Available olie at www.sciecedirect.com ScieceDirect Eergy Procedia 88 (6 ) 69 66 CUE5-Applied Eergy Symposium ad Summit 5: Low carbo cities ad urba eergy systems A Slidig Mode Observer SOC Estimatio Method Based o Parameter Adaptive Battery Model Bo Nig, Ju Xu*, Biggag Cao, Bi Wag, Guagca Xu State Key Laboratory for Maufacturig Systems Egieerig, School of Mechaical Egieerig, Xi a Jiaotog Uiversity, Xi a 749Chia Abstract Errors of a battery model will dramatically elarge as the iteral parameters of a battery varyig. To reduce the systematic errors, a parameter adaptive battery model is proposed. Based o it, slidig mode algorithm is adopted to estimate the SOC of a battery. The experimetal platform is costructed ad the UDDS drivig cycles is used to verify the method. The results show the error of SOC estimatio is less tha % ad it idicates the moitorig algorithm is of great value to power batteries which are geerally used i variable eviromet. 6 5 The The Authors. Published by Elsevier by Elsevier Ltd. This Ltd. is a ope access article uder the CC BY-NC-ND licese (http://creativecommos.org/liceses/by-c-d/4./). Selectio ad/or peer-review uder resposibility of CUE Peer-review uder resposibility of the orgaizig committee of CUE 5 Keywords: battery model; parameter adaptive battery model; slidig mode observer; SOC estimatio Nomeclature E V V z R R C C Ope Circuit Voltage Termial Voltage Polarizatio Voltage SOC Ohm Resistace Polarizatio Resistace Polarizatio Capacitor Nomial Battery Capacity * Ju Xu. Tel.: +86-9-8668835; fax: +86-9-8668835. E-mail address: xuju8@gmail.com. 876-6 6 The Authors. Published by Elsevier Ltd. This is a ope access article uder the CC BY-NC-ND licese (http://creativecommos.org/liceses/by-c-d/4./). Peer-review uder resposibility of the orgaizig committee of CUE 5 doi:.6/j.egypro.6.6.88
6 Bo Nig et al. / Eergy Procedia 88 ( 6 ) 69 66 i i V e Z Noise Feedback Coefficiet e The Observable Error of Termial Voltage V The Observable Error of SOC e The Observable Error of Polarizatio Voltage. Itroductio Battery maagemet system (BMS) is oe of the most importat parts of a electric vehicle. As the core of BMS, state of charge (SOC) estimatio has a extremely cosiderable effect o safety, dyamic ad ecoomy of the electric vehicles. If a accurate SOC ca be obtaied, the SOC rage ca be used of batteries could be exteded[]. Thus, a smaller battery pack will be able to satisfy the demad of electric vehicles. It meas the price for buildig low-carbo cities by improvig the market peetratio of electric vehicles could be dramatically decreased. The precisio of SOC estimatio rely o the accuracy of the battery model[]. Curretly, static battery models are geerally adopted i implemet, such as Rit RC[] Thevei[3] PNGV[4] ad oliear equivalet circuit model[5]. However, static battery models iitialized i laboratory are uable to adapt variable actual usig eviromet[6]. Though may robust SOC observer have bee built to reduce the egative impacts, such as slidig mode observer[7], proportioal itegral observer[8] ad exteded Kalma filter observer[9], the model systemic error led from the variatio of iteral parameters is hard to be elimiated. Thus, keepig the coherece of a battery model ad its actual characteristics uder actual usig eviromet becomes the key poit to esure the accuracy of SOC