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Communication Dans Un Congrès Année : 2019

Extended flow control in large pressure dependent demand models

Contrôle étendu des flux avec modèle de grande taille d'un réseau dépendant de la pression

Jochen Deuerlein
  • Fonction : Auteur
Sylvan Elhay

Résumé

Flow control is an important tool for providing an adequate volume of water to all the consumers, especially in the case when natural resources are limited. In real systems different kinds of flow control devices can be distinguished. One of the simplest is the tap control, where the outflow can be directly adjusted by the user. More sophisticated devices are normally used by water supply companies in order to control the flow within the pipe system. Here, the feedback loop is between a flow measuring sensor and the state of the control valve. Using such flow control devices, it is possible to limit the flow through the pipe to a justifiable threshold. Flow control is an important measure providing at least a limited water supply to the entire population, especially in regions that suffer from water scarcity where the demand is higher than the available resources. Thus, flow control could, in combination with proper rehabilitation of leaking pipes, replace the current wide-spread occurrence of intermittent water supply, which poses a high risk for human health (contaminant intrusion due to regular emptying of pipes) as well as the physical state of the system (transients, water hammer). Hydraulic simulation models are invaluable tools for proper planning of distribution network design. The difficulties that result from the presence of control devices in hydraulic simulation models are well reported in the literature. One prominent problem arises from the fact that mathematically flow control devices add inequality constraints to the hydraulic system equations. For example, the hydraulic steady-state can be formulated as the minimum of the convex Content function. Considering flow control devices, the unconstrained nonlinear optimization problem is replaced by a constrained nonlinear optimization problem where the flow control is represented by box constraints for the link flow. As has been previously shown [1] in demand driven analysis, the existence of a feasible flow distribution can be guaranteed if the links with flow control are part of the cotree. If this condition does not hold the non-emptiness of the feasible set can be proved by solving an LP-problem. In the more realistic case of pressure dependent modelling [2, 3], the constrained problem always has a solution if 1.) the consumer behaviour is modelled by pressure dependent demands and 2.) the general box constraints for links with flow control include the point 0. In the first part of this paper, the methods that are used to check the existence of a feasible flow distribution are discussed with respect to their applicability for large networks. Even in the case where the existence of a solution has been proved, the iterative active set method for calculation of the hydraulic steady-state may fail to converge. This is often caused by the linear dependency of the active link flow constraints of and nodal outflow constraints. In the second part of the paper a method for avoiding such linear dependence is presented and discussed with respect to its applicability to large networks. If the pressure deficiency is great, possibly due by large failures such as massive pipe bursts or failure of pumping stations, entire subregions of the network may be without supply. In such cases, there often exists, mathematically speaking, degenerate solutions where the Lagrangian multipliers of the active constraints and the constraints themselves are zero. This paper presents examples for large networks with extensive flow controls as well as proposals on how to deal with such cases numerically.
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Dates et versions

hal-02610104 , version 1 (16-05-2020)

Identifiants

Citer

Jochen Deuerlein, Olivier Piller, Sylvan Elhay, Angus Simpson. Extended flow control in large pressure dependent demand models. 17th International Computing & Control for the Water Industry Conference, Sep 2019, Exeter, United Kingdom. pp.2. ⟨hal-02610104⟩
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