SOC Estimation of Lithium-ion Battery Packs Based on Thevenin Model Yuanqi Fang 1,a, Ximing Cheng 1,b, and Yilin Yin 1,c. Corresponding author

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1 Appled Mechancs and Materals Onlne: ISSN: , Vol. 299, pp do: / Trans Tech Publcatons, Swtzerland SOC Estmaton of Lthum-on Battery Pacs Based on Thevenn Model Yuanq Fang 1,a, Xmng Cheng 1,b, and Yln Yn 1,c 1 Natonal Engneerng Laboratory for Electrc Vehcle, Bejng Insttute of Technology, Bejng, Chna Correspondng author a E-mal: fangyuanq1988@163.co b E-mal: cxm2004@bt.edu.cn, c E-mal: ynyln2008@126.com Keywords: lthum-on battery, EKF, SOC estmaton, Thevenn model Abstract. Due to the mmeasurablty of SOC n battery and nevtablty of error n current collecton, SOC estmaton of Lthum-on battery has become a focus of EV research. Wth Thevenn equvalent crcut model, ths paper employs EKF algorthm to estmate SOC, whch taes nto consderaton both precson requrement of the estmaton and amount of computaton nvolved n onlne estmaton. Based on above-mentoned objectves and prncples, a test platform composed of Dgatron battery test system and thermostat was bult. Expermental result has confrmed that the combnaton of EKF algorthm wth Thevenn model can mprove precson and reduce amount of computaton. Introducton As an mportant component of EVs, battery management system can acheve real tme montorng and manage the battery s worng condton [1][2].One of the most fundamental and also the most mportant functon of the management system s the estmaton of SOC. However, due to the mmeasurablty of SOC [3], accurate estmaton of SOC n power battery has long been a challengng tas, and more and more methods are appled nto ths ssue, for example, the Ampere-Hour ntegral [4], the open-crcut- voltage(ocv) measurement. The result of Ah approach s substantally nfluenced by the precson of current measurement and the ntal value. OCV measurement requres long tme of standng before operaton [5]. The applcaton of EKF nto the estmaton of SOC can by contrast effectvely mae up for the defcences of the above-mentoned approaches. Establshment of Equvalent Crcut Model It s mportant to establsh a battery model of hgh precson for the applcaton of EKF nto the estmaton of SOC. Thevenn model s adopted n ths paper, whch taes the polarzaton phenomena of battery nto consderaton, shown n Fg.1. R 0 + u oc p Rp c C + uc u o Fg.1: Thevenn equvalent crcut mode Fg.2: Battery test bench All rghts reserved. No part of contents of ths paper may be reproduced or transmtted n any form or by any means wthout the wrtten permsson of Trans Tech Publcatons, (# , Pennsylvana State Unversty, Unversty Par, USA-18/09/16,15:23:50)

2 212 Mechancal Engneerng, Industral Electroncs and Informatzaton In Fg.1, R 0 s used to descrbe ohmc polarzaton effect, u 0 represents the voltage of R 0, u oc represents OCV, whch s a functon of SOC. u o represents the load voltage, resstance Rp and capacty C represent polarzaton phenomena, u c represents the voltage of Rp. Parameter Determnaton of Thevenn Model The determnaton of battery model parameters should consder the followng two aspects, fttng of open OCV-SOC curve and determnaton of R 0, R p, C, both of whch must be conducted after HPPC test. Battery Test Bench. To acqure expermental data, a battery test bench was establshed. Battery pacs composed of 36 battery cells produced by Chna BAK Battery Inc. serves as experment object. Informaton of the battery cell s shown n Table 1. Table 1: Informaton of battery cell Nomnal capacty [mah] Nomnal voltage [V] Maxmum chargng/ dschargng current [ma] Maxmum chargng/ dschargng temperature [ ] / /75 Fg.2 s the schematc dagram of the battery test bench. The test system adopted Dgatron EVT , whch can collect data such as tme, voltage, current, charge and dscharge energy, charge and dscharge capacty of the battery wth ts maxmum samplng frequency beng as hgh as 10 Hz. Parameter Determnaton. The current exctaton and voltage response n HPPC test are shown n Fg. 3. The cutoff condton of the experment s set as SOC0.2 to avod over-dscharge. Fg. 3: HPPC test Fg. 4: Voltage responses at SOC0.7 As s shown n Fg. 4, the value of OCV and R 0 can be wored out wth Eq. (1) and Eq. (2). Durng V2~V3, load voltage s shown as Eq. (3). Accordng to the least square method, the target functon has been dervate shown n Eq. (4). R p and C can be calculated wth fmnsearch functon n Matlab. The dschargng current has been set as I. uoc V1 (1) R0 ( V2 V1 )/ I (2) t/ uo uocr0 Rp(1 e τ ) (3) 2 J mn( ( v ve, ) ) (4) where τ RpC, 1,2,3, n, n represents the number of samplng pont, v and ve, represent measured and calculated load voltage at respectvely.

