On the use of change constraints in reservoir design and operation modeling

Abstract

This work examines (1) the set of probabilistic and deterministic constraints binding the objective function of a reservoir design and operation problem, (2) the conditions under which the solution of a reservoir design and operation problem becomes infeasible, and (3) the discrepancies between the exact chance constrained formulation of the reservoir design and operation problem and alternative models. The crux of the paper is the difference between chance‐constrained feasibility sets that restrict reservoir levels to be within zero and maximum capacity with probability one and those sets that impose a less stringent chance constraint on reservoir levels. We derive the probability that a reservoir solution computed with the less stringent feasibility set is physically feasible (i.e., reservoir levels are bounded by zero and reservoir capacity). Such probability is found to be a function of prespecified reliability levels, the length of the planning horizon, the joint distribution of streamflows and initial reservoir storage, reservoir capacity, and two chance‐constrained parameters. It is concluded that physically feasible solutions yielded by alternative models are valuable if they serve as guidelines that are updated (as they are implemented) in response to unforeseen, uncontrollable events.