estimatio. It meas dyamic battery models are eeded to adapt the chage of iteral parameters of a battery. Plett proposed a dual exteded Kalma filter method[] ad Sog proposed a dual slidig mode observer to estimate SOC ad state of health (SOH) of a battery[]. However, these kids of battery models have obvious drawbacks: ) igorig the variatio of other parameters except for iteral resistace, ) igorig the trasmissio error s impacts o parameter estimatio, 3) a complex idetificatio of parameters is eeded. Thus, research o dyamic battery model ad related SOC estimatio methods are still iadequate. To solve the problems stated above, a adaptive battery model is established ad a slidig mode observer for SOC estimatio is proposed i this paper. As show i Figure, parameters estimatio, model updatig ad SOC estimatio are sychroous. Compared with previous models, advatages are obvious: ) elimiatig systemic error of battery model effectively, ) olie estimatio of parameters, 3) o eed of accurate iitial parameters, 4) trasmissio errors are avoided by idepedet parameter observer, 5) simple mathematical operatio. load. Theoretical aalysis Thermostat battery curret voltage voltage curret Parameters estimatio observer Movig average filter Adaptive battery model SOC Slidig mode Observer for SOC Fig.. Parameter adaptive battery model ad slidig mode SOC estimatio method
Bo Nig et al. / Eergy Procedia 88 ( 6 ) 69 66 6.. Equivalet circuit of a battery A simple first order RC equivalet circuit battery model is adopted for a further study i this paper. The RC model is show i Figure. It cosists of a voltage source ( E ), a resistor ( R ), ad a parallel capacitor ( C ) ad resistor ( R ). V R V R E C I V E Fig.. Oe order RC equivalet circuit battery model E is a oliear fuctio of SOC[]. The relatioship of E ad SOC could be decomposed as z by liear iterpolatio. The related parameters are listed i Table. Table. Relatioship betwee E ad SOC z -..-..-.3.3-.4.4-.5.59.46.6.73.79 3.4 3.43 3.38 3.348 3.34 z.5-.6.6-.7.7-.8.8-.9.9-.64.65.76.87.6 3.399 3.393 3.36 3.8 3.47 I Figure, the relatioship betwee polarizatio voltage ad curret ca be obtaied accordig to Kirchhoff's law V V ( RC ) I C () Termial voltage V could be writte as follow V E IR V () C is assumed to be costat i this paper. SOC ca be depicted by derivatio z I C (3).. Olie estimatio of model parameters As termial voltage varies slightly i a short period, R R C ad E are assumed to be slowly varyig parameters. The derivative of equatio () ca be rewritte by substitutig equatio () ad (4) ito itself V RI [( RR) I] ( RC ) V ( RC ) E ( RC ) T [ R ( R R) ( RC) ( RC) E ( RC)][ I I V ] (4) T T [ ][ ] 3 4 3 4 ( E, R, R, C ) [ ] is a matrix cosists of parameters uder estimatio. Defie where 3 4
6 Bo Nig et al. / Eergy Procedia 88 ( 6 ) 69 66 error e ˆ V V V, the a V observer is costructed T Vˆ ˆ ev (5) ˆ ˆ ˆ ˆ T [ 3 4][ II V ] ev If e ˆ, equatio (6) ad (7) are eeded for the covergece of the parameters lime (6) t lime (7) Defiite Lyapuov fuctio as follow t Where is a positive defiite matrix. Thus V e e e e V V e e e (8) V V T V T e [ ( ˆ e )] e ( ˆ ) T T T T V V T T e ( ˆ ev ) e V I order to satisfy the law of Lyapuov s stability criterio, V shoule be egative defiite. Thus, a model for estimatio of parameters is costructed ˆ ˆ IV ( V) ˆ ˆ IV ( V) ˆ ˆ 3 3V( VV) ˆ ˆ 4( V V) 4 () ˆR ˆ () ˆR ˆ ˆ ˆ 3 () Ê ˆ ˆ 4 3 (3) Cˆ [( Rˆ Rˆ ) I V Eˆ ] /[( V IRˆ ) Rˆ ] (4) As battery iteral parameters vary slowly i a short period, a movig average filter is built to reduce oise of parameters for the ext step of operatio..3. Adaptive slidig mode SOC observer The cotiuous state space equatio of the battery model is established accordig to the equatio (), (),(4) V V ( RC ) E ( RC ) [ I( RR)] ( RC ) z ( V E V) ( RC ) (5) V V ( RC) I C 3 Ad it ca be updated dyamically by parameters olie (9)
Bo Nig et al. / Eergy Procedia 88 ( 6 ) 69 66 63 V V ( RC ˆ ˆ ) Eˆ ( RC ˆ ˆ ) [ I( Rˆ ˆ ˆ ˆ R)] ( RC ) z ( V ˆ ˆ E V) ( RC ) (6) V ˆ ˆ ˆ V ( RC) I C 3 State variables of the battery model are observable, because the observatio matrix is positive defiite. A state observer ca be costructed as follow Vˆ V ( RC ˆ ˆ ) Eˆ ˆ ˆ ˆ ˆ ˆ ˆ ( RC ) [ I( RR)] ( RC ) sg( ev ) zˆ ( V Eˆ Vˆ ) ( RC ˆ ) sg( e ) (7) Vˆ Vˆ ˆ ˆ ( Rˆ C) I C 3sg( ev ) Where e V ca be easily got through a voltage sesor, however e V ad ev could ot be got directly. Accordig to the law of Lyapuov s stability criterio, whe formula (9) is satisfied, the relatioship betwee e Z ad e V, e V ad e V ca be costructed sg( e ˆ ˆ Z) sg[ RCsg( ev ) ] sg( e ) sg{ ˆ ˆ ˆ V RC sg[ RCsg( ev ) ]} (8), ev sg( ev ), ev 3 (9) The a adaptive slidig mode SOC observer could be described as follow Vˆ V ( RC ˆ ˆ ) Eˆ ˆ ˆ ˆ ˆ ˆ ˆ ( RC ) [ I( RR)] ( RC ) sg( ev ) zˆ ( V Eˆ Vˆ ) ( RC ˆ ) sg[ Rˆ Cˆ sg( e ) ] V Vˆ Vˆ ( RC ˆ ˆ ) I Cˆ ˆ ˆ ˆ 3sg{ RC sg[ RC sg( ev ) ]}, ev sg( ev ), ev 3 Z () 3. Experimetal verificatio NCR865 lithium-io battery is adopted i the experimet. It has a rated voltage of 3.7V ad a cut off voltage of.8v. Urba dyamometer drivig schedule (UDDS) curret profile show i Figure 3 is used to verify the accuracy of the algorithm for olie parameter idetificatio ad SOC estimatio of the power battery. 5 UDDS Curret profile I/A -5 - -5 4 6 8 4 T/s Fig. 3. UDDS curret profile
64 Bo Nig et al. / Eergy Procedia 88 ( 6 ) 69 66 Iitializatio parameters ad feedback coefficiets ˆ () ˆ (). ˆ 3(). ˆ 4()...5 3.5 4.5. Compariso betwee curves of parameters ad actual curves filtered by slidig average filter are show i Figure 4. The referece curve is calculated ad iterpolated offlie through hybrid pulse power characterizatio (HPPC) test. I Figure 4, the curves of parameters quickly coverge to the referece curves with small fluctuatios. The they are used to dyamically update the SOC estimatio model. The termial voltage based o parameter adaptive battery model proposed before ad the actual oe are compared i Figure 5. The curves fit well, which idicates that the adaptive battery model updated olie could truly reflect the characteristics of the battery. R/Ohm..8.6 referece.4 5 5 5 3 35 4 45 5.5 (a) Ohm resistace estimatio curve R/Ohm referece -.5 5 5 5 3 35 4 45 5 9 (b) Polarizatio resistace estimatio curve C/F 8 7 6 referece 5 5 5 5 3 35 4 45 5 (c) Polarizatio capacitace estimatio curve Fig. 4. Olie parameter estimatio curves 4.6 4.4 4. actual V/v 4 3.8 3.6 3.4 4 6 8 4 Fig. 5. Termial voltage uder UDDS curret Iitialize state variable z.8 V V 4, iitialize coefficiets.5. 3.5. I order to verify the estimatio accuracy of the SOC uder ukow iitial situatio, the iitial error of SOC is set to be %. The compariso of the SOC curve ad the actual curve are show i Figure 6.
