Evaluating Real-Life Performance of Lithium-Ion Battery Packs in Electric Vehicles. V. Klass, M. Behm, and G. Lindbergh

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1 / The Electrochemical Society Evaluating Real-Life Performance of Lithium-Ion Battery Packs in Electric Vehicles V. Klass, M. Behm, and G. Lindbergh Applied Electrochemistry, Department of Chemical Engineering and Technology, KTH Royal Institute of Technology, Stockholm, Sweden In regard to the increasing market launch of plug-in hybrid electric vehicles (PHEVs), understanding battery pack performance under electric vehicle (EV) operating conditions is essential. As lifetime still remains an issue for battery packs, it is a necessity to monitor the battery pack s state-of-health (SOH) on-board. Standard performance tests for health evaluation do not apply since operation interruptions and additional testing equipment are beyond question during ordinary EV usage. We suggest a novel methodology of performance estimation from real-life battery data. On the basis of battery pack data collected during PHEV operation, a support vector machine model is constructed that serves as source for performance evaluation figures. The SOH indicator 10 s discharge resistance as known from hybrid pulse power characterization (HPPC) tests is chosen to exemplify how performance degradation can be followed over a year. Introduction Lithium-ion batteries have raised high expectations as energy storage in electric vehicles (EVs). In such challenging applications, it is essential to know how long the battery pack lasts - both in the short term, until the next charge, and in the long run in terms of lifetime. In order to soundly predict lifetime, the performance and degradation of batteries as a function of their use in plug-in hybrid electric vehicles (PHEVs) has to be better understood. On the way to understanding EV battery performance, batteries are conventionally tested in laboratory environments with standard driving cycles as load profiles mimicking electric vehicle operation (1,2). Recently, even thermal cycling has been added (3). In terms of modeling, both simple data-fitting models from laboratory data, for instance equivalent circuits from impedance measurements (4), and mathematical models on the basis of physical and chemical processes in the battery (2,5) are common. Laboratory tests can provide fundamental insight into calendar and cycle life of batteries revealing dependencies on temperature, cycling depth, and state-of-charge (SOC) (6,7). However, those tests have limited validity for real-life applications as the conditions during vehicle operation are complex. Field testing of traction battery packs is thus an important complement. In this way, the behavior of the battery pack can be monitored in its actual application instead of moving it into laboratory environment. Real-life battery testing in electric vehicles is scarcely represented in literature. Svens et al. presented a method for single battery cell field testing recently (8) and Liaw s research group analyzed data from nickel-metal hydride (NiMH) electric vehicle battery 1

2 packs with the help of driving and duty cycles (9,10). The difficulties with on-board battery testing lie in the constant battery pack operation and the poorly defined operating conditions. As a result, reference test procedures (e.g. capacity, hybrid pulse power characterization (HPPC), energy efficiency tests (11,12)), well-established in laboratory testing and commonly used for battery state-of-health (SOH) estimation, are not available in field tests. In this paper, we show how standardized reference tests can be applied to real-life plug-in hybrid electric vehicle (PHEV) battery data with the help of a statistical learning approach. By this, figures of merit for evaluation of on-board performance can be computed. Preliminary results for a HPPC test are presented as example of such an evaluation figure. On-Board Battery Pack Data Methods The data that underlies this project is CAN-bus data from a Volvo V70 plug-in hybrid electric vehicle prototype tested by ETC Battery and FuelCells Sweden AB during one year within the scope of a joint Volvo Cars Vattenfall project. The car has been equipped with a 32 Ah Li-ion battery pack whose specifications are summarized in table I. Both the behavior of the battery pack and information on the operating conditions were collected from January to December 2010 (13). The data was logged with a 2 Hz frequency whenever the ignition was started or the charging cable was connected to the grid. TABLE I. Specifications of Li-ion battery pack as used in the joint Volvo Cars Vattenfall project. Type PHEV Li-ion Number of cells 192 Thermal management Cabin air cooled Weight 150 kg Volume 150 l Cathode Nickel manganese cobalt oxide (NMC) Anode Hard carbon Nominal voltage 350 V Nominal capacity 32 Ah Maximum voltage 395 V Minimum voltage 270 V Maximum charge/discharge current 250 A The logged signals that are most important to this battery performance study are battery pack voltage, battery pack current, battery pack temperature (average of cell temperatures) and battery pack state-of-charge (SOC). The first three variables were measured whereas the SOC was estimated by the battery management system (BMS) provided by the manufacturer. Note that discharge current is defined as positive and charge current thus is negative. Apart from information on the battery behavior, operating condition variables such as date, time, vehicle speed, ambient temperature, and PHEV 2

