Elektrochemische Modelle für Lithium-Ionen Batterien

Transkript

1 Modellbildung elektrochemischer Systeme Elektrochemische Modelle für Lithium-Ionen Batterien André Weber - IAM-WET Adenauerring 20b, Geb (FZU), Raum 314 phone: 0721/ , fax: 0721/ andre.weber@kit.edu KIT Universität des Landes Baden-Württemberg und nationales Forschungszentrum in der Helmholtz-Gemeinschaft

2 Elektrochemisches Modell Stand der Technik & Motivation Differentialgleichungen & FEM c = t ( 1 α ) ( D c) zf j = j0 exp ( U U 0 ) RT physikalisch motiviertes Ersatzschaltungsmodell I batt U OCV U batt Verhaltensmodell U OCV R 1 R 0 C1 I batt U batt hohe örtliche Auflösung nicht echtzeitfähig Parametrierung aufwendig geringe örtliche Auflösung echtzeitfähig Parametrierung mittel geringe örtliche Auflösung echtzeitfähig Parametrierung einfach Simulation von unbekannten Strukturen und Materialien Inter-/Extrapolation des Parameterraums Diagnose durch Simulation Fehler-/Degradationsfälle Inter-/Extrapolation des Parameterraums grobe Verhaltensprädiktion im vermessenen Parameterraum Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 2,

3 Distribution of Relaxation Times as Basis for Time-Domain Models of Li-Ion Batteries Impedance Measurement Time-Domain Simulation Physically Motivated Model Model Targets: Good Real-time Capabilities Scalability Automization of Parameterization - model structure deployable on microcontroller - accuracy and computational effort easy adaptable - model quality does not depend on human expertise Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 3,

4 Introduction Battery Modeling Today EIS Measurement electrochemical impedance measurements non parametric representation of linear dynamics variation of operating points (SOC,T) Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 4,

5 Introduction Battery Modeling Today EIS Measurement Model selection and fit a priori knowledge necessary stabilization of fit procedure critical subtraction of differential capacity R 0 RQ 1 RQ 2 RQ 3 Z GFLW C 0 R 0 RQ 1 RQ 2 RQ 3 Z GFLW C 0 fractional impedance elements differential capacity Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 5,

6 Introduction Battery Modeling Today EIS Measurement Model selection and fit Approximation of fractional impedance elements Fractional impedance elements cannot be simulated directly in time domain Approximation with sum of RC-Elements: RQ empirical relation [1] analytical expansion to sum discretization of the distribution of relaxation times RC 1 RC 2 RC 3 Analytical expression for the measured impedance has to be known! [1] Stephan Buller, Phd-Thesis, Aachener Beitrage des ISEA, Shaker Verlag GmbH, 2002 Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 6,

7 Introduction Battery Modeling Today EIS Measurement Model selection and fit Approximation of fractional impedance elements Time Domain Model and Simulation time effort Loss of accuracy I U OCV OCV + U t SOC PLECS t Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 7,

8 The Distribution of Relaxation Times The Continuous Distribution of Relaxation Times g( τ ) Z pol ( jω) = R dτ 1+ jωτ pol 0 g(τ): distribution function of relaxation times (DRT) H. Schichlein, A.C. Müller, M. Voigts, A. Krügel and E. Ivers-Tiffée, Journal of Applied Electrochemistry, Vol. 32, No. 8, pp , 2002 ideal process: RC-Elements real process: RQ-Elements RC 1 RC 2 g R R 1 p o l R R τ 1 τ 2 g(τ): Dirac pulses 2 p o l t RQ 1 RQ 2 Calculation of the Discrete Distribution of Relaxation Times Z pol ( jω) = N n= 1 g( τ ) n 1+ jωτ n δ τ g g τ 1 τ 2 general distribution function t N is the Number of RC-Elements discrete distribution: is logarithmical equally spaced g( n ) = 0 at highest and lowest n log(τ) Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 8,

9 Introduction Battery Modeling Today EIS Measurement Model selection and fit Approximation of fractional impedance elements Time Domain Model and Simulation time effort Loss of accuracy I U OCV OCV + U t SOC PLECS t Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 9,

10 Introduction Battery Modeling Today EIS Measurement Method of the Distribution of Relaxation Times Im(Z th ) deconvolution of EIS Z pol ( jω) = R N pol n= 1 g( τ ) n 1+ jωτ n distribution of relaxation times Re(Z th ) Time Domain Model and Simulation I U OCV OCV + U t SOC PLECS t Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 10,

11 Verification of the DRT Model Experimental 2 Ah Li-ion cell from KOKAM Pouch-cell Anode: Graphite Cathode: NCA/LCO-Blend Anode: Graphite Cathode: NCA / LiCoO2 Blend LiCoO2 REM: Anode 2µm NCA 2µm Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 11,

