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ISEE’Cap09 June 29 July 2, 2009 Nantes, France Testing of Supercapacitors: Capacitance, Resistance, and Energy Energy and Power Capacity Andrew Burke Institute of Transportation Studies University of California Davis Outline of the Presentation Introduction and objectives Approaches • USABC • IEC • UCDavis UC Davis test procedures and data Determination of resistance Summary and modification to test procedures IEC Committee on testing EDLCs • Proposed procedures • Application of procedures and test data • Theoretical basis • Methods Introduction and objectives There is a need to standardize the test procedures for determining the capacitance, resistance, and energy density of supercapacitors Statements concerning the power capability of supercapacitors are particularly confusing and unreliable There are a number of approaches to determining the performance of supercapacitors and relating the device characteristics to requirements for various applications Ultracapacitor testing approaches • cyclic voltametry ( small currents) • AC impedance tests at various frequencies ( small currents) • DC with variable large currents ****** Performance of Electrochemical Capacitor Devices Energy density ( Wh/ kg vs. W/ kg) Cell voltage ( V) and capacitance ( F) Series and parallel resistance ( Ohm and Ohmcm2) Power density ( W/ kg) for a charge/ discharge at 95% efficiency Temperature dependence of resistance and capacitance especially at low temperatures ( 20 deg C) Cycle life for full discharge Self discharge at various voltages and temperatures Calendar life ( hours) at fixed voltage and high temperature ( 40 60 deg C) Test procedures Constant current charge/ discharge Capacitance and resistance for discharge times of 60 sec to 5 sec. Pulse tests to determine resistance Constant power charge/ discharge Determine the Ragone Curve for power densities between 100 and at least 1000 W/ kg for the voltage between Vrated and ½ Vrated. Test at increasing W/ kg until discharge time is less than 5 sec. The charging is often done at constant current with a charge time of at least 30 sec. Sequential charge/ discharge step cycling Testing done using the PSFUDS test cycle with the max. power step being 500 W/ kg. From the data, the roundtrip efficiency for charge/ discharge is determined. Tests modules with at least 15 20 cells in series Device V rated C ( F) R ( mOhm) RC ( sec) Wh/ kg ( 1) W/ kg ( 95%) ( 2) W/ kg Match. Imped. Wgt. ( kg) Vol. lit. Maxwell* 2.7 2885 .375 1.08 4.2 994 8836 .55 .414 Maxwell 2.7 605 .90 .55 2.35 1139 9597 .20 .211 ApowerCap** 2.7 55 4 .22 5.5 5695 50625 .009  Apowercap** 2.7 450 1.3 .58 5.89 2766 24595 .057 .045 Ness 2.7 1800 .55 1.00 3.6 975 8674 .38 .277 Ness 2.7 3640 .30 1.10 4.2 928 8010 .65 .514 Ness ( cyl.) 2.7 3160 .4 1.26 4.4 982 8728 .522 .379 Asahi Glass ( propylene carbonate) 2.7 1375 2.5 3.4 4.9 390 3471 .210 ( estimated) .151 Panasonic ( propylene carbonate) 2.5 1200 1.0 1.2 2.3 514 4596 .34 .245 EPCOS 2.7 3400 .45 1.5 4.3 760 6750 .60 .48 LS Cable 2.8 3200 .25 .80 3.7 1400 12400 .63 .47 BatScap 2.7 2680 .20 .54 4.2 2050 18225 .50 .572 Power Sys. ( activated carbon, propylene carbonate) ** 2.7 1350 1.5 2.0 4.9 650 5785 .21 .151 Power Sys. ( graphitic carbon, propylene carbonate) ** 3.3 3.3 1800 1500 3.0 1.7 5.4 2.5 8.0 6.0 486 776 4320 6903 .21 .23 .15 .15 JSR Micro ( AC/ graphitic carbon) 3.8 1000 2000 4 1.9 4 3.8 11.2 12.1 900 1038 7987 9223 .113 .206 .073 .132 ( 1) Energy density at 400 W/ kg constant power, Vrated  1/ 2 Vrated ( 2) Power based on P= 9/ 16*( 1 EF)* V2/ R, EF= efficiency of discharge * Except where noted, all the devices use acetonitrile as the electrolyte ** all device except those with ** are packaged in metal containers Summary of the characteristics of various ultracapacitors being developed all over the world All these ultracapacitors have been tested at UC Davis Approach USABC • United States vehicle manufacturers • FreedomCAR Ultracapacitor Test Manual • Characterization tests based on a Imax value set by manufacturer ( somewhat arbitrary) • Procedures are not well tailored to testing ultracapacitors – often are closely related to testing batteries • Pulse power characterization tests are vehicle application oriented and not easily applied to proto type devices • Procedures not well suited for device evaluation in general Calculation of the pulse power characteristics of ultracapacitors using the USABC and energy efficiency methods USABC method PABC = Vmin ( Vnom. OC – Vmin)/ R = 1/ 8 Vrated / R discharge PABC = Vmax ( Vmax  Vnom. OC )/ R = 1/ 4 Vrated / R charge VnomOC is the open circuit voltage at a mid range voltage ( 3/ 4 Vrated ) Vmin is the minimum discharge voltage for the cap ( 1/ 2 Vrated ) Vmax is the maximum regen voltage for the cap ( Vrated) R is the effective pulse resistance of the