cal- endar lifetime of the LFP/C battery cells (possible inter- action between stress factors is not considered). Table 5.1: Accelerated calendar lifetime tests - testing conditions.

Figure 5.4: LFP/C battery cells stored in oven during one of the accelerated calendar lifetime tests. 3 Accelerated cycling lifetime tests Accelerated cycling lifetime tests were performed in order to determine the lifetime of the LFP/C battery cells for cycling at different conditions. As shown in Chapter 4.1.2, the stress factors, which are influencing the cycling lifetime of the Li-ion batteries are: the temperature, the cycle depth, the SOC-level, and the chatging/discharging C-rate. However, all the accelerated cycling TC were performed considering a C-rate equal to 4C (10A), which can be treated as a worst case scenario for these battery cells (4C-rate is the maximum continuous charging current, which the battery can withstand - see Appendix A). ee i Hs etc peepee & DS a De. wT. Cw ee Ce. DD OE

Figure 5.5: Complex test matrix for determining the cy- cle lifetime of the LFP/C battery cells (temperature, cycle depth, and SOC-Level ageing stress factors). Figure 5.6: Reduced test matrix for determining the cy- cle lifetime of the LFFP/C battery cells (possible interaction between stress factors is not considered).

uture during the tests. Moreover, the temperature values summarized in Table 5.2 re- fer to the average temperature measured on the battery cell during cycling and not to the ambient temperature inside the various temperature chambers. The SOC parame- rer mentioned in Table 5.2 refers to the average SOC of the LFP/C battery cell during charging-discharging cycles; for exemplification, Fig. 5.7 illustrates the cycling process with different cycle depths considering the average SOC-value equal to 50%. with different cycle depths considering the average SOC-value equal to 50%.

Figure 5.8: LFP/C battery cells placed in a temperature chamber during one of the accelerated cycling lifetime tests.

CHAPTER 5. ACCELERATED AGEING TESTING OF LIFEPO4/C BATTERY CELL Figure 5.9: Current pulse profile applied to measure the internal resistance of the LFFP/C battery cell at each dmebrawensd Te OT

Figure 5.10: Current (top) and voltage (bottom) profiles measured on the LFP/C battery cells during the RPT. 14. Relaxation of the battery cell for 15 minutes;

Figure 5.11: Distribution of the discharge capacity val- ues measured at the BOL of the LFEP/C battery cells (T=25°C, I=2.5A).

Figure 5.12: Distribution of the internal resistance val- ues measured at the BOL of the LFP/C battery cells (T=25°C, I=10A, SOC=50%).

Figure 6.1: Procedure for determining the degradation of the LFP/C battery cell's performance parameters during storage at various conditions.

Figure 6.2: Exemplification of the effect of the accelerated calendar ageing on the discharging voltage profile of th studied LFP/C battery cells (calendar ageing: T=55° C, SOC=50%; RPT: T=25°C, [=2.5A). The capacity of the LFP/C battery cells were measured during the RPTs for both charg: ng and discharging conditions with 1C-rate and 4C-rate; nevertheless, in this work, fot inalysing the degradation behaviour of this parameter, only the measurements carried yut during discharging with 1C-rate current (2.5 A) will be considered. The measured apacity fade as function of the battery cell voltage is presented in Fig. 6.2 for one of the »erformed accelerated calendar lifetime tests. As illustrated, the shape of the discharging oltage curve did not change, while the calendar ageing process of the LFP/C battery ee be ee ee |

Table 6.1: Dependence of the capacity fade on the storage time. Fitting functions and accuracy measured capacity fade characteristics obtained for the LFP/C battery cells.

Figure 6.3: Dependence on the storage temperature of the capacity fade measured on the LFP/C cells subjected to accelerated calendar lifetime tests. CHAPTER 6. CALENDAR AGEING RESULTS FOR THE LIFEPO4/C BATTERY CELL

Figure 6.5: Dependence on the storage SOC-level of the capacity fade measured on the LFP/C cells subjected to accelerated calendar lifetime tests.

Figure 6.7: Estimation of capacity fade for LFP/C battery cells stored at different temperature and SOC values (the EOL criterion was set at 20% capacity fade). normal operating temperature (i.e., 25°C), as presented in Fig. 6.7. ) Pulse power capability decrease developed model which is able to predict the calendar lifetime in terms of capacity fade

Figure 6.8: Voltage profile during the periodical in- ternal resistance measurements, performed throughout | the accelerated calendar lifetime tests (calendar ageing: | T=55°C, SOC=50%; RPT: T=25°C, I=10A). The effect of calendar ageing on the voltage drop of the LFP/C cells that was ob-

Figure 6.9: Internal resistance of the LFP/C battery cells, derived based on Ohm's Law from the voltage pro- files illustrated in Fig.6.8 (calendar ageing: T=55°C, SOC=50%; RPT: T=25°C, I=10A).

Figure 6.10: Pulse power capability measured for an 18 seconds discharging current pulse during accelerated calendar ageing tests (calendar ageing: T=55°C, SOC=50%; RPT: T=25°C, I=10A, various SOC-levels). CHAPTER 6. CALENDAR AGEING RESULTS FOR THE LIFEPO4/C BATTERY CELL decrease characteristics for all performed TCs are summarized in Appendix E.

Figure 6.11: Discharging PPC decrease of LFP/C battery cells aged under Calendar 1 conditions (RPT: T=25°C, I=10A, various SOC )

Table 6.2: Dependence of the PPC decrease on the storage time. Fitting functions and accuracy

Figure 6.13: Exponential relationship between the curve fitting coefficients (see Table 6.2) and the storage temperature. Figure 6.12: Dependence on the storage temperature of the PPC decrease measured on the LFP/C cells subjected to accelerated calendar lifetime tests.

Table 6.3: Evaluation of various functions for fitting the dependence of PPC decrease on SOC-level

and 90% SOC) are illustrated in Fig. 6.14. 5.3.3. Dependence on storage SOC-level

Figure 6.17: Dependence of LFP/C battery cells' EIS spectra on the storage time (ageing conditions: T=55°C, SOC=50%, RPT conditions: T=25° C, SOC=20%).

