Comparison between RLS-GA and RLS- PSO For Li-ion battery SOC and SOH estimation: a simulation study

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1 Comparson between RLS-GA and RLS- PSO For L-on battery SOC and SOH estmaton: a smulaton study Rozaq, L, Rjanto, E & Kanarachos, S Publshed PDF deposted n Coventry Unversty s Repostory Orgnal ctaton: Rozaq, L, Rjanto, E & Kanarachos, S 2017, 'Comparson between RLS-GA and RLS- PSO For L-on battery SOC and SOH estmaton: a smulaton study' Journal of Mechatroncs, Electrcal Power, and Vehcular Technology, vol 8, no. 1, pp DOI /j.mev.2017.v ISSN ESSN Publsher: Elsever Ths s an open access artcle under the CC BY-NC-SA lcense( Copyrght and Moral Rghts are retaned by the author(s) and/ or other copyrght owners. A copy can be downloaded for personal non-commercal research or study, wthout pror permsson or charge. Ths tem cannot be reproduced or quoted extensvely from wthout frst obtanng permsson n wrtng from the copyrght holder(s). The content must not be changed n any way or sold commercally n any format or medum wthout the formal permsson of the copyrght holders.

2 Journal of Mechatroncs, Electrcal Power, and Vehcular Technology 8 (2017) Journal of Mechatroncs, Electrcal Power, and Vehcular Technology e-issn: p-issn: Comparson between RLS-GA and RLS-PSO for L-on battery SOC and SOH estmaton: A smulaton study Latf Rozaq a, *, Estko Rjanto a, Strats Kanarachos b a Research Center for Electrcal Power and Mechatroncs, Indonesan Insttute of Scences (LIPI) Kampus LIPI, Jalan Sangkurang, Gd.20, Bandung 40135, Indonesa b Centre for Moblty & Transport, Coventry Unversty Prory Street, Coventry, CV1 5FB, Unted Kngdom Receved 22 March 2017; receved n revsed form 31 May 2017; accepted 03 July 2017 Publshed onlne 31 July 2017 Abstract Ths paper proposes a new method of concurrent SOC and SOH estmaton usng a combnaton of recursve least square (RLS) algorthm and partcle swarm optmzaton (PSO). The RLS algorthm s equpped wth multple fxed forgettng factors (MFFF) whch are optmzed by PSO. The performance of the hybrd RLS-PSO s compared wth the smlar RLS whch s optmzed by sngle objectve genetc algorthms (SOGA) as well as mult-objectves genetc algorthm (MOGA). Open crcut voltage (OCV) s treated as a parameter to be estmated at the same tme wth nternal resstance. Urban Dynamometer Drvng Schedule (UDDS) s used as the nput data. Smulaton results show that the hybrd RLS-PSO algorthm provdes lttle better performance than the hybrd RLS-SOGA algorthm n terms of mean square error (MSE) and a number of teraton. On the other hand, MOGA provdes Pareto front contanng optmum solutons where a specfc soluton can be selected to have OCV MSE performance as good as PSO Research Centre for Electrcal Power and Mechatroncs - Indonesan Insttute of Scences. Ths s an open access artcle under the CC BY-NC-SA lcense ( Keywords: L-Ion; battery; state of charge (SOC); state of health (SOH); recursve least square (RLS); partcle swarm optmzaton (PSO); genetc algorthm (GA) I. Introducton Battery states of charge (SOC) and state of health (SOH) have to be estmated properly n order to buld a good battery management system (BMS) for electrc vehcles. It s known that Lthum battery has tme varyng nonlnear dynamcs where the speed of parameter values change s dfferent on each parameter. There have been many SOC estmaton methods proposed by other researchers. A mxed coulombcountng and model-based algorthm was proposed for SOC estmaton of LFePO 4 battery [1, 2, 3]. Current and termnal voltages are measured, and an ntegral feedback controller s used to compensate termnal voltage and SOC estmaton errors. A PI observer was proposed for SOC estmaton of L-Ion battery where * Correspondng Author. Tel: E-mal address: latefrozaqe@gmal.com the SOC and polarzaton voltage are used