An interval joint-probabilistic stochastic flexible programming method for planning municipal-scale energy-water nexus system under uncertainty

Abstract In this study, an interval joint-probabilistic stochastic flexible programming method is proposed by integrating interval joint-probabilistic stochastic programming and flexible programming into one framework. It can not only be effective for handling interval-fuzzy information associated with flexible constraints, but also be efficient for reflecting interactions among correlated random variables as well as the resulting joint risk. It is applied to the real-world energy-water nexus system management problem in Zhengzhou City, China. A series of management schemes are investigated through the proposed approaches, including (i) five satisfaction degrees linked to the flexible constraints of water resources availability and electricity demand-supply balance, (ii) five satisfaction degrees related to the flexible constraint of power output limit, and (iii) ten scenarios for different combinations of joint and individual constraint-violation levels between water resources availability and electricity demand. Results reveal that capacity expansion of renewable energy can increase with time, and the installed capacity of renewable energy at the end planning period can increase by 29.94%. Under consideration of energy and water resources availability, maximum power output limit, electricity demand-supply balance, pollutant and CO2 emissions control, and capacity expansion, decision makers in Zhengzhou can achieve a minimum system cost under the scenario of low water resources availability and high electricity demand (i.e. S10 ( p =0.2, p 1 =0.19, p 2 =0.01)). These results can effectively support the 13th Five-Year Plan of Henan Province for Energy Development, which is required to choose more renewable energies with low water consumption.