Integrated PSO-MILP water–energy planning and operation under flexibility constraints and water scarcity: Application to an off-grid Mediterranean island

Rising water demand and global energy transition represent two of the most pressing systemic challenges. Where freshwater is scarce, supply increasingly depends on electricity-intensive desalination, while power systems themselves are undergoing rapid transformation driven by the growing penetration of variable renewable energy sources. Both dynamics impose a major need for flexibility: desalination adds large, inflexible loads, and variable renewables amplify operational uncertainty. Although often treated separately, these issues are deeply interconnected—both at the planning and operational levels. This work introduces a hybrid PSO-MILP framework that jointly optimizes long-term investment and short-term operation in coupled power and water systems. The model explicitly accounts for desalination flexibility, hydrogen production and storage, unit commitment, and downward reserve requirements. By linking water demand and availability with power dispatch and reserve provision, desalination is modeled as a demand-side management resource, effectively substituting for conventional storage and enabling higher renewable penetration. The framework is demonstrated on Pantelleria, a non-interconnected Mediterranean island. Results show that enabling reserve provision from clean technologies such as batteries and desalination plants reduces total system costs by nearly 47% and raises the renewable share from 41% to 87%. Flexible desalination scheduling further cuts costs by up to 30%. Even when freshwater demand doubles, renewable penetration falls only 6%, with modest increases in offshore wind capacity. These findings confirm the strategic relevance of integrated planning in water-constrained energy systems.