Model Order Reduction for Battery Simulation. Xiao Hu, PhD Confidence by Design Detroit June 5, 2012

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1 Model Order Reduction for Battery Simulation Xiao Hu, PhD Confidence by Design Detroit June 5, 202

2 Outline ANSYS model order reduction (MOR) technique Different types of battery simulation Transfer function based MOR (aka LTI method) System matrix based MOR Conclusion 2

3 ANSYS MOR Techniques Model order reduction (MOR) for linear problems Transfer function based (or LTI method) System matrix based Model order reduction (MOR) for non-linear problems Proper orthogonal decomposition (POD) 3

4 ANSYS MOR Techniques Model order reduction (MOR) for linear problems Transfer function based (or LTI method) System matrix based Model order reduction (MOR) for non-linear problems Proper orthogonal decomposition (POD) 4

5 Different Types of Battery Simulations Electrical circuit model Battery system level thermal management simulation Battery P2D electrochemistry model Battery 3-D micro-scale electrochemistry model Mechanical, aging, Li + Jump Li+ Li + Li x C 6 e Li + e Lix -Metal-oxide 5

6 MOR for Battery Simulations Battery system level thermal management simulation Battery P2D electrochemistry model Li + Li x C 6 e Li + Jump Li+ Li + e Lix -Metal-oxide Li + Li + Li + Jump Li + e Li x C 6 e Li x -Metal-oxide 6

Motivation of Using MOR for Battery System

transient CFD analysis MOR can significantly

7 Motivation of Using MOR for Battery System Level Thermal Management CFD as a general thermal analysis tool is accurate Can be expensive for large system level repeated transient CFD analysis MOR can significantly reduce the model size for system level thermal analysis 7

Battery Thermal Management Using CFD Full Hybrid Electrical

Front view of the pack with the two bricks assembled and inlet

outlet plenum Airflow path into the battery pack. D.

Zhu, " Design and CFD Simulation of a Battery Module for a

Ghosh, 20 K. King, ANSYS, B. Schwemmin, Inc. D.

8 Battery Thermal Management Using CFD Full Hybrid Electrical Vehicle Battery Pack System Design, CFD Simulation and Testing Front view of the pack with the two bricks assembled and inlet busbar Velocity contours of airflow through the brick, inlet and outlet plenum Airflow path into the battery pack. D. Ghosh, P. D. Maguire, and D. X. Zhu, " Design and CFD Simulation of a Battery Module for a Hybrid Electric Vehicle Battery Pack, SAE D. Ghosh, 20 K. King, ANSYS, B. Schwemmin, Inc. D. June Zhu, 7, Full 202 Hybrid Electrical Vehicle Battery Pack System Design, CFD Simulation and Testing, SAE Airflow path and air outlet

9 Introduction to Transfer Function Based MOR Input DT LTI Output This is a Discrete Time example. 0 Impulse Input t LTI Impulse response t 2 0 Input t LTI Output 2 3 t 0 Input t LTI Output t 2 0 Input t LTI Output t 9

10 Introduction to Transfer Function Based MOR Input Output of a LTI system is completely LTI Output characterized by its impulse response *! 0 Input t LTI 2 2 If two LTI 0 systems 2 3 t have the same impulse LTI 0 Impulse t Input response, response the two systems are equivalent Output 2 3 t 0 Input t Make a small LTI model have the 2 same LTI impulse t response as the Output 0 LTI t 0 modeled large LTI system! Input Output t 0 * Under the condition of initial rest

11 Why Is It Called Transfer Function Based? Impulse response, step response, or system transfer function contains the same amount of information. Laplace transfer of impulse response is system transfer function. Time derivative of step response is impulse response.