3 mode (battery discharge, battery regenerative charge, battery grid charge, diesel drive) have been monitored. Support Vector Based Battery Data Analysis The complexity of battery systems impedes a description by mathematical equations. Empirical inference is a way to nevertheless find patterns in a large amount of battery data by substantially building a model from examples. In this article, the applicability of support vector machines (SVM), a supervised method based on statistical learning theory that is able to deal with non-linear systems, is explored. SVM, which has been developed by Vapnik (14), has traditionally been used for classification, but it is also applicable for regression problems such as in the present case. Just the most important SVM equations are given in the following; a detailed derivation can be found in (15). A training data set consists of L points with input x of dimensionality D and output y, { x i, y i } where i =, D 1,..., L, y i R x R. [1] In the case of nonlinear regression, a kernel trick is used to increase the dimensionality of the input space to a feature space where the system is linear. Here, we apply a radial basis function (RBF), i j a x i x = e γ a b j K( x, x ), [2] where a and b represent the kernel s parameters and γ is the kernel option. The idea of SVM is then to find a hyperplane that best describes the training data by finding the optimal offset b and the normal vector to the hyperplane w, y = w φ ( x ) b, [3] i i + where Φ(x i ) is the Kernel mapping of the input. A Matlab SVM toolbox developed by Canu (16) has been adjusted for our purposes and used to predict battery voltage from two input variables that are known to influence voltage, namely current and SOC. Voltage prediction with the help of SVM is uncommon so far (17), but SVM is used for SOC estimation quite frequently (18,19). For the voltage prediction, SVM is applied according to the following procedure: 1. Training run: selection of data sample and creation of SVM model, 2. Test run: selection of another data sample and prediction of the test voltage from test current and SOC from interpolation of the SVM model from 1), 3. Error estimation: evaluation of the difference of the predicted from the true voltage values by computing the maximum relative error and the root mean square error (RMSE). 3

4 The performance of a SVM depends on the choice of parameters. Apart from the chosen kernel function and its parameters, there is C, the soft-margin parameter, and ε, the size of the intensive loss region. The best choice of parameters is still an open research issue (20). We use an empirical method where the aforementioned procedure is applied on different sets of parameters in order to find the optimum set with minimized error. Virtual Test for Battery State-of-Health Estimation Apart from testing a SVM model with another set of current and SOC input data in order to estimate its voltage prediction error, we use SVM models as voltage look-up tables for hypothetical inputs. By choosing the current and SOC vectors of a standard battery performance test as input (figure 1), the resulting voltage prediction can serve as source for computing performance figures. We call this novel concept a virtual test. Similar to an ordinary laboratory test, a virtual test can be performed on the basis of reallife data SVM models and figures of merit that estimate the battery s SOH can subsequently be computed. Internal resistance and capacity are important performance figures with respect to battery pack health (7) that can be derived from a HPPC test and a constant current discharge test respectively. We focus here on the HPPC test from the ISO test manual (11) to estimate the 10 s discharge resistance, R 10sdisch U = 0s U I max 10s, [4] where U 0s and U 10s are the voltages at the start of the test and after 10 s on the voltage response curve and I max is the current during the discharge current pulse according to figure 1a. The theoretical SOC input vector (figure 1b) is derived from the current-time integral, the nominal capacity of the battery pack (32 Ah) and the chosen SOC start value SOC start : ( 32 ) 100 SOC( t) = SOC + idt start 100. [5] 32 (a) (b) Figure 1. Hypothetical (a) current and (b) SOC curves versus time as to the HPPC test from (11). The battery pack current and SOC vectors are supposed to be used in a socalled virtual test in order to estimate the battery pack s 10 s discharge resistance. 4

