  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
due to 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.
