Two-stage adjustable robust optimisation for unit commitment under uncertainty

A new adjustable robust optimisation formulation to solve unit commitment (UC) problems under uncertainty is proposed. Unlike the stochastic programming or chance-constrained approaches, the robust formulation does not require information on the exact probability distributions. This method protects power systems against all possible scenarios within a deterministic uncertainty set. The degree of conservatism can be conveniently controlled by the parameters of the uncertainty set. The formulation is divided into two stages, where here-and-now UC decisions are determined in the first stage, and the second stage makes wait-and-see dispatch decisions. The second-stage problems are reformulated into the equivalent form, so that a practical cutting-plane algorithm can be used to solve the proposed two-stage problems in an iterative manner. Numerical studies show that the robust formulation offers more consistent performance than the stochastic method when the underlying distribution of demand or generating unit reliability varies.