SOC estimation performance comparison based on the equivalent circuit model using an EKF in commercial LiCoO 2 and LiFePO 4 cells

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1 EVS28 KINTEX, Korea, May 3-6, 2015 SOC estimation performance comparison based on the equivalent circuit model using an EKF in commercial LiCoO 2 and LiFePO 4 cells Hyun-jun Lee 1, Joung-hu Park 1 Jonghoon Kim 2 1 Department of Electrical Engineering, Soongsil University, Seoul, wait4u@ssu.ac.kr 2 Department of Electrical Engineering, Chosun University, Gwangju, qwzxas@hanmail.net Abstract This study gives a comparison of an Equivalent Circuit-Model (ECM)-based SOC performance using an Extended Kalman Filter (EKF) algorithm for commercial LiCoO 2 and LiFePO 4 cells with an emphasis on the model considering parameterization and noise-modeling with data rejection technique. Firstly, introduces the difference in modelling between both of the cells caused by the Open-Circuit-Voltage(OCV) characteristics. Secondly, this works attempt to show the difference of SOC performance with an increased RC-ladder number in the EKF, namely parameterization. Additionally, comparison of SOC performance with and without noise model and data rejection are implemented to reduce the model error caused by the simplified ECM. Keywords: Comparison, state-of-charge(soc), extended Kalman filter(ekf), LiCoO 2, LiFePO 4 1 Introduction Currently, market demand for high energy density of lithium rechargeable cells applicable to electric-powered transportation such as electric vehicle (EV) and hybrid electric vehicle (HEV) has gradually been increased. Two representative lithium rechargeable cells are the lithium cobalt oxide (LiCoO 2 ) cell and the lithium iron phosphate (LiFePO 4 ) cell. One of these cells is properly selected according to the specific target specification. In general, in order to describe electrochemical characteristics of lithium rechargeable cells, an equivalent circuit model (ECM) plays an important role for the efficient model-based state-of-charge (SOC) estimation that enables to provide an outstanding battery management system (BMS). Nowadays, depending on battery cell s experimental condition, much noticeable approaches committed to the development of model-based SOC estimation have been individually investigated. However, relatively little attention was paid to SOC performance comparison between LiCoO 2 cell and LiFePO 4 cell with respect to the model considering parameterization and noise-modeling with data rejection technique. Thus, this work introduces the ECM-based SOC performance comparison using the Extended Kalman Filter (EKF) algorithm between commercial LiCoO 2 and LiFePO 4 cells. The conventional ECM is basically comprised of simple OCV, resistance and a RC-ladder. However, the OCV characteristic for a LiFePO 4 cell exhibits very flat curves over the SOC ranges and also pronounced hysteresis phenomena in comparison to the LiCoO 2 physics [1]-[4]. Firstly, this paper EVS28 International Electric Vehicle Symposium and Exhibition 1

2 will introduce the difference in modelling between both of cells. Secondly, this works attempt to show the differences of SOC performance with an increased RC-ladder number in the EKF, namely parameterization. Since the number of RC-ladder determines the performance of the model. Finally, this work develops more the aforementioned results investigated by comparison of SOC performance with and without the noise using a data rejection technique. The real charging/discharging profiles of the battery voltage/currents are included in order to verify the performance of the SOC estimation varied by the modeling differences. From the result verification, it will be concluded that this approach describe an effort to provide a fundamental solution for implementation of the cell s electrochemical characteristics. 