power Load flow equations

Hi,

So, I implemented the code based on your header and code snippet provided by defining symbolic variables for voltage magnitudes (vmag1, vmag2, etc.), voltage angles (vang1, vang2, etc.), and power variables (Pg, Qg, Pd, Qd). The real and reactive power demands at bus 1 are set to 100 MW and 50 MVAR, respectively. The admittance matrix components are also defined with example values. Two power balance equations are formulated in which the first equation makes sure that the real power generated (Pg) equals the real power demand (Pd) plus the power losses in the system. The second equation does the same for reactive power. Afterwards, the solve function is called with the constraints and the list of variables to find the solution. Finally, the results are displayed, showing the generated power, reactive power, voltage magnitudes, and angles at each bus.

% Define symbolic variables
syms vmag1 vmag2 vmag3 vmag4 vang1 vang2 vang3 vang4 Pg Qg Pd Qd   
Qd1 Qd2 Qd3 Qd4 Ymag1 Ymag2 Ymag3 Ymag4 Yang1 Yang2 Yang3 Yang4

% Define known parameters (example values)
Pd = 100; % Real power demand at bus 1
Qd = 50;  % Reactive power demand at bus 1

% Admittance matrix components (example values)
Ymag = [0.5; 0.4; 0.3; 0.2]; % Magnitude of admittance
Yang = [30; 45; 60; 90];     % Angle of admittance in degrees

% Constraints
constraints = [
  Pg - Pd == vmag1 * (vmag1 * Ymag(1) * cosd(Yang(1)) + ...
                  vmag2 * Ymag(2) * cosd(Yang(2) + vang1) + ...
                  vmag3 * Ymag(3) * cosd(Yang(3) + vang1 + vang2) + ...
                  vmag4 * Ymag(4) * cosd(Yang(4) + vang1 + vang2 +                     vang3));
  Qg - Qd == -vmag1 * (vmag1 * Ymag(1) * sind(Yang(1)) + ...
                  vmag2 * Ymag(2) * sind(Yang(2) + vang1) + ...
                  vmag3 * Ymag(3) * sind(Yang(3) + vang1 + vang2) + ...
                  vmag4 * Ymag(4) * sind(Yang(4) + vang1 + vang2 +                     vang3));
];

% Solve equations
vars = [Pg, Qg, vmag1, vmag2, vmag3, vmag4, vang1, vang2, vang3, vang4];
sol = solve(constraints, vars);

% Display results
disp('Results:');
disp(['Pg: ', char(sol.Pg)]);
disp(['Qg: ', char(sol.Qg)]);
disp(['Voltage Magnitudes: ', num2str(double([sol.vmag1, sol.vmag2,     
sol.vmag3, sol.vmag4]))]);
disp(['Voltage Angles: ', num2str(double([sol.vang1, sol.vang2, 
sol.vang3,sol.vang4]))]);

Please see attached.

Please let us know if you have any further questions.