Model Order Reduction for Thermal Management in Battery and Power Electronics
Xiao Hu, Ph.D.
Principal Engineer
ANSYS Inc.
Outline
• Motivation of model order reduction (MOR)
• Introduction to ANSYS MOR
• Linear and time‐invariant (LTI) based MOR
• Examples
• Conclusion
Motivation of MOR
• CFD as a general thermal analysis tool is accurate.
• Can be computationally expensive for large cases running transient CFD analysis • MOR can significantly reduce the model size and simulation time.
FLUENT
Maxwell
Icepak
Mechanical
Introduction to ANSYS MOR Technology
• Model order reduction (MOR) for linear problems
• LTI based (aka transfer function based)
• System matrix based
• Model order reduction (MOR) for non‐linear problems
• Proper orthogonal decomposition (POD)
• Currently investigating other technologies
Introduction to ANSYS MOR Technology
• Model order reduction (MOR) for linear problems
• LTI based (aka transfer function based)
• System matrix based
E
.z
Temperature 1
Total Battery Power Dissipated
Temperature 2
LTI
…
Temperature n
x
≈ V
Er
Foundation of LTI Based MOR
Output of an 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.
Seek a simple LTI system to represent the original complex LTI system
MOR Using Icepak‐Simplorer
Coupling
1. Create the CFD model
2. Generate step responses
 Use Icepack Parameters and Optimization tool
3. Extract LTI model
 Use Simplorer
4. Simulate inside Simplorer
Icepak
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.
X. Hu, S. Lin, S. Stanton, W. Lian, “A Foster Network Thermal Model for HEV/EV Battery Modeling,” IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 4, JULY/AUGUST 2011
X. Hu, S. Lin, S. Stanton, W. Lian, “A State Space Thermal Model for HEV/EV Battery Modeling", SAE 2011‐01‐1364
LTI Approach 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 10,000 is observed. Huge time saving if the error, which is about 1.4%, is acceptable.
X. Hu, S. Lin, S. Stanton, W. Lian, “A State Space Thermal Model for HEV/EV Non‐Linear and Time‐Varying Battery Thermal Systems,” Proceedings of the ASME 2011 International Mechanical Engineering Congress & Exposition IMECE2011, Nov 11‐17, 2011, Denver, Colorado, USA
Simplorer 9/10 Limitations
• Simplorer uses a simplified state space model .
• Can NOT model systems with complex conjugate poles
• Can NOT model systems with oscillatory step response
• This limitation does not affect thermal applications
• Simplorer performs the fitting using the time domain LM method.
• Only robust for lower order state space models
• Reduces accuracy for more complex problems
• None of the limitations shown are limitations of LTI approach. Rather, they are all limitations of Simplorer 9 current implementation.
• These limitations can be removed by using a better technique, called vector fitting (VF).
Electronics/Battery Cooling • For some cooling applications, a higher order LTI model is needed. The current Simplorer 9 implementation gives large numerical error.
Prismatic battery cells example
Electronics cooling example
Introduction of Vector Fitting
• Idea: A signal, for instance impulse response, and its Fourier transform have the same amount of information. So, instead of curve‐fitting in the time domain, the curve‐fitting is done in the frequency domain for Fourier transform of the impulse response. Time Domain
Impulse response of the thermal
system
Impulse response of the simple
system
Frequency Domain
FFT
Inv. FFT
FFT
Inv. FFT
Fourier transform of impulse response of the thermal system
Fourier transform of impulse response of the simple system
Match these two
using VF
Vector Fitting in Simplorer 11
• Provides matrices A, B, C, and D
• Provides tools to plot fitting results
Electronics Cooling • The vector fitting method gives much more accurate results for the electronics cooling example.
X. Hu, L. Chaudhari, S. Lin, S. Stanton, and S. Asgari “A State Space Thermal Model for HEV/EV Battery Using Vector Fitting,” Paper number IT‐0065, IEEE ITEC Conference, Dearborn, 2012
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 1 input and 20 outputs.
X. Hu, L. Chaudhari, S. Lin, S. Stanton, and S. Asgari “A State Space Thermal Model for HEV/EV Battery Using Vector Fitting,” Paper number IT‐0065, IEEE ITEC Conference, Dearborn, 2012
Velocity magnitude
GM Battery Module Test Case
• Using VF only two equations are solved in the reduced model. The run time reduces from 5 seconds to less than 1 second. X. Hu, L. Chaudhari, S. Lin, S. Stanton, and S. Asgari “A State Space Thermal Model for HEV/EV Battery Using Vector Fitting,” Paper number IT‐0065, IEEE ITEC Conference, Dearborn, 2012
MOR for Newman P2D Electrochemistry 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 LTI modeling technique to model the diffusion process and keep the rest non‐linear equations intact.
Li+
Li+
Jump
Li+
LixC6
Li+
e
 ( e ce )
1  t  Li
j
    De  ce  
F
t
• Electrochemical Kinetics
• Solid‐State Li Transport
• Electrolytic Li Transport
e
Lix-Metal-oxide
• Charge Conservation/Transport
• (Thermal) Energy Conservation
Solid‐Phase Diffusion Validation of LTI
 Even the 3rd order model gives good accuracy.