3 Appled Mechancs and Materals Vol Fg. 5: OCV-SOC curves fttng Fg. 6 R 0 -SOC curve Fg. 7 R p -SOC curve Fg. 8 τ -SOC curve Fg. 5 shows the result of quartc-polynomal fttng of OCV and SOC curves. It s clear that polynomal fttng result meets the precson requrement, and error s just 5. R 0, R p and C have been shown n Fg. 6~Fg. 8. R 0, R p and τ have been defned as the average of all values at dfferent SOC pont respectvely, shown n Table 2. Table 2 Values of model parameters R 0 [Ω] R p [Ω] τ [sec] Valdaton of Parameters. As s shown n Fg. 9, to valdate the accuracy of the model parameters, the termnal voltage s smulaton values and expermental values are compared n the exctaton of the current values composed of ECE, FTP and J1015 cycle condton. Relatve error s to evaluate the model precson, whch s shown n Eq. (5). relatve_ error v v / v (5) e, Where 1, 2, 3, n, n represents the number of samplng pont, v and ve, represent measured and calculated load voltage at respectvely. Fg. 9 llustrates that the vast majorty of relatve error o s below 5%. Calculatons have shown that the average relatve error s only 0.64%. Therefore, quartc-polynomal fttng can be appled to SOC estmaton. Fg. 9 Valdaton of model parameters Fg. 10 The rusult of combned worng condton test

4 214 Mechancal Engneerng, Industral Electroncs and Informatzaton SOC Estmaton Usng EKF Algorthm EKF algorthm s a recursve approach to get the status value of nonlnear system utlzng Lnear Mnmum Square Error estmaton method [6]. In Eq. (6) and (8), state and observaton equaton are formulated by combnng Ampere-Hour ntegral model and Thevenn model. x 1 A x B + w (6) uo, G(, x) + v (7) G( x, ) u u R (8) oc, c, 0 s 1 0 ηts / Cn T Where x u A c, 0 α B s / τ T / β α e (1 s τ β Rp e ).T s s the samplng perod. C n s the nomnal capacty. S s the SOC value and u c, s the voltage value of R p at samplng nstant of T s. ω s the system s random dsturbance. ν s the measurement nose. SOC estmaton utlzng EKF algorthm can be formulated. The recurson s shown as follws: A + B a), P A P A + Q T b), c) K P C [ C P C + R ] T T 1, 1, 1 d) ˆ ˆ ˆ, 1 + L,, 1 1 e) P [ I KC] P / 1 Where x x K [ u G( x,, t)] C dg( x, ) dg( x, ) 0, x, G G dr +,, 1 dx dx x R dx G 2 3 v,1 + 2v,2 s + 3v,3 s + 4v,4s 1 x 0, G R 0,, [ 0 0] 0, dr dx. Experment Analyss As s shown n Fg. 10, combned cycle worng condton s taen as an example to evaluate EKF algorthm. SOC estmaton precson s evaluated by absolute error, as s shown n Eq. (9). absolute_ error s s / max( s ) mn( s ) (9) { } e, Where 1, 2, 3, n, n represents the number of samplng pont, s and se, represent measured and calculated SOC at respectvely. Intal values of EKF flterng s shown as follow: P Q , R R 0 s defned as 0.8 R 0,0.9 R 0, R 0,1.1 R 0,1.2 R 0, the nfluence of nternal resstance has been shown n Fg.11, whch manfests that the more the nternal resstance devates from the exact value R 0, the lower the estmaton precson becomes. Fg.11: Influence of nternal resstance Fg. 12(a): Influence of ntal value Fg. 12(b): Intal stage

5 Appled Mechancs and Materals Vol It s clearly shown from Fg. 12 that the nfluence of ntal value s only mnmal. Estmated SOC can qucly follow the trac of the measured SOC. As s show n Fg. 13, the comparson between measured SOC and estmated SOC at the tme R 0 s set as R 0, only exhbts the maxmum absolute error of 1.42% and the mean absolute error of 0.52%. Fg. 13: Measured SOC and estmated SOC Fg.14: Measured voltage and calculated voltage Fg.14 s the comparson between estmated and measured termnal voltage value, the former s calculated wth estmated SOC value. For the most part the relatve error s below 5% wth a mean relatve error of 0.72%. Ths has lad the foundaton for subsequent onlne dentfcaton of battery parameters and wll further facltate the applcaton of double Kalman flter nto the smultaneous onlne estmaton of battery parameter and SOC. Concluson Expermental results have manfested that the applcaton of EKF algorthm nto Thevenn equvalent crcut model can realze relatvely hgh SOC estmaton precson. The method also acheves a balance between amount of computaton and precson. In addton, ths paper also confrms that the accurate estmaton of nternal resstance has a drect bearng on the mprovement of SOC estmaton precson, and ntal values only exert nfluence at the ntal stage, whch effectvely overcome the defcences facng Ampere-Hour ntegral. References [1] Rujn Nan, Fengchun Sun, Janqun Wang, Electrc Vehcle Battery Management System[J], Journal of Tsnghua Unversty (Natural Scence), 2007, 47(S2): [2] Wenhua Huang, Xaodong Han, Qaunsh Chen, ect., A Study on SOC Estamton Algorthm and Battery Management System for Electrc Vehcle[J], Automotve Engneerng, 2007, 29(3): [3] Xaosong Hu, Module dentfcaton, optmzaton and state estmaton of L on Battery for Electrc Vehcle[D], Bejng: Bejng Insttute of Technology, [4] Zhe L, Languang Lu, Mnggao Ouyang, Comparson of Methods for Improvng SOC Estmaton Accuracy through an Ampere-hour Approach[J], Journal of Tsnghua Unversty (Natural Scence), 2010, 50(8): [5] Chengtao Ln, Junpng Wang, Quansh Chn, Methods for state of charge estmaton of EV batteres and ther applcaton[j], Battery, 2004,34(5): [6] Wenyao Song, Ya Zhang, Juchun Zhang, Kalman Flterng [M]. Bejng: Scence Press, 1991.