An Asynchronous Distributed Algorithm for Solving Stochastic Unit Commitment

We present an asynchronous algorithm for solving the stochastic unit commitment (SUC) problem using scenario decomposition. The algorithm is motivated by the scale of problem and significant differences in run times observed among scenario subproblems, which can result in inefficient use of distributed computing resources by synchronous parallel algorithms. Dual iterations are performed asynchronously using a block-coordinate subgradient descent method which allows performing block-coordinate updates using delayed information. We provide convergence guarantees for the asynchronous block-coordinate subgradient method based on previous results for incremental subgradient methods and stochastic subgradient methods. The algorithm recovers candidate primal solutions from the solutions of scenario subproblems using recombination heuristics. The asynchronous algorithm is implemented in a high performance computing cluster and we conduct numerical experiments for two-stage SUC instances of the Western Electricity Coordinating Council (WECC) system and of the Central Western European (CWE) system. The WECC system that we study consist of 130 thermal generators, 182 nodes and 319 lines with hourly resolution and up to 1000 scenarios, while the CWE system consist of 656 thermal generators, 679 nodes and 1073 lines, with quarterly resolution and up to 120 scenarios. When using 10 nodes of the cluster per instance, the algorithm provides solutions that are within 2% of optimality to all problems within 47 minutes for WECC and 3 hours, 54 minutes for CWE. Moreover, we find that an equivalent synchronous parallel subgradient algorithm would leave processors idle up to 84% of the time, an observation which underscores the need for designing asynchronous optimization schemes in order to fully exploit distributed computing on real world applications.