Yasha Parvini 1 Jason B. Siegel 2 Anna G. Stefanopoulou 2 Ardalan Vahidi 1

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1 4 Ameican Contol Confeence (ACC) June 4-6, 4. Potland, Oegon, USA Peliminay Results on Identification of an Electo-Themal Model fo Low Tempeatue and High Powe Opeation of Cylindical Double Laye Ultacapacitos Yasha Pavini Jason B. Siegel Anna G. Stefanopoulou Adalan Vahidi Abstact The capability of ultacapacitos in deliveing high powe at low tempeatue applications such as cold stating is the motivation of this pape. A two state equivalent electic cicuit model coupled with a two state themal model is defined and paameteized to develop a fou state contol oiented electo-themal model fo cylindical double laye ultacapacitos. The poposed two state equivalent electic cicuit model mimics the teminal voltage dynamics and could be used to evaluate the powe capability and efficiency of the cell. The electic model paametes ae estimated by pulseelaxation tests fo sub-zeo tempeatues as low as -4 C. The two state themal model povides a tool to estimate the suface and coe tempeatue dynamics. The two models ae then coupled though the evesible plus ievesible heat geneation and also via tempeatue dependence of the equivalent cicuit model paametes. The modeled teminal voltage and suface tempeatue dynamics ae in good ageement with expeimental obsevations fo fixed envionmental tempeatue with foced ai cooling. I. INTRODUCTION Electic double laye capacitos (EDLC) ae the pemie electochemical devices in tems of powe density, long cycle life, and exteme tempeatue opeation. Mateials used fo the electode ange fom activated cabon to metal oxides and polymes. The electolyte could be eithe aqueous o non-aqueous depending on the mateials and application. The high powe capability aises fom the low equivalent seies esistance (ESR) as a esult of high electolyte conductivity, low electonic esistance of the electode and the inteface between electodes and cuent collectos. Fomation of electic double layes at the inteface of the electode and electolyte is due to electostatic foces and as no chemical o phase changes occus, the pocess is highly evesible and the chage-dischage cycle can be epeated vitually without limit [. Highe capacity in EDLC compaed to dielectic capacitos is achieved by inceasing the suface aea using poous electodes with an extemely lage intenal effective suface [. In eal wold application of ultacapacitos, it s vital to pedict the electical and themal dynamics in a eal time manne in ode to meet the pefomance equiements of the load while maintaining the module in safe opeating Yasha Pavini and Adalan Vahidi ae with the Depatment of Mechanical Engineeing, Clemson Univesity, Clemson, SC 9634, USA spavin@clemson.edu, avahidi@clemson.edu Jason B. Siegel and Anna G. Stefanopoulou ae with the Depatment of Mechanical Engineeing, Univesity of Michigan, Ann Abo, MI 489, USA siegeljb@umich.edu, annastef@umich.edu conditions. Effots have been made on modeling the teminal voltage behavio of ultacapacitos in the fequency domain mainly using electochemical impedance spectoscopy (EIS) [3. Bulle et al. s equivalent electic cicuit model has fou paametes to be detemined and consides dependence on fou voltage levels and tempeatues fom -3 C to 5 C. The poposed equivalent cicuit model in this pape consists of a seies esistance in seies with a single R-C pai. This model has two states. The fist state is the state of chage (SOC) of the ultacapacito which is the amount of chage stoed in the cell at each time ove the maximum stoable chage. The second state is the voltage acoss the R-C pai. The electic model has thee paametes to be identified. Due to the wide ange of opeating conditions, tempeatue dependent model paametes ae needed to accuately pedict the system esponse. The paametes of the equivalent cicuit