Contributions to the electromechanics of unbalanced magnetic pull in a synchronous hydropower generator

Abstract: Misalignment between the rotor geometrical axis and the geometrical stator axis in a hydropower generator is usually present at standstill and when the machine is under operation. Now, rotor-stator eccentricity in a rotating electrical machine is a harbinger to abnormal operating conditions of the machine. This rotor-stator eccentricity gives rise to a phenomenon called the unbalanced magnetic pull (UMP). Though the topic of UMP has been studied for more than a century, little attention has been paid to another phenomenon which is whirling and more specifically to non-synchronous whirling. Whereas the rotor-stator standstill misalignment can be cured to an acceptable level, a rotor when under operation normally entails whirling as well. Whirling is a reality in hydropower generators which are vertical machines and the latter are studied in this thesis work. It turns out that studying the effects of whirling in conjunction with the UMP can lift off pre-conceived ideas and hence provide a more qualitative and quantitative assessment of the effects of the nature and consequences of having a hydropower generator operating with UMP present. This thesis work provides simple theoretical conceptualisations that capture the phenomena of whirling and of the UMP, and purports to provide mechanical and electrical engineers with information on the necessity of studying these two phenomena simultaneously. With only the rotor eccentricity type considered in this work, the contributions are limited to mechanical dynamic simulations in the first part of the research work in addition to electromagnetic (EM) simulations in the second part of the research work. The validity of these EM simulations has been verified with an actual reported measurement. As for the mechanical dynamic analyses that cover the first part of the research work and which concern in essence one case of rotor eccentricity, valuable information such as the maximum rotor centre displacements inside the stator of the generator together with stability characteristics of the rotor motion are arrived at. These analyses indicate how stable the hydropower generator is under operation when UMP is present due to rotor eccentricity. It shows that one needs to consider both components of the UMP which are the radial UMP and the tangential UMP. Leaving out the tangential UMP component and/or considering a simplified whirling-independent model of the radial UMP lead(s) to a false representation of the dynamics of the generator when treated as a mechanical system. The analyses are new as a model that is used cares for both components of the UMP. In the second part of the research work, an electromechanics approach is preferred and emphasis is put on showing that important EM parameters such as force or the UMP, currents and ohmic losses are affected when non-synchronous whirling exists. The consideration of whirling as intimately linked to the UMP leads in the last stages of the research work to a robust and reliable method to compute the steady state UMP magnitude(s) up to sufficiently large eccentricities when two primary types of eccentricities, which are a purely static eccentricity and a purely dynamic eccentricity, co-exist. This novel computation method is of utmost importance and is a breakthrough in this area for four reasons: Firstly, there is no other work in the literature that has looked at mixed eccentricities motion of the geometric centre of the rotor in conjunction with simultaneous consideration of the UMP and the whirling phenomena. Secondly, it is fast as it is a semi-analytical method that rests on some previously done EM simulations which can be obtained with certain commercial EM field modelling software packages. Thirdly, it dispenses the analyst to have one of the rare contemporary commercial EM software products that can handle such intricate rotor centre motion since the proposed method rests upon less complicated EM simulations. And fourthly, it enables an analyst to obtain very good estimates of the UMP for a rotor centre motion that better mimics the true motion occurring in practice inside the stator of a hydropower generator. Altogether, the contributions in this thesis work can profoundly shape the strategies for better machine designs and analysis of the UMP without discounting previous knowledge that has been amassed since the end of the nineteenth century in this field. It is hoped that the research work carried out will help in the long interdisciplinary pursuit and allegiance to honing hydropower technology through creating an awareness of the need to study non-synchronous whirling effects as opposed to only looking at the usual synchronous whirling motion.