Improved formulation for long-duration storage in capacity expansion models using representative periods

Abstract

With the increasing complexity and size of capacity expansion models, temporal aggregation has emerged as a common method to improve computational tractability. However, this approach inherently complicates the inclusion of long-duration storage (LDS) systems, whose operation involves the entire time horizon connecting all time steps. This work presents a detailed investigation of LDS modelling with temporal aggregation. We propose a novel compact formulation to reduce the number of constraints of the linear programming problem, thus enabling a reduction in runtime and memory use. Our formulation incorporates dedicated constraints to track the storage content and enforce limits on the state of charge throughout the entire time horizon, including non-representative periods. The developed method is compared with the two leading state-of-the-art formulations. We implement all three methods in the Dolphyn capacity expansion model and test them on a case study for the continental United States, considering different configurations in terms of spatial resolutions and representative periods. The performance is assessed with both the commercial solver Gurobi and the open-source solver HiGHS. Results show that our compact formulation consistently outperforms the state-of-the-art methods in terms of both runtime (30%–70% faster) and memory usage (1%–9% lower).

The authors' abstract, as published at the source. Journal of Energy Storage, 2026 · DOI ↗