Optimal Long-term Operation of Reservoir-river Systems under Hydrologic Uncertainties: Application of Interval Programming

Long-term basin-wide reservoir-river operation optimization problems are usually complex and nonlinear especially when the water quality issues and hydrologic uncertainties are incorporated. It is due to non-convex functions in water quality modeling and a large number of computational iterations required by most of stochastic programming methods. The computational burden of uncertainty modeling can be reduced by a special combination of uncertainty modeling and interval programming, though the problem solution is still a challenge due to model nonlinearity. In this paper, an integrated water quantity-quality model is developed for optimal water allocation at river-basin scale. It considers water supply and quality targets as well as hydrologic, water quality and water demand uncertainties within the nonlinear interval programming (NIP) framework to minimize the slacks in water supply and quality targets during a long-term planning horizon. A fast iterative linear programming (ILP) method is developed to convert the NIP into a linear interval programming (LIP). The ILP resolves two challenges in NIP, first converting the large non-linear programming (NLP) into a linear programming (LP) with minimum approximation and second reducing the iterations needed in interval programming for NLP into just two iterations for the upper and lower limits of decision variables. This modeling approach is applied to the Zayandehrood river basin in Iran that has serious water supply and pollution problems. The results show that in this river basin at dry conditions when available surface water resources are below 85 % of normal hydrologic state and water demands are 115 % of current water demands, the total dissolved solids (TDS) concentration can be reduced by 50 % at the inlet of the Gavkhuni wetland located downstream of the river basin.