Optimal design of aggregated energy systems with (N-1) reliability: MILP models and decomposition algorithms

This work investigates the design optimization of aggregated energy systems (multi-energy systems, microgrids, energy districts, etc.) with (N-1)-reliability requirements. The problem is formulated as a two-stage stochastic Mixed Integer Linear Program which optimizes design (first stage variables) and operation variables (second stage variables) simultaneously considering a set of typical and extreme days. The analysis proposes and compares different approaches to include the (N-1) reliability requirement in the optimization problem. Moreover, the paper proposes two effective decomposition algorithms to solve the large-scale Mixed Integer Linear Program suitable for design problems with and without (N-1) reliability requirements. Depending on the instance, such decomposition algorithms allow reducing the computational time by one or more orders of magnitude (from days to a few hours, in the worst cases tested in this work). The proposed methodology is tested to design the aggregated energy system for a real case study considering both a grid-connected and off-grid installation. Results indicate that the actual reliability of the design solutions depends by the profiles of energy demand and renewable production considered in the failure scenarios included in the design problem. Including N-1 reliability requirements causes an increase in the total annual cost in the range 15–20%, due to the increase in capital costs.