125 lines
4.4 KiB
Matlab
125 lines
4.4 KiB
Matlab
% 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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%
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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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% - 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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% Input parameters
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SOC = 0:0.02:1; % [-] Input state of charge (0...1)
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X_Li_an = (0.75-0.01)*SOC+0.01; % anode balancing
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X_Li_ca = (0.99-0.49)*(1-SOC)+0.49; % cathode balancing
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I_app = 0; % [A] Externally-applied current
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R_elyt = 0; % [Ohm] Electrolyte resistance
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T = 300; % [K] Temperature
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P = oneatm; % [Pa] Pressure
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inputCTI = 'lithium_ion_battery.cti'; % cantera input file name
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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 = Solution(inputCTI, 'anode');
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cathode = Solution(inputCTI, 'cathode');
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elde = Solution(inputCTI, 'electron');
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elyt = Solution(inputCTI, 'electrolyte');
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anode_interface = Interface(inputCTI, 'edge_anode_electrolyte', anode, elde, elyt);
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cathode_interface = Interface(inputCTI, 'edge_cathode_electrolyte', cathode, elde, elyt);
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% Set the temperatures and pressures of all phases
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set(anode,'T',T,'P',P);
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set(cathode,'T',T,'P',P);
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set(elde,'T',T,'P',P);
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set(elyt,'T',T,'P',P);
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set(anode_interface,'T',T,'P',P);
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set(cathode_interface,'T',T,'P',P);
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% Calculate cell voltage, separately for each entry of the input vectors
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E_cell = zeros(length(SOC),1);
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for i = 1:length(SOC)
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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),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),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 state of charge:
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figure(1);
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plot(SOC*100,E_cell,'linewidth',2.5)
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ylim([2.5,4.3])
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xlabel('State of charge / %')
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ylabel('Cell voltage / V')
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set(gca,'fontsize',14)
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%--------------------------------------------------------------------------
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% Helper functions
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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,anode,elde,elyt,anode_interface,S_an)
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global F
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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*96485*S_an*1; % F = 96485 C/mol Faraday's constant
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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,cathode,elde,elyt,cathode_interface,S_ca)
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global F
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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*96485*S_ca*(-1); % F = 96485 C/mol Faraday's constant
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end
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