model also depend on state of chage and cuent diection. In ode to pedict the module tempeatue we also need an accuate model of the heat tansfe. The heat tansfe poblem can be educed to a linea two state system simila to the model developed fo cylindical batteies in [4. Fo ELDC howeve the evesible heat geneation effect must also be consideed. Expeimental obsevation of the themal dynamics and the elative contibution of evesible heat geneation was shown in [5. The themal dynamics can be pedicted by numeically solving the govening patial diffeential equations as investigated in [6-[7. Howeve these complex fist pinciple based themodynamic models can not be solved in eal time and theefoe ae not suitable fo contol applications. Utilizing a educed ode model with sufficient accuacy [5 is moe pefeable fo the puposes of this study. The electical and themal models will be coupled to develop a computationally efficient electo-themal model fo cylindical EDLC. This model can be used in pecisely calculating the efficiency of ultacapacitos unde diffeent loads following the study conducted in [8. Also the model could be utilized in system integation and contol studies in the vehicle level. II. ULTRACAPACITOR ELECTRICAL MODEL In this section the electic model fo the ultacapacito is pesented. An equivalent electic cicuit model is poposed with the following chaacteistics: Fewe paametes to be identified compaed with the detailed electochemical model /$3. 4 AACC 4

2 Computational efficiency and suitability fo contol oiented studies. Accuate pediction of dynamic teminal voltage. In this section the expeimental setup fo paametization tests and also the identification esults ae pesented. A. Equivalent Electic Cicuit Model In this study the galvanostatic appoach is used in the whole modeling pocedue whee cuent is the input to the system and the output is the teminal voltage. Fig. shows the schematic of the equivalent electic cicuit model. It consists of an equivalent seies esistance which epesents the intenal esistance of the ultacapacito and also R- C banches that captue the voltage behavio of the cell duing elaxation. Positive cuent coesponds to chaging and negative sign is fo dischaging. The dynamic model is deived by applying kichhoff s voltage law (KVL) to the cicuit shown in Fig.. The equation govening the teminal voltage could be witten as follows: V T = OCV (SOC) + IRs + n V RC,j () j= In (), OCV is the open cicuit voltage which is a linea function of state of chage fo an ideal capacito. The SOC is detemined by coulomb counting by the following state equation: dsoc dt = I CV max () whee C and V max ae the nominal capacitance of the ultacapacito in Faads and the voltage acoss the ultacapacito at maximum chage. The second pat in (), is the voltage dop ove the ohmic esistance and the last pat is the sum of voltage dops acoss paallel R-C cicuits connected in seies. The voltage dynamics of each R-C pai is descibed as: dv RC,j dt = R j C j V RC,j + I C j (3) whee R j and C j ae the equivalent esistance and capacitance espectively. Fo example the state space epesentation of an ideal ultacapacito knowing that OCV = V max SOC and assuming a single R-C pai (j = ) with V voltage dop acoss it, is as follows: [. SOC. V = [ R C B. Expeimental Setup [ SOC V [ CV + max C I Expeiments have been conducted on a Maxwell BCAP3 cylindical cell with activated cabon as electodes. The nominal capacitance of the cell is 3 Faads. The cell contains non-aqueous electolyte allowing the maximum ated voltage of.7 Volts. All the expeiments elated (4) Fig.. Schematic of the equivalent electic cicuit model with n numbe of RC banches to paametization and validation of both the electical and themal models ae conducted using the following set of equipments: Powe supply: Bitode FTV-/5/-6 cycle which is capable of supplying up to A suitable fo unning