A Distributed Randles Circuit Model for Battery Abuse Simulations Using LS-DYNA

Transcription

1 Page 1 A Distributed Randles Circuit Model for Battery Abuse Simulations Using LS-DYNA Pierre L Eplattenier 1, Iñaki Çaldichoury 1 James Marcicki 2, Alexander Bartlett 2, Xiao Guang Yang 2, Valentina Mejia 2, Min Zhu 2, Yijung Chen 2 1 LSTC, Livermore, CA, USA 2 Ford Research and Innovation Center, Dearborn, MI, USA

2 Introduction Car crash Mechanical EM Thermal CPM => Battery crush => local short circuits => large localized current densities => Joule heating => temperature increase => thermal runaway => fire, explosion

3 Case Study Development Assumptions Page 3 Mechanics Time Scale Crash < 100 ms Regulatory Crush > 10 s Overcharge/External Short/Thermal Ramp > 10 s EM/thermal Time Scale ms to minutes Deformation Mode Out-of-Plane or In- Plane Compression; Bending; Shear Out-of-Plane Compression; In-Plane Compression Internal Swelling; Separator Melting Solver Assumption Explicit to Implicit Implicit Implicit 3-D, transient finite element code needed to span these target applications Models that resolve mechanical properties of individual layers have higher potential robustness to multiple deformation modes In-Plane Out-of-Plane

4 Page 4 Outline Li-ion cell in an electric car The distributed Randles circuit model Validation on various electrical cycling experiments ( benign use) Presentation of external short cases Presentation of internal short cases

5 Vehicle Li-ion cell Dual-Packs Cell Module Pack 180μm Cell (zoomed in z) Unit cell (zoomed in z) 20cm Page 5 15cm

6 Page 6 Outline Li-ion cell in an electric car The distributed Randles circuit model Validation on various electrical cycling experiments ( benign use) Presentation of external short cases Presentation of internal short cases

7 Distributed Equivalent Circuit (1st Order Randles) Cu Current Collector Page 7 Al Current Collector Negative (Anode) Separator Li + Discharge Positive (Cathode) Current collectors transport electrons to/from tabs; modeled by resistive elements Jelly roll (anode separator cathode) transports Li+ ions; modeled with Randle circuit r 0 : Ohmic & kinetic r 10 & c 10 : Diffusion u: Equilibrium voltage (OCV) r m : Current collectors

8 Page 8 Standard EM resistive solver ϕ : potential E = - grad(ϕ) : electric field V = ϕ 2 ϕ 1 : voltage J = σ E : current density (σ = electric conductivity) div (J) = 0 => Δ ϕ = 0 + boundary conditions (Δ ϕ) 1 current flowing out at N 1 V= ϕ 2 ϕ 1 : voltage between nodes 1 and 2 - (Δ ϕ) 2 current flowing out at N 2

9 Introduction of randles circuits in resistive solver R ϕ 2 ϕ 1 = u - r 0 *I V c r 0 *i + ϕ 2 ϕ 1 = u - V c i + (ϕ 2 ϕ 1 ) / r 0 = (u - V c ) / r 0 FEM solve: (S 0 + D) * ϕ = b Where S 0 is the Laplacian operator (nds x nds) D has 1/r 0 at (N 1,N 1 ) and (N 2,N 2 ) -1/r 0 at (N 1,N 2 ) and (N 2,N 1 ) 0 elsewhere b has 1/r 0 (u-v c ) at N 1-1/r 0 (u-v c ) at N 2 0 elsewhere ϕ 2 ϕ 1 Actualization of randle circuits: r 0 i i= (S u 0 * ϕ)(n 1 ) V c V c (t+dt)=v c (t)+dt*(i/c 0 -V c (t)/r 10 /c 10 ) Randle circuit Page 9 soc(t+dt)=soc(t)-dt*i*c Q /Q u=u(soc) Page 9

10 Page 10 EM/thermal connection T from thermal for r 0, r 10, c 10 vs T Randle circuit Cu collector : EM+Thermal Al collector : EM+Thermal Anode : cathode : Thermal Thermal Separator: Thermal r 0 * i 2 added to thermal ITdU/dT added to thermal Allow correct material mass, heat capacity and thermal conductivity

11 EM/thermal/mechanical connections Page 11 Electrochemical Ordinary differential equations (Randles circuit model) Finite element analysis Thermal Finite element analysis; 3-D Heat diffusion with source terms Structural Finite element analysis; Nonlinear continuum mechanics

