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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.
Maxwell
Mechanical
FLUENT
Icepak
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
LTI
Temperature 1
Temperature 2
…Total Battery Power Dissipated
Temperature n
E
x Vz
≈.
Er
Foundation of LTI Based MOR
If two LTI systems have the same impulse or step response, the two
systems are equivalent.
Output of an LTI system is completely characterized by its impulse or step response!
Seek a simple LTI system to represent the original complex LTI system
Icepak
MOR Using Icepak‐SimplorerCoupling
1. Create the CFD model2. Generate step responses Use Icepack Parameters and
Optimization tool
4. Simulate inside Simplorer
3. Extract LTI model Use Simplorer
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 2011X. 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
• 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.
Introduction of Vector Fitting
Impulse response of the thermalsystem
FFTInv. FFT
Fourier transform of impulse response of the thermal system
Impulse response of the simplesystem
Fourier transform of impulse response of the simple system
Match these twousing VF
FFTInv. FFT
Time Domain
Frequency Domain
Vector Fitting in Simplorer 11
• Provides matrices A, B, C, and D• Provides tools to plot fitting results
Electronics Cooling
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
• The vector fitting method gives much more accurate results for the electronics cooling example.
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.
Velocity magnitudeX. 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
GM Battery Module Test Case
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
• Using VF only two equations are solved in the reduced model. The run time reduces from 5 seconds to less than 1 second.
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.
• Electrochemical Kinetics• Solid‐State Li Transport• Electrolytic Li Transport
• Charge Conservation/Transport• (Thermal) Energy Conservation
Li+
e
Li+
Li+ Li+
LixC6LixC6 Lix-Metal-oxideLix-Metal-oxidee
Jump
Liee
ee jF
tcDtc
1)(
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, 2012X. 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
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=Ln+Ls+Lp
x=Ln+Ls
x=Ln
x=0
x=Ln+Ls+Lp
x=Ln+Ls
x=Ln
x=0Rate0.1C0.5C1C3C5C10C
Rate0.1C0.5C1C3C5C10C
X. Hu, S. Stanton, L. Cai, R. White, J. of Power Sources, vol. 214, p. 40‐50, 2012X. 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, 2012X. Hu, S. Stanton, L. Cai, R. White, J. of Power Sources, vol. 218, p. 212‐220, 2012
• 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.
What is LPV Modeling?
LPV for Simple Battery Thermal System
LPVBattery Temperature
Battery Heat
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
• 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.
LPV Test Conditions
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
• 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 1 Cell 2
Cell 3 Cell 4
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
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
0
0
0
0
0
00
CONST
H00RT_LRT_S
CT_LCT_SIBattCcapacity
Rseries
VOC
E1
R1
C1 I7C2 C3
R2 R3
CONST
H01
E2
R5
C4 I8C5 C6
R6 R7
CONST
H02
E3
R9
C7 I9C8 C9
R10 R11
CONST
H03
E4
R13
C10 I10C11 C12
R14 R15
CONST
H04
E5
R17
C13 I11C14 C15
R18 R19
CONST
H05
RLoad
SIMPARAM1
Qcell1
Qcell2Qcell3
Qcell4
Qcell5
Qcell6Tambien
Temp_block_1
Temp_block_2Temp_block_3
Temp_block_4
Temp_block_5
Temp_block_6
0.00 2000.00 4000.00 6000.00 8000.00Time [s]
300.00
310.00
320.00
330.00
340.00
350.00
Y1
[kel
]
Curve InfoU1.Temp_block_1
TR
U1.Temp_block_3TR
U1.Temp_block_5TR
0
0
0
0
0
00
CONST
H00RT_LRT_S
CT_LCT_SIBattCcapacity
Rseries
VOC
E1
R1
C1 I7C2 C3
R2 R3
CONST
H01
E2
R5
C4 I8C5 C6
R6 R7
CONST
H02
E3
R9
C7 I9C8 C9
R10 R11
CONST
H03
E4
R13
C10 I10C11 C12
R14 R15
CONST
H04
E5
R17
C13 I11C14 C15
R18 R19
CONST
H05
RLoad
SIMPARAM1
Qcell1
Qcell2Qcell3
Qcell4
Qcell5
Qcell6Tambien
Temp_block_1
Temp_block_2Temp_block_3
Temp_block_4
Temp_block_5
Temp_block_6
0.00 2000.00 4000.00 6000.00 8000.00Time [s]
300.00
310.00
320.00
330.00
340.00
350.00
Y1
[kel
]
Curve InfoU1.Temp_block_1
TR
U1.Temp_block_3TR
U1.Temp_block_5TR
Voc=f(SOC, U1.Temp_block_1)
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.
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