FERRITE PERMANENT MAGNET HYSTERESIS LOSS IN ROTATING ELECTRICAL MACHINERY

Dmitry Egorov

ACTA UNIVERSITATIS LAPPEENRANTAENSIS 873

Dmitry Egorov

FERRITE PERMANENT MAGNET HYSTERESIS LOSS IN ROTATING ELECTRICAL MACHINERY

Acta Universitatis Lappeenrantaensis 873

Dissertation for the degree of Doctor of Science (Technology) to be presented with due permission for public examination and criticism in Room 1316 at Lappeenranta–Lahti University of Technology LUT, Lappeenranta, Finland on the 15th of November, 2019, at noon.

Supervisors Professor Juha PyrhönenLUT School of Energy SystemsLappeenranta–Lahti University of Technology LUTFinland

Dr. Ilya PetrovLUT School of Energy SystemsLappeenranta–Lahti University of Technology LUTFinland

Reviewers Professor Peter SergeantDepartment of Electrical Energy, Systems and AutomationUniversity of GentBelgium

Professor Bulent SarliogluDepartment of Electrical and Computer EngineeringUniversity of Wisconsin–MadisonUnited States

Opponents Professor Peter SergeantDepartment of Electrical Energy, Systems and AutomationUniversity of GentBelgium

Professor Bulent SarliogluDepartment of Electrical and Computer EngineeringUniversity of Wisconsin–MadisonUnited States

ISBN 978-952-335-428-9ISBN 978-952-335-429-6 (PDF)

ISSN-L 1456-4491ISSN 1456-4491

Lappeenranta–Lahti University of Technology LUTLUT University Press 2019

AbstractDmitry EgorovFerrite Permanent Magnet Hysteresis Loss in Rotating Electrical MachineryLappeenranta 201944 pagesActa Universitatis Lappeenrantaensis 873Diss. Lappeenranta–Lahti University of Technology LUTISBN 978-952-335-428-9, ISBN 978-952-335-429-6 (PDF), ISSN-L 1456-4491, ISSN1456-4491

Electrical machines with permanent magnets (PMs) find numerous applications in presentenergy-efficient technologies. A reasonable compromise in terms of costs and efficiencymakes electrical machines with ferrite PMs a viable alternative to the widely usedinduction motors in some cases.

The loss analysis requires knowledge of all possible loss sources in an electrical machine.The hysteresis loss in the PM magnetic poles of a PM motor is usually excluded from theconventional loss analysis in the electrical machine design. However, there is someevidence that this loss may take place in the PM material under operating conditionsrelevant to electrical machinery.

In this doctoral dissertation, the focus of study is on the hysteresis behavior of ferrite PMsused in electrical machinery. Extensive measurements were performed by means of aVibrating Sample Magnetometer (VSM) based system. The measurement procedure forthe VSM was developed to be a relevant option in terms of electrical machine design. Thedetected magnetic phases with a reduced coercivity may introduce an additional losssource in the PM material when it is placed in a magnetic circuit of a PM electricalmachine.

The hysteresis behavior of the ferrite magnets was simulated by the static History-Dependent Hysteresis Model (HDHM) with a newly introduced analytical equation forreversal curves. The HDHM concept was further developed to enable the simulation offerrite magnets consisting of multiple magnetic phases with markedly different magneticproperties. The results of the study clearly indicate that the ferrite PM hysteresis loss doesnot play a significant role in most electrical machine designs. Nevertheless, the ferrite PMmaterial can be a source of considerable hysteresis loss under unfortunate operatingconditions in the region of the BH plane relevant to the electrical machine design.

Keywords: permanent magnet materials, hysteresis, modeling, losses, design of anelectrical machine

AcknowledgmentsThis work was carried out at the Department of Electrical Engineering at Lappeenranta–Lahti University of Technology LUT, Finland, between 2016 and 2019.

