Advanced Loop-flow Method for Fast Hydraulic Simulations Z. Vasilic - PowerPoint PPT Presentation

Advanced Loop-flow Method for Fast Hydraulic Simulations Z. Vasilic 1 / M. Stanic 2 / Z. Kapelan 3 / D. Prodanovic 2 1 University of Belgrade, zvasilic@grf.bg.ac.rs 2 University of Belgrade 3 University of Exeter

OUTLINE  Introduction  Methods for hydraulic analysis  Overview of Loop-flow method  Advanced Loop-flow method (TRIBAL-∆Q)  Minimal basis loops identification alg.  Efficient implementation of loop-flow method  Examples, results & discussion  Conclusions

INTRODUCTION  Water Distribution Network (WDN)  Purpose of Hydraulic simulation ?  Essential prerequisite for any type of general WDN analysis is Mathematical model of the WDN  Modification of the existing WDN  Expansion of the existing WDN Multiple  Optimisation process is usually involved Adopted scenarios/alternatives solution  Need for the hydraulic simulation method Optimization Result efficient in terms of computational speed

METHODS for HYDRAULIC ANALYSIS  Systematization of the methods Ref. Todini & Rossman 2013  Depending of the unknown variable:  Q method GGA (EPANET) Node based equations  H method  ∆Q method (loop-flow) Loop based equations

METHODS for HYDRAULIC ANALYSIS  Node vs. Loop based methods Node based Easy to „code“ (system of non-linear eqs.) Don’t require loop identification Loop based Less number of BWSN2 Network – Large unknowns (eqs) Network (Ostfeld et.al 2008): Solving branched 14 831 Links network is easier (No 12 523 Nodes iterative procedure) 2 308 Loops

Loop-flow ( ∆ Q) method  Initial flows satisfy nodal continuity equations  Loop head-loss equations are formed      n 1 ( ) o ( ) o        f Q , Q R Q Q Q Q ... 2 1 2 45 2 2 45 45    n 1 ( ) o ( ) o       R Q Q Q Q ... 52 52 2 52 2    n 1 ( ) o ( ) o          R Q Q Q Q Q Q ... 12 12 1 2 12 1 2    n 1 ( ) o ( ) o       R Q Q Q Q 0 41 2 2 41 41  Non-linear system for the network         n 1   T T T     f ΔQ M R  Q M ΔQ  Q M ΔQ A H   o o o o  

Loop-flow ( ∆ Q) method  Non-linear system for the         n 1   T T T     f ΔQ M R  Q M ΔQ  Q M ΔQ A H   o o o o   network  NR Linearization of the -1 ΔQ = ΔQ - J f  i 1 i i i system yields iterative solution form 4 loops X 4 links  Structure of identified loops has great influence on solver’s efficiency 2 loops X 4 links 2 loops X 6 links

TRIBAL – ∆ Q method  Combines: 1. New algortihm for optimal loop identification (TRIBAL) 2. Efficient implementation of loop-flow based hyd.solver ( ∆ Q)  TRI angulation BA sed L oops (TRIBAL) identification algorithm is based on constrained Delaunay triangulation and Graph Theory

TRIBAL – ∆ Q method  TRIBAL algorithm

TRIBAL – ∆ Q method  TRIBAL – D Q method implementation

TRIBAL – ∆ Q method  TRIBAL – D Q method implementation (1 st Block – Pre-processing)

TRIBAL – ∆ Q method  TRIBAL – D Q method implementation (2 nd Block – Hyd. Simulation)  ENRunLoops uses:  linsolve routine to solve non-linear system  newcoeff routine to calculate links coeffs Data from the 1 st Block  1    f 1 ij        n 1 Q   nR Q ij ij ij   f  f f  n 1    ij  0   ij   nR Q Q m J ( , ) m k ij ij k    Q Q Q  ij m k k k

TRIBAL – ∆ Q method  TRIBAL – D Q method implementation (2 nd Block – Hyd. Simulation)  newcoeff updates only links in loops

BENCHMARKING RESULTS  2 Case study networks PES BIN Network N n N l N s n RL n PL n L LF BIN 447 454 4 8 3 11 0.36 PES 71 98 3 28 2 30 0.96

BENCHMARKING RESULTS  Comparison is made between 3 solvers: 1. GGA solver – as implemented in EPANET 2. TRIBAL – D Q solver 3. ASL – D Q solver  Comparison criteria: t GGA ( ) 1. Computational efficiency (total time & speedup )  SPU F  t ( Q ) 2. Convergence (num of iter)  Reported calculation times are execution times for 2 nd Block  Times are averaged over 10 series of 10,000 cumulative runs  Target convergence for the discharge is eps=10 -3

BENCHMARKING RESULTS  Convergence  Computational efficiency BIN network BIN network 3.859 Number of Iterations 6 6 6 Simulation time (s) 1.111 1.087 GGA TRIBAL-DQ D Q ASL-DQ D Q GGA TRIBAL-DQ D Q ASL-DQ D Q

BENCHMARKING RESULTS  Convergence  Computational efficiency BIN network PES network BIN network PES network 7 7 3.859 Number of Iterations 6 6 6 Simulation time (s) 5 1.111 1.087 0.712 0.675 0.563 D Q GGA TRIBAL-DQ D Q ASL-DQ D Q GGA TRIBAL-DQ D Q ASL-DQ

BENCHMARKING RESULTS  Efficiency of loop-based solvers compared to GGA BIN network PES network BIN network PES network NNZ elements in Cholesky factor 1035 3.551 3.475 2.14 % SPU F (-) 1.265 1.055 236 16.61 % 141 90 29 27 D Q D Q D Q D Q GGA TRIBAL-DQ ASL-DQ TRIBAL-DQ ASL-DQ

CONCLUSIONS  New loop-flow based TRIBAL- D Q method is presented  Computationally faster than GGA for steady state simulations  Achieved speedups are result of: 1. Highly sparse solution matrix obtained with TRIBAL algorithm 2. Efficient implementation of D Q hydraulic solver  Well suited for substantially branched networks  Convenient for use in optimization tasks and networks with unchanged topology  Accounting flow control devices and pressure-driven analysis

Advanced Loop-flow Method for Fast Hydraulic Simulations Z. Vasilic 1 / M. Stanic 2 / Z. Kapelan 3 / D. Prodanovic 2 1 University of Belgrade, zvasilic@grf.bg.ac.rs 2 University of Belgrade 3 University of Exeter