Logo: to the web site of Uppsala University

This article serves as an overview of existing models of permanent magnets (PMs) for electrical machines. The review study starts with the linear recoil model, which is commonly used to describe the reversible part of the demagnetizing curve. It is a simple model, especially useful for representing materials with high anisotropy, such as ferrite, NdFeB, and SmCo. The model is harder to apply for nonlinear materials, such as Alnico, but still possible since their recoil curves are linear. The study shows how the linear recoil model could be extended to include irreversible demagnetization, temperature dependence, and angular dependence. All such models have their advantages and disadvantages, which will be discussed further. Both the magnetization and the risk of demagnetization are temperature-dependent. It could be noted that NdFeB has an increased risk of demagnetization at high temperatures, while ferrite has it at very low temperatures. The temperature dependence is described and compared for several materials, also including simplifying models. There are different methods to include the inclination angle of an applied magnetic field when studying the demagnetization of PMs. Several models describe different phenomena associated with the underlying dynamics of magnetism. Such models could then consider coercivity mechanisms and coherent rotation of magnetization, both with the Stoner-Wohlfarth model and models of domain wall motions.

This paper will analyze how the energy flux of Poynting's vector is compared to the power flow in electrical engineering, where the power, instead, is defined by voltages and currents. There are alternatives to Poynting's energy flux vector that agree more with circuit theory methods such that the energy flow is in the current conductor and not in the insulation surrounding it. One such basic formulation would only consist of the total current density and the voltage potential, but it would need an alternative theorem for energy transfer. Another formulation proposed by Slepian would instead still agree with Poynting's energy transfer theorem, but it needs to add the power of alternating magnetic vector potential. The alternatives to Poynting's vector may better illustrate the energy flow in electrical engineering, but two things could be considered in their generality. First, since they are expressed by potentials, they are gauge invariant and depend on the definition of the potentials. Second, Poynting's vector is used to formulate the electromagnetic momentum, and any alternative energy flow vectors would not. These two notes are of minor importance in electrical engineering, and the alternatives could be used as good alternatives for describing power flow. The main purpose of this paper is to bridge the differences between the physical theory of energy flux and the methods in electrical power engineering. This could simplify the use of energy flux and Poynting's vector in engineering problems.

Hybrid excitation is a technology that combines the advantages of field windings and permanent magnets for inducing magnetic flux. This article studies the benefits of hybrid excitation and provides an outlook on their possible applications, such as wind power generators and electric vehicle motors. Compared to permanent magnet-based machines, hybrid excitation gives a variable flux while still using the advantage of the permanent magnets for a portion of the flux. This article also looks into some different categories of machines developed for hybrid excitation. The categories are based on the reluctance circuit, the relative geometrical location of the field windings relative to the permanent magnets, or the placement of the excitation system.

This paper shows how to model the force density in electrical machines based on the field lines of the magnetic flux density. The force density is written as two vector components: the magnetic tension force and the magnetic pressure gradient force. This approach has been applied in physics but never to forces in engineering problems. The magnetic tension force acts to straighten bent field lines, based on the curvature of the flux density. The magnetic pressure gradient force acts from regions of high flux density to regions of low flux density. Both force densities are derived from the Lorentz force using the tnb-frame of Frenet–Serret formulas and shown to be equivalent to the divergence of the Maxwell stress tensor. It is shown how the force density could describe the forces in a synchronous machine, including both the angular torque of the load and the radial forces between the rotor and the stator. It could also be linked to the power flow and thereby to the energy flux of Poynting’s vector. The force densities could be used to improve the understanding of the Maxwell stress tensor, since they are easier to illustrate as vectors compared to the matrix form of the Maxwell stress tensor. It also shows the location of the force density, which could improve the use of enclosing volumes when calculating the force based on the divergence theorem with the Maxwell stress tensor.

