Model Order Reduction for Thermal Management in … · Model Order Reduction for Thermal Management...

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


Impact of Particle Shapes on Cell Performance


• 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


LPV Test Results


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


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.


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)

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.

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