ultracapacitor Pulse efficiency method PEF = 9/ 16( 1 EF) V 2 rated / R both charge and discharge pulses at ¾ Vrated Differences in the maximum peak power predicted by the USABC and the EF methods for supercapacitors discharge PEF / PABC = 9/ 2 ( 1 EF) charge PEF / PABC = 9/ 4 ( 1 EF) Example: Ultracapacitor V rated = 2.7 , Vmin = 1.35, Vmax = 2.7, Vnom = 2.025 Efficiency EF Discharge PEF/ PABC charge PEF/ PABC .95 .225 .11 .90 .45 .23 .85 .675 .34 .80 .9 .45 .75 1 .56 .70 1 .68 Calculation the pulse power characteristics of batteries using the USABC and energy efficiency methods USABC method PABC = Vmin ( Vnom. OC – Vmin)/ R discharge PABC = Vmax ( Vmax  Vnom. OC )/ R charge VnomOC is the open circuit voltage at a mid range SOC Vmin is the minimum voltage at which the battery is to be operated in discharge Vmax is the maximum voltage at which the battery is to be operated in charge ( regen) R is the effective pulse resistance of the battery Pulse efficiency method PEF = EF( 1 EF) V 2 nomOC / R both charge and discharge pulses Differences in the maximum peak power predicted by the USABC and the EF methods discharge PEF / PABC = EF( 1 EF)/ [( Vmim/ VnomOC)( 1 Vmin / VnomOC)] charge PEF / PABC = [( VnomOC/ Vmax, ch) 2/ ( 1 VnomOC/ Vmax, ch)] EF( 1 EF) Example: Iron Phosphate VnomOC = 3.2, Vmin = 2, Vmax = 4.0 Efficiency EF( 1 EF) Discharge PEF/ PABC charge PEF/ PABC .95 .0475 .20 .15 .90 .09 .38 .29 .85 .1275 .54 .41 .80 .16 .68 .51 .75 .1875 .80 .60 .70 .21 .90 .67 Example: Nickel Cobalt VnomOC = 3.7, Vmin = 2.5, Vmax = 4.3 Efficiency EF( 1 EF) Discharge PEF/ PABC charge PEF/ PABC .95 .0475 .22 .25 .90 .09 .41 .48 .85 .1275 .58 .68 .80 .16 .73 .85 .75 .1875 .86 1.0 .70 .21 .96 .1.0 56 V, 90 F Power Systems Nano Storage Carbon Ultracapacitor USABC UC10 test 4 sec discharge at 54A ( 100C) 4 sec rest 4 sec charge at 54A Repeat 5 times Repeat 10 times Roundtrip efficiency 95.8% USABC Pulse Characterization 5 sec at 100 A ( 211C) 55 sec rest I= 0 5 sec at 75 A Time step sec Full power kW Cell test power W W/ kg Net energy W sec 9 10 disch 117 557 1053 27 rest 0 0 1053 2 16 charge 188 895 677 4 11 charge 129 614 161 4 6 charge 71 338  121 26 rest 0 0  121 USABC Pulse Efficiency test 125 Wh unit  15 kg cells Roundtrip efficiency 93.5% PSFUDS test 500 W peak power pulse 12 seconds three cycles 91%, 91.9%, 92% 1000W peak power pulse 6 seconds three cycles 84.9%, 85.2%, 86% Pulse cycle tests of the Power Systems 14 cell module 0 5 10 15 20 25 30 35 40 45 50 0 200 400 600 800 1000 1200 1400 1600 1800 Time ( secs) Discharge 89.9 0.0247 95.7 Charge 67.9  0.0216 Discharge 84.3 0.0239 94.8 Charge 62.5  0.0221  87.5 Discharge 79.0 0.0234 94.1 Charge 57.4  0.0224  89.8 Discharge 73.8 0.0232 93.2 Charge 52.3  0.0228  92.0 Discharge 68.6 0.0228 91.5 Charge 47.3  0.0240  94.0 Discharge 63.6 0.0223 88.7 Charge 42.1  0.0251  95.5 Discharge 58.8 0.0217 84.6 Charge 36.7  0.0267  96.2 Discharge 54.0 0.0216 80.5 Charge 30.9  0.0289  96.2 Discharge 49.1 0.0210 75.2 Charge 24.6  0.0312  94.0 Discharge 44.3 0.0208 69.2 Charge 17.9  0.0340  91.7 Discharge 39.6 0.0205 61.6 Charge 10.4  0.0372  88.2 USABC Pulse Characterization Test of the PS14 cell module SOC= V Vmin/ Vmax Vmin Vmax= 3.3, Vmin= 2.0 Approach IEC ( International Electrotechnical Commission) New test procedure recently voted on and approved Device oriented application neutral Assumes ideal EDLC to derive test conditions 95% efficient charge and discharge; constant current test Ich = Vr/ 38R, Idisch = Vr/ 40R Determination of capacitance from discharge between .9Vr and .7Vr Determination of resistance from initial IR drop at initiation of the discharge Maximum power is given as P= Vr2/ 4R ( matched impedance) – determining useful power is still a key issue No consideration of energy density or effect of discharge rate on capacitance or energy stored included LS Cable 300 A Constant Current 0 0.5 1 1.5 2 2.5 3 0 20 40 60 80 100 120 140 160 Time ( sec) Voltage ( Volts)  400  300  200  100 0 100 200 300 Current ( Amps) Current Voltage Voltage vs. time for a carbon/ carbon capacitor Power Systems 55V NSC  40  30  20  10 0 10 20 30 40 50 60 0 20 40 60 80 100 120 140 160 180 time sec Amps, V Voltage vs time at constant current ( 30A) Fuji 200A Constant Current 0 0.5 1 1.5 2 2.5 3 3.5 4 0 20 40 60 80 100 120 140 Time ( sec) Voltage ( Volts)  250  200  150  100  50 0 50 100 Current ( Amps) Current Voltage Voltage vs. time for a hybrid capacitor ( carbon/ met. Oxide) Voltage, current traces for the C/ PbO2 device Carbon PbO2 ( 42 cm 2 ) Constant Current ( 2 A) 0 0.5 1 1.5 2 2.5 0 50 100 150 200 250 300 350 400 Time ( sec) Voltage ( volts)  2.5  2  1.5  1  0.5 0 0.5 1 1.5 Current ( amps) Voltage Current Test data for application of the IEC test procedures IEC Test Cycle Maxwell Capacitor  200  150  100  50 0 50 100 150 200 250 0 100 200 300 400 500 600 700 Time ( seconds) Current ( amps) 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Voltage ( volts) Current Voltage Cap ( F) IEC Full V Eff ( 1) Eff ( 2) R mOhm R mOhm meas Av. cur. A LS Cable round trip eff. 3045 3071 83.5 85 0.37 0.44 194 ch/ disch eff 0.91 0.92 Maxwell round trip eff. 3202 3168 88.4 89.2 0.44 0.45 157 ch/ disch eff 0.94 0.94 Ness round trip eff. 3254 3285 86.9 88.6 0.47 0.45 147 ch/ disch eff 0.93 0.94 Ness term conn round trip eff. 3253 3266 85 87 0.28 0.275 245 ch/ disch eff 0.92 0.93 JSR round trip eff. 2070 1900 89.1 89.5 2.6 2.7 37 ch/ disch eff 0.94 0.95 charge or discharge efficiency = sqroot ( roundtrip efficiency) Capacitance from 0.9 Vmax to 0.7 Vmax ( 2.43  1.89) For JSR from 3.48 to 2.84 Full V means the discharge from Vrated to 1.35 V Sample IEC test data for several supercapacitors Approach UCDavis ( Burke) Based on constant current, constant power, and pulse tests of devices Capacitance determined from constant current tests using the simple relation C= Q/( V1 V2) Resistance determined from the constant current tests using the data at the initiation of the discharge by extrapolating the linear voltage curve back to t= 0. Pulse tests done to check resistance determined from the constant current tests Energy density determined from the constant power tests over voltage range Vr and Vr/ 2 or that set by device manufacturer in the case of hybrid supercapacitors. Peak pulse power calculated from the relationship P = 9/ 16 ( 1 Eff) Vr 2 / R ( pulse at V = ¾ Vr ) 57 gm, 45 cm3 ApowerCap AC/ AC 450F device Test data for the Pouch packaged APowerCap device Constant current discharge data 2.7V  0 Current A Time sec Capacitance F Resistance mOhm 10 120.5 450 Not calculate 20 60.3 453 Not calculate 40 30 453 Not calculate 80 14.7 452 1.4 120 9.6 455 1.4 160 7.1 456 1.3 Constant power discharges data 2.7 – 1.35V Power W W/ kg * Time sec Wh Wh/ kg Ceff 12.5 219 95.5 .332 5.82 437 22 385 54.9 .336 5.89 442 41.5 728 28.8 .332 5.82 437 80.5 1412 14.6 .326 5.72 429 120 2105 9.1 .303 5.31 399 * weight of device  57 gm as tested Ceff = 2( W sec)/. 75 ( 2.7) 2 Maxwell 3000F and 650F devices Test data for the 3000F Maxwell device Constant current discharge data 2.7V  0 Current A Time sec Capacitance F Resistance mOhm 50 153.4 2869 Not calculate 100 76.7 2883 Not calculate 200 38 2900 .375 300 25 2885 .333 400 18.4 2886 .40 Constant power discharges data 2.7 – 1.35V Power W W/ kg * Time sec Wh Wh/ kg Ceff 63 115 135.3 2.349 4.27 3093 102 186 82.7 2.332 4.24 3071 201 365 40.8 2.278 4.14 3000 301 547 26.5 2.216 4.03 2918 400 727 19.4 2.156 3.92 2839 500 909 15.1 2.097 3.81 2761 * weight of device  .55 kg Ceff = 2( W sec)/. 75( 2.7) 2 Nesscap 2.7V, 3000F Supercapacitor Test data for the 3000F Nesscap cylindrical device Constant current discharge data 2.7V to 0 Current A Time sec Capacitance Resistance mOhm 50 171 3190  100 84.3 3181 .44 ( 1) 200 41.3 3157 .42 300 27 3140 .37 400 20 3150 .40 Constant power discharge data 2.7 1.35 V Power W W/ kg * Time sec Wh Wh/ kg Ceff 100 192 84.8 2.36 4.52 3107 200 383 41.8 2.32 4.44 3055 300 575 27.1 2.26 4.33 2976 400 766 19.7 2.19 4.20 2884 500 958 15.4 2.14 4.1 2818 700 1341 10.9 2.12 4.06 2792 * Weight of device .522 kg , Dimensions of the device 6 cm D, 13.4 cm length Ceff = 2( W sec)/. 75( 2.7) 2 ( 1) voltage probes connected to the bus bar 2000F Low R 2000 F 1000 F JSR  Mixed carbon lithium capacitors High energy density – 12 Wh/ kg Characteristics of the JSR Micro 2000F ultracap cell Constant Current discharge 3.8V – 0V Current ( A) Time ( sec) C( F) Resistance ( mOhm) ** 30 102.2 2004  50 58.1 1950  80 34.1 1908  130 19.1 1835 2.0 200 11.1 1850 1.9 250 8.2 1694 1.84 ** resistance is steady state value from linear V vs. time discharge curve Constant Power discharges 3.8V – 2.2V Power ( W) W/ kg Time( sec) Wh Wh/ kg * Ceff Wh/ L * 102 495 88.3 2.5 12.1 1698 18.9 151 733 56 2.35 11.4 1596 17.8 200 971 40 2.22 10.8 1508 16.9 300 1456 24.6 2.05 10.0 1392 15.7 400 1942 17 1.89 9.2 1283 14.4 500 2427 12.5 1.74 8.5 1181 13.3 * based on the weight and volume of the active cell materials Cell weight 206 gm, 132 cm3 Ceff = 2( W sec)/( 3.82  2.22 ) Pulse resistance tests results Resistance ( mOhm) Current ( A) Pulse test ( 5sec) RC ( sec) 100 2 3.8 200 1.9 3.5 Peak pulse power at 95% efficiency R= 1.9 mOhm P= 9/ 16*. 05* ( 3.8) 2 /. 