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Further improved Li-ion battery example

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MATLAB example: better comments, faster calculation, consistent signs; CTI file: thermally-activated kinetics
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wbessler 2019-06-25 08:29:38 +02:00 • committed by Ray Speth
parent bc6dd4ddc0
commit cceb12b01b
2 changed files with 61 additions and 47 deletions
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12
data/inputs/lithium_ion_battery.cti
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@ -279,9 +279,15 @@ ideal_interface(
#==============================================================================
# Electrochemical reactions
#
# We use Butler-Volmer kinetics by setting rate_coeff_type = "exchangecurrentdensity".
# The preexponential factors and activation energies are converted from
# Guo et al., J. Electrochem. Soc. 158, A122 (2011)
#==============================================================================
# Use Butler-Volmer kinetics (rate_coeff_type = "exchangecurrentdensity").
edge_reaction("Li[anode] <=> Li+[elyt] + V[anode] + electron", [4, 0.0, (0, 'kJ/mol')], rate_coeff_type = "exchangecurrentdensity", beta = 0.5,id="anode_reaction")
edge_reaction("Li+[elyt] + V[cathode] + electron <=> Li[cathode]", [100, 0.0, (0, 'kJ/mol')], rate_coeff_type = "exchangecurrentdensity", beta = 0.5,id="cathode_reaction")
# Graphite/electrolyte interface
edge_reaction("Li+[elyt] + V[anode] + electron <=> Li[anode]", [2.028e4, 0.0, (20, 'kJ/mol')], rate_coeff_type = "exchangecurrentdensity", beta = 0.5,id="anode_reaction")
# LCO/electrolyte interface
edge_reaction("Li+[elyt] + V[cathode] + electron <=> Li[cathode]", [5.629e11, 0.0, (58, 'kJ/mol')], rate_coeff_type = "exchangecurrentdensity", beta = 0.5,id="cathode_reaction")

96
samples/matlab/lithium_ion_battery.m
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@ -1,44 +1,53 @@
% This example file calculates the open-circuit voltage for a lithium-ion
% battery over a range of compositions.
% This example file calculates the cell voltage of a lithium-ion % battery
% at given temperature, pressure, current, and range of state of charge (SOC).
%
% The thermodynamics are based on a graphite anode and a LiCoO2 cathode,
% modeled using the 'BinarySolutionTabulatedThermo' class.
% Further required cell parameters are the electrolyte ionic resistance, the
% stoichiometry ranges of the active materials (electrode balancing), and the
% surface area of the active materials.
%
% Note that the function 'E_cell' below has even greater capabilities than
% what we use, here. It calculates the steady state cell voltage, at a
% given composition and cell current, for a given electrolyte ionic
% resistance. This functionality is presented in greater detail in the
% The functionality of this example is presented in greater detail in the
% reference (which also describes the derivation of the
% BinarySolutionTabulatedThermo class):
%
% Reference:
% M. Mayur, S. DeCaluwe, B. L. Kee, W. G. Bessler, "Modeling
% thermodynamics and kinetics of intercalation phases for lithium-ion
% batteries in Cantera", under review at Electrochimica Acta.
%
% The routine below returns the cell voltage (in Volt) of a lithium-ion
% cell for a given cell current and active material lithium stoichiometries.
%
% Input:
% - stoichiometries X_Li_ca and X_Li_an [-] (can be vectors)
% - temperature T [K]
% - pressure P [Pa]
% - externally-applied current I_app [A]
% - electrolyte resistance R_elyt [Ohm]
% M. Mayur, S. DeCaluwe, B. L. Kee, W. G. Bessler, "Modeling and simulation of
% the thermodynamics of lithium-ion battery intercalation materials in an
% open-source software", under review at Electrochimica Acta (2019).
% -----------------------------------------------------------------------------
% Input
% -----------------------------------------------------------------------------
% Input parameters
SOC = 0:0.02:1; % [-] Input state of charge (0...1)
X_Li_an = (0.75-0.01)*SOC+0.01; % anode balancing
X_Li_ca = (0.99-0.49)*(1-SOC)+0.49; % cathode balancing
I_app = 0; % [A] Externally-applied current
R_elyt = 0; % [Ohm] Electrolyte resistance
T = 300; % [K] Temperature
% Operation parameters
SOC = 0:0.02:1; % [-] Input state of charge (0...1) (can be a vector)
I_app = -1; % [A] Externally-applied current, negative for discharge
T = 293; % [K] Temperature
P = oneatm; % [Pa] Pressure
inputCTI = 'lithium_ion_battery.cti'; % cantera input file name
% Cell properties
inputCTI = 'lithium_ion_battery.cti'; % Cantera input file name
R_elyt = 0.0384; % [Ohm] Electrolyte resistance
S_ca = 1.1167; % [m^2] Cathode total active material surface area
S_an = 0.7824; % [m^2] Anode total active material surface area
% Electrode balancing: The "balancing" of the electrodes relates the chemical
% composition (lithium mole fraction in the active materials) to the macroscopic
% cell-level state of charge.
