Applying High Performance Computing to Multi-Area Stochastic Unit Commitment for Renewable Penetration

We present a parallel implementation of a Lagrangian relaxation algorithm for solving stochastic unit commitment subject to uncertainty in wind power supply and generator and transmission line failures. We present a scenario selection algorithm inspired by importance sampling in order to formulate the stochastic unit commitment problem and validate its performance by comparing it to a stochastic formulation with a very large number of scenarios, that we are able to solve through parallelization. We examine the impact of narrowing the duality gap on the performance of stochastic unit commitment and compare it to the impact of increasing the number of scenarios in the model. We examine the relation between duality gap in Lagrangian relaxation and the number of scenarios in the model and relate that to theoretical results provided in the literature. We finally report results regarding speedup and efficiency and discuss the scalability of our proposed algorithm.