Solar Panel Tilt Angle Optimization

This project demonstrates the use of mathematical methods to optimize the tilt angle of solar panels for maximum efficiency. We use a polynomial model to represent the solar panel efficiency as a function of the tilt angle and implement both Lagrange interpolation and the Dichotomy method for root finding.

Project Structure

• racinef.m: Plots the efficiency of the solar panel as a function of the tilt angle.
• lagrange.m: Implements Lagrange interpolation to predict solar efficiency at intermediate tilt angles.
• dichotomie.m: Finds the optimal tilt angle using the Dichotomy (Bisection) method.

How It Works

1. Plotting Solar Efficiency: racinef.m generates a plot of the solar panel efficiency over a range of tilt angles (0° to 90°). The efficiency curve is modeled using a polynomial approximation.

2. Lagrange Interpolation: lagrange.m allows us to estimate the efficiency of the solar panel at any tilt angle, even if we only have data for a few angles. For example, if we know the efficiency at 0°, 30°, 60°, and 90°, we can use this method to estimate the efficiency at 45°.

3. Dichotomy Method for Optimization: dichotomie.m uses the Bisection method to find the tilt angle that maximizes the solar panel efficiency. The method works by finding the root of the derivative of the efficiency function.

How to Run the Code

1. Open MATLAB.
2. Run racinef.m to visualize the solar panel efficiency curve.
3. Use lagrange.m to predict solar efficiency at specific tilt angles.
4. Use dichotomie.m to find the optimal tilt angle for your solar panel installation.

Example

• Plot the efficiency curve using racinef.m.
• Predict the efficiency at 45° using lagrange.m:

  angles = [0, 30, 60, 90];
  efficiency = [0.5, 0.75, 0.8, 0.6];
  predicted_efficiency = lagrange(angles, efficiency, 45);
  

• Find the optimal tilt angle using dichotomie.m:

  [optimal_angle, iterations] = dichotomie(20, 70, 1e-4);
  

License

This project is licensed under the GNU General Public License.