I would like to express my deepest gratitude to my supervisors prof. Juha Pyrhönen andDr. Ilya Petrov for their guidance during this research. I would like to thank Dr. Pia Lindh,Dr. Hanna Niemelä, and Dr. Julia Vauterin for their advice during the journal publicationprocess.

My sincere thanks are due to prof. Raivo Stern and Dr. Joosep Link from the NationalInstitute of Chemical Physics and Biophysics, Tallinn, Estonia for their altruistic andenthusiastic contribution to the vibrating sample magnetometer measurements of thepermanent magnet samples. This work made it possible to detect the performance of themagnet samples, and it was priceless for my research.

Dr. Sami Ruoho from Nordmag and Dr. Harri Kankaanpää from NEOREM magnets alsodeserve my thanks for numerous discussions and help in understanding the permanentmagnet behavior.

I thank my honored pre-examiners and opponents prof. Peter Sergeant and prof. BulentSarlioglu for their valuable comments, which helped to emphasize the importance of theresearch done in this dissertation.

Finally, I would like to thank my family and true friends for continuous support in all mylife.

Dmitry EgorovJune 2019Lappeenranta, Finland

Contents

Abstract

Acknowledgements

Contents

List of publications 9

Nomenclature 11

1 Introduction 131.1 Previous work ...................................................................................... 151.2 Outline of the doctoral dissertation ....................................................... 181.3 Scientific contribution .......................................................................... 20

2 Publications 212.1 Publication I ......................................................................................... 212.2 Publication II ........................................................................................ 232.3 Publication III ...................................................................................... 242.4 Publication IV ...................................................................................... 262.5 Publication V ....................................................................................... 28

3 Conclusions and future work 333.1 Conclusions .......................................................................................... 333.2 Suggestions for future work .................................................................. 34

References 35

Publications

9

List of publicationsThis doctoral dissertation is based on the following papers. The rights have been grantedby the publishers to include the papers in the dissertation.

I. Egorov, D., Uzhegov, N., Petrov, I., and Pyrhönen, J., Factors affecting hysteresisloss risk in rotor-surface-magnet PMSMs. Conference article. In: XXIIInternational Conference on Electrical Machines (ICEM), pp. 1735–1741.Lausanne: IEEE.

II. Petrov, I., Egorov, D., Link, J., Stern, R., Ruoho, S., and Pyrhönen, J., (2017).Hysteresis losses in different types of permanent magnets used in PMSMs. IEEETransactions on Industrial Electronics, 64(3), pp. 2502–2510.

III. Egorov, D., Petrov, I.; Link, J., Stern, R., and Pyrhönen, J. J., (2018). Model-basedhysteresis loss assessment in PMSMs with ferrite magnets. IEEE Transactions onIndustrial Electronics, 65(1), pp. 179–188.

IV. Egorov, D., Petrov, I., Pyrhönen, J. J., Link, J., and Stern, R., (2018). Hysteresisloss in ferrite permanent magnets in rotating electrical machinery. IEEETransactions on Industrial Electronics, 65(12), pp. 9280–9290.

V. Egorov, D., Petrov, I., Pyrhönen, J., Link, J., and Stern, R., Linear recoil curvedemagnetization models for ferrite magnets in rotating machinery. Conferencearticle. In: IECON 2017 - 43rd Annual Conference of the IEEE IndustrialElectronics Society, pp. 2046–2052. Beijing: IEEE.

Author's contributionDmitry Egorov is the principal author and investigator in Publications I and III–V. InPublication II, Dr. Ilya Petrov was the corresponding author and Dmitry Egorovconducted the studies on the basic idea of the measurement procedure and thepostprocessing of the measurement data.

