I need MATLAB code that plots the aerodynamic power generated by a wind turbine vs the generator rotation speed for different wind speeds

I need a new MATLAB code or patch for the following code that draws the aerodynamic power generated by the wind turbine versus the generator's rotation speed for different wind speeds:

clear; clc; close all;

% Define constants
rho = 1.225;  % Air density [kg/m^3]
R = 35.25;       % Radius of wind turbine [m]

% Define wind speeds
wind_speeds = [5 10 15 20];  % Wind speeds [m/s]

% Define generator rotation speeds
rotation_speeds = 0:1000:2000;  % Rotation speeds [rpm]

% Calculate aerodynamic power for each wind speed and rotation speed
power = zeros(length(rotation_speeds), length(wind_speeds));
for i = 1:length(wind_speeds)
    for j = 1:length(rotation_speeds)
        wind_speed = wind_speeds(i);
        rotation_speed = rotation_speeds(j) * (2*pi/60);  % Convert rpm to rad/s
        
        % Calculate aerodynamic power
        power(j, i) = 0.5 * rho * pi * R^2 * (wind_speed^3) * rotation_speed;
    end
end

% Plot the aerodynamic power
figure;
hold on;
colors = {'b', 'g', 'r', 'm'};
for i = 1:length(wind_speeds)
    plot(rotation_speeds, power(:, i), colors{i});
end
hold off;

% Set plot properties
title('Aerodynamic Power vs. Generator Rotation Speed');
xlabel('Generator Rotation Speed [rpm]');
ylabel('Aerodynamic Power [W]');
legend(cellstr(num2str(wind_speeds', 'Wind Speed = %d m/s')));

% Adjust plot limits, if needed
% xlim([0 max(rotation_speeds)]);
% ylim([0 max(power(:))]);

% Save the plot as an image, if desired
% saveas(gcf, 'aerodynamic_power_plot.png');

[itouchene]

[Nikhil]

Could you explain the issue with this code?

[itouchene]

I want to give results like the attached image in the comment, but I don't know where the error is

[Alan Stevens]

Your expression for power is linearly proportional to rotation speed, so you are only ever going to get straight line outputs from it!

Answer 1

[Image Analyst]

Looks like you're not plotting out far enough on the x axis to see the parabolic shape. You're only going out on the relatively flat upward sloping side of the parabola. Try increasing the range of the rotation speeds so that you can see the full parabola shape.

[David Goodmanson]

what parabola?

[Image Analyst]

His desired curves look roughly like parabolas or Gaussians. Perhaps his equations are not right and won't ever give the desired shapes (not sure, didn't delve into it too deeply to figure it out). Maybe he needs to check his equation.

[David Goodmanson]

His code is well annotated and is an obvious straight line.

[Image Analyst]

Yes we know he's getting straight lines but what he wants is curvy lines like

so that's why I suggested he may have the wrong equation. It looks like Sam did some research and perhaps has found the proper equation to use.

Answer 2

[Sam Chak]

Hi @itouchene

You can clearly identify the relationship here:

If the aerodynamic power is y, the rotation speed is x, and this term is a constant, then mathematically, you are plotting , which is a straigh line.

After checking the facts in the Variable speed wind turbine, the correct formula should be

where the coefficient of power, is a nonlinear function of lambda (λ), given by

with ω is the tip rotational speed.