Online Monitoring of Supercapacitor Ageing Authors: ZhihaoSHI, François AUGER, Emmanuel SCHAEFFER, Philippe GUILLEMET, Luc LORON Réunion inter GDR inter GT 2//203
Content Introduction Applications of EDLCs (Electric Double Layer Capacitors) Advantages of EDLCs EDLCs models EDLCs Ageing Online Identification Principle Mathematical model of EDLCs system Observability of EDLCs system Identification methods Experimental Results Conclusion and future work 2
Applications Electronics PC Mobile Phone Digital Camera Energy Solar Cell Wind Power Fuel Cell Transportation Electric Vehicle (EV) Supercapacitor Bus Global market for supercapacitors for 2008-205 3
EDLCs (Electric double layer capacitors) Electric double layer High C -> Higher energy density than a conventional capacitor High Power Density -> Faster charging/discharging than a battery Long life cycle
EDLCs Ageing Initial and aged Activated-carbon surfaces AFM photographs of the positive polarizing electrode by T. Umemura etc. CAUSE: Parasitic electrochemical reactions Eg. Decomposition of the electrolyte CONSEQUENCE: Reduce the life expectancy of EDLCs RESEARCH AIM: Monitor the ageing process of the EDLCs Detect when the end of life criteria occurs Replace the old EDLC to avoid catastrophic events 5
EDLCs models Classic RC model [] Transmission line model [2] N-branch model [3] Multi-pore model [] [] D. R. Cahela and B. J. Tatarchuk, Overview of electrochemical double layer capacitors, Proceedings of the IECON 97 23 rd International Conference on Industrial Electronics, Control and Instrumentation, Vol. 3, pp. 068-073, November 997 [2] R. de Levie, On porous electrodes in electrolyte solutions: I. Capacitance effects, Electrochimica Acta, vol. 8, no. 0, pp. 75 780, Oct. 963. [3] R. M. Nelms, D. R. Cahela, and B. J. Tatarchuk, Modeling double-layer capacitor behavior using ladder circuits, IEEE Transactions on Aerospace and Electronic Systems, vol. 39, no. 2, pp. 30 38, Apr. 2003. [] R. German, P. Venet, A. Sari, O. Briat, J. M. Vinassa, Comparison of EDLC impedance models used for ageing monitoring, in 202 st International Conference on REVET, pp. 22 229, 202. 6
Quantification of EDLCs Ageing Ageing Visible by Variation of Parameters An example: End of life C R S End of life Estimate State of Health (SOH) State of Charge (SOC) E 2 CV 7
Identification EDLCs Ageing Diagnoisis EDLCs Parameter Identification Offline Identification Laboratory technique Require EDLCs to be removed from their application Online Identification In situ More practical in an application 8
Online Identification Particular charge to provide an accurate parameter estimation. Charge Discharge Monitor Load Power Supply EDLCs Online identification does not disturb the way the load consumes the energy stored in the EDLC. 9
Online Identification Charge Discharge U c Load Power Supply EDLCs I c Model based Observer Estimated Parameters R s, C, R p 0
Extended state space model of EDLCs Unknown Parameters u& = u + I C RpC U = u + R I c s c Linear state space model c Add three state variables: x : u x 2 : R s x 3 : /C x : -/(R p C) Extend to 2 3 Σ: = x x + x u 3 2 3 y = x + x2u Nonlinear model u = Ic y = Uc
Online state and parameter estimation Model based Observer? Estimated parameters Estimated internal state R s ; /C; -/(R p C) State of charge estimation Σ: = x x + x u 3 2 3 y = x + x2u Extended state space model x = u x 2 = R s x 3 = /C x = -/(R p C) u = Ic y = Uc 2
Nonlinear Observability The observability of the nonlinear system If Jacobian matrix J at x 0 has full rank: J h( x, u) ( L f h)( x, u) = x n ( L f h)( x, u ) M 0, Locally Observable [] rank( J ) x = n If EDLC system satisfies x ( x ( u&& uu &&&& ) + x ( u& + u &&& u 2 uuu &&&) 3 2 2 2 + x ( x + x ) ( u& uu&& ) + x ( x + x )( uu &&& uu &&& ) 2 2 3 3 + x x + x u u&& uu& 2 2 ( 3 )( )) 0 locally observable Eg. When u = Constant; Sinusoidal signal; Exponential signal; system is locally unobservable. When u = I +I 2 sin(ωt); (with I I 2 and x 0) system is locally observable. Σ: = x x + x u 3 2 3 y = x + x u 2 Nonlinear EDLC system = f ( x, u) y = h( x, u) x = u x 2 = R s x 3 = /C x = -/(R p C) u = Ic y = Uc 3 [] R. Hermann and A. Krener, Nonlinear controllability and observability, IEEE Transactions on Automatic Control, vol. 22, no. 5, pp. 728 70, Oct. 977.
