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Ultracapacitor Distributed Model Equivalent Circuit for Power Electronic Circuit Simulation John M. Miller Dragan Nebrigic Michael Everett Maxwell Technologies Inc. San Diego, CA Ansoft Leading Insights Workshop Los Angles, CA 19 Oct. 2006 Southfield, MI 24 Oct. 2006 Ultracapacitors Microelectronics High-Voltage Capacitors July 18, 2006 Outline • Introduction to Maxwell • Facilities and Business Units • Introduction to Ultracapacitors • The technology • Ultracapacitor model • Ultracapacitor Model Basics • Transmission line “moment matched” approach • Extending PWB circuit router nonlinear model to Ultracapacitor • Model Validation • Model parameter extraction and validation: MC2600 model • Simulation validation tests: D Cell model • Automotive Application – Engine Cold Cranking Ultracapacitors Microelectronics High-Voltage Capacitors Slide 2 Introduction Founded in 1965 Manufacturing in Switzerland, USA & China – capacity 20-25M cells per year Worldwide distribution Own electrode & electrolyte so technology and quality is controlled in-house Driving ultracapacitor costs down Recognised by Frost & Sullivan as pioneer manufacturer of ultracapacitors 16949 Certified Wide range of cells and standard/bespoke modules Ultracapacitors Microelectronics High-Voltage Capacitors Slide 3 Introduction • Cells tested to highest specs possible – some to MIL standards • Cells – mechanical shock & vibration • Crush & penetration • Temperature & humidity cycling • Salt fog & ambient pressure • Charge/discharge abuse • Self discharge characterisation • DC Life • Modules • Shock and Vibration • Thermal and Humidity • Pressure • Crash testing • Penetration • Fire Testing • Strong experience with traction/ buses/ coaches/ wind turbines/ fork lift trucks/ Vehicles Ultracapacitors Microelectronics High-Voltage Capacitors Slide 4 About Maxwell Capacitor Manufacturer since 1965 Manufacturing facilities: Maxwell is a leading developer US, Europe, Asia and manufacturer of innovative, cost-effective energy storage and power delivery solutions. Certifications: ISO 9001:2000 ISO/TS 16949 ISO 9002 Ultracapacitors Microelectronics High-Voltage Capacitors Slide 5 Maxwell Products Ultracapacitor Business Unit Automotive Consumer Applications Transportation Industrial Ultracapacitors Microelectronics High-Voltage Capacitors Slide 6 Ultracapacitor Market • Applications are proliferating rapidly because manufacturing capability is now in place for ultracapacitors • Ultracapacitor markets to grow 300% and Lithium battery markets to grow 1500% by 2012 –Frost & Sullivan report 2005 2012 Market growth UC’s by 300% Lithium by 1500% Frost & Sullivan Industry Outlook and Growth Strategies 2006 Meeting Hyatt Hill Country, San Antonio, 24-27 Sept 2006, Ultracapacitors Microelectronics High-Voltage Capacitors Slide 7 Maxwell Products Ultracapacitor Product Range Range of Cell Products (30 and growing) • From 2F to 10F (PC) • From 150 – 350F (BC) • From 650 – 3000F (MC) Ultracapacitors Microelectronics High-Voltage Capacitors Slide 8 Maxwell Products Ultracapacitor Modules 15-50V Modules Ultracapacitors Microelectronics High-Voltage Capacitors Slide 9 Ultracapacitor Introduction • Double layer capacitor technology • Ultracapacitor equivalent circuit model Ultracapacitors Microelectronics High-Voltage Capacitors Slide 10 Ultracapacitor Technology • The electrode is fundamental to ultracapacitor performance. Source: IEEE Spectrum, Jan 2005 Ultracapacitors Microelectronics High-Voltage Capacitors Slide 11 Ultracapacitor Model Basics • The ultracapacitor model commonly applied is that of the series combination of two DLC’s at the electrode - solvent compact layer. _ Ionic Resistance _ + Separator + electrolyte + Electrical Resistance: Helmholtz layers Helmholtz layers Collector foil + Separator _ _ + Foil to Carbon+ _ _ + + + C-particle to _ _ + C-particle + + _ _ + _ + _ + _ _ + + + ++ _ _ + + + + _ _ _ _ _ + + _ + _ _ _ + + Electrode Electrolyte Electrode Electric conductivity Ionic conductivity Electric conductivity Ultracapacitors Microelectronics High-Voltage Capacitors Slide 12 Ultracapacitor Model Basics • Extreme capacitance is available from the carbon electrochemical double layer capacitor • Activated carbon has very high specific area (S) • The compact layer interface between the carbon particles and electrolyte ions, the Helmholtz layer, is on the order of 1 atom thickness. 3ε 10 ( m2 ) 3 εS g C= = d 10 −9 Scale * 1012 ( ) Ultracapacitors Microelectronics High-Voltage Capacitors Slide 13 Ultracapacitor Model Basics 1. Non-purely resistive short term behaviors during first few milliseconds PC10F MC2600 -100 Amps Constant Current Charge - 0.03V Initial Voltage 0.35 0.3 Voltage 0V 0.25 Vo ltag e (V 0.2 2. A varying slope of voltage respond 0.15 during charge 3. Phenomenon of energy redistribution 0.1 after charge 0.05 4. Long term time constant (voltage dependent charge recovery) 0 10.0 60.0 110.0 160.0 210.0 260.0 310.0 360.0 410.0 460.0 510.0 560.0 610.0 660.0 710.0 760.0 810.0 860.0 910.0 960.0 1010.0 5. Significant inaccuracies can be observed since extraction conditions are different Especially initial states Time (100/sec) Ultracapacitors Microelectronics High-Voltage Capacitors Slide 14 Electrode as Transmission Line • Simple RC model is therefore inadequate to describe the nonlinear DLC electrode behavior. •Complex network of voltage dependent capacitors connected by the distributed resistances •Supercapacitor theoretical model could be treated as a transmission line with the voltage dependent distributed capacitance Ultracapacitors Microelectronics High-Voltage Capacitors Slide 15 3 L-section Moment Matched Model • Transfer function of any linear system respond on impulse function. Three non-uniform L segment model Two uniform L segment model 13% more accurate: Moment Matching => Transfer function coefficients for the Linear system transmission line transfer function that reacts on impulse have corresponding polynomial coefficients identical to the second Coefficient of the non-uniform distributed RC line Ultracapacitors Microelectronics High-Voltage Capacitors Slide 16 Ultracapacitor Model • Maxwell Technologies nonlinear, multiple time constant, equivalent circuit model derived from transmission line theory • Ultracapacitor electrode is a distributed RC network • Three nonlinear time constants are sufficient Power MC2600-Cell Transmission Model R1 Rtran1 0.3R Rtran2 0.2R Rtran3 0.5R 0.0008 Ohm 0.4C(v) 0.414C(v) 0.16C(v) 100 # # + # -250 A I1 C XY_LINT2 C1 C2 V XY_LINT1 XY_LINT3 XY XY XY VM1 Ultracapacitors Microelectronics High-Voltage Capacitors Slide 17 MC2600 Ultracapacitor Model • R’s and C’s are transmission line moment method derived parameters • C(U) is table lookup – increases with voltage Charge & Capacitance vs. Voltage 1000 Q(Uc) Capacitance (C) 800 Coulomb (Q), C(Uc)=Q(Uc)/Uc 600 400 200 0 0.00 0.50 1.00 1.50 2.00 2.50 3.00 Voltage (V) Ultracapacitors Microelectronics High-Voltage Capacitors Slide 18 MC2600 Ultracapacitor Model • Validation test: constant current • Evaluate ESR and average capacitance, Co • Discharge to ~ ½ Umx • Ic =250A discharge for T=15s • 2.85V 2.765V 1.365V in 15s • ESR= δU/Ic= 340µΩ and <Co> = Ic/(Ucf-Uci) = 2665F C urrentSourc TerminalV o lts 0 2.85 -25.000 -50.000 -75.000 2.50 -100.000 -125.000 I1.I [A] -150.000 -175.000 VM1... -200.000 2.00 -225.000 -250.000 0 5.00 10.00 15.00 20.00 25.00 1.50 1.36 0 10.00 20.00 25.00 Ultracapacitors Microelectronics High-Voltage Capacitors Slide 19 MC2600 Ultracapacitor Model • Validation test: constant current • Evaluate ESR and average capacitance, Co • Discharge to ~ ¼ Umx • Ic =250A discharge for T=20s • 2.85 2.765V 0.844V in 20s • ESR = δU/Ic = 340 µΩ and <Co> = Ic/(Ucf-Uci) = 2604F C urrentSourc TerminalV o lts 0 -25.000 2.85 -50.000 -75.000 -100.000 -125.000 I1.I [A] -150.000 2.00 -175.000 VM1... -200.000 -225.000 -250.000 0 5.00 10.00 15.00 20.00 25.00 1.00 840.00 m 0 10.00 20.00 25.00 Ultracapacitors Microelectronics High-Voltage Capacitors Slide 20 MC2600 Ultracapacitor Validation • Laboratory test and validation of MC2600 MC-2600 Nonlinearity -100Amps Cons ec tant Charge, 5s Charnge 0.35 Voltage 0V-100Amps Processed Voltage 0.5V-100Amps 0.3 Processed Voltage 1V-100Amps Processed Voltage 1.5V-100Amps Processed Voltage 2V-100Amps 0.25 Processed Voltage 2.5V-100Amps Processed Voltage 2.7V-100Amps Processed Voltage 3.0V-100Amps MC-2600 Voltage Variat 0.2 0.15 0.1 0.05 0 0 200 400 600 800 1000 1200 -0.05 Time (sec*100) Plot shows nonlinear response of ultracapacitor due to initial state (state-of-c Ultracapacitors Microelectronics High-Voltage Capacitors Slide 21 MC2600 Ultracapacitor Validation • Total transmission line capacitance (DLC) as function of voltage. MC-2600 Total Capacitance -Voltage Dependance 3500 y = -61.66x2 + 508.35x + 1946.4 3000 Capacitance (V) 2500 Poly. (Capacitance (V)) Variation in Capacitance 2000 1500 1000 500 0 0 0.5 1 1.5 2 2.5 3 3.5 Voltage (V) Ultracapacitors Microelectronics High-Voltage Capacitors Slide 22 D Cell Model Performance Tests • Summary of constant power tests • Evaluate at the following points: 0.1 Pml = 34W; 0.4 Pml = 135W; 1.0 Pml = 336W; and 1.6 Pml = 538W D Cell Module Pml = 5.6kW/kg or 336W per cell 2.5V, 2.2mOhm, 60g Power D-Cell Transmission Model R1 Rtran1 0.3R Rtran2 0.2R Rtran3 0.5R PSRC1 -500 W 0.0008 Ohm Power 0.4C(v 0.44C(v 0.16C(v Rsd VM1 560 Ohm + # # V C XY_LINT2 C1 XY_LINT3 # AM1 XY_LINT1 C2 A XY XY XY Power loading Load Watts Voltage cut-off Uco, Time to Uco Useable Energy (J) Delivered Energy Energy Eff. (W) (V) (s) (P*t) 0.1 Pml = 34 0.45 31 1260.6 1054 0.83 0.4 Pml = 135 0.9 6.56 1230.5 885.6 0.72 1.0 Pml = 336 1.42 1.78 1180 598.1 0.507 1.6 Pml = 538 1.8 0.653 1120.6 351.3 0.313 Total stored energy at Uc = Umx is: 1295 J. Ultracapacitors Microelectronics High-Voltage Capacitors Slide 23 D Cell Model Performance Tests • Cell cut-off voltage, Uco, is determined as follow under constant power conditions: U c 0 = 2 ESR * P0 • D Cell model performance at Po = 34W and at 336W Load_Vand_ Load_Vand_ 81.00 400.00 300.00 PSRC1.V [V] PSRC1.I [A] PSRC1.V [V] PSRC1.I [A] 50.00 -10.0... -10.0... 200.00 -1.00... -1.00... 25.00 100.00 4.00 8.00 0 20.00 31.00 0 1.00 1.78 Initial current: 12.3A 122A Ultracapacitors Microelectronics High-Voltage Capacitors Slide 24 D Cell Model Performance Tests • Model internal time constants and response: 34W Probe1 2.76 P robe3 P robe4 2.76 2.76 2.25 2.20 2.00 1.75 1.80 C.V [V] C1.V ... C2.V ... 