Predicting the dynamic behavior of Francis turbine generating units

To reduce CO2 emissions and tackle global warming, an increasing amount of electrical power consumed around the world must be obtained from renewable sources. Among these sources, hydropower has not only the advantage of leaving a very small carbon footprint, but also the ability to be flexible and compensate for the intermittent nature of other sources like solar and wind. For these qualities, a large number of new hydropower projects is foreseen in the near future. Hydropower still has a large potential for new projects worldwide. Furthermore, many already existing plants have also the possibility to modernize its facilities and increase its available installed capacity. For both new plants and modernization projects, thorough investigations are necessary to decide if the project is technically viable and economically relevant. Nevertheless, in the very early design stage, some key information regarding the properties of the future generating unit is often unknown or sometimes estimated with high uncertainty levels. One of these unknown aspects is the turbine efficiency: it can only be known with high accuracy after performing measurements on a reduced scale physical turbine model homologous to the future turbine prototype. The turbine complete characteristics of torque and discharge is also necessary for a proper dimensioning of the generating unit, as it impacts notably the overpressure in the water conduits and the overspeed of the rotating parts. Francis turbines operating at part load and full load conditions feature the so-called cavitation vortex rope in their draft tube cone. Therefore, two additional dynamic aspects can impact the performance of a Francis turbine generating unit: (1) a possible resonance between the hydraulic circuit first eigenfrequency and the excitation frequency from the vortex rope, and (2) the occurrence of high amplitude power swings and pressure surge induced by the cavitation vortex rope in unstable full load operating conditions. Currently, these two additional aspects usually remain completely unknown until the prototype enters into operation. This thesis objective is then to develop and validate new empirical models, testing and calculation procedures able to perform accurate predictions of a Francis turbine prototype dynamic behavior still in the early stage of a hydropower plant project. They can be used by engineers working in the design of Francis generating units to estimate with accuracy the final dynamic behavior of these units as a whole and, consequently, optimize the unit design to reduce costs and minimize risks related to the occurrence of undesired dynamic behavior of the cavitation vortex rope. The complete database of reduced scale physical model measurements available in the Laboratory for Hydraulic Machines (LMH) at the École Polytechnique Fédérale de Lausanne (EPFL) is used to construct empirical models able to estimate the turbine efficiency and complete characteristics. The obtained standard error in estimating peak efficiency values is then less than 1%. Extensive measurements and 1-D eigenvalue calculations are performed to better understand the dynamic behavior of the cavitation vortex in a specific test case. As a result, procedures to predict with accuracy part load resonance and full load instability are presented. These predictions can then be made soon after reduced scale model testing, i.e., usually years before the prototype enters into operation.