12 Three Approaches Are Possible Make sure the reduced model has the same impulse response as the original model Make sure the reduced model has the same step response as the original model Make sure the reduced model has the same transfer function as the original model 2

13 Two Approaches Are Implemented Step response of the reduced model is curvefitted to that of the original model in the timedomain Used in current Simplorer 0 Transfer function of the reduced model is curve-fitted to that of the original model in the frequency-domain Will be added in future Simplorer 3

14 LTI Modeling Using Simplorer 0. Create step responses From CFD / Test 2. Generate.simpinfo file Automatic using Icepak 3. Extract LTI model Use Simplorer 4. Simulate inside Simplorer 4

GM Battery Module Example Using LTI Modeling MOR is Used to Drastically Reduce Runtime of Long Transient Simulations The LTI model gives the same results as CFD.

15 GM Battery Module Example Using LTI Modeling MOR is Used to Drastically Reduce Runtime of Long Transient Simulations The LTI model gives the same results as CFD. The LTI model runs in less than a few seconds while the CFD runs 2 hours on one single CPU.. X. Hu, S. Lin, S. Stanton, and W. Lian, "A Foster Network Thermal Model for HEV/EV Battery Modeling," IEEE Trans. on Industry Appl., vol. 47, no. 4, p , X. Hu, S. Lin, S. Stanton, W. Lian, A State Space Thermal Model for HEV/EV Battery Modeling", SAE X. Hu, S. Lin, S. Stanton, and W. Lian, A State Space Thermal Model for HEV/EV Non-Linear and 5 Time-Varying Battery Thermal Systems, IMECE , 20

16 LTI Modeling for Non-Linear Problems GM Module Non-linear CFD: Ideal gas law plus temperature dependent properties are used. Full Navier- Stokes equations are solved LTI: Assumes the system is linear and time invariant. A speed-up factor of 0,000 is observed. Huge time saving if the error, which is about.4%, is acceptable. 6

Average temperature of each cell is monitored.

17 Battery Example with Prismatic Cells The battery module has 20 prismatic cells. Water cooling is used. Average temperature of each cell is monitored. The LTI model has input and 20 outputs. 7 Velocity magnitude

18 One Cell Battery Example with Changing Flow Rate Three sets of LTI models are identified at flow rates of 0.06, 0.075, and 0.09 kg/s. Interpolation used for intermediate flow rates. Transient heat source and mass flow rate are applied for testing the model with changing flow rate. 8

19 Six Cell Battery Example with Changing Flow Rate Cell Cell 2 Power dissipation inputs are sinusoidal functions Flow rate changes at time of 000 second. Results are excellent for the entire duration. A small difference is seen during transition period. Cell 3 Cell 4 9

GM Battery Module Example with Changing Flow Rate The model gives similar results as CFD. The model runs in less than 20 seconds while the CFD runs a couple of days on 6 CPUs.

20 GM Battery Module Example with Changing Flow Rate The model gives similar results as CFD. The model runs in less than 20 seconds while the CFD runs a couple of days on 6 CPUs. X. 20 Hu, S. Asgari, 20 S. ANSYS, Lin, S. Stanton, Inc. A Linear June Parameter-Varying 7, 202 Model for HEV/EV Battery Thermal Modeling, IEEE ECCE Conference, paper no. 04, 202.

21 Electro-Themeral Coupled Analysis Voc=f(SOC, U.Temp_block_) Rseries RT_S RT_L H00 SIMPARAM Ccapacity IBatt VOC CT_S CT_L CONST C 0 I7 E R R2 C2 R3 C3 H0 CONST Qcell Qcell2 Qcell3 Temp_block_ Temp_block_2 Temp_block_3 Qcell4 Temp_block_4 C4 0 I8 E2 R5 R6 C5 R7 C6 RLoad H02 CONST Qcell5 Qcell6 Tambien Temp_block_5 Temp_block_6 0 R9 R0 R H C7 I9 E3 C8 C9 CONST C0 0 I0 E4 R3 R4 C R5 C2 H04 CONST Y [kel] TR Curve Info U.Temp_block_ C3 0 I E5 R7 R8 C4 R9 C5 H05 CONST Time [s] TR TR U.Temp_block_3 U.Temp_block_

22 Newman P2D Electrochemistry Model Li + Jump Li+ Lithium Ion Batteries Li + Li x C 6 e ( ece ) t e e t F Li D c j Li + e Li x -Metal-oxide Electrochemical Kinetics Solid-State Li Transport Electrolytic Li Transport Charge Conservation/Transport (Thermal) Energy Conservation x=0 δ n δ s δ p x=l Negative Electrode Separator Positive Electrode X. 22 Hu, S. Lin, 20 S. Stanton, ANSYS, Simulating Inc. Rechargeable June 7, 202 Lithium-Ion Battery Using VHDL-AMS, SAE paper , 202.

