Data-driven Adaptive Benders Decomposition for the Stochastic Unit Commitment Problem

Abstract

This paper proposes a data-driven version of the Benders decomposition algorithm applied to the stochastic unit commitment (SUC) problem. The proposed methodology aims at finding a trade-off between the size of the Benders master problem and the number of iterations until convergence. Using clustering techniques, we exploit the information contained in the Lagrange multipliers of the Benders subproblems in order to aggregate the optimality cuts, without compromising the critical information that is passed to the master problem. In addition, we develop an outer parallelization scheme that finds the optimal solution of the SUC problem by solving a series of less computationally intensive SUC instances for certain partitions of the scenario set. Our computational results on the IEEE 3-Area RTS-96 power system, illustrate the improved performance of our data-driven Benders algorithm, in terms of solution time and problem size, compared both to the SUC extensive formulation and to the prevailing single- and multi-cut Benders formulations.