as state varables [4]. More robust and advanced methods such as Kalman flter [5, 6] and Sldng Mode Observer [7] have also been used. However, the above methods assumed that the battery parameter values are constant or constant at some specfed regon, and treated the parameter values varance as a dsturbance. A deeper nvestgaton s requred to evaluate the stablty and estmaton performance when the parameter values vary largely. Recursve Least Square (RLS) has also been appled for battery SOC estmaton. It was appled to a sngle RC Thevenn model of Lthum-Ion battery whose open crcut voltage (OCV) was depcted by Nernst equaton [8]. It was appled to a double polarzaton RC Thevenn model of a LFePO 4 battery of whch the SOC s estmated by onlne dentfcaton of OCV and the predetermned OCV-SOC look up table [9]. Movng wndow least square (MWLS) method was developed and appled to sngle RC do: / Research Centre for Electrcal Power and Mechatroncs - Indonesan Insttute of Scences (RCEPM LIPI). Ths s an open access artcle under the CC BY-NC-SA lcense ( Accredtaton Number: (LIPI) 633/AU/P2MI-LIPI/03/2015 and (RISTEKDIKTI) 1/E/KPT/2015.

3 L. Rozaq et al. / Journal of Mechatroncs, Electrcal Power, and Vehcular Technology 8 (2017) Thevenn models of L-Ion and L-Polymer batteres [10]. The SOC and battery parameters are coestmated usng a combnaton of MWLS and lnear observer. All the above RLS based SOC estmaton methods use sngle forgettng factor. RLS wth multple fxed forgettng factors (MFFF) has been used to estmate SOC of a L-Ion battery. The forgettng factors were optmzed usng Genetc Algorthm (GA), and t was proved that the algorthm provded better performance than RLS wth sngle forgettng factor [11]. An nterestng result has been reported on the estmaton of battery SOH usng RLS wthout forgettng factor. Estmaton speed and relablty have been compared between nternal ohmc resstance based estmaton and capacty based estmaton. It can be concluded that SOH estmaton based on nternal resstance s faster and more relable [12]. Many researchers have used PSO algorthm for estmatng battery SOC n dfferent ways. Support Vector Regresson (SVR) was used to estmate SOC of a Lead-acd battery n whch hyperparameters of the SVR are determned usng PSO [13]. A hybrd model whch combned multvarate adaptve regresson splnes (MARS) and PSO was used to estmate SOC of a LFeMnPO 4 battery cell. PSO was used to fnd the optmal parameters of the MARS model. As a result, SOC s represented by 29 pars of bass functons and ther coeffcents [14]. Stepwse method consderng multcollnearty was used to predct battery SOC. PSO was used to fnd optmum coeffcent values, and the SOC can be expressed usng 9 varables [15]. Some methods for concurrent estmaton of battery SOC and SOH have been proposed. Dual Kalman Flter (DKF) was used for adaptve state and parameter estmaton of Lthum-Ion batteres. Dffuson voltage, state of charge, and nternal resstance are selected as state varables, whle cell capacty, dffuson resstance, and dffuson capactance are chosen as parameters. One Kalman flter s used for state estmaton and the other Kalman flter s used for parameter values [16]. A hybrd battery model was proposed whch conssts of an enhanced Coulomb countng algorthm and an electrcal crcut model. The Coulomb countng algorthm s used for SOC estmaton whle the electrcal crcut model s used for electrcal mpedance estmaton. Fve parameters are used n the electrcal model those are nternal resstance, one par of resstance and capactance whch governs shortterm dynamcs, and one par of resstance and capactance whch governs long-term dynamcs. A set of nonlnear dscrete tme dynamc equatons are formulated usng battery termnal voltage and current as measured sgnals as well as sx unknown parameters. The unknown parameters nclude nternal resstance, open crcut