23 Motivation of Using MOR for Newman P2D Electrochemistry Model x=0 x=l δ n δ s δ p c s, c s2, c s3, c s4, c s5, c s,2 c s2,2 c s3,2 c s4,2 c s5, c s,3 c s2,3 c s3,3 c s4,3 c s5,3 Negative Electrode Separator Positive Electrode The model is pseudo 2D due diffusion equation solved for each particle. Many particles exist c c 2 c 3 c 4 c 5 φ, φ 2, i, i 2, x=0 φ,2 φ 2,2 i,2, i 2,2 h φ,3 φ 2,3 i,3 i 2,3 φ,4 φ 2,4 i,4 i 2,4 φ,5 φ 2,5 i,5 i 2,5 φ,6 φ 2,6 i,6 i 2,6 x=δ n. M. Doyle, T.F. Fuller, and J. Newman, Journal of Electrochem. Soc., 40, 526 (993) C. R. Pals and 20 J. ANSYS, Newman Inc. Journal of Electrochem. June 7, 202 Soc., 42 (0), (995) 3. M. Doyle, J. Newman, Journal of Electochem. Soc., 43, 890 (996)

24 Observations of the Newman P2D Model Equations are highly non-linear overall. However, solid-phase diffusion equations are linear. And solid-phase diffusion is the most time consuming part of the P2D model. Use transfer function based MOR to model the diffusion process and keep the rest non-linear equations intact. 24

25 Hu, S. Stanton, 20 L. ANSYS, Cai, R. Inc.

25 CFD Geometry/Mesh and Solution for the Diffusion Process in a Spherical Particle Use CFD to solve the diffusion process ONCE and then use model order reduction to characterize the diffusion process. X. 25 Hu, S. Stanton, 20 L. ANSYS, Cai, R. Inc. White, A Linear June 7, Time-Invariant 202 Model for Solid-Phase Diffusion in Physics-Based Lithium Ion Cell Models, J. of Power Sources, vol. 24, p , 202

26 Reduced Order Model Validation Even the 3 rd order model gives good accuracy. 3 rd order model solves only 3 equations for diffusion Log scale shows that dynamics near time of zero is captured accurately by the reduced order model X. 26 Hu, S. Stanton, 20 L. ANSYS, Cai, R. Inc. White, A Linear June 7, Time-Invariant 202 Model for Solid-Phase Diffusion in Physics-Based Lithium Ion Cell Models, J. of Power Sources, vol. 24, p , 202

Validation for P2D Electrochemistry Model Rate 0.C 0.5C C 3C 5C 0C x=0 x=l n x=l n +L s x=l n +L s +L p The reduced order model runs approximately 6 times faster.

27 Validation for P2D Electrochemistry Model Rate 0.C 0.5C C 3C 5C 0C x=0 x=l n x=l n +L s x=l n +L s +L p The reduced order model runs approximately 6 times faster. Excellent accuracy is retained by using the reduced order model Reduced order model allows for non-spherical particles X. 27 Hu, S. Stanton, 20 L. ANSYS, Cai, R. Inc. White, A Linear June 7, Time-Invariant 202 Model for Solid-Phase Diffusion in Physics-Based Lithium Ion Cell Models, J. of Power Sources, vol. 24, p , 202

Inc. White, A Linear June 7, Time-Invariant 202 Model for Solid-Phase Diffusion

28 Impact of Particle Shapes on Cell Performance Impact of different particle shapes only show up at high discharge rates. X. 28 Hu, S. Stanton, 20 ANSYS, L. Cai, R. Inc. White, A Linear June 7, Time-Invariant 202 Model for Solid-Phase Diffusion in Physics-Based Lithium Ion Cell Models, J. of Power Sources, vol. 24, p , 202

