make a newton raphson code for 3 bus power systems in matlab

To implement the Newton-Raphson method for a 3-bus power system in MATLAB, you can follow these steps:

1. Define the system parameters:

   • Define the admittance matrix Ybus, which represents the network topology and all the branches.
   • Define the power injections P and Q for each bus.
   • Define the initial values for voltage magnitudes (V) and angles (theta) for each bus.

2. Initialize the iteration variables:

   • Set the maximum number of iterations (max_iter) and the convergence tolerance (tol).
   • Set the iteration counter (iter) and the convergence flag (converged).

3. Implement the Newton-Raphson algorithm:

   • Start a loop for the maximum number of iterations:
     • Calculate the power mismatches (delta_P and delta_Q) for each bus using equations: delta_P = P - (G * V.^2 - B * V .* cos(theta)) delta_Q = Q - (-B * V.^2 - G * V .* sin(theta))
     • Calculate the Jacobian matrix J using equations: J11 = -B * V .* sin(theta) J12 = G * V + B * V .* cos(theta) J21 = B * V.^2 + G * V .* sin(theta) J22 = G * V - B * V .* cos(theta)
     • Solve the linear equations J * delta_theta = delta_P and J * delta_V = delta_Q for delta_theta and delta_V.
     • Update the voltage angles (theta) and magnitudes (V).
     • Check for convergence by calculating the maximum power mismatch and comparing it to the convergence tolerance. If the maximum mismatch is below the tolerance, set the converged flag to true and exit the loop.
   • End the loop.

4. Display the results:

   • Display the final voltage magnitudes (V) and angles (theta).
   • Display the convergence status (converged) and the number of iterations (iter).

Here is an example implementation of the Newton-Raphson method for a 3-bus power system in MATLAB:

main.m
% Step 1: Define the system parameters
Ybus = [3 -1 -2; -1 2 -1; -2 -1 5];
P = [1.4; 0.6; 0.2];
Q = [0.4; 0.3; 0.1];
V = [1; 1; 1]; % initial voltage magnitudes
theta = [0; 0; 0]; % initial voltage angles

% Step 2: Initialize the iteration variables
max_iter = 20;
tol = 1e-6;
iter = 0;
converged = false;

% Step 3: Implement the Newton-Raphson algorithm
while iter < max_iter
    % Calculate power mismatches
    delta_P = P - (real(Ybus) * V.^2 - imag(Ybus) * V .* cos(theta));
    delta_Q = Q - (-imag(Ybus) * V.^2 - real(Ybus) * V .* sin(theta));

    % Calculate Jacobian matrix
    J11 = -imag(Ybus) * V .* sin(theta);
    J12 = real(Ybus) * V + imag(Ybus) * V .* cos(theta);
    J21 = imag(Ybus) * V.^2 + real(Ybus) * V .* sin(theta);
    J22 = real(Ybus) * V - imag(Ybus) * V .* cos(theta);
    J = [J11 J12; J21 J22];

    % Solve linear equations
    delta_theta = J \ [delta_P; delta_Q];
    delta_V = delta_theta(3:end);
    delta_theta = delta_theta(1:2);

    % Update voltage angles and magnitudes
    theta = theta + delta_theta;
    V = V + delta_V;

    % Check convergence
    max_mismatch = max(max(abs([delta_P; delta_Q])));
    if max_mismatch < tol
        converged = true;
        break;
    end

    iter = iter + 1;
end

% Step 4: Display the results
if converged
    disp('Converged!');
else
    disp('Not converged!');
end

disp('Final voltage magnitudes:');
disp(V);
disp('Final voltage angles:');
disp(theta);
disp('Number of iterations:');
disp(iter);
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Make sure to adjust the system parameters and initial values according to your specific 3-bus power system. This code provides a basic implementation of the Newton-Raphson method and can be expanded or modified to suit your specific needs or for larger power systems.