Accurate sizing of supercapacitors storage system considering its capacitance variation.

Transcription

1 Aurate izing of ueraaitor torage ytem onidering it aaitane. Sony Triete, Salvy Bourguet, Jean-Chritohe Olivier, Lu Loron, Jean-Claude Le Claire To ite thi verion: Sony Triete, Salvy Bourguet, Jean-Chritohe Olivier, Lu Loron, Jean-Claude Le Claire. Aurate izing of ueraaitor torage ytem onidering it aaitane.. IEEE. Euroean Conferene Power Eletroni and Aliation - EPE th, Aug 011, Birmingham, United Kingdom , 011. <hal > HAL Id: hal htt://hal.arhive-ouverte.fr/hal Submitted on 11 Ot 01 HAL i a multi-diilinary oen ae arhive for the deoit and diemination of ientifi reearh doument, whether they are ublihed or not. The doument may ome from teahing and reearh intitution in Frane or abroad, or from ubli or rivate reearh enter. L arhive ouverte luridiilinaire HAL, et detinée au déôt et à la diffuion de doument ientifique de niveau reherhe, ublié ou non, émanant de établiement d eneignement et de reherhe françai ou étranger, de laboratoire ubli ou rivé.

2 Aurate izing of ueraaitor torage ytem onidering it aaitane S. Triete, S. Bourguet, J.C. Olivier, L. Loron, J.C. Le Claire Intitut de Reherhe en Eletrotehnique et Eletronique de Nante Atlantique (IREENA) 37 Bd de l univerité BP406, 4460 Saint-Nazaire, Frane Tel.: +33 / (0) Fax: +33 / (0) ony.triete@univ-nante.fr Keyword Energy torage, Sueraaitor, Ultra aaitor, Tration aliation, Meaurement, Effiieny, Devie modeling, Devie haraterization. Abtrat Thi aer highlight the energy error made for the deign of ueraaitor ued a a main energy oure. Firt of all, the aer reent the two definition of aaitane of a aaitane-voltage deendent material. The number of ueraaitor i imortant for the aliation urhaing ot. That i why the aer introdue an analytial model and an eletrial model along with an identifiation method for the aaitane. Thi i reented and omared to the manufaturer value in order to underore the energy error between the manufaturer, the ontant aroximation and the firt order aroximation whih interet u here. Thi aer alo reent the izing aet onidering the loe aoiated to a ontant-urrent harging mode in order to minimize the eletrial loe. At lat, an aliation ae omare the number of ueraaitor for different aroximation of the aaitane. Introdution The ueraaitor ha a high ower denity of 1000W/kg, a high eifi ower of 1000W/l and a low eifi energy of 10Wh/kg. Thee ower harateriti make thi energy torage unit uitable for eak ower aliation uh a the voltage omenation into the eletrial network [1], for reovery of braking energy [4] and for hybridization with other eletrial ytem with low eifi ower and low ower denity. Thi energy torage ytem i more and more rooed into tranortation aliation thank of it ability to ave regenerating eak ower energy into a fulleletri or a hybrid eletri drive train. Today, mot of full-eletrial tranortation drive train ue batterie a main energy torage unit. Indeed, the eifi energy of battery i high (hundred of Wh/kg for lithium batterie) and it allow a medium autonomy for a reaonable ize. While the relaement rie i high beaue the lifetime of thi eletrohemial energy torage unit i only around few 1000 yle regarding the bet available tehnology uh a lithium-ion battery. In hybrid tranortation ytem and in full-eletri tranortation aliation (lifetime > 15 year), the lifetime yle of the energy torage i highly imortant for the whole-life ot of the tranortation aliation. In thee artiular ae [6][9] where the uer doe not want to hange often the main energy unit, the ueraaitor i highly uitable beaue it lifetime i around yle. Even if it eifi energy ot i higher omared to a lithium-ion battery, the harateriti of ueraaitor an make it referable veru batterie a a main on-board energy oure. Thi kind of ue of ueraaitor i a hallenge beaue the behaviour of the ueraaitor i different from the exiting eletrohemial batterie. Moreover regarding the ueraaitor rie ae, the ueraaitor bank ha to be harly deigned to tay more ometitive againt a battery deign. EPE Birmingham ISBN: P.1

