How to update variables in a simple iteration

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Kamilu Sanusi
Kamilu Sanusi 2023-1-24
编辑： per isakson 2023-1-24
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
  2 个评论
John D'Errico
John D'Errico 2023-1-24
编辑：John D'Errico 2023-1-24
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
Kamilu Sanusi 2023-1-24
@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

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