Slide 1: High Power Supercapacitor Performance
High Power Supercapacitor Performance Peter J. Mahon & George Paul cap-XX Pty. Ltd. December 1999
Slide 2: Supercap Characterisation
Supercap Characterisation aConstant Current (R,C) aElectrochemical Impedance Spectroscopy (R,C, Figure of Merit) aPower Capability (R,C) cap-XX 2
Slide 3: Analysis Models
Analysis Models aSimple RC Model 1 Z (ω ) = R + iωC aRCPE Model 1 Z (ω ) = R + T (iω ) p cap-XX 3
Slide 4: cap-XX Supercap
cap-XX Supercap V = 5V mass = 12.0g C = 0 .5 F size = 40x35x7mm R = 30mΩ FOM = 5.83kW / kg cap-XX 4
Slide 5: Linearized Constant Current
Linearized Constant Current 6 5 1A 4 Voltage (V) 3 2 1 E xpt R egr 0 0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 T im e ( s ) cap-XX 5
Slide 6: Linearized Constant Current
Linearized Constant Current 6 5 30A 4 Voltage (V) 3 2 1 E xpt R egr 0 0 .0 0 0 .0 2 0 .0 4 0 .0 6 0 .0 8 T im e ( s ) cap-XX 6
Slide 7: Linearized RC Model
Linearized RC Model aConstant Current It V = + IR C cap-XX 7
Slide 8: Linearized Constant Current
Linearized Constant Current 0 .0 5 0 .0 4 Resistance (ohm) 0 .0 3 0 .0 2 0 .0 1 R 0 .0 0 1 .0 Capacitance (F) 0 .8 0 .6 0 .4 C 0 .2 0 5 10 15 20 25 30 35 C u rre n t (A ) cap-XX 8
Slide 9: Non-linear RCPE Model
Non-linear RCPE Model aConstant Current p It V= + IR T Γ(1 + p ) aApply Marquardt Non-Linear Least Squares Method cap-XX 9
Slide 10: Non-linear Constant Current
Non-linear Constant Current 0 .0 5 0 .0 4 Resistance (ohm) 0 .0 3 0 .0 2 0 .0 1 R 0 .0 0 1 .0 0 .8 T,p 0 .6 0 .4 T p 0 .2 0 5 10 15 20 25 30 35 C u rre n t (A ) cap-XX 10
Slide 11: Impedance Spectroscopy
Impedance Spectroscopy 102 101 |Z| 100 10-1 10-2 10-2 10-1 100 101 102 103 Frequency (Hz) -100 -50 theta 0 50 100 10-2 10-1 100 101 102 103 Frequency (Hz) cap-XX 11
Slide 12: Impedance Spectroscopy
Impedance Spectroscopy 0 .0 5 0 .0 4 Resistance (ohm) 0 .0 3 0 .0 2 0 .0 1 R 0 .0 0 1 .0 0 .8 T p T,p 0 .6 0 .4 0 .2 0 1 2 3 4 5 V o lt a g e ( V ) cap-XX 12
Slide 13: Constant Power Cycling
Constant Power Cycling 40 30 30W Current (A), Voltage(V) & Power (W) 20 10 V o lt a g e 0 C u rre n t Pow er -1 0 -2 0 -3 0 -4 0 0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 T im e ( s ) cap-XX 13
Slide 14: Constant Power Cycling
Constant Power Cycling 80 60 70W Current (A), Voltage(V) & Power (W) 40 20 V o lt a g e 0 C u rre n t Pow er -2 0 -4 0 -6 0 -8 0 0 .0 0 .2 0 .4 0 .6 0 .8 T im e ( s ) cap-XX 14
Slide 15: Linearized RC Model
Linearized RC Model aConstant Power Q =C [V − Vo ] − RC I I cap-XX 15
Slide 16: Linearized Constant Power
Linearized Constant Power 0 .3 0 .2 30W 0 .1 Q/I 0 .0 -0 .1 -0 .2 E x p t. R egr -0 .3 -0 .5 -0 .4 -0 .3 -0 .2 -0 .1 0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 [V -V o]/I cap-XX 16
Slide 17: Linearized Constant Power
Linearized Constant Power 0 .1 0 70W 0 .0 5 Q/I 0 .0 0 -0 .0 5 E x p t. Regr -0 .1 0 -0 .2 -0 .1 0 .0 0 .1 0 .2 [V -V o]/I cap-XX 17
Slide 18: Linearized Constant Power
Linearized Constant Power 0 .0 5 0 .0 4 Resistance (ohm) 0 .0 3 0 .0 2 0 .0 1 R 0 .0 0 1 .0 Capacitance (F) 0 .8 0 .6 0 .4 C 0 .2 0 20 40 60 80 100 P o w e r (W ) cap-XX 18
Slide 19: Non-linear RCPE Model
Non-linear RCPE Model aConstant Power V = (I * Z ) d dt aApply Marquardt Non-Linear Least Squares Method cap-XX 19
Slide 20: Convolution Algorithm
Convolution Algorithm aA Straightforward Summation d 1 L −1 dt (I * Z ) = I L z1 + ∑ I L −λ ( zλ−1 − 2 zλ + zλ+1 ) t = L∆ ∆ λ=1 for L = 1,2,..., N t p t awhere z = ∫ Z dt and Z= +R 0 T Γ(1 + p ) cap-XX 20
Slide 21: Non-Linear Constant Power
Non-Linear Constant Power 6 5 30W 4 Voltage (V) 3 2 E xpt R e s id u a l T h e o ry 1 0 -1 0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 T im e ( s ) cap-XX 21
Slide 22: Non-Linear Constant Power
Non-Linear Constant Power 6 5 70W 4 Voltage (V) 3 2 E xpt R e s id u a l T h e o ry 1 0 -1 0 .0 0 .2 0 .4 0 .6 0 .8 T im e ( s ) cap-XX 22
Slide 23: Non-linear Constant Power
Non-linear Constant Power 0 .0 5 0 .0 4 Resistance (ohm) 0 .0 3 0 .0 2 0 .0 1 R 0 .0 0 1 .0 0 .8 T,p 0 .6 T 0 .4 p 0 .2 0 20 40 60 80 100 P o w e r (W ) cap-XX 23
Slide 24: Ragone Plot
Ragone Plot 10 C h a rg e D is c h a r g e 5 ρ (kW/kg) 2 P 1 0 .5 0 .0 2 0 .0 5 0 .1 0 .2 ρ E (W h /k g ) cap-XX 24
Slide 25: EIS Model of Power Data
EIS Model of Power Data 100 Discharge Power Density (kW/kg) 10 Charge EIS Model 1 0.1 0.01 0.1 1 Energy Density (Wh/kg) cap-XX 25
Slide 26: Summary of Analyses
Summary of Analyses "RC" Time Model R C,T Constant Condition Constant Current (Lin) 0.0273 0.545 0.015 15A Constant Current (Non-Lin) 0.0225 0.621 0.014 10-30A Impedance 0.0288 0.487 0.014 0V Constant Power (Lin) 0.0269 0.557 0.015 50-100W Constant Power (Non-Lin) 0.0355 0.597 0.021 20-100W acap-XX
Slide 27: cap-XX Pty. Ltd.
cap-XX Pty. Ltd. aBuilding 5, Gate 4, 105 Delhi Road aNorth Ryde, NSW 2113, Australia a+612 9490 5312 (phone) a+612 9490 5311 (fax) ageorge.paul@cap-xx.com awww.cap-xx.com cap-XX 27