3 Uually, the manufaturer give an equivalent aaitane value whih i for a ower eak aliation [3]. To ue a ueraaitor a an energy torage ytem, it i imortant to know the real available energy whih do not orreond to the formula [3] beaue of the aaitane along with the aaitane voltage [4-5][7-8]. Thi make the deign more tringent for energy aliation uh a highlight in the aer [4] and [7] and the ontant aaitane deign reent ome hortoming. In fat, the tored energy in the aaitane deend on the voltage range, the lifetime of the vehiular aliation and the deth of the voltage diharge. Furthermore, the uual analytial relation have to be orreted beaue of the of the aaitane aording to it voltage. Indeed few aer on the deign of the ueraaitor bank have taken into aount the aaitane. For the other value of deth of diharge and urrent, thi aer how the error done and how to avoid it. In the firt art of thi aer, the modified analytial model of the energy for a variable aaitane and the benh ued for the identifiation of the ueraaitor are reented. We reall the two ueful eletrial aaitane definition and we introdue a aaitane identifiation method. In the eond art, the energy rofile obtained with two aroximation of the aaitane are deribed and omared to the manufaturer value. At lat, thi aer reent the total loe for a ontanturrent harging method. In the lat art, a numerial aliation on a full-eletrial vehile i to highlight the imortane of taking the aaitane into aount for an aurate izing. Analytial model develoed for the izing method We built an analytial model whih maintain the artiularity of the dynamial equation to harge and diharge a aaitane. The voltage and urrent equation have to be modified for the non-water oluble ueraaitor. Indeed the aaitane value varie along it voltage range [4-5][7-8] and o the voltage-time arameter u (t) ha no exat-analytial olution whatoever the kind of harge and diharge. Thee voltage aaitane have two main definition whih ondut to the ame energy reult. Definition of eletrial aaitane Beaue of the of the aaitane, we have to define what we all the aaitane of the ueraaitor beaue the equation of the energy tored i not a a ontant aaitane. There are two main definition of a nonlinear aaitane material. The firt aaitane definition introdue the total eletrial harge a a voltage-deendent funtion q(u). Thi funtion i defined at a voltage tate to give a ontant aaitane C T [11]. Thi equivalent ontant aaitane of the equation (1) i the total aaitane for the tate-voltage. If we ugget the deomoition of the eletrial harge a the rodut of a aaitane C T (u) and the tate voltage u, therefore we an write the equation (1) of the total harge Q. ( C u u) dq = d T ( ) (1) With thi aaitane definition, the equation () give the inremental harge whih flow into the eletrial double layer. i () t = dq dt d = ( C ( u) u) C ( u) du + d( C ( u) ) T dt = T The eond definition ue the loal definition of the relation between the loal eletrial harge dq and the inremental voltage du uh a reented in the equation (3). The aaitane i the oeffiient whih link the eletrial harge to the differential eletri otential. Thi oeffiient an be a voltagedeendent oeffiient or a olynomial funtion C(u). ( u) du dt T u () dq = C (3) EPE Birmingham ISBN: P.

