# Rotor dynamical modelling and analysis of hydropower units

Abstract (Summary)

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 crucial parts. During the last century the machines for production of electricity have been developed from a few megawatts per unit, up to several hundreds megawatts per unit. The development and increased size of the hydropower machines has 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 measurement is still the most reliable and commonly used method for avoiding failure during commissioning, for periodic maintenance, and for protection of the systems. Knowledge of the bearing forces at 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. This method was used in Paper C to investigate bearing stiffness and damping. 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 due to misalignment between stator and rotor. These two methods are described in appended papers B and D. 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 force acting on the rotor is assumed to be proportional to the rotor displacement. In Paper D, a non-linear model is proposed for analysis of an eccentric rotor subjected to radial magnetic forces. 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 position of the rotor rim relative to the rotor hub is included in the analysis. The analysis also shows that natural frequencies can decrease and the rotor response can increase if the position of the rotor rim in relation to the rotor spider is considered. In Paper E, the effect of damping rods was included in the analysis of the magnetic pull force. The resulting force was found to be reduced significantly when the damper rods were taken into account. An interesting effect of the rotor damper rods was that they reduced the eccentricity forces and introduced a force component perpendicular to the direction of eccentricity. The results from the finite-element simulations were used to determine how the forces affect the stability of the generator rotor. Damped natural eigenfrequencies and the damping ratio for load and no-load conditions were investigated. When applying the forces computed in the time- dependent model, the damped natural eigenfrequencies were found to increase and the stability of the generator rotor was found to be reduced, compared with when the forces were computed in a stationary model. Damage due to contact between the runner and the discharge ring have been observed in several hydroelectric power units. The damage can cause high repair costs to the runner and the discharge ring as well as considerable production losses. In Paper F a rotor model of a 45 MW hydropower unit is used for the analysis of the rotor dynamical phenomena occurring due to contact between the runner and the discharge ring for different grades of lateral force on the turbine and bearing damping. The rotor model consists of a generator rotor and a turbine, which are connected to an elastic shaft supported by three isotropic bearings. The discrete representation of the rotor model consist of 32 degrees of freedom. To increase the speed of the analysis, the size of the model has been reduced with the IRS method to a system with 8 degrees of freedom. The results show that a small gap between the turbine and discharge ring can be dangerous, due to the risk of contact with high contact forces as a consequence. It has also been observed that backward whirl can occur and in some cases the turbine motion becomes quasi-periodic or chaotic. 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 rotor dynamics, are often the most powerful methods available to improve understanding of the cause of the dynamic load. The method for measurement of the bearing load presented in this thesis makes it possible to investigate the dynamic as well as the static loads acting on the bearing brackets. This can be done using the suggested method with high accuracy and without re-designing the bearings. During commissioning of a hydropower unit, measurement of shaft vibrations and forces is the most reliable methods for investigating the status of the rotating system. Generator rotor models suggested in this work will increase the precision of the calculated behaviour of the rotor. Calculation of the rotor behaviour is important before a generator is put in operation, after overhaul or when a new machine is to be installed.
Bibliographical Information:

Advisor:

School:Luleå tekniska universitet

School Location:Sweden

Source Type:Doctoral Dissertation

Keywords:

ISBN:

Date of Publication:01/01/2008