0019 = 214 W, 1038 W/ kg Determination of the capacitance No problem if capacitance is constant with voltage, but it is not the case even for carbon/ carbon devices Calculation of the capacitance from the data is dependent on voltage range considered Effect of voltage range on the determination of the capacitance of devices from test data Vmax to 0V Vmax to 1.35V Device/ developer 3000F/ Maxwell 100A 2880F 200A 2893F 100A 3160F 200A 3223F 3000F/ Nesscap 50A 3190F 200A 3149F 50A 3214F 200A 3238F 450F/ ApowerCap 20A 450F 40A 453F 20A 466F 40A 469F 3.8 to 2.2V 3.8 to 2.6V 2000F/ JSR Micro 80A 1897F 200A 1817F 80A 1941F 200A 1938F Seems appropriate to use the same voltage range for calculating C as used in the energy density tests – that is V max to V rated / 2. Effective capacitance from the discharge energy W sec and from charge ( A sec) are not in good agreement for the hybrid carbon capacitor Cap ( F) IEC Full V Eff ( 1) Eff ( 2) R mOhm R mOhm meas LS Cable round trip eff. 3045 3071 83.5 85 0.37 0.44 ch/ disch eff 0.91 0.92 Maxwell round trip eff. 3202 3168 88.4 89.2 0.44 0.45 ch/ disch eff 0.94 0.94 Ness round trip eff. 3254 3285 86.9 88.6 0.47 0.45 ch/ disch eff 0.93 0.94 JSR round trip eff. 2070 1900 89.1 89.5 2.6 2.7 ch/ disch eff 0.94 0.95 Capacitance from 0.9 Vmax to 0.7 Vmax ( 2.43  1.89) For JSR from 3.48 to 2.84 Full V is from roughly when current reaches full value to 1.35 V For JSR from roughly when current reaches full value to 2.2 V Sample IEC test data for several supercapacitors Methods of determining the resistance IR drop at the initiation of a constant current discharge Constant current pulse (< 5sec) at a specified voltage Bounce back of voltage at end of constant current discharge AC Hz impedance ( often at 1000 Hz) Transient constant current solution Solution of the partial differential equations for the electron current in the solid carbon and the ion current in the electrolyte through the porous electrode. Derive the voltage and currents as a function of x ( position in electrode) and time. The solution for V is the following: V= V0 – I* t/ Ccell  I* Rss { 1 – ( 4/ π2 ( 2/ 3+ Lsep / Lelectrode )) * A( t’)} * ∞ where A( t ´ ) = Σ 1/ n2 e – n2 t ´ , A( t ´ = ∞) = 0 n= 0 t ´ = t/ τ , τ = 3/ π2 Rss Ccell * Assumes capacitance per unit volume and conductivities are constant. Rss = 2/ 3 * Lelectrode * effective resistivity of electrolyte + contact resistance R( t= 0) = contact resistance + 2Lelectrode / Ax ( σcarbon + σelectrolyte ) + Lsep / Ax σelectrolyte ), R0 = 2L/ AX σcarbon Transient Power Losses in Electrochemical Capacitors during Galvanostatic Cycling by C. J. Farahmandi, published ? Mathematical Modeling of electrochemical Capacitors by Srinivasan, V. and Weidner, J. W., published in Journal of Electrochemical Society, 1998 Mathematical solution for constant current charge/ discharge t/ RC Constant current data Method of determining the resistance of devices from V vs. time Apowercap 450F cell RC= .58 sec 0.1 0 2.06 0.2 0 2.06 0.3 0 2.06 0.4 0 2.06 0.5 0 2.06 0.6  0.3 2.06 0.7  0.3 2.06 0.8  71.6 2.04 0.9  192.3 1.99 1  270 1.95 1.1  313.6 1.93 1.2  299.9 1.92 1.3  299.9 1.9 1.4  300 1.89 1.5  300 1.88 1.6  300 1.88 1.7  300 1.86 1.8  300 1.85 1.9  300 1.84 2  300 1.83 2.1  300 1.82 2.2  300 1.81 2.3  300 1.8 2.4  300 1.79 2.5  300 1.78 2.6  300 1.77 2.7  300 1.76 2.8  300 1.75 2.9  300 1.74 3  300 1.73 Time current voltage Sec A R = ( 2.06 – 1.95  delta Q/ C )/ 300 Delta Q/ C= 53.4 A sec/ 3100 = .017 V R = ( 2.06 1.95. 017)/ 300 = .31 mOhm Resistance from pulse test data Nesscap 3000F device Question? What value of resistance should be used to assess the performance of a supercapacitor unit? By performance is meant  losses/ efficiency and heat dissipation/ thermal management My experience indicates that Rss is the proper measured resistance to use and it is a well defined value for all devices This is consistent with the IEC procedure and the 95% efficiency of the charge/ discharge cycle test Summary and recommendations There is a need to standardize test procedures to determine the capacitance, resistance, and energy density of supercapacitors The uncertainty is largest for the resistance of devices; the steady state resistance determined from the initiation of discharge is well defined and relatively easily determined from constant current discharge data The effective capacitance of microporous carbon/ carbon devices is well defined from constant current data, but varies with the voltage range used to determine it ; it is recommended that the voltage range of Vr and Vr/ 2 be used. Further work is needed to determine the effective capacitance and resistance of hybrid supercapacitors. The energy density should be measured in constant power discharges and not calculated from E= 1/ 2CV2 ; this is especially the case for hybrid supercapacitors
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Title  Testing of supercapacitors capacitance, resistance, and energy and power capacity 
Subject  SupercapacitorsTesting. 
Description  Text document in PDF format.; PowerPoint slide show.; Title from PDF title page (viewed on August 25, 2009).; "ISEE'Cap09, June 29July 2, 2009, Nantes, France."; "July 2009." 
Creator  Burke, Andrew F. 
Publisher  Institute of Transportation Studies, University of California, Davis 
Contributors  University of California, Davis. Institute of Transportation Studies. 
Type  Text 
Language  eng 
Relation  http://worldcat.org/oclc/433191696/viewonline; http://pubs.its.ucdavis.edu/publication_detail.php?id=1308 
DateIssued  [2009] 
FormatExtent  42 p. : digital, PDF file (2.22 MB) with col. ill., col. charts. 
RelationRequires  Mode of access: World Wide Web. 
RelationIs Part Of  Research report ; UCDITSRR0919; Research report (University of California, Davis. Institute of Transportation Studies) ; UCDITSRR0919. 
Transcript  ISEE’Cap09 June 29 July 2, 2009 Nantes, France Testing of Supercapacitors: Capacitance, Resistance, and Energy Energy and Power Capacity Andrew Burke Institute of Transportation Studies University of California Davis Outline of the Presentation Introduction and objectives Approaches • USABC • IEC • UCDavis UC Davis test procedures and data Determination of resistance Summary and modification to test procedures IEC Committee on testing EDLCs • Proposed procedures • Application of procedures and test data • Theoretical basis • Methods Introduction and objectives There is a need to standardize the test procedures for determining the capacitance, resistance, and energy density of supercapacitors Statements concerning the power capability of supercapacitors are particularly confusing and unreliable There are a number of approaches to determining the performance of supercapacitors and relating the device characteristics to requirements for various applications Ultracapacitor testing approaches • cyclic voltametry ( small currents) • AC impedance tests at various frequencies ( small currents) • DC with variable large currents ****** Performance of Electrochemical Capacitor Devices Energy density ( Wh/ kg vs. W/ kg) Cell voltage ( V) and capacitance ( F) Series and parallel resistance ( Ohm and Ohmcm2) Power density ( W/ kg) for a charge/ discharge at 95% efficiency Temperature dependence of resistance and capacitance especially at low temperatures ( 20 deg C) Cycle life for full discharge Self discharge at various voltages and temperatures Calendar life ( hours) at fixed voltage and high temperature ( 40 60 deg C) Test procedures Constant current charge/ discharge Capacitance and resistance for discharge times of 60 sec to 5 sec. Pulse tests to determine resistance Constant power charge/ discharge Determine the Ragone Curve for power densities between 100 and at least 1000 W/ kg for the voltage between Vrated and ½ Vrated. Test at increasing W/ kg until discharge time is less than 5 sec. The charging is often done at constant current with a charge time of at least 30 sec. Sequential charge/ discharge step cycling Testing done using the PSFUDS test cycle with the max. power step being 500 W/ kg. From the data, the roundtrip efficiency for charge/ discharge is determined. Tests modules with at least 15 20 cells in series Device V rated C ( F) R ( mOhm) RC ( sec) Wh/ kg ( 1) W/ kg ( 95%) ( 2) W/ kg Match. Imped. Wgt. ( kg) Vol. lit. Maxwell* 2.7 2885 .375 1.08 4.2 994 8836 .55 .414 Maxwell 2.7 605 .90 .55 2.35 1139 9597 .20 .211 ApowerCap** 2.7 55 4 .22 5.5 5695 50625 .009  Apowercap** 2.7 450 1.3 .58 5.89 2766 24595 .057 .045 Ness 2.7 1800 .55 1.00 3.6 975 8674 .38 .277 Ness 2.7 3640 .30 1.10 4.2 928 8010 .65 .514 Ness ( cyl.) 2.7 3160 .4 1.26 4.4 982 8728 .522 .379 Asahi Glass ( propylene carbonate) 2.7 1375 2.5 3.4 4.9 390 3471 .210 ( estimated) .151 Panasonic ( propylene carbonate) 2.5 1200 1.0 1.2 2.3 514 4596 .34 .245 EPCOS 2.7 3400 .45 1.5 4.3 760 6750 .60 .48 LS Cable 2.8 3200 .25 .80 3.7 1400 12400 .63 .47 BatScap 2.7 2680 .20 .54 4.2 2050 18225 .50 .572 Power Sys. ( activated carbon, propylene carbonate) ** 2.7 1350 1.5 2.0 4.9 650 5785 .21 .151 Power Sys. ( graphitic carbon, propylene carbonate) ** 3.3 3.3 1800 1500 3.0 1.7 5.4 2.5 8.0 6.0 486 776 4320 6903 .21 .23 .15 .15 JSR Micro ( AC/ graphitic carbon) 3.8 1000 2000 4 1.9 4 3.8 11.2 12.1 900 1038 7987 9223 .113 .206 .073 .132 ( 1) Energy density at 400 W/ kg constant power, Vrated  1/ 2 Vrated ( 2) Power based on P= 9/ 16*( 1 EF)* V2/ R, EF= efficiency of discharge * Except where noted, all the devices use acetonitrile as the electrolyte ** all device except those with ** are packaged in metal containers Summary of the characteristics of various ultracapacitors being developed all over the world All these ultracapacitors have been tested at UC Davis Approach USABC • United States vehicle manufacturers • FreedomCAR Ultracapacitor Test Manual • Characterization tests based on a Imax value set by manufacturer ( somewhat arbitrary) • Procedures are not well tailored to testing ultracapacitors – often are closely related to testing batteries • Pulse power characterization tests are vehicle application oriented and not easily applied to proto type devices • Procedures not well suited for device evaluation in general Calculation of the pulse power characteristics of