2 Equivalent-Circuit Modeling 2.1 Comparison of OCV characteristic is explored to study. Maximum charge voltages are 4.2V in LiCoO 2 and 3.65V in LiFePO 4 cell. Maximum discharge voltages are 2.8V in LiCoO 2 and 2V in LiFePO 4 cell. LiFePO 4 cell has a very unusual OCV characteristics compared to LiCoO 2 cell caused by hysteresis effect. Figure 1(a)-(b) shows two OCV curves at 4A, 25 C in the discharging/charging. At the LiCoO 2 cell, the OCV is almost the same between discharging and charging curves, as illustrated in Figure 1(a). However, at the LiFePO 4 cell, the charging OCV curve is higher than the discharging curve, as shown in Figure 1(b). These unusual OCV characteristics are to be considered in this paper with the equivalent-circuit model. Figure 2(a)-(b) are simplified ECMs. Figure 2(a) is a basic ECM for SOC estimation of LiCoO 2 cell. Figure 2(b) is a previously developed equivalent circuit model [4]. It consists of discharging and charging OCVs selected by the current flow direction. These models will be used for SOC estimation performance based on an EKF algorithm. (a) LiCoO 2 cell (a) LiCoO 2 cell (b) LiFePO 4 cell Figure 1: Discharging/Charging OCV curves. (a) Discharging/Charging OCV curves in LiCoO 2 cell. (b) Discharging/Charging OCV curves in LiFePO 4 cell. In present work, both of a fresh LiCoO 2 and a LiFePO 4 cell with high capacity 1.3Ah and 14Ah (b) LiFePO 4 cell Figure 2: Simplified electrical equivalent circuit model. (a) Simplified equivalent circuit model of the LiCoO 2 cell. (b) Simplified equivalent circuit model of the LiFePO 4 cell [4]. 2.2 Number of RC-ladder Figure 3 shows an electrical ECM considering the second order RC-ladder. EVS28 International Electric Vehicle Symposium and Exhibition 2

3 - t C n [ SOC k V ] = [ 1 0 t diff,k 0 1- ] [ SOC k-1 ] + [ V t ] i k-1 (1) R diff C diff diff,k-1 C diff SOC k [ V diff1,k ] = V diff2,k (a) LiCoO 2 cell t 0 1- SOC k-1 0 R diff C diff V diff1,k-1 4 t R diff C diff ] [ [ ] + V diff2,k-1 [ - t C n 2 t C diff 2 t C diff ] i k-1 (2) V k = h k (OCV, V diff ) - R i i k = OCV - V diff - R i i k (3) V k = h k (OCV, V diff1, V diff2 ) = OCV - V diff1 - V diff2 - R i i k (4) (b) LiFePO 4 cell Figure 3: Electrical equivalent circuit model with two RC-ladders. (a) Equivalent circuit model of the LiCoO 2 cell with two RC-ladders [5]. (b) Equivalent circuit model of the LiFePO 4 cell with two RC-ladders. Since the charge transfer phenomenon of the battery has a fast response speed in the equivalent circuit model organization, the charge transfer can be expressed with the basic resistance R i. The diffusion region is expressed as an RC-ladder, the parallel connection of R diff and C diff. The resistance becomes small, inversely proportional to the n 2, where n is in the number of the RC-ladder. Due to the relationship, the effect of the time constant of the RC-ladder is decreased. Therefore, the effect of the capacitance is reduced gradually with the increase of the order of RC-ladder. Therefore, the resistance can be simplified if the error is negligible. For the final goal of this paper, electrical equivalent circuit model is constructed using single and double RC-ladders, as illustrated in Figure 2(a)-(b) and Figure 3(a)-(b). Based on these models, this work will implement state equations and measurement equation for the equivalent circuit model based Extended Kalman Filter. 3 Extended Kalman Filter (EKF) The Extended Kalman Filter (EKF) is an optimum state estimator, which is widely used these days. The equations (1)-(2) show the state equations of the EKF when the number of RCladders are one and two, respectively. We can see the number of the state variable increase by one when increasing RC-ladders. The equations (3)-(4) express the measurement equations of the EKF when the number of RC-ladder is one and two, respectively. 