Solving the hydro unit commitment problem via dual decomposition and sequential quadratic programming

This paper presents an algorithm that achieves the hydro unit commitment in hydrothermal systems. This problem is difficult to solve since several constraints with continuous and discrete variables exist, including hydraulic coupling, storage and released flow limits of the reservoirs, and unit forbidden operation zones. The forbidden zones cause a noncontinuous operation of the generating units, making the solution of the problem more difficult, due to the associated combinatorial nature. Moreover, there exists the presence of nonlinear functions that represent the tailrace level, the hydraulic losses, and the unit efficiency. To solve a problem that contains all of these characteristics is a challenging task. Within this scenario, an algorithm is presented that makes use of Lagrangian relaxation, in which some variables are artificially duplicated in order to separate the problem into simpler subproblems. The idea is to relax the spatial and temporal coupling present in the constraints associated with the forbidden zones. In order to solve the subproblems of nonlinear continuous nature that result from the relaxation, this paper presents a sequential quadratic programming algorithm. To update the Lagrange multipliers, an algorithm based on the Bundle Method is used. We assess our approach on a real-life hydroelectric configuration, proving the conceptual and practical feasibility of the proposed algorithm.