A dam management problem with energy production as an optimal switching problem

Author:

Chevalier Etienne12,Di Girolami Cristina3ORCID,Gaïgi M'hamed4,Giovannini Elisa5,Scotti Simone6

Affiliation:

1. Laboratoire de Modélisation Mathématique d'Evry (LaMME) Université d'Evry Val d'Essonne Evry France

2. UMR CNRS Université Paris Saclay Gif‐sur‐Yvette France

3. Dipartimento di Matematica Università Alma Mater Studiorum Bologna Bologna Italy

4. Ecole Nationale d'Ingénieurs de Tunis ENIT‐LAMSIN Université de Tunis El Manar Tunis Tunisia

5. Dipartimento di Scienze per l'Economia e l'Impresa Università degli Studi di Firenze Firenze Italy

6. Dipartimento di Economia e Management Università di Pisa Pisa Italy

Abstract

AbstractWe consider an optimal stochastic control problem for a dam. Electrical power production is operating under an uncertain setting for electricity market prices and water level which has to be kept under control. Indeed, the water level inside the basin cannot exceed a certain threshold for safety reasons, and at the same time cannot decrease below another threshold in order to keep power production active. We model this situation as a mixed control problem with regular and switching controls under constraints. We characterize the value function as solution of an HJB equation and provide some numerical approximating methods. We shall illustrate by numerical examples the main achievements of the present approach.

Funder

Università di Pisa

Publisher

Wiley

Subject

Management Science and Operations Research,General Business, Management and Accounting,Modeling and Simulation

Reference27 articles.

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