Joint chance constrained programming for hydro reservoir management

Abstract

In this paper, we deal with a cascaded reservoir optimization problem with uncertainty on inflows in a joint chance constrained programming setting. In particular, we will consider inflows with a persistency effect, following a causal time series model with Gaussian innovations. We present an iterative algorithm for solving similarly structured joint chance constrained programming problems that requires a Slater point and the computation of gradients. Several alternatives to the joint chance constraint problem are presented. In particular, we present an individual chance constraint problem and a robust model. We illustrate the interest of joint chance constrained programming by comparing results obtained on a realistic hydro valley with those obtained from the alternative models. Despite the fact that the alternative models often require less hypothesis on the law of the inflows, we show that they yield conservative and costly solutions. The simpler models, such as the individual chance constraint one, are shown to yield insufficient robustness and are therefore not useful. We therefore conclude that Joint Chance Constrained programming appears as an approach offering a good trade-off between cost and robustness and can be tractable for complex realistic models.