fmincon for Battery Parameter Estimation

Question

Gokul Gopakumar 2024-3-21

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https://ww2.mathworks.cn/matlabcentral/answers/2097251-fmincon-for-battery-parameter-estimation

编辑： Torsten 2024-3-21

Hello,

I am trying to build Thevenin Model for ym LFP Cell. I am attaching the programme. When you run the programme, graph with comparison of simulated and measured voltage will be displayed. But as you can see from the graph, it is not exactly correct. Can somebody help me regarding this.

load("WLTP.mat")

onecyclevoltage = WLTP.VoltageV;

onecyclecurrent = WLTP.CurrentA;

onecycletime = WLTP.Time;

dt =0.1;

% Define initial parameter guesses

initial_guesses = [0.00116 , 0.00126 , 0.0043 , 59.982 , 0.0213 ,300.0103]; % [RCha, RDch, R1, Tau1, R2, Tau2]

% Define optimization options

%options = optimoptions(@fmincon, 'Algorithm', 'active-set', 'MaxIterations', 18101, 'MaxFunEvals', 18101);

options = optimoptions(@fmincon, 'MaxIterations', 40000, 'MaxFunEvals', 40000);

% Define optimization options

%options = optimoptions(@ga, 'MaxGenerations', 1851958, 'PopulationSize', 50);

% Perform parameter estimation using fmincon

[estimated_params, min_rmse,estimated_capacity,~] = fmincon(@(params) objective_function(params, onecyclecurrent, onecyclevoltage, onecycletime), initial_guesses, [], [], [], [], [], [],[],options);

Solver stopped prematurely. fmincon stopped because it exceeded the function evaluation limit, options.MaxFunctionEvaluations = 4.000000e+04.

% Display estimated parameters

disp('Estimated Parameters:');

Estimated Parameters:

disp(estimated_params);

0.0012 0.0012 0.0043 59.9820 0.0213 300.0103

disp(['Minimum RMSE: ', num2str(min_rmse)]);

Minimum RMSE: 0.028285

% Simulate the Thevenin model using the estimated parameters

[~, U2, Uoc, simulated_voltage] = simulate_thevenin_model(estimated_params, onecyclecurrent, onecycletime);

simulated_voltage(1) = Uoc(1);

% Plot the measured and simulated voltage

figure;

plot(onecycletime, onecyclevoltage, 'b-', 'LineWidth', 2);

hold on;

plot(onecycletime, simulated_voltage, 'r--', 'LineWidth', 2);

xlabel('Time (s)');

ylabel('Voltage (V)');

title('Measured vs Simulated Voltage');

legend('Measured', 'Simulated');

grid on;

hold off;

function error = objective_function(params, onecyclecurrent, onecyclevoltage, onecycletime)

% Simulate the Thevenin model with the given parameters

[U1, U2, Uoc, sim_volt,capacity] = simulate_thevenin_model(params, onecyclecurrent, onecycletime);

% Calculate the root mean square error (RMSE) between measured and simulated voltage

error = sqrt(mean((onecyclevoltage - sim_volt).^2));

end

function [U1, U2, Uoc, sim_volt,capacity] = simulate_thevenin_model(params, onecyclecurrent, ~)

% Extract parameters

RCha = params(1);

RDch = params(2);

R1 = params(3);

Tau1 = params(4);

R2 = params(5);

Tau2 = params(6);

% Initialize variables

U1 = zeros(size(onecyclecurrent));

U2 = zeros(size(onecyclecurrent));

Uoc = zeros(size(onecyclecurrent)) ;

Uoc(1) = 3.3398;

sim_volt = zeros(size(onecyclecurrent));

dt =0.1;

% Initialize capacity

capacity = 20;

% Simulation loop

for k = 2:length(onecyclecurrent)

U1(k) = U1(k - 1) * exp(-dt/ (Tau1)) + onecyclecurrent(k) * R1 * (1 - exp(-dt/ Tau1));

U2(k) = U2(k - 1) * exp(-dt / Tau2) + onecyclecurrent(k) * R2 * (1 - exp(-dt / Tau2));

Uoc(k) = Uoc(k - 1) + onecyclecurrent(k) * (RCha - RDch);

sim_volt(k) = Uoc(k) + U1(k) + U2(k);

% Accumulate charge/discharge to estimate capacity

capacity = capacity + abs(onecyclecurrent(k)) * dt ; % Convert current from A to Ah

end

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Torsten 2024-3-21

编辑：Torsten 2024-3-21

One thing that is obvious is that (RCha - RDch) must be reduced to one parameter so that 5 instead of 6 parameters are left to estimate.

I don't see at the moment if the same can be done for R1 and R2 resp. Tau1 and Tau2.

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fmincon for Battery Parameter Estimation

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