how to substitute multiple variables of syms toolbox into matrix elements using subs function.

Hello dear community,

I would like to create a matrix (5,1) of functions using variables that are defined in syms toolbox using for loop to decrease manual work. yet, when I try to assign the function into a cell value by subs I get an error as follow: Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters. In attach you can see my code, and related info. Thnak you very much for your valuable time and help in advance.

PS: The image shows the formula that I am trying to obtain at the end to analyze a system, which has 6 nodes in total.

clc, clear all

syms u1 u2 u3 u4 u5 u6 phi1 phi2 phi3 phi4 phi5 phi6

r = 0.01; %ohm/km
x = 0.1; %ohm/km

l13 = 200; %km
l24 = 160; %km
l34 = 80; %km
l35 = 100; %km
l46 = 125; %km

z13 = l13*(r+1j*x); %ohm
z24 = l24*(r+1j*x); %ohm
z34 = l34*(r+1j*x); %ohm
z35 = l35*(r+1j*x); %ohm
z46 = l46*(r+1j*x); %ohm

g13 = 1/z13; %S
g24 = 1/z24; %S
g34 = 1/z34; %S
g35 = 1/z35; %S
g46 = 1/z46; %S

%addmittance matrix
G = [g13 0 -g13 0 0 0;...
     0 g24 0 -g24 0 0;...
     -g13 0 g13+g34+g35 -g34 -g35 0;...
     0 -g24 -g34 g24+g34+g46 0 -g46;...
     0 0 -g35 0 g35 0;...
     0 0 0 -g46 0 g46];
display(G);

[Yang, Ymag] = cart2pol(real(G), imag(G));

display(Ymag);
display(Yang);

%input data
p1 = -2e6; %W
q1 = -1j*0.5e6; %VAr
s1 = p1 + q1; %MVA

p2 = -2.5e6; %W
q2 = +1j*1e6; %VAr
s2 = p2 + q2; %MVA

p3 = 0e6; %W
q3 = +1j*0e6; %VAr
s3 = p3 + q3; %MVA

p4 = 0e6; %W
q4 = +1j*0e6; %VAr
s4 = p4 + q4; %MVA

u5 = 20e3*exp(1j*deg2rad(0)); %V
u5mag = abs(u5); %V
phi5 = angle(u5); %rad

u6mag = 20e3; %V

p6 = 2.9e6; %W

u = [u1; u2; u3; u4; u5; u6];
phi = [phi1; phi2; phi3; phi4; phi5; phi6];

% F = matlabFunction([F1; F2; F3; F4; F6]);                                   

F = zeros(5,1);
for j=1:5
    for k=1:5
        if k~=j
            F(j) = subs(Ymag(j,j)*u(j)^2*cos(-Yang(j,j))-(u(j)*(Ymag(j,k)*u(k)*cos(phi(j)-phi(k)-Yang(j,k))));
        end
    end
end

disp([F]);

Answer 1

[Sulaymon Eshkabilov]

Note that you don't need subs instead you'd need to save all calc values in a cell array. Here is the corrected part of your code:

...

H = cell(5,1);
for j=1:5
    for k=1:5
       if k~=j
      F= Ymag(j,j)*u(j)^2*cos(-Yang(j,j))-(u(j)*(Ymag(j,k)*u(k)*cos(phi(j)-phi(k)-Yang(j,k))));   
      H(j) ={F}; 
      end
    end
end
celldisp(H);

[Vatan Bedel]

Thank you very much for your time and help. That was a very creative and easy approach. Thanks again.

[Sulaymon Eshkabilov]

Most welcome!

Answer 2

[Walter Roberson]

F(j) = subs(Ymag(j,j)*u(j)^2*cos(-Yang(j,j))-(u(j)*(Ymag(j,k)*u(k)*cos(phi(j)-phi(k)-Yang(j,k))));
 1 0       1    2   1  2 1      2     3   21 2 3 2 3    4   3  4 3    4   5 4    5 4     5   4321 

The digit is the number of open bracket levels "after" the character the digit is below.

Notice at the end the digit is 1. There is one unclosed bracket. You are missing one )