Estimation of state-of-charge of Li-ion batteries in EV using the genetic particle filter

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1 IOP Coferece Seres: Earth ad Evrometal Scece PAPER OPEN ACCESS Estmato of state-of-charge of L-o batteres EV usg the geetc partcle flter To cte ths artcle: Ju B et al 207 IOP Cof. Ser.: Earth Evro. Sc Vew the artcle ole for updates ad ehacemets. Ths cotet was dowloaded from IP address o 6/0/208 at 2:26

2 IOP Publshg IOP Cof. Seres: Earth ad Evrometal Scece (207) 0283 do :0.088/755-35/8//0283 Estmato of state-of-charge of L-o batteres EV usg the geetc partcle flter Ju B, 2, Hag Gao2, Yogxg Wag2, Xaome Zhao2.Bejg Jaotog Uversty, Weha 2.School of Traffc ad Trasportato, Bejg Jaotog Uversty Abstract: Estmatg the state of charge (SOC) of electrc vehcle (EV) batteres accurately ad tmely s of great sgfcace to the safe trp of pure EV. Based o the olear propertes of the battery, ad the stadard partcle flter (PF) has certa adaptablty for ths feature, so t ca be used to accurately estmate the SOC of the batteres. However, the stadard PF has partcle degeeracy pheomeo, whch wll mae the accuracy of predcto lower. Therefore, ths paper, the geetc algorthm s appled to the stadard PF, ad the estmato of SOC s optmzed, whch maes the mproved flter algorthm more accurate. Based o the measured data of Bejg pure electrc satato vehcle, a expermet s defed to verfy the algorthm. The expermetal results show that the geetc partcle flter (GPF) ca crease the dversty of partcles ad has better predcto accuracy ad tmeless tha the PF. Itroducto Pure EV s the future developmet drecto of automoble. However, power batteres are the oly source of pure EV eergy, order to mae better use of power battery ad prolog ts lfe, t s ecessary to accurately estmate the most mportat parameter SOC EV battery maagemet system. SOC s the rato of the curret battery remag power to the rated capacty of the battery, whch ca t be measured drectly. It ca be estmated merely by parameters of the batteres, such as voltage, resstace, curret ad temperature. At preset, estmatg methods of SOC are dscharge test, ope-crcut voltage, the Amper-Hour tegral, eural etwor, Calma flterg etc. I these methods, the dscharge test s ot sutable for applcato [0]; Amper-Hour tegral requres hgh curret accuracy [5]; ope-crcut voltage ca oly be used a stable state of the voltage, the actual measuremet s ot coveet [6, 8]; eural etwor uses a large umber of referece data for trag, the error the applcato s affected by the trag data ad methods [2]; Calma flterg explots the mea ad varace to characterze the state probablty dstrbuto, however, whch ca t guaratee the estmated accuracy for olear ad o Gauss dstrbuted state models [3, 4]. Tradtoal PF ca deal wth olear problems well, whch s applcable to the olear stochastc system represeted by varous state space models ad effectvely mproves the effect of optmal estmato [7]. But, PF has partcle degradato pheomea ad affects the predcto precso. Therefore, ths paper attempts to apply the prcple of geetc algorthm to the PF. Usg the uque optmzato ablty of geetc algorthm to optmze the resamplg process, ad the mprove the utlzato of partcles to esure that the algorthm has a hgher accuracy. Ths paper s orgazed as follows. Secto 2 proposes the battery model. Secto 3 shows the descrpto of GPF. Secto 4 carres out expermets ad compares the results. Fally, Secto 5 gves some coclusos. Cotet from ths wor may be used uder the terms of the Creatve Commos Attrbuto 3.0 lcece. Ay further dstrbuto of ths wor must mata attrbuto to the author(s) ad the ttle of the wor, joural ctato ad DOI. Publshed uder lcece by IOP Publshg Ltd

