Design optimization of multi-energy systems using mixed-integer linear programming: Which model complexity and level of detail is sufficient?

Designing sustainable, cross-sectoral energy supply systems is a challenging task. A widespread and proven planning approach is mathematical optimization and in particular mixed-integer linear programming (MILP). While numerous MILP models have been presented in literature, there is no convention which level of detail is necessary to obtain reliable energy system designs. In this paper, a systematic performance comparison of 24 MILP models for designing multi-energy systems is conducted. The models include different combinations of five widely used model features: Piece-wise linear investment curves, multiple component resolution, minimum partload limitations, part-load efficiencies, and start-up costs. The operational performances of the optimal system designs are compared by using a unit commitment optimization with high level of detail. In a district heating case study, the total annualized costs of the unit commitment optimizations differ substantially from 391 to 481 kEUR and the computation times of the design optimizations range from 10 s to more than 10 h. Models that consider part-load efficiencies lead to the lowest system costs but the highest computation times. In addition, simple design heuristics are identified which lead in combination with fast-solving linear models to energy systems with low total annualized costs (410 kEUR, 5% cost increase).

Automated summary

This study compares the performance of 24 MILP models for designing multi-energy systems, examining the impact of different combinations of features on the final system design. It was found that models considering part-load efficiencies have the lowest costs but longest computation times, while simple design heuristics combined with fast-solving linear models can achieve lower total costs.