An efficient cell balancing method for LiFeP04 batteries based on inductors

BACHELOR PAPER Te m pape submi ed in pa ial ul illmen o he equi emen s o he deg ee o Bachelo o Science in Enginee ing a he Uni e si y o Applied Sciences Technikum Wien - Deg ee P og am: Mecha onics/Robo ics. AN EFFICIENT CELL BALANCING METHOD FOR LiFePO4 BATTERIES BASED ON INDUCTORS By: Blanco Riesco, Ángel – Deg ee in Au oma ic and Elec onic Enginee ing S uden Numbe : 693041892 Supe iso : Raue , Johannes Nikolaus, MSc Wien, 16/06/2021 Decla a ion o Au hen ici y “As au ho and c ea o o his wo k o hand, I con i m wi h my signa u e knowledge o he ele an copy igh egula ions go e ned by highe educa ion ac s (see U hebe ech sgese z/ Aus ian copy igh law as amended as well as he S a u e on S udies Ac P o isions / Examina ion Regula ions o he UAS Technikum Wien as amended). I he eby decla e ha I comple ed he p esen wo k independen ly and ha any ideas, whe he w i en by o he s o by mysel , ha e been ully sou ced and e e enced. I am awa e o any consequences I may ace on he pa o he deg ee p og am di ec o i he e should be e idence o missing au onomy and independence o e idence o any in en o audulen ly achie e a pass ma k o his wo k (see S a u e on S udies Ac P o isions / Examina ion Regula ions o he UAS Technikum Wien as amended). I u he decla e ha up o his da e I ha e no published he wo k o hand, no ha e I p esen ed i o ano he examina ion boa d in he same o simila o m. I a i m ha he e sion submi ed ma ches he e sion in he upload ool.” Wien, 17/06/2021 Place, Da e Signa u e Abs ac Nowadays, anspo a ion is li ing h ough a g ea ans o ma ion mo i a ed, among many o he easons, by he pollu ion caused by combus ion ehicles. Faced wi h his change, o he mo e enewable o ms o anspo , such as he elec ic ca , a e inc easing and being in oduced weigh y in he ma ke . Due o he g ea monopoly o he combus ion ca in ecen yea s, his ype o echnology is no ye ully de eloped and he e a e many a eas o imp o emen , especially in he plo o elec ic ba e ies. Wi hin hese de ices, mos o he s udies and e o s a e ocusing on hese wo opics: - New ma e ials o ba e y cons uc ion wi h be e chemical cha ac e is ics, such as g aphene. - New sys ems o supe iso and con ol he ba e y in a mo e e icien way, BMS (Ba e y Managemen Sys em). Cu en ly mos companies design hei BMS h ough capaci o s, which dec ease he cos and complexi y o sys em con ol, in exchange o inc easing he balancing ime. This ac educes he use ul li e o he cells. Mo i a ed by he dissa is ac ion o a ma ke ha ends o lead mobili y soon, his hesis is s udying, implemen ing, and de eloping an inno a i e cell balancing ci cui h ough induc o s. I is heo e ically ( h ough equa ions) and p ac ically ( h ough simula ions) c ea ed o simula e he beha io o an elec ic ehicle ba e y. To ob ain simula ions and esul s ha will make he indus y hink abou he possible inco po a ion o his sys em o he elec ic ehicle, wo ypes o balancing (wi h induc o s and wi h capaci o s), ha e been simula ed and compa ed in he PSIM ool in h ee di e en si ua ions .A e isualizing he g aphs o he h ee cell ol ages, he cell powe , and he o al cu en o he ci cui , i can be concluded ha wi h he induc o me hod, mo e p ecision and speed is achie ed when cha ging he induc o s. The ealiza ion o a PSIM ci cui wi h he same design bu wi h a la ge numbe o cells, as well as he in eg a ion o his h ee-cell ci cui wi h physical elemen s, is being conside ed o u u e s udies. Keywo ds: ba e ies, BMS, cell balancing, induc o s, PSIM ci cui . Table o con en s 1. In oduc ion ............................................................................................................ 