This paper serves as an overview of existing models of permanent magnets 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 dependency 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 permanent magnets. 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 with models of domain wall motions.

Low speed, high torque machines are used in wind turbines where the turbine rotor is directly connected to the generator. A permanent magnet synchronous generator using high-energy rare-earth permanent magnets (PMs) is one common choice for this application, but rare-earth PMs have supply insecurities and cost risks. A rare-earth free 32-pole PM generator, using ferrite PMs in a spoke-type rotor, for use in a 12 kW experimental wind turbine is built and tested. Voltages and currents at load and no load are measured, as well as the magnetic field in the end regions of the machine. The generator can deliver the required power at nominal speed and has low harmonic content in the output. The electrical measurements are compared to two-dimensional finite element design calculations and the experimental results are lower than expected from simulations. The measured voltage is lower than expected, requiring a higher current than calculated for the rated power. Three-dimensional magnetic field simulations show that there are leakage flux paths in the end-regions that the two-dimensional design calculations overlook, explaining the discrepancy between simulations and measurements.

Within the area of permanent magnet electrical machines, there is an ongoing focus on replacing the rare earth permanent magnets with alternatives. An option is hard ferrites, commonly used in other applications. The relatively low coercive field strength of the ferrite magnets makes irreversible demagnetization an area that should not be neglected. In this paper, a methodology is proposed for the optimization of a slow-moving linear generator simulated in a finite element environment. The no-load phase voltage is maximized while accounting for iron saturation and permanent magnet irreversible demagnetization. This demagnetization is considered when the translator is alongside either the stator or air. The inclination angle between magnetization and magnetic field strength is accounted for by adjusting the intrinsic coercivity for each element of the permanent magnets. Characteristics for the magnet grades Y30 and Y40 are used in the optimization process. The velocity of the translator is set to resemble a speed common to wave power applications. Commercial finite element software is used together with two optimization algorithms: the genetic algorithm and the particle swarm optimization. The results of these optimization algorithms reach similar optimal solutions for the considered objective function, assuring a result close to a global maximum. The results also show a great difference in the optimal geometry for the two magnet grades and highlight the need to account for irreversible demagnetization when designing generators with ferrite magnets.

The wave energy converter (WEC) studied and developed at Uppsala University in Sweden is a point absorbing buoy connected to a linear generator (LG) on the seabed. Previous studies have improved the sustainability of the generator, changing its magnets from Nd₂Fe₁₄B-magnets to ferrites. In this paper, the magnetic circuit of the linear generator is further studied. Ferrite magnets of two different types (Y30 and Y40) are studied along with different shapes of pole shoes for the system. The finite element method (FEM) simulations in a program called Ace are performed. The results show that a linear generator including both Y30 and Y40 magnets and shortened T-shaped pole shoes can generate a similar magnetic energy in the airgap as a linear generator only containing Y40 magnets and rectangular pole shoes. This shows that the magnetic circuit can be altered, opening up sizes and strengths of magnets for different retailers, and thereby possibly lowering magnet cost and transportation. This work was previously presented as a conference at the European Wave and Tidal Energy Conference (EWTEC) 2017 in Cork, Ireland; this manuscript has been carefully revised and some discussions, on magnet costs for example, have been added to this paper.

Electromagnetic modelling of electrical machines through finite element analysis is an important design tool for detailed studies of high resolution. Through the usage of finite element analysis, one can study the electromagnetic fields for information that is often difficult to acquire in an experimental test bench. The requirement for accurate result is that the magnetic circuit is modelled in a correct way, which may be more difficult to maintain for rare earth free permanent magnets with an operating range that is more likely to be close to non-linear regions for the relation between magnetic flux density and magnetic field strength. In this paper, the inclination angles of the magnetic flux density, magnetic field strength and magnetization are studied and means to reduce the inclination angles are investigated. Both rotating and linear machines are investigated in this paper, with different current densities induced in the stator windings. By proper design of the pole shoes, one can reduce the inclination angles of the fields in the permanent magnet. By controlling the inclination angles, one can both enhance the performance of the magnetic circuit and increase the accuracy of simpler models for permanent magnet modelling.

Electricity production from ocean waves with different solutions is a topic of major research interest. Many of such designs are based on linear generators that inherently introduce end forces. In this paper, detent force using Maxwell Stress Tensor and induced voltage is initially investigated for two different winding patterns for a generator topology with buried magnets in a finite element software. Two ways of overcoming the end forces are further examined: the first method reduces the magnetic flux variations of the translator between stator and air. The second method aims at countering the end forces at both ends for full active stator area. A comparison is then made between buried and surface-mounted topologies for the second end effect compensation method. Both no-load and load conditions are investigated in the comparison. The end effect compensation shows promising results for both topologies. Some clear similarities of the extended stator used to counter the end forces are also apparent, where the stator extensions completely cover the outer poles of both topologies. The results also indicate a longer full active stator area for the buried topology for the same pole-pitch and stroke length, resulting in a higher average voltage for partial stator overlap.