Hybrid Approach for the Modeling of Magnetic Force Excitations in Multipole Wind Turbine Generators Considering Air Gap Imperfections

Magnetic force excitations in the air gap of generators can lead to tonal noise emissions of direct-drive wind turbines. Besides the magnetic circuit design, the generator air gap topology has an impact on the excited vibration modes and their frequencies, respectively. For the model-based analysis of the excited force density waves, the spatial and temporal distribution of the air gap magnetic flux density has to be modeled accurately, since it is directly linked with the interfacial forces by the Maxwell stress tensor. Electromagnetic simulations by finite elements consider nonlinear effects, as e.g. saturation, and are therefore convenient for the quantitative analysis. The processing of finite element meshes for the stated purpose is however cumbersome, since many full-models of huge structures (multipole) are necessary. Semi-analytical approaches using conformal maps are efficient for analyzing air gap deformations linearly, even though they do not consider the saturation behavior implicitly. In this work, an efficient hybrid approach for the modeling of force excitations by multipole generators considering air gap imperfection is presented. The calculation method combines electromagnetic 2D-finite-element results of symmetrical units with permeance functions of deformed air gaps obtained by conformal mapping to study the spatial and temporal shape of excited force density waves along the whole generator circumference.