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© 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
© 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
© 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
© 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
© 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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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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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
© 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
© 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)
© 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.
© 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)
© 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)
© 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
© 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)
© 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.
© 2011 ANSYS, Inc. September 22, 2011
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Results of a Prismatic Lithium-Ion Cell
Geometry & Mesh
Temperature Current Density
© 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
© 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
© 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!!
© 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
© 2011 ANSYS, Inc. September 22, 2011
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Discharge Curves in Time
These results are from Newman electrochemistry model in Simplorer.
© 2011 ANSYS, Inc. September 22, 2011
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Discharge Curves in DOD
© 2011 ANSYS, Inc. September 22, 2011
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Sampled Discharge Curves in DOD
Simplorer offers nice sampling tools shown above.
© 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
© 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
32
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.
© 2011 ANSYS, Inc. September 22, 2011
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Curve Fitting Results
U Results Y Results
© 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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Thank you !!