1 1.1 Topic/Mo i a ion .................................................................................................. 1 1.2 P oblem/Goal ...................................................................................................... 1 1.3 S uc u e o he wo k ........................................................................................... 2 2. S a e o he A ....................................................................................................... 3 2.1 BMS (Ba e y Managemen Sys em) ................................................................... 3 2.2 Techniques used o cell balancing. ..................................................................... 4 2.2.1 Passi e me hods ........................................................................................... 4 2.2.2 Ac i e me hods ............................................................................................. 4 3. Ci cui de eloped in PSIM. ..................................................................................... 5 3.1 Solu ion Ap oach ................................................................................................. 6 3.1.1 Cells (C1,C2,C3) ........................................................................................... 7 3.1.2 Con ol ci cui ................................................................................................ 8 3.1.3 Powe supply ci cui .................................................................................... 19 4.Ci cui p og amming ................................................................................................. 20 5.Resul s and discussion ............................................................................................ 21 5.1 Case 1: Vcell1> Vcell2> Vcell3 .......................................................................... 22 5.2 Case 2: Vcell2> Vcell3> Vcell1 .......................................................................... 25 5.3 Case 3: Vcell3> Vcell 1> Vcell2 ........................................................................ 25 6. Conclusions ............................................................................................................ 26 Bibliog aphy ................................................................................................................ 27 Lis o igu es .............................................................................................................. 29 1 1. In oduc ion This sec ion will explain he eason o w i ing he hesis, he goals o be achie ed by doing i and will summa ize he o he sec ions ha make up he hesis. 1.1 Topic/Mo i a ion Nowadays, anspo a ion is li ing h ough a g ea ans o ma ion mo i a ed, among many o he easons, by he pollu ion caused by combus ion ehicles. Faced wi h his change, o he mo e enewable o ms o anspo , such as he elec ic ca , a e inc easing and being in oduced weigh y in he ma ke . Due o he g ea monopoly o he combus ion ca in ecen yea s, his ype o echnology is no ye ully de eloped and he e a e many a eas o imp o emen , especially in he plo o elec ic ba e ies. Wi hin hese de ices, mos o he s udies and e o s a e ocusing on hese wo opics: - The ma e ials o which he ba e y is composed. Disco e ing and de eloping new ma e ials, such as g aphene. Mo e o ien ed o he ield o chemical enginee ing. - Sys ems o supe ise and con ol he ba e y in a mo e e icien way, BMS (Ba e y Managemen Sys em). Cu en ly many la ge companies in his sec o we e in es ing la ge amoun s o economic esou ces o ind new sys ems ha could eplace he use o capaci o s, wi h which, al hough good esul s a e ob ained, he balancing ime is s ill high. Be ween he o he possible me hods (induc o s and ans o me s) o pe o m he balancing o cells in an elec ic ba e y. This hesis will ocus on s udy a ci cui h ough induc o s, since wi h he use o ans o me s a e y e icien balancing is pe o med, bu he p ice inc eases a lo , and i would no be p o i able o he elec ic ehicle companies. 