2011 ANSYS, Inc. September 22,. 2011. 1. Battery Cell Electrochemical and. Thermal Modeling. Xiao Hu, PhD. Lead Technical Services Engineer. ANSYS Inc ...
Battery Cell Electrochemical and Thermal Modeling
Xiao Hu, PhD Lead Technical Services Engineer ANSYS Inc 1
© 2011 ANSYS, Inc.
September 22, 2011
Outline Battery electrochemical modeling using Simplorer VHDL-AMS Battery cell thermal modeling using FLUENT From electrochemistry model to cell thermal model 2
© 2011 ANSYS, Inc.
September 22, 2011
Newman Pseudo 2d Electrochemistry Model Lithium Ion Batteries
Li+
Li+ Jump Li+
LixC6
Li+ e
∂ (ε e ce ) 1 − t + Li j = ∇ ⋅ ( De ∇ce ) + F ∂t
• Electrochemical Kinetics • Solid-State Li Transport • Electrolytic Li Transport
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• Charge Conservation/Transport • (Thermal) Energy Conservation
Results from Simplorer
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September 22, 2011
e
Lix-Metal-oxide
Results from Newman
What is VHDL-AMS Very High Speed Integrated Circuit Hardware Description Language – Analog and Mixed-Signal Description & simulation of eventdriven systems
Description & simulation of analog and mixed signal circuits and systems IEEE 1076 VHDL
IEEE 1076.1 VHDL-AMS
1993
1999
VHDL-AMS is a strict superset of IEEE Std. 1076
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September 22, 2011
VHDL-AMS Model Construct Entity
Architecture
• Interface description of a
• Behavior description • Can be dataflow, structural,
subsystem or physical device • Specifies input and output ports to the model
procedural, etc • Modeling can deal with both analog (continuous) and digital (discrete) domains
Entity input ports
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Architecture 1 Architecture 2 Architecture 3
September 22, 2011
In-out ports output ports
VHDL-AMS Model for a Capacitor
• Entity
• Architecture
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
ARCHITECTURE arch_cap OF cap IS QUANTITY voltage ACROSS current THROUGH p TO n; BEGIN IF (domain = quiescent_domain) USE
voltage == init_v; ELSE
current == capacitance * voltage'dot;
); END ENTITY cap;
END USE; END ARCHITECTURE arch_cap;
The capacitor entity has one model constant, one input, and two terminals 6
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September 22, 2011
The model description essentially has two lines, one for initial condition and one for the equation!!
VHDL-AMS Model for Heat Conduction Example:
• Entity ENTITY transient_diffusion IS generic ( rho: real := 2000.0; k: real := 2.0; Cp: real := 1000.0); END ENTITY transient_diffusion;
• Architecture (main part) IF (domain = quiescent_domain) USE T1 T2 T3 T4 T5
== == == == ==
20.0; 60.0; 100.0; 60.0; 20.0;
ELSE rho*Cp*T1'dot rho*Cp*T2'dot rho*Cp*T3'dot rho*Cp*T4'dot rho*Cp*T5'dot END USE 7
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September 22, 2011
== == == == ==
-(N1p -(N2p -(N3p -(N4p -(N5p
-
N0p)/h; N1p)/h; N2p)/h; N3p)/h; N4p)/h;
VHDL-AMS Model for Electrochemistry The governing equations of porous electrode model of the lithiumion battery (Electrochemical Systems, 3rd by John Newman)
(
∂c i2 ⋅ ∇t +0 ajn 1 − t +0 + ε = ∇ ⋅ (εD∇c ) − ∂t z+ν +F v+ κRT ( i2 = −κ∇φ2 + 1 − t +0 )∇ ln c F I − i2 = −σ∇φ1 aFjn = ∇ ⋅ i2 αaF α c F = − η s exp − η s jn i0 exp RT RT 8
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September 22, 2011
)
PDE: initial value
A coupled set of PDE: The boundary PDEs. wayvalue to solve them with VHDL-AMS uses PDE: boundary value the same technique as before. PDE: boundary value Algebraic
Model Implementation Ref: Newman et al (1993, 1995, 1996)
x=0
x=L δn
δs
δp
1
1
1
1
1
1
cs1,1
cs2,1
cs3,1
cs4,1
cs5,1
2
2
2
2
2
cs1,2
cs2,2
cs3,2
cs4,2
cs5,2
3 cs1,3
3 cs2,3
3 cs3,3
3 cs4,3
3 cs5,3
1
2 c1
Negative Electrode
Separator
Positive Electrode
2
3 c2
φ1,2 φ2,2 i1,2, i2,2
φ1,1 φ2,1 i1,1 i2,1
3
4 c3
φ1,3 φ2,3 i1,3 i2,3
4
5 c4
φ1,4 φ2,4 i1,4 i2,4
5
6 c5
φ1,5 φ2,5 i1,5 i2,5
φ1,6 φ2,6 i1,6 i2,6
h x=0 x=δn
•Reference: M. Doyle, T.F. Fuller, and J. Newman, Journal of Electrochem. Soc., 140, 1526 (1993) C. R. Pals and Journal22, of Electrochem. Soc., 142 (10), 3274-3281 (1995) © 2011 ANSYS, Inc. J. Newman September 9 M. Doyle, J. Newman, Journal of Electochem. Soc., 143, 1890 (1996) 2011
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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Newman Model – Dual Insertion
Simplorer’s Results © 2011 ANSYS, Inc.
