On the Practical Use of Generalized Adaptive Partition Methods: Application to the Stochastic Unit Commitment Problem

Stochastic programming has been a crucial mathematical framework for many operational and planning problems in power systems. The increase of renewable generation sources in many countries has accelerated academia and practitioners’ interest in such a tool. Limitations on solving stochastic programs to optimality are well known. By far, the most common solution strategies have been focused on representing or approximating uncertainty by a finite and tractable set of scenarios. In general, no a priori optimality bound is guaranteed, or if so, it is impractical for use in real applications. We leverage recent advances in adaptive partition methods for dealing with a class of two-stage stochastic programming problems. In particular, we introduce a recently proposed generalized adaptive partition method (GAPM) that guarantees $\epsilon$-optimal solutions. We provide insights on the GAPM and propose two new algorithms. We run extensive numerical experiments for the stochastic unit commitment problem on systems of 24 and 118 buses. More than 30 indicators were benchmarked. The proposed algorithms showed better computational performance than the existing adaptive partition method in many of those indicators. Finally, conclusions and recommendations are drawn on the basis of numerical experiments.