model order reduction for battery simulation - ansys model order reduction (mor) technique different...

© 2011 ANSYS, Inc. June 7, 2012 1

Model Order Reduction for Battery Simulation

Xiao Hu, PhD

Confidence by Design

Detroit June 5, 2012

© 2011 ANSYS, Inc. June 7, 2012 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

© 2011 ANSYS, Inc. June 7, 2012 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)

© 2011 ANSYS, Inc. June 7, 2012 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)

© 2011 ANSYS, Inc. June 7, 2012 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+

e

Li+

Li+ Li+

LixC6 Lix-Metal-oxide

e

Jump

© 2011 ANSYS, Inc. June 7, 2012 6

MOR for Battery Simulations

Battery system level thermal management simulation

Battery P2D electrochemistry model

Li+

e

Li+

Li+ Li+


e

Jump

Li+

e Li+

Li+ Li+


e

Jump

© 2011 ANSYS, Inc. June 7, 2012 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

© 2011 ANSYS, Inc. June 7, 2012 8

Full Hybrid Electrical Vehicle Battery Pack System Design, CFD Simulation and Testing

Velocity contours of airflow through the brick, inlet and outlet plenum

Airflow path into the battery pack Airflow path and air outlet

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

Battery Thermal Management Using CFD

1. 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 2009-01-1386 2. D. Ghosh, K. King, B. Schwemmin, D. Zhu, “Full Hybrid Electrical Vehicle Battery Pack System Design, CFD Simulation and Testing,” SAE 2010-01-1080

© 2011 ANSYS, Inc. June 7, 2012 9

Introduction to Transfer Function Based MOR

LTI

Impulse Input

t

1

0

Impulse response

t

2

1

0 1 2 3

Input t

1

LTI 0 1

Input t

2

LTI 1

0

Input t

1

LTI 0 1

2

Output t

2

1

4

3

1 2 3 0

Output t 1 2 3 4

2

1

4

3

0 Output t

2

1

0 1 2 3 4

DT LTI Output Input

This is a Discrete Time example.

© 2011 ANSYS, Inc. June 7, 2012 10

LTI Output Input

LTI

Input t

1

0

Input t

1

LTI 0 1

Input t

2

LTI 1

0

LTI

Output t

2

1

4

3

1 2 3 0

Output t

2

1

0 1 2 3 4

Impulse response

t

2

1

0 1 2 3

Output t 1 2 3 4

2

1

4

3

0

Input t

1

0 1

2

Output of a LTI system is completely characterized by its impulse response*!

If two LTI systems have the same impulse

response, the two systems are equivalent.

* Under the condition of initial rest

Make a small LTI model have the same impulse response as the

modeled large LTI system!

Introduction to Transfer Function Based MOR

© 2011 ANSYS, Inc. June 7, 2012 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.

© 2011 ANSYS, Inc. June 7, 2012 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

© 2011 ANSYS, Inc. June 7, 2012 13

Two Approaches Are Implemented

Step response of the reduced model is curve-fitted to that of the original model in the time-domain

Used in current Simplorer 10

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

© 2011 ANSYS, Inc. June 7, 2012 14

LTI Modeling Using Simplorer 10

1. Create step responses • From CFD / Test

2. Generate .simpinfo file • Automatic using Icepak

4. Simulate inside Simplorer

3. Extract LTI model • Use Simplorer

© 2011 ANSYS, Inc. June 7, 2012 15

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.

1. 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. 1692-1699, 2011 2. X. Hu, S. Lin, S. Stanton, W. Lian, “A State Space Thermal Model for HEV/EV Battery Modeling", SAE 2011-01-1364 3. X. Hu, S. Lin, S. Stanton, and W. Lian, “A State Space Thermal Model for HEV/EV Non-Linear and Time-Varying Battery Thermal Systems,” IMECE2011-62022, 2011

GM Battery Module Example Using LTI Modeling

© 2011 ANSYS, Inc. June 7, 2012 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 10,000 is observed. Huge time saving if the error, which is about 1.4%, is acceptable.

© 2011 ANSYS, Inc. June 7, 2012 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 1 input and 20 outputs.

Velocity magnitude

© 2011 ANSYS, Inc. June 7, 2012 18

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.

One Cell Battery Example with Changing Flow Rate

© 2011 ANSYS, Inc. June 7, 2012 19

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

© 2011 ANSYS, Inc. June 7, 2012 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. Hu, S. Asgari, S. Lin, S. Stanton, “A Linear Parameter-Varying Model for HEV/EV Battery Thermal Modeling,“ IEEE ECCE Conference, paper no. 1041, 2012.

© 2011 ANSYS, Inc. June 7, 2012 21

Electro-Themeral 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

Qcell2

Qcell3

Qcell4

Qcell5

Qcell6

Tambien

Temp_block_1

Temp_block_2

Temp_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 [k

el]

Curve InfoU1.Temp_block_1

TR

U1.Temp_block_3TR

U1.Temp_block_5TR

Voc=f(SOC, U1.Temp_block_1)

© 2011 ANSYS, Inc. June 7, 2012 22

Lithium Ion Batteries

• Electrochemical Kinetics • Solid-State Li Transport • Electrolytic Li Transport

