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

TL;DR

The work develops an analytical framework for optimally scheduling water-desalination plants colocated with renewables, treating them as hybrid generator-load resources that bidirectionally interact with water and electricity markets. It derives a threshold-based dispatch policy with explicit, off-line computable thresholds Γ_IM, Γ_NZ1, Γ_NZ2, Γ_EX that govern water and power setpoints across four regions, including a net-zero regime that absorbs renewable fluctuations without grid switching. The contribution includes closed-form expressions for optimal desalination outputs, structural properties, and comparative statics showing how tariff and technology parameters shape profits and operation, supported by numerical results that demonstrate significant gains over benchmark schemes. This framework offers actionable insights for grid-integrated water-energy systems under high renewables, highlighting operational flexibility, grid-friendly transitions, and avenues for scalable deployment and planning. It also outlines future extensions, such as energy storage integration and joint long-horizon planning, to further enhance adaptability and economic performance.

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.

Figures (7)

• 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 $g \in \mathbb{R}_+$, and $z \in \mathbb{R}$.
• Figure 2: Optimal WDP water dispatch across electricity operating modes (IM: import, NZ: net-zero, EX: export).
• Figure 3: Depiction of the optimal WDP dispatch in Theorem \ref{['thm:optimal']}, i.e., when $f_r' \pi^w \in [\pi^-, \pi^+]$, and Proposition \ref{['prop:SpecialCases']}, i.e., when $f_r' \pi^w \notin [\pi^-, \pi^+]$. Top row: Optimal TDP and RODP water dispatch (when $w^{\sf{IM}}_h<\overline{w}_r$) versus renewable generation. Bottom row: WDP's water and power transactions with the water and electric utilities versus renewable generation.
• Figure 4: WDP hourly dispatch and profits under the optimal joint dispatching (left), max-RODP algorithm (center), and passive-TDP algorithm (right).
• Figure 5: WDP hourly dispatch and profits under the optimal policy, when $\pi^w=\$2/m^3$ (left) and $\pi^w=\$0.2/m^3$ (right).

Theorems & Definitions (14)

• Lemma 1: Concavity of $\Pi(\cdot)$
• proof
• Theorem 1: Optimal WDP dispatch
• proof
• Corollary 1: Thresholds relationship
• proof
• Proposition 1: Optimal grid exchange
• proof
• Proposition 2: Optimal dispatch under special tariff cases
• proof