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.

Optimization Methods and Algorithms for Solving Of HydroThermal Scheduling Problems.

“…However, there is an important disadvantage: for nonconvex problems, the LR fails to find a feasible solution. On the other hand, with AL, it is possible to obtain a feasible solution or a near-feasible solution [89].…”

“…Chang [77] reports that FAPSO generates better solutions than other methods, mainly because it is implemented to dynamically adjust the inertia weight by using "IF-THEN" rules, this can improve the global and local search ability of the PSO and overcome the disadvantages of the PSO. Although almost all works which use dual decomposition in the Short-Term Scheduling (STS) problem are based on either Lagrangian Relaxation (LR) [42,[80][81][82][83][84][85] or Augmented Lagrangian (AL) [86][87][88], Rodrigues et al [89] proposed a two-phase approach similar to [90,91], but introduced contributions. In the first phase, LR was used to obtain (Infeasible) primal solution, and in the second phase the AL was used to obtain a solution whose quality can be assessed by the LR.…”

“…Nevertheless, using this strategy, the hydro-subproblem remains coupled in time and space [89]. An alternative approach consists in combining LR with Variable Splitting-LRVS method [92,44], where the decomposition is achieved by duplicating some variables.Rodrigues et al [89]used the LRVS to duplicate thermal and hydrovariables, as well as the turbined outflow and spillage variables, thusobtaining four subproblems: thermal, hydro, hydrothermal, and hydraulic. The first two subproblems take into account the unit commitment constraints (thermal and hydro).…”

Augmented Lagrangian Algorithm for Hydrothermal Scheduling

“…Baslis et al [8] proposed a MIP approach to the yearly scheduling problem of a mixed hydro thermal system. Rodrigues et al [9] solved the short-term scheduling problem of hydrothermal systems via Lagrangian Relaxation and augmented Lagrangian Methods. Borghett et al [10] proposed a MILP approach for shortterm hydro scheduling and unit commitment with headdependent reservoir.…”

Hydro unit commitment and loading problem for day-ahead operation planning problem

“…The method applied in this paper is similar to [19]. Firstly, we apply the Lagrangian Relaxation (LR) [20,21] to obtain a primal point, which solves a certain convexified form of the HUCL problem.…”