Abstract
The synthesis of energy systems necessitates simultaneous optimization of both design and operation across all components within the energy system. In real-world applications, this synthesis poses a mixed-integer nonlinear programming (MINLP) problem, considering nonlinear behaviours such as investment cost curves and part-load performance. The complexity increases further when seasonal energy storage is involved, as it requires temporal coupling of the full time series. Although numerous solution approaches exist to solve the synthesis problems simplified by linearization, methods for solving a full-scale problem are currently missing. In this work, we introduce a rigorous method, RiNSES4, to manage the nonlinear aspects of energy system synthesis, particularly focusing on long-term time-coupling constraints. RiNSES4 calculates the upper and lower bounds of the initial synthesis problem in two separate branches. The proposed method yields feasible solutions through upper bounds, while evaluating the solution quality via lower bounds. The solution quality is iteratively enhanced by increasing the resolution for calculating upper bounds and tightening the relaxations for computing lower bounds. Both branches work simultaneously and independently, with their outcomes compared after each iteration within each branch. The iterations continue until a predefined optimality gap is reached. We apply RiNSES4 to design a photovoltaic and battery energy system, considering the seasonality of both energy supply and demand sides. In comparison with a state-of-the-art commercial solver, RiNSES4 enables to solve the MINLP synthesis problem with great temporal detail and shows high potential.