why does this says converged to an infeasible point

Question

TSAM KIT CHAN 2024-4-1

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2101366-why-does-this-says-converged-to-an-infeasible-point

关闭： Dyuman Joshi 2024-4-2

i am running below code. it is still to be able to output matrix of x, and fval. but it says this. then im not sure if the values makes sense.

Converged to an infeasible point.

fmincon stopped because the size of the current step is less than

the value of the step size tolerance but constraints are not

satisfied to within the value of the constraint tolerance.

Consider enabling the interior point method feasibility mode.

Converged to an infeasible point.

fmincon stopped because the size of the current step is less than

the value of the step size tolerance but constraints are not

satisfied to within the value of the constraint tolerance.

Optimization stopped because the relative changes in all elements of x are

less than options.StepTolerance = 1.000000e-10, but the relative maximum constraint

violation, 9.267884e-01, exceeds options.ConstraintTolerance = 1.000000e-06.

a = 0.001;
b = 10;
c = 0.01;
d = 0.01;
e = 0.05;
f = 0.005;
g = 1;
h = 1;
% Define function to calculate impedance
function Impedance = Z(R, L)
w = 2*pi*50; % Assuming 50 Hz power system
Impedance = R + L*1j*w;
end
% Calculate impedances
Z12 = Z(88e-3, 130e-6);
Z15 = Z(13e-3, 280e-6);
Z35 = Z(78e-3, 50e-3);
Z45 = Z(29e-3, 467e-6);
Z6 = Z(30e-3, 147e-6);
Y12 = 1/Z12;
Y15 = 1/Z15;
Y35 = 1/Z35;
Y45 = 1/Z45;
Y6 = 1/Z6;
% Construct admittance matrix
Y = [Y15+Y12, -Y12, 0, 0, -Y15, 0;
    -Y12, Y12, 0, 0, 0, 0;
    0, 0, Y35, 0, -Y35, 0;
    0, 0, 0, Y45, -Y45, 0;
    -Y15, 0, -Y35, -Y45, Y15+Y35+Y45+Y6, -Y6;
    0, 0, 0, 0, -Y6, Y6];
G = real(Y);
B = imag(Y);
% Define objective function
fun = @(x) a*x(13) + b*x(13)^2 + c*x(14) + d*x(14)^2 + e*x(15) + f*x(15)^2 + g*x(18) + h*x(18)^2;
% Set up constraints
A = [];
b = [];
Aeq = [];
beq = [];
lb = [0;0;0;0;0;0;
    230;230;230;230;230;230;
    24000;41000;34000;0;0;0;
    -89600;-89600;-89600;0;0;-89600];
ub = [0;2*pi;2*pi;2*pi;2*pi;2*pi;
    240;240;240;240;240;240;
    89600;89600;89600;0;0;89600;%89600
    89600;89600;89600;0;0;89600;
    ];
% Define nonlinear constraints
nonlcon = @(x) power(x, G, B);
% Provide initial point for fmincon closer to feasible region
x0 = [0.1; 0.1; 0.1; 0.1; 0.1; 0.1;   % angles
    230; 230; 230; 230; 230; 230;  % voltages
    1; 1; 1; 0; 0; 1;               % active powers
    1; 1; 1; 0; 0; 1];              % reactive powers
% Set solver options
%options = optimoptions('fmincon', 'Algorithm', 'interior-point', 'Display', 'iter');
options = optimoptions('fmincon', 'Algorithm', 'interior-point', 'Display', 'iter','MaxFunctionEvaluations',4e3)
% Call fmincon with updated options
[x, fval, exitflag, output] = fmincon(@(x) fun(x), x0, A, b, Aeq, beq, lb, ub, nonlcon, options);
% Display exit message
disp(output.message);
% Define power flow equations
function [c, ceq] = power(x, G, B)
w = 2*pi*50;
% Define power injections
PL = [24e3; 41e3; 50e3; 44e3];
QL = [18e3; 28e3; 34e3; 0];
% Calculate active and reactive powers
P = zeros(6, 1);
Q = zeros(6, 1);
P(1) = x(7)*(x(11)*(G(1,5)*cos(x(1)-x(5))+B(1,5)*w*sin(x(1)-x(5)))+x(8)*(G(1,2)*cos(x(1)-x(2))+B(1,2)*w*sin(x(1)-x(2))))-x(13);
Q(1) = x(7)*(x(11)*(G(1,5)*sin(x(1)-x(5))+B(1,5)*w*cos(x(1)-x(5)))+x(8)*(G(1,2)*sin(x(1)-x(2))+B(1,2)*w*cos(x(1)-x(2))))-x(19);
P(2) = x(8)*(x(7)*(G(2,1)*cos(x(2)-x(1))+B(2,1)*w*sin(x(2)-x(1))))-x(14);
Q(2) = x(8)*(x(7)*(G(2,1)*sin(x(2)-x(1))+B(2,1)*w*cos(x(2)-x(1))))-x(20);
P(3) = x(9)*(x(11)*(G(3,5)*cos(x(3)-x(5))+B(3,5)*w*sin(x(3)-x(5))))-x(15);
Q(3) = x(9)*(x(11)*(G(3,5)*sin(x(3)-x(5))+B(3,5)*w*cos(x(3)-x(5))))-x(21);
P(4) = x(10)*(x(11)*(G(4,5)*cos(x(4)-x(5))+B(4,5)*w*sin(x(4)-x(5))));
Q(4) = x(10)*(x(11)*(G(4,5)*sin(x(4)-x(5))+B(4,5)*w*cos(x(4)-x(5))));
P(5) = x(11)*(x(7)*(G(1,5)*cos(x(5)-x(1))+B(1,5)*w*sin(x(5)-x(1)))+...
    x(9)*(G(3,5)*cos(x(5)-x(3))+B(3,5)*w*sin(x(5)-x(3)))+...
    x(10)*(G(4,5)*cos(x(5)-x(4))+B(4,5)*w*sin(x(5)-x(4)))+...
    x(12)*(G(5,6)*cos(x(5)-x(6))+B(5,6)*w*sin(x(5)-x(6))));
Q(5) = x(11)*(x(7)*(G(1,5)*sin(x(5)-x(1))+B(1,5)*w*cos(x(5)-x(1)))+...
    x(9)*(G(3,5)*sin(x(5)-x(3))+B(3,5)*w*cos(x(5)-x(3)))+...
    x(10)*(G(4,5)*sin(x(5)-x(4))+B(4,5)*w*cos(x(5)-x(4)))+...
    x(12)*(G(5,6)*sin(x(5)-x(6))+B(5,6)*w*cos(x(5)-x(6))));
P(6) = x(12)*(x(11)*(G(6,5)*cos(x(6)-x(5))+B(6,5)*w*sin(x(6)-x(5))));
Q(6) = x(12)*(x(11)*(G(6,5)*sin(x(6)-x(5))+B(6,5)*w*cos(x(6)-x(5))));
% Set up nonlinear equality constraints
ceq = [P(1) + PL(1);
    Q(1) + QL(1);
    P(2) + PL(2);
    Q(2) + QL(2);
    P(3) + PL(3);
    Q(3) + QL(3);
    P(4) + PL(4);
    Q(4) + QL(4);
    P(5) - x(17);
    Q(5) - x(23);
    P(6) - x(18);
    Q(6) - x(24);
    sum(P)+sum(PL)-x(17)-x(18);
    sum(Q)+sum(QL)-x(23)-x(24);];
% Set up nonlinear inequality constraints (none in this case)
c = [];
end
display(x);
display(fval);