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Nomenclature

Latin alphabetB magnetic flux density TBr permanent magnet remanence TBHmax maximum energy product J/m3

H magnetic field strength A/mHa applied magnetic field strength A/mHd demagnetizing field A/mHi intrinsic magnetic field strength A/mHcB normal coercivity A/mHcJ intrinsic coercivity A/mHmax maximum value of the magnetic field strength in the magnet when the

magnetic field varies between Hmin and Hmax A/mHmin minimum value of the magnetic field strength in the magnet when the

magnetic field varies between Hmin and Hmax A/mH variation of the external magnetic field strength A/m

J magnetic polarization TNm magnetometric demagnetizing factorS surface area m2

V volume m3

r relative permeability0 permeability of vacuum, 4 × 10-7 H/m

electrical resistivity m

Abbreviations2D two-dimensionalAC alternating currentDC direct currentFEA finite element analysisHDHM history-dependent hysteresis modelLRC linear recoil curveMEC magnetic equivalent circuitNMRSD normalized root mean square deviationPM permanent magnetPMSM permanent magnet synchronous machineRSM rotor surface magnetRE rare earthTCW tooth coil windingVSM vibrating sample magnetometer

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1 IntroductionThe global trend in improvement in the energy-efficiency technology directly affects thedevelopment of electrical machinery. At the moment, electrical machines consumearound 45% of the total generated electrical energy [1], being thus an object of significantresearch interest in terms of efficiency improvement. The progress in the permanentmagnet (PM) technology has boosted the development of PM-based electrical machinedesigns. The high maximum energy product BHmax in rare-earth (RE) based PM materialsenables electrical machine designs with a higher power or torque density compared withother electrical machine alternatives operating at a similar power and speed but withoutpermanent magnet material [2].

The penetration of electrical machine designs with RE PMs into the market issignificantly constrained by the high price of the RE-based magnet materials. After theconsiderable price rise in 2011–2013, the cost of the raw RE materials for RE PMproduction (i.e., Samarium, Dysprosium, Neodymium) remains at a relatively high levelor even demonstrates an increasing price trend [3]–[5]. An additional difficulty associatedwith the use of RE PMs in electrical machinery is caused by their unsustainableproduction process, price volatility, and possible threats of the supply chain of the REraw materials [6]–[8]. The challenges related to the mass production of electrical motorsbased on RE PMs has boosted the research aiming to find alternative hard magneticmaterials, which can be used in electrical machine design keeping the cost of the electricalmachine at an acceptable level. Ferrite PM materials enable viable electrical machinedesigns in some applications where the machine volume has no strict limitations [9]. Theprice of the ferrite PMs remains significantly lower in comparison with RE-basedmagnets because of the relatively high abundance of raw materials needed for the ferritePM production [10]–[12]. The relatively low BHmax and intrinsic coercivity HcJ of ferritePMs require thoughtful designs to achieve a competitive performance in comparison withother possible electrical machine designs [13]. The latest literature review clearlyindicates that ferrite PM electrical machines can be an attractive option in someapplications, such as electric propulsion systems [6], [14], hybrid electric vehicles [13],[15], high-speed motors [16], [17], submersible water pumps [18], wind power generators[19], [20], and others [21]–[24].

A detailed efficiency analysis requires evaluation of all possible loss sources in themagnetic and mechanical parts of an electrical machine. In traditional distributed windingmachines applying RE PMs, the losses in PMs were initially not considered as they hardlycontribute to the overall efficiency of the electrical machine [2]. However, the relativelylow electrical resistivity of RE-based PMs within one to two hundred cm [12], [25]brought the PM loss into consideration in the context of eddy current loss theory. Inparticular, Rotor Surface Magnet (RSM) and Tooth Coil Winding (TCW) PermanentMagnet Synchronous Machine (PMSM) designs are in the scope of the research, as theyenhance the presence of flux density harmonics penetrating through the magnets [26]–[29]. Nowadays, both analytical and finite-element-based approaches are available forcalculation of eddy current losses in PMs [30]–[34]. Most of the commercial tools for

1 Introduction14

electrical machine design include eddy-current-theory-based calculation of losses in PMs[22], [35]–[39].

