An integrated MILP framework for co-optimizing energy and water systems with up and downward reserve constraints: Application to an off-grid small island

High shares of variable renewable energy sources (vRES) pose growing challenges for power system planning. While these issues are expected to intensify in large-scale systems with increasing vRES deployment, they are already critical in isolated or weakly interconnected areas, where balancing resources are scarce and operational flexibility is limited. Simultaneously, water-intensive infrastructures such as desalinators impose a substantial and often inflexible electricity demand, further stressing system stability. These dual pressures call for a coordinated planning approach that captures energy-water interdependencies while explicitly accounting for reserve adequacy and operational constraints. This study presents an integrated MILP-based framework for co-optimizing energy and water systems. The model incorporates upward and downward reserve requirements and the detailed operational behavior of key technologies, including fuel-fired generators, battery energy storage, and desalination units. Applied to the off-grid island of Pantelleria, the framework quantifies the isolated effects of core features—such as reserve directionality, unit commitment, and flexible desalination scheduling—on system costs, sizing, and dispatch. Results show that explicitly modeling both upward and downward reserves leads to substantially different system configurations, increasing total system costs by up to 55 % compared to scenarios with only upward reserves. Introducing desalination flexibility via load shifting further decreases costs by 10 % while supporting greater vRES penetration. Neglecting these aspects leads to inefficient use of dispatchable assets and suboptimal planning outcomes. While demonstrated on Pantelleria, the proposed methodology applies broadly to systems where flexibility, sector coupling, and reserve provision are critical. The model is implemented in the open-source PyPSA framework, enabling transparent and extensible energy-water co-planning.