12 Contact for Internal Short Models R R R r s R R r s R R Replace randle circuit by resistance r s R s * i 2 added to thermal Experiment + simulation (voltage, current, temperature) should give good models

13 Randle circuits in LS-PREPOST Scalar potential Current density Randle r0 Randle SOC

14 Connection to external circuits Page 14 Isopotentials can be defined and connected: The connectors do not need to be meshed. Enables alignment of cell simulations with experimental conditions (low rate cycling, HPPC, continuous discharge, ). R(t) V(t) i(t)

15 Page Type B Capacity (Ah) C/10 capacity tests Cell Voltage 3.8 Evaluation of the circuit Discharge Charge Average parameters 3.4 Current (A) Time (s) Time (s) 3.8 Voltage (V) HPPC tests Time (s) x 10 4

16 Page 16 Outline Li-ion cell in an electric car The distributed Randles circuit model Validation on various electrical cycling experiments ( benign use) Presentation of external short cases Presentation of internal short cases

17 Benchmarking with experimental results Page 17 Image Type Cathode Chemistry Dimensions Number of Elements A NMC/LMO 195 mm x 145 mm 151k B NMC 195 mm x 125 mm 153k Table 1: Cell characteristics for experimental benchmarking study. 2 types of cells Various electrical cycling experiments Quick tests : transient response Longer tests: coupling between thermal and electrochemical

18 Page 18 RMS Voltage Error (V) HPPC validation Type A, 25 C Voltage (V) Voltage (V) Type B, 25 C Experimental 80% SOC 60% SOC 20% SOC Time (s) HPPC tests at different current magnitude (different SOC) State of Charge (%) Type A, 25 C Type B, 25 C Type A, 40 C Type B, 40 C Type A, 50 C Type B, 50 C Simulation/experiment voltage error for different SOC for each cell

19 Multi-rate capacity test validation Page 19 Experiments on longer time scale => the temperature effects are more important Voltage (V) Voltage (V) Type A, 25 C Type B, 25 C Experimental 2C 5C 10C Capacity (Ah) Temperature ( C) Temperature ( C) Type A, 25 C Type B, 25 C Experimental 2C 5C 10C Time (s)

20 Page 20 Outline Li-ion cell in an electric car The distributed Randles circuit model Validation on various electrical cycling experiments ( benign use) Presentation of external short cases Presentation of internal short cases

21 External Short Model Setup Page 21 Cells and Bus Bar A B Short circuit resistance applied between A and B creates current pathway Inactive Components

22 Page 22 External Short Thermal Fringe Plot a) b) Average short resistance is 6.5 mohm, equivalent to ~2 mm 2 steel connection across terminals Heat propagates from bus to cells; higher bus temperatures observed where cells are not connected.

23 Page 23 External Short Circuit Validation Current (A) Model Predicted Current versus Experiment Numerical Measured Time (s) Temperature ( C) Model Predicted (Dashed) Temperatures versus Experiment (Solid) Outer Cell 30 Bus Inner Cell Time (s) Good agreement between numerical and measured data for electrical variables Thermal predictions demonstrate agreement of 5-10 C between numerical and experimental data (excluding >550 s for inner cell)

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25 Page 25 Outline Li-ion cell in an electric car The distributed Randles circuit model Validation on various electrical cycling experiments ( benign use) Presentation of external short cases Presentation of internal short cases

26 Page 26 Internal short case 3 Cell Crush Case Study Boundary Conditions Vz = -20 m/s Mech + Electrical + Thermal tf = 50 μs dt = 0.2 μs Vz = 0 R = 100 Ω V = 0 Thermal boundary conditions same as previous simulations Failure criteria is unit cell compressive strain threshold Randles circuits replaced by direct short once failure criteria is exceeded Freeze mechanics Electrical + Thermal tf = 50 s dt = 1 s

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28 Page 28 Internal short case 3 Short Circuit Characteristics Current Density Vector Plots Shorted Area versus Time 0.09 Before Internal Short After Internal Short Shorted Area (m 2 ) Shorted Area (m 2 ) Time (ms) Time (s) Shorted area increases upon application of external load, then stabilizes Resistivity combines with shorted area to compute corresponding current response

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30 Summary A three-dimensional finite element model has been developed for battery abuse case studies The model is parameterized using benign experiments on cells and cell components The model is available on solid and thick shells as a beta version Validation activities are underway Future Work Add a Battery packaging in LS-PREPOST to easily create the models Extend the model to composite thick shells Develop higher-fidelity failure models and examine more complex loading conditions Improve models for short resistance, based on comparisons with experiments Replace empirical inputs with an increasingly analytical approach Page 30