Optimal management of pumped hydroelectric production with state constrained optimal control

TL;DR

This paper introduces a new method for optimally managing pumped hydroelectric storage by transforming the state-constrained control problem into an unconstrained one using a level-set approach, enabling classical dynamic programming solutions.

Contribution

The paper develops a novel technique that applies a level-set approach to solve state-constrained stochastic optimal control problems in hydroelectric management.

Findings

Effective transformation of constrained problem into unconstrained form

Application of classical dynamic programming to the transformed problem

Potential for improved management strategies in hydroelectric systems

Abstract

We present a novel technique to solve the problem of managing optimally a pumped hydroelectric storage system. This technique relies on representing the system as a stochastic optimal control problem with state constraints, these latter corresponding to the finite volume of the reservoirs. Following the recent level-set approach presented in O. Bokanowski, A. Picarelli, H. Zidani, "State-constrained stochastic optimal control problems via reachability approach", SIAM J. Control and Optim. 54 (5) (2016), we transform the original constrained problem in an auxiliary unconstrained one in augmented state and control spaces, obtained by introducing an exact penalization of the original state constraints. The latter problem is fully treatable by classical dynamic programming arguments.