Dynamic consequences of shape deviations in hydropower generators

Abstract: Earlier measurements on hydropower generators have indicated the existence of backward whirling motion, and, also relatively large shape deviations in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called unbalanced magnetic pull (UMP). The target of this thesis is to analyse the dynamic consequences of shape deviations in hydropower generators. A mathematical model is developed to describe the shapes of the rotor and stator, and the corresponding UMP is obtained through the law of energy conservation. Theorems about the existence of stable equilibria and whirling motion of the rotor response are proved mathematically for certain cases. The results indicate that different whirling motions, including both backward and forward whirling can occur. Generator dynamics are further investigated by simulating the basin of attraction, giving a measure of the robustness of the attractors. From this, the magnitudes are approximately obtained when the shape deviations become dangerous for the generator. It is concluded which shape deviations that are more dangerous than others. In hydropower generator maintenance the shapes of the rotor and stator are frequently measured. The results from this thesis can be used to evaluate such measurements and explain the existence of complicated whirling motion.