29 Introduction to System Matrix Based MOR What is a state? What is a state trajectory? What is change of basis? What is a projection? x 2 x 2 Initial state at t=t 0 What is the main goal of system matrix based MOR? x x 2 Find x x 2 x 2 x x x x 29

30 Introduction to System Matrix Based MOR Obtain the original system matrix Ex Kx Bu E Find and project onto lowdimensional subspace x Vz Substitute and solve the reduced system matrix. z V T EVz V T KVz V T Bu x V E r 30

31 Workflow of System Matrix Based MOR E x V. z E r 3

32 Example: Battery Pack Thermal FE Model 4 Cells Cooling by 3 air channels 3D FEM model in ANSYS Uniform heat generation in each cell D fluid channels Coupling by heat transfer coefficient Fixed velocity FLUID6 32

Reduced vs Full Solution VALUE=0 H VALUE=0 H VALUE=0 H VALUE=0 H Cell Cell2 Cell3 Cell4 T_Ref Q VALUE=20 Temperature [cel].00 0.50 Error <% TR Curve Info TCell.

33 Reduced vs Full Solution VALUE=0 H VALUE=0 H VALUE=0 H VALUE=0 H Cell Cell2 Cell3 Cell4 T_Ref Q VALUE=20 Temperature [cel] Error <% TR Curve Info TCell.T ansys_cell Imported Step response of W per cell Y [kel] Curve Info THM.T TR THM2.T TR THM3.T TR THM4.T TR Time [s] Reduced Time [s] Simulation time [s] (00 time steps) Full Dimension 40 (0 x Input) elements CPU time [s] < ~20 min 33

34 Example: Electro-Thermal Response Heat Temperature Battery Pack 34

35 Recover the Original Solution From the reduced results back to the original results whenever desired Expansion pass Get reduced vectors z(t) and multiply by the matrix V x 2. z x V x 35

36 REDUCED Recover the Temperature Field FULL 36

More Complex Battery Pack Model 3 layers of 33 cells = 99

max :400s Δt min : ms Dimension of reduced order model

37 More Complex Battery Pack Model 3 layers of 33 cells = 99 inputs! Each cell is a source of heat Outputs: Temperature of the cell center Numerics FEM: DOFs 4000s, adaptive time step Δt max :400s Δt min : ms Dimension of reduced order model 0*Number of inputs MOR time is less than one transient simulation Results W/per cell step response CPU time in Simplorer: 5mim 48s 37

38 Comparison Transfer Function Based System Matrix Based Linear systems (linearized non-linear systems, small non-linearity) Need to create the CFD or FEA model and run flow solution Needs transient step response Could use testing data Only specified outputs Extremely short run time (sec) Can handle very large problems Extremely accurate Most efficient with SISO systems (can be extended to MIMO systems) Needs system matrices Can not use testing data Field solution is possible Short run time (sec, min) Challenging for large problems Very accurate MIMO systems can be handled efficiently 38

39 Conclusion Both transfer function based and system matrix based ROM are available with ANSYS MOR can significantly reduce the transient simulation time while retaining excellent accuracy. MOR can be applied to battery system level thermal simulation. MOR can also be used for battery Newman P2D electrochemistry modeling. 39

40 Acknowledgement Ralph E. White (University of South Carolina) Long Cai (University of South Carolina) Wenyu Lian (General Motors) Lucas Kostetzer (ESSS) Evgeny Rudnyi (CADFEM) 40

Reduction of Model Order Based on LTI for Battery System Thermal Simulation Xiao Hu, PhD Lead Technical Services Engineer ANSYS Inc

Reduction of Model Order Based on LTI for Battery System Thermal Simulation Xiao Hu, PhD Lead Technical Services Engineer ANSYS Inc 1 ANSYS, Inc. September 21, Motivation of Using Model Order Reduction