[Paper Review] Optimal Scheduling of Electricity and Water in Renewable-Colocated Desalination Plants

Ahmed S. Alahmed, Audun Botterud+2 more|arXiv (Cornell University)|Jan 5, 2026

Membrane Separation Technologies0 citations

TL;DR

The paper develops an analytical framework for optimally dispatching water and electricity in renewable-integrated desalination plants, modeling WDPs as hybrid generator-load resources with a threshold-based, closed-form dispatch policy.

ABSTRACT

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.

Motivation & Objective

• Motivate the need for flexible, bidirectional water-energy resources at the water-energy nexus.
• Develop an analytical framework to optimally dispatch WDPs as hybrid generator-load resources.
• Characterize the structural properties of the optimal dispatch and provide offline thresholds for scalable deployment.
• Quantify how tariffs and technology parameters affect WDP profit and operation.

Proposed method

• Model TDP and RODP as coupled desalination units producing water and electricity under capacity constraints.
• Formulate a profit-maximization dispatch problem with water revenue and bidirectional electricity payments.
• Prove concavity of the profit function to guarantee a globally optimal solution.
• Derive a four-threshold (for TDP) and two-threshold (for RODP) structure governing optimal dispatch.
• Provide closed-form expressions for optimal setpoints and thresholds as functions of tariffs and conversion factors.
• Analyze special tariff cases and conduct simulations to compare with benchmarks.

Figure 1: WDP as a hybrid generator-load resource. The water (power) output of the thermal desalination plant (TDP) and reverse osmosis desalination plant (RODP) is denoted by $w_{h},w_{r}\;(q_{h},q_{r})\in\mathbb{R}_{+}$ , respectively. The renewable generation and net consumption are denoted by $g

Experimental results

Research questions

• RQ1 How should a renewable-colocated desalination plant optimally dispatch its water and electricity outputs to maximize profit under bidirectional grid interactions?
• RQ2 What is the structure of the optimal dispatch (thresholds, modes) and how does it depend on tariffs, conversion factors, and renewable generation?
• RQ3 How do special tariff cases affect the optimal dispatch and profitability of WDPs?
• RQ4 What is the impact of on-site renewable generation levels on water and electricity exchange with utilities and overall profit?
• RQ5 How does the WDP behave as a flexible grid resource (import, net-zero, export) across different renewable scenarios?

Key findings

• The optimal WDP dispatch exhibits a four-threshold structure for TDP water and a two-threshold structure for RODP water, segmented by renewable generation levels.
• The WDP can operate in three grid-interaction modes—import, net-zero, and export—via threshold-based transitions that depend on tariffs and conversion factors rather than renewables alone.
• Water and power dispatch are monotone and piecewise-linear in renewable output, enabling closed-form setpoints.
• RDP (RODP) grid dispatch is independent of import/export prices, while TDP decisions depend on combined marginal values of water and electricity.
• The thresholds are computable offline and provide monotone profit with increasing renewable generation, with profits increasing in water price, export price, and conversion factors while decreasing in import price.
• Special tariff cases yield simplified two-threshold policies for RODP and TDP, illustrating boundary behaviors.
• Simulations show significant improvements in operation, profit, and water-electricity exchange against benchmark strategies.

Figure 2: Optimal WDP dispatch across electricity operating modes (IM: import, NZ: net-zero, EX: export).