Optimal Control Formulations for the Unit Commitment Problem

Abstract

The unit commitment (UC) problem is a well-known combinatorial optimization problem arising in operations planning of power systems. It involves deciding both the scheduling of power units, when each unit should be turned on or off, and the economic dispatch problem, how much power each of the on units should produce, in order to meet power demand at minimum cost while satisfying a set of operational and technological constraints. This problem is typically formulated as nonlinear mixed-integer programming problem and has been solved in the literature by a huge variety of optimization methods, ranging from exact methods (such as dynamic programming and branch-and-bound) to heuristic methods (genetic algorithms, simulated annealing, and particle swarm). Here, we discuss how the UC problem can be formulated with an optimal control model, describe previous discrete-time optimal control models, and propose a continuous-time optimal control model. The continuous-time optimal control formulation proposed has the advantage of involving only real-valued decision variables (controls) and enables extra degrees of freedom as well as more accuracy, since it allows to consider sets of demand data that are not sampled hourly.