Micro Water–Energy Nexus: Optimal Demand-Side Management and Quasi-Convex Hull Relaxation

In some countries and regions, water distribution and treatment consume a considerable amount of electric energy. This paper investigates the water network's potential ability to provide demand response services to the power grid for the management of renewable resources under the framework of a distribution-level water-energy nexus (micro WEN). In particular, the hidden controllable water loads, such as irrigation systems, were closely studied as virtual energy storage to improve the flexibility of electrical grids. An optimization model is developed for the demand-side management (DSM) of micro WEN, and the simulation results assert that grid flexibility indeed benefits from taking controllable water loads into account. Although the proposed optimal DSM model is a computationally intractable mixed-integer nonlinear programming (MINLP) problem, quasi-convex hull techniques were developed to relax the MINLP into a mixed-integer convex programming (MICP) problem. The numerical study shows that the quasi-convex hull relaxation is tight and that the resulting MICP problem is computationally efficient.