Aghezzaf, El-Houssaine

Verleye, Derek

English

Ghent University Academic Bibliography

A hybrid piecewise-linear/Newton's method withcorrected Jacobian matrix for multi-period waterproduction and distribution in large networksD. VerleyeGhent University, Departement of Industrial Managementderek.verleye@ugent.beE.-H. AghezzafGhent University, Departement of Industrial Managementelhoussaine.aghezzaf@ugent.beIncreasing prices for production of drinking water - in terms of energy as wellas resources - make optimization tools for its production and distribution in-valuable. Nowadays, many drinking water companies rely on simulation softwarepackages (EPANET, Infoworks) for the daily operation of their network. Thissoftware allows the user to make accurate and thus reliable simulations of thenetwork for a chosen conﬁguration. However, the user-deﬁned scenario's do notnecessarily lead to the lowest costs. More often than not the pumps are workingat a suboptimal point in the system curve and water towers are not being usedenergy-eﬃciently.The typical underlying optimisation model for the planning problem of waterproduction and distribution operations is an MINLP, that is very hard to solve inpractice. The nonlinearities are imposed by hydraulic pressure losses in pipes andpower output in pumps. Additionally, switching the pumps on/oﬀ and allowingreverse ﬂow at water towers introduce binary variables in the model. To ﬁnd asolution in acceptable computation time, authors typically relax some of thesehydraulic functions. This can however result in practically infeasible solutions.Heuristics work well in practice but do not guarantee a global optimal or evenclose to optimal solution.In [1] a piecewise linear approach to solve the resulting optimisation model inan acceptable computation time is presented. The computation time is short butthe convergence speed depends greatly on the desired accuracy. Here, we use thismethod to ﬁnd fast (slightly inaccurate) solutions that give us an estimate on theproduction totals and the storage in buﬀers. Starting from this (slightly infeasi-ble) result, a feasible and economically acceptable solution is then derived usingNewton's method. This method, in which the values of pressure and ﬂow are up-dated iteratively, was introduced by Todini and Pilati [2] and implemented in theEPANET framework by Rossini [3]. Recently, Simpson and Elhay presented thecorrected formulation for the Jacobian matrix, restoring quadratic convergenceof the method [4].1The model is tested on several diﬀerent conﬁgurations with diﬀerent levels ofaccuracy. It is shown that when the parameters are carefully tuned, results canbe found in less computation time and with a better objective value than thosefound by commercial solvers. Initialization through Lagrangian relaxation canspeed up the process as well.References[1] D. Verleye & E.-H. Aghezzaf. Optimising production and distribution op- erations in large water supply networks:A piecewise linear optimisation approach. International Journal of Production Research, 51(23-24):7170-7189,2013.[2] E. Todini & S. Pilati. A gradient algorithm for the analysis of pipe networks. pages 1-20, 1988[3] Lewis A. Rossman. EPANET 2 Users Manual. U.S. ENVIRONMENTAL PROTECTION AGENCY, Cincinnati,OH 45268, September 2000.[4] Angus Simpson & Sylvan Elhay. Jacobian matrix for solving water distri- bution system equations with thedarcy-weisbach head-loss model. Journal of Hydraulic Engineering, 137(6):696-700, 2010.

A hybrid piecewise-linear/Newton's method with corrected Jacobian matrix for multi-period water production and distribution in large networks

https://biblio.ugent.be/publication/4292442/file/6977863

A hybrid piecewise-linear/Newton's method with corrected Jacobian matrix for multi-period water production and distribution in large networks

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