Figure 6.16: Estimation of pulse power capability decrease caused by calendar ageing at various conditions (the predictions are made for a battery lifetime of 20 years at the considered conditions).

Figure 6.18: Dependence of LFP/C battery cells’ EIS spectra on the storage time (ageing conditions: T=55°C, SOC=50%, RPT conditions: T=25° C, SOC=50%).

Figure 6.19: Dependence of LFP/C battery cells’ EIS spectra on the storage time (ageing conditions: T=5 5° C, SOC=50%, RPT conditions: T=25° C, SOC=80%). CHAPTER 6. CALENDAR AGEING RESULTS FOR THE LIFEPO4/C BATTERY CELL

Table 6.4: Dependence of the series resistance Ry increase on the storage time. Fitting functions and accuracy 4.1 Ageing evaluation of series resistance R, The functions describing the dependence of the series resistance R, increase on the

Figure 6.20: Dependence on the storage temperature of the Rs increase measured on the LEP/C cells subjected to accelerated calendar lifetime tests. CHAPTER 6. CALENDAR AGEING RESULTS FOR THE LIFEPO4/C BATTERY CELL

Figure 6.21: Dependence on the storage SOC-kevel of the Rs increase measured on the LFP/C cells subjected to accelerated calendar lifetime tests.

Table 6.5: Dependence of the resistance Ry increase on the storage time. Fitting functions and accuracy

Figure 6.23: Dependence on the storage SOC-level of the Ry increase measured on the LFP/C cells subjected to accelerated calendar lifetime tests. Figure 6.22: Dependence on the storage temperature of the Ry increase measured on the LFP/C cells subjected to accelerated calendar lifetime tests. resistance Ry depends following a power law on the storage SOC-level (see Fig. E.82).

Table 6.6: Dependence of the generalized capacitance OQ, increase on the storage time. Fitting functions and The dependence of the generalized capacitance Q, on the storage temperature (fo: 0% SOC) and on the SOC-level (for T=55°C) are illustrated in Fig. 6.24 and Fig. 6.25 espectively. Similar to the cases of the other two EEC parameters, which have beer reviously analysed, the decrease of the capacitance Q, over time depends exponentially n the storage time, as illustrated in Fig. E.83. Furthermore, it was found out that a powe: aw function estimates with relative-high accuracy (R* = 0.9647) the dependence of Q n the storage SOC-level (see Fig. E.84).

Figure 6.24: Dependence on the storage temperature of the generalized capacitance QO increase measured on the LFP/C cells subjected to accelerated calendar lifetime tests.

Figure 6.26: Measured self-discharge of LFP/C battery during calendar ageing at 50% SOC and three different

Figure 6.27: Measured self-discharge of LFP/C battery during calendar ageing at 55°C and three different SOC Levels. Similar to the case of the other studied parameters of the LFP/C battery cells, the

Table 6.7: Fitting results for estimating the self-discharge dependence on temperature with an exponential function

Figure 6.29: Exponential relationship between storag SOC-kevel and self-discharge rate at different ages of th LFP/C battery cells. Figure 6.28: Exponential relationship between storage temperature and self-discharge rate at different ages of the LFP/C battery cells.

Table 6.8: Fitting results for estimating the self-discharge dependence on SOC with an exponential function.

The results, obtained from the accelerated lifetime tests, for the capacity, PPC, and evolution of the EIS plots ( EEC parameters) were analysed similar to the case of the results obtained from accelerated calendar lifetime tests. Based on the considered two- steps fitting procedure, individual lifetime models have been developed for the capacity fade, PPC decrease, and parameters of the EEC, which were found to consistently follow the ageing conditions.

Table 7.1: Dependence of the capacity fade on the number of cycles. Fitting functions and accuracy

Figure 7.2: Dependence on the cycle depth of the capacity Jade measured on the LFP/C cells subjected to accelerated cycling lifetime tests. The influence of the cycle depth on the capacity fade of the tested cells was investigated during TC7, TC2, and TC; for these TCs the temperature was set at 50°C and the average SOC-level at 50% SOC. The measured and fitted capacity fade characteristics for the LFP/C cells tested based on the aforementioned conditions are illustrated in Fig. 7.2. The results are showing that the capacity fade of the tested Li-ion cells is accelerated by increasing the cycle depth.

Figure 7.3: Power-law relationship between the curve fitting coefficients (see TC1, TC2, and TC3 - Table 7.1) and the considered cycle depths.

Figure 7.5: Exponential relationship between the curve fitting coefficients (see TC3, TC6, and TC9 - Tabk 7.1) and the cycling temperature. The measured and fitted capacity fade characteristics for the LFP/C battery cells used to investigate the influence of the cycling temperature on the capacity fade are presented in Fig. 7.4. As expected, the capacity fade of the tested battery cells is strongly influenced by the cycling temperature, decreasing quickly when the temperature was increased. Figure 7.4: Dependence on the temperature of the ca- pacity fade measured on the LFP/C cells subjected to ac- celerated cycline lifetime tests. by the cycling temperature, decreasing quickly when the temperature was increased. 7.2.3 Dependence on temperature

Se ee ee ee ee ae Se 2 ee ee ee ee Se Re The measured and fitted capacity fade characteristics of the Li-ion battery cells used 9 investigate the effect of average SOC-level on the capacity degradation are shown in ‘ig. 7.6. The obtained characteristics are showing that the decrease of the capacity of ne LFP/C battery cells is strongly dependent on the average SOC-level and the capac- y loss is accelerated by decreasing average SOC-level. These results are in opposition ith the capacity fade results obtained for calendar ageing conditions (see Chapter 6.2), rhich were showing a decrease of the capacity fade rate when the storage SOC-level was arrancearl in Table 7.1 went for a second round of fitting as illustrated in Fig. 7.7. Thus, it wa:

Figure 7.8: Estimation of the cycle lifetime of LFP/C battery cells cycled at different temperature and average SOC-kevels considering a 20% cycle depth (the EOL criterion was set at 20% capacity fade). for different operating conditions as presented in Fig. 7.8.

