How to update variables in a simple iteration

Hello everone,

I am trying to solve an equation of which i want to be using the new value as an update. The idea is to use the P and Q calculated in 1 and 2 in equation 3, and the values obtained in 3 is then used in equation 1 and 2 untill delta in equation 3 converges. Is the undelined letters P and Q in 1 and 2 respectively correct?

The expected result is to display P, Q and delta.

% P(i) = P(i) + formula....  % trying to update P and Q
% Q(i) = Q(i) + formula...

THANK YOU

% The formula for calculating the P and Q at each buses 1 & 2
%{
        P(i) = sum(j=1->n) |Vi||Vj|(Gij * cos(delta_i - delta_j) + 
                                    Bij * sin(delta_i - delta_j)
        Q(i) = sum(j=1->n) |Vi||Vj|(Gij * sin(delta_i - delta_j) - 
                                    Bij * cos(delta_i - delta_j)
%}
% ........................................................................................................
delta = zeros(2,1);
Ybuskron = [Y11 - Y12*inv(Y22)*Y21];
G = real(Ybuskron); % conductance (G) <- real part of admittance 
B = imag(Ybuskron); % susceptance (B) <- the imaginary part of admittance
while (delta_tolerance > 1e-7 || E_angle_tol > 1e-7)
    for i = 1:2
        for j = 1 : 2
            P(i) = P(i) + E(i)*E(j)*(G(i,j)*cos(delta(i)-delta(j)) + ...        equation (1)
                B(i,j)*sin(delta(i)-delta(j)))
            Q(i) = Q(i) + E(i)*E(j)*(G(i,j)*sin(delta(i)-delta(j)) - ...      equation (2)
                B(i,j)*cos(delta(i)-delta(j)));
        end  
    end  
    delta(2) = 0;
    delta(1) = delta(2) + atan((P(1)/Q(1)));                                  equation (3)
    E11(iteration+1,1:2)= abs(E);
    E_tolerance = max(abs((E)-(Eprev)));
    E_angle_tol = max(abs((angle(E))- angle(Eprev)));
    delta_tolerance = max(abs(delta - delta_prev));
    Eprev = E;  % Vprev is required for next iteration
    delta_prev = delta;
    iteration = iteration + 1;      % Increment iteration count
end
ybus;
E;
delta;
P
Q

[John D'Errico]

I doubt I'd call it Gauss-Seidel, since that has a very well defined meaning in mathematics. But you are just performing a simple fixed point iteration.

Anyway, why would you not consider a solving tool, like fsolve instead? Use a tool that is designed to solve a class of problems, rather than trying to invent a possibly poorly convergent tool your own.

[Kamilu Sanusi]

@John D'Errico, thank you so much. First I am still a learner and I need it seriously for my research. I later removed the Gauss Siedel from the title. In order to determine P1, P2, Q1, and Q2, delta(1) and delta(2) must be specified in equations (1 and 2). So, i am using equation (3) to determine delta(2) while delta(1) is set to zero (i.e refrence). I want to be using new values of delta(2) to update equations 1 & 2. My expected results is to display delta(1), delta(2), P1, P2, Q1, and Q2. Please any assistance to improve the program would be highly appreciated