 Log scale shows that dynamics near time of zero is captured accurately by the LTI model
X. Hu, S. Stanton, L. Cai, R. White, J. of Power Sources, vol. 214, p. 40‐50, 2012
X. Hu, S. Stanton, L. Cai, R. White, J. of Power Sources, vol. 218, p. 212‐220, 2012
Newman P2D Electrochemistry Model Validation for LTI Method
Rate
0.1C
0.5C
1C
3C
5C
10C
x=0
x=Ln
x=Ln+Ls
x=Ln+Ls+Lp
 The LTI model reduces the problem size by a factor of 7 and the reduced model runs approximately 6 times faster.
 The accuracy is retained by using the LTI approach
 LTI modeling allows for non‐spherical particles
X. Hu, S. Stanton, L. Cai, R. White, J. of Power Sources, vol. 214, p. 40‐50, 2012
X. Hu, S. Stanton, L. Cai, R. White, J. of Power Sources, vol. 218, p. 212‐220, 2012
Impact of Particle Shapes on Cell Performance
X. Hu, S. Stanton, L. Cai, R. White, J. of Power Sources, vol. 214, p. 40‐50, 2012
X. Hu, S. Stanton, L. Cai, R. White, J. of Power Sources, vol. 218, p. 212‐220, 2012
What is LPV Modeling?
• LTI models can only handle one value of a scheduling parameter (think of flow rate).
• LPV stands for linear parameter‐varying. LPV models are used to model LTI systems with changing scheduling parameters.
• Methodology: a set of LTI models are identified corresponding to a set of scheduling parameter values. Interpolation is then used for intermediate values.
LPV for Simple Battery Thermal System
Battery Heat
LPV
Flow Rate
(Parameter)
X. Hu, S. Asgari, S. Lin, S. Stanton, “A Linear Parameter‐Varying Model for HEV/EV Battery Thermal Modeling” IEEE Energy Conversion Congress and Expo, Raleigh, NC, Sep 16‐20, 2012
Battery Temperature
LPV Test Conditions • 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.
• A rather random heat source and mass flow rate are applied.
X. Hu, S. Asgari, S. Lin, S. Stanton, “A Linear Parameter‐Varying Model for HEV/EV Battery Thermal Modeling” IEEE Energy Conversion Congress and Expo, Raleigh, NC, Sep 16‐20, 2012
LPV Test Results
X. Hu, S. Asgari, S. Lin, S. Stanton, “A Linear Parameter‐Varying Model for HEV/EV Battery Thermal Modeling” IEEE Energy Conversion Congress and Expo, Raleigh, NC, Sep 16‐20, 2012
Six Cell Battery Example with Changing Flow Rate
Cell 1
•
•
•
Power 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.
Cell 3
X. Hu, S. Asgari, S. Lin, S. Stanton, “A Linear Parameter‐Varying Model for HEV/EV Battery Thermal Modeling” IEEE Energy Conversion Congress and Expo, Raleigh, NC, Sep 16‐20, 2012
Cell 2
Cell 4
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. Hu, S. Asgari, S. Lin, S. Stanton, “A Linear Parameter‐Varying Model for HEV/EV Battery Thermal Modeling” IEEE Energy Conversion Congress and Expo, Raleigh, NC, Sep 16‐20, 2012
Electro‐Thermal Coupled Analysis
Voc=f(SOC, U1.Temp_block_1)
Rseries
IBatt
CT_S
VOC
0
C1
R1
I7
0
C4
H01
C3
R6
C5
I9
R7
C6
R10
C8
E3
C10
R3
H02
Qcell1
Temp_block_1
Qcell2
Temp_block_2
Qcell3
Temp_block_3
Qcell4
Temp_block_4
Qcell5
Temp_block_5
Qcell6
Temp_block_6
Tambien
R9
0
CONST
CONST
E2
0
C7
R2
R5
I8
H00
CT_L
C2
E1
SIMPARAM1
RT_L
RLoad
R11
CONST
H03
CONST
R13
I10
R14
C11
E4
350.00
C9
R15
C12
H04
CONST
340.00
330.00
Y1 [kel]
Ccapacity
RT_S
Curve Info
320.00
TR
0
C13
R17
I11
E5
R18
C14
R19
310.00
TR
H05
TR
C15
CONST
0
U1.Temp_block_3
U1.Temp_block_5
300.00
0.00
0
U1.Temp_block_1
2000.00
4000.00
Time [s]
6000.00
8000.00
System Model Involving Reduced Thermal Model
Conclusion
• LTI based MOR has shown to be applicable to many applications including electrochemistry problems.
• Icepak‐Simplorer coupling uses a simplified version of this methodology for thermal problems.
• Vector fitting is shown to be much more flexible than the method implemented in Simplorer 9.
• A natural extension from LTI to LPV is discussed.