voltage, two parameters as a functon of short-term dynamcal resstance and capactance, and two parameters as a functon of longterm dynamcal resstance and capactance. PSO s used to fnd a set of values of the unknown parameters whch mnmzes the selected ftness functon. The OCV s then used for SOC estmaton usng the enhanced Coulomb countng method [17]. The DKF nvolves extended Kalman flter for parameter dentfcaton whch adds computatonal burden. The use of PSO n the hybrd model requres executon of the PSO teraton ndependently to the SOC calculaton routne whch may rse a problem snce there s no guarantee that the stoppng crteron s fulflled n the samplng perod of SOC calculaton. An adaptve algorthm whch can estmate SOC and SOH concurrently and can work under sngle samplng tme and less computng burden s necessary. In ths paper, such requrement s answered by proposng a new algorthm named hybrd Recursve Least Square Partcle Swarm Optmzaton (RLS- PSO). RLS s equpped wth multple fxed forgettng factors whose the values are tuned by PSO. PSO s smple and nexpensve computatonal effort compared to other artfcal ntellgence (AI) methods. The PSO s used to fnd the optmum values of these forgettng factors n an offlne manner usng AI to avod the tedous effort nstead of tral and error. Once optmum forgettng factor λ s obtaned, the RLS wll run onlne wth these determned optmum forgettng factor. SOC s predcted based on Open Crcut Voltage (OCV) whle SOH s predcted based on nternal resstance. Moreover, n order to evaluate the performance of hybrd RLS-PSO, a hybrd RLS-GA (Sngle objectve GA (SOGA)) whch s a more common method and had already used by the author on prevous paper s employed [11]. Furthermore, hybrd RLS wth mult-objectves GA (MOGA) s also ntroduced. In Secton II, battery dynamcal model, RLS, and problem formulaton descrbed. Secton III presents optmzaton methods to calculate values of forgettng factors usng PSO, SOGA, and MOGA. Smulaton results and dscusson are reported n Secton IV. Fnally, concluson s drawn n Secton V. II. Modelng and problem formulaton Fgure 1 shows an equvalent crcut model usng sngle RC [3]. V t and I represent the battery termnal voltage and current, respectvely. R 0 s the battery nternal resstance, R p s dffuson resstance, and C p s dffuson capactance. U d denotes the voltage drop n the dffuson resstance. By usng a conventon that the current s postve when t flows nto the battery, the dynamcs of the battery model can be expressed n the followng dscrete tme equatons. U d (k) = a 1 U d (k 1) + b 0 I(k) + b 1 I(k 1) (1) V t (k) = U d (k) + OCV(k) (2) where: R 0 = b 0 ; R p = ( b 1 a 1 b 0 ) ; C 1+a p = ( 1 T ) b 1 a 1 b 0

4 42 L. Rozaq et al. / Journal of Mechatroncs, Electrcal Power, and Vehcular Technology 8 (2017) SOC estmaton s optmzed usng performance ndex J 1, whle SOH estmaton s optmzed by performance ndex J 2 as follows. J 1 = 1 N s (OCV (k) OCV(k)) 2 N s k=1 (11) J 2 = 1 N s (R N 0 (k) R 0 (k)) 2 s k=1 (12) Termnal voltage and current are measurable, but U d (k) and OCV(k) can not be measured n real tme manner. OCV of the battery s known to be a nonlnear functon of ts SOC [8]. The nternal battery parameters are dependent on SOC and they are tme varyng n nature. Termnal voltage estmate V t(k) can be expressed n the followng lnear equaton. y k = V t(k) = θ kt x k (3) where the regressor x k and the parameter estmates θ k are gven below. x k = [U d (k 1); I(k); I(k 1); 1] θ k = [ a 1 (k); b 0 (k); b 1 (k); OCV(k)] The measured termnal voltage s assumed to follow the followng formula. y k = V t (k) = V t(k) + e k (4) The parameter estmates are calculated usng RLS wth multple fxed forgettng factors (MFFF-RLS) as follows [18, 19]. e k = y k x T k θ k 1 (5) K k = P x k 1 k λ +x T (6) kpk 1 x k P k = (1 K k x k T )P k 1 (7) L k = Fgure 1. Sngle RC equvalent crcut