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

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. A novel compact formulation is proposed to reduce the number of constraints while effectively tracking the storage content and enforcing limits on the state of charge throughout the entire time horizon. The developed method is compared with two leading state-of-the-art formulations. All three methods are implemented in the Dolphyn capacity expansion model and tested 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 the developed compact formulation consistently outperforms the other methods in terms of both runtime (30%-70% faster than other methods) and memory usage (1%-9% lower than other methods).