1.2 P oblem/Goal The p esen hesis aims o demons a e h ough equa ions and simula ions hanks o he PSIM p og am ha he use o induc o s o balance he cells can p o ide he same o be e esul s han using capaci o s. This is because wi h capaci o s good balancing is ob ained, bu some imes i akes a long ime o pe o m he balancing o cells, besides when he cell ol ages ha e e y 2 simila alues i is e y di icul o une i mo e by discha ging o cha ging hem. I is belie ed ha using induc o s can achie e g ea e accu acy when balancing, and i is a opic ha we wan o s udy and demons a e. 1.3 S uc u e o he wo k This sec ion will b ie ly explain how he o he chap e s o he hesis will be dis ibu ed: S a e o he a : I will be explained: why is undamen al he use o BMS in an elec ic ehicle, he di e en echniques o pe o m he balancing (passi e and ac i e) and he wo possible ways o pe o m he balancing o cells, using induc o s. Ci cui de eloped in PSIM: In his sec ion i will be explained: how he ci cui has been de eloped in PSIM and he di e en blocks ha con o m i . In addi ion, i will be explained how he elemen s ha e been pa ame e ized, h ough a heo e ical s udy o he powe , se ling ime and sensi i i y, and he p og amming ha has been ca ied ou o pe o m he balancing. Ci cui p og amming In his sec ion we will s udy he p og amming ha has been ca ied ou o ob ain a co ec cell balancing Resul s and discussion: The ci cui will be simula ed in h ee possible si ua ions (Vcell1> Vcell2> Vcell3, Vcell2> Vcell3> Vcell1 and Vcell3> Vcell1> Vcell2) And h ough o g aphs o he cell cu en , cell ol ages... i will be demons a ed i he ci cui has been pe o med co ec ly and i i is well pa ame e ized. Conclusions: E e y hing s udied in he hesis will be compiled and i will be e i ied ha he objec i es ha we e in he sec ion "P oblem /Goal" ha e been achie ed. 3 2. S a e o he A To see he impo ance o he me hod de eloped in he hesis, we will explain he unc ions o a BMS in an elec ic ehicle, and he di e en o ms o balancing ha exis oday. 2.1 BMS (Ba e y Managemen Sys em) Be o e ocusing on he de elopmen o he ci cui , i will be explained he eason why he BMS is so impo an o he co ec ope a ion o he ba e y. Ini ially, he BMS ge eme ge like an elec onic ci cui o con ol ha he cells o hese did no go ou o hei ope a ing ange, since his could cause acciden s o e en he explosion o he ba e y. O e he yea s, his concep has been changed and cu en ly a BMS in an elec ic ehicle is a sys em whose main pu pose is s ill he sa e y o he ba e y, bu now i also akes in o ma ion and pa ame e s ha imp o e he ope a ion and e iciency o he ehicle. [1][2] As can be seen in Figu e 1, he BMS measu es pa ame e s (such as cu en , ol age, empe a u e…) o each o he ba e y cells and ansmi s his in o ma ion, h ough he CAN communica ion p o ocol, o he ehicle's cen al compu e . In his way, i o example BMS ecei es a e y high Tº alue, i will ansmi his in o ma ion o he cen al compu e which will ac i a e a an o o he cooling sys em, o y o main ain his pa ame e be ween op imal alues. [4][5] Al hough he BMS moni o s many pa ame e s such as: heal h s a us, load capaci y o discha ge capaci y, all o hem depend on a co ec balancing o he cells. Tha is why he de elopmen o he hesis will ocus on his aspec , cause s udying he cell balancing o he aspec s will be imp o ed indi ec