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Hydraulic modeling is the classical approach to investigate and describe complex fluid motion. Many empirical formulas in the literature used for the hydraulic design of river training measures and structures have been developed using experimental data from the laboratory. Although computer capacities have increased to a high level which allows to run complex numerical simulations on standard workstation nowadays, non-standard design of structures may still raise the need to perform physical model investigations. These investigations deliver insight into details of flow patterns and the effect of varying boundary conditions. Data from hydraulic model tests may be used for calibration of numerical models as well. As the field of hydraulic modeling is very complex, this chapter intends to give a short overview on capacities and limits of hydraulic modeling in regard to river flows and hydraulic structures only. The reader shall get a first idea of modeling principles and basic considerations. More detailed information can be found in the references.
Using optimization to design a renewable energy system has become a computationally demanding task as the high temporal fluctuations of demand and supply arise within the considered time series. The aggregation of typical operation periods has become a popular method to reduce effort. These operation periods are modelled independently and cannot interact in most cases. Consequently, seasonal storage is not reproducible. This inability can lead to a significant error, especially for energy systems with a high share of fluctuating renewable energy. The previous paper, “Time series aggregation for energy system design: Modeling seasonal storage”, has developed a seasonal storage model to address this issue. Simultaneously, the paper “Optimal design of multi-energy systems with seasonal storage” has developed a different approach. This paper aims to review these models and extend the first model. The extension is a mathematical reformulation to decrease the number of variables and constraints. Furthermore, it aims to reduce the calculation time while achieving the same results.