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.

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. These formulations differ in terms of dimensionality, computational cost, and solution accuracy. The literature presents different formulations of heads-flows equations to derive the flows and heads in WDN. 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. Simulation of Water Distribution Networks (WDNs) constitutes a key element for the planning and management of water supply systems. In the latter, the new formulation leads to compact optimization problems that result in better performance in terms of the objective function, run time, and rate of successful optimization runs. In the former, the method demonstrates improved scalability and accuracy as compared with other widely known formulations. The advantages of the proposed method are demonstrated in simulation and optimization settings. The literature presents different formulations of heads-flows equations that differ in terms of dimensionality, computational cost, and solution accuracy. Simulation of water distribution networks (WDNs) constitutes a key element for the planning and management of water supply systems.

Age of water mains