Modelling and analysis of hydropower generator rotors

Sammanfattning: In almost all production of electricity the rotating machines serves as an important part of the energy transformation system. In hydropower units, a hydraulic turbine connected to a generator converts the potential energy stored in the water reservoir into electrical energy in the generator. An essential part of this energy conversion is the rotating system of which the turbine and the generator are part. During the last century the machines for electricity production have been developed from a few mega watts per unit up to several hundreds mega watts per unit. The development and increasing of size of the hydropower machines have also brought a need for new techniques. The most important developments are the increased efficiency of the turbines and generators, new types of bearings and the introduction of new materials. Vibration measurements are still the most reliable and commonly used method to avoid failure during commissioning, for periodic maintenance, and as protection of the systems. Knowledge of the bearing forces in different operational modes is essential in order to estimate the degeneration of components and to avoid failures. In the appended Paper A, a method has been described for measurement of bearing load by use of strain gauges installed on the guide bearing bracket. This technique can determine the magnitude and direction of both static and dynamic loads acting on the bearing. This method also makes it possible to find the cause of the radial bearing force among the various eccentricities and disturbances in the system. A principal cause of many failures in large electrical machines is the occurrence of high radial forces due to misalignment between rotor and stator, rotor imbalance or disturbance from the turbine. In this thesis, two rotor models are suggested for calculation of forces and moments acting on the generator shaft depending on misalignment between stator and rotor. These two methods are described in appended papers B and C. In Paper B, a linear model is proposed for an eccentric generator rotor subjected to a radial magnetic force. Both the radial force and the bending moment affecting the generator shaft are considered when the centre of the rotor spider hub deviates from the centre of the rotor rim. The magnetic pull force acting on the rotor is assumed to be proportional to the rotor displacement. In Paper C, a non-linear model is proposed for analysis of an eccentric rotor subjected to radial magnetic force. Both the radial and bending moments affecting the generator shaft are considered when the centre of the generator spider hub deviates from the centre of the generator rim. The magnetic forces acting on the rotor are assumed to be a non-linear function of the air-gap between the rotor and stator. The stability analysis shows that the rotor can become unstable for small initial eccentricities if the rotor rim position relative to the rotor hub is included in the analysis. The analysis also shows that the natural frequencies can decrease and the rotor response can increase if the rotor rim position in relation to the rotor spider is considered. The endurance of hydropower rotor components is often associated with the dynamic loads acting on the rotating system and the number of start-stop cycles of the unit. Measurements together with analysis of the rotordynamics are often the most powerful methods available to improve understanding of the cause of the dynamic load. The method for measurement of bearing load presented in this thesis makes it possible to investigate the dynamic as well as the static loads as acting on the bearing brackets. This can be done using the suggested method with high accuracy and without redesign of the bearings. During commissioning of hydropower unit, measurements of shaft vibrations and forces are the most reliable method to investigate the status of the rotating system. Generator rotor models suggested in this work will increase the precision of the calculated behavior of the rotor. Calculation of the rotor behavior is important before the generator is put in operation, after rehabilitation or when new machines will be installed.