Battery Cell Electrochemical and Thermal Modeling - · PDF fileBattery Cell Electrochemical...

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© 2011 ANSYS, Inc. September 22, 2011 1 Battery Cell Electrochemical and Thermal Modeling Xiao Hu, PhD Lead Technical Services Engineer ANSYS Inc

Transcript of Battery Cell Electrochemical and Thermal Modeling - · PDF fileBattery Cell Electrochemical...

Page 1: Battery Cell Electrochemical and Thermal Modeling -  · PDF fileBattery Cell Electrochemical and Thermal Modeling ... Electrochemical Kinetics ... (Electrochemical Systems, 3 rd

© 2011 ANSYS, Inc. September 22, 2011

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Battery Cell Electrochemical and Thermal Modeling

Xiao Hu, PhD

Lead Technical Services Engineer

ANSYS Inc

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© 2011 ANSYS, Inc. September 22, 2011

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Battery electrochemical modeling using Simplorer VHDL-AMS

Battery cell thermal modeling using FLUENT

From electrochemistry model to cell thermal model

Outline

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© 2011 ANSYS, Inc. September 22, 2011

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Newman Pseudo 2d Electrochemistry Model

Lithium Ion Batteries

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

• Charge Conservation/Transport• (Thermal) Energy Conservation

Li+

e

Li+

Li+ Li+

LixC6 Lix-Metal-oxidee

Jump

Results from Simplorer Results from Newman

( ) Liee

ee jF

tcDtc +−

+∇⋅∇=∂

∂ 1)(ε

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© 2011 ANSYS, Inc. September 22, 2011

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What is VHDL-AMS

VHDL-AMS is a strict superset of IEEE Std. 1076

Very High Speed Integrated Circuit Hardware Description Language – Analog and Mixed-Signal

1993 1999

IEEE 1076VHDL

IEEE 1076.1VHDL-AMS

Description & simulation of event-driven systems

Description & simulation of analog and mixed signal circuits and systems

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© 2011 ANSYS, Inc. September 22, 2011

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Architecture 3Architecture 2Architecture 1

VHDL-AMS Model Construct

Entity• Interface description of a

subsystem or physical device

• Specifies input and output ports to the model

Architecture• Behavior description

• Can be dataflow, structural, procedural, etc

• Modeling can deal with both analog (continuous) and digital (discrete) domains

output portsinput ports

In-out ports

Architecture 2Architecture 1

Entity

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© 2011 ANSYS, Inc. September 22, 2011

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VHDL-AMS Model for a Capacitor

LIBRARY Ieee;use Ieee.electrical_systems.ALL;ENTITY cap IS

GENERIC (capacitance : capacitance := 1.0e-3);PORT (QUANTITY init_v : IN voltage := 0.0;TERMINAL p : electrical;TERMINAL n : electrical);

END ENTITY cap;

ARCHITECTURE arch_cap OF cap ISQUANTITY voltage ACROSS current THROUGH p TO n;BEGIN

IF (domain = quiescent_domain) USE

voltage == init_v;

ELSE

current == capacitance * voltage'dot;

END USE;

END ARCHITECTURE arch_cap;

The capacitor entity has one model constant, one input, and two terminals

The model description essentially has two lines, one for initial condition and one for the equation!!

•Entity •Architecture

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© 2011 ANSYS, Inc. September 22, 2011

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VHDL-AMS Model for Heat Conduction

Example:

ENTITY transient_diffusion ISgeneric (

rho: real := 2000.0;k: real := 2.0;Cp: real := 1000.0);

END ENTITY transient_diffusion;

IF (domain = quiescent_domain) USE

T1 == 20.0;T2 == 60.0; T3 == 100.0; T4 == 60.0; T5 == 20.0;

ELSE

rho*Cp*T1'dot == -(N1p - N0p)/h;rho*Cp*T2'dot == -(N2p - N1p)/h;rho*Cp*T3'dot == -(N3p - N2p)/h;rho*Cp*T4'dot == -(N4p - N3p)/h;rho*Cp*T5'dot == -(N5p - N4p)/h;

END USE

• Architecture (main part)• Entity

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© 2011 ANSYS, Inc. September 22, 2011

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VHDL-AMS Model for Electrochemistry

The governing equations of porous electrode model of the lithium-ion battery (Electrochemical Systems, 3rd by John Newman)

( ) ( )+

+

++

+ −+

∇⋅−∇⋅∇=

∂∂

vtaj

FzticD

tc n

002 1ν

εε

( ) ctFRTi ln1 0

22 ∇−+∇−= +κφκ

−−

= s

cs

an RT

FRT

Fij ηαηα expexp0

12 φσ∇−=− iI

2iaFjn ⋅∇=

A coupled set of PDEs. The way to solve them with VHDL-AMS uses the same technique as before.

PDE: initial value

PDE: boundary value

PDE: boundary value

PDE: boundary value

Algebraic

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© 2011 ANSYS, Inc. September 22, 2011

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Model ImplementationRef: Newman et al (1993, 1995, 1996)

Negative Electrode

Positive Electrode

Separator

δsδn δp

x=0 x=L

h

x=0

2 3 4 51

φ1,1

φ2,1

i1,1

i2,1

c1

3

2

1cs1,1

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

1cs2,1

cs2,2

cs2,3

3

2

1cs3,1

cs3,2

cs3,3

3

2

1cs4,1

cs4,2

cs4,3

3

2

1cs5,1

cs5,2

cs5,3

φ1,6

φ2,6

i1,6

i2,6

2 3 4 51 6

x=δn

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

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© 2011 ANSYS, Inc. September 22, 2011

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How to Use a VHDL-AMS Model in Simplorer?

