A Modified Takács Model to Formulate the Anisotropic Behavior of Grain-Oriented Laminations

It is essential to consider the anisotropic behavior of soft-magnetic materials to accurately estimate the core losses in the machine parts, wherein the direction of the magnetic field is a function of time and space. At T joints of transformers and tooth-yoke joints of rotating machines, the direction of magnetic fields changes as a function of time. Directional dependency of magnetic properties results in additional losses. Various formulations to model the anisotropic behavior of hysteresis characteristics and corresponding losses of soft-magnetic materials are available in the literature. The Takács model is a computationally efficient mathematical formulation to model the hysteresis behavior. In this work, an analytical extension to the Takács model is proposed to formulate the anisotropic behavior of these materials. The variation of the model parameters with direction is studied, and their directional dependencies are formulated using suitable functions. The anisotropic behavior of the grain-oriented (GO) materials along arbitrary directions is investigated using the proposed approach, and it is found to be in agreement with measurements. This model can be used to formulate the complicated magnetic behavior at joints in transformers and electrical machines.