Global Sensitivity Analysis-Based Dimension Reduction for Stochastic Unit Commitment

The uncertainty in the stochastic unit commitment (UC) problem for a real-world power grid is driven by a large number of stochastic input variables. This article develops a method for estimating the contribution of uncertainty in different input variables to the uncertainty in the quantities of interest (QoIs) corresponding to a unit commitment decision. The stochastic (input) variables are ranked based on their contribution to the uncertainty in the QoI by computing a global sensitivity index. Stochastic variables with small contributions are then selected to be treated as deterministic variables fixed at their mean values, which effectively reduces the dimension of the random input vector. A systematic methodology, which compares the risk and cost profiles obtained with and without dimension reduction, is developed to determine the acceptable degree of dimension reduction. It is shown that even though the dimension reduction may introduce some changes in the UC decision, it does not significantly change the operating cost or risk profile of the system. The dimension reduction methodology has the potential to reduce the computational burden of stochastic unit commitment problem for large power grids. The ranking of drivers of uncertainty in the system can also be used for optimal resource allocation for improved forecasting or for identifying optimal storage locations.