  We consider electricity capacity expansion models, which optimize investment
and retirement decisions by minimizing both investment and operation costs. In
order to provide credible support for planning and policy decisions, these
models need to include detailed operations and time-coupling constraints, and
allow modeling of discrete planning decisions. Such requirements result in
large-scale mixed integer optimization problems that are intractable with
off-the-shelf solvers. Hence, practical solution approaches often rely on
carefully designed abstraction techniques to find the best compromise between
reduced temporal and spatial resolutions and model accuracy. Benders
decomposition methods offer scalable approaches to leverage distributed
computing resources and enable models with both high resolution and
computational performance. Unfortunately, such algorithms are known to suffer
from instabilities, resulting in oscillations between extreme planning
decisions that slows convergence. In this study, we implement and evaluate
several level-set regularization schemes to avoid the selection of extreme
planning decisions. Using a large capacity expansion model of the Continental
United States with over 70 million variables as a case study, we find that a
regularization scheme that selects planning decisions in the interior of the
feasible set shows superior performance compared to previously published
methods, enabling high-resolution, mixed-integer planning problems with
unprecedented computational performance.
