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C. N. Ashtiani D. A. Lowther Computational Analysis and Design Laboratory Department of Electrical Engineering McGill University |
Simulation of the Steady-State Reactances of a Large Water-Wheel Generator by Finite ElementsFinite elements and finite differences in the past have been extensively used for the prediction of turbo generators steady-state reactances at the design stage. Compared with the technical progress made in the past decade in the computational methods used, little attention has been given to the modeling as well as the postprocessing of the engineering and physical insight into the specific problem of concern. The numerical field analyst does not concern himself with the specific applications of the methods and leaves the application engineer with the task of modeling and the interpretation of results. On the other hand, the application engineer, being traditionally oriented towards classical methods, tends to model his problem in ways which are often in contrast with the essence of the new tools of analysis. Replacing the actual current distribution in the slot conductors of the stator with sinusoidal distribution, or replacing the armature winding of a generator with an equivalent d-q sinusoidally distributed winding, are examples of this tendency in the field of electric machines.This paper reports a successful computation of the steady-state reactances of a modern large water-wheel generator. Because of the short stack length and asymmetric rotor magnetic properties, hydrogenerators pose serious problems not noticeable in turbogenerators. A significant third-harmonic may arise in the flux space waveform at high active loads which makes the computation of quadrature axis reactance prone to error. The present work takes this effect into account by employing the concept of space phasors. It is shown that the instantaneous values of time varying phasal attributes can easily be transformed into a vector, independent of the frame of reference, which is free from significant third space harmonic. The projections of this vector at instant, retrieve the instantaneous values of the quantity of concern at all desired points. It is also shown that the theoretical test setups for measurement of direct and quadrature axis reactances, can be easily simulated by this method. The computed reactances are matched against the measured quantities and a detailed explanations of the results is presented. It is concluded that the finite element method is a powerful tool for the computer-aided analysis of electric machines. However, careful modeling of the problems as well as postprocessing of the results remains the key to a successful outcome. |
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