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

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Gauss-Jordan Simplification Linearization of model • Starting point for subsequent linearization is Λ ) T Q ( Λ h = q nod • After linearization we get dQ Λ Λ d∆h T nod nod ⋅ ( h − h( t0 )) = ( q − q ( t0 )) • • Using Q ij = g ij | ∆ ij h | 0.54 sign( ∆ ij h) © ABB Group June 28, 2010 | Slide 60 • we obtain dQ = d∆h diag −0.46 [ 0.54g ] J j | ∆h j | j = 1
Gauss-Jordan Simplification Setup of linearized equations system • Defining Matrix A as dQ A = Λ Λ d∆h • We obtain for each element A [ n, m] ∑ T ⎧− Anm for n = m ⎪ m≠n ⎪ − = ⎨ − 0.54gn, m | hn − hm | ⎪ ⎪ ⎩ 0 for n ≠ m and 0.46 = : −g~ ( n, m) nm for n ≠ m and ( n, m) connected by a not connected by a link link • and can therefore build the following equations system nod ⎛ g~ − g~ − g~ 11 1,2 ... 1, N ⎞⎛ δh1 ⎞ ⎛δq ⎞ 1 ⎜ ⎟⎜ ⎟ ⎜ ⎟ nod ⎜ − g~ g~ − g~ 2,1 22 ... 2, N ⎟⎜ δh2 ⎟ ⎜δq2 ⎟ ⎜ ⎟⎜ ⎟ = ... ... ... ... ... ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ... ⎟ nod ⎝− g~ N − g~ N ... g~ ,1 ,2 NN ⎠⎝δhN ⎠ ⎝δq N ⎠ © ABB Group June 28, 2010 | Slide 61
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Alexander Horch Angewandte Regelung
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Wasserversorgung - Globale Sicht Kl
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Wasserverwendung weltweit Schlüsse
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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
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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: Gauss-Jordan Simplification Determi
Page 63 and 64: 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/
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Angewandte Regelung und Optimierung in der ... - uni-stuttgart

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