A stabilised scenario decomposition algorithm applied to stochastic unit commitment problems

In recent years the expansion of energy supplies from volatile renewable sources has triggered an increased interest in stochastic optimisation models for hydro-thermal unit commitment. Several studies have modelled this as a two-stage or multi-stage stochastic mixed-integer optimisation problem. Solving such problems directly is computationally intractable for large instances, and alternative approaches are required. In this paper we use a Dantzig–Wolfe reformulation to decompose the stochastic problem by scenarios. We derive and implement a column generation method with dual stabilisation and novel primal and dual initialisation techniques. A fast, novel schedule combination heuristic is used to construct very good primal solutions, and numerical results show that knowing these from the start improves the convergence of the column generation method significantly. We test our method on a central scheduling model based on the British National Grid and illustrate that convergence to within 0.1% of optimality can be achieved quickly.