Bo Nig et al. / Eergy Procedia 88 ( 6 ) 69 66 65.8 referece SOC.6.4. 5 5 5 3 35 4 45 5 (a) SOC estimatio curve..5 SOC Error % Boud SOC Error..5 -.5 5 5 5 3 35 4 45 5 (b) SOC estimatio error curve Fig. 6. The results of the proposed method It shows that the SOC curve rises rapidly ad coverges to the actual SOC curve i 4 secods. The rapid covergece ad small overshoot reflect a great robustess of the algorithm. After 4 secods the SOC teds to be stable with few mior fluctuatios. The error of SOC estimatio is less tha % as show i Figure 6 (b). Differet iitial SOC error has a cosiderable effect o the covergece time. Uder ormal coditios, the iitial SOC error of a battery is led from self-discharge, which is geerally much lower tha %. So the covergece time should be less tha 4 secods. To apply the algorithm i implemetatio, a hardware platform icludig curret cesorsvoltage sesors ad a digital sigal processor is eeded. As the variatio of the parameters is small i a short period, the model could be updated periodically usig a multi-time dimesio method to reduce the computatio of DSP. At the begiig of the estimatio period, the parameters are ot stable, so the historical parameters are used to replace them. 4. Coclusio I this paper, a complete adaptive battery model is established based o battery parameters idetified olie to take the variatio of battery iteral characteristics uder variable eviromet ito cosideratio. Based o it, the slidig mode SOC observer is costructed to elimiate the error of the battery model ad reduce the oise of measuremet. The battery evirometal platform is built ad Lithium-io battery is adopted to verify the effectiveess of the proposed method i estimatig battery iteral parameters ad SOC uder the UDDS drivig cycles. The experimet results idicates that the olie parameters all coverged to the true value i 4 secods ad the SOC estimatio error is less tha %. Ackowledgemets
66 Bo Nig et al. / Eergy Procedia 88 ( 6 ) 69 66 This work was supported by the Natioal Natural Sciece Foudatio of Chia (Grat No. 545374) ad the Postdoctoral Sciece Foudatio of Chia (Grat No. 4M56763). Referece Wag JP, Che QS, Cao BG. Study o the chargig ad dischargig model of Ni/MH battery module for electric vehicle. Joural of Xi'a Jiaotog Uiversity 6,4(),5-5 Li C, Shag AN. Research o secod-order RC circuit model of Ni-MH battery for EV. Chiese Joural of Power Sources,35(): 95-97. Fag YQ, Cheg XM, Yi YL. SOC Estimatio of Lithium-Io Battery Packs Based o Thevei Model. Mechaical Egieerig, Idustrial Electroics ad Iformatizatio 3, 99():-5. Gao WG, Jiag M, Hou YM. Research o PNGV model parameter idetificatio of LiFePO4 Li-io battery based o FMRLS. Idustrial Electroics ad Applicatios (ICIEA). Beijig, Chia: 6th IEEE Coferece o,49():94-97. Li CT, Qiu B, Che QS. A study o oliear equivalet circuit model for battery of electric vehicle. Automotive Egieerig 6,8(): 38-4. Wag JP, Cao BG, Che QS. Self-adaptive filterig based state of charge estimatio method for electric vehicle batery Chiese Joural of Mechaical Egieerig 8, 44(5): 76-79. Che X, She W. Slidig mode observer for state of charge estimatio based o battery equivalet circuit i electric vehicles Australia Joural of Electrical & Electroic Egieerig, 5-34. Xu J, Mi CC, Cao BG. The State of Charge Estimatio of Lithium-Io Batteries Based o a Proportioal Itegral Observer Vehicular Techology, IEEE Trasactios o 4, 63(4):64-6. Plett GL. Exteded Kalma filterig for battery maagemet systems of LiPB-based HEV battery packs: Part. Backgroud. Joural of Power Sources 4, 34(): 5-6. Plett GL. Exteded Kalma filterig for battery maagemet systems of LiPB-based HEV battery packs. Part 3. State ad parameter estimatio. Joural of Power Sources 4, 34(): 77-9. IL-SONG K. A Techique for Estimatig the State of Health of Lithium Batteries Through a Dual Slidig Mode Observer. Power Electroics, IEEE Trasactios o, 5(4):3-. XU J, MI CC, CAO BG. A ew method to estimate the state of charge of lithium-io batteries based o the battery impedace model. Joural of Power Sources 3, 33(4): 77 84. 5. Author Artwork Nig Bo received the B.S. degree i mechaical egieerig from Xi a Jiaotog Uiversity,Xi a, Chia, i, where he is curretly workig toward the M.S. degree with the School of Mechaical Egieerig. From 3 to 5, he focused o the battery maagemet system for electric vehicle. His research iterests iclude desig, aalysis, testig, ad state estimatio of battery systems, icludig battery modelig ad battery state estimatio. Ju Xu received his BS ad PhD degrees i Mechaical Egieerig from Xi a Jiaotog Uiversity, Xi a, Shaaxi, Chia i 9 ad 3, respectively. He is a assistat professor at the Istitute for Electric Vehicle ad System Cotrol i Xi a Jiaotog Uiversity. His research iterests iclude battery system desig, aalysis, ad state estimatio for electric vehicles.