Optimal Scheduling of Electricity and Water in Renewable-Colocated Desalination Plants

We develop a mathematical framework for the optimal scheduling of flexible water desalination plants (WDPs) as hybrid generator-load resources. WDPs integrate thermal generation, membrane-based controllable loads, and renewable energy sources, offering unique operational flexibility for power system operations. They can simultaneously participate in two markets: selling desalinated water to a water utility, and bidirectionally transacting electricity with the grid based on their net electricity demand. We formulate the scheduling decision problem of a profit-maximizing WDP, capturing operational, technological, and market-based coupling between water and electricity flows. The threshold-based structure we derive provides computationally tractable coordination suitable for large-scale deployment, offering operational insights into how thermal generation and membrane-based loads complementarily provide continuous bidirectional flexibility. The thresholds are analytically characterized in closed form as explicit functions of technology and tariff parameters. We examine how small changes in the exogenous tariff and technology parameters affect the WDP's profit. Extensive simulations illustrate the optimal WDP's operation, profit, and water-electricity exchange, demonstrating significant improvements relative to benchmark algorithms.