4 Thi aaitane, alled the Rowe inremental aaitane [10-11], an be diretly meaured from voltage and urrent arameter if we ue the equation (4) between the eletrial harge er time-unit and the urrent flow. i dq du = (4) dt dt () t = C( u) In thi aer, we ue the Rowe definition to identify the eletrial aaitane beaue it i very imle to aoiate the urrent into the aaitane and the voltage inrement er time-unit. It i well-uited for our identifiation roe whih onit to reord the voltage for a ontant te urrent I SC0. We alo introdue an aurate aaitane method with multile ignal te with ontant urrent likewie all MuSSiCC. Eletrial model and identifiation method MuSSiCC The figure 1 reent the branh analytial model baed on the aroah of the ueraaitor a energy ytem with it tranfer loe r, balaning and/or elf-diharge loe r. All balaning iruit whih ommonly go with ueraaitor module an be modeled by r. The value of r deend on the balaning iruit, r i infinite if there i no balaning iruit or for a voltage-withed reitive iruit, finite for a reitive iruit or bound to u in the ae of an ative iruit. The aaitane C =f(u ) reflet the real tored energy. In thi aer, we how the influene of the hoie to introdue the voltage-aaitane deendeny. Figure 1 - Sueraaitor eletrial model of one branh Thank to the analytial model of the figure 1, we write the eletrial and energy equation (5-7). Thee eletrial equation are ueful to know the exreion of the energy inide the ueraaitor during a harging mode. Thee equation alo how the imle relation between the arameter voltage u and the aaitane voltage u. The voltage u i alo the idle voltage tate arameter. The lat ontrollable arameter i i divided in two art, i to harge the real aaitane and i to balane the voltage u. P = u i = r i + u i + r i (5) u = r i + u = r i (6) u i dt = u i dt + r i dt + Inut Energy Stored Energy Tranfer Energy r i dt Balaning Energy (7) With a elf-diharge tet, we know the value of r and with high ontant-urrent te we know the r value. The aaitane i identified with the MuSSiCC method that we deribe later. In thi method, we onider a high value of r and a low value of r. In order to limit the tranfer loe into the internal reitane r, the aaitane identifiation tet are made at low urrent range. We onider the influene of the urrent on the aaitane a negligible for our urrent range. EPE Birmingham ISBN: P.3

5 In the identifiation MuSSiCC method, we et multile ontant-urrent te with ontant idle time between them in order to meaure the elevation voltage between eah idle tate. During an idle tate, the ueraaitor voltage u and the aaitane voltage u are equal. To undertate the loe in r and the loe in r, we hooe a ontant urrent ignal with ative tate and an idle tate eriod of 5 eond. The figure illutrate the urrent and the voltage during the MuSSiCC method. The uer art how the voltage u during the multile ontant-urrent te while the lower art how the ontant-urrent i evolution. In order to minimize the voltage meaurement dierion, we alulate the u mean voltage during the idle tate ([P10; P11] and [P0; P1]) with: u P1 1 P11 1 t = u Δt P 10 t t t P P11 [ P11 P10] = u dt = u dt P1 We alo alulate the average urrent value of i between eah idle tate. The time aoiated to eah 1 1 idle tate are t P1 = ( tp 11 + tp10 ) and t P = ( tp1 + tp0 ), they orreond to the middle of eah idle egment. Thu, the aaitane i determined by equation (9) and the aaitane attahed 1 u = u = u + u. voltage [ ] ( ) PP1 P; P1 P P1 P11 P10 10 (8) C ( u ) [ P; P1] i Δt = Δu = tp i dt tp1 (9) u P u P1 Comutation oint Figure - Voltage and urrent evolution during MuSSiCC method Benh ued for the aurate izing of a ueraaitor bank The method deribed in thi aer i baed on the energy model develoed on the figure 3 and in the aer [8]. For vehiular aliation, the eletrial dynami i low enough to onider a quai-tati mode. We are aware that in the deign of thi kind of ueraaitor aliation, the balaning iruit hould have the highet reitive value while avoiding the voltage ell overflow. The benh ued to identify the aaitane i omoed of a ower onverter with it moothing indutane and Maxwell BOOSTCAP unit (BMOD Serie) on the figure 3. The ueraaitor ue non-water oluble eletrolyte (aetonitrile) tehnology. The energy torage bank i omoed of a branh with eah 7 ueraaitor under 105 V with a reitive balaning. Aording to the manufaturer information, the branh of ueraaitor omoe an 8.3 F 105 V ueraaitorbaed energy torage unit. EPE Birmingham ISBN: P.4