Table 7.2: Dependence of the PPC degradation on the number of cycles. Fitting functions and accuracy

Figure 7.9: Dependence on the cycle depth of the PPC decrease measured on the LFP/C cells subjected to accel- erated cycling lifetime tests. linear fitting as function of number of cycles are presented in Fig. 7.9.

cells was found to decrease exponentially with increasing the temperature (see Fig. 7.12 7.3.3 Dependence on temperature

Figure 7.14: Dependence of LFP/C battery cells EIS spectra on the number of cycles (ageing conditions T=50C, cycle depth=10%, average SOC=50%, RPT conditions: T=25° C, SOC=50%). Figure 7.13: Dependence of LFP/C battery cells' EIS spectra on the number of cycles (ageing conditions: T=50C, cycle depth=10%, average SOC=50%, RPT conditions: T=25° C, SOC=20%). to TC7 accelerated ageing conditions, are presented in Fig. 7.13 , Fig. 7.14, and Fig. 7.15

Figure 7.15: Dependence of LFP/C battery cells' EIS spectra on the number of cycles (ageing conditions: T=50°C, oele depth=10%, average SOC=50%, RPT conditions: T=25°C, SOC=80%).

Table 7.4: Dependence of the resistance Ry increase on the performed number of cycles. Fitting functions and accuracy of resistance Ry during cycling at 55°C with different cycle depths amplitude is given by:

ptocess are summarized in Table 7.5. [n contrast with the resistance Rg, the generalized capacitance Q» is decreasing during cycling ageing, independent on the applied conditions. The degradation of the gener. lized capacitance Q» during cycling for all the considered conditions is presented in \ ppendix E.2.6 (see Fig. E.150 - Fig. E.149). Even though Q> is decreasing during cy- ling, the same first degree polynomial function, as in the case of resistance Ry, was used ‘o fit the degradation pace as function of the number of cycles. The results of the fitting ee imereceaanan: rusian: enmamadimmiaumpeditioame,>d saw UE ale ten 7 o£

Figure 7.19: Dependence on the cycling temperature of the Ro increase measured on the LFP/C cells subjected to accelerated cycling lifetime tests. Figure 7.18: Dependence on the cycle depth of the Ro increase, measured on the LFP/C cells subjected to accel- erated cycling lifetime tests.

Figure 7.21: Dependence on the cycling temperature of the Oo decrease measured on the LFP/C cells subjected to accelerated cycling lifetime tests. Figure 7.20: Dependence on the cycle depth of the Or lecrease, measured on the LFP/C cells subjected to accel- rated cycling lifetime tests. The dependence of the generalized capacitance Q» on the cycle depth (for 50°C) and on the temperature (for 60% cycle depth) are shown in Fig. 7.20 and Fig. 7.21, respec- tively. As in the case of the resistance Ro, the decrease of Qo during cycling depends linearly on the amplitude of the cycle depth, as presented in Fig. E.162. So, the function, which expresses the influence of the number of cycles and their cycle depths on the capacitance decrease, is given in (7.21).

Figure 8.1: Structure of the performance-degradation model for the LFP/C battery cell

gure 8.4: Field-measured SOC mission profile for the Figure 8.5: P/C battery cell, characteristic to the PFR service. profile preseni Figure 8.5: 3D-histogram extracted from the SOC- profile presented in Fig. 8.4 of cycles and their corresponding cycle depths and average SOC-level is illustrated.

Figure 8.6: Lifetime estimation for the LFP/C battery cell stored at different temperatures and SOC-levels, before the EOL criterion (i.e., 20% capacity fade) is reached. CHAPTER 8. LIFEPO4/C BATTERY CELL PERFORMANCE-DEGRADATION MODEL and theit cycle depth, on the average SOC-level and on the temperature. Since

Figure 8.11: Estimation of PPC decrease during cycling with different cycle depths and at different temperatures; a 10 000 full cycles cycling lifetime was considered. Figure 8.10: Estimation of PPC decrease during stor- age at various SOC-levels and temperatures; a 20 years calendar lifetime was considered, in Fig. 8.10 and Fig. 8.11 for the calendar and cycling dimensions, respectively.

Figure 8.8: Lifetime estimation for the LFP/C bat- tery cell cycled at different temperatures and different cycle depths, before the EOL criterion (i.e., 20% capacity fade) is reached. Figure 8.9: Number of cycles that the LFP/C batten cell can withstand at different cycle depths until EOL eri terion (i.¢., capacity fade) is reached; T=25°C, average SOC=50%. 8.2. INCREMENTAL DECREASE OF LFP/C BATTERY CELL PERFORMANCE PARAMETERS cell can withstand at different cycle depths until EOL eri-

factors is illustrated in Fig. 8.12 and in Fig. 8.13.

Figure 8.13: Estimation of Rs increase during cycling with different cycle depths and at different temperatures; a 10 000 full cycles cycling lifetime was considered.

Figure 8.15: Comparison betveen capacity fade and PPC decrease of cycling aged LFP/C battery cells at 25°C and 100% cycle depth. Figure 8.14: Comparison between capacity fade and PPC decrease of calendar aged LFP/C battery cells at 25°C and SOC=50%. 8.3. VERIFICATION OF THE PERFORMANCE-DEGRADATION MODEL and Fig. 8.8.

Figure 8.16: Procedure for verification of the developed LFP/C battery cell performance-degradation model.