ly. [6] Figu e 1:Func ions o he BMS in an EV [3] 4 In o de o unde s and he concep o cell balancing, a simila i y will be made wi h he ope a ion o a ho se-d awn ca iage. Le us imagine ha ou ba e y is he ca and he di e en cells ha compose i a e he ho ses, o he ca o ad ance all he ho ses mus go a he same speed, his happens in he same way in he ba e y pack, all he cells will ha e o be in he same ol age ange o he ba e y o wo k co ec ly. [7] This can be achie ed h ough di e en echniques, which will be shown below: 2.2 Techniques used o cell balancing. Depending on how his balancing is done, wo me hods can be ound: 2.2.1 Passi e me hods In hese me hods, he SOC (S a e o Cha ge) o all cells is ma ched o he cell wi h he lowes SOC, in he case o Figu e 2, o cell 1. Al hough he design and p og amming o hese me hods a e e y easy, due o he use o esis o s, much unusable ene gy is los in he o m o hea du ing balancing. [8][9] Figu e 2:Balancing wi h passi e me hods [12][13] 2.2.2 Ac i e me hods In hese me hods balancing is pe o med by ans e ing ene gy om one cell o ano he , so ha all cells ha e he same SOC alue. In his way, he balancing ime is educed by inc easing he complexi y o he sys em and i s p og amming. [10][11] 5 Figu e 3:Balancing wi h ac i e me hods [12][13] Wi hin he ac i e me hods he e a e h ee di e en me hods depending on he elemen s used o ans e ene gy: capaci o s, induc o s, and ans o me s. In his hesis we will s udy he balancing h ough induc o s, depending on he numbe o induc o s used, wo o he me hods can be di e en ia ed: 2.2.2.1 Single induc o equaliza ion ci cui Balancing is done by discha ging and cha ging only one induc o and ans e can be made be ween any o he ba e y cells. Sys em cos is inc eased due o he use o many swi ches. [14][15] 2.2.2.2 Mul iple induc o equaliza ion ci cui In his me hod, each cell is connec ed o he nex h ough an induc o and ene gy can only be ans e ed be ween wo adjacen cells. Balancing is done as e han using capaci o s and cos s less han using ans o me s, which is why we wan o implemen cell balancing in elec ic ehicles. Al hough he e a e many ad an ages o his me hod, he balancing ime becomes longe he g ea e he dis ance be ween he cells whe e he ene gy is ans e ed. This ime will be impe cep ible in he ci cui de eloped in he hesis since he e will only be h ee cells, bu i is a ac o o conside when he ba e y consis s o many cells.[16][17]. 3. Ci cui de eloped in PSIM. In his sec ion he ci cui is modelled wi h i s h ee undamen al blocks (cells, con ol ci cui and powe supply ci cui ), making he equa ions in he s a ing si ua ion, and pa ame e izing he elemen s by pe o ming: powe s udies, se ling ime and sensi i i y. In conclusion, he objec i e o his sec ion is o ob ain he mos e icien and as ci cui , o be able o model i and o ob ain conclusions abou i . 12 I is subs i u ed in o del a equa ion 11 wi h L= R√3 o see wha he smalles alue del a is will be able o ha e: 𝜕= (3𝑅2 𝑅√3+𝑅√3) 4𝑅 =√3 2 [16] Tha is, wi h his alue o L an unde damped sys em is ob ained. Be o e pe o ming any powe calcula ion, he op ion in which L= R√ 3 can be p e iously disca ded, since, being an o e damped sys em, i is always going o ha e a slowe beha io han he wo o he op ions ha a e c i ically damped. Bo h si ua ions (L=R and L=3R) will be s udied o see whe e he maxima and minima o he in ensi y a e ob ained, and how quickly hey a e eached Case L = 3R Subs i u ing in he exp ession [12] we ob ain: 𝐼𝑡(s) = 𝑉𝑐𝑒𝑙𝑙 2𝑅 𝒔+𝑉𝑐𝑒𝑙𝑙 3𝑅 +𝑉𝑐𝑒𝑙𝑙 2𝑅 𝒔𝟐+2𝒔+1 =𝑉𝑐𝑒𝑙𝑙 𝑅(𝑠2+1 3+1 2𝑠) 𝑠2+2𝑠+1 = 𝑉𝑐𝑒𝑙𝑙 𝑅(6𝑠2+4𝑠+6 12𝑠) 𝑠2+2𝑠+1 [17] Applying Laplace's in e se: 𝐼𝑡(𝑡)=𝑉𝑐𝑒𝑙𝑙 𝑅𝐿−1{𝑉𝑐𝑒𝑙𝑙 𝑅(6𝑠2+4𝑠+6 12𝑠) 𝑠2+2𝑠+1 }=𝑉𝑐𝑒𝑙𝑙 𝑅(1 2𝜕(𝑡)−2 3𝑒−𝑡𝑡) [18] To