Utilizing Matrix Completion for Simulation and Optimization of Water Distribution Networks

Simulation of Water Distribution Networks (WDNs) constitutes a key element for the planning and management of water supply systems. This simulation involves estimating the flows and pressures by solving a linear set of mass conservation equations and a nonlinear set of energy conservation equations. The literature presents different formulations of heads-flows equations to derive the flows and heads in WDN. These formulations differ in terms of dimensionality, computational cost, and solution accuracy. Whereas this problem has been the subject of active research in the past, in the last decades a state of stagnation was reached and no new formulations were introduced. In this study, we propose a novel formulation that utilizes a matrix completion technique to construct a reduced-size nonlinear system of equations that guarantees both mass and energy conservation. Unlike former formulations that rely on the topology of the network, in the proposed method we employ a matrix completion technique in which arbitrary entries are added to the equation system to facilitate its solution. The advantages of the proposed method are demonstrated in simulation and optimization settings. In the former, the method demonstrates improved scalability and accuracy as compared with other widely known formulations. In the latter, the new formulation leads to smaller optimization problems, which are otherwise intractable when the classical formulation is used. Our results reopen an old debate on the best formulation for WDN simulation and optimization tasks and show that the matrix completion technique is a viable solution option for the problem.