Sectoral and spatial decomposition methods for multi-sector capacity expansion models

Multi-sector capacity expansion models play a crucial role in energy planning by providing decision support for policymaking in technology development. To ensure reliable support, these models require high technological, spatial, and temporal resolution, leading to large-scale linear programming problems that are often computationally intractable. To address this challenge, conventional approaches rely on simplifications that trade accuracy for computational efficiency. Benders decomposition has been widely explored to improve computational efficiency in electricity capacity expansion models. Specifically, state-of-the-art methods have primarily focused on improving performance through temporal decomposition. However, multi-sector models introduce additional complexity, requiring new decomposition strategies. In this work, we propose a budget-based formulation to extend decomposition to the sectoral and spatial domains. We test the developed sectoral and spatial Benders decomposition algorithms on case studies of the continental United States, considering different configurations in terms of spatial and temporal resolution. Results show that our algorithms achieve substantial performance improvement compared to existing decomposition algorithms, with runtime reductions of 15% to 70%. The proposed methods leverage the generic structure of multi-sector capacity expansion models, and can thus be applied to most existing energy planning models, ensuring computational tractability without sacrificing resolution.