How can i get the optimum point from this curve ?

Question

Muhamed 2024-1-25

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2074431-how-can-i-get-the-optimum-point-from-this-curve

评论： Muhamed 2024-1-25

采纳的回答： Hassaan

在 MATLAB Online 中打开

Vrev = 1.229;

A = 0.25;

n = 1;

s = 0.185;

t1 = 1.002;

t2 = 8.424;

t3 = 247.3;

r1 = 8.05e-5;

r2 = -2.5e-7;

T = [40, 60, 80].';

Iplot = linspace(0,350,100);

nc=1;

Z=2;

F=96485;

f1=[150 200 250].';

f2=[0.99 0.985 0.98].';

I = (((r1 + r2 * T) ./ A) .* Iplot.* A) ./ ((r1 + r2 .* T));

Vact = s * log10(((((t1 + (t2 ./ T)) + (t3 ./ T.^2)) ./ A) .* I) + 1);

Vohm = ((r1 + r2 * T) ./ A) .* I;

Y = Vrev + s * log10((((t1 + (t2 ./ T) + (t3 ./ T.^2)) ./ A) .* I) + 1) + ((r1 + r2 * T) ./ A) .* I;

EF=(((I./A).^2).*f2)./(f1+(I./A).^2);

ndotH=EF.*((nc.*I)/(Z*F));

Q=ndotH*3600*0.022414;

tiledlayout("flow")

nexttile

plot(Iplot,Y)

title('Current denisty vs Voltage cell')

legend('T=40','T=60','T=80');

xlabel("Current Density ,mA/cm^2");

ylabel("cell Voltage ,voltage");

grid on;

nexttile

plot(Iplot,Vohm)

legend('T=40','T=60','T=80');

title ('Current denisty vs Ohmic voltage')

xlabel("Current Density ,mA/cm^2");

ylabel("ohmic voltage ,(Vohmic)");

grid on;

nexttile

plot(Iplot,Vact)

title('Current denisty vs Actual Voltage')

legend('T=40','T=60','T=80');

xlabel("Current Density ,mA/cm^2");

ylabel("Activation voltage ,Vact");

grid on;

nexttile

plot(Iplot,EF)

title ('Current denisty vs Faraday efficiency')

legend('T=40','T=60','T=80');

xlabel("Current Density ,mA/cm^2");

ylabel("Faraday efficiency");

grid on;

nexttile

plot(Iplot,Q)

title ('current denisty vs H2 flowrate')

legend('T=40','T=60','T=80');

xlabel("Current Density ,mA/cm^2");

ylabel("flow rate ,m^3/sec");

grid on;

How can i get the optimum point from this curve and the otimum temp operated on it ?

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Answer 1

Hassaan 2024-1-25

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2074431-how-can-i-get-the-optimum-point-from-this-curve#answer_1397591

在 MATLAB Online 中打开

I assumed you want to optimize for a balance between high hydrogen flow rate and high Faraday efficiency while maintaining a reasonable cell voltage.

% your parameters and equations as you have already done.
Vrev = 1.229;
A = 0.25;
s = 0.185;
t1 = 1.002;
t2 = 8.424;
t3 = 247.3;
r1 = 8.05e-5;
r2 = -2.5e-7;
T = [40, 60, 80].'; % Temperatures
Iplot = linspace(0, 350, 100); % Current Density
f1 = [150 200 250].';
f2 = [0.99 0.985 0.98].';
nc = 1;
Z = 2;
F = 96485;
% Calculate parameters for each temperature
optimalPoints = zeros(length(T), 3); % To store optimum points for each temperature
for i = 1:length(T)
    I = (((r1 + r2 * T(i)) / A) * Iplot * A) / ((r1 + r2 * T(i)));
    Vact = s * log10(((((t1 + (t2 / T(i))) + (t3 / T(i).^2)) / A) * I) + 1);
    Vohm = ((r1 + r2 * T(i)) / A) * I;
    Y = Vrev + Vact + Vohm;
    EF = (((I/A).^2) * f2(i)) / (f1(i) + (I/A).^2);
    ndotH = EF * ((nc * I) / (Z * F));
    Q = ndotH * 3600 * 0.022414;
    % Define optimization criteria (example: maximize Q and EF, minimize Y)
    % You can adjust these criteria based on your specific needs
    score = Q .* EF ./ Y; % Example scoring function
    [maxScore, idx] = max(score); % Find index of maximum score
    % Store the optimum point for each temperature
    optimalPoints(i, :) = [Iplot(idx), Q(idx), T(i)];
end
% Display the optimal points
optimalPoints
optimalPoints = 3×3
  350.0000    0.1449   40.0000
  350.0000    0.1441   60.0000
  350.0000    0.1434   80.0000

-----------------------------------------------------------------------------------------------------------------------------------------------------

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It's important to note that the advice and code are based on limited information and meant for educational purposes. Users should verify and adapt the code to their specific needs, ensuring compatibility and adherence to ethical standards.

