Abstract This paper presents a fractional order equivalent circuit model and uses fractional order Kalman filter (FOKF) method for state of charge (SOC) estimation of lithium-ion power batteries in electric vehicles. Firstly, a fractional order battery model was established based on second-order equivalent circuit and the fractional orders were identified by genetic algorithm. The SOC was estimated depending on the FOKF method. Compared with extend Kalman filter (EKF) method, it is shown that the maximum absolute error of the terminal voltage is 0.014V under constant current discharge test. The maximum SOC estimation error is under 2% by FOKF, which has higher accuracy and faster convergence speed. The fractional order model proposed in this paper not only presents an accurate and reliable battery model, but also provides an effective means for improving the accuracy of SOC estimation in battery management system.
Liu Shulin,Cui Naxin,Li Yan等. Modeling and State of Charge Estimation of Lithium-Ion Battery Based on Theory of Fractional Order for Electric Vehicle[J]. Transactions of China Electrotechnical Society, 2017, 32(4): 189-195.
[1] 刘艳莉, 戴胜, 程泽, 等. 基于有限差分扩展卡尔曼滤波的锂离子电池SOC估计[J]. 电工技术学报, 2014, 29(1): 221-228. Liu Yanli, Dai Sheng, Cheng Ze, et al. Estimation of state of charge of lithium-ion battery based on finite difference extended Kalman filter[J]. Transactions of China Electrotechnical Society, 2014, 29(1): 221-228. [2] Seaman A, Dao T S, Mcphee J. A survey of mathematics-based equivalent-circuit and electro- chemical battery models for hybrid and electric vehicle simulation[J]. Journal of Power Sources, 2014, 256(3): 410-423. [3] 陈息坤, 孙冬, 陈小虎. 锂离子电池建模及其荷电状态鲁棒估计[J]. 电工技术学报, 2015, 30(15): 141-147. Chen Xikun, Sun Dong, Chen Xiaohu. Modeling and state of charge robust estimation for lithium-ion batteries[J]. Transactions of China Electrotechnical Society, 2015, 30(15): 141-147. [4] 孙朝晖, 成晓潇, 陈冬冬, 等. 计及非线性容量效应的锂离子电池混合等效电路模型[J]. 电工技术学报, 2016, 31(15): 156-162. Sun Zhaohui, Cheng Xiaoxiao, Chen Dongdong, et al. Hybrid equivalent circuit model of lithium-ion battery considering nonlinear capacity effects[J]. Transactions of China Electrotechnical Society, 2016, 31(15): 156-162. [5] Hu X, Li S, Peng H. A comparative study of equivalent circuit models for Li-ion batteries[J]. Journal of Power Sources, 2012, 198: 359-367. [6] Gandolfo D, Brandão A, Patiño D, et al. Dynamic model of lithium polymer battery-load resistor method for electric parameters identification[J]. Journal of the Energy Institute, 2014, 88(4): 470-479. [7] Seaman A, Dao T S, Mcphee J. A survey of mathematics-based equivalent-circuit and electro- chemical battery models for hybrid and electric vehicle simulation[J]. Journal of Power Sources, 2014, 256(3): 410-423. [8] Unterrieder C, Zhang C, Lunglmayr M, et al. Battery state-of-charge estimation using approximate leasts- quares[J]. Journal of Power Sources, 2015, 278(15): 274-286. [9] Yin C, Zhong Q S, Chen Y Q, et al. Estimating the state of charge of lithium batteries based on fractional-order sliding-mode observer[C]//2014 Inter- national Conference on Fractional Differentiation and Its Applications (ICFDA), 2014: 1-6. [10] Riu D, Montaru M, Bultel Y. Time domain simulation of Li-ion batteries using non-integer order equivalent electrical circuit[J]. Communications in Nonlinear Science & Numerical Simulation, 2013, 18(6): 1454- 1462. [11] 杨晴霞, 曹秉刚, 徐俊, 等. 一种估计锂电池充电状态的分数阶阻抗模型[J]. 西安交通大学学报, 2015, 49(8): 128-132. Yang Qingxia, Cao Binggang, Xu Jun, et al. A fractional impedance model for charge state esti- mation of lithium battery[J]. Journal of Xi’an University, 2015, 49(8): 128-132. [12] Yuan S, Wu H, Zhang X, et al. Online estimation of electrochemical impedance spectra for lithium-ion batteries via discrete fractional order model[C]// IEEE Vehicle Power and Propulsion Conference (VPPC), 2013: 1-6. [13] Sabatier J, Merveillaut M, Francisco J M, et al. Fractional models for lithium-ion batteries[C]//European Control Conference (ECC), 2013: 3458- 3463. [14] Zhong F, Li H, Zhong S, et al. An SOC estimation approach based on adaptive sliding mode observer and fractional order equivalent circuit model for lithium-ion batteries[J]. Communications in Non- linear Science & Numerical Simulation, 2015, 24: 127-144. [15] Westerlund S, Ekstam L. Capacitor theory[J]. IEEE Transactions on Dielectrics & Electrical Insulation, 1994, 1(5): 826-839. [16] Macdonald J R. Impedance spectroscopy[M]. Cali- fornia: Society of Photo-Optical Instrumentation Engineers, 1981. [17] Wang B, Li S E, Peng H, et al. Fractional-order modeling and parameter identification for lithium-ion batteries[J]. Journal of Power Sources, 2015, 293(20): 151-161. [18] 李江, 王义伟, 魏超, 等. 卡尔曼滤波理论在电力系统中的应用综述[J]. 电力系统保护与控制, 2014, 42(6): 135-144. Li Jiang, Wang Yiwei, Wei Chao, et al. A survey on the application of Kalman filtering method in power system[J]. Power System Protection and Control, 2014, 42(6): 135-144. [19] Micea M V, Ungurean L, CaRstoiu G N, et al. Online state-of-health sssessment for battery management systems[J]. IEEE Transactions on Instrumentation & Measurement, 2011, 60(6): 1997-2006. [20] Zhang Y, Pu Y, Zhang H, et al. An extended fractional Kalman filter for inferring gene regulatory networks using time-series data[J]. Chemometrics & Intelligent Laboratory Systems, 2014, 138: 57-63.
2017, Vol. 32 
