Mechanistic model for Francis turbines in OpenModelica

Often, simulation tools use an empirical turbine model, typically based on look-up tables for turbine efficiency. Such look-up tables can be based on dimensionless hill charts which again require experimental data, or can be directly fitted to experimental data. Thus, empirical models require extensive experiments on real turbines, and it is not straightforward to adapt such models to other systems. Instead of using an empirical model, it is of interest to use a simple mechanistic model based on the Euler equations for the Francis turbine. Such a simple mechanistic model still holds a number of design parameters which must be found. However, the design parameters have a physical interpretation, and algorithmic design rules exist for choosing these parameters based on information such as nominal water head and nominal flow rate for the hydropower plant. In consequence, the use of such a mechanistic model enables simulation of hypothetical systems with reasonable accuracy, without having to wait until the system is built. This paper describes as the mechanistic model and a design algorithm for the Francis turbine. The results of the design algorithm and model dynamics (shaft power and hydraulic efficiency) are also compared to designs and turbine behaviors found from the commercial turbine design software Alab. These comparisons show good fitting (using a least squares error method) that leads to a good confidence in both the design algorithm, and the mechanistic model. The dynamics comparison is done by simulating two different turbine descriptions using OpenModelica and our in-house hydropower library. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.