model 1+ P 1 x2 k 1 1k 1 λ1 1 k 1 x 2 k 1 + +P λ [ P 1k 1 x 1k 1 λ 1 P k 1 x k 1 λ ] (8) θ k = θ k 1 + L k e k (9) where subscrpt ndcates the scalar components = 1, 2... n. For the battery model addressed n ths paper n = 4. λ denotes forgettng factor. By assumng that OCV changes faster than the nternal parameters, t s reasonable to select dfferent values of forgettng factors among them. A computer scrpt code (m fle n Matlab ) has been bult to realze the MFFF-RLS algorthm accordng to the above descrpton and formulae. The followng performance ndex s used to evaluate the MFFF-RLS algorthm. J 0 = 1 N {V N t (k) V t(k)} 2 s k=1 (10) s OCV and R 0 represent true values of OCV and nternal resstance, respectvely. The problem of determnng optmum forgettng factor values s formulated as follows. Mnmze: J 1 (λ ) Mnmze: J 2 (λ ) Where: 0 < λ < 1 I(k) s generated by UDDS } (13) III. Optmzaton methods usng PSO and GA The optmzaton problem s solved usng partcle swarm optmzaton (PSO) and genetc algorthm (GA). Fgure 2 shows the block dagram of the optmzaton method proposed n ths paper. Three methods are elaborated.e. optmzaton based on PSO (method 1), optmzaton based on SOGA (method 2), and optmzaton based on MOGA (method 3). Ther results are analyzed and compared. PSO s a knd of evolutonary computaton technques whch resembles the socal behavour of fsh schoolng or brd flockng. Its basc conceptual framework was orgnally proposed n 1995 for optmzaton of contnuous nonlnear functons [20]. The term swarm was selected because t artculated well fve basc prncples of swarm ntellgence n artfcal lfe, those are the proxmty prncple, the qualty prncple, the prncple of dverse response, the prncple of stablty, and the prncple of adaptablty. It nvolves cooperaton and competton among ndvduals throughout generatons. Each ndvdual remembers the best poston whch had found, and the nformaton of the global best poston that an ndvdual had found was shared to all members. Snce then t has been experencng varous developments [21, 22]. In PSO, a partcle represents a soluton, and a swarm of partcles s referred to as populaton of solutons. Each partcle s characterzed by ts velocty and poston. Every tme a new poston s acheved the best postons and veloctes are updated. Each partcle adjusts ts velocty based on ts experences. The followng equatons are used n PSO to fnd optmum values of forgettng factors. λ 0 = λ mn + Rand(λ max λ mn ) (14) v 0 = λ 0 v k+1 t s (15) = wv k + c 1 Rand ( p λ k t s ) + c 2 Rand ( p g k λk )(16) t s λ k+1 = λ k + v k+1 t s (17)

5 L. Rozaq et al. / Journal of Mechatroncs, Electrcal Power, and Vehcular Technology 8 (2017) Fgure 2. The optmzaton method of forgettng factors values λ k and v k represent the th partcle at tme k of the postons and veloctes, respectvely. The upper and lower bounds on the postons are denoted by λ max and λ mn. Rand s a unformly dstrbuted random varable whose value s between 0 and 1. t s denotes a postve scalar. The ntal postons λ 0 and ntal veloctes v 0 are randomly generated by Equaton (14) and (15). For the next teraton, veloctes of each partcle s gven by Equaton (16). p s the best postons of each partcle over tme n current and all prevous moves. p k g s the best global postons of a certan partcle n the current swarm wth respect to a predefned ftness functon. The new search drecton ncorporates three peces of nformaton whch have each own weght factor. The frst part s current moton whch s multpled by ts nerta factor w. The second part s partcle memory nfluence whch s multpled by ts cogntve factor c 1, and the thrd part s swarmed nfluence whch s multpled by ts socal factor c 2. Poston update of each partcle s gven by Equaton (17). In order to mnmze mean square error values of open crcut voltage and nternal resstance, the followng ftness functon s used. F