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

Transcription

1 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,

2 Motivation of Using Model Order Reduction CFD as a general thermal analysis tool is accurate but Can be expensive for large system level repeated transient CFD analysis Can be cumbersome to couple with electrical circuit model for large system analysis 2 ANSYS, Inc. September 21,

3 Motivation of Using Model Order Reduction Seek reduced order models for system level transient analysis Thermal network (use thermal resisters and capacitors, etc) Compromised accuracy Needs careful calibration and calculation of thermal resistance, capacitance LTI method (state space) Can be as accurate as CFD or even testing No need to calculate thermal resistance, capacitance Rely on linearity and time invariance I1 V R1 VM1 R2 C1 C2 0 3 ANSYS, Inc. September 21,

4 What is an LTI system? A LTI system is a Linear Time Invariant (LTI) system Output of such a system is completely characterized by its impulse (or step) response in that the output of the system under any input is simply the convolution of the impulse response and the input. Battery cooling problem can be treated like a system, in which the inputs are the power dissipation by individual batteries and the outputs are temperatures at user specified locations Battery1 Heat Battery2 Heat Battery12 Heat LTI Temperature1 Temperature2 Temperature12 4 ANSYS, Inc. September 21,

5 Characteristics of LTI Systems Output of a LTI system is completely characterized by its impulse or step response *! If two LTI systems have the same impulse or step response, the two systems are equivalent!! Use the simple state space LTI model to represent the complex thermal LTI system. 5 ANSYS, Inc. September 21, * Under the condition of initial rest

6 State Space Approach for One Input One Output System State space model is an LTI system x y Ax Cx Bu Du x :internal states, no physical u : heat dissipated, input y : temperature, output meaning Goal: Find coefficient matrices A, B, C, and D such that the state space model gives the same step response as the thermal system. 6 ANSYS, Inc. September 21,

7 An One Input and One Output LTI Battery Thermal System Battery Heat LTI Battery Temperature 7 ANSYS, Inc. September 21, CFD results shown are pressure contour and velocity vectors

8 State Space Model vs FLUENT CFD Input Comparison Identical results obtained between FLUENT CFD calculation and state space model State space takes a fraction of second to compute 8 ANSYS, Inc. September 21,

9 Multiple Inputs/Outputs LTI System For multiple inputs and outputs, use superposition since the system is linear. A matrix of state space is used. x Ax Bu x Ax Bu x Ax Bu y Cx Du y Cx Du y Cx Du x y Ax Cx Bu Du Represents the relationship x Ax Bu between y Cx2 nd Du input and 1 st output x y Ax Cx Bu Du x Ax Bu x Ax Bu x Ax Bu y Cx Du y Cx Du y Cx Du 9 ANSYS, Inc. September 21,

10 Reduced Order Model Extraction Process Using Simplorer Create step responses From CFD / Test 2. Generate.simpinfo file 3. Extract equivalent thermal model Use Simplorer 4. Simulate inside Simplorer 10 ANSYS, Inc. September 21,

11 Six-Cell Module Test Case Geometry/Mesh Inputs: heat source to each battery Outputs: battery volume average temperature 11 ANSYS, Inc. September 21,

12 State Space vs FLUENT Cell 1 Cell 2 Cell 3 12 Cell 4 Cell 5 Cell 6 State space and Fluent give identical solution under arbitrary sinusoidal power inputs State space model runs in a few seconds while the full CFD model could take a couple of hours to run. ANSYS, Inc. September 21,

13 LTI Model Extraction for a General Motors Battery Module Example State space model gives the same results as CFD. State space model runs in less than 5 seconds while the CFD runs 2 hours on one single CPU. 1. X. Hu, S. Lin, S. Stanton, W. Lian, A Novel Thermal Model for HEV/EV Battery Modeling Based on CFD Calculation IEEE Energy Conversion Congress and Expo, Atlanta, Sep 12-16, X. Hu, S. Lin, S. ANSYS, Stanton, Inc. W. Lian, September A State Space 21, Thermal Model for HEV/EV Battery Modeling", SAE

14 Example: A Battery Module Coupled Analysis Vocf(SOC, U1.Temp_block_1) 14 ANSYS, Inc. September 21,

15 LTI Approach for Flow Rate Change of 100% Cell 1 Cell 2 Cell 3 Cell 4 Cell 5 Cell 6 Heat dissipation inputs are sinusoidal functions Flow rate changes at time of 1000 second. Results are excellent for the entire duration. A small difference is seen during transition period. 15 ANSYS, Inc. September 21,

16 LTI Approach for Non-Linear Problems 6 Cell 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 10,000 is observed. Huge time saving if the error, which is about 2%, is acceptable. 16 ANSYS, Inc. September 21,

17 LTI Approach for Non-Linear Problems GM Module 17 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 10,000 is observed. Huge time saving if the error, which is about 1.4%, is acceptable. ANSYS, Inc. September 21,

18 Conclusion Battery system level thermal management can be greatly simplified by using state space model. Results show that the state space approach gives identical solution compared with the Fluent CFD calculation under LTI assumption. State space approach, however, is much faster than CFD calculation. Seconds rather than hours of run time has been shown on a few test cases. Multiple flow rates can be handled with multiple sets of state space model with good accuracy. Non-linearity is not strong to affect thermal performance for the temperature range seen in battery application. 18 ANSYS, Inc. September 21,

19 Thank you!! 19 ANSYS, Inc. September 21,