Double interior-point regularization for large-scale capacity expansion

Abstract

Capacity expansion is a key tool for planning future energy systems. However, weather-dependent generation and long-duration storage result in problem sizes that exceed the computational limits of conventional interior-point solvers, making it impossible to plan renewable systems that are cost-efficient and reliable across a wide range of weather conditions. To tackle such large problems, this paper introduces the double interior-point regularization (DIP-set) for Benders Decomposition, combining the advantages of traversing the interior of the solution space while remaining close to a reference solution. We benchmark the method on a power-sector problem and an energy-system problem, varying problem size and the level of foresight during operations. Results demonstrate that DIP-set outperforms competing regularizations in all test cases. The speed-up increases with size, reaching 30-50% for the largest problems, which are the most critical for planning renewable systems and are too large for state-of-the-art methods. The key benefit of DIP-set is its ability to mitigate the sharp decrease in convergence as BD approaches the optimal solution.