• Drag and drop the VHDL-AMS model as if it is built-in.

• Double click to launch the property window as if it is built-in.

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© 2011 ANSYS, Inc. September 22, 2011

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Newman Model – Dual Insertion

Simplorer’s Results Newman’s Results•Reference: M. Doyle, J. Newman, Journal of Electochem. Soc., 143, 1890 (1996)

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© 2011 ANSYS, Inc. September 22, 2011

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Newman Model – Temperature Impact

Concentration profiles due to different temperatures

Discharge curves due to different temperatures

•Reference: C. R. Pals and J. Newman Journal of Electrochem. Soc., 142 (10), 3274-3281 (1995)

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© 2011 ANSYS, Inc. September 22, 2011

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Newman Model – Quantitative Comparison

Simplorer’s Results

x=0

x=Lp+Ls+Ln

x=Lp+Ls

x=Lp

1/10 C1/2 C1 C2 C4 C6 C8 C10 C

•Reference: Long Cai, Ralph E. White, Journal of Electrochem. Soc., 156 (3), A154-A161 (2009)

White’s Results

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© 2011 ANSYS, Inc. September 22, 2011

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Newman Model - Quantitative Comparison

Simplorer’s Results White’s Results

•Reference: Long Cai, Ralph E. White, Journal of Electrochem. Soc., 156 (3), A154-A161 (2009)

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© 2011 ANSYS, Inc. September 22, 2011

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- Newman & Tidemann (1993); - Gu (1983) ; - Kim et al (2008)*

( ) J=∇⋅∇ φσ

)()( TfUYJ np −−= φφ

Cathode Anode

Current Current

ip= Current Vectorsat Cathode plate in= Current Vectors

at Anode plate

J = Current DensityJ (t, x, y, T )

Cathode Anode

Current Current

ip= Current Vectorsat Cathode plate in= Current Vectors

at Anode plate

J = Current DensityJ (t, x, y, T )

Transfer current

U and Y are derived from experimentally obtained polarization curve, dependent on Depth of Discharge (DOD) & Temperature

Single Battery Cell Thermal Model

The model is based on the work of:

* Reference: U. S. Kim, C. B. Shin , C. S. Kim, “Effect of electrode configuration on the thermalbehavior of a lithium-polymer battery”, Journal of Power Sources 180 (2008) 909–916.

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© 2011 ANSYS, Inc. September 22, 2011

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Results of a Prismatic Lithium-Ion Cell

Geometry & Mesh

Temperature Current Density

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© 2011 ANSYS, Inc. September 22, 2011

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Inputs to Single Cell Thermal Model

• U and Y curves are the inputs to the cell thermal model. U and Y curves are converted from battery performance data.

• A small program has been written to convert the performance data into the U and Y curves needed by Fluent.

Performance data A program

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© 2011 ANSYS, Inc. September 22, 2011

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What Performance Data Needed?

• Short answer: Battery discharge curves. (aka polarization characteristics)

• Precise answer: Battery cell potential as a function of depth of discharge (DOD) for different discharge rates sampled in the way demonstrated in Gu’s paper Figure 3.

• The required data can be from either testing or electrochemistry model.

•Reference: H. Gu , “Mathematical Analysis of a Zn/NiOOH Cell” J of Electrochem. Soc., Vol. 130, No.7, 1983

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© 2011 ANSYS, Inc. September 22, 2011

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Battery Discharge Curves

Battery discharge curves are battery cell potential as a function of capacity, time, or DOD for different discharge rates.

The two examples use capacity and time. But we need DOD!!

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© 2011 ANSYS, Inc. September 22, 2011

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What is DOD?

Definition of depth of discharge (DOD) used:

What is Qt?

• The theoretical capacity per unit area of the electrodes.

• Achieved when cell potential is lower than certain value discharged at a rate close to zero.

t

t

Q

JdtDOD ∫= 0

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© 2011 ANSYS, Inc. September 22, 2011

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Discharge Curves in Time

These results are from Newman electrochemistry model in Simplorer.

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© 2011 ANSYS, Inc. September 22, 2011

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Discharge Curves in DOD

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© 2011 ANSYS, Inc. September 22, 2011

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Sampled Discharge Curves in DOD

Simplorer offers nice sampling tools shown above.

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© 2011 ANSYS, Inc. September 22, 2011

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Data Input File Format to the Program

Matrix Size

Not Used

Current Density

DOD Main Data

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© 2011 ANSYS, Inc. September 22, 2011

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Program Output : Polynomial Coefficients for U and Y

Coefficients for U

Coefficients for Y

32

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9.1894.16876.890.157676.2661.2659.1187.4

DODDODDODYDODDODDODU

⋅+⋅−⋅−=

⋅−⋅+⋅−=

Note that the extraction code allows you to select the order of

polynomial. An order of 3 is used for both U and Y.

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© 2011 ANSYS, Inc. September 22, 2011

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Curve Fitting Results

U Results Y Results

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© 2011 ANSYS, Inc. September 22, 2011

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Summary

Battery electrochemistry can be modeled using VHDL-AMS in Simplorer.

Battery cell thermal analysis can be performed using a simplified model in FLUENT.

Model inputs for the cell thermal model can be calculated from battery electrochemistry model.

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© 2011 ANSYS, Inc. September 22, 2011

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Thank you !!