1.60 1.25 1.40 1.20 560.00m 1.00 610.00m 630.00m 0 5.00 15.00 31.00 t 0 5.00 15.00 31.00 0 10.00 31.00 Voltage across the nonlinear capacitance branches in the model. C_Amps C1_Amps C2_Amps -5.00 -3.55f -4.93m -15.00 -10.00 -4.00 -15.00 C2.I [A] -20.00 C.I [A] C1.I [A] -6.00 -20.00 -25.00 -8.00 -25.00 -35.40 -34.00 -11.55 0 5.00 15.00 31.00 0 5.00 15.00 31.00 0 5.00 15.00 31.00 Currents through the nonlinear capacitance branches in the model Ultracapacitors Microelectronics High-Voltage Capacitors Slide 25 D Cell Model Performance Tests • Internal time constant and response: 336W Probe1 P robe3 P robe4 2.76 2.76 2.76 2.40 2.40 2.40 2.20 C.V [V] C1.V ... C2.V ... 2.00 2.20 2.20 2.00 1.56 2.00 1.75 1.84 0 400.00m 1.00 1.78 t 0 400.00m 1.00 1.78 0 400.00m 1.00 1.78 Voltage across each nonlinear branch capacitance in the model. C_Amps C1_Amps C2_Amps -62.50 -1.78f -4.92m -100.00 -40.00 -15.00 -120.00 -60.00 -140.00 C.I [A] C1.I [A] C2.I [A] -80.00 -25.00 -160.00 -100.00 -180.00 -35.00 -211.00 -145.00 -45.00 0 400.00m 1.00 1.78 0 400.00m 1.00 1.78 0 400.00m 1.00 1.78 Currents through each nonlinear branch capacitance in the model. Ultracapacitors Microelectronics High-Voltage Capacitors Slide 26 D Cell Model Performance Tests • D Cell constant power experimental versus modeled response data @ Po=7.5W Measured Measured Model Model Initial time 0 Final time (s) 178.8 Initial time 0 Final time (s) 148.2 Initial Current 2.72 Final Current (A) 38.25 Initial Current 2.72 Final Current (A) 36.4 Initial Voltage 2.8 Final Voltage (V) 0.186 Initial Voltage 2.76 Final Voltage (V) 0.188 • There appears to be some discrepancy in final time, tf: • Model contains an additional external resistance that lab test does not. 2 CU mx P0 t f ≅ • The final time at constant power discharge can be approximated as: 2 2 CU mx 340(2.8) 2 tf = = = 177.7 Consistent with laboratory test 2 P0 2(7.5) Ultracapacitors Microelectronics High-Voltage Capacitors Slide 27 Engine Cold Cranking Example • The ultracapacitor model is readily scaleable to arbitrary module size. Np C mod = C cell Ns Ns ESRmod = ESRcell Np • The “diesel” engine is modeled as friction and inertia elements in Simplorer • The starter motor is modeled as a gyrator: cross coupled electro-mechanical system. Ultracapacitors Microelectronics High-Voltage Capacitors Slide 28 Engine Cold Cranking Example • Overall Simplorer model Power MC2600-Cell in 6s x 2p Module Rtran1 = 0.3R Rtran2 = 0.2R L1 Rtran1 0.3R Rtran2 0.2R Rtran3 0.5R Rtran3 = 0.5R R_Cable12F 0.611 mOhm 102 nH Ctran1=0.4*C(v) 0.4C(v) 0.414C(v) 0.16C(v) + # 100 # Rleak 1650 Ohm Ctran2=0.414*C(v) # S1 VM1 V XY_LINT1 C XY_LINT2 C1 XY_LINT3 C2 Ctran3=0.16*C(v) XY XY XY C = C(v) R = 5mOhms Ra 2.2 mOhm MASS_roto SystemGearin WM_Cran La + MASS_Cran % 0.0005 kg m 100 % 0.15 mH 2 W 2.6 kg m% 1 GAIN_ke 60 + Ea GAIN ω DAMP_ROT VM_Arm_Sp 0.0003 Nms/ra GAIN_kt AM1 DAMP_Cran A GAIN T F_arm 25 Nms/rad Engine nonlinear torque model State machine to actuate and terminate cranking event TRANS1 STATE2 TRANS2 STATE1 STATE3 Starter motor electro-mechanical model K1:=0 t>=1.5 K1:=1 t>=9.5 K1:=0 Ultracapacitors Microelectronics High-Voltage Capacitors Slide 29 Engine Cold Cranking Example • Engine cranking simulation ultracapacitor only: 16 liter CI engine • Electrical performance • Starter Motor: Armature speed & current Arm Speed(r. 2DGraphS.. Ultracapacitor: UC 1.11k Voltage 1.93k 12.8 AM1.I [A] VM_... 1.00k AM1... VM1.. 500.00 10.0 0 0 8.36 0 5.00 8.00 0 5.00 8.00 0 5.00 8.00 • Mechanical performance Arm Torque (Nm) 18.40 Engine Crank Speed (r/s) 21.00 • Starter motor torque (Nm) Engine speed (rad/s) 10.00 10.00 -1.00... WM_... 