check which o all he solu ions is he op imal one, i will be analysed when he de i a i e o he inpu cu en becomes ze o, since i is an in lec ion poin in he speed o he sys em: 𝑑𝐼𝑡 (𝑡) 𝑑𝑡 =0→−2𝑉𝑐𝑒𝑙𝑙 3𝑅 (𝑒−𝑡−𝑒−𝑡)=0→𝑒−𝑡=𝑒−𝑡𝑡→𝑡=1 [19] The second de i a i e is equalled o ze o, subs i u ing he alue ob ained in he i s de i a i e ( =1): 𝑑2𝐼𝑡(𝑡) 𝑑𝑡 (𝑡=1)> 0→−2𝑉𝑐𝑒𝑙𝑙 3𝑅 (𝑡−2)𝑒−𝑡>0→2𝑉𝑐𝑒𝑙𝑙 3𝑅𝑒 >0→𝑀𝐼𝑁𝐼𝑀𝑈𝑀 [20] 13 Figu e 8: esul ing ci cui when he swi ches con olled by signal S1 a e closed, si ua ion L=3R To e i y ha wha has been sol ed heo e ically also happens in p ac ice, he ci cui will be simula ed in PSIM wi h he da a L=3R and we will see how he o al cu en beha es: 𝑹=1𝛺 L=3H C= 1/L= 1/3 F VDC=1 V In Figu e 9 one can see he I du ing he i s h ee seconds du ing he simula ion: Figu e 9:I g aph when he swi ches con olled by signal S1 a e closed, si ua ion L=3R Equa ion 18 will be s udied in wo si ua ions ( =0 and =1): I ( =0)=Vcell R(1 2∂( )−2 3e−00)=Vcell 2R =0.5A [21] I ( =1)=Vcell R(1 2∂( )−2 3e−11)=Vcell 2R −2Vcell 3R =0.2547A [22] 14 As can be seen, he esul s ob ained heo e ically coincide pe ec ly wi h he da a ob ained in he simula ion (ma ked wi h a do in he g aphs), so i can be concluded ha he simula ion o he sys em has been de eloped in a co ec way. Case L = R Subs i u ing in he exp ession [12] we ob ain: 𝐼𝑡(𝑠)=𝑉𝑐𝑒𝑙𝑙 2𝑅 𝒔+𝑉𝑐𝑒𝑙𝑙 𝑅+𝑉𝑐𝑒𝑙𝑙 2𝑅𝑠 𝒔𝟐+(3𝑅2 𝑅+𝑅 2𝑅 )𝒔+1 = 𝑉𝑐𝑒𝑙𝑙 2𝑅 𝒔+𝑉𝑐𝑒𝑙𝑙 𝑅+𝑉𝑐𝑒𝑙𝑙 2𝑅𝑠 𝒔𝟐+2𝒔+1 =𝑉𝑐𝑒𝑙𝑙 𝑅(2𝑠2+4𝑠+2 4𝑠 𝒔𝟐+2𝒔+1 )= 𝑉𝑐𝑒𝑙𝑙 2𝑅𝑠 [23] Applying he in e se o LaPlace we ob ain: 𝐼𝑡(𝑡)=𝑽𝒄𝒆𝒍𝒍 𝟐𝑹 𝝏(𝒕) [24] The I plo will be obse ed in he ci cui o Figu e 8, his ime wi h he L=R ela ionship: Figu e 10:I g aph when he swi ches con olled by signal S1 a e closed, si ua ion L=R S udying equa ion 24 wi h he da a L=R=C=1 we ob ain: 𝐼𝑡(𝑡)=𝑽𝒄𝒆𝒍𝒍 𝟐𝑹 =𝟎.𝟓𝑨 [25] Being a cons an e m, i is e iden ha he i s and second de i a i es will be ze o. Only ha ing s udied he sys em in e ms o speed i can be concluded ha when L=R he 15 sys em will beha e in a as e way han wi h L=3R and he e o e he sys em will be op imized. E en so, o co obo a e ha we a e ollowing he igh pa h and p ocedu e we will s udy he ci cui in powe . Powe s udy In his sec ion we will s udy which pa ame e s o he elemen s a e he bes o achie e mo e powe . To ob ain he bes sys em, he powe exp ession will be ob ained: 𝑃(𝑠)=𝑉2∙𝐼𝑡(𝑠)= 𝑉2∙𝑉2 (𝑅+𝐿𝑠)+𝐶𝑠𝑉2∙𝑉2 (𝑅𝐶𝑆+1)=𝑉𝑐𝑒𝑙𝑙2−2𝑅𝐼𝑡+𝑅2𝐼𝑡2 (𝑅+𝐿𝑠)+𝐶𝑠(𝑉𝑐𝑒𝑙𝑙2−2𝑅𝐼𝑡+𝑅2𝐼𝑡2) (𝑅𝐶𝑠+1) [26] I is he leas common mul iple: 𝑃(𝑠)= 𝐴 𝑅𝐶𝐿𝑠2+(𝑅2𝐶+𝐿)𝑠+𝑅= 𝐴 𝑠2+(𝑅2𝐶+𝐿 𝑅𝐶𝐿 )𝑠+1 𝐶𝐿 [27] The nume a o is ep esen ed wi h a alue o A because i is independen , since wha is impo an is he denomina o om which he na u al equency and he damping coe icien will be ob ained: 𝒘𝒏= √1 𝐿𝐶→𝑤𝑛=1→ 𝐿𝐶=1 [28] 2𝜕𝑤𝑛=𝑅2𝐶+𝐿 𝑅𝐶𝐿 → 𝜕= 12(𝑅 𝐿+𝐿 𝑅) [29] In u n, as in he case o he ime s udy, he e a e wo ways: • Assume c i ical damping, ∂=1 : 2=𝑅2+𝐿2 𝑅𝐿 →𝐿2−2𝑅𝐿+𝑅2=0→𝐿=2𝑅±√4𝑅2−4𝑅2 2→ 𝑳=𝑹 [30] • Find he minimum o maximum alue o ∂ as a unc ion o L: 𝑑𝜕 𝑑𝐿=0→1 2𝑑 𝑑𝐿(𝑅 𝐿+𝐿 𝑅)=0→1 2(−𝑅 𝐿2+1 𝑅)=0→𝑅 𝐿2=1 𝑅→ 𝑳=𝑹 [31] S udying how he powe would be i we subs i u e L=R: 𝑃(𝑡)=𝑉𝑐𝑒𝑙𝑙2−2𝑅𝐼𝑡+𝑅2𝐼𝑡2→𝐿−1{𝑃}=2(𝑉𝑐𝑒𝑙𝑙 2 𝑅 )𝑡 [32] 16 As i was known be o e ca ying ou he powe s udy, he bes op ion is L=R, since being a cons an alue i has a se ling ime equal o 0 and always deli e s he maximum powe . Once he ela ionship be ween he pa ame e s is ob ained, hese should be passed o he equency a which he ci cui is wo king, because i we implemen in he PSIM ci cui a equency o 1Hz he balancing will be e y slow, and i will ne e wo k. In his case a andom equency o 1000Hz has been chosen, wi h which he balancing will be done in a as way and will no gene a e much noise. Th oughou he heo e ical s udy an angula eloci y o 1 ad/s has been assumed, wi h his alue and ha o he angula eloci y, we ob ain a pa ame e α ha ela es hem: 𝛼=𝜔𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝜔𝑢𝑛𝑖𝑡𝑠 =2𝜋103 1=2𝜋103 [33] By de eloping he exp ession o he angula eloci y o he ci cui , a ela ionship be ween he componen s ob ained heo e ically and hose o be implemen ed in p ac ice will be achie ed. 