Angewandte Regelung und Optimierung in der ... - uni-stuttgart

More documents

Recommendations

Info

© ABB Group June 28, 2010 | Slide 62 Gauss-Jordan Simplification Elimination of nodes • Eliminating node 1 from the equations system leads to a reduced equation system ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ − − − − − − nod N nod nod N NN N N N N q q q h h h g g g g g g g g g δ δ δ δ δ δ ... ... ~ ... ~ ~ ... ... ... ... ~ ... ~ ~ ~ ... ~ ~ 2 1 2 1 ,2 ,1 2, 22 2,1 1, 1,2 11 ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + + = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − nod N nod N nod nod N N N N N N N N q g g q q g g q h h g g g g g g g g g g g g g g g g 1 1 ,1 1 1 2,1 2 2 1, 11 ,1 1,2 11 ,1 ,2 1, 11 2,1 2, 1,2 11 2,1 22 ~ ~ ... ~ ~ ... ~ ~ ~ ~ ... ~ ~ ~ ~ ... ... ... ~ ~ ~ ~ ... ~ ~ ~ ~ δ δ δ δ δ δ
Gauss-Jordan Simplification Setup of linearized equations system • Once all nodes selected have been eliminated, the equation system can be reconverted to a nonlinear one using following assumptions • R n,m = 100 (Roughness) • D=L (D)iameter and (L)ength of pipe ⎛ ⎛ ⎜ ⎜ ⎜ g~ ⎝ ⎜ ⎜⎛ ⎜ ⎜ ⎜− g~ ⎝⎝ 22 N ,2 g~ 2,1 − g~ g~ 1,2 11 ... g~ N ,1 − g~ g~ 11 ⎞ ⎟ ⎠ 1,2 ⎞ ⎟ ⎠ ... ... ... ⎛ ⎜− g~ ⎝ ⎛ ⎜ g~ ⎝ 2, N 0.54g g~ −0.46 n, m | hn − hm | = N g~ − g~ ... g~ − g~ N ,1 11 2,1 11 g~ nm g~ 1, N 1, N ⎞⎞ ⎟ ⎟ ⎟⎛ δh ⎠ ⎜ ⎟ ⎜ ... ⎞ ⎟ ⎜ ⎟ ⎟ ⎝δh ⎠ ⎟ ⎠ 2 N ⎛ ⎜ δq ⎞ ⎟ ⎜ ⎟ = ⎜ ⎟ ⎜ ⎠ ⎜δq ⎝ nod 2 nod N + + g~ g~ ... g~ g~ 2,1 1 N ,1 1 δq δq nod 1 nod 1 ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ D n, m ⎛ g ⎜ ⎝ 3.58821⋅10 n, m = Ln, m = −4 ⎞ ⎟ ⎠ 1 2.09 © ABB Group June 28, 2010 | Slide 63
Page 1 and 2:
Alexander Horch Angewandte Regelung
Page 3 and 4:
Wasserversorgung - Globale Sicht Kl
Page 5 and 6:
Wasserverwendung weltweit Schlüsse
Page 7 and 8:
Randnotiz Beispiel - Verluste in eu
Page 9 and 10:
Wichtige Marktreiber Worauf sich Wa
Page 11 and 12: Wasser Aktueller Megatrend mit Folg
Page 13 and 14: Nachhaltige und effiziente Wasserve
Page 15 and 16: Integriertes Wassermanagement Ausga
Page 17 and 18: Randnotiz Zeitlicher Verlauf „Feh
Page 19 and 20: Integriertes Wassermanagement Konze
Page 21 and 22: © ABB | 21 Betrieb und Instandhalt
Page 23 and 24: Advanced Solutions in Water Network
Page 33 and 34: Decision Support System for Burst L
Page 35 and 36: Burst Localisation Risk-based appro
Page 37 and 38: Burst Localisation Pipe burst predi
Page 39 and 40: Burst Localisation Information Proc
Page 41 and 42: •41
Page 43 and 44: •43
Page 45 and 46: Burst Localisation Case Study 2 •
Page 47 and 48: Hydraulic model •47
Page 49 and 50: •49
Page 51 and 52: Network Simplification Why use simp
Page 53 and 54: Preprocessing Substitute valves tha
Page 55 and 56: Preprocessing Remove dead-end pipes
Page 57 and 58: Preprocessing Combine pipes in seri
Page 59 and 60: Gauss-Jordan Simplification Determi
Page 61: Gauss-Jordan Simplification Setup o
Page 65 and 66: Example of Water Distribution Netwo
Page 67 and 68: Simplified network Comparison • A
Page 69 and 70: Example: network with 12527 nodes
Page 71 and 72: Water Network Optimization Pumpen-
Page 73 and 74: Pump & Valve scheduling Optimizatio
Page 75 and 76: Pump & Valve scheduling Current ope
Page 77 and 78: Anwendung Wassernetz Basel Problemb
Page 79 and 80: Anwendung Wassernetz Basel Implemen
Page 81 and 82: Referenzen • http://www.zvei.org/
show all

Angewandte Regelung und Optimierung in der ... - uni-stuttgart

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?