Nonlinear Observability The observability of the linearized system Jacobian matrix of f(x,u) : Jacobian matrix of h(x,u) : f ( x, u) F = x h( x, u) H = x Observability Matrix O O H HF HF 3 HF = 2 det ( O ) Linearization Unobservable! Σ: = x x + x u 3 2 3 y = x + x u 2 Nonlinear EDLC system = f ( x, u) y = h( x, u) x = u x 2 = R s x 3 = /C x = -/(R p C) u = Ic y = Uc
Charging Current Design I Charging Discharging t Solution: Add PRBS (Pseudo Random Binary Signal) to the charging current 5
Extended Kalman Observer (EKO) Extended system dynamics : Measured output : = f ( x, u) + w y = h( x, u) + v w : Process noise v : Sensor noise I c EDLCs U c n v K y yˆ + Parameter Estimation n i EKO yˆ = h( xˆ, u) xˆ & = f ( xˆ, u) + K( y yˆ ) - xˆ xˆ xˆ xˆ 2 3 for x = u x 2 = R s x 3 = /C x = -/(R p C) ˆx : states estimated by the observer Calculation of K: K = T PH R, with & T T P = FP + PF PH R HP + Q 6
Interconnected Observers (IOs) [] Σ: = x x + x u 3 2 3 y = x + x u 2 Nonlinear EDLC system x x 2 x 3 : 2 : = xx + x3u 2 3 y = x + x u 2 = xx + x3u y = x + x u 2 x 2 x 3 x x = u x 2 = R s x 3 = /C x = -/(R p C) u = Ic y = Uc [] G. Besançon and H. Hammouri, On observer design for interconnected systems, Journal of Mathematical Systems, Estimation, and Control, vol. 8, no. 3, pp. 25, 998. 7
Interconnected Observers (IOs) - Kalman-like observer X& = F( X, u) X 2 y = H ( u) X = x x + x3u 3 y = x + x u X K 2 2 n i 2 u : I c ˆX 2 Kalman-like observer y yˆ yˆ = h( xˆ, u) n v ˆ& X = F( Xˆ, u) Xˆ + K( y yˆ ) 2 + - y : V c ˆX xˆ xˆ xˆ 2 3 X = xx + x3u y = x + x u 2 Calculation of K : K ( ˆ, ) ( ˆ T S& = S F X u S SF X, u) + H H T = S H, with ρ T 2 2 8
Interconnected Observers (IOs) - Reduced order Luenberger observer X 2 = x x + x3u 2 3 y = x + x u 2 X = xx + x3u y = x + x u 2 9
Interconnected Observers (IOs) - Reduced order Luenberger observer = xx + x3u y = x + x u 2 New output : y ' = Order is reduced! y ' = = ( y x u) x + x u 2 3 x can be deduced from y: x = y x2u Luenberger observer: xˆ & = K ( y ' yˆ ') = K ( yˆ ') 2 2 xˆ & K = K yˆ ' 2 2 yˆ ' = xˆ ( y xˆ u) + xˆ u 2 3 ˆ5 y : V c u : I c 5 2 2 xˆ & ˆ ˆ ˆ ˆ 5 = K2 ( y x2u) K2( y x2u) x5 K2x3u ˆX ˆx xˆ = xˆ + K ( y xˆ u) 5 2 2 ˆx ˆX 2 xˆ ˆ = y x2u ˆx 20
Convergence of IOs Estimation error from KLO: e = X Xˆ Estimation error from ROLO: e2 = X ˆ 2 X2 Convergence? Lyapunove Function Definition For KLO: For ROLO: V V = e Se T = e T e T 2 2 2 2 For Whole Observer: V0 = V + V2 V& If : δ ( ρ, K ) V and δ ( ρ, K2) < 0 0 2 0 Estimations of IOs are convergent. 2
Comparison of the two kinds of observers Extended Kalman Observer (EKO) Interconnected Observers (IOs) Is able to estimate the parameters online Is able to estimate the parameters online It is difficult to prove its convergence. More tuning parameters The convergence is guaranteed Less tuning parameters 22
Ageing Experiments EDLC tested: Nichicon UM series 2,7V/F Ageing test bench: Stoves Voltage source VSP Thermostat 60 C Ageing Acceleration 2 weeks ageing 23
Experimental Results Offline characterization by EIS [] 2 weeks 9 weeks 6 weeks 3 weeks Before ageing EDLCs ageing [] EIS: Electrochemical Impedance Spectroscopy 2
Experimental Results - Current and Voltage record Charging current Discharging Current 25
Experimental Results - Parameters estimation before ageing 2.5 R (ohm) s 2.5 by EKO by IOs 200 205 2050 2055 2060 2065 2070 2075 2080 time(s) /C(F - ).35.3.25.2 by EKO by IOs C) (s- ) -/(R p.5 200 205 2050 2055 2060 2065 2070 2075 2080 time(s) 0.0 0-0.0 by EKO by IOs -0.02 200 205 2050 2055 2060 2065 2070 2075 2080 time(s) 26
Experimental Results - Parameters estimation during ageing Rs/ohm 8 7 6 5 3 2 0 207% 87% 3% 58% 0 3 6 9 2 Ageing Weeks EKO IOs C/F 0,86 0,8 0,82 0,8 0,78 0,76 0,7 0,72 0,7 0,68 3,2% 5,% 0 3 6 9 2 EKO IOs Rp/ohm 60 0 20 00 80 60 0 20 0 2,%,6% 0 3 6 9 2 EKO IOs Ageing Weeks Ageing Weeks 27
Conclusions An online in situ monitoring method by means of real-time observers is proposed to monitor the EDLCs ageing. To monitor the parameter evolution online, two kinds of real time observers(eko and IOs) are designed. Compared to EKO, IOs have a lower computational cost and a guaranteed convergence. Real ageing experimental data showed that both observers succeed to estimate the parameters in real time and to perceive their evolution. Future Work Better EDLCs models will be used to the online observation of the ageing of EDLCs. ( This work has already been presented at the IEEE IECON 203 conference in Vienna in Nov. 203) 28
Thank you for your attention! E-mail: zhihao.shi@univ-nantes.fr