Synergetic management of energy-water nexus system under uncertainty: An interval bi-level joint-probabilistic programming method

Synergic management of energy-water nexus (EWN) system is essential for coping with the dilemma of joint shortage of energy and water and supporting socio-economic sustainable development. The system is full of multiple uncertainties, making deterministic analysis methods infeasible. In this study, an interval bi-level joint-probabilistic programming (IBJP) approach is first developed through incorporating bi-level programming (BP) and interval joint-probabilistic programming (IJP) within a framework. IBJP has advantages in balancing the tradeoff between two-level decision makers under uncertainty, tackling uncertainties expressed as joint probabilities and interval values, and examining the risk of violating joint-probabilistic constraints. Then, the developed method is applied to planning China’s EWN system over a long-term planning horizon (2021–2050). Multiple scenarios related to different groups of constraint-violation levels for violating electricity demand and/or water availability constraints are examined. Results reveal that uncertainties associated with joint and individual probabilities have effects on the synergic management of EWN system. Results also disclose that limited water resource can promote electricity generation structure toward a low water-intensity, clean and sustainable pattern, in which the share of clean energy would increase to 66.25% by 2050 and the corresponding water withdrawal would save 41.20%.