<p>This paper introduces the concept of structure-preserving aggregations to address a family of large-scale linear programming (LP) problems for which aggregation preserves the problem’s essential constraint-and-variable structure. We derive sufficient conditions under which a solution to an aggregated problem can be extended to an optimal solution of the original LP. Building on these results, we propose a heuristic that progressively refines an initial coarse aggregation: each aggregated problem is solved, and its solution is used as a warm start for the next refinement, iteratively obtaining tighter lower bounds. To illustrate the approach, we apply it to a capacity expansion problem for electricity grids with renewable generation and hydrogen storage, where scenario-based uncertainty and fine temporal resolution lead to extremely large LP instances. We also propose three strategies to guide the refinement: two heuristics based on a net-power-production index derived from our theoretical framework, and a Rolling Horizon (RH) validation method that identifies intervals where feasibility fails. Computational experiments show that these strategies improve upon random interval selection and highlight the potential of our approach as a scalable alternative to directly solving the monolithic LP.</p>