Table 8.1: Considered test conditions for the symmetrical charging-discharging mission profile. Following the same procedute as in the case of the accelerated cycling ageing tests see Table 5.2), the incremental degradation of the performance parameters of the tested FP/C battery cells was quantified by performing RPTs at regular time intervals (after ach 670 cycles for this verification case). The capacity of the cells considered for this etification TC and their corresponding capacity fade, which was measured during the geing process ate presented in Fig. F.1 and Fig. F.2 (see Appendix F.1), respectively Jue to time constraints and considering that the capacity degradation at the considered emperatute (i.e., 30°C) is relatively slow, the LFP/C battery cells subjected to the this

The first approach used to verify the performance-degradation model was based on a symmetrical charging/ discharging SOC mission profile, presented in Fig. 8.17. Thus, the same approach as it was used for the cycling TCs, which were performed for developing the lifetime models for the performance parameters (e.g., capacity, PPC etc.). However, in ordet to ensure for a non-biased verification, the conditions used for this verification TC were different than the ones used for the accelerated ageing tests; the conditions of the verification TC using asymmetrical charging/discharging SOC mission profile are summarized in Table 8.1.

Figure 8.18: Comparison between measured and esti- mated capacity fade of the LFP/C battery cells, obtained for the ageing conditions presented in Fig. 8.17. Figure 8.19: Capacity fade estimation error (absolute error), between model and measurements for LFP/C cells tested under the conditions presented in Fig. 8.17. petiod, are presented in Fig. 8.18.

Figure 8.20: One week mission profile used for verifi- cation of the developed LFP/C battery cell performance- degradation model. time was extracted, totalling approximately 80% of the operation time. In order to perform the evaluation of the developed model, a representative period of the mission profile, with a length of one week, was selected. This one week mission profile, illustrated in Fig. 8.20, was applied to the LFP/C battery cells for seven weeks, and RPT measurements were carried out after each week. In order to be applied to the developed model, the SOC mission profile, shown in Fig. 8.20, was decomposed using the rainflow cycle counting algorithm, following the procedure presented in Fig. 8.3. The cycling mission profile expressed in number of cycles of different cycle depths, performed at various average SOC-levels is presented in Fig. 8.21; additionally, the idling time was extracted. totalling approximatelv 80°% of the operation time.

Table 8.2: Considered test conditions for the mission profile characteristic to the PFR service. As presented in Table 8.2, for this verification TC, only two LFP/C battery cells were used. Consequently, in this case, the average degradation is computed only from the results obtained for two cells. The capacity of the LFP/C battery cells considered for this second verification TC and their corresponding capacity fade, which was measured during seven weeks of ageing process, are presented in Fig. F.3 and Fic. F.4 (see Ap- pendix F.2), respectively. Because the verification profile has been com posed of periods when the battery cells were cycled and periods when they were idling, both at 25°C, the measured capacity fade was relatively reduced (i.e., approx. 4.5%). hee AARARACAK Kearncaan che K~anaries fade oencneed nn the TRD/C hartcare Kelle

Table 8.3: Accuracy of the LFP/C battery cell performance-degradation model for two different mission profiles error. As illustrated in Fig. 8.23, the short observation period (i.e., seven weeks) does not low to conclude if a clear trend of underestimation or overestimation the capacity fade s present. Nevertheless, the proposed performance-degradation model is able to predict vith good accuracy the capacity fade of LFP/C battery cells, which are "providing PFR service" with a maximum error, for the consider period, of 1.33% capacity fade, and an iverage relative estimation error of 10.24%. average telative estimation error of 10.24%.

Figure 9.1: Characteristics of primary frequency regulation in Western Denmark.

Figure 9.2: Grid frequency values, recorded during one_year, sorted according to their values.

Figure 9.3: Accumulated duration of under-frequencies, divided in frequency intervals, for a period of one year. Fig. 9.3 shows the distribution of the under-frequencies, expressed as accumulated time, during each quarter of the considered year. As one can observe, most of the fre- quency deviations from the lower accepted values (i.e., 49.98 Hz), are having a reduced amplitude. Consequently, this has resulted in cycle depths with reduced amplitude for the Li-ion battery ESS. the Li-ion battery ESS.

Figure 9.5: Distribution of cycles according to their depths and average-SOC, corresponding to the SOC pro- file presented in 9.4. Fig. 9.4. profile to which the LFP/C battery cell is subjected was obtained and is presented in

Figure 9.6: Estimated calendar capacity fade and cy. cling capacity fade of the LFP/C battery cells for each month of providing PFR service.

Figure 9.8: Decrease of the capacity fade rate when the same mission profile is applied to the performance- degradation model at different ageing levels of the LFP/C battery cell (example for "Month9"). the ageing process evolves. This behaviour can be also observed in Fig. 9.6

Figure 9.10: Contribution of calendar and cycling oper- ation to the total estimated PPC decrease of the LFP/C battery cells subjected to the PFR mission profile. crease were observed for both cycling and calendar dimensions.

Figure 9.11: Decrease of the PPC decrease rate when the same mission profile is applied to the performance- degradation model at different ageing levels of the LFP/C battery cell (example for "Month9"). CHAPTER 9. EVALUATION OF THE LIFEPO4/C BATTERY CELL LIFETIME IN VPP

Table A.1: Parameters of the studied LiFePO4/C battery cells. The parameters of the LFP/C battery cells under test are listed in the table below. ratrameters of the LirerUy,/ battery cells under study battery cells under study

Figure B.1: Fue/Con battery test station.

Figure B.2: Maccor battery test station.

Figure B.3: Memmert UNP 500 universal oven used for accelerated calendar ageing tests.

Figure B.4: LFP/C battery cells placed inside one of the Memmert UNPP 500 universal ovens.

Figure C.3: Voltage recovery during 24 hours relaxation, after charging (SOC=20%) both charging and discharging conditions ate presented in Fig. C.3 - Fig. C.10.

Figure C.4: Voltage recovery during 24 hours relaxation, after discharging (SOC=20%)

Figure C.7: Voltage recovery during 24 hours relaxation, after charging (SOC=80%) Figure C.5: Open-circuit voltage error depending on the relaxation time (charging case, SOC=20%)

Figure C.8: Voltage recovery during 24 hours relaxation, after discharging (SOC=80%) Figure C.6: Open-circuit voltage error depending on the relaxation time (discharging case, SOC=20%)

Figure C.10: Open-circuit voltage error depending on the relaxation time (discharging case, SOC=80%)

Table C.4: Voltage of the LFP/C battery cell measured at 20% SOC after various relaxation time periods measurements is only slightly dependent on the relaxation period.