This paper studies the properties of the Preisach model and the play model, and compare their similarities. Both are history-dependent hysteresis models that are used to model magnetic hysteresis. They are described as discrete sums of simple hysteresis operators but can easily be reformulated as integral equations of continuous distribution functions using either a Preisach weight distribution function or a play distribution function. The models are mostly seen as phenomenological or mathematical tools but can also be related to friction-like pinning of domain-wall motions, where Rayleigh’s law of magnetic hysteresis can be seen as the simplest case on either the play model or the Preisach model. They are poor at modeling other domain behavior, such as nucleation-driven hysteresis. Yet another hysteresis model is the stop model, which can be seen as the inverted version of the play model. This type of model has advantages for expressions linked to energy and can be related to Steinmetz equation of hysteresis losses. The models share several mathematical properties, such as the congruency property and wiping-out property, and both models have a history of dependence that can be described by the series of past reversal points. More generally, it is shown that the many models can be expressed as Preisach models, showing that they can be treated as subcategories of the Preisach type models. These include the play model, the stop model and also the alternative KP-hysteron model.

This paper gives a broad overview of methods to model core losses from the magnetization of soft magnetic iron cores in electrical machines. The review study starts with some commonly used models of loss separation for hysteresis losses and eddy current losses. The study links the models to physical models of magnetization, considering domain behaviour such as nucleation, formation and rotation, and also pinning and damping of domain wall motions. Both the non-linear behaviour of hysteresis and excess eddy currents is better understood by these underlying physical domain mechanisms.

Classical eddy currents usually only consider the resistivity and the thickness of the lamination steel plates, but core losses are also related to several material properties, such as texture, crystal grain size, type of alloy and alignment of the crystal anisotropy. These dependencies could be considered by some adoptions of the loss models.

The common approaches to core loss modelling neglects non-sinusoidal fields and multi-dimensional fields and assumes an ideal sine wave which only is directed along one direction. This paper also discusses non-sinusoidal losses, both for hysteresis and eddy current losses. It also covers two- dimensional rotational losses, and how they could be handled by simplified models based on ellipse trajectories.

The relation between iron losses and external physical factors is presented, such as dependence on the direction of an applied field, dependence on the temperature, dependence on cutting degradation and dependence on an applied stress.

There are several models for magnetic hysteresis. Their key purposes are to model magnetization curves with a history dependence to achieve hysteresis cycles without a frequency dependence. There are different approaches to handling history dependence. The two main categories are Duhem-type models and Preisach-type models. Duhem models handle it via a simple directional dependence on the flux rate, without a proper memory. While the Preisach type model handles it via memory of the point where the direction of the flux rate is changed. The most common Duhem model is the phenomenological Jiles–Atherton model, with examples of other models including the Coleman–Hodgdon model and the Tellinen model. Examples of Preisach type models are the classical Preisach model and the Prandtl–Ishlinskii model, although there are also many other models with adoptions of a similar history dependence. Hysteresis is by definition rate-independent, and thereby not dependent on the speed of the alternating flux density. An additional rate dependence is still important and often included in many dynamic hysteresis models. The Chua model is common for modeling non-linear dynamic magnetization curves; however, it does not define classical hysteresis. Other similar adoptions also exist that combine hysteresis modeling with eddy current modeling, similar to how frequency dependence is included in core loss modeling. Most models are made for scalar values of alternating fields, but there are also several models with vector generalizations that also consider three-dimensional directions.

In this paper, hard magnetic materials for future use in electrical machines are discussed. Commercialized permanent magnets used today are presented and new magnets are reviewed shortly. Specifically, the magnetic MnAl compound is investigated as a potential material for future generator designs. Experimental results of synthesized MnAl, carbon-doped MnAl and calculated values for MnAl are compared regarding their energy products. The results show that the experimental energy products are far from the theoretically calculated values with ideal conditions due to microstructure-related reasons. The performance of MnAl in a future permanent magnet (PM) generator is investigated with COMSOL, assuming ideal conditions. Simplifications, such as using an ideal hysteresis loop based on measured and calculated saturation magnetization values were done for the COMSOL simulation. The results are compared to those for a ferrite magnet and an NdFeB magnet. For an ideal MnAl hysteresis loop, it would be possible to replace ferrite with MnAl, with a reduced weight compared to ferrite. In conclusion, future work for simulations with assumptions and results closer to reality is suggested.