Updates to samples/matlab/lithium_ion_battery.m
Added some context and higher level functionality to lithium_ion_battery.m sample, such that it now uses some of the already-present functionality to calculate and plot the open circuit voltage for a lithium ion battery for a range of active material compositions.
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Steven DeCaluwe
Ray Speth
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1 changed files with 77 additions and 39 deletions
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@ -1,6 +1,29 @@
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function E_cell = lithium_ion_battery(X_Li_ca, X_Li_an, T, P, I_app, R_elyt)
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% Returns the cell voltage (in Volt) of a lithium-ion cell for a given cell
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% current and active material lithium stoichiometries.
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% This example file calculates the open-circuit voltage for a lithium-ion
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% battery over a range of compositions.
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%
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% The thermodynamics are based on a graphite anode and a LiCoO2 cathode,
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% modeled using the 'BinarySolutionTabulatedThermo' class.
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%
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% Note that the function 'E_cell' below has even greater capabilities than
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% what we use, here. It calculates the steady state cell voltage, at a
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% given composition and cell current, for a given electrolyte ionic
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% resistance. This functionality is presented in greater detail in the
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% reference (which also describes the derivation of the
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% BinarySolutionTabulatedThermo class):
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%
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% Reference:
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% M. Mayur, S. DeCaluwe, B. L. Kee, W. G. Bessler, "Modeling
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% thermodynamics and kinetics of intercalation phases for lithium-ion
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% batteries in Cantera", under review at Electrochimica Acta.
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% For the sake of simplicity, we're going to assume that the anode and
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% cathode capacities are perfectly balanced (i.e. if the cathode lithium
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% content is X percent of it's max possible (i.e. its capacity), then we
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% will assume that the anode is at 1-X percent. Without loss of
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% generality, we will define the anode composition:
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% The routine below returns the cell voltage (in Volt) of a lithium-ion
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% cell for a given cell current and active material lithium stoichiometries.
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%
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% Input:
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% - stoichiometries X_Li_ca and X_Li_an [-] (can be vectors)
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@ -8,13 +31,16 @@ function E_cell = lithium_ion_battery(X_Li_ca, X_Li_an, T, P, I_app, R_elyt)
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% - pressure P [Pa]
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% - externally-applied current I_app [A]
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% - electrolyte resistance R_elyt [Ohm]
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%
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% Reference:
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% M. Mayur, S. DeCaluwe, B. L. Kee, W. G. Bessler, "Modeling
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% thermodynamics and kinetics of intercalation phases for lithium-ion
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% batteries in Cantera", under review at Electrochimica Acta.
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X_Li_an = [0.005:0.025:0.995];
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X_Li_ca = 1 - X_Li_an;
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I_app = 0;
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R_elyt = 0;
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T = 300;
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P = oneatm;
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global F
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% Parameters
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inputCTI = 'lithium_ion_battery.cti'; % cantera input file name
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F = 96485; % Faraday's constant [C/mol]
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@ -42,58 +68,70 @@ for i = 1:length(X_Li_ca)
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phi_s_an = 0;
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% Calculate anode electrolyte potential
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phi_l_an = fzero(@(E) anode_curr(phi_s_an,E,X_Li_an(i))+I_app, 0);
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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);
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% Calculate cathode electrolyte potential
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phi_l_ca = phi_l_an + I_app*R_elyt;
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% Calculate cathode electrode potential
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phi_s_ca = fzero(@(E) cathode_curr(E,phi_l_ca,X_Li_ca(i))+I_app, 0);
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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);
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% Calculate cell voltage
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E_cell(i) = phi_s_ca - phi_s_an;
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end
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% Let's plot the cell voltage, as a function of the cathode stoichiometry:
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plot(X_Li_ca,E_cell,'linewidth',2.5)
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ylim([2.5,4.3])
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xlabel('Li Fraction in Cathode')
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ylabel('Cell potential [V]')
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set(gca,'fontsize',14)
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%--------------------------------------------------------------------------
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% Sub-functions
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% Helper functions
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% This function returns the ThermoPhase class instance from CTI file
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function phase = importThermoPhase(inputCTI, name)
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doc = XML_Node('doc', inputCTI);
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node = findByID(doc, name);
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phase = ThermoPhase(node);
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end
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function phase = importThermoPhase(inputCTI, name)
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doc = XML_Node('doc', inputCTI);
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node = findByID(doc, name);
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phase = ThermoPhase(node);
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end
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% This function returns the Cantera calculated anode current (in A)
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function anCurr = anode_curr(phi_s,phi_l,X_Li_an)
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% Set the active material mole fraction
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set(anode,'X',['Li[anode]:' num2str(X_Li_an) ', V[anode]:' num2str(1-X_Li_an)]);
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function anCurr = anode_curr(phi_s,phi_l,X_Li_an,anode,elde,elyt,anode_interface,S_an)
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% Set the electrode and electrolyte potential
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setElectricPotential(elde,phi_s);
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setElectricPotential(elyt,phi_l);
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global F
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% Get the net reaction rate at the cathode-side interface
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r = rop_net(anode_interface).*1e3; % [mol/m2/s]
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% Set the active material mole fraction
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set(anode,'X',['Li[anode]:' num2str(X_Li_an) ', V[anode]:' num2str(1-X_Li_an)]);
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% Calculate the current
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anCurr = r*F*S_an*1;
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end
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% Set the electrode and electrolyte potential
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setElectricPotential(elde,phi_s);
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setElectricPotential(elyt,phi_l);
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% Get the net reaction rate at the cathode-side interface
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r = rop_net(anode_interface).*1e3; % [mol/m2/s]
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% Calculate the current
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anCurr = r*F*S_an*1;
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end
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% This function returns the Cantera calculated cathode current (in A)
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function caCurr = cathode_curr(phi_s,phi_l,X_Li_ca)
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% Set the active material mole fractions
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set(cathode,'X',['Li[cathode]:' num2str(X_Li_ca) ', V[cathode]:' num2str(1-X_Li_ca)]);
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function caCurr = cathode_curr(phi_s,phi_l,X_Li_ca,cathode,elde,elyt,cathode_interface,S_ca)
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% Set the electrode and electrolyte potential
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setElectricPotential(elde,phi_s);
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setElectricPotential(elyt,phi_l);
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global F
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% Get the net reaction rate at the cathode-side interface
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r = rop_net(cathode_interface).*1e3; % [mol/m2/s]
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% Set the active material mole fractions
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set(cathode,'X',['Li[cathode]:' num2str(X_Li_ca) ', V[cathode]:' num2str(1-X_Li_ca)]);
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% Calculate the current
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caCurr = r*F*S_ca*(-1);
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end
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end
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% Set the electrode and electrolyte potential
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setElectricPotential(elde,phi_s);
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setElectricPotential(elyt,phi_l);
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% Get the net reaction rate at the cathode-side interface
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r = rop_net(cathode_interface).*1e3; % [mol/m2/s]
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% Calculate the current
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caCurr = r*F*S_ca*(-1);
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end
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