0 0 0 5.00 8.00 0 5.00 8.00 Ultracapacitors Microelectronics High-Voltage Capacitors Slide 30 Summary • The Maxwell Technologies ultracapacitor large signal equivalent circuit model provides very good agreement with products • Constant current validation • Constant power validation • The model is readily scalable to industrial applications • Ultracapacitor and battery hybrid energy storage systems are currently under evaluation Ultracapacitors Microelectronics High-Voltage Capacitors Slide 31 References • Andrew B. Kahng, Sudhakar Mudd, “Optimal Equivalent Circuits for Interconnect Delay Using Moments,” published in Association for Computing Machinery, 1994 ACM 0-89791-687-5 • Russel L. Spyker, Robert M. Nelms, “Analysis of Double Layer Capacitors Supplying Constant Power Loads,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 36, Nr. 4, Oct. 2000 • George L. Paul, Anthony M. Vassallo, “Effect of Time Constant on Power Capability of Supercapacitors,” authors are with CapXX and CSIRO Energy Technology respectively of Villawood and North Ryde, Australia Ultracapacitors Microelectronics High-Voltage Capacitors Slide 32 Maxwell Technologies The Ultracapacitor Company Thank You! Ultracapacitors Microelectronics High-Voltage Capacitors Slide 33 Appendix Supplementary material Ultracapacitors Microelectronics High-Voltage Capacitors Slide 34 Hybrid Energy Storage Systems • The new combination! • High power density component plus • High energy density component Ultracapacitors Microelectronics High-Voltage Capacitors Slide 35 Energy and Power Density • Specific energy 2 CU mx • E [=] Wh/kg E= 2 3600 M • Specific power 2 • Pd [=] W/kg 0.12U mx ESRdc Pd = M • M = cell mass, kg Ultracapacitors Microelectronics High-Voltage Capacitors Slide 36 Energy Relationships • Energy storage systems are typically compared using the Ragone relationship BCAP0650 P Ragon ne Umx=2.7V, Umin=2.2V 16.178 100 Energy Density at point (Wh/kg) E E ML E Es 10 T0 = = s γ E = γ ES − mγ P i PML 2 PML E ML E ml i 1 Es/2 0.1 0.1 1 .10 1 .10 1 .10 3 4 5 1 10 100 1.123 P, P s 1×10 5 i Power Density tested (W/kg) Ultracapacitors Microelectronics High-Voltage Capacitors Slide 37 Normal and Abuse Operation • Normal operation range of the ultracapacitor is from no load to matched power loading. Beyond • 16.178 100 matched power load is abuse tolerance BCAP0650 P Ragon ne Umx=2.7V, Umin=2.2V region Energy Density at point (Wh/kg) E Es i 10 η => 100% Normal Operation η => 50% Abuse E ML γ E = γ ES − mγ P Tolerance E ml 1 Rapid i Discharge η => 0% Regime 0.1 0.1 1 .10 1 .10 1 .10 3 4 5 1 10 100 1.123 P, P s 1×10 5 i Power Density tested (W/kg) Ultracapacitors Microelectronics High-Voltage Capacitors Slide 38 Hybrid Markets and Trends The HEV Application matrix Mild (42V & 144V): 100.000 • <1kWh; 10 15kW Electric Energy per cycle in Wh • 7% to 12% FE Electric vehicle 10.000 Plug In Full Strong Hybrid (>200V): min Hybrid 120 Hybrid • low storage ~ 1 kWh bus • battery heavy <3 kWh 1000 min Mild Strong • Storage: 20kW...60kW 20 Hybrid + Hybrid • 20% to >50% FE Comfort Features Plug-In Hybrid (300V) 100 in 2m (AER:all electric range) Mild Hybrid c • 10...20kWh; 20 40mi 10 20se • Storage: 50kW..100kW Micro Hybrid c 10se Full Hybrid Bus: • 2...20kWh 1 10 100 1000 • 80kW 200kW Electric Power in kW Ultracapacitors Microelectronics High-Voltage Capacitors Slide 39 Ultracapacitor Power Cells • Ultracapacitor cell design • Trends are for τ <1s and PML 10 kW/kg C= 650 1200 1500 2000 2600 3000 F ESRac = 0.6 0.44 0.35 0.26 0.21 0.20 mΩ τ= 0.39 0.528 0.525 0.520 0.546 0.60 s Irms = 105 110 115 125 130 150+ Arms Micro-Hybrid Industrial Applications Heavy Transportati Ultracapacitors Microelectronics High-Voltage Capacitors Slide 40