5 PHEV Battery Pack Data Statistics Results and Discussion Statistics have been computed in order to provide an overview over the ranges of collected signal values and the frequencies of value levels. A selection is presented in the following. The monitored battery pack voltage in January as shown in figure 2a gives an impression of how the raw signal looks like. Consecutive charges and discharges of varying depth resulting in increasing and decreasing voltage can be distinguished. The voltage does not feature a continuous line as data only was logged when either the ignition was on or the charging cable was connected. As the monitored cars were PHEVs, the actual operating time was divided into PHEV modes. Figure 2b illustrates the division into the different PHEV modes in January The battery pack was mainly connected to the grid, while actual driving only accounts for about 16 % of the operating time. This time is divided between diesel drive and battery discharge propulsion whereas regenerative braking occurred during both operating modes. (a) (b) Figure 2. (a) Monitored PHEV battery pack voltage in January (b) Operating time at PHEV modes in January Breaking down the operating time into the four PHEV modes and subsequently into battery pack current and SOC levels reveals further features of PHEV usage. From figure 3a it can be observed that the current mainly ranged in the interval between -10 and 10 A. For diesel drive, the current was obviously zero, but also 100 % of the battery grid charge operating time show up in the same interval as the grid charging current was around -2.5 A. During battery discharge the current was primarily under 10 A, too. The operating time percentage decreases for increasing currents - approaching the maximum discharge current of 250 A. On the side of negative currents, regenerative charge currents appear although the largest operating time percentage is close to zero as well. Figure 3b shows the same type of graph for battery pack SOC levels. It should be noted that there is an increased appearance of regenerative charging at low SOC levels. Furthermore, the driver of this specific car seems to have chosen diesel drive over battery discharge mode frequently in January as 54 % of the diesel drive operating time took place at 90 to 100 % SOC. 5

6 (a) (b) Figure 3. Operating time at (a) battery pack current levels (intervals of 20 A) (b) battery pack SOC levels (intervals of 10 %) for the different PHEV modes in January Figure 4 presents the battery pack, in-car and ambient temperature in January, July and December Although the ambient temperature reached -15 C in January and December, the battery pack itself was not exposed to such low temperatures. Note that the car seems to have been parked in an indoor parking space in January (ambient temperature up to 25 C), but not in December where the ambient temperature did not exceed 0 C. In July, the battery pack has been warmed up to a maximum of around 35 C. The average battery pack temperatures in January, July and December were 9.3 C, 27.7 C and 10.7 C. (a) (b) (c) Figure 4. Histogram for battery pack, in-car, and ambient temperature in (a) January, (b) July and (c) December Support Vector Machine Model Following the previously presented three-step procedure, data samples for SVM training and test runs have been selected. About 2000 data points corresponding to 1000 s were found to be an appropriate sample vector length. As this study focuses on battery performance analysis, only data from the PHEV modes battery discharge and regenerative charge have been included in the data selection. Data from diesel drive and grid charge have been omitted. Of course, a SVM model is only able to predict within the range of the training run variables. It was thus important to match the range of the input variables of training and test run. In addition, as only two input variables (current, SOC) and one output variable (voltage) were supposed to be included in the SVM model, it was important to choose a consistent range for other operating condition variables with impact on battery pack voltage (primarily battery pack and ambient temperature) when selecting 6

7 a corresponding pair of training and test data. In that way, a comparability of the modeling results could be ensured. The derived error values depended greatly on the chosen SVM parameters. In the parameter tuning process, the kernel function had the largest impact on the nature of the SVM model. Gaussian and polynomial kernel functions yielded higher error values than the heavy-tailed radial basis function (RBF) kernel (RMSE of 1.46 %, see figure 6b). Optimization of the other SVM parameters yielded C = 1000 = 0.05 kerneloptiε on= [ 0.3,0.3]. A SVM with those parameters was trained with voltage, current, and SOC data from a 15 min driving event in April 2010 with an average battery pack temperature of 23 C. Figure 5 presents the resulting hyperplane. The overall trends are a voltage decrease with decreasing SOC and with increasing currents, which is in accordance with fundamental battery characteristics (6,7). Figure 5. SVM model based on training data from the driving event in figure 4 (3D plot). Current and SOC have been used as input, voltage as output. This SVM model was subsequently tested with SOC, current and voltage data from another driving event in March where the battery temperature was similar (average battery pack temperature = 19 C). The comparison between predicted and actual battery pack voltage is illustrated in figure 6a. The relative error for the voltage prediction (figure 6b) showed a maximum of 1.72 % right in the beginning of the driving event. SOC inaccuracies are common directly after the logging start when the battery has been at rest and the SOC value from the prior logging does not coincide with reality. The RMSE thus was lower, 1.46 %; a good result for such a small data sample. Additionally, the error of the predicted voltage does not seem to increase with time or follow any other trend. 7