4 Noise model and data rejection The estimation error of the electrical circuit model is unavoidable when using a simplified model for implementation of the electrochemical properties of the battery. SOC estimation of the EKF is determined by the Kalman gain (K k ), which is a function of the measurement error variance, that is, the value of K k is determined by the value of the measurement error. Note this, since we use the noise model in the following two conditions in order to reduce the error from the simplified model. It is one of the objective of this paper to enhance the performance of SOC estimation by adjusting the value of Kalman gain. When a high current greater than the C-rate of battery, the SOC estimation should be applied to the measurement noise model corresponding to the current level. And, also when a step current is applied to battery, the dynamic characteristics of the RC-ladder generates a significant model error. Therefore, the decision to accept or reject the data depends on the current step magnitude. Finally, data rejection technique is utilized in order to exclude the experimental data from the estimation algorithm, where the model error grows high. That EVS28 International Electric Vehicle Symposium and Exhibition 3

4 is, the infinite value of the measurement error variance sets the value of the K k zero. Four measurement noise models and two data rejection technique are listed in Table 1 and 2. Table 1: Noise model and data rejection for LiCoO 2 cell in the EKF Measurement noise model by battery current R k+1 = R k, reliable current ( i < 5A) R k+1 = R k [1+G i ( i -5A)], unreliable current ( i > 5A) G i = 2A -1 Measurement noise model by dynamic of RCladder R k+1 = R k [1+G step (step_time)] G step = 0.1sec -1 Data rejection technique R k =, reject time (ΔI > 5A) reject time = 10ms Table 3: The average error on the SOC estimation of the LiCoO 2 cell ECM Average error One RC-ladder One Rc-ladder/Data rejection Two RC-ladder Two RC-ladder/Data rejection Table 2: Noise model and Data rejection for LiFePO 4 cell in the EKF Measurement noise model by battery current R k+1 = R k, reliable current ( i < 10A) R k+1 = R k [1+G i ( i -10A)], unreliable current ( i > 10A) G i = 4A -1 Measurement noise model by dynamic of RC-ladder R k+1 = R k [1+G step (step_time)] G step = 0.1sec -1 Data rejection technique R k =, reject time (ΔI > 10A) reject time = 100ms 5 Experimental results Figure 4: SOC estimation results of LiCoO 2 Figure 5: SOC estimation results of LiFePO 4 Table 4: The average error on the SOC estimation of the LiFePO 4 cell ECM Average error One RC-ladder One RC-ladder/Data rejection Two RC-ladder Two RC-ladder/Data rejection This paper compares the SOC performance between LiCoO 2 cell and LiFePO 4 cell according to the number of RC-ladder in the EKF algorithms. And, comparison of SOC estimation with and without noise model and data rejection is also presented. For the estimation, charging/discharging voltage data of LiCoO 2 and LiFePO 4 cell were obtained by applying the scale-down current profile for a hybrid vehicle to the real batteries. Figure 4 shows a result of SOC performance in LiCoO 2 cell. And, the average error was calculated with the SOC. Model error to confirm the experimental results shown in Figure 4 in detail. The calculation result is shown in Table 3. Based on the analysis of Table 3, SOC estimation is negligibly improved when the order of RC-ladder becomes two, compared with when it is one. Whereas, the SOC estimation using the noise model and data rejection technique is improved significantly improved, compared to that without the noise model and data rejection technique. EVS28 International Electric Vehicle Symposium and Exhibition 4

5 Figure 5 and Table 4 show the result of SOC estimation in LiFePO 4 cell. The analysis of Table 4, SOC performance is improved significantly, when the number of RC-ladder becomes two, compared to that of the first order RC-ladder. Also, the SOC estimation using the noise model and data rejection technique is improved significantly, compared to that without the noise model and data rejection technique. From both of the results, increasing number of RC-ladder in equivalent-circuit-model and using the noise model and data rejection technique in EKF algorithm play an important role in the SOC estimation of LiFePO 4 cells. On the other hand, it can be seen that the order of RC-ladder does not affect the accuracy of the SOC estimation of LiCoO 2 cells. However, noise model and the data rejection are very important to the SOC estimation of the LiCoO 2 cell. 6 