6 Figure 3- Sueraaitor benh ued for the aurate izing method After the identifiation of the reitane r, r and the aaitane C(u), in order to aroximate the of the aaitane aording to the voltage [5][7-8], we omared a firt order aroximation, a nd order aroximation, a 3 rd olynomial aroximation, the average value of the aaitane meaured on the thorough voltage range and the manufaturer aaitane value. We ue the MuSSiCC method to identify the arameter a 1 and 1 of the firt order funtion: C ( u ) a1 u 1 = (10) + The figure 4 how the linear olynomial aroximation and it average value obtained by the MuSSiCC identifiation. We add the manufaturer aaitane value whih i the minimum value of the aaitane and it uoed maximum aaitane. We know that the manufaturer give the average aaitane for the thorough range [1] and thi value annot outrun the maximum value (8.3F+0%). Indeed the manufaturer identifiation method [1] i the MuSSiCC ued with two omutation oint (U min, U max ). Figure 4 - Benh aaitane aroximation veru voltage (branh n 3) Of oure the aroximation i imortant for the energy tored auray but thi aroximation ha to be a imle a oible. We omute the reidual norm of eah aroximation and the table 1 onfirm that the 3 rd order olynomial aroximation have a lower reidual norm than the 1 t order olynomial. EPE Birmingham ISBN: P.5

7 Table 1 - reidual norm of the aroximation order Contant 1 t nd 3 rd Reidual norm.1 F 0.1 F 0.11 F 0.10 F Reidual norm on average value (%) We agreed to ue the 1 t order olynomial aroximation beaue it i the bet omromie. Thank to the identifiation on 6 rak, it i oible to omute an average firt order aroximation with maximum relative error of 10% on the arameter a 1 and a maximum relative error of 1.3% for the arameter 1. The identifiation data are ummarized in the table. To omute the energy error and the total loe, we ued the average value of the arameter a 1 and 1. Table - Firt order oeffiient of the 6 ueraaitor branhe (105 V F) n 1 n n 3 n 4 n 5 n 6 Average a 1 (10-3 F/V) Error (%) (F) Error (%) Aurate izing and energy error With thi ueraaitor branh model, it i oible to give the equation (11) of the energy related to the linear aroximation aaitane aording the voltage deth of diharge γ(%)=100*(u initial /u final ) when we fou only on the tored energy without the balaning and tranfer loe. 3 3 ( 1 γ ) + a u ( γ ) 1 E 1 = 1 u final 1 final 1 (11) 3 The uual equation for a ontant aaitane i defined by the equation (1). In the variable aaitane ae, there i an additional art due to the firt order aaitane aroximation. Thi i why we have to aurate the izing method beaue for ome tarting and ending voltage it may aue imortant error. ( γ ) 1 E 0 = 0 u final 1 (1) The laial izing method i enough for a mall ower aliation when it doe not require many ueraaitor. In our ae, we need to harly deign the energy torage bank beaue the number of ueraaitor i very imortant for the whole-life ot of the aliation. In addition, we added the imortane of the deth of diharge and the extreme voltage value for the energy tranfer. In ertain ae, the relative energy tored in the aaitane ould reah an error value u to 0% in the wort ae (figure 5) or the energy tored ould be underetimated if a failing voltage range i ued. The figure 5 how the energy tored error veru the initial voltage. Thi energy tored error i omuted between the average aaitane C 0 or the manufaturer value C 83 = 8.3 F and the firt order aaitane aroximation C(u). Thee error are omuted for one rak of the figure 3. The energy tored error E r = E 1 - E 0 (right art of figure 5) between the linear aaitane aroximation and it average value onfirm the exitene of an energy error. Thi error i greater if we omare the EPE Birmingham ISBN: P.6