8 (a) (b) Figure 6. (a) Battery pack voltage prediction curve based on the SVM model from figure 5. An 810 seconds driving event from March served as test data (measured). (b) Relative error for voltage prediction from figure 6a. The maximum relative error is 1.72 %, the RMSE is 1.46 %. Setting the derived model error results in context by comparing to other SVM battery voltage prediction studies, does not allow straightforward conclusions. There are several studies on SVM based SOC estimation (18,19), but just one other study on SVM based voltage prediction (17). In (17), the relationship between voltage and current under different temperature and state-of-charge conditions has been predicted for a NiMH battery pack. The authors used a LS-SVM (least square) method with a RBF kernel for a training set of 3000 points and a test set of 6500 points. No information on the used software or the SVM parameters is given, but a maximum relative error of 3.61 % is mentioned. A direct comparison of the maximum relative errors is however difficult as (17) used a larger sample, a different system (Li-ion vs. NiMH) and an additional input (temperature). Battery State-of-Health Estimation After having proven the applicability of SVM for voltage prediction of real-life battery pack data in the previous section, SVM models from data selections from different points in time have been constructed in order to follow if and how battery behavior changes with time. The SVM models for driving events from January, July and December 2010 have been prepared with the SVM parameter set as displayed in the previous section and are presented in figure 7. A virtual HPPC test that matches the ranges of all three SVM models was prepared. Therefore, the HPPC test as suggested by (11) has been modified. As the maximum current of 250 A is hardly reached in real-life operation, a current of 175 A was chosen for the discharge pulse instead. The SOC start value was set to 90 %. The resulting current and SOC vectors can be found in figure 1. Figure 8 demonstrates the voltage response of this HPPC test for the three SVM models from figure 7. A look at the voltage behavior during the discharge pulse reveals a voltage drop as expected. The constant voltage during the rest subsequent to the discharge pulse does not coincide with normal battery characteristics on the other hand. The absence of a time-dependent voltage relaxation can be explained by the lack of time dependence in the model. 8

9 (a) (b) (c) Figure 7. SVM models based on training data from driving events in (a) January, (b) July and (c) December Current and SOC have been used as input, voltage as output. Figure 8. Voltage output from virtual tests on SVM models from figure 6 with SOC and current input from figure 1 for January, July and December The discharge resistances derived according to equation [4] from the plots in figure 8 are depicted in figure 9. Comparing the 10 s discharge resistance values for January, July and December, we observe that, starting from 0.13 Ohm in January, the resistance is lower in July and higher in December. This result makes sense considering the battery pack temperatures. The average battery pack temperature for the driving event in July (28.7 C) was about 13 C higher than the ones in January (15.9 C) and December (14.3 C) explaining the decreased resistance. The average battery pack temperatures for January and December on the other hand are close. It seems likely that the small temperature difference between January and December is not the reason for the increase in resistance. Aging seems to be at least partially responsible for the resistance increase. A comparison of the derived 10 s discharge resistances with a mathematical model (0.09 Ohm at 175 A, 20 C, April 2010 (2)) and a laboratory test (0.11 Ohm at 65 A, 28 C, 86.4 % SOC, June 2011 (13)) shows that the results lie within the correct order of magnitude. Still, more laboratory tests are needed to soundly validate the model. 9

