Analysis of Orbital Eccentricity and UMP in Large Salient Pole Synchronous Machines

The problem with unbalanced magnetic pull (UMP), often analyzed for induction motors, is also a huge issue in large hydro generators. This paper focuses on large vertical shaft synchronous machines describing the UMP as a function of eccentricity, irrespective of its origin on the rotor, stator, or both. The static and the dynamic eccentricity impact on the air-gap length is described through an original mathematical model in which the magnetic flux density spatial distribution is amplitude modulated and the UMP is calculated applying Maxwell's tensor. This process allows including the machine saturation when calculating the no-load rated voltage. Hence, with constant rotor excitation current, corresponding to the rated generator voltage at no-load, the magnetic field amplitude variation results in a linear function of the air-gap length variation. Seven case studies are presented comparing traditional methodology with the proposed one. Two of them are also calculated by applying the finite element method (FEM). The proposed methodology gets more realistic answers if FEM results are taken as a reference. Finally, UMP triggered by a dynamic eccentricity is shown, and the resulting force that followed the orbital eccentricity is depicted clearly.