How does the fcn2optimexpr() really work, for non-linear expressions. Confused.

Hi,

I am have an non linear equation problem, in which I am using the problem based approuch. I have gotten solutions, but some of the solutions where just awkward. I have found where the error can be be. It lies in the calls to to fcn2optimexpr().

So little of my code.

This function below creates the non-linear equations.

function [Pkj_expr,Qkj_expr] = PowerFlow_func(U,Theta,G,B,Nodes)
%power flows in the system
    for m = 1:length(Nodes)
        for n = 1:length(Nodes)
            Pkj_expr(m,n) = U(m)*U(n)*(G(m,n)*cos(Theta(m)-Theta(n))+B(m,n)*sin(Theta(m)-Theta(n)));
            Qkj_expr(m,n) = U(m)*U(n)*(G(m,n)*sin(Theta(m)-Theta(n))-B(m,n)*cos(Theta(m)-Theta(n)));
        end
    end
end

Then in my main code I use the func2optimexpr() to form the non-linear constrain. Then I sum rows of Pkj and Qkj. See code below.

[Pkj_expr, Qkj_expr] = fcn2optimexpr(@PowerFlow_func,U,Theta,G,B,Nodes);
Flow_P_eq = Pkj == Pkj_expr; 
Flow_Q_eq = Qkj == Qkj_expr;
for tt = 1:length(Nodes)
    P_Injected_eq(tt)  = Pk(tt) == sum(Pkj(tt,:));
    Q_Injected_eq(tt)  = Qk(tt) == sum(Qkj(tt,:));
end

When I solve the problem. I get follwowing

% Equation problem has bound constraints. Reformulating as a least squares problem.
% 
% Solving problem using lsqnonlin.
% 
% Equation solved, inaccuracy possible.
% 
% lsqnonlin stopped because the vector of function values is near zero, as measured by the value
% of the function tolerance. However, the last step was ineffective.
% 
% <stopping criteria details>

So the problem is solved. With inaccuracy. When I investigate the soltuion, it seem resonable, until I inspect the sol.Pkj and sol.Qkj variables. These are unrealistic. So the question, is how to obtain correct expression from the func2optimexpr().

Cheers!