10 Figure s discharge resistance as derived from HPPC tests for driving events in January, July and December SOC and current are just two out of a number of important variables that influence battery pack voltage. Adding battery pack temperature as input variable would help in order to distinguish between the impacts of aging and temperature on the resistance value. Apart from instantaneous values, such as battery pack temperature and ambient operating conditions, battery pack voltage also depends on the battery s operation history. Especially mass transport (mainly diffusion in electrolyte and electrodes) is a timedependent process that is responsible for a large part of the polarization in lithium-ion batteries (2). The time dependence that could be caught by a moving average of the battery current, for instance, should add the so far missing time-dependent voltage relaxation in the HPPC test voltage response (figure 8). Conclusions We have presented a proof of concept for the evaluation of battery performance from on-board data without additional testing equipment or interruptions of the ordinary operation. Support vector machines are identified as a powerful method to handle large amounts of real-life battery data. From on-board battery pack data, SVM models with battery behavior information can be conveniently constructed. The models allow us to perform virtual tests that estimate SOH figures of merit of the battery pack, e.g. internal resistance. This procedure opens up the possibility to enhance the comparability between laboratory and field tests and a mapping of real-life battery performance. The method offers the potential to further explore battery performance in real applications i.e. a platform to increase understanding. The model as presented in this article does not take into account all variables with high impact on battery voltage. In addition to current and SOC, time dependence and temperature are important. Those variables should be included in future models in order to further improve the voltage prediction accuracy. 10

11 Putting the suggested method into practice, a SVM model like the one described may be implemented in the BMS of an electric vehicle. The support vectors can be updated continuously from operation history, and a prediction of future voltage development depending on the operating conditions can be accomplished. Acknowledgments This work is supported by the Swedish Hybrid Vehicle Centre (SHC). We would like to thank ETC Battery and FuelCells Sweden AB for providing us with field test data and battery pack laboratory test results, Tommy Zavalis for applying his mathematical model on battery pack data, and Stefan Arnborg for discussing support vector machines. References 1. J. Belt, V. Utgikar, I. Bloom, J. Power Sources, 196, (2011). 2. A. Nyman, T. Zavalis, R. Elger, M. Behm, G. Lindbergh, J. Electrochem. Soc., 157, A1236 (2010). 3. K. Gering, S. Sazhin, S. Jamison, D. Michelbacher, B. Liaw, M. Dubarry, M. Cugnet, J. Power Sources, 196, 3395 (2011). 4. D. Andre, M. Meiler, K. Steiner, H. Walz, T. Soczka-Guth, D. Sauer, J. Power Sources, 196, 5349 (2011). 5. M. Safari, C. Delacourt, J. Electrochem. Soc., 158, A562 (2011). 6. J. Vetter, P. Novák, M. Wagner, C. Veit, K. Möller, J. Besenhard, M. Winter, M. Wohlfahrt-Mehrens, C. Vogler, A. Hammouche, J. Power Sources, 147, 269 (2005). 7. S. Brown, K. Ogawa, Y. Kumeuchi, S. Enomoto, M. Uno, H. Saito, Y. Sone, D. Abraham, G. Lindbergh, J. Power Sources, 185, 1444 (2008). 8. P. Svens, J. Lindstrom, O. Gelin, M. Behm, G. Lindbergh, Energies, 4, 741 (2011). 9. B. Liaw, M. Dubarry, J. Power Sources, 174, 76 (2007). 10. M. Dubarry, V. Svoboda, R. Hwu, B. Liaw, J. Power Sources, 174, 366 (2007). 11. Electrically propelled road vehicles Test specifications for lithium-ion traction battery packs and systems Part 1: High-power applications, ISO (2011). 12. Battery test manual for plug-in hybrid electric vehicles, INL/EXT (2008). 13. ETC Battery and FuelCells Sweden AB, Vattenfall AB, Volvo Technology AB, Volvo Personvagnar AB, Plug-in hybrid project PHEV, financed by the Swedish Energy Agency under project number until (2010). 14. C. Cortes, V. Vapnik, Mach. Learn., 20, 273 (1995). 15. N. Cristianini, J. Shawe-Taylor, An Introduction to Support Vector Machines and other Kernel-based Learning Methods, Cambridge University Press (2000). 16. S. Canu, Y. Grandvalet, V. Guigue, A. Rakotomamonjy, SVM and Kernel Methods Matlab Toolbox, INSA de Rouen, Rouen, France, (2005). 17. W. Junping, C. Quanshi, C. Binggang, Energ. Convers. Manage., 4, 858 (2006). 18. T. Hansen, C. Wang, J. Power Sources, 141, 351 (2005). 19. X. Wu, L. Mi, W. Tan, J. Qin, M. Zhao, Adv. Mat. Res., , 1204 (2011). 20. O. Maimon, L- Rokach, Data mining and knowledge discovery handbook, Springer (2005). 11