the pulse-elaxation and also the diving cycle validation tests. Themal chambe: Cincinnati sub-zeo ZPHS SCT/AC capable of contolling the ambient tempeatues as low as -4 C. C. Electic Model Paameteization The open cicuit voltage V ocv, capacitance C, seies esistance R s, esistance and capacitance of the R-C pais ae the paametes to be identified. V ocv and C fo chaging ae obtained by chaging the ultacapacito fom zeo to its maximum nominal voltage unde a low cuent of.5a. The ultacapacito is then dischaged to zeo with simila cuent ate to obtain the capacity and OCV fo dischaging. The diffeence between chaging and dischaging OCV is small due to low cuent and small intenal esistance. The paametes of the equivalent cicuit including R s, R j, and C j, ae identified using pulse-elation expeiments. Fou cuent levels, 9, 35, 67.5 and.5 Ampees, ae applied. In ode to investigate the dependence of the paametes on SOC, sub-zeo tempeatue, and also the diection of cuent, appopiate tests have been designed to sweep the whole SOC ange (fom to with 5% intevals) and tempeatues anging fom -4 C to C (-4, -, C ) fo both chaging and dischaging. Fig. is one example of an SOC sweep at fixed tempeatue. In this specific test the tempeatue is -4 C and the ultacapacito cell is chaged with constant cuent of 9A fom % SOC to 5% SOC. Afte a est peiod of seconds the same step is epeated in 5% SOC intevals till % SOC. Similaly the same pocedue is epeated fo dischaging to also investigate the effect of cuent diection. The identification is pefomed by minimizing the squae eo between the measued and simulated teminal voltages at each time instant at each fixed tempeatue level. The cost function is: J = k (V m (k) V T (k)) (5) 43

3 Cuent(A) Cuent Voltage Time (s) Fig.. Pulse-elaxation test at -4 C and 9A cuent whee V m (k) is the measued teminal voltage at each time and V T (k) is the simulated teminal voltage fom equation (). The numbe of R-C banches will be detemined based on the fitting esults in the next section. D. Electic Model Identification Results In this section the paameteization esults ae discussed. Fistly we stat with a simple OCV R s model and in the next steps the R-C banches ae added, evaluating the pefomance of the model at each level. The paametes, (Rs, R-C) in the equivalent cicuit model ae tempeatue dependent, howeve though caeful design of the expeiments, by holding the tempeatue constant, they can be identified at a fixed tempeatue without consideing the coupled themal model. The OCV of an ideal ultacapacito as mentioned befoe is a linea function of SOC. In eality the OCV of the double laye ultacapacito unde investigation has a nonlinea elationship with SOC. Fig. 3 shows the OCV as a function of SOC in both the ideal and eal cases at -4 C. 3 Voltage(V) the model using a lookup table. The oot mean squae eo (RMSE) numbes in Table I show that the eal nonlinea OCV pofile should be integated in the model which deceases the RMSE eo by 8%. The next step is to add an R-C banch to the OCV R s model and evaluate the model accuacy. Fig. 4 compaes the teminal voltage esults fom the OCV R s RC model and the expeimental data fo the expeiment conducted at - C and 35A of cuent. The teminal voltage dynamics deived fom the OCV R s RC model is in ageement with expeimental data with a RMSE eo of only 9 mv. This esult shows that the OCV R s RC model is accuate enough and will be used as the final electical model. Similaly the paameteization is pefomed fo the othe tests with diffeent cuent ates and tempeatues. Table II lists the values of the identified paametes fo the tests with tempeatues at -4,- and C and 35A of cuent. Results show that the total impedance of the ultacapacito inceases as tempeatue deceases. This tempeatue dependence of identified electic paametes indicates the necessity of coupling the electic and themal