Modeling Reservoir Evaporation Losses by Generalized Networks

Using a generalized network formulation, the nonlinear evaporation loss function of a reservoir is directly incorporated in a water-supply-optimization model. The nonlinear function is first piecewise-linearized and the resulting line segments are represented by a series of arcs. An appropriate arc-flow multiplier is used to reflect the slope in each line segment. A convex penalty function is then used to preserve the order of arc-flow fulfillment. The proposed formulation can be applied to model other forms of losses in a water-supply system and it eliminates iterative solutions as required by a pure network formulation. The overall management model is solved by an embedded generalized network algorithm (EMNET), which is designed to solve a linear-programming problem with an embedded generalized network substructure. Together with our previous study EMNET is proven to be an efficient tool in solving general water-supply-optimization problems.