ultracapacitors using the USABC and energy efficiency methods USABC method PABC = Vmin ( Vnom. OC – Vmin)/ R = 1/ 8 Vrated / R discharge PABC = Vmax ( Vmax  Vnom. OC )/ R = 1/ 4 Vrated / R charge VnomOC is the open circuit voltage at a mid range voltage ( 3/ 4 Vrated ) Vmin is the minimum discharge voltage for the cap ( 1/ 2 Vrated ) Vmax is the maximum regen voltage for the cap ( Vrated) R is the effective pulse resistance of the ultracapacitor Pulse efficiency method PEF = 9/ 16( 1 EF) V 2 rated / R both charge and discharge pulses at ¾ Vrated Differences in the maximum peak power predicted by the USABC and the EF methods for supercapacitors discharge PEF / PABC = 9/ 2 ( 1 EF) charge PEF / PABC = 9/ 4 ( 1 EF) Example: Ultracapacitor V rated = 2.7 , Vmin = 1.35, Vmax = 2.7, Vnom = 2.025 Efficiency EF Discharge PEF/ PABC charge PEF/ PABC .95 .225 .11 .90 .45 .23 .85 .675 .34 .80 .9 .45 .75 1 .56 .70 1 .68 Calculation the pulse power characteristics of batteries using the USABC and energy efficiency methods USABC method PABC = Vmin ( Vnom. OC – Vmin)/ R discharge PABC = Vmax ( Vmax  Vnom. OC )/ R charge VnomOC is the open circuit voltage at a mid range SOC Vmin is the minimum voltage at which the battery is to be operated in discharge Vmax is the maximum voltage at which the battery is to be operated in charge ( regen) R is the effective pulse resistance of the battery Pulse efficiency method PEF = EF( 1 EF) V 2 nomOC / R both charge and discharge pulses Differences in the maximum peak power predicted by the USABC and the EF methods discharge PEF / PABC = EF( 1 EF)/ [( Vmim/ VnomOC)( 1 Vmin / VnomOC)] charge PEF / PABC = [( VnomOC/ Vmax, ch) 2/ ( 1 VnomOC/ Vmax, ch)] EF( 1 EF) Example: Iron Phosphate VnomOC = 3.2, Vmin = 2, Vmax = 4.0 Efficiency EF( 1 EF) Discharge PEF/ PABC charge PEF/ PABC .95 .0475 .20 .15 .90 .09 .38 .29 .85 .1275 .54 .41 .80 .16 .68 .51 .75 .1875 .80 .60 .70 .21 .90 .67 Example: Nickel Cobalt VnomOC = 3.7, Vmin = 2.5, Vmax = 4.3 Efficiency EF( 1 EF) Discharge PEF/ PABC charge PEF/ PABC .95 .0475 .22 .25 .90 .09 .41 .48 .85 .1275 .58 .68 .80 .16 .73 .85 .75 .1875 .86 1.0 .70 .21 .96 .1.0 56 V, 90 F Power Systems Nano Storage Carbon Ultracapacitor USABC UC10 test 4 sec discharge at 54A ( 100C) 4 sec rest 4 sec charge at 54A Repeat 5 times Repeat 10 times Roundtrip efficiency 95.8% USABC Pulse Characterization 5 sec at 100 A ( 211C) 55 sec rest I= 0 5 sec at 75 A Time step sec Full power kW Cell test power W W/ kg Net energy W sec 9 10 disch 117 557 1053 27 rest 0 0 1053 2 16 charge 188 895 677 4 11 charge 129 614 161 4 6 charge 71 338  121 26 rest 0 0  121 USABC Pulse Efficiency test 125 Wh unit  15 kg cells Roundtrip efficiency 93.5% PSFUDS test 500 W peak power pulse 12 seconds three cycles 91%, 91.9%, 92% 1000W peak power pulse 6 seconds three cycles 84.9%, 85.2%, 86% Pulse cycle tests of the Power Systems 14 cell module 0 5 10 15 20 25 30 35 40 45 50 0 200 400 600 800 1000 1200 1400 1600 1800 Time ( secs) Discharge 89.9 0.0247 95.7 Charge 67.9  0.0216 Discharge 84.3 0.0239 94.8 Charge 62.5  0.0221  87.5 Discharge 79.0 0.0234 94.1 Charge 57.4  0.0224  89.8 Discharge 73.8 0.0232 93.2 Charge 52.3  0.0228  92.0 Discharge 68.6 0.0228 91.5 Charge 47.3  0.0240  94.0 Discharge 63.6 0.0223 88.7 Charge 42.1  0.0251  95.5 Discharge 58.8 0.0217 84.6 Charge 36.7  0.0267  96.2 Discharge 54.0 0.0216 80.5 Charge 30.9  0.0289  96.2 Discharge 49.1 0.0210 75.2 Charge 24.6  0.0312  94.0 Discharge 44.3 0.0208 69.2 Charge 17.9  0.0340  91.7 Discharge 39.6 0.0205 61.6 Charge 10.4  0.0372  88.2 USABC Pulse Characterization Test of the PS14 cell module SOC= V Vmin/ Vmax Vmin Vmax= 3.3, Vmin= 2.0 Approach IEC ( International Electrotechnical Commission) New test procedure recently voted on and approved Device oriented application neutral Assumes ideal EDLC to derive test conditions 95% efficient charge and discharge; constant current test Ich = Vr/ 38R, Idisch = Vr/ 40R Determination of capacitance from discharge between .9Vr and .7Vr Determination of resistance from initial IR drop at initiation of the discharge Maximum power is given as P= Vr2/ 4R ( matched impedance) – determining useful power is still a key issue No consideration of energy density or effect of discharge rate on capacitance or energy stored included LS Cable 300 A Constant Current 0 0.5 1 1.5 2 2.5 3 0 20 40 60 80 100 120 140 160 Time ( sec) Voltage ( Volts)  400  300  200  100 0 100 200 300 Current ( Amps) Current Voltage Voltage vs. time for a carbon/ carbon capacitor Power Systems 55V NSC  40  30  20  10 0 10 20 30 40 50 60 0 20 40 60 80 100 120 140 160 180 time sec Amps, V Voltage vs time at constant current ( 30A) Fuji 200A Constant Current 0 0.5 1 1.5 2 2.5 3 3.5 4 0 20 40 60 80 100 120 140 Time ( sec) Voltage ( Volts)  250  200  150  100  50 0 50 100 Current ( Amps) Current Voltage Voltage vs. time