Table C.5: Voltage of the LFP/C battery cell measured at 80% SOC after various relaxation time periods

The measured voltage profiles during the capacity test of the LFP/C battery cell are

Figure C.12: The OCV vs SOC characteristic 0 the LFP/C battery cell measured at 15 °C.

Figure C.13: The OCV vs SOC characteristic of the LFP/C battery cell measured at 35 °C.

Figure C.16: Maximum charging PPC of the LFP/C battery cell measured for the entire SOC range at various temperatures (measurements performed with nominal cur- rent, 10 A). re almost independent on the operating temperature. battery cell measured for the entire SOC range at various

Figure C.17: Maximum discharging PPC of the LFP/C battery cell measured for the entire SOC range at various temperatures (measurements performed with nom- inal current, 10 A).

Table C.9: Procedure followed during the EIS test.

Figure C.18: Dependence of the impedance spectra on the SOC (measured at T = 25°C for whole SOC interval). a decrease of the first semi-circle of the Nyquist curve was observed. In Fig. C.19 and Fig. C.20, there are presented the measured impedance spectra of

Figure C.19: Dependence of the impedance spectra on the temperature (measured at SOC = 20%). temperature is not changing with the SOC level.

Figure C.20: Dependence of the impedance spectra on the temperature (measured at SOC = 80%).

Figure D.1: Current profile applied to the LFP/C battery cell during the verification of the performance model The procedure used to validate the developed LFP/C battery cell performance model using a dynamic charge/dischatge current pulses profile is summarized in Table D.1. The current profile applied to the LFP/C battery cell is presented in Fig. D.1. The current profile applied to the LFP/C battery cell is presented in Fig. D.1.

Table D.2: Procedure based on PFR current profile for verification of the developed performance model.

Table E.1: Accelerated calendar and cycling lifetime tests - testing conditions. The obtained accuracy values for fitting the measured capacity fade with the consid. ted functions are summarized in Table E.2. The best fitting accuracies were obtained ot the power law and for the power law with fixed coefficient functions; however, be- use the difference in the obtained accuracy values is extremely small between these wo fitting functions (Le. 0.9989 vs. 0.9978), the power law with fixed coefficient was elected since it involves only one free parameter.

Figure E.1: Capacity values measured on LFP/C cells Fig subjected to Calendar 1 ageing conditions. Jecte

gure E.3: Capacity values measured on LFP/C cells Figure E.4: C. bected to Calendar 2 ageing conditions. jected to Calenda

Figure E.2: Capacity fade of LFP/C battery cells sub- jected to Calendar 1 ageing conditions. APPENDIX E. RESULTS OF THE ACCELERATED AGEING TESTS

Figure E.4: Capacity fade of LFP/C battery cells sub- jected to Calendar 2 ageing conditions.

Figure E.5: Capacity values measured on LFP/C cells subjected to Calendar 3 ageing conditions.

Figure E.9: Capacity values measured on LFP/C cells subjected to Calendar 5 ageing conditions. ‘igure E.7: Capacity values measured on LFP/C cells Fig ubjected to Calendar 4 ageing conditions. Jectea

Figure E.10: Capacity fade of LFP/C battery cell subjected to Calendar 5 ageing conditions. Figure E.8: Capacity fade of LFP/C battery cells sub- jected to Calendar 4 ageing conditions.

Figure E.6: Capacity fade of LFP/C battery cells sub- jected to Calendar 3 ageing conditions.

Figure E.13: Measured and fitted capacity fade of the LFP/C cells subjected to Calendar 2 ageing conditions. Figure E.12: Measured and fitted capacity fade of the LFP/C cells subjected to Calendar 1 ageing conditions.

Figure E.11: Comparison of results obtained from fitting the capacity fade of LFP/C battery cells with differeni functions (capacity fade results obtained from Calendar 1 test used for curve fitting selection).

Table E.2: Accuracy obtained for fitting the capacity fade with various functions.

Figure E.17: Discharge PPC values measured on LFP/C cells subjected to Calendar 1 ageing conditions (RPT: SOC=20%, Tac=10A). Figure E.16: Measured and fitted capacity fade of the LFP/C cells subjected to Calendar 5 ageing conditions.

Figure E.14: Measured and fitted capacity fade of the LFP/C cells subjected to Calendar 3 ageing conditions. E.1, RESULTS FROM ACCELERATED CALENDAR AGEING TESTS

Figure E.15: Measured and fitted capacity fade of the LFP/C cells subjected to Calendar 4 ageing conditions.

Figure E.19: Discharge PPC values measured on LFP/C cells subjected to Calendar 2 ageing conditions (RPT: SOC=20%, 1,.=10.A).

Figure E.21: Discharge PPC values measured on LFP/C cells subjected to Calendar 3 ageing conditions (RPT: SOC=20%, Idc=10A).

Figure E.23: Discharge PPC values measured on LFP/C cells subjected to Calendar 4 ageing conditions (RPT: SOC=20%, Tac=10A).

Figure E.20: Discharge PPC decrease of LFP/C bat- tery cells subjected to Calendar 2 ageing conditions (RPT: SOC=20%, Lic=10A). APPENDIX E. RESULTS OF THE ACCELERATED AGEING TESTS

Figure E.22: Discharge PPC decrease of LFP/C bat- tery cells subjected to Calendar 3 ageing conditions (RPT: SOC=20%, Ite=10A).

Figure E.24: Discharge PPC decrease of LFP/C bat- tery cells subjected to Calendar 4 ageing conditions (RPT: SOC=20%, Tae=10A).

Figure E.27: Discharge PPC values measured on LFP/C cells subjected to Calendar 1 ageing conditions (RPT: SOC=50%, Ige=10A). Measured PPC and PPC decrease at 50% SOC

Figure E.29: Discharge PPC values measured on LFP/C cells subjected to Calendar 2 ageing conditions (RPT: SOC=50%, Tac=10A).