September 22,
Newman’s Results
11 •Reference: M. Doyle, J. Newman, Journal of Electochem. Soc., 143, 1890 (1996) 2011
Newman Model – Temperature Impact
Concentration profiles due to different temperatures
Discharge curves due to different temperatures
© 2011 ANSYS, Inc. September 22, 12 •Reference: C. R. Pals and J. Newman Journal of Electrochem. Soc., 142 (10), 3274-3281 (1995) 2011
Newman Model – Quantitative Comparison x=Lp+Ls+Ln x=Lp+Ls x=Lp x=0
1/10 C 1/2 C 1C 2C 4C 6C 8C 10 C
Simplorer’s Results
White’s Results
© 2011 ANSYS, Inc. September 22, 13 •Reference: Long Cai, Ralph E. White, Journal of Electrochem. Soc., 156 (3), A154-A161 (2009) 2011
Newman Model - Quantitative Comparison
Simplorer’s Results
White’s Results
© 2011 ANSYS, Inc. September 22, 14 •Reference: Long Cai, Ralph E. White, Journal of Electrochem. Soc., 156 (3), A154-A161 (2009) 2011
Single Battery Cell Thermal Model The model is based on the work of: - Newman & Tidemann (1993);
- Gu (1983) ; - Kim et al (2008)*
∇ ⋅ (σ∇φ ) = J
Transfer current
J = Y (φ p − φn − U ) f (T ) Current
Current
ip= Current Vectors at Cathode plate
in= Current Vectors
U and Y are derived from experimentally obtained polarization curve, dependent on Depth of Discharge (DOD) & Temperature
at Anode plate
J = Current Density J (t, x, y, T )
Cathode
Anode
* Reference: U. S. Kim, C. B. Shin , C. S. Kim, “Effect of electrode configuration on the thermal © 2011 ANSYS, Inc. September 22, 15 behavior of a lithium-polymer 2011 battery”, Journal of Power Sources 180 (2008) 909–916.
Results of a Prismatic Lithium-Ion Cell Geometry & Mesh
Temperature
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Current Density
September 22, 2011
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
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A program September 22, 2011
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. © 2011 ANSYS, Inc. September 22, 18 •Reference: H. Gu , “Mathematical Analysis of a Zn/NiOOH Cell” J of Electrochem. Soc., Vol. 130, No.7, 1983 2011
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!! 19
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What is DOD? Definition of depth of discharge (DOD) used: t
Jdt ∫ DOD = 0
Qt
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. 20
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September 22, 2011
Discharge Curves in Time
These results are from Newman electrochemistry model in Simplorer. 21
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September 22, 2011
Discharge Curves in DOD
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September 22, 2011
Sampled Discharge Curves in DOD
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September 22, 2011
Simplorer offers nice sampling tools shown above.
Data Input File Format to the Program Matrix Size
Current Density
Not Used
DOD 24
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Main Data September 22, 2011
Program Output : Polynomial Coefficients for U and Y Coefficients for U
Coefficients for Y
Note that the extraction code allows you to select the order of polynomial. An order of 3 is used for both U and Y.
U = 4.187 − 1.659 ⋅ DOD + 2.661 ⋅ DOD 2 − 2.676 ⋅ DOD 3 Y = 157.0 − 89.76 ⋅ DOD − 168.4 ⋅ DOD 2 + 189.9 ⋅ DOD 3 25
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September 22, 2011
Curve Fitting Results
U Results 26
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September 22, 2011
Y Results
Summary Battery electrochemistry can be modeled using VHDLAMS 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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September 22, 2011
Thank you !!
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© 2011 ANSYS, Inc.
September 22, 2011