X_Li_an_0 = 0.01; % [-] anode Li mole fraction at SOC = 0 %
X_Li_an_1 = 0.75; % [-] anode Li mole fraction at SOC = 100 %
X_Li_ca_0 = 0.99; % [-] cathode Li mole fraction at SOC = 0 %
X_Li_ca_1 = 0.49; % [-] cathode Li mole fraction at SOC = 100 %
% -----------------------------------------------------------------------------
% Calculations
% -----------------------------------------------------------------------------
% Calculate mole fractions from SOC
X_Li_an = (X_Li_an_1-X_Li_an_0)*SOC+X_Li_an_0; % anode balancing
X_Li_ca = (X_Li_ca_0-X_Li_ca_1)*(1-SOC)+X_Li_ca_1; % cathode balancing
% Import all Cantera phases
anode = Solution(inputCTI, 'anode');
cathode = Solution(inputCTI, 'cathode');
@ -56,27 +65,29 @@ set(anode_interface,'T',T,'P',P);
set(cathode_interface,'T',T,'P',P);
% Calculate cell voltage, separately for each entry of the input vectors
E_cell = zeros(length(SOC),1);
V_cell = zeros(length(SOC),1);
phi_l_an = 0;
phi_s_ca = 0;
for i = 1:length(SOC)
% Set anode electrode potential to 0
phi_s_an = 0;
% Calculate anode electrolyte potential
phi_l_an = fzero(@(E) anode_curr(phi_s_an,E,X_Li_an(i),anode,elde,elyt,anode_interface,S_an)+I_app, 0);
phi_l_an = fzero(@(E) anode_curr(phi_s_an,E,X_Li_an(i),anode,elde,elyt,anode_interface,S_an)-I_app, phi_l_an);
% Calculate cathode electrolyte potential
phi_l_ca = phi_l_an + I_app*R_elyt;
% Calculate cathode electrode potential
phi_s_ca = fzero(@(E) cathode_curr(E,phi_l_ca,X_Li_ca(i),cathode,elde,elyt,cathode_interface,S_ca)+I_app, 0);
phi_s_ca = fzero(@(E) cathode_curr(E,phi_l_ca,X_Li_ca(i),cathode,elde,elyt,cathode_interface,S_ca)-I_app, phi_s_ca);
% Calculate cell voltage
E_cell(i) = phi_s_ca - phi_s_an;
V_cell(i) = phi_s_ca - phi_s_an;
end
% Let's plot the cell voltage, as a function of the state of charge:
figure(1);
plot(SOC*100,E_cell,'linewidth',2.5)
plot(SOC*100,V_cell,'linewidth',2.5)
ylim([2.5,4.3])
xlabel('State of charge / %')
ylabel('Cell voltage / V')
@ -85,12 +96,10 @@ set(gca,'fontsize',14)
%--------------------------------------------------------------------------
% Helper functions
% -----------------------------------------------------------------------------
% This function returns the Cantera calculated anode current (in A)
function anCurr = anode_curr(phi_s,phi_l,X_Li_an,anode,elde,elyt,anode_interface,S_an)
global F
% Set the active material mole fraction
set(anode,'X',['Li[anode]:' num2str(X_Li_an) ', V[anode]:' num2str(1-X_Li_an)]);
@ -98,18 +107,16 @@ function anCurr = anode_curr(phi_s,phi_l,X_Li_an,anode,elde,elyt,anode_interface
setElectricPotential(elde,phi_s);
setElectricPotential(elyt,phi_l);
% Get the net reaction rate at the cathode-side interface
r = rop_net(anode_interface).*1e3; % [mol/m2/s]
% Get the net reaction rate at the anode-side interface
% Reaction according to cti file: Li+[elyt] + V[anode] + electron <=> Li[anode]
r = rop_net(anode_interface)*1e3; % [mol/m2/s] . Factor 1e3 for kmol->mol
% Calculate the current
anCurr = r*96485*S_an*1; % F = 96485 C/mol Faraday's constant
% Calculate the current. Should be negative for cell discharge.
anCurr = r*96485*S_an; % F = 96485 C/mol Faraday's constant
end
% This function returns the Cantera calculated cathode current (in A)
function caCurr = cathode_curr(phi_s,phi_l,X_Li_ca,cathode,elde,elyt,cathode_interface,S_ca)
global F
% Set the active material mole fractions
set(cathode,'X',['Li[cathode]:' num2str(X_Li_ca) ', V[cathode]:' num2str(1-X_Li_ca)]);
@ -118,8 +125,9 @@ function caCurr = cathode_curr(phi_s,phi_l,X_Li_ca,cathode,elde,elyt,cathode_int
setElectricPotential(elyt,phi_l);
% Get the net reaction rate at the cathode-side interface
r = rop_net(cathode_interface).*1e3; % [mol/m2/s]
% Reaction according to cti file: Li+[elyt] + V[cathode] + electron <=> Li[cathode]
r = rop_net(cathode_interface)*1e3; % [mol/m2/s] . Factor 1e3 for kmol->mol
% Calculate the current
% Calculate the current. Should be negative for cell discharge.
caCurr = r*96485*S_ca*(-1); % F = 96485 C/mol Faraday's constant
end