for a hybrid capacitor ( carbon/ met. Oxide) Voltage, current traces for the C/ PbO2 device Carbon PbO2 ( 42 cm 2 ) Constant Current ( 2 A) 0 0.5 1 1.5 2 2.5 0 50 100 150 200 250 300 350 400 Time ( sec) Voltage ( volts)  2.5  2  1.5  1  0.5 0 0.5 1 1.5 Current ( amps) Voltage Current Test data for application of the IEC test procedures IEC Test Cycle Maxwell Capacitor  200  150  100  50 0 50 100 150 200 250 0 100 200 300 400 500 600 700 Time ( seconds) Current ( amps) 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Voltage ( volts) Current Voltage Cap ( F) IEC Full V Eff ( 1) Eff ( 2) R mOhm R mOhm meas Av. cur. A LS Cable round trip eff. 3045 3071 83.5 85 0.37 0.44 194 ch/ disch eff 0.91 0.92 Maxwell round trip eff. 3202 3168 88.4 89.2 0.44 0.45 157 ch/ disch eff 0.94 0.94 Ness round trip eff. 3254 3285 86.9 88.6 0.47 0.45 147 ch/ disch eff 0.93 0.94 Ness term conn round trip eff. 3253 3266 85 87 0.28 0.275 245 ch/ disch eff 0.92 0.93 JSR round trip eff. 2070 1900 89.1 89.5 2.6 2.7 37 ch/ disch eff 0.94 0.95 charge or discharge efficiency = sqroot ( roundtrip efficiency) Capacitance from 0.9 Vmax to 0.7 Vmax ( 2.43  1.89) For JSR from 3.48 to 2.84 Full V means the discharge from Vrated to 1.35 V Sample IEC test data for several supercapacitors Approach UCDavis ( Burke) Based on constant current, constant power, and pulse tests of devices Capacitance determined from constant current tests using the simple relation C= Q/( V1 V2) Resistance determined from the constant current tests using the data at the initiation of the discharge by extrapolating the linear voltage curve back to t= 0. Pulse tests done to check resistance determined from the constant current tests Energy density determined from the constant power tests over voltage range Vr and Vr/ 2 or that set by device manufacturer in the case of hybrid supercapacitors. Peak pulse power calculated from the relationship P = 9/ 16 ( 1 Eff) Vr 2 / R ( pulse at V = ¾ Vr ) 57 gm, 45 cm3 ApowerCap AC/ AC 450F device Test data for the Pouch packaged APowerCap device Constant current discharge data 2.7V  0 Current A Time sec Capacitance F Resistance mOhm 10 120.5 450 Not calculate 20 60.3 453 Not calculate 40 30 453 Not calculate 80 14.7 452 1.4 120 9.6 455 1.4 160 7.1 456 1.3 Constant power discharges data 2.7 – 1.35V Power W W/ kg * Time sec Wh Wh/ kg Ceff 12.5 219 95.5 .332 5.82 437 22 385 54.9 .336 5.89 442 41.5 728 28.8 .332 5.82 437 80.5 1412 14.6 .326 5.72 429 120 2105 9.1 .303 5.31 399 * weight of device  57 gm as tested Ceff = 2( W sec)/. 75 ( 2.7) 2 Maxwell 3000F and 650F devices Test data for the 3000F Maxwell device Constant current discharge data 2.7V  0 Current A Time sec Capacitance F Resistance mOhm 50 153.4 2869 Not calculate 100 76.7 2883 Not calculate 200 38 2900 .375 300 25 2885 .333 400 18.4 2886 .40 Constant power discharges data 2.7 – 1.35V Power W W/ kg * Time sec Wh Wh/ kg Ceff 63 115 135.3 2.349 4.27 3093 102 186 82.7 2.332 4.24 3071 201 365 40.8 2.278 4.14 3000 301 547 26.5 2.216 4.03 2918 400 727 19.4 2.156 3.92 2839 500 909 15.1 2.097 3.81 2761 * weight of device  .55 kg Ceff = 2( W sec)/. 75( 2.7) 2 Nesscap 2.7V, 3000F Supercapacitor Test data for the 3000F Nesscap cylindrical device Constant current discharge data 2.7V to 0 Current A Time sec Capacitance Resistance mOhm 50 171 3190  100 84.3 3181 .44 ( 1) 200 41.3 3157 .42 300 27 3140 .37 400 20 3150 .40 Constant power discharge data 2.7 1.35 V Power W W/ kg * Time sec Wh Wh/ kg Ceff 100 192 84.8 2.36 4.52 3107 200 383 41.8 2.32 4.44 3055 300 575 27.1 2.26 4.33 2976 400 766 19.7 2.19 4.20 2884 500 958 15.4 2.14 4.1 2818 700 1341 10.9 2.12 4.06 2792 * Weight of device .522 kg , Dimensions of the device 6 cm D, 13.4 cm length Ceff = 2( W sec)/. 75( 2.7) 2 ( 1) voltage probes connected to the bus bar 2000F Low R 2000 F 1000 F JSR  Mixed carbon lithium capacitors High energy density – 12 Wh/ kg Characteristics of the JSR Micro 2000F ultracap cell Constant Current discharge 3.8V – 0V Current ( A) Time ( sec) C( F) Resistance ( mOhm) ** 30 102.2 2004  50 58.1 1950  80 34.1 1908  130 19.1 1835 2.0 200 11.1 1850 1.9 250 8.2 1694 1.84 ** resistance is steady state value from linear V vs. time discharge curve Constant Power discharges 3.8V – 2.2V Power ( W) W/ kg Time( sec) Wh Wh/ kg * Ceff Wh/ L * 102 495 88.3 2.5 12.1 1698 18.9 151 733 56 2.35 11.4 1596 17.8 200 971 40 2.22 10.8 1508 16.9 300 1456 24.6 2.05 10.0 1392 15.7 400 1942 17 1.89 9.2 1283 14.4 500 2427 12.5 1.74 8.5 1181 13.3 * based on the weight and volume of the active cell materials Cell weight 206 gm, 132 cm3 Ceff = 2( W sec)/( 3.82  2.22 ) Pulse resistance tests results Resistance ( mOhm) Current ( A) Pulse test ( 5sec) RC ( sec) 100 2 3.8 200 1.9 3.5 Peak pulse power at 95% efficiency R= 1.9 mOhm P= 9/ 16*. 05* ( 3.8) 2 /. 