Why do i met converged to an infeasible point

I have met this problem while doing power flow optimization.

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.

<stopping criteria details>

i tried both sqp and interior point method. they showed similar results. like below

i am not sure how to solve this

codes are provided below.

a=1;
b=1;
c=1;
d=1;
e=1;
f=1;
g=1;
h=1;
function  Impedance= Z(R,L,C)
w = 3.141592653589793e+02;
Impedance = R+L*w*j-C*w*j;
end
Z12 = Z(88e-3,130e-6,0);
Z15 = Z(13e-3,280e-6,0);
Z35 = Z(78e-3,50e-3,0);
Z45 = Z(29e-3,467e-6,0);
Z6 = Z(30e-3,147e-6,0);
Y12 = 1/Z12;
Y15 = 1/Z15;
Y35 = 1/Z35;
Y45 = 1/Z45;
Y6 = 1/Z6;
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 = full(real(Y));
B = full(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 Parameters for fmincon
A = [];
b = [];
Aeq = [];
beq = [];
lb = [0;0;0;0;0;0;
    220;220;220;220;220;220;
    0;0;0;0;0;0;
    -89600;-89600;-89600;0;0;-89600];
ub = [2*pi;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;0;0;89600;
    ];
%% Define Nonlinear Constraints
nonlcon = @(x)power(x,G,B);
%% Provide Initial Point for fmincon
x0 = zeros(24,1);
%An=x(1:6);
%V=x(7:12);
%P=x(13:18);
%Q=x(19:24);
% x1~6angle, x7~12V, x13~18P,x19~24Q
% V1   V2   V3   V4     V5    V6
%x(7) x(8) x(9) x(10) x(11) x(12)
%% Set Parameters for fmincon and Call fmincon
%options = optimoptions('fmincon','Algorithm','interior-point','OptimalityTolerance',1e-9,'StepTolerance',1e-9,'ConstraintTolerance',1e-9);
options = optimoptions('fmincon','Algorithm','sqp');
[x,fval] = fmincon(@(x)fun(x),x0,A,b,Aeq,beq,lb,ub,nonlcon,options);
function [c,ceq] = power(x,G,B)
w = 3.141592653589793e+02;
PL1 = 24e3;
QL1 = 18e3;
PL2 = 41e3;
QL2 = 28e3;
PL3 = 50e3;
QL3 = 34e3;
PL4 = 44e3;
ceq=[x(7)*(x(11)*(G(1,5)*cos(x(1)-x(5))+w*B(1,5)*sin(x(1)-x(5)))+x(8)*(G(1,2)*cos(x(1)-x(2))+w*B(1,2)*sin(x(1)-x(2))))+PL1-x(13);%P1
    x(7)*(x(11)*(G(1,5)*sin(x(1)-x(5))+w*B(1,5)*cos(x(1)-x(5)))+x(8)*(G(1,2)*sin(x(1)-x(2))+w*B(1,2)*cos(x(1)-x(2))))+QL1-x(19);%Q1
    x(8)*(x(1)*(G(2,1)*cos(x(2)-x(1))+w*B(2,1)*sin(x(2)-x(1))))+PL2-x(14);%P2
    x(8)*(x(1)*(G(2,1)*sin(x(2)-x(1))+w*B(2,1)*cos(x(2)-x(1))))+QL2-x(20);%Q2
    x(9)*(x(11)*(G(3,5)*cos(x(3)-x(5))+w*B(3,5)*sin(x(3)-x(5))))+PL3-x(15);%P3
    x(9)*(x(11)*(G(3,5)*sin(x(3)-x(5))+w*B(3,5)*cos(x(3)-x(5))))+QL3-x(21);%Q3
    x(10)*(x(11)*(G(4,5)*cos(x(4)-x(5))+w*B(4,5)*sin(x(4)-x(5))))+PL4;%P4
    x(10)*(x(11)*(G(4,5)*sin(x(4)-x(5))+w*B(4,5)*cos(x(4)-x(5))));%Q4
    x(11)*(x(7)*(G(1,5)*cos(x(5)-x(1))+w*B(1,5)*sin(x(5)-x(1)))+x(9)*(G(3,5)*cos(x(5)-x(3))+w*B(3,5)*sin(x(5)-x(3)))+x(10)*(G(4,5)*cos(x(5)-x(4))+w*B(4,5)*sin(x(5)-x(4)))+x(12)*(G(5,6)*cos(x(5)-x(6))+w*B(5,6)*sin(x(5)-x(6))))-x(17);%P5
    x(11)*(x(7)*(G(1,5)*sin(x(5)-x(1))+w*B(1,5)*cos(x(5)-x(1)))+x(9)*(G(3,5)*sin(x(5)-x(3))+w*B(3,5)*cos(x(5)-x(3)))+x(10)*(G(4,5)*sin(x(5)-x(4))+w*B(4,5)*cos(x(5)-x(4)))+x(12)*(G(5,6)*sin(x(5)-x(6))+w*B(5,6)*cos(x(5)-x(6))))-x(23);%Q5
    x(12)*(x(11)*(G(6,5)*cos(x(6)-x(5))+w*B(6,5)*sin(x(6)-x(5))))-x(18);%P6
    x(12)*(x(11)*(G(6,5)*sin(x(4)-x(5))+w*B(6,5)*cos(x(6)-x(5))))-x(24);%Q6
    ];
c=[];
end

[Mitchell Thurston]

I don't know very much about this problem, but my guess is its in your lower bound and upper bounds. For example, the 16th, 17th, 22nd, and 23rd index of the bounds define your parameters to be zero. When I get rid of the bounds, it's able to converge

x = [3.82, 4.79, 3.87, 3.39, 4.96, 4.97, -13.87, -9.59, 984.72, 7.46, 2.86, 4.43, -0.50, -0.50, -0.50, 0.00, -32347.81, -0.50, 63686.87, 0.00, 60053.68, 0.00, 28775.68, 60729.14]'

Answer 1

[Nipun]

Hi Tsam,

I understand that you are facing an "infeasible point" error while doing power flow optimization using "fmincon" in MATLAB.

"fmincon" is a gradient based solver based on the bounds provided. Upon careful investigation of the given information, I can confirm that the lower bound and upper bounds force the parameters to be zero. I recommend reconsidering the provided bounds to get a feasible point.

Another possible resolution for this problem is using the gradient as "GradObj" in the "fmincon" solver. This can be done by setting the "GradObj" in "optimoptions. For more information on available options for "fmincon" function, refer to the following MathWorks documentation:

https://in.mathworks.com/help/optim/ug/fmincon.html#busog7r-options

You may find the following MATLAB answer useful that addresses dealing with infeasible solutions given the "fmincon" solver:

https://in.mathworks.com/matlabcentral/answers/213340-why-getting-infeasible-solutions-using-fmincon-update

Hope this helps.

Regards,

Nipun