3 IOP Publshg IOP Cof. Seres: Earth ad Evrometal Scece (207) 0283 do :0.088/755-35/8// Battery Modelg State space model s the basc of GPF. The State space model cossts of the state equato ad observato equato. 2. State equato The state equato s determed by the SOC defto the paper. I geeral, the expresso of SOC uses Amper-Hour tegral method, the specfc calculato formula: t ( ) SOC( t) SOC0 d( ) 0 C () Where, SOC(t) s the value of SOC at tme t, SOC 0 s the tal value of SOC, (t) s the stataeous curret at tme t ( (t)> 0 for dscharge, (t)< 0 for charge). C s the rated capacty, s the Columbc effcecy ( = for dscharge ad for charge). The state equato s derved as Eq.(2): V x x t C Where, x s the value of SOC at tme, s the stataeous curret at tme, Dt s the samplg terval. 2.2 Observato equato The paper selects the smplfed electrochemcal model [4] applyg to L-o battery as the observato equato whch s a aalytcal model ad easy to estmate voltage or SOC x (2) y R x l x l x (3) Where, y s the battery termal voltage at tme, R s the battery resstace ad 0,, 2, 3, 4 are a set of parameters to ft. Above all, the structure of battery model cosstg of Eq. (2) ad Eq. (3) s overall descrbed Eq. (4). V t x x w C (4) y 0 R 2x+ 3l x 4 l x v x The model has the advatages of smple operato, small computato, easy to be realzed the mcro cotroller, ad easy to detfy the parameters of the model. As log as N battery data obtaed, t ca be obtaed by the least squares detfcato model parameters. 3 Geetc Partcle Flter 3. The ratoale for geetc partcle flter Compared wth PF ad geetc algorthm, ther smlartes are as follows: frstly, both algorthms have a talzed group, ad each dvdual the populato represets a feasble soluto of the system; secodly, each dvdual chages accordg to certa crtera ad copy the dvdual wth hgh ftess. Therefore, ths paper attempts to apply the adaptve geetc algorthm to the PF, ad use the geetc algorthm to optmze the tradtoal resamplg process, so as to acheve the purpose of 2

4 IOP Publshg IOP Cof. Seres: Earth ad Evrometal Scece (207) 0283 do :0.088/755-35/8//0283 hbtg partcle degradato ad creasg partcle dversty. I ths algorthm, we cosder the partcle swarm as a group, each partcle s regarded as a chromosome, the mportace of the weght of the partcles as a persoal ftess value. The uque search ablty of the geetc algorthm greatly mproves the utlzato of the partcles, so that the umber of partcles requred to approxmate the true posteror probablty desty fucto s greatly decreased, whch ot oly reduces the computatoal complexty of the algorthm, but also mproves the algorthm real-tme. 3.2 The steps of geetc partcle flter Step: Italzato Step2: Partcle Sample Sample from the tal probablty desty fucto ad yeld a set of partcles cotag N partcles wth a tal weght of /N [] for each partcle. Step3: Predctg Use the Eq. (2) to predct the value of x { =,2, N}. Step4: Weght update Usg Eq. (5), the weght (w ) s computed. The ormalzato of weght w s calculated accordg to Eq. (6). w 2 ( y y) 2 2s e (5) 2 ps w w N w Step5: Resamplg Accordg to the Eq. (7) to determe whether the partcles eed to geetc resamplg. If yes, go to Step6. If ot, go to Step0. N 2 eff / ( ) threshold (6) N x N (7) Step6: Crossover ad mutato The weght (w ) s tae as the ftess of the dvdual. f = w { =,2,, N} Accordg to adaptve geetc algorthm [9], the correspodg crossover probablty (p c ) ad mutato probablty (p m ) are calculated by Eq. (8) ad Eq. (9). p p c m p ( fmax fc ) fc f fmax favg p3 fc f p2( fmax fm) fm f fmax favg p4 fm f avg avg avg avg (8) (9) 3

5 IOP Publshg IOP Cof. Seres: Earth ad Evrometal Scece (207) 0283 do :0.088/755-35/8//0283 Where f max s the maxmum ftess value of the dvdual, f c s the larger ftess value the two tersectg dvduals, f m s the ftess value of the varat dvdual, ad f avg s the average of the dvdual ftess the populato. Usg Eq. (0) ad Eq. () to perform the crossover ad mutato operatos. ' j ( x ) x ( ) x j ' j ( x ) x ( ) x (0) ' ( x ) t g G x r ( N x ) p 0.5 t g G x r ( x M ) p 0.5 Where β s a radom umber evely dstrbuted over tervals 0 to, to be crossed, ad ' j ' ( x),( x) () x, x are the ew partcles that are produced after crossg. j are the two partcles Step7: Determe whether the evoluto of algebra has reached. If yes, go to Step8, or bac to Step6. Step8: Partcle optmzato The roulette method s used to optmze the partcle to obta a ew set {(x, w j ),=,,N} of partcles. Step9: State estmato The estmated state s gve as N x w x (2) Step0: Determe whether the algorthm s over. If t s out of the algorthm, otherwse, bac to Step3. 4 Expermetal Results Of Soc Estmato I ths expermet, the dscharge data of two dfferet perods of the same satato electrc vehcle was collected from 8:3 am to 0:2 am o May 9, 204 ad from 4:23 pm to 6:30 pm o May 20, 204.The partcles are ecoded usg real umbers, ad the parameters requred for the expermet are show Table. The formula of the weght of the partcle s used as the ftess fucto. The parameters of the battery model are detfed by the recursve least squares method of forgettg factor. The put ad output data of the model are the measured data of the pure electrc satato vehcle. The battery model parameters are show Table 2. Table : Crossover ad mutato probablty calculato formula parameter values. N represets the populato sze. N p p 2 p 3 p Table 2: The fal estmated parameter values P