Figure E.30: Discharge PPC decrease of LFP/C bat- tery cells subjected to Calendar 2 ageing conditions (RPT: SOC=50%, Tac=10A). Figure E.28: Discharge PPC decrease of LFP/C bat- tery cells subjected to Calendar 1 ageing conditions (RPT: SOC=50%, Tac =10A).

Figure E.31: Discharge PPC values measured on LFP/C cells subjected to Calendar 3 ageing conditions (RPT: SOC=50%, Ige=10A).

Figure E.35: Discharge PPC values measured on LFP/C cells subjected to Calendar 5 ageing conditions (RPT: SOC=50%, Tac=10A). Figure E.33: Discharge PPC values measured on LFP/C cells subjected to Calendar 4 ageing conditions (RPT: SOC=50%, Tde=10A).

Figure E.32: Discharge PPC decrease of LFP/C bat- tery cells subjected to Calendar 3 ageing conditions (RPT: SOC=50%, Lye=10A).

Figure E.34: Discharge PPC decrease of LFP/C bat- tery cells subjected to Calendar 4 ageing conditions (RPT: SOC=50%, Iac=10A).

Figure E.39: Discharge PPC values measured on LFP/C cells subjected to Calendar 2 ageing conditions (RPT: SOC=80%, Tac=10A). Figure E.37: Discharge PPC values measured on LFP/C cells subjected to Calendar 1 ageing conditions (RPT: SOC=80%, Ige=10A).

Measured PPC and PPC decrease at 80% SOC

Figure E.40: Discharge PPC decrease of LFP/C bat- tery cells subjected to Calendar 2 ageing conditions (RPT: SOC=80%, Tac=10A). Figure E.38: Discharge PPC decrease of LFP/C bat- tery cells subjected to Calendar 1 ageing conditions (RPT: SOC=80%, Tae =10A).

Figure E.41: Discharge PPC values measured on LFP/C cells subjected to Calendar 3 ageing conditions (RPT: SOC=80%, Ige=10A).

Figure E.45: Discharge PPC values measured on LFP/C cells subjected to Calendar 5 ageing conditions (RPT: SOC=80%, Ide=10A). Figure E.43: Discharge PPC values measured on LFP/C cells subjected to Calendar 4 ageing conditions (RPT: SOC=80%, Tac=10A).

Figure E.42: Discharge PPC decrease of LFP/C bat- tery cells subjected to Calendar 3 ageing conditions (RPT: SOC=80%, Ljec=10A).

Figure E.46: Discharge PPC decrease of LFP/C bat- tery cells subjected to Calendar 5 ageing conditions (RPT: SOC=80%, Tac=10A). Figure E.44: Discharge PPC decrease of LFP/C bat- tery cells subjected to Calendar 4 ageing conditions (RPT: SOC=80%, Igce=10A).

Figure E.49: Measured and fitted PPC decrease of the LFP/C cells subjected to Calendar 3 ageing conditions. Figure E.47: Measured and fitted PPC decrease of the LFP/C cells subjected to Calendar 1 ageing conditions.

The results obtained for fitting the PPC decrease over time of the LFP/C battery cells

Figure E.48: Measured and fitted PPC decrease of the LFP/C cells subjected to Calendar 2 ageing conditions.

Figure E.50: Measured and fitted PPC decrease of the LFP/C cells subjected to Calendar 4 ageing conditions.

Figure E.51: Measured and fitted PPC decrease of the LFP/C cells subjected to Calendar 5 ageing conditions.

Figure E.52: Dependence of LFP/C battery cells' EIS spectra on the storage time (calendar ageing conditions: T=47.5°C, SOC=50%, RPT conditions: T=25°C, SOC=20%).

Figure E.54: Dependence of LFP/C battery cells' EIS spectra on the storage time (calendar ageing conditions: T=47.5°C, SOC=50%, RPT conditions: T=25°C, SOC=80%). Figure E.53: Dependence of LFP/C battery cells' EIS spectra on the storage time (calendar ageing conditions: T=47.5°C, SOC=50%, RPT conditions: T=25°C, SOC=50%).

Figure E.55: Dependence of LFP/C battery cells’ EIS spectra on the storage time (calendar ageing conditions: T=40°C, SOC=50%, RPT conditions: T=25°C, SOC=20%).

Figure E.58: Dependence of LFP/C battery cells’ EIS spectra on the storage time (calendar ageing conditions: T=55°C, SOC=10%, RPT conditions: T=25°C SOC=20%). Spectra on the storage time (calendar ageing conditions: Figure E.57: Dependence of LFP/C battery cells' EIS spectra on the storage time (calendar ageing conditions: T=40°C, SOC=50%, RPT conditions: T=25°C, SOC=80%).

Figure E.56: Dependence of LFP/C battery cells’ EIS spectra on the storage time (calendar ageing conditions: T=40°C, SOC=50%, RPT conditions: T=25°C, SOC=50%).

Figure E.59: Dependence of LFP/C battery cells' EIS spectra on the storage time (calendar ageing conditions: T=55°C, SOC=10%, RPT conditions: T=25°C, SOC=50%). spectra on the storage time (calendar ageing conditions:

Figure E.61: Dependence of LFP/C battery cells' EIS spectra on the storage time (calendar ageing conditions: T=553°C, SOC=90%, RPT conditions: T=25°C, SOC=20%). Figure E.60: Dependence of LFP/C battery cells' EIS spectra on the storage time (calendar ageing conditions: T=55°C, SOC=10%, RPT conditions: T=25°C, SOC=80%).

Figure E.63: Dependence of LFP/C battery cells' EIS spectra on the storage time (calendar ageing conditions: T=55°C, SOC=90%, RPT conditions: T=25°C, SOC=80%). Figure E.62: Dependence of LFP/C battery cells' EIS spectra on the storage time (calendar ageing conditions: T=55°C, SOC=90%, RPT conditions: T=25°C, SOC=50%).

