Content-Based Active-Set Method for the Pressure-Dependent Model of Water Distribution Systems

Abstract

A new content based, box constrained, active set projected Newton method is presented which solves for the heads, the pipe flows and the nodal outflows of a water distribution system in which nodal outflows are pressure dependent. The new method is attractive because, by comparison with the weighted least squares energy and mass residuals (EMR) damped Newton method previously published by the authors, (i) it typically takes fewer iterations, (ii) it does not require damping, (iii) it takes less wall-clock time, (iv) it does not require the addition of any virtual elements and (v) it is algorithmically easier to deal with. Various pressure outflow relationships (PORs ), which model nodal outflows, are considered and two new PORs are presented. The new method is shown, by application to eight previously published case study networks with up to about 20,000 pipes and 18,000 nodes, to be up to 5 times faster than the EMR method and to take between 34% and 70% fewer iterations than the EMR method.

A Content-Based Active-Set Method for Pressure-Dependent Models of Water Distribution Systems with Flow Controls

“…A regularization of the Schur complement may be necessary in some cases. The new method is applicable to all the PORs for which the ASM of Deuerlein et al (2019) is applicable provided the special methods introduced there to account for irregularities in the inverse POR are invoked.…”

“…The derivative assignment technique described in Deuerlein et al (2019), which is part of the implementation code for these tests was automatically invoked for the unregularized Wagner POR to overcome the di culties created by the fact that the derivative of that POR is undefined when h = h m = 0. Where the (unreasonable) demand magnification factor of 40 was used to engineer a more di cult problem, a larger Schur complement regularization parameter was, in 2 cases, necessary to ensure convergence.…”

“…Hydraulic simulation solvers are used by water engineers in the design and management of large, complex, water distribution system (WDS) networks. Newton-type methods are frequently used to solve the non-linear model equations for the steady-state demand dependent 1 model (DDM) link flows and nodal heads (Todini & Rossman 2013) and very good methods now exist for pressure dependent model (PDM) WDSs in which there are no control devices (Deuerlein et al 2019). However, real WDSs normally utilize control devices such as throttle control valves (TCVs), check valves (CHVs), flow control valves (FCVs), pressure sustaining valves (PSVs), pressure reducing valves (PRVs) and pumps but early methods developed for models which include some or all of these elements had considerable shortcomings.…”

“…The authors did not apply this method to PDM problems although the method can be extended to these models. In a later development, Deuerlein et al (2019) presented a content-based active set method (ASM) for PDM problems without link flow constraints which is fast and reliable for a wide range of pressure outflow relations (PORs ). The ASM solves an optimization problem with equality and inequality constraints.…”

“…In this paper, the content function used in Deuerlein et al (2019) forms the basis of a new ASM for PDM WDSs with FCVs and pumps. It was shown there that if a solution exists the flows are unique because of the strict convexity of the system content function.…”