t = αf 1 + (1 α)f 2 (18) where F 1 = 1 N s (1 OCV(k) N s k=1 (19) OCV (k) )2 F 2 = 1 N s (1 R 0(k) N s k=1 (20) R 0 (k) )2 0 < α < 1 (21) By normalzng performance ndexes n Equaton (11) and (12), ther correspondng dmensonless ftness functons are obtaned n Equaton (19) and (20). The total ftness functon n Equaton (18) s a sum of the weghted normalzed ftness functons. Values of the weght α are lsted n Table 1. Genetc Algorthm (GA) s an evolutonary algorthm whch mtates evoluton of lvng creature. Many varants of GAs exsts dependng on evaluaton method of new chromosomes, a calculaton method usng seral or parallel processors, combnaton wth some local optmzaton algorthms (hll clmbng, etc), and other factors [23]. A computer code scrpt (m fle n Matlab ) has been bult to realze a GA accordng to the followng procedure: Frst, defne parameter values ncludng number of ntal populaton/chromosomes N p, number of genes n a chromosome s 4, boundary value of each gene (0 < λ < 1 ), and number of bts for each genotype to construct phenotype N b.second, defne probablty rate values ncludng selecton probablty rate P s, crossover probablty rate P c, and mutaton probablty rate P m. Each probablty rate s dvded nto three sets whch are generated randomly, namely small (random value from 0.1 to 0.3), medum (random value from 0.4 to 0.6), and large (random value from 0.7 to 0.9). Thus, there exst 27 sets of probablty rate values whch yeld 27 best chromosomes from 27 dfferent evolutons. Thrd, create ntal random chromosomes. Fourth, evaluate ftness of each chromosome usng ftness functon n Equaton (18), and select best ndvduals usng rankng method. Ffth, create matng pool and generate offsprngs by applyng a sngle pont crossover. Sxth, reproduce and gnore few chromosomes. Seventh, performs mutaton by bt flppng operaton randomly accordng to the mutaton probablty rate. Eltsm prncple s used to control mutaton. Fnally, back to step 4, untl termnaton crteron s acheved. Method 1 and method 2 above are used to solve the sngle objectve functon n Equaton (18). In order to solve the orgnal multple objectves optmzaton problem descrbed n the problem formulaton at the prevous secton, multple objectves GA (MOGA) s also mplemented. A fast eltst multobjectve GA known as nondomnated sortng genetc algorthm II (NSGAII) s used to solve ths problem snce ths algorthm has three advantages,.e. a fast nondomnated sortng procedure, a fast crowded dstance estmaton process, and a smple crowded comparson operator. The man loop of the NSGA II procedure s descrbed below [24]. Frst, combne parent and offsprng populaton and saved as R t. Second, execute the fast non-domnated sortng procedure aganst R t, and save the result of all non-domnated fronts of R t nto F = (F 1, F 2, ). Thrd, set ntal values of parent populaton P t+1 = 0, and generaton counter = 1. Fourth, run teraton of generaton untl the parent populaton s flled and P t+1 + F N. Execute the crowded dstance estmator n F, nclude -th nondomnated front n the parent populaton, then check the next front for ncluson = + 1. Ffth, sort F n Table 1. Weght of fness functon No α

6 44 L. Rozaq et al. / Journal of Mechatroncs, Electrcal Power, and Vehcular Technology 8 (2017) descendng order usng the crowded comparson operator. Sxth, choose the frst (N P t+1 ) elements of F and nclude them nto the parent populaton. Seventh, use selecton, crossover, and mutaton to create offsprng Q t+1. Fnally, ncrement the generaton counter t = t + 1. More detals about the algorthm can be seen n [24]. IV. Results and dscusson In order to valdate the proposed method, computer smulaton has been conducted. The swarm sze n PSO and ntal populaton n GA s set to 64. The populaton sze s chosen based on the crossover operaton n GA, t s easer to choose a 2 n number. Larger n needs more calculaton tme