Angewandte Regelung und Optimierung in der ... - uni-stuttgart
Angewandte Regelung und Optimierung in der ... - uni-stuttgart
Angewandte Regelung und Optimierung in der ... - uni-stuttgart
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Gauss-Jordan Simplification<br />
Setup of l<strong>in</strong>earized equations system<br />
• Def<strong>in</strong><strong>in</strong>g Matrix A as<br />
dQ<br />
A = Λ Λ<br />
d∆h<br />
• We obta<strong>in</strong> for each element<br />
A<br />
[ n,<br />
m]<br />
∑<br />
T<br />
⎧−<br />
Anm<br />
for n = m<br />
⎪ m≠n<br />
⎪<br />
−<br />
= ⎨<br />
− 0.54gn,<br />
m<br />
| hn<br />
− hm<br />
|<br />
⎪<br />
⎪<br />
⎩ 0 for n ≠ m and<br />
0.46<br />
= : −g~<br />
( n,<br />
m)<br />
nm<br />
for n ≠ m and<br />
( n,<br />
m)<br />
connected by a<br />
not connected by a l<strong>in</strong>k<br />
l<strong>in</strong>k<br />
• and can therefore build the follow<strong>in</strong>g equations system<br />
nod<br />
⎛ g~<br />
− g~<br />
− g~<br />
11<br />
1,2<br />
...<br />
1, N ⎞⎛<br />
δh1<br />
⎞ ⎛δq<br />
⎞<br />
1<br />
⎜<br />
⎟⎜<br />
⎟ ⎜ ⎟<br />
nod<br />
⎜ − g~<br />
g~<br />
− g~<br />
2,1 22<br />
...<br />
2, N ⎟⎜<br />
δh2<br />
⎟ ⎜δq2<br />
⎟<br />
⎜<br />
⎟⎜<br />
⎟ =<br />
... ... ... ... ...<br />
⎜ ⎟<br />
⎜<br />
⎟⎜<br />
⎟ ⎜<br />
...<br />
⎟<br />
nod<br />
⎝−<br />
g~<br />
N<br />
− g~<br />
N<br />
... g~<br />
,1<br />
,2<br />
NN ⎠⎝δhN<br />
⎠ ⎝δq<br />
N ⎠<br />
© ABB Group<br />
June 28, 2010 | Slide 61
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