models. TABLE I RMSE BETWEEN MODEL AND EXPERIMENT Model RMSE (mv) Linea-OCV-R s 8 Nonlinea-OCV-R s 6 OCV-R s-rc 9 TABLE II IDENTIFIED PARAMETERS FOR TEMPERATURES -4,- AND C AND 35A OF CURRENT 4 C - C C R s(mω) R (mω) C (F ) Expeimental Ideal SOC Fig. 3. Open cicuit voltage vs state of chage fo ideal and eal cases at -4 C This nonlinea OCV vesus SOC pofile is integated into III. ULTRACAPACITOR THERMAL MODEL The themal model used in this study is adopted fom a computationally efficient model oiginally developed fo cylindical batteies by Kim et al. [4. Fist the two state themal model is descibed. In the consecutive sections entopic heat geneation and electo-themal coupling ae intoduced. Finally paameteization esults ae pesented. A. Two State Themal Model The model is based on one dimensional heat tansfe along the adial diection of a cylinde with convective heat tansfe bounday conditions as illustated in Fig. 5. A cylindical ultacapacito, so-called a jelly-oll, is fabicated by olling a stack of cathode/sepaato/anode layes. Assuming a symmetic cylinde, constant lumped themal popeties such as cell density, conduction heat tansfe and specific heat coefficient ae used [4. Unifom heat geneation 44

4 Voltage Eo (V).5.5 Measuement Model Time (S) Fig. 4. Compaison between teminal voltage fom expeiments and the OCV R s RC model Heat geneation heat tansfe at the suface of the cell foms the bounday condition in (8). Hee T is the ambient ai tempeatue and h is the heat tansfe coefficient fo convective cooling. With unifom heat geneation distibution the solution to (6) is assumed to satisfy the following polynomial tempeatue distibution as poposed in [: T (, t) = α (t) + α (t)( R ) + α 3 (t)( R )4 (9) The volume-aveaged tempeatue T, and volume aveaged tempeatue gadient γ ae chosen as the states of the themal model. These quantities can be elated to the tempeatue distibution as follows: T = R [ R γ= [ R R T d ( T ) d () () Using (9) the suface T s and coe T c tempeatue of the cell ae expessed by: h T inf Tempeatue Fig. 5. Given the assumption of unifom heat geneation with a convective cooling bounday condition at the suface, the adial tempeatue distibution can be modeled as a 4th ode polynomial [4. along the adial diection is a easonable assumption accoding to [9. The tempeatue distibution in the axial diection is moe unifom than the adial due to highe themal conductivity [. The adial -D tempeatue distibution is govened by the following PDE: ρc p T (, t) t = k t T (, t) with bounday conditions: T (, t) T (, t) + k t T (, t) Tc Ts R R + Q(t) V cell (6) = = (7) =R = h k t (T (R, t) T ) (8) whee t, ρ, c p and k t ae time, volume-aveaged density, specific heat, and conduction heat tansfe coefficients, espectively. The heat geneation ate inside the cell is Q, The cell volume is V cell and R is the adius of the cell. The fist bounday condition in (7) is to satisfy the symmetic stuctue of the ultacapacito aound the coe. Convective T s = α (t) + α (t) + α 3 (t), T c = α (t) () The tempeatue distibution T (, t) can be witten as a function of T s, T and γ afte some algebaic manipulation. The oiginal PDE (6), can be educed to a set of two linea ODEs with the state space epesentation of: ẋ = Ax + Bu, y = Cx + Du (3) whee x = [ T γ T, u = [Q T T, and y = [T c T s T ae state, input and output vectos espectively. The paamete β = kt ρc p is the themal diffusivity. Finally the linea system matices A, B, C, and D ae: A = 48βh R() 3βh R () B = C = β k tv cell 4k t 3Rh 4k t D = 5βh β(4k t+rh) R () 48βh R(4k ) t+rh 3βh R () Rkt+5R h 8() 5Rk t 48k t+rh 4Rh Rh This linea two state model is easy to paameteize as shown in the following sections. 45

5 B. Ievesible and Revesible Heat Geneation The inclusion of evesible heat geneation in the model is equied to accuately pedict the dynamic tempeatue esponse fo cycling ove diffeent SOC anges at both low and high cuents. Fig. 6 shows a set of fou expeiments at - C and pulse cuent of 4A that highlights the effect of est peiod between the chage and dischage cycle and depth of dischage on the dynamics of tempeatue ise. All pofiles show an oveall incease in the cell tempeatue duing the test which is due to the ievesible heat geneation ate due to esistive losses and is equal to: feeds back into the esistance of the equivalent cicuit. The esulting coupled model is non-linea. Figue 7 illustates the coupled electo-themal model. Q joule = R s I + V RC I (4) whee V RC is the voltage acoss the single R-C pai. The incease in tempeatue depends on the depth of dischage only when thee is a est peiod between the chage and dischage cycle. In this case the RMS cuent is lowe and theefoe Q joule is smalle. While in the case without any est between chaging and dischaging the aveage steady state tempeatue is not a function of SOC ange. A close look at the inset in Fig. 6 will also eveal that thee is an obvious non-lineaity in the tempeatue ipple. This is due to the evesible heat geneation which is a esult of entopy change duing chage and dischage peiod. The tempeatue change is exothemic duing chaging and endothemic duing dischaging. The entopic heat geneation ate is govened by [5: Q ev = δ T I(t) (5) The evesible heat geneation ate is popotional to cuent and the volume aveage tempeatue T with the unit of ( K). The constant of popotionality δ is elated to the physical popeties of the cell and will be estimated fom the tempeatue measuements. Tempeatue ( o C ) SOC(5 ),Rest=9s SOC( ),Rest=9s SOC(5 ),Rest=s SOC( ),Rest=s Time (S) Fig. 6. Themal pulse tests at - C and 4A fo diffeent SOC anges and ests C. Electo-Themal Coupling The electical and themal models ae coupled to fom the complete system model. The total heat geneation ate is calculated fom the equivalent cicuit model, and the tempeatue (which is the output of the themal model) Fig. 7. Coupling of the electical and themal models D. Themal Test Pocedue and Paameteization Results fo the Themal Model Repeated cycling of the ultacapacito is used to induce self heating. This tempeatue ise can be used fo paameteization of the themal model. The set of expeiments in the themal chambe ae conducted at the tempeatue of - C. The themocouple used fo tempeatue measuements is T-type and is mounted on the suface of the cell. The coe tempeatue is not measued in this study and theefoe must be pedicted by the model. Thee cuent levels (4,, and 5 Amps) and two SOC anges (-% and 5-% ) ae used to geneate a ich data set. In each set of expeiments a dischaged o a half chaged cell undegoes cycles of chage-est-dischage until the suface tempeatue of the cell eaches steady state followed by a long est peiod till the suface tempeatue elaxes to its initial value. Fig. 8 shows the tempeatue and voltage evolution unde a pulse test with cuent of 4A. In this test the cell is cycled in the uppe half of the voltage ange (5-% SOC) with an ambient tempeatue of C and 9 seconds of est between evey chage and dischage peiod. The tempeatue eaches steady state afte appoximately h. The tempeatue elaxation data is also useful fo paameteizing the heat capacity and coefficient of convective cooling in the model. Cell Tempeatue(C) Tempeatue Cuent Time (s) Fig. 8. Test pocedue fo themal model paameteization Cuent(A) 46