The electrical resistivity of ferrite PMs is around 1010 cm (100 m) [11]. Such a highelectrical resistivity has established a common engineering practice to neglect any eddycurrent losses in this type of a hard magnetic material in rotating electrical machinery [9],[13], [40], [41].

Hysteresis loss generated by an alternating magnetic field in the electrical steel of themagnetic circuit of a machine is a well-known source of losses, and has been included inthe efficiency analysis of machines for decades [2], [42]–[45]. The conventionalrepresentation of the PM as a material consisting of only one hard magnetic phase leaves,in principle, almost no space for a similar loss type within the normal operating range ofan electrical machine. Nevertheless, the relative permeability r slightly higher than unityimplies a possibility of some hysteresis behavior in PMs [46]. Deviation from thepermeability of vacuum indicates that there are some soft magnetic phases in permanentmagnet materials.

Further, a magnet may include regions of magnetic phases with considerably weakermagnetic properties in comparison with the expected hard magnetic phase [47]–[51].These regions can be located either in the PM volume or on the surface of the magnet[47], [48], [52]. The volumetric defects can originate from formation of some magneticphases and local imperfections in the production of the PM [47], [48], [53]. The grainswith a reduced coercivity on the surface are mostly an adverse effect of the machiningproduction step [12], [52], [54].

A schematic comparison of the ideal and real hysteresis behavior of PMs is provided inFig. 1. The main JH curve of an ideal magnet (dashed line) has µr = 1 and remains inparallel with the H-axis within the 1st and the 2nd quadrants of the intrinsic JH plane upto the normal coercivity of the main hard magnetic phase HcJ,1. This region of an initiallyfully polarized magnet is called linear region. If the external demagnetizing field exceedsHcJ,1, the PM loses its polarization irreversibly. The value of µr for a typical PM is slightlyhigher than unity. This indicates at least a possibility of some hysteresis behavior of themain hard magnetic phase and results in some angle between the H-axis and the part ofthe PM main JH curve within the linear region. The magnetic phases with smallercoercivities (HcJ,2 and HcJ,3) compared with the expected main magnetic phase may bepresent on the surface and in the inner volume of the magnet. The resulting main JH curveof the PM within the linear region (solid black line) may have a considerable polarizationdecrease near the J-axis. The magnetic phases with reduced coercivities are able to formhysteresis loops in the linear region of the JH plane of the magnet under variation in theexternal magnetic field strength. The hysteresis loop (hatched region) may include aconsiderable amount of energy if the variation in the external magnetic field strength His able to modulate the PM operating point from the 2nd to the 1st quadrant and back.

15

Figure 1: Idealized and actual hysteresis behavior of a PM.

Regions with a reduced coercivity are able to form hysteresis loops under time-periodicvariation in the magnetic flux in the PMs used in an electrical machine under unfortunateoperating conditions [46]. Fluctuation in the flux density of the magnets in a synchronouselectrical machine during operation is caused by space harmonics that are not insynchronism with the fundamental of the armature reaction field. These harmonicsoriginate mostly from the spatial distribution of the armature reaction field caused by thecurrent fundamental [13], [35], slotting effect [55], [56], tooth tip flux leakage, and localtooth saturation [57], [58]. The resulting magnetic field variation in the PM can magnetizeand demagnetize the magnet regions with a reduced coercivity and thereby modulate thetime periodic hysteresis loops that contain a considerable amount of energy. Thehysteresis loss produced by the main magnetic phase and the regions with considerablyweaker magnetic properties of the magnet are usually excluded from the conventionalloss analysis of PM electrical machines.

1.1 Previous work

Several studies have been completed before this work on the hysteresis loss phenomenonin the PM magnetic poles of electrical machines. The study in [59] used a magneticallyshorted system to measure losses in the neodymium iron boron (NdFeB) PM. Thehysteresis loss and eddy current loss were estimated from the total measured loss by atwo-frequency method. The determined hysteresis loss was converted into a function ofelectrical frequency and maximum flux density. Then, this hysteresis loss dependencewas applied in the postprocessing of the Finite Element Analysis (FEA), where the fluxvariation in the PMs was estimated in an actual machine. The calculated hysteresis lossexceeded the eddy current loss by about 100% when the machine was running at the 50Hz frequency.

