Faculté des sciences et techniques de l'ingénieur STI, Programme doctoral Energie, Institut des sciences de l'énergie ISE (Laboratoire de machines électriques LME)

## Large low speed hydrogenerators - UMP and additional damper losses in eccentricity conditions

### Keller, Stefan ; Simond, Jean-Jacques (Dir.) ; Tu Xuan, Mai (Dir.)

### Thèse sciences Ecole polytechnique fédérale de Lausanne EPFL : 2007 ; no 3773.

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- The present thesis is an advanced contribution to the design process of large synchronous generators with high number of poles. It proposes two original contributions, the first one allowing a very precise prediction of the no-load voltage and of the no-load losses in the damper winding, the second one allowing a rigorous calculation of the unbalanced magnetic pulls and of the associated losses in the damper winding in the case of a machine in eccentricity conditions or with any kind of rotor and stator deformation. Both contributions are based on the same strategy, apart from the fact that it has to be taken into account that the geometry is not the same in both cases, it is supposed perfect in the first case and damaged in the second. The magnetostatic 2D finite element method (FEM) is used to determine the magnetic coupling of the machine conductors as a function of the rotor position. These values of magnetic coupling are then used in the voltage equations of the machine which are solved using a numerical method. A particularity is the calculation of the magnetic flux coupled with a conductor in two situations, once with only the field winding currents, fixing the levels of saturation, and once with field winding currents and a current in one damper bar. This strategy leads to the concept of differential inductances. The two contributions are different because for the first one the geometric, cyclic periodicity of the machine is of one stator slot pitch and for the damaged machine no short cyclic periodicity can be found. In the first case the values of flux linkage and the inductances necessary for the voltage prediction are therefore calculated only for some rotor positions within one stator slot pitch. These values are then reused for all other rotor positions. This method allows to predict the currents and the losses in the damper winding, as well as the no-load voltage waveform with the same precision as a transient magnetic FEM simulation but reducing the simulation time by a factor of about 20. Comparisons with measurements and with transient magnetic FEM simulations on several operating units prove the precision of this approach. As in the case of the calculation of the unbalanced magnetic pulls and of the associated losses in the damper winding for a machine with damaged geometry one can not take advantage of a short geometric periodicity, the procedure has to be different. Again the magnetic coupling of the different circuits is calculated in advance using the magnetostatic FEM, but in this case without rotation of the rotor. The stator slotting can be neglected because it does not influence the aimed results. Any kind of geometric deformation is represented by contiguous segments, placed on the interior stator surface, which can be displaced radially in both directions. A correct adjustment in time of the air gap value of each segment allows to represent any combination of static and dynamic deformation of the air gap for any position of the rotor. The use of a linear superposition of the linearized influences of all segments on the values of magnetic coupling and on the inductances allows to reduce the number of preliminary magnetostatic FEM calculations to the minimum. It has to be specified that the preliminary magnetostatic 2D FEM calculations are carried out only once for a given machine. They can then be used for different deformations of the geometry. If one wants to use the transient magnetic 2D FEM the whole approach has to be repeated for every geometric deformation to be analyzed. The results obtained haven been systematically compared to results obtained through transient magnetic FEM calculations. The agreement is excellent and the reduction of calculation time is enormous. Both contributions were implemented in highly automatized tools; they are therefore well adapted to an industrial application.