6 The convective h and conductive k t heat coefficients, specific heat coefficient C p and a paamete associated with evesible heat geneation δ ae identified fo the themal model. The physical paametes of the cell that ae measuable ae summaized in Table III. TABLE III PHYSICAL PARAMETERS OF THE ULTRACAPACITOR CELL Mass (Kg) length Radius Volume Density.5Kg.38m.34m 4E-4m 3 77 Kg m 3 TABLE IV IDENTIFIED THERMAL PARAMETERS FOR THE TEST AT - C,4A, ZERO REST AND SOC RANGE OF TO P aamete V alue Unit h 68.8 W/m.K c p 56 J/kgK k t.4 W/mK δ. J/coulomb.K The paameteization is pefomed by minimizing the squae eo between the measued and simulated suface tempeatues. The cost function to be minimized is: J = k (T m (k) T s (k)) (6) Fig. 9 shows the paameteization esults fo the test conducted at - C ambient ai tempeatue and pulse cuent of 4A with zeo est and SOC anging fom to. The total heat geneation ate is calculated though the electical model and fed into the themal model. The electical model paametes ae fixed and ae deived fom the - C and 35A pulse-elaxation test. The RMS eo is only.3 C which is an indicato of the themal model accuacy. Table IV shows the esults fo the identified themal paametes. Tempeatue (C) Measued Estimated Time (s) Fig. 9. Paameteization esult fo - C,4A, zeo est and SOC ange of to The value estimated fo h is in the ange of foced convective heat tansfe coefficient fo ai which is between to W/(m K). The specific heat coefficient is 56 W/(m K) which is expected to be close to the amount of the cell s oganic based electolyte (Acetonitile c p =59 J/kgK at - C). The themal conductivity of.4w/mk at C is a esult of the combined themal conductivity of activated cabon, electolyte, sepaato and the aluminum cuent collectos fomed in a jelly oll shape. The value of. fo δ at - C is compaable to.33 J coulomb K epoted in [5 fo a.7 V, 5 F pismatic cell with oganic electolyte at oom tempeatue. IV. CONCLUSIONS This pape shows the paameteization of a fou state electo-themal model fo cylindical double laye ultacapacitos including entopic (evesible) heat geneation that is accuate fo sub-zeo tempeatues. In the futue this computationally efficient model can be used fo eal time vehicle level contol such powe management, battey life extension though hybidization, cold stating of engines and also efficiency analysis of ultacapacitos. ACKNOWLEDGMENT The authos wish to acknowledge the technical and financial suppot of automotive eseach cente (ARC) in accodance to ageement W56HZV-4-- with TARDEC. REFERENCES [ J. B. Goodenough, H. Abuna, and M. Buchanan, Basic eseach needs fo electical enegy stoage, in Repot of the basic enegy sciences wokshop fo electical enegy stoage, vol. 86, 7. [ R. Kötz and M. Calen, Pinciples and applications of electochemical capacitos, Electochim. Acta, vol. 45, no. 5, pp ,. [3 S. Bulle, E. Kaden, D. Kok, and R. W. De Doncke, Modeling the dynamic behavio of supecapacitos using impedance spectoscopy, IEEE Tansactions on Industy Applications, vol. 38,. [4 Y. Kim, S. Mohan, J. Siegel, A. Stefanopoulou, and Y. Ding, The estimation of tempeatue distibution in cylindical battey cells unde unknown cooling conditions, Contol Systems Technology, IEEE Tansactions on, vol. PP, no. 99, pp., 4. [5 J. Schiffe, D. Linzen, and D. U. Saue, Heat geneation in double laye capacitos, J. Powe Souces, vol. 6, no., pp , 6. [6 H. Gualous, H. Louahlia, and R. Gallay, Supecapacito chaacteization and themal modelling with evesible and ievesible heat effect, Powe Electonics, IEEE Tansactions on, vol. 6, no., pp ,. [7 A. d Entemont and L. Pilon, Fist-pinciples themal modeling of electic double laye capacitos unde constant-cuent cycling, J. Powe Souces, vol. 46, pp , 4. [8 Y. Pavini and A. Vahidi, Optimal chaging of ultacapacitos duing egeneative baking, in Electic Vehicle Confeence (IEVC), IEEE Intenational. IEEE,, pp. 6. [9 D. H. Jeon and S. M. Baek, Themal modeling of cylindical lithium ion battey duing dischage cycle, Enegy Convesion and Management, vol. 5, no. 8, pp ,. [ H. Maleki, S. Al Hallaj, J. R. Selman, R. B. Dinwiddie, and H. Wang, Themal popeties of lithium-ion battey and components, J. Electochem. Soc., vol. 46, no. 3, pp , 999. [ V. R. Subamanian, V. D. Diwaka, and D. Tapiyal, Efficient macomico scale coupled modeling of batteies, J. Electochem. Soc., vol. 5, no., pp. A A8, 5. 47