Optimal unit commitment in simulations of hydrothermal power systems: an augmented Lagrangian approach

Abstract This paper describes a new approach to Unit Commitment under supply-demand, load/frequency control margin and spinning reserve constraints in simulations of hydrothermal power systems. This problem belongs to the class of large-scale mixed real-integer mathematical programming problems, because some integer start-up and shut-down decision variables have to be taken into account. The suggested algorithm is based on both the duplication of variables, which may be used in both linear and nonlinear cases, and the use of an augmented Lagrangian approach. Despite the fact that Unit Commitment problems are both nonconvex and nondifferentiable, numerical tests show some good convergence and stability properties. The main advantages of this approach are: decomposition of a large-scale problem, elimination of the combinatorial explosion due to the integer decision variables, possible use of this algorithm for solving other nonlinear mixed real-integer programming problems, improved numerical performances versus ordinary Lagrangian approaches.