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The paper describes the vector magnetic characteristic analytical method using the vector magnetic hysteretic engineering model. By this method, various kinds of vector magnetic properties, for example vector hysteretic loop, coercive force, magnetic power loss, vector behavior of magnetic flux density B, and magnetic field strength H, can be obtained on electrical machines and apparatus. Index Terms--E&S model, FEM, magnetic characteristic analysis, magnetic modeling, vector magnetic property.

This paper presents the two-dimensional vector magnetic property of the grain-oriented electrical steel sheet. The local magnetic characteristics are varied with the interaction of domain structure in the crystal grains, because the grain-oriented electrical steel sheets are composed of many crystal grains. Therefore, it is necessary to evaluate the local magnetic characteristic of electrical steel sheet to improve the magnetic properties. However, the local magnetic characteristic, including hysteresis, was difficult to express numerically with the conventional constitutive relation. In this paper, the influence of the specific magnetic permeability of the grain boundary on the magnetic power loss properties has been investigated numerically. In the numerical simulation, the finite-element method with the E&SS modeling is used to consider the grain structure and its orientation. Index Terms--Crystal grain, E&SS modeling, finite-element method (FEM), grain-oriented electrical steel sheet, magnetic power loss, two-dimensional (2-D) vector magnetic property.