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The massive penetration of the electrical network by renewable energy sources, such as wind and solar, pushes the operators to extend hydropower plant units operating range to meet the transmission system operator requirements. However, in off-design operating conditions, flow instabilities are developing in Francis turbines, inducing cavitation, pressure pulsations and potentially resonance that can threaten the stability of the whole system. Reduced scale model testing is commonly performed to assess the hydraulic behaviour of the machine for industrial projects. However, it is not possible to directly transpose pressure pulsations and resonance conditions from model to prototype since the characteristics of the hydraulic circuits are different from model to prototype. In this paper, a methodology developed in the framework of the HYPERBOLE European research project for predicting the eigenfrequencies of hydropower plant units operating in off-design conditions is introduced. It is based on reduced scale model testing and proper one-dimensional modelling of the hydraulic circuits, including the draft tube cavitation flow, at both the model and prototype scales. The hydro-acoustic parameters in the draft tube are identified at the model scale for a wide number of operating conditions and, then, transposed to the full-scale machine, together with the precession frequency for part load conditions. This enables the prediction of the eigenfrequencies and resonance conditions of the full-scale generating unit.

Reduced scale model testing for prediction of eigenfrequencies and hydro-acoustic resonances in hydropower plants operating in off-design conditions