0019 = 214 W, 1038 W/ kg Determination of the capacitance No problem if capacitance is constant with voltage, but it is not the case even for carbon/ carbon devices Calculation of the capacitance from the data is dependent on voltage range considered Effect of voltage range on the determination of the capacitance of devices from test data Vmax to 0V Vmax to 1.35V Device/ developer 3000F/ Maxwell 100A 2880F 200A 2893F 100A 3160F 200A 3223F 3000F/ Nesscap 50A 3190F 200A 3149F 50A 3214F 200A 3238F 450F/ ApowerCap 20A 450F 40A 453F 20A 466F 40A 469F 3.8 to 2.2V 3.8 to 2.6V 2000F/ JSR Micro 80A 1897F 200A 1817F 80A 1941F 200A 1938F Seems appropriate to use the same voltage range for calculating C as used in the energy density tests – that is V max to V rated / 2. Effective capacitance from the discharge energy W sec and from charge ( A sec) are not in good agreement for the hybrid carbon capacitor Cap ( F) IEC Full V Eff ( 1) Eff ( 2) R mOhm R mOhm meas LS Cable round trip eff. 3045 3071 83.5 85 0.37 0.44 ch/ disch eff 0.91 0.92 Maxwell round trip eff. 3202 3168 88.4 89.2 0.44 0.45 ch/ disch eff 0.94 0.94 Ness round trip eff. 3254 3285 86.9 88.6 0.47 0.45 ch/ disch eff 0.93 0.94 JSR round trip eff. 2070 1900 89.1 89.5 2.6 2.7 ch/ disch eff 0.94 0.95 Capacitance from 0.9 Vmax to 0.7 Vmax ( 2.43  1.89) For JSR from 3.48 to 2.84 Full V is from roughly when current reaches full value to 1.35 V For JSR from roughly when current reaches full value to 2.2 V Sample IEC test data for several supercapacitors Methods of determining the resistance IR drop at the initiation of a constant current discharge Constant current pulse (< 5sec) at a specified voltage Bounce back of voltage at end of constant current discharge AC Hz impedance ( often at 1000 Hz) Transient constant current solution Solution of the partial differential equations for the electron current in the solid carbon and the ion current in the electrolyte through the porous electrode. Derive the voltage and currents as a function of x ( position in electrode) and time. The solution for V is the following: V= V0 – I* t/ Ccell  I* Rss { 1 – ( 4/ π2 ( 2/ 3+ Lsep / Lelectrode )) * A( t’)} * ∞ where A( t ´ ) = Σ 1/ n2 e – n2 t ´ , A( t ´ = ∞) = 0 n= 0 t ´ = t/ τ , τ = 3/ π2 Rss Ccell * Assumes capacitance per unit volume and conductivities are constant. Rss = 2/ 3 * Lelectrode * effective resistivity of electrolyte + contact resistance R( t= 0) = contact resistance + 2Lelectrode / Ax ( σcarbon + σelectrolyte ) + Lsep / Ax σelectrolyte ), R0 = 2L/ AX σcarbon Transient Power Losses in Electrochemical Capacitors during Galvanostatic Cycling by C. J. Farahmandi, published ? Mathematical Modeling of electrochemical Capacitors by Srinivasan, V. and Weidner, J. W., published in Journal of Electrochemical Society, 1998 Mathematical solution for constant current charge/ discharge t/ RC Constant current data Method of determining the resistance of devices from V vs. time Apowercap 450F cell RC= .58 sec 0.1 0 2.06 0.2 0 2.06 0.3 0 2.06 0.4 0 2.06 0.5 0 2.06 0.6  0.3 2.06 0.7  0.3 2.06 0.8  71.6 2.04 0.9  192.3 1.99 1  270 1.95 1.1  313.6 1.93 1.2  299.9 1.92 1.3  299.9 1.9 1.4  300 1.89 1.5  300 1.88 1.6  300 1.88 1.7  300 1.86 1.8  300 1.85 1.9  300 1.84 2  300 1.83 2.1  300 1.82 2.2  300 1.81 2.3  300 1.8 2.4  300 1.79 2.5  300 1.78 2.6  300 1.77 2.7  300 1.76 2.8  300 1.75 2.9  300 1.74 3  300 1.73 Time current voltage Sec A R = ( 2.06 – 1.95  delta Q/ C )/ 300 Delta Q/ C= 53.4 A sec/ 3100 = .017 V R = ( 2.06 1.95. 017)/ 300 = .31 mOhm Resistance from pulse test data Nesscap 3000F device Question? What value of resistance should be used to assess the performance of a supercapacitor unit? By performance is meant  losses/ efficiency and heat dissipation/ thermal management My experience indicates that Rss is the proper measured resistance to use and it is a well defined value for all devices This is consistent with the IEC procedure and the 95% efficiency of the charge/ discharge cycle test Summary and recommendations There is a need to standardize test procedures to determine the capacitance, resistance, and energy density of supercapacitors The uncertainty is largest for the resistance of devices; the steady state resistance determined from the initiation of discharge is well defined and relatively easily determined from constant current discharge data The effective capacitance of microporous carbon/ carbon devices is well defined from constant current data, but varies with the voltage range used to determine it ; it is recommended that the voltage range of Vr and Vr/ 2 be used. Further work is needed to determine the effective capacitance and resistance of hybrid supercapacitors. The energy density should be measured in constant power discharges and not calculated from E= 1/ 2CV2 ; this is especially the case for hybrid supercapacitors 



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