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COMPEL 28,3

700

Comparison of a simple and a detailed model of magnetic hysteresis with measurements on electrical steel
Hanif Tavakoli
School of Electrical Engineering, Royal Institute of Technology, Stockholm, Sweden

Dierk Bormann
˚ ¨ ABB AB – Corporate Research, PowerTechnologies, Vasteras, Sweden, and

¨ ¨ David Ribbenfjard and Goran Engdahl
School of Electrical Engineering, Royal Institute of Technology, Stockholm, Sweden
Abstract
Purpose – For efficient magnetic field calculations in electrical machines, the hysteresis and losses in laminated electrical steel must be modeled in a simple and reliable way. The purpose of this paper is to investigate anddiscuss the potential of a simple complex-permeability model. Design/methodology/approach – A frequency dependent complex-permeability model as well as a more detailed model (describing hysteresis, classical eddy current effects, and excess losses separately) are compared to single-sheet measurements on laminated electrical steel. It is discussed under which circumstances the simple complex-m model isan adequate substitute for the more detailed model. Findings – A satisfactory agreement of the simple complex-m model was found with both detailed model and measurements, improving with increasing frequencies. This is true not only for the effective permeability function, but holds also for the detailed H-B characteristics (hysteresis). Originality/value – It is demonstrated that the complex-mmodel is a reliable and convenient starting point for the estimation of flux distribution and losses in complicated magnetic core geometries. Keywords Electrical machines, Steel, Permeability, Eddy currents, Electromagnetism Paper type Research paper

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Vol. 28 No. 3, 2009 pp. 700-710 q EmeraldGroup Publishing Limited 0332-1649 DOI 10.1108/03321640910940954

1. Introduction Recent research has resulted in detailed models of the magnetic hysteresis and loss ¨ ¨ mechanisms in a wide frequency range (Bertotti, 1998; Ribbenfjard, 2007; Ribbenfjard and Engdahl, 2008). Although these models provide a good description of magnetic material properties or of simple reluctance circuits based onthem, they are too demanding numerically to be incorporated into a full-scale magnetic field simulation of a realistic geometry, as with a FEM or FDM calculation tool. In other words, while such a detailed simulation of the H-B relation of a single or a few interacting cells is still perfectly feasible, simulating thousands or ten thousands of them simultaneously may be inconvenient or impossible.Moreover, in many practical situations a detailed description is not required either. Often, the goal is to obtain a good estimate of some local or global quantity containing much less information than the detailed local H-B relation, such as the local losses causing dangerous hot spots, or simply the total losses in a machine relevant for cooling or economic reasons. For such applications, itis desirable to use a simple model of magnetic hysteresis and losses, which can easily be incorporated in field calculation tools but which at the same time is sufficiently close to reality, within the frequency range of interest for the specific application. Such a model is the description of magnetic (meta-)materials by a suitable frequency dependent complex permeability, which is the most generallinear description of a local and isotropic H-B relation. If desired, it can easily be extended to a nonlocal and/or aniso-tropic H-B relation by turning m from a scalar function of position into a distance dependent integral kernel and/or tensor, respectively, (Jackson, 1998). In this paper, we discuss to which extent the measurement results obtained with a single-sheet tester on strips of...