SOC estimation performance comparison based on the ...

1 EVS28 International Electric Vehicle Symposium and Exhibition 1 EVS28 KINTEX, Korea, May 3-6, 2015 SOC estimation performance comparison based on the equivalent circuit model using an EKF in commercial LiCoO2 and LiFePO4 cells Hyun-jun Lee1, Joung-hu Park1 Jonghoon Kim2 1 Department of Electrical Engineering, Soongsil University, Seoul, 2 Department of Electrical Engineering, Chosun University, Gwangju, Abstract This study gives a comparison of an Equivalent Circuit-Model (ECM)- based SOC performance using an Extended Kalman Filter (EKF) algorithm for commercial LiCoO2and LiFePO4 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.

2 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), LiCoO2, LiFePO41 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 (LiCoO2) cell and the lithium iron phosphate (LiFePO4) 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).

3 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 LiCoO2 cell and LiFePO4 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 LiCoO2 and LiFePO4 cells. The conventional ECM is basically comprised of simple OCV, resistance and a RC-ladder. However, the OCV characteristic for a LiFePO4 cell exhibits very flat curves over the SOC ranges and also pronounced hysteresis phenomena in comparison to the LiCoO2 physics [1]-[4]. Firstly, this paper EVS28 International Electric Vehicle Symposium and Exhibition 2 will introduce the difference in modelling between both of cells.

4 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 comparison of OCV characteristic (a) LiCoO2 cell (b) LiFePO4 cell Figure 1: Discharging/Charging OCV curves. (a) Discharging/Charging OCV curves in LiCoO2 cell.

5 (b) Discharging/Charging OCV curves in LiFePO4 cell. In present work, both of a fresh LiCoO2 and a LiFePO4 cell with high capacity and 14Ah is explored to study. Maximum charge voltages are in LiCoO2 and in LiFePO4 cell. Maximum discharge voltages are in LiCoO2 and 2V in LiFePO4 cell. LiFePO4 cell has a very unusual OCV characteristics compared to LiCoO2 cell caused by hysteresis effect. Figure 1(a)-(b) shows two OCV curves at 4A, 25 C in the discharging/charging. At the LiCoO2 cell, the OCV is almost the same between discharging and charging curves, as illustrated in Figure 1(a). However, at the LiFePO4 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 LiCoO2 cell.

6 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) LiCoO2 cell (b) LiFePO4 cell Figure 2: Simplified electrical equivalent circuit model. (a) Simplified equivalent circuit model of the LiCoO2 cell. (b) Simplified equivalent circuit model of the LiFePO4 cell [4]. Number of RC-ladder Figure 3 shows an electrical ECM considering the second order RC-ladder. EVS28 International Electric Vehicle Symposium and Exhibition 3 (a) LiCoO2 cell (b) LiFePO4 cell Figure 3: Electrical equivalent circuit model with two RC-ladders. (a) Equivalent circuit model of the LiCoO2 cell with two RC-ladders [5]. (b) Equivalent circuit model of the LiFePO4 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 Ri.

7 The diffusion region is expressed as an RC-ladder, the parallel connection of Rdiff and Cdiff. The resistance becomes small, inversely proportional to the n2, 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) [SOCkVdiff,k]= [1001- tRdiffCdiff][SOCk-1 Vdiff,k-1]+[- tCn tCdiff]ik-1 (1) [SOCkVdiff1,kVdiff2,k]= [ 10001- tRdiffCdiff0001-4 tRdiffCdiff] [SOCk-1 Vdiff1,k-1 Vdiff2,k-1]+[ - tCn2 tCdiff2 tCdiff] ik-1 (2) Vk = hk (OCV, Vdiff) - Riik = OCV - Vdiff - Riik (3) Vk = hk (OCV, Vdiff1, Vdiff2) = OCV - Vdiff1 - Vdiff2 - Riik (4) The Extended Kalman Filter (EKF) is an optimum state estimator, which is widely used these days.

8 The equations (1)-(2) show the state equations of the EKF when the number of RC-ladders 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 (Kk), which is a function of the measurement error variance, that is, the value of Kk 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.

9 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 4 is, the infinite value of the measurement error variance sets the value of the Kk 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 LiCoO2 cell in the EKF Measurement noise model by battery current Rk+1 = Rk, reliable current (|i| < 5A) Rk+1 = Rk[1+Gi(|i|-5A)], unreliable current ( |i| > 5A) Gi = 2A-1 Measurement noise model by dynamic of RC-ladder Rk+1 = Rk[1+Gstep(step_time)] Gstep = Data rejection technique Rk = , reject time ( I > 5A) reject time = 10ms Table 2: Noise model and Data rejection for LiFePO4 cell in the EKF Measurement noise model by battery current Rk+1 = Rk, reliable current (|i| < 10A) Rk+1 = Rk[1+Gi(|i|-10A)], unreliable current ( |i| > 10A) Gi = 4A-1 Measurement noise model by dynamic of RC-ladder Rk+1 = Rk[1+Gstep(step_time)] Gstep = Data rejection technique Rk = , reject time ( I > 10A) reject time = 100ms 5 Experimental results Figure 4: SOC estimation results of LiCoO2 Table 3.

10 The average error on the SOC estimation of the LiCoO2 cell ECM Average error One RC-ladder One Rc-ladder/Data rejection Two RC-ladder Two RC-ladder/Data rejection Figure 5: SOC estimation results of LiFePO4 Table 4: The average error on the SOC estimation of the LiFePO4 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 LiCoO2 cell and LiFePO4 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 LiCoO2 and LiFePO4 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 LiCoO2 cell. And, the average error was calculated with the SOC. Model error to confirm the experimental results shown in Figure 4 in detail.