• Charge Conservation/Transport • (Thermal) Energy Conservation

Li+

e

Li+

Li+ Li+


e

Jump

Li

eeee j

F

tcD

t

c

1)(

Newman P2D Electrochemistry Model

Negative Electrode

Positive Electrode

Separator

δs δn δp

x=0 x=L

X. Hu, S. Lin, S. Stanton, “Simulating Rechargeable Lithium-Ion Battery Using VHDL-AMS,“ SAE paper 2012-01-0665, 2012.

© 2011 ANSYS, Inc. June 7, 2012 23

Motivation of Using MOR for Newman P2D Electrochemistry Model

Negative Electrode

Positive Electrode

Separator

δs δn δp

x=0 x=L

h

x=0

2 3 4 5 1

φ1,1 φ2,1 i1,1

i2,1

c1

3

2

1 cs1,1

c2 c3 c4 c5

φ1,2 φ2,2 i1,2,

i2,2

φ1,3 φ2,3 i1,3

i2,3

φ1,4 φ2,4 i1,4

i2,4

φ1,5 φ2,5 i1,5

i2,5

cs1,2

cs1,3

3

2

1 cs2,1

cs2,2

cs2,3

3

2

1 cs3,1

cs3,2

cs3,3

3

2

1 cs4,1

cs4,2

cs4,3

3

2

1 cs5,1

cs5,2

cs5,3

φ1,6 φ2,6 i1,6

i2,6

2 3 4 5 1 6

x=δn

1. M. Doyle, T.F. Fuller, and J. Newman, Journal of Electrochem. Soc., 140, 1526 (1993) 2. C. R. Pals and J. Newman Journal of Electrochem. Soc., 142 (10), 3274-3281 (1995) 3. M. Doyle, J. Newman, Journal of Electochem. Soc., 143, 1890 (1996)

The model is pseudo 2D due diffusion equation solved for each particle.

Many particles exist

© 2011 ANSYS, Inc. June 7, 2012 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.

© 2011 ANSYS, Inc. June 7, 2012 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. Hu, S. Stanton, L. Cai, R. White, “A Linear Time-Invariant Model for Solid-Phase Diffusion in Physics-Based Lithium Ion Cell Models,“ J. of Power Sources, vol. 214, p. 40-50, 2012

© 2011 ANSYS, Inc. June 7, 2012 26

Reduced Order Model Validation

Even the 3rd order model gives good accuracy.

3rd 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


© 2011 ANSYS, Inc. June 7, 2012 27

Validation for P2D Electrochemistry Model

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=Ln+Ls+Lp

x=Ln+Ls

x=Ln

x=0

Rate 0.1C 0.5C 1C 3C 5C 10C


© 2011 ANSYS, Inc. June 7, 2012 28

Impact of Particle Shapes on Cell Performance


Impact of different particle shapes only show up at high discharge rates.

© 2011 ANSYS, Inc. June 7, 2012 29

Introduction to System Matrix Based MOR

What is a state?

x1

x2

Initial state at t=t0

x1

x2

x1

x2

x1

x2

x1

x2

What is the main goal of system matrix based MOR?

What is a state trajectory?

What is change of basis?

What is a projection?

Find x1’

© 2011 ANSYS, Inc. June 7, 2012 30

Introduction to System Matrix Based MOR

Obtain the original system matrix

zx V

uxx BKE

uzz BVKVVEVV TTT

E

Er x V

z

≈

.

Substitute and solve the reduced system matrix

Find and project onto low-dimensional subspace

© 2011 ANSYS, Inc. June 7, 2012 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

• 1D fluid channels

Coupling by heat transfer coefficient

Fixed velocity

FLUID116

© 2011 ANSYS, Inc. June 7, 2012 33

Reduced vs Full Solution

Reduced Full

Simulation time [s] 4000 4000 (100 time steps)

Dimension 40 (10 x Input) 48500 elements

CPU time [s] <1 ~20 min

0000

Cell1

Cell2

Cell3

Cell4 T_Ref

HVALUE=0

HVALUE=0

HVALUE=0

Q

VALUE=20HVALUE=10

0.00 1000.00 2000.00 3000.00 4000.00 5000.00Time [s]

293.00

294.25

295.50

296.75

297.50

Y1 [k

el]

Curve InfoTHM1.T

TRTHM2.T

TRTHM3.T

TRTHM4.T

TR

0.00 1000.00 2000.00 3000.00 4000.00Time [s]

0.00

0.50

1.00

Tem

pera

ture

[cel

]

Curve InfoTCell1.T

TR

ansys_Cell1Imported

Error <1%

Step response of 1W per cell

© 2011 ANSYS, Inc. June 7, 2012 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

x1

x2

x V

z

≈

.

© 2011 ANSYS, Inc. June 7, 2012 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: 68000 DOFs

• 4000s, adaptive time step

Δtmax:400s

Δtmin : 1ms

• Dimension of reduced order model

10*Number of inputs

• MOR time is less than one transient simulation

Results • 1W/per cell step response

• CPU time in Simplorer: 5mim 48s

© 2011 ANSYS, Inc. June 7, 2012 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 Needs system matrices

Could use testing data Can not use testing data

Only specified outputs Field solution is possible

Extremely short run time (sec) Short run time (sec, min)

Can handle very large problems Challenging for large problems

Extremely accurate Very accurate

Most efficient with SISO systems (can be extended to MIMO systems)

MIMO systems can be handled efficiently

© 2011 ANSYS, Inc. June 7, 2012 39

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.

Conclusion

© 2011 ANSYS, Inc. June 7, 2012 40

Ralph E. White (University of South Carolina)

Long Cai (University of South Carolina)

Wenyu Lian (General Motors)

Lucas Kostetzer (ESSS)

Evgeny Rudnyi (CADFEM)

Acknowledgement

model order reduction for battery simulation - ansys model order reduction (mor) technique different...

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