99 lines
No EOL
3.4 KiB
Matlab
99 lines
No EOL
3.4 KiB
Matlab
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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%
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% Input:
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% - stoichiometries X_Li_ca and X_Li_an [-] (can be vectors)
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% - temperature T [K]
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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", Computer Physics Communications
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% Parameteres
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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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S_ca = 1.1167; % [m^2] Cathode total active material surface area
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S_an = 0.7824; % [m^2] Anode total active material surface area
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% Import all Cantera phases
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anode = importThermoPhase(inputCTI, 'anode');
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cathode = importThermoPhase(inputCTI,'cathode');
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elde = importThermoPhase(inputCTI,'electron');
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elyt = importThermoPhase(inputCTI,'electrolyte');
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anode_interface = importEdge(inputCTI, 'edge_anode_electrolyte', anode, elde, elyt);
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cathode_interface = importEdge(inputCTI, 'edge_cathode_electrolyte', cathode, elde, elyt);
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% Set the temperatures and pressures of all phases
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phases = [anode elde elyt cathode];
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for ph = phases
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set(ph,'T',T,'P',P);
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end
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% Calculate cell voltage, separately for each entry of the input vectors
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E_cell = zeros(length(X_Li_ca),1);
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for i = 1:length(X_Li_ca)
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% Set anode electrode potential to 0
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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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% 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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% 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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%--------------------------------------------------------------------------
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% Sub-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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% 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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% 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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% 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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end |