Solving a matrix with multiple unknowns

I am trying to solve this set of equations knowning a solution must exist for such set. However, Matlab does not give the needed solution and results in an empty sym variable.

syms Vpri Vpc Vsec Vsc I6 I7 I8 I9
I_op = [100 100 100 100 -100 I6 I7 I8 I9 (I6+I7+I8+I9)/4];
V_op = [Vpri Vpri Vpri Vpri Vpc Vsec Vsec Vsec Vsec Vsc]
eq = LL_mat * I_op' - V_op' == 0;
MYMY = (solve(eq))

The solution is empty for all symbolic variables

>> MYMY.I6
 
ans =
 
Empty sym: 0-by-1

>> MYMY

MYMY = 

  struct with fields:

      I6: [0×1 sym]
      I7: [0×1 sym]
      I8: [0×1 sym]
      I9: [0×1 sym]
     Vpc: [0×1 sym]
    Vpri: [0×1 sym]
     Vsc: [0×1 sym]
    Vsec: [0×1 sym]

Is there a way to solve this system in matlab?

[Walter Roberson]

What is LL_mat?

[user3490]

LL_mat is a symetric non zero 10*10 matrix

Answer 1

[Walter Roberson]

LL_mat is a symetric non zero 10*10 matrix

You have 10 equations in 8 variables. There will seldom be a solution.

[Walter Roberson]

You can solve equations 1 to 7 and 10 for variables in the order I6, I7, I8, I9, Vpc, Vpri, Vsec, Vsc . However, after you have solved equations 1 to 7 for I6, I7, I8, I9, Vpc, Vpri, Vsec and substituted that in, before you have solved for Vsc, then equations 8 and 9 are independent of Vsc -- so equations 8 and 9 are not full rank.

The solutions are generally of the form

(very long expression in elements of LL_mat) / (long expression in elements of LL_mat)

For example Vsc has a numerator that is the sum of 18696 combinations of products of 5 variables at a time from LL_mat, and a denominator that is the sum of 936 combinations of products of 4 variables at a time from LL_mat . For example, terms in the numerator include

-100*L1_10*L2_6*L4_10*L4_7*L6_8 + 100*L1_10*L2_6*L4_10*L4_7*L7_8 + 100*L1_7*L2_10*L4_10*L4_8*L6_6 - 100*L2_10*L2_8*L3_10*L4_6*L6_9 + 100*L2_10*L2_8*L3_10*L4_6*L7_9

and terms in the denominator include

L1_10*L2_6*L3_7*L6_8 - L1_10*L2_6*L3_7*L6_9 - L1_10*L2_6*L3_7*L7_8 + L1_10*L2_6*L3_7*L7_9 - L1_10*L2_6*L3_8*L6_7 + L1_10*L2_6*L3_8*L6_9 + L1_10*L2_6*L3_8*L7_7 - L1_10*L2_6*L3_8*L7_9