each teraton but yelds smaller number of generaton. Based on ths consderaton we choose n=6. For the sake of equalty and comparablty, the swarm sze n PSO s chosen the same number. The optmzaton s executed teratvely untl a termnaton crteron s acheved. Ftness functon tolerance s set to 10e -6 whle stall teraton s set to 50. For method 1, the cogntve factor and socal factor are set c 1 = 1.49 and c 2 = In order to mantan the speed of convergence whle avodng local optma, the nerta factor s changed lnearly wth teraton counter k as follows. w = w (w w f ) k (22) N In ths smulaton, parameter values related to nerta factors are set as follows: w = 1.1, w f = 0.1, and N = 50. Fgure 3 shows trajectores of ftness functon F t as a functon of generaton for 9 dfferent weght values n Table 1. Fgure 3(a) plots the results of method 1 whle Fgure 3(b) those of method 2. In method 2, every sngle weght produces 27 sets of solutons accordng to the values of selecton, crossover, and (a) (b) Fgure 3. Trajectores of ftness functon F t ; (a) PSO; (b) SOGA

7 L. Rozaq et al. / Journal of Mechatroncs, Electrcal Power, and Vehcular Technology 8 (2017) mutaton probablty rates. The best soluton s selected among 27 choces. Therefore, n Fgure 3(b) we have 9 curves of the best-selected solutons. It s obvous that the value of weght affects the ftness functon value sgnfcantly. The best result of method 1 and method 2 n Fgure 3 are plotted together n Fgure 4. From Fgure 4, some mportant results can be summarzed as follows: Frst, the SOGA and PSO provde smlar performance ndex values at the end of generaton (after 52 teratons). Second, at the 3 rd and 4 th generaton, SOGA provdes better performance than PSO. Thrd, the 5 th generaton, SOGA and PSO provde smlar performance. Fourth, at the 6 th generaton, PSO gves better performance than SOGA, and ths condton remans untl the 43 rd generaton. Durng ths condton, the performance dfference s around 10-8 ths mples that PSO provdes better performance than SOGA n terms of less generaton number. Dependng on the engneerng problem solved, a performance dfference of 10-8 may be consdered as substantally small, so that one may argue that SOGA and PSO have the same capablty for solvng optmzaton problem such as ths paper. However, n ths paper, the cogntve and socal factor values of PSO are fxed. Investgaton of the mpact of dfferent cogntve and socal factor on the performance s left for further study. Fgure 5 shows the Pareto front obtaned by NSGA II. From ths result, t can be seen that NSGA II provdes several optmal solutons of the orgnal mult-objectves optmzaton problem stated n Equaton (13). In other words, ths mples that NSGA II leaves the fnal decson to us to select a soluton. In ths paper, a soluton s selected whch gves the smlar performance of ftness functons F 1 and F 2 from PSO and SOGA above. Thus, F 1 = e 6 and F 2 = e 6. In respect to the tme consumed or a number of generaton durng teraton, the followng results are obtaned: Frst, PSO requres a smaller number of generaton to yelds better MSE performance than Table 2. Forgettng factors obtaned through optmzaton Method λ 1 λ 2 λ 3 λ 4 PSO SOGA NSGA II Table 3. Performance ndex value No Performance Index Values PSO SOGA NSGAII 1 J e e e-08 2 J e e e-05 3 J e e e-10 SOGA. Second, MOGA requres much longer tme than PSO and SOGA because t computes Pareto front contanng several numbers of optmum solutons. Table 2 lsts up the forgettng factors obtaned by PSO, SOGA, and NSGA II. These forgettng factors are used together wth MFFF-RLS to estmate battery termnal voltage, OCV, SOC, and nternal resstance R 0. Fgure 6 shows battery termnal voltage and ts estmaton error durng the UDDS testng usng the forgettng factors n Table 2. Red lne s the results of PSO, the blue lne s the results of SOGA, and the green lne s the results of NSGA II. Fgure 7 shows the correspondng OCV whle Fgure 8 shows the correspondng SOC and ts estmaton error. Fgure 9 shows tme hstory of nternal resstance estmate R 0(k) and ts error er 0(k) = R 0 (k) R 0(k). Table 3 lsts performance ndex values obtaned from these results. As expected PSO, SOGA and NSGA II gve smlar performances n terms of mean square error. However, PSO and MOGA provde a lttle better performance than SOGA n terms of OCV MSE value. Fgure 4. The best performance ndex F t of PSO and SOGA