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2 个评论
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Muhamed 2024-1-25

thanks bro but how can i identify this point on the curve ? i want to know how to identify this point on the curve

Muhamed 2024-1-25

as data of curve

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Answer 2

Hassaan 2024-1-25

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2074431-how-can-i-get-the-optimum-point-from-this-curve#answer_1397611

在 MATLAB Online 中打开

% your parameters and equations as you have already done.

Vrev = 1.229;

A = 0.25;

s = 0.185;

t1 = 1.002;

t2 = 8.424;

t3 = 247.3;

r1 = 8.05e-5;

r2 = -2.5e-7;

T = [40, 60, 80].'; % Temperatures

Iplot = linspace(0, 350, 100); % Current Density

f1 = [150 200 250].';

f2 = [0.99 0.985 0.98].';

nc = 1;

Z = 2;

F = 96485;

% Calculate parameters for each temperature

optimalPoints = zeros(length(T), 3); % To store optimum points for each temperature

for i = 1:length(T)

I = (((r1 + r2 * T(i)) / A) * Iplot * A) / ((r1 + r2 * T(i)));

Vact = s * log10(((((t1 + (t2 / T(i))) + (t3 / T(i).^2)) / A) * I) + 1);

Vohm = ((r1 + r2 * T(i)) / A) * I;

Y = Vrev + Vact + Vohm;

EF = (((I/A).^2) * f2(i)) / (f1(i) + (I/A).^2);

ndotH = EF * ((nc * I) / (Z * F));

Q = ndotH * 3600 * 0.022414;

% Define optimization criteria (example: maximize Q and EF, minimize Y)

% You can adjust these criteria based on your specific needs

score = Q .* EF ./ Y; % Example scoring function

[maxScore, idx] = max(score); % Find index of maximum score

% Store the optimum point for each temperature

optimalPoints(i, :) = [Iplot(idx), Q(idx), T(i)];

end

% Display the optimal points

optimalPoints

optimalPoints = 3×3

350.0000 0.1449 40.0000 350.0000 0.1441 60.0000 350.0000 0.1434 80.0000

% Now plot the curves and highlight the optimal points

figure; % Create a new figure

% Plotting Current Density vs. Total Cell Voltage (Y)

subplot(2,2,1);

hold on;

for i = 1:length(T)

Y = Vrev + s * log10((((t1 + (t2 ./ T(i)) + (t3 ./ T(i).^2)) ./ A) .* Iplot) + 1) + ((r1 + r2 * T(i)) ./ A) .* Iplot;

plot(Iplot, Y);

% Marking the optimal point

plot(optimalPoints(i, 1), Vrev + s * log10((((t1 + (t2 / T(i)) + (t3 / T(i).^2)) / A) * optimalPoints(i, 1)) + 1) + ((r1 + r2 * T(i)) / A) * optimalPoints(i, 1), 'o');

end

hold off;

title('Current Density vs Total Cell Voltage');

xlabel('Current Density (mA/cm^2)');

ylabel('Total Cell Voltage (V)');

legend('T=40','T=60','T=80','Optimal Points');

grid on;

% Similarly, you can plot for other parameters like Vohm, Vact, EF, and Q

% Just remember to use the subplot and plot commands to create each plot and mark the optimal points

% Example for plotting Current Density vs Hydrogen Flow Rate (Q)

subplot(2,2,2);

hold on;

for i = 1:length(T)

EF = (((Iplot/A).^2) * f2(i)) / (f1(i) + (Iplot/A).^2);

ndotH = EF * ((nc * Iplot) / (Z * F));

Q = ndotH * 3600 * 0.022414;

plot(Iplot, Q);

% Marking the optimal point for Q

plot(optimalPoints(i, 1), optimalPoints(i, 2), 'o');

end

hold off;

title('Current Density vs Hydrogen Flow Rate');

xlabel('Current Density (mA/cm^2)');

ylabel('Hydrogen Flow Rate (m^3/sec)');

legend('T=40','T=60','T=80','Optimal Points');

grid on;

% Continue for other plots as needed...

-----------------------------------------------------------------------------------------------------------------------------------------------------

If you find the solution helpful and it resolves your issue, it would be greatly appreciated if you could accept the answer. Also, leaving an upvote and a comment are also wonderful ways to provide feedback.

It's important to note that the advice and code are based on limited information and meant for educational purposes. Users should verify and adapt the code to their specific needs, ensuring compatibility and adherence to ethical standards.

Professional Interests