𝜔𝑐𝑖𝑟𝑐𝑢𝑖𝑡=1 √𝐿´𝐶´→𝐿´𝐶´= 1 (𝜔𝑐𝑖𝑟𝑐𝑢𝑖𝑡)2=1 𝛼2𝜔𝑢𝑛𝑖𝑡𝑠 2=1 𝛼2∙1 𝐿𝐶→(𝛼𝐿´)(𝛼𝐶´)=𝐿𝐶 [34] Since wi h exp ession 29 he e a e wo unknowns, o acili a e he esolu ion, a alue o he induc ance will be andomly assumed: 𝑅=0.2Ω 𝑳´=𝑳=𝟎.𝟐𝑯𝒓 Knowing ha L equals L', his alue will be ob ained o he ci cui capaci o : 𝐶´=𝐶 𝛼2=1 𝐿 𝛼2=1 𝐿𝛼2=1 0.2∙(2𝜋103)2→ 𝑪´=𝟏𝟐𝟔𝒏𝑭 [35] Once ob ained hese alues o he componen s ha o m he ci cui , i is known ha wi h hem he ci cui will beha e in he as es way and ob aining he highes possible powe . Now i only emains o ca y ou a p og amming (chap e : “Ci cui p og amming”) ha allows us o con ol he ol age o he cells and ha i s load is ca ied ou in he mos simila way o he one ha eally akes place in a ba e y o an elec ic ca . 17 Sensibili y s udy: Sensi i i y analysis is one o he mos widely used ools o p edic he expec ed esul s o a p ojec . Wi h hem, decision making will be acili a ed, and he alues o he ci cui elemen s will be assigned in a mo e app op ia e way. In igu e 7 i has been assumed ha all he esis ances o he ci cui a e he same and ha e he alue o R. Bu i is no qui e ue since he esis ance o he cell depends on o he pa ame e s. Tha is why o s udy he sensi i i y o ou sys em we will s udy he sys em in his way. Figu e 11:Resul ing ci cui when he swi ches con olled by signal S1 a e closed, di e en ia ing esis o s. The alue o R1 will be: R1=Rin e n+Rwi ing+ RMos e The Rwi ing and RMos e hei alue can be known, on he o he hand o he Rin e n is unknown, he e o e he alue o R1 will be exp essed: R1= R+∆R The exp ession o he sensi i i y will be s udied: Sensi i i y=𝐈𝐭(𝐑)−𝐈𝐭(𝐑+∆𝐑) 𝑹𝟏−𝑹 [36] De eloping each exp ession o he nume a o : I (R)=Vcell 2R [37] I (R+∆R)=V2+LIL0 (R+Ls)+c(sV2−Vc0) (RCS+1) = Vcell−R1I +LIL0 (R+Ls)+VcellCs−R1CsI −CVC0 (RCS+1) [38] I (R+∆R)((RCL+R1CL)s2+(2RCR1+R2C+L)s+(R+R1))=LCVcells2+2RCVcells+Vcell [39] 18 Subs i u ing ,CL=1 R=L: I (R+∆R)((R+R1)s2+(2R1+R+R)s+(R+R1))=Vcells2+2Vcells+Vcell [40] Subs i u ing R1= R + ∆R: I (R+∆R)((2R+∆R)s2+(4R+2∆R)s+(2R+∆R))=Vcells2+2Vcells+Vcell [41] G ouping e ms: I (R+∆R)=Vcell(s2+2s+1) (2R+∆R)(s2+2s+1)=Vcell (2R+∆R) [42] Finally, he exp ession is ob ained: Sensi i i y=Vcell 2R −Vcell (2R+∆R) (R+∆R)−R =Vcell 2R(2R+∆R) [43] This inc ease in esis ance is in e sely p opo ional o he sensi i i y, so ha when he sensi i i y inc eases he sys em will be less accu a e and he balancing will be pe o med in a wo se way. Figu e 12 shows he cell ol ages when R has a alue o 5Ω,as one can see, no balancing is pe o med: Figu e 12: Cell ol ages g aphs when Vcell1>Vcell2> Vcell3, when ∆𝑅=5 . Tha is why in he sec ion ("3.2 Theo e hical S udy”) we ha e assumed all he R o he ci cui o be equal, because his means ha ∆R=0 and hus he maximum possible sensi i i y is ob ained 19 Figu e 13:S ages o ba e y cha ging 3.1.3 Powe supply ci cui Be o e explaining he p og amming ha has been ca ied ou , i is necessa y o ha e clea how he p ocess o load akes place in an elec ical ba e y. This p ocess is ca ied ou in 3 main phases [20][21]: Bulk: his is he i s cha ging s age, in which, wi h cons an cu en and a p og essi ely inc easing ol age, 90% o he ba e y cha ge is achie ed. I is ecommended by la ge companies (BMW, Tesla …) ha he cu en o load in his s age is a en h pa o he o al capaci y o he ba e y. Knowing ha in he ci cui o PSIM his