4.10 Complex Networks
155
(continued)
Matrix of the system function (F i )
Function
Q 14
Q 12
Q 24
Q 34
Q 23
Ind. term = Q a
F i
Jacobian of the system
Variable
Q 14
Q 12
Q 24
Q 34
Q 23
F 1
1
−1
0
0
0
F 2
0
1
−1
0
−1
F 3
0
0
0
−1
1
F 4
52.571429 50.571429 10.428571 0
0
F 5
0
0
−10.42857 28.892857 15.553571
Inverse matrix calculation
Solution
0.5288858 0.0756944 0.0492059 0.0089614 0.001703
Q 14 = −3.12
−0.471114 0.0756944 0.0492059 0.0089614 0.001703
Q 12 = −3.12
−0.381583 −0.748648 −0.486667 0.0072584 −0.016844 Q 24 = −11.14
−0.089532 −0.175657 −0.464127 0.001703
0.0185469 Q 34 = 8.02
−0.089532 −0.175657 0.5358725 0.001703
0.0185469 Q 23 = 8.02
Branch
14
12
24
34
23
R ij
0.4
0.3
0.8
0.2
0.1
Q i + Q i −68.83
81.17
−4.62
−64.21
85.79
…
Iteration 4
Branch
14
12
24
34
23
R ij
0.4
0.3
0.8
0.2
0.1
Q i + Q i
−69.30
80.70
−6.40
−62.90
87.10
Iteration 5
Branch
14
12
24
34
23
R ij
0.4
0.3
0.8
0.2
0.1
Q i + Q i
−69.30
80.70
−6.40
−62.90
87.10
(b) Solution by substitution of variables.
The initial approach is the same as outlined in the previous section. However, since
we have two meshes we can simplify matters by select two arbitrary variables (in
this case Q 12 , Q a ) and allow all other variables to depend on these, such that: