Enhancing reliability of integrated electricity-water systems with data centers via decentralized robust planning considering decision-dependent uncertainties

The rapid expansion of Internet Data Centers (IDCs) has significantly intensified the operational pressure on urban electricity and water infrastructures, necessitating the development of cross-system collaborative planning mechanisms to enhance overall system reliability. This paper proposes a tri-level robust planning framework for the coordinated optimization of IDCs and the integrated electricity-water system (IEWS) under multiple uncertainties. The upper-level model optimizes IDC resource deployment and IEWS infrastructure reinforcement investments. The middle-level model constructs decision-dependent uncertainty (DDU) and decision-independent uncertainty (DIU) sets to jointly capture the endogenous and exogenous coupling mechanisms among load fluctuations, power grid failure scenarios, and renewable energy outputs. The lower-level model addresses system operation scheduling under worst-case disturbances to ensure operational safety and cost-effectiveness. To enhance tractability and convergence efficiency, a hybrid solution approach is developed by integrating Parametric Column-and-Constraint Generation (PC&CG), Analytical Target Cascading (ATC), and Alternating Optimization Process (AOP), enabling synchronized decentralized solving across heterogeneous stakeholders. Case studies demonstrate that the proposed framework significantly improves system reliability under multiple disturbance scenarios, reducing electricity and water load shedding rates from 4.31% to 1.29% and from 6.33% to 2.15%, respectively, while enhancing system adaptability and robustness. This work provides a scalable and privacy-preserving theoretical foundation and methodological tool for robust multi-agent co-planning in integrated IDC-IEWS environments.