A Constraint Disaggregation Method for Structure-Preserving Aggregations in LP Problems: Application to Renewable Energy Grids with Hydrogen Storage

In recent years, the integration of renewable energy sources into electrical grids has become a critical area of research due to the increasing need for sustainable and resilient energy systems. To address the variability of wind and solar power output over time, electricity grids expansion plans need to account for multiple scenarios over large time horizons. This significantly increases the size of the resulting Linear Programming (LP) problem, making it computationally challenging for large scale grids. To tackle this, we propose an approach that aggregates time-steps to reduce the problem size, followed by an iterative refinement of the aggregation, in order to converge to the optimal solution. Using the previous iteration's solution as a warm start, we introduce and compare methods to select which time intervals to refine at each iteration. The first method selects time-steps based on the proportion of net power production within each interval. We provide a general theoretical justification for its use and sufficient conditions under which an optimal solution of an aggregated linear problem can extend to an optimal solution of the original problem. The second method employs a Rolling Horizon (RH) method to evaluate the feasibility of the aggregated solutions, and selects the time interval on which the validation fails. These selection methods are then compared against a random interval selection approach. Mathematics Subject Classification (2020) 90-10 · 90B15