This paper aims to address the challenges of solving complex nonlinear optimization problems that simultaneously involve sizing and control of energy systems. The objective is to obtain realistic and computationally efficient solutions suitable for real-world applications. The study focuses on demonstrating the advantages of a bilevel approach compared to conventional single-level formulations, particularly in systems characterized by strong nonlinear interactions between design and operational variables.
A bilevel optimization framework is proposed, in which the lower level solves the control problem through a combination of nonlinear programming (NLP) and dynamic programming (DP). The upper level handles the sizing variables and coordinates the results from multiple control subproblems. The decomposition allows for a significant reduction in computational complexity while maintaining high accuracy. The methodology is validated and benchmarked against a classical linear programming (LP) approach.
The results show that the proposed bilevel NLP–DP methodology achieves performance close to that of linear programming in terms of energy cost while effectively handling nonlinearities inherent to real systems. It demonstrates strong robustness and stability over long-term optimization horizons, with deviations below 0.3% compared to LP. Moreover, the approach ensures physically realistic control trajectories and operational feasibility under nonlinear constraints.
This work introduces a unified bilevel optimization framework combining nonlinear and dynamic programming to jointly address sizing and control problems in complex energy systems. The originality lies in the decomposition strategy, which makes it possible to preserve nonlinear behavior while ensuring computational tractability. The proposed approach provides a practical and reliable tool for the optimal design and control of hybrid infrastructures, such as railway substations or microgrids.