Conclusion In this paper, the first order and the second order RC-ladder electrical equivalent circuit model were applied to LiCoO 2 and LiFePO 4 cells for SOC estimation based on EKF. Also, various SOC estimation performances was compared and analysed with and without data rejection. As the number of RC-ladder increases and the noise model and data rejection technique are used, the SOC estimation is improved. In particular, when LiFePO 4 cell is applied, the error is significantly increased in accordance with the simplified model. Therefore, the accurate modeling and error correction technique are more important to the LiFePO 4 than to the LiCoO 2 cell. However, as to the realization of algorithm, certainly the simplification of the algorithm by simplification of the algorithm is required. In the future work, research of the trade-off between the SOC estimation accuracy and the calculation from EKF algorithm is necessary. The objective is to compensate correct the simplified ECM error by using more correct noise model and data rejection. Acknowledgments This work was supported by the Human Resources Development program (No ) of the Korea Institute of Energy Technology Evaluation and Planning(KETEP) grant funded by the Korea government Ministry of Trade Industry and Energy. References [1] A. Awarke, S. Lauer, S. Pischinger, and M. Wittler, Percolation-tunneling modeling for the study of the electric conductivity in LiFePO4 based Li-ion battery cathodes, J. Power Sources, vol. 196, pp , Feb [2] Y. Zhang, C.-Y. Wang, and X. Tang, Cycling degradation of an automotive LiFePO4 lithium-ion battery, J. Power Sources, vol. 196, pp , Feb [3] M. A. Roscher, J. Assfalg, and O. S. Bohlen, Detection of Utilizable Capacity Deterioration in Battery Systems, IEEE Trans. Veh. Technol., vol. 60, no. 1, pp , Jan [4] J. H. Kim, G. S. Seo, C. C. Chun and B. H. Cho, OCV hysteresis effect-based SOC estimation in extended Kalman filter algorithm for a LiFePO 4 /C cell, Electrical Vehicle Conference (IEVC), 2012 IEEE International., ISBN (2012) pp. 1-5, March [5] H. J. Lee, J. H. Park, J. H. Kim, Comparison of equivalent-circuit-model-based SOC estimation using the EKF, Power Electronics Autumn Conference 2014., p , November Authors Hyun-jun Lee He received his B.S. degree from the Department of Electrical Engineering of Soongsil University, Seoul, Korea, in He is currently pursuing his M.S. degree at Soongsil University. His current research interests include the equivalent circuit model based SOC performance using the EKF. Joung-hu Park He received his B.S., M.S., and Ph.D. degrees from the Department of Electrical Engineering and Computer Science of Seoul National University, Seoul, Korea, in 1999, 2001, and 2006, respectively. He is currently an assistant professor at Soongsil University, Seoul, Korea. His current research interests include the analysis of high-frequency switching converters and renewable energy applications. Jonghoon Kim He received the B.S. degree in Electrical Engineering from Chungnam National University, Daejeon, Republic of Korea and Ph.D degrees in Electrical Engineering and Computer Science from Seoul EVS28 International Electric Vehicle Symposium and Exhibition 5

6 National University, Republic of Korea, in 2005 and 2012, respectively. From 2012 to 2013, he was a Senior Research Engineer in Energy Storage System (ESS) Development Group, Energy Solution (ES) Division, Samsung SDI, Cheonnan, Republic of Korea. He is currently an assistant professor with the Department of Electrical Engineering, Chosun University, Gwangju, Republic of Korea. His main research interests include battery management system (BMS; modelling, screening, equalization, SOC/SOH estimation), Lithium-air, and fuel cell system (ripple current analysis, fault diagnosis, SOH prediction, and modelling). He is a member of IEEE and the Korean Institute of Power Electronics (KIPE). In addition, he is currently an Associate Editor of the Journal of Power Electronics (JPE). He received the Student Paper Award from IPEC- 10. EVS28 International Electric Vehicle Symposium and Exhibition 6