Figure E.64: Increase of series resistance Rs during cal- endar ageing (ageing conditions: T=55°C, SOC=50%, RPT conditions: T=25°C, different SOCS).

Figure E.66: Increase of series resistance Rs during cal- endar ageing (ageing conditions: T=40° C, SOC=50%, RPT conditions: T=25° C,different SOCS).

Figure E.65: Increase of series resistance Rs dur- ing calendar ageing (ageing conditions: T=47.5°C, SOC=50%, RPT conditions: T=25°C, different SOC).

Figure E.67: Increase of series resistance Rs during cal- endar ageing (ageing conditions: T=55°C, SOC=10%, RPT conditions: T=25°C, different SOC).

Figure E.69: Increase of resistance Ry during calendar ageing (ageing conditions: T=55°C, SOC=50%, RPT conditions: T=?25°C. different SOG). Dependence of resistance R; on storage time, temperature, and SOC-level

Figure E.71: Increase of resistance Ry during calendar ageing (ageing conditions: T=40°C, SOC=50%, RPT conditions: T=25° Cdifferent SOC).

Figure E.70: Increase of resistance Ry during calen- dar ageing (ageing conditions: T=47.5°C, SOC=50%, RPT conditions: T=25° C, different SOCS).

Figure E.72: Increase of resistance Ry during calendar ageing (ageing conditions: T=55°C, SOC=10%, RPT conditions: T=25°C, different SOC).

Figure E.76: Decrease of gen. capacitance QO, during calendar ageing (ageing conditions: T=40°C, SOC=50%, RPT conditions: T=25°C, different SOCS). Figure E.74: Decrease of gen. capacitance QO, during calendar ageing (ageing conditions: T=55°C, SOC=50%, RPT conditions: T=25°C, different SOCS).

Dependence of generalized capacitance Q; on storage time, temperature, and SOC-level

Figure E.75: Decrease of gen. capacitance Q, dur- ing calendar ageing (ageing conditions: T=47.5°C, SOC=50%, RPT conditions: T=25°C, different SOCS).

Figure E.77: Decrease of gen. capacitance QO, during calendar ageing (ageing conditions: T=55°C, SOC=10%, RPT conditions: T=25°C, different SOCS).

Figure E.79: Exponential relationship between the curve fitting coefficients (see Table 6.4) and the storage temperature. 1.7 Dependence of EEC parameters’ time evolution on storage temperature and SOC-level

Figure E.81: Exponential relationship between the curve fitting coefficients (see Table 6.5) and the storage temperature.

Figure E.80: Power-/aw relationship between the curve fitting coefficients (see Table 6.4) and the storage SOC- level

Figure E.83: Exponential relationship between the curve fitting coefficients (see Table 6.6) and the storage temperature.

APPENDIX E. RESULTS OF THE ACCELERATED AGEING TESTS

Figure E.87: Capacity values measured on LFP/C cells subjected to TC2 ageing conditions. Figure E.85: Capacity values measured on LFP/C cells subjected to TC1 ageing conditions.

Figure E.86: Capacity fade of LFP/C battery cells subjected to Calendar TC1 ageing conditions.

Figure E.88: Capacity fade of LFP/C battery cells subjected to Calendar TC2 ageing conditions.

Figure E.89: Capacity values measured on LFP/C F¥ cells subjected to TC3 ageing conditions. Si

Figure E.93: Capacity values measured on LFP/C Figure E cells subjected to TC6 ageing conditions. subjected to ‘igure E.91: Capacity values measured on LFP/C Figur Mls subjected to TCS ageing conditions. subjecte

Figure E.92: Capacity fade of LFP/C battery cells subjected to Calendar TC5 ageing conditions. Figure E.90: Capacity fade of LFP/C battery cells subjected to Calendar TC? ageing conditions.

Figure E.94: Capacity fade of LFP/C battery cells subjected to Calendar TC6 ageing conditions.

Figure E.95: Capacity values measured on LFP/C cells subjected to TC9 ageing conditions.

Figure E.97: Capacity values measured on LFP/C cells subjected to TC10 ageing conditions.

Figure E.99: Capacity values measured on LFP/C cells subjected to TC11 ageing conditions.

Figure E.100: Capacity fade of LFP/C battery cells subjected to Calendar TC11 ageing conditions. Figure E.98: Capacity fade of LFP/C battery cells subjected to Calendar TC10 ageing conditions.

Figure E.96: Capacity fade of LFP/C battery cells subjected to Calendar TC9 ageing conditions.

Figure E.101: Comparison of results obtained from fitting the capacity fade of LFP/C battery cells with different functions (capacity fade results obtained from TC9 test used for curve fitting selection). FE.2.2 Dependence of capacity fade on the number of cycles

Table E.3: Accuracy obtained for fitting the capacity fade measured on TC9 cells with various functions.

‘igure E.102: Capacity values measured on LFP/C Figure lls subjected to TC1 ageing conditions. subjected Fig. E.117.

Figure E.105: Capacity fade of LFP/C battery cells subjected to TC2 ageing conditions.

Figure E.103: Capacity fade of LFP/C battery cells subjected to TC1 ageing conditions.

Figure E.106: Capacity values measured on LFP/C cells subjected to TC3 ageing conditions.

Figure E.108: Capacity values measured on LFP/C cells subjected to TC5 ageing conditions.

Figure E.110: Capacity values measured on LFP/C cells subjected to TC6 ageing conditions.

Figure E.111: Capacity fade of LFP/C battery cells subjected to TC6 ageing conditions. Figure E.109: Capacity fade of LFP/C battery cells subjected to TCS ageing conditions.

Figure E.107: Capacity fade of LFP/C battery cells subjected to TC3 ageing conditions.

Figure E.112: Capacity values measured on LFP/C cells subjected to TC9 ageing conditions.

