A Nested Cross Decomposition Algorithm for Power System Capacity Expansion with Multiscale Uncertainties

Modern electric power systems have witnessed rapidly increasing penetration of renewable energy, storage, electrical vehicles, and various demand response resources. The electric infrastructure planning is thus facing more challenges as a result of the variability and uncertainties arising from the diverse new resources. This study aims to develop a multistage and multiscale stochastic mixed integer programming (MM-SMIP) model to capture both the coarse-temporal-scale uncertainties, such as investment cost and long-run demand stochasticity, and fine-temporal-scale uncertainties, such as hourly renewable energy output and electricity demand uncertainties, for the power system capacity expansion problem. To be applied to a real power system, the resulting model will lead to extremely large-scale mixed integer programming problems, which suffer not only the well-known curse of dimensionality but also computational difficulties with a vast number of integer variables at each stage. In addressing such challenges associated with the MM-SMIP model, we propose a nested cross decomposition algorithm that consists of two layers of decomposition-that is, the Dantzig-Wolfe decomposition and L-shaped decomposition. The algorithm exhibits promising computational performance under our numerical study and is especially amenable to parallel computing, which will also be demonstrated through the computational results.