67087f874d
Corrected one typo (stray mid-line comment symbol) and converted hard-coded faraday constant to the corresponding Matlab toolbox function (added with PR #640).
133 lines
5.3 KiB
Matlab
133 lines
5.3 KiB
Matlab
% This example file calculates the cell voltage of a lithium-ion battery
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% at given temperature, pressure, current, and range of state of charge (SOC).
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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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% Further required cell parameters are the electrolyte ionic resistance, the
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% stoichiometry ranges of the active materials (electrode balancing), and the
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% surface area of the active materials.
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%
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% The functionality of this example 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 and simulation of
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% the thermodynamics of lithium-ion battery intercalation materials in an
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% open-source software", under review at Electrochimica Acta (2019).
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% -----------------------------------------------------------------------------
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% Input
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% -----------------------------------------------------------------------------
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% Operation parameters
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SOC = 0:0.02:1; % [-] Input state of charge (0...1) (can be a vector)
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I_app = -1; % [A] Externally-applied current, negative for discharge
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T = 293; % [K] Temperature
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P = oneatm; % [Pa] Pressure
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% Cell properties
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inputCTI = 'lithium_ion_battery.cti'; % Cantera input file name
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R_elyt = 0.0384; % [Ohm] Electrolyte resistance
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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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% Electrode balancing: The "balancing" of the electrodes relates the chemical
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% composition (lithium mole fraction in the active materials) to the macroscopic
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% cell-level state of charge.
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X_Li_an_0 = 0.01; % [-] anode Li mole fraction at SOC = 0 %
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X_Li_an_1 = 0.75; % [-] anode Li mole fraction at SOC = 100 %
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X_Li_ca_0 = 0.99; % [-] cathode Li mole fraction at SOC = 0 %
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X_Li_ca_1 = 0.49; % [-] cathode Li mole fraction at SOC = 100 %
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% -----------------------------------------------------------------------------
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% Calculations
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% -----------------------------------------------------------------------------
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% Calculate mole fractions from SOC
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X_Li_an = (X_Li_an_1-X_Li_an_0)*SOC+X_Li_an_0; % anode balancing
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X_Li_ca = (X_Li_ca_0-X_Li_ca_1)*(1-SOC)+X_Li_ca_1; % cathode balancing
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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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V_cell = zeros(length(SOC),1);
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phi_l_an = 0;
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phi_s_ca = 0;
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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, phi_l_an);
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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, phi_s_ca);
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% Calculate cell voltage
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V_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,V_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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% -----------------------------------------------------------------------------
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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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% 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 anode-side interface
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% Reaction according to cti file: Li+[elyt] + V[anode] + electron <=> Li[anode]
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r = rop_net(anode_interface); % [kmol/m2/s]
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% Calculate the current. Should be negative for cell discharge.
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anCurr = r*faradayconstant*S_an; %
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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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% 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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% Reaction according to cti file: Li+[elyt] + V[cathode] + electron <=> Li[cathode]
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r = rop_net(cathode_interface); % [kmol/m2/s]
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% Calculate the current. Should be negative for cell discharge.
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caCurr = r*faradayconstant*S_ca*(-1); %
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end
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