capaci y is o 10Ah he cu en will be o 1A. Abso b: in his s age he o al cha ge o he ba e y is comple ed. Unlike he p e ious s age, in his one he ol age emains cons an a i s maximum alue and he cu en will be dec easing li le by li le. The pu pose o his s age is o eco e he elec oly e (conduc o used o anspo he elec ic ions om he posi i e pla e o he nega i e pla e). The du a ion o his s age will inc ease, depending on how de e io a ed he elec oly e is. The ol age p o ided should be highe han he o al ol age o he ba e y. In his case he ol age is 10.95 V, since he 3.6 V o each cell make up 10.8 V. Floa : in his phase he ba e y is al eady 100% cha ged and only he necessa y in ensi y is p o ided o compensa e he sel -discha ge ha can be ealized. In he ci cui o be implemen ed in PSIM his s age will no be conside ed, since he simula ions and conclusions o be ob ained a e o e y sho imes and his s age is a ac o ha needs a e y long simula ion ime. Once he 3 phases ha e been explained, we will p oceed o he explana ion o he p og amming hanks o a lowcha : 20 4.Ci cui p og amming In his sec ion we will s udy he p og amming ha has been ca ied ou o ob ain a co ec cell balancing: I g_nS epCoun = 100 I IMBALANCE I g_nS epCoun =1000 10001 I V_ba e y < 9.9 START Commu a o = 0 Commu a o = 1 BMS = 0 BMS = 1 YES YES YES YES NO NO NO NO g_nS epCoun ++ Figu e 14:Flowcha o cell balancing p og amming. BULK ABSORB 21 Be o e s a ing he simula ion, hese pa ame e s will be de ined: VA e age = (Vcell1 +Vcell2 +Vcell3)/3 A a iable will be de ined wi h he name g_nS epCoun which will ac as a coun e . Once i eaches a alue o 100 ( andom alue), i will be checked i he sys em is in balance o no . I will be unde s ood ha he sys em is no balanced i he sub ac ion be ween Va e age and any o he cells is g ea e han he a iable de ined as Imbalance. As explained in he con ol ci cui , he swi ches a e egula ed by wo signals S1 and S2. These pe iodic signals a e 180º ou o phase and bo h ha e he same pe iod and a e mul iplied by he BMS signal. In his way, when he BMS signal is equal o 1, balancing will be pe o med, while he BMS signal has a alue equal o 0, no ene gy ans e s will be pe o med, and all swi ches will be open. When he a iable g_nS epCoun eaches he alue o 1000 ( andom alue), he s a e o cha ge o he ba e y will be checked. I he ba e y is less han 90% o i s o al cha ge (in his case 10.8*0.9= 9.72 V), a alue o 9.9 V is se in he ci cui o ha e a ce ain ma gin o ope a ion, a cons an cu en will be applied h ough he swi ch since i is in he bulk s age. O he wise, i he ba e y ol age alue is highe han 90%, a cons an ol age will be applied since we a e in he abso b s age. Now he ci cui will be simula ed in di e en si ua ions o check i s co ec ope a ion. 5.Resul s and discussion The ci cui will be s udied in h ee possible si ua ions: - Vcell1> Vcell2> Vcell3 - Vcell2> Vcell3> Vcell1 - Vcell3> Vcell 1> Vcell2 In each si ua ion he maximum ol age has a di e en cell, in his way i will be possible o see i he ci cui wo ks in all possible ope a ing si ua ions. 28 [15] J.P. Xie, X.Z. Wei, H. F. Dai,” Induc o -based ac i e balancing o Li-ion ba e y”, Appl Mech Ma e . 