Figure E.116: Capacity values measured on LFP/C Fig cells subjected to TC11 ageing conditions. suby Figure E.114: Capacity values measured on LFP/C Fign cells subjected to TC10 ageing conditions. subje

FP/C Figure E.115: Capacity fade of LFP/C battery cells subjected to TC10 ageing conditions. Figure E.113: Capacity fade of LFP/C battery cells subjected to TC9 ageing conditions.

Figure E.117: Capacity fade of LFP/C battery cells subjected to TC11 ageing conditions.

Figure E.118: Measured and fitted PPC decrease of the LFP/C cells subjected to TC1 ageing conditions. The results obtained for fitting the PPC decrease over time of the LFP/C battery cells

Figure E.120: Measured and fitted PPC decrease oj the LFP/C cells sulyected to TC3 ageing conditions.

Figure E.121: Measured and fitted PPC decrease of the LFP/C cells subjected to TC5 ageing conditions. Figure E.119: Measured and fitted PPC decrease of the LFP/C cells subjected to TC2 ageing conditions.

figure E.122: Measured and fitted PPC decrease of Figu he LFP/C cells subjected to TC6 ageing conditions. the L.

of Figure E.125: Measured and fitted PPC decrease of the LFP/C cells sulyected to TC11 ageing conditions.. Figure E.123: Measured and fitted PPC decrease of the LFP/C cells subjected to TC9 ageing conditions..

Figure E.126: Dependence of LFP/C battery cells' EIS spectra on the number of cycles (cycling ageing condi- tions: T=50°C, cycle depth = 10% average SOC=50%, RPT conditions: T=25°C, SOC=80%).

Figure E.129: Dependence of LFP/C battery cells' EIS spectra on the number of cycles (cycling ageing conditions: T=42.5°C, cycle depth = 35% average SOC=50%, RPT conditions: T=25° C, SOC=80%). Figure E.127: Dependence of LFP/C battery cells' EIS spectra on the number of cycles (cycling ageing condi- tions: T=50°C, oycle depth = 35% average SOC=50%, RPT conditions: T=25° C, SOC=80%).

Figure E.132: Dependence of LFP/C battery cells’ EIS spectra on the number of cycles (cycling ageing conditions: T=42.5°C, cde depth = 35% average SOC=27.5%, RPT conditions: T=25°C, SOC=80%). Figure E.130: Dependence of LFFP/C battery cells' EIS spectra on the number of cycles (cycling ageing conditions: T=42.5°C, cycle depth = 60% average SOC=50%, RPT conditions: T=25° C, SOC=80%).

Figure E.133: Dependence of LFP/C battery cells’ EIS spectra on the number of cycles (cycling ageing conditions: T=42.5°C, cyde depth = 35% average SOC=72.5%, RPT conditions: T=25°C, SOC=80%). Figure E.131: Dependence of LFP/C battery cells' EIS spectra on the number of cycles (cycling ageing condi- tions: T=35°C, cycle depth = 60% average SOC=50%, RPT conditions: T=25° C, SOC=80%).

Figure E.134: Increase of series resistance Rs during accelerated calendar ageing TC1. Dependence of series resistance R, on cycling conditions

Figure E.136: Increase of series resistance Rs during accelerated calendar ageing TC3.

Figure E.137: Increase of series resistance Rs during accelerated calendar ageing TC5. Figure E.135: Increase of series resistance Rs during accelerated calendar ageing TC2.

Figure E.138: Increase of series resistance Rs during accelerated calendar ageing TC6.

figure E.140: Increase of series resistance Rs during Fi wcelerated calendar ageing TC10. a

Figure E.141: Increase of series resistance Rs during accelerated calendar ageing TC11. Figure E.139: Increase of series resistance Rs during accelerated calendar ageing TC9.

Figure E.144: Increase of resistance Ra during acceler- ated calendar ageing TC3. Figure E.142: Increase of resistance Ro during acceler- ated calendar ageing TC1.

Figure E.146: Increase of resistance R2 during acceler- Fis ated calendar ageing TCO. ate

Dependence of resistance R2 on cycling conditions

Figure E.147: Increase of resistance Ry during acceler- ated calendar ageing TC9. Figure E.145: Increase of resistance Ro during acceler- ated calendar ageing TCS.

Figure E.143: Increase of resistance Ro during acceler- ated calendar ageing TC2.

Figure E.148: Increase of resistance Rz during acceler- ¥ ated calendar ageing TC10. a

Figure E.154: Decrease of generalized capacitance Or during accelerated calendar ageing TCO. Figure E.152: Decrease of generalized capacitance Or during accelerated calendar ageing TC3.

Figure E.150: Decrease of generalized capacitance Or during accelerated calendar ageing TC1.

Dependence of generalized capacitance Q) on cycling conditions

Figure E.153: Decrease of generalized capacitance Ro during accelerated calendar ageing TC.

Figure E.151: Decrease of generalized capacitance Oo during accelerated calendar ageing TC2.

Figure E.160: Exponential relationship between the curve fitting coefficients (see Table 7.4) and the cycle depth.

Figure E.158: Exponential relationship between the curve fitting coefficients (see Table 7.3) and the cycle depth.

Figure E.161: Power-/aw relationship between the curve fitting coefficients (see Table 7.4) and the cycling tempera-

Figure E.159: Power-law relationship between the curve fitting coefficients (see Table 7.3) and the cycling tem- perature. .7 Dependence of EEC parameters' on cycle depth and cy- cling temperature

Figure E.162: Exponential relationship between the curve fitting coefficients (see Table 7.5) and the cycle depth.

Figure F.1: Capacity values measured on LFP/C cells subjected to verification TC with a symmetrical charging- discharging SOC profile. Figure F.2: Capacity fade of LFP/C battery cells subjected to verification TC with a symmetrical charging- discharging SOC profile.

Figure F.3: Capacity values measured on LFP/C cells subjected to verification TC with profile characteristic to PFR service.

Figure F.4: Capacity values measured on LEP/C cells subjected to verification TC with profile characteristic to PFR service.

Figure G.1: Frequency signal measured between June 2013 and May 2014.

Table G.1: Grid frequency statistical data for the considered one year.

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