Chance-Constrained Model of System of Reservoirs

Abstract

In this paper chance-constrained programming is used to model a system of linked multipurpose reservoirs. The objective of the model is to determine an optimal operating policy for a given time sequence of minimum and maximum reservoir levels. The unregulated inflows into the reservoirs are assumed to be stochastic with a known distribution for each time frame. The chance-constraints, based on material balance equations, are converted to an equivalent linear deterministic constraint set. The linked system model is a natural extension of the single reservoir model. The problem of stochastic demands as well as stochastic inflows is shown to be a straightforward generalization of the stochastic inflow problem. Since the resulting constraints for these models are linear and the decision variables are deterministic rather than random variables, linear, quadratic, and even general convex objective functions can be readily handled.