6 IOP Publshg IOP Cof. Seres: Earth ad Evrometal Scece (207) 0283 do :0.088/755-35/8//0283 The process ose ad measuremet ose are subject to the ormal dstrbuto of Q = ad P = 5, respectvely. The varace of the measured ose s R = 5. Accordg to the specfc steps of the GPF ad PF, through the Matlab software to acheve the estmato process of the SOC, after repeated debuggg ad rug, the fal predcto results ad error curves are as follows: PF Ture SOC(%) Tme(m) Fgure.: The results of SOC estmato based o PF (May 9th) GPF Ture SOC(%) Tme(m) Fgure.2: The results of SOC estmato based o GPF (May 9th) 5

7 IOP Publshg IOP Cof. Seres: Earth ad Evrometal Scece (207) 0283 do :0.088/755-35/8// PF Ture SOC(%) Tme(m) Fgure 2.: The results of SOC estmato based o PF (May 20th) GPF Ture SOC(%) Tme(m) Fgure 2.2: The results of SOC estmato based o GPF (May 20th) Based o the above expermetal data, ths paper uses the root-mea-square error (RMSE) ad root-mea-square-relatve error (RMSRE) to further evaluate the estmato results. The mathematcal expressos are as follows. RMSE ( y y) 2 (3) RMSRE y y ( ) y 2 (4) I the above equato, y s the true value ad y s the predcted value. Table 3 ad table 4 show the results of the comparso. Table 3: Partcle flter performace evaluato Idex RMSE Date PF GPF May 9th

8 IOP Publshg IOP Cof. Seres: Earth ad Evrometal Scece (207) 0283 do :0.088/755-35/8//0283 May 20th Table 4: Partcle flter performace evaluato Idex RMSRE Date PF GPF May 9th May 20th The expermetal results show that the SOC estmato curve of the GPF s closer to the real curve tha the PF. A further comparso shows that the RMSE ad RMSRE of the GPF are reduced by about 40% relatve to the stadard PF. Therefore, the GPF s more effectve tha the PF the estmato of the SOC of the electrc vehcle batteres. 5 Cocluso I ths paper, a ew PF optmzato method, the geetc partcle flter, s proposed to predct the SOC of the batteres, whch effectvely suppresses the degradato of partcles the stadard PF. The statstcal results of the battery dscharge expermet based o the data of the actual operato of EV show that the geetc partcle flter ca effectvely crease the dversty of the partcles ad ow hgher accuracy of the predcto tha the stadard PF, ad has better SOC estmated characterstcs. Acowledgemets Ths research s supported by Key research ad developmet project of Shadog Provce (206GGX05004). Refereces [] Arulampalam, M. S., S. Masell, & N. Gordo (2002). A tutoral o partcle flters for ole olear/o-gaussa Bayesa tracg. IEEE Tras. SgalProcess. 50 (2), [2] Charhgard, M. & M.Farroh (200). State-of-Charge Estmato for Lthum-Io Batteres Usg Neural Networs ad EKF. J. IEEE Trasactos o Idustral Electrocs. 57(2), [3] Daum, F. E. (2005). Nolear flters: beyod the Kalma flter. Aerosp. Electro. Syst. Mag. 20 (8), [4] Plett, G. L. (2004). Exteded Kalma flterg for battery maagemet systems of LPB-based HEV battery pacs: Part 3. State ad parameter estmato. J. Power Sources. 34 (2), [5] Pop, V., Bergveld, H. J. & P. H. Notte (2009). Accuracy aalyss of the State-of-Charge ad remag ru-tme determato for lthum-o batteres. J. Measuremet. 42(8),3-38. [6] Roscher, M.A. & D.U. Sauer (20). Dyamc electrc behavor ad ope crcut voltage modelg of LFePO4-based lthum o secodary batteres. J. PowerSources. 96 (), [7] Schwu, S., N. Armbruster, & S.Straub (203). Partcle flter for state of charge ad state of health estmato for lthum ro phosphate batteres. J. Joural of Power Sources. 203, 239: [8] Shr, Irya (2006). Battery ope-crcut voltage estmato by a method of statstcal aalyss. J. Power Sources. 59 (2), [9] Srvas, M. & L.M. Pata (994). Adaptve Probabltes of Crossover ad Mutato Geetc Algorthm. J. IEEE Tras. o Systems, Ma ad Cybemetcs. 24(4), [0] ZHAO, X. C., L. ZHANG, & W. X. HUANG (2006). Study o relato betwee the capacty ad dyamc resstace of aeral storage battery by dyamc electroc load. J. Chese joural of power source. 30(2),