12 Verification of the DRT Model Experimental Electrochemical Measurements quasi stationary OCV discharge/charge at C/40 f = [100kHz 5mHz] U ampl = 10mV / 5mV pulse height 1C pulse length = 10s transformation to frequency domain 1 merger of high and low frequency range impedance spectra f = [100kHz 10µHz] completely automated process Variation of I max = C/4 2C 0.5A 4A average discharge with I max /2, D. Klotz, M. Schönleber, J. P. Schmidt, and E. Ivers-Tiffée, Electrochim. Acta, 56, 8763 (2011). Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 12,

13 Impedance Measurements in the Frequency and Time Domain impedance spectroscopy time domain measurements -Z [Ω] Z [Ω] SOC = 100 % Û = 10 mv f min = 5,88 µhz f max = 10 khz SOC = 1,95 % t Mess = 19 days n Integration = Z [Ω] Z [Ω] SOC = 100 % U = 50 mv f min = 6,84 µhz f max,zb = 8,63 Hz f max = 10 khz SOC = 5,01 % t Mess = 4 days -Z [Ω] cell LiCoO 2 / C -Z [Ω] cell LiCoO 2 / C Z [Ω] C = 120 mah Z [Ω] C = 120 mah Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 13,

14 Measurement Results EIS f 0 f 0 f 10mHz SOC [%] extended frequency range via pulse measurements Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 14,

15 Measurement Results DRT SOC SOC? Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 15,

16 Measurement Results DRT complex SOC-dependence beneficial use of the DRT for identification and separation of Processes 1,2 interpretation not necessary for parameterization of time domain model [1] J.P. Schmidt, T. Chrobak, M. Ender, J. Illig, D. Klotz, and E. Ivers-Tiffée, J. Power Sources, 196 (2010) [2] J. Illig, T. Chrobak, D. Klotz, and E. Ivers-Tiffée, ECS Trans., 33 (2011) Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 16,

17 Measurement Results Comparison: EIS / DRT-Model Measurement DRT Model SOC [%] Very good accordance of measurement and DRT-model Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 17,

18 Verification of the DRT-Model Scalability EIS Measurement / DRT-Model Variation of N Z pol ( jω) = N n= 1 g( τ ) 1+ n jωτ n Results N = RC / decade N = 20 N = 10 N = RC / decade 1.1 RC / decade 0.5 RC / decade 20 RC-elements show no significant difference to 100 RC-elements 10 RC-elements show slight deviations 4 RC-elements result in a bad fit of the impedance data Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 18,

19 Verification of the DRT-Model Scalability Time Domain Simulation Comparison of dynamic behavior I max -I max Currrent seconds-timescale shows significant differences for 4 RC-model slight increase of accuracy between 10 and 20 RC-model no visible difference for 20 and 100 RC-model 10 RC-Model shows good accordance and modest calculation effort Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 19,

20 DRT-Model Real-Time Capability Comparison of Simulation Time Model Order RCs / decade T sim / T meas [%] % 0.8% 0.5% 0.3% Simulation Environment PLECS Matlab R2009a PLECS Hardware: Intel Core i7 CPU 4GB RAM Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 20,

21 Measurement Results Validation Profile and Time Domain Simulation Measurement I max = 2C I max = 1C I max = C/2 I max = C/4 significant increase of surface temperature Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 21,

22 Elektrochemisch-thermische Modellierung Elektrochemisches Modell Setup Messung Kapazität: 2Ah Pouch-Gehäuse max. Strom ±3,2A Anode: Graphit Kathode: NCA-LCO mittlerer Strom -2A Klimakammer: 25 C Vierpunktkontaktierung Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 22,

23 Elektrochemisch-thermische Modellierung Elektrochemisches Modell: Validierung Setup Messung Kapazität: 2Ah Pouch-Gehäuse Anode: Graphit Kathode: NCA-LCO T=38 C Klimakammer: 25 C T=25 C Vierpunktkontaktierung Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 23,

24 Elektrochemisch-thermische Modellierung Kopplungsansatz SOC OCV Entropie ETIS U OCV S/T SOC Im(Z th ) SOC Re(Z th ) I cell Zustandsraum Elektrochemie U cell q rev q irrev Zustandsraum Temperatur DRT EIS T g(f) Im(Z) SOC f Re(Z) Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 24,

25 Elektrochemisch-thermische Modellierung Validierung Setup Messung Kapazität: 2Ah Pouch-Gehäuse Anode: Graphit Kathode: NCA-LCO Klimakammer: 25 C Vierpunktkontaktierung Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 25,

26 Elektrochemisch-thermische Modellierung Validierung Setup Messung Kapazität: 2Ah Pouch-Gehäuse Anode: Graphit Kathode: NCA-LCO Klimakammer: 25 C Vierpunktkontaktierung Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 26,