8 46 L. Rozaq et al. / Journal of Mechatroncs, Electrcal Power, and Vehcular Technology 8 (2017) Fgure 5. Pareto front of NSGA II (a) (b) Fgure 6. Trackng performance of varous methods; (a) Termnal voltage; (b) estmaton error

9 L. Rozaq et al. / Journal of Mechatroncs, Electrcal Power, and Vehcular Technology 8 (2017) Fgure 7. Open crcut voltage (a) (b) Fgure 8. Trackng performance of varous methods; (a) Tme hstory of state of charge; (b) SoC error

10 48 L. Rozaq et al. / Journal of Mechatroncs, Electrcal Power, and Vehcular Technology 8 (2017) (a) (b) Fgure 9. Trackng performance of varous methods (a) Internal resstance; (b) Error n nternal resstance V. Conclusons From the computer smulaton results, the followng concluson can be drawn. By selectng proper probablty rates of selecton, crossover, and mutaton, SOGA was able to produce almost smlar performance wth PSO n terms of MSE. Consderng the number of generaton, PSO provdes better performance than SOGA n terms of less generaton number. MOGA provdes Pareto fronts contanng optmum solutons where a specfc soluton can be selected to have MSE performance as good as PSO. However, the MOGA requres much longer tme than PSO and SOGA because t computes Pareto fronts contanng several numbers of optmum solutons. Acknowledgement The authors thank to the Indonesan Insttute of Scences (LIPI) for provdng fnancal support n the scheme of excellent research programme wth the contract number /D3/PG/2016 of the fnancal year of They also delver grattude to the Mnstry of Scence, Technology, and Hgher Educaton of the Republc of Indonesa n provdng fnancal support for conductng ndvdualzed mmerson programme at Centre for Moblty & Transport, Coventry Unversty, Unted Kngdom n References [1] F. Codeca et al., "On battery state of charge estmaton: A new mxed algorthm," n Proc. IEEE Int. Conf. Control Appl., pp , [2] F. Codeca et al., "The mx estmaton algorthm for battery State-of-Charge estmator Analyss of the senstvty to measurement errors," pp , [3] A. Nugroho et al., "Battery state of charge estmaton by usng a combnaton of Coulomb Countng and dynamc model wth adjusted gan," n Internatonal Conference on Sustanable Energy Engneerng and Applcaton (ICSEEA), pp.54-58, [4] J. Xu et al., "The state of charge estmaton of lthum-on batteres based on a proportonal-ntegral observer," IEEE Trans. Veh. Technol., vol. 63, no. 4, pp , [5] R. Xong et al., "A robust state-of-charge estmator for multple types of lthum-on batteres usng adaptve extended Kalman flter," J. Power Sources, vol. 243, pp , [6] D. L et al., "State of charge estmaton for LMn2O4 power battery based on strong trackng sgma pont Kalman flter," J. Power Sources, vol. 279, pp , [7] X. Chen et al., "A novel approach for state of charge estmaton based on adaptve swtchng gan sldng mode observer n electrc vehcles," J. Power Sources, vol. 246, p , [8] X. Hu et al., "Onlne Estmaton of an Electrc Vehcle Lthum-Ion Battery Usng Recursve Least Squares wth Forgettng," [9] H. He et al., "Onlne model-based estmaton of state-ofcharge and open-crcut voltage of lthum-on batteres n electrc vehcles," Energy, vol. 39, no. 1, p , [10] H. R. Ech and M. Chow, "Adaptve parameter dentfcaton and State-of-Charge estmaton of lthum-on batteres,"

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