Solving the Short‐Term Scheduling Problem of Hydrothermal Systems via Lagrangian Relaxation and Augmented Lagrangian

Abstract

This paper addresses the short‐term scheduling problem of hydrothermal power systems, which results in a large‐scale mixed‐integer nonlinear programming problem. The objective consists in minimizing the operation cost over a two‐day horizon with a one‐hour time resolution. To solve this difficult problem, a Lagrangian Relaxation (LR) based on variable splitting is designed where the resulting dual problem is solved by a Bundle method. Given that the LR usually fails to find a feasible solution, we use an inexact Augmented Lagrangian method to improve the quality of the solution supplied by the LR. We assess our approach by using a real‐life hydrothermal configuration extracted from the Brazilian power system, proving the conceptual and practical feasibility of the proposed algorithm. In summary, the main contributions of this paper are (i) a detailed and compatible modelling for this problem is presented; (ii) in order to solve efficiently the entire problem, a suitable decomposition strategy is presented. As a result of these contributions, the proposed model is able to find practical solutions with moderate computational burden, which is absolutely necessary in the modern power industry.