2011;80-81:255-260. [16] X. Cui, W. Shen, Y. Zhang, and C. Hu, “Fas mul i-swi ched induc o balancing sys em based on a uzzy logic con olle o li hium-ion ba e y packs in elec ic ehicles”, Ene gies. 2017; 10:1–16. [17] Y. Dou, Z. Ouyang, and M. A. E. Ande sen, "In eg a ed Coupled Induc o s wi h Func ionali y o Cu en Balancing T ans o me o Two-Phase Synch onous DC–DC Con e e s," in IEEE T ansac ions on Powe Elec onics, ol. 35, no. 5, pp. 4472-4476, May 2020, doi: 10.1109/TPEL.2019.2948882. [18] C. Liao, H. Li and L. Wang, "A dynamic equi alen ci cui model o LiFePO4 ca hode ma e ial o li hium-ion ba e ies on hyb id elec ic ehicles," 2009 IEEE Vehicle Powe and P opulsion Con e ence, 2009, pp. 1662-1665, doi: 10.1109/VPPC.2009.5289681. [19] J. Pa k, G. Kim, W. Na, C. Lim, and J. Kim, "Nonlinea Obse e and Simpli ied Equi alen Ci cui Model-based EKF-SOC Es ima o o a Recha geable LiFePo4 cell," 2019 10 h In e na ional Con e ence on Powe Elec onics and ECCE Asia (ICPE 2019 - ECCE Asia), 2019, pp. 1467-1472, doi: 10.23919/ICPE2019- ECCEAsia42246.2019.8796922. [20] S. A ms ong, M. E. Gla in and W. G. Hu ley, "Compa ison o ba e y cha ging algo i hms o s andalone pho o ol aic sys ems," 2008 IEEE Powe Elec onics Specialis s Con e ence, 2008, pp. 1469-1475, doi: 10.1109/PESC.2008.4592143. [21] A. Kim and S. Lee,2021 15 h In e na ional Con e ence on Ubiqui ous In o ma ion Managemen and Communica ion (IMCOM), 10.1109/IMCOM51814.2021.9377368, (1- 6), (2021). 29 Lis o igu es Figu e 1:Func ions o he BMS in an EV [3] ................................................................................... 3 Figu e 2:Balancing wi h passi e me hods [12][13] ....................................................................... 4 Figu e 3:Balancing wi h ac i e me hods [12][13] ......................................................................... 5 Figu e 4:Ci cui simula ing he beha io o a LiFePO4 ba e y in PSIM. ....................................... 6 Figu e 5:Ci cui simula ing a cell in an elec ic LiFePO4 ba e y. .................................................. 7 Figu e 6:Si ua ions o cha ge and discha ge in induc o s ............................................................. 8 Figu e 7:Resul ing ci cui when he swi ches con olled by signal S1 a e closed. ........................ 9 Figu e 8: esul ing ci cui when he swi ches con olled by signal S1 a e closed, si ua ion L=3R13 Figu e 9:I g aph when he swi ches con olled by signal S1 a e closed, si ua ion L=3R ........... 13 Figu e 10:I g aph when he swi ches con olled by signal S1 a e closed, si ua ion L=R ........... 14 Figu e 11:Resul ing ci cui when he swi ches con olled by signal S1 a e closed, di e en ia ing esis o s. ...................................................................................................................................... 17 Figu e 12: Cell ol ages g aphs when Vcell1>Vcell2> Vcell3, when ∆𝑅=5 .................. 18 Figu e 13:S ages o ba e y cha ging .......................................................................................... 19 Figu e 14:Flowcha o cell balancing p og amming. ................................................................ 20 Figu e 15:Cell ol ages g aphs when Vcell1>Vcell2> Vcell3 ....................................................... 22 Figu e 16:Zoom o cells ol ages g aphs display when Vcell1>Vcell2> Vcell3. ........................... 22 Figu e 17:Cells powe g aphs when Vcell1>Vcell2> Vcell3 ......................................................... 23 Figu e 18:Cells (blunk, abso b and ol age ba e y) g aphs when Vcell1>Vcell2> Vcell3. ......... 23 Figu e 19:g aphs o capaci o and induc o cu en s in cell 1 when Vcell1>Vcell2> Vcell3. ...... 24 Figu e 20:Zoom o g aphs o capaci o and induc o cu en s in cell 1 when Vcell1>Vcell2> Vcell3. .......................................................................................................................................... 24 Figu e 21:Cell ol ages g aphs when Vcell2>Vcell3> Vcell1 ....................................................... 25 Figu e 22:Cell ol ages g aphs when Vcell2>Vcell3> Vcell1 ....................................................... 25