Calculate dV/dQ to plot differential voltage analysis curve?

57 views (last 30 days)
ekagra gupta on 3 Jun 2022
I have all the required data but do not know how to differentiate my voltage with respect to discharge/charge capacity given.
Alberto Cuadra Lara on 3 Jun 2022
My mistake, I thought I posted it as an answer. Thanks @John D'Errico!

Alberto Cuadra Lara on 3 Jun 2022
Hello Ekagra,
I guess you have numerical values of the voltage as a function of the discharge/charge capacity, right? In this case, you can compute the first derivative numerically, e.g., using finite central differences as follows, where x and y will be Q and V, respectively.
% Definitions
x = linspace(0, 2*pi);
y = sin(x);
% Compute first derivative
dydx = compute_first_derivative(y, x);
% Plot
figure; hold on;
plot(x, y);
plot(x(2:end), dydx);
xlabel('x', 'interpreter', 'latex')
ylabel('y', 'interpreter', 'latex')
legend({'y(x)', 'dy(x)/dx'}, 'interpreter', 'latex', 'location', 'northeastoutside');
% SUB-PASS FUNCTION
function dxdy = compute_first_derivative(x, y)
% Compute first central derivate using a non-uniform grid
%
% Args:
% x (float): Values for the corresponding grid
% y (float): Grid values
%
% Returns:
% dxdy (float): Value of the first derivate for the given grid and its corresponding values
%
h = y(2:end) - y(1:end-1);
hmax = max(h);
mu = h / hmax;
dxdy = zeros(1, length(h));
dxdy(1) = ((x(2) - x(1)) ./ h(1));
for i = 2:length(mu)-1
dxdy(i) = (mu(i)^2 * x(i+1) - (mu(i)^2 - mu(i+1)^2) * x(i) - mu(i+1)^2 * x(i-1)) / ((mu(i)^2 * mu(i+1) + mu(i) * mu(i+1)^2) * hmax);
end
% Direct method
% dxdy(2:end-1) = (mu(2:end-1).^2 .* x(3:end-1) - (mu(2:end-1).^2 - mu(3:end).^2) .* x(2:end-2) - mu(3:end).^2 .* x(1:end-3)) ./ ((mu(2:end-1).^2 .* mu(3:end) + mu(2:end-1) .* mu(3:end).^2) * hmax);
dxdy(end) = ((x(end) - x(end-1)) ./ h(end));
end

Categories

Find more on Solver Outputs and Iterative Display in Help Center and File Exchange

R2022a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!