Coordinated optimal scheduling of island micro water–energy nexus considering multi-source uncertainty and extreme risks

This paper investigates coordinated day-ahead scheduling of an island micro water–energy nexus (MWEN) under multi-source uncertainties, where low-probability but high-impact composite extreme conditions may lead to severe tail risks in system operating costs. To explicitly address this issue, a two-stage stochastic scheduling framework is developed with an objective function formulated based on conditional value at risk (CVaR), enabling systematic control of tail-risk exposure beyond conventional expected-cost minimization. A hierarchical scenario processing pipeline that integrates extreme-scenario retention with k-medoids clustering is further proposed to preserve risk-relevant characteristics while maintaining computational tractability. The MWEN model leverages water storage and water-treatment/desalination flexibility as cross-domain buffering resources to enhance system resilience under adverse conditions. Comparative case studies demonstrate that deterministic scheduling can result in pronounced cost deterioration under uncertainty, with the worst-case daily operating cost reaching $3401.78. In contrast, the proposed strategy significantly suppresses tail risk: at a 95% confidence level, value-at-risk (VaR) is reduced from $2642.22 to $2593.81 and CVaR from $2735.10 to $2684.22. These results highlight the importance of explicitly modeling extreme risks in MWEN scheduling and provide practical decision support for resilient island microgrids with high renewable penetration.