  The deep penetration of wind and solar power is a critical component of the
future power grid. However, the intermittency and stochasticity of these
renewable resources bring significant challenges to the reliable and economic
operation of power systems. Motivated by these challenges, we present a
multistage adaptive robust optimization model for the unit commitment (UC)
problem, which models the sequential nature of the dispatch process and
utilizes a new type of dynamic uncertainty sets to capture the temporal and
spatial correlations of wind and solar power. The model also considers the
operation of energy storage devices. We propose a simplified and effective
affine policy for dispatch decisions, and develop an efficient algorithmic
framework using a combination of constraint generation and duality based
reformulation with various improvements. Extensive computational experiments
show that the proposed method can efficiently solve multistage robust UC
problems on the Polish 2736-bus system under high dimensional uncertainty of 60
wind farms and 30 solar farms. The computational results also suggest that the
proposed model leads to significant benefits in both costs and reliability over
robust models with traditional uncertainty sets as well as deterministic models
with reserve rules.
