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

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Gauss-Jordan Simplification Full nonlinear model Use point in time with max. number of pipes with flow > 0 to linearize network Linearize model Full linear model Use Gauss-Jordan algorithm to reduce number of nodes and pipes Simplify model Simplified linear model Convert back to nonlinear model © ABB Group June 28, 2010 | Slide 58 Calculate new nonlinear pipe parameters using incidence matrix (C=100, D=L) Simplified nonlinear model
Gauss-Jordan Simplification Determine nonlinear model reservoir demand demand • Setup incidence matrix to describe model of water network tank demand demand ⎡ 1 ⎢ ⎢ −1 ⎢ 0 Λ = ⎢ ⎢ 0 ⎢ 0 ⎢ ⎣ 0 | 0 1 −1 0 0 0 0 0 1 −1 0 0 h | 0.54 0 0 1 0 −1 0 0 0 0 1 −1 0 sign( ∆ 0 ⎤ 0 ⎥ ⎥ 0 ⎥ ⎥ 1 ⎥ 0 ⎥ ⎥ −1 ⎦ The Hazen-Williams equation describes the flow-head relationship in a pipe Q ij = g ij ∆ ij ij h) Λq = q nod Mass balance equation ∆h T = Λ h Headloss equation © ABB Group June 28, 2010 | Slide 59
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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: Preprocessing Combine pipes in seri
Page 61 and 62: Gauss-Jordan Simplification Setup o
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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