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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© ABB Group<br />
June 28, 2010 | Slide 62<br />
Gauss-Jordan Simplification<br />
Elim<strong>in</strong>ation of nodes<br />
• Elim<strong>in</strong>at<strong>in</strong>g node 1 from the equations system leads to a reduced<br />
equation system<br />
⎟<br />
⎟<br />
⎟<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
⎜<br />
⎜<br />
⎜<br />
⎝<br />
⎛<br />
=<br />
⎟<br />
⎟<br />
⎟<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
⎜<br />
⎜<br />
⎜<br />
⎝<br />
⎛<br />
⎟<br />
⎟<br />
⎟<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
⎜<br />
⎜<br />
⎜<br />
⎝<br />
⎛<br />
−<br />
−<br />
−<br />
−<br />
−<br />
−<br />
nod<br />
N<br />
nod<br />
nod<br />
N<br />
NN<br />
N<br />
N<br />
N<br />
N<br />
q<br />
q<br />
q<br />
h<br />
h<br />
h<br />
g<br />
g<br />
g<br />
g<br />
g<br />
g<br />
g<br />
g<br />
g<br />
δ<br />
δ<br />
δ<br />
δ<br />
δ<br />
δ<br />
...<br />
...<br />
~<br />
...<br />
~<br />
~<br />
...<br />
...<br />
...<br />
...<br />
~<br />
...<br />
~<br />
~<br />
~<br />
...<br />
~<br />
~<br />
2<br />
1<br />
2<br />
1<br />
,2<br />
,1<br />
2,<br />
22<br />
2,1<br />
1,<br />
1,2<br />
11<br />
⎟<br />
⎟<br />
⎟<br />
⎟<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
⎜<br />
⎜<br />
⎜<br />
⎜<br />
⎝<br />
⎛<br />
+<br />
+<br />
=<br />
⎟<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
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⎝<br />
⎛<br />
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⎠<br />
⎞<br />
⎜<br />
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⎜<br />
⎝<br />
⎛<br />
⎟<br />
⎟<br />
⎠<br />
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⎜<br />
⎜<br />
⎝<br />
⎛<br />
−<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
⎝<br />
⎛<br />
−<br />
−<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
⎝<br />
⎛<br />
−<br />
−<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
⎝<br />
⎛<br />
−<br />
nod<br />
N<br />
nod<br />
N<br />
nod<br />
nod<br />
N<br />
N<br />
N<br />
N<br />
N<br />
N<br />
N<br />
N<br />
q<br />
g<br />
g<br />
q<br />
q<br />
g<br />
g<br />
q<br />
h<br />
h<br />
g<br />
g<br />
g<br />
g<br />
g<br />
g<br />
g<br />
g<br />
g<br />
g<br />
g<br />
g<br />
g<br />
g<br />
g<br />
g<br />
1<br />
1<br />
,1<br />
1<br />
1<br />
2,1<br />
2<br />
2<br />
1,<br />
11<br />
,1<br />
1,2<br />
11<br />
,1<br />
,2<br />
1,<br />
11<br />
2,1<br />
2,<br />
1,2<br />
11<br />
2,1<br />
22<br />
~<br />
~<br />
...<br />
~<br />
~<br />
...<br />
~<br />
~<br />
~<br />
~<br />
...<br />
~<br />
~<br />
~<br />
~<br />
...<br />
...<br />
...<br />
~<br />
~<br />
~<br />
~<br />
...<br />
~<br />
~<br />
~<br />
~<br />
δ<br />
δ<br />
δ<br />
δ<br />
δ<br />
δ
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