Network analysis, control valve placement and optimal control of flow velocity for self-cleaning water distribution systems

In this paper, we consider the proactive control of flow velocities to maximise the self-cleaning capacity of the drinking water distribution systems under normal operations both through a change of the network topology and through an optimal control of pressure reducing valve (PRV) settings. Inspired by line outage flow distribution in electrical networks, we show how a fast network graph analysis of link closures can be used to estimate the potential changes in flow velocities, which are then used to determine the most favourable pipes for closure. Where closing of pipes cannot be used because of other conflicting objectives, we consider the optimal control of PRVs to maximise self-cleaning at peak demand periods. We formulate a novel optimisation problem to maximise the network operations for increased self-cleaning capacity, while satisfying hydraulic and regulatory pressure constraints at demand nodes. A new smooth objective function approximation for cleaning capacity of the network is proposed along with a scalable sequential convex programming method to solve the resulting valve optimization problems. We use a published benchmark network as a case study to show the efficacy of these new approaches

Constraint preconditioned inexact Newton method for hydraulic simulation of large-scale water distribution networks

Many sequential mathematical optimization methods and simulation-based heuristics for optimal control and design of water distribution networks rely on a large number of hydraulic simulations. In this paper, we propose an efficient inexact subspace Newton method for hydraulic analysis of water distribution networks. By using sparse and well-conditioned fundamental null space bases, we solve the nonlinear system of hydraulic equations in a lower-dimensional kernel space of the network incidence matrix. In the inexact framework, the Newton steps are determined by solving the Newton equations only approximately using an iterative linear solver. Since large water network models are inherently badly scaled, a Jacobian regularization is employed to improve the condition number of these linear systems and guarantee positive definiteness. After presenting a convergence analysis of the regularised inexact Newton method, we use the conjugate gradient (CG) method to solve the sparse reduced Newton linear systems. Since CG is not effective without good preconditioners, we propose tailored constraint preconditioners that are computationally cheap because they are based only on invariant properties of the null space linear systems and do not change with flows and pressures. The preconditioners are shown to improve the distribution of eigenvalues of the linear systems and so enable a more efficient use of the CG solver. Since contiguous Newton iterates can have similar solutions, each CG call is warm-started with the solution for a previous Newton iterate to accelerate its convergence rate. Operational network models are used to show the efficacy of the proposed preconditioners and the warm-starting strategy in reducing computational effort