8 leat aaitane value and C(u). Thi figure 5 onfirm the interet for aliation with many ueraaitor to take into aount the linear beaue the eletrial deigner ould ave ueraaitor module and imrove the urhaing ot of it aliation. Thi relative energy error E rr = (E 1 E 0 )/E 0 rereent at leat 7% but if we omare to the manufaturer value it ould reah 0%. Obviouly, we fou on the energy error between the firt order aaitane aroximation and it average value beaue it i only related to take or not into aount the firt order. Figure 5 - Relative energy tored error (left) and the energy tored error (right) veru initial voltage The figure 6 ontain the relative error urfae howing the energy differene between the aaitane C 0 and the aaitane C(u) for the tored energy aording to the tarting and the ending voltage value. Thi figure 6 i a rereentation of multile omutation of the figure 5 for different final voltage. It highlight the error in the ae of ueraaitor bank over izing. In thi ae, the energy an be underetimated. Figure 6 - Relative energy tored error urfae veru initial and final voltage EPE Birmingham ISBN: P.7

9 Aurate izing and harging arameter hoie We fou on the ommon ontant-urrent harging mode for the ueraaitor ontrolled by the arameter i of the figure 1. From a tarting voltage to a final voltage, the mode i aoiated with an effiieny of the mode whih i diretly link to the balaning and the tranfer energy loe. Thi aer rooed to undertand the bet hoie of the harging arameter i to reah the bet effiieny. Thi arameter hoie an hange aording to the aaitane aroximation hoie. We baed thi energy tored etimation on the equation (10-1). We um u the total loe a the um of the tranfer energy and the balaning energy. Thee loe are alulated by the Matlab olver ode15i on the (13) differential equation. Here after i the differential equation (13) whih determine the evolution of u (t) aording to the I 0 arameter value. du r r r r ( a1 u + 1 ) + u = I 0 (13) dt r + r r + r The omutation method i a traezoidal method. We hooe two tyial deth of diharge related with the maximum harging voltage: a deth of diharge γ = 50% (u initial = 5.5 V) a deth of diharge γ = 70% (u initial = 31.5 V) On the figure 7, the urrent-ontant reult for 100% of deth of diharge how the dereae of the effiieny out of 5A to 10A. The tranfer energy i link to the arameter I 0 wherea the balaning energy i related to the voltage u during the harging mode. Thi figure i alo aliable if there i no balaning iruit. In thi ae, the total loe would be equal only to the tranfer loe. Figure 7 - Total loe with firt order aroximation for γ = 70% For a ontant-urrent harging mode, the otimal energy zone i only related to the ueraaitor arameter (r,r ) and not to the aroximation order a the figure 8 how. The deth of diharge doe not have a great influene on the energy loe minimum oint. So the aurate izing of the ueraaitor bank ould et a number arallel branhe to have the bet harging effiieny and then the eletrial deigner hooe the number of module in erial aoiation. Thi ueraaitor EPE Birmingham ISBN: P.8

10 module aoiation will be otimize after when we try to otimize the deign of the ower onverter and it attahed ueraaitor bank. Figure 8 - Total loe veru ontant-urrent harging aording to the deth of diharge (50%, 70%) The meaurable voltage i u o the final voltage deend on the u value. Of oure, for harging hae the u final voltage at 50 A i lower than the u voltage at 5 A. Otherwie, the hoie of the balaning tehnology i very imortant beaue it deend on the aliation yle. Of oure, the balaning tehnology avoid overtaking the maximum admiible voltage. It ha alo to are about the energy lot during a harging yle. Aliation In order to illutrate the energy error between the manufaturer aaitane and the zero order aroah veru the firt order aroximation onto the ueraaitor bank deign, we ized a bank of BMOD Maxwell ueraaitor for a bu. The energy delivered i 8.6 kwh to the eletrial motor. All bu harateriti are available in the aer [9]. The um u the izing reult the relative error are the ame than the table 3 reult reented. Thank to firt order aroximation, it i oible to ave between 9% and 13% of ueraaitor module aording to the deth of diharge. Table 3 - Number of ueraaitor module needed for 8.6 kwh and a final voltage of 105V Number of needed branhe Manufaturer aaitane Contant aroximation Firt order aroximation Relative Error Manufaturer/Firt Order (%) Relative Error Contant/ Firt Order (%) Deth of 50 % Deth of 70% We know the number of ueraaitor module and we an otimize the erial and arallel onnetion of the module. Thi otimization alo deend on the aliation and the ueraaitor hoie. For ontant urrent harge, we want to harge around it minimum loe oint while tay EPE Birmingham ISBN: P.9

11 unhanged the harging time (1 to 15 minute). Thi onnetion otimization ha to take into aount the ower eletroni. Conluion Thank to the firt order aroximation, it i oible to ave ueraaitor module. Thi i very imortant for the aliation urhaing ot. Thi aurate method alo define the bet aurate ontant-urrent to harge the ueraaitor bank and thank to the aer we are aware of the bet erial and arallel onnetion to reah the otimal effiieny zone. Thi otimal urrent harging value deend mainly on the internal loe arameter of the ueraaitor module. In thi artiular ae, the harging-diharging yle reahe u to 15 minute. That i why, the eletrial deigner hoie ha an imat only on the balaning loe arameter and thi aer highlight how the hoie of the balaning tehnology influene the otimal loe zone. Referene [1] A. Rufer, P. Barrade, A ueraaitor-baed energy torage ubtation for voltage omenation in weak tranortation network, 003 IEEE Bologna Power Teh Conferene, 3 rd - 6 th June 003 [] O. Koerner, J. Bran, Energy effiient drive ytem for a dieel eletri hunting loomotive, EPE 005, Dreden, 005 [3] A. Rufer, P. Barrade, A ueraaitor-baed energy-torage ytem for elevator with oft ommutated interfae, IEEE Tranation on aliation, Volume 38 n 5, age , Set-Ot 00 [4] P. Kurzweil, M. Chwitek, R. Gallay, Eletrohemial and etrooi tudie on rated aaitane and aging mehanim of ueraaitor, ESSCAP 006, Lauanne, -3 November 006 [5] E. Harzfold, R. Gallay, M. Mahn, Caaitane and erie reitane determination in high ower ultraaaitor, ESSCAP 04, Belfort, 004 [6] S.R. Beale, R. Geron, The ue of ultraaaitor a the Sole Power Plant in an autonomou eletri railguided vehile, Alied Power Eletroni Conferene and Exoition, APEC '04. Nineteenth Annual IEEE, Volume age , ISBN: , 004 [7] F. Rafik, H; Gualou, A. Berthon, R. Gallay, Contribution to the izing of ueraaitor and their aliation, ESSCAP 004, Belfort, 004 [8] N. Rizoug, P. Bartholomeu, P. Le Moigne, Modelling and haraterizing ueraaitor uing an online method, IEEE indutrial eletroni magazine, 009 [9] I.N. Varakin, A.V. Dzenkevith, A.D. Klementov, N.F. Starodoubtev, Eletrial drive bu and eletri drive truk, with eletrohemial aaitor a the only on-board ower oure, reented at the 17th International Eletri Vehile Symoium, EVS-17, Otober 000, Montreal, Quebe, 000 [10] H. Heffner, Caaitane definition for arametri oeration, IRE Tranation on Mirowave Theory and Tehnique, Volume 9, Iue 1, age() 98-99, January 1961 [11] H.E. Rowe, Some general roertie of nonlinear element II. Small ignal theory, IRE Tranation on Mirowave Theory and Tehnique, Volume 46, age() , May 1958 [1] Maxwell Tehnologie, Rereentative Tet Proedure for Cutomer Evaluation, Aliation note doument , Marh 00 EPE Birmingham ISBN: P.10