1 Introduction16

The procedure applied in [59] is somewhat questionable from an electrical machinedesigner’s point of view. The magnetically closed measurement circuit of the PM aloneis not a valid condition for a permanent magnet material in PM electrical machines asthey have an air gap in their magnetic circuit. In addition, there is often a negativearmature reaction present that opposes the magnetization of the PM and furtherdemagnetizes the magnets. The air gap is seen as a considerable demagnetizing fieldacting on the magnet, and thus, the operating point of a magnet shifts to the secondquadrant of the BH plane. The possible time-periodic modulation of the magnetic field inthe PM becomes nonsymmetric with respect to the B axis of the BH plane. Moreover, thehysteresis phenomenon implies a history-dependent magnetic behavior of a material, thatis, the area of the recoil loop is significantly affected by the previous magnetic states ofthe system. Therefore, the hysteresis loss in every part of the PM pole cannot only becharacterized by the maximum flux density that was obtained in a closed magnetic circuit.

The study of [54] used a closed circuit and measurement procedure like the ones used in[59] to estimate the total loss in two NdFeB PM grades. A considerable proportion of themeasured loss cannot be explained by the classical eddy current loss theory. Thepermagraph (Magnet-Physik C-300) with a closed magnetic circuit measured thehysteresis behavior of two bulk samples. The considerable polarization decrease near theJ-axis clearly demonstrates the presence of different magnetic phases with significantlydifferent magnetic properties. The phases with a smaller coercivity are associated withthe damaged grains on the surfaces of the samples. This claim is supported by the Kerrmicroscopy surface images (Evico magnetics GmbH) for both samples in the remanentstate of initially fully polarized PM samples. The measurements were provided after theapplication of a DC demagnetizing field with a magnitude that is far from the nominalintrinsic coercive force HcJ of the studied grades; in other words, the magnets were notexposed to any notable irreversible demagnetization. The images, however, clearlyindicate the partial irreversible demagnetization of the surface grains, thereby supportingthe idea of the surface origin of the hysteresis loss in NdFeB magnets. The importantresults in [54] are the measured total loss under simultaneously applied sinusoidalalternating current (AC) and demagnetizing direct current (DC) magnetic fields. Theapplied DC field was used to simulate the operating conditions similar to those in theactual machine, which had an air gap and demagnetizing armature reaction. The measuredloss under the simultaneously applied demagnetizing DC field and the AC field show asmall difference compared with the eddy-current-loss-theory-calculated loss. Theobtained result clearly indicates the minor contribution of the hysteresis loss to the totalPM loss if the operating point of the magnet remains in the second quadrant of theintrinsic BH plane of the magnet. Nevertheless, the measured data in [54] onlydemonstrate the common trend for hysteresis loss in a PM material. Exact calculation ofthe hysteresis loss in PMs of actual electrical machines was not provided.

The magnetic properties of small sintered NdFeB magnets were studied in [52]. Thesurface-to-volume ratio S/V of the samples was varied within 5–36 mm-1. It was reportedthat the magnetic phases with a reduced coercivity were located on the surface of thesample. The thickness of the damaged layer was estimated in the range of the mean grain

17

size. Coating with powders and further heat treatment of samples at temperatures higherthan the melting point of the Nd-rich phase resulted in a considerable reduction in themagnetic phases with a reduced coercivity. The total hysteresis behavior of the treatedbulk sample still included a notable contribution of the magnetic phases with a smallercoercivity, in other words, it was shown that no PM sample consists of a uniform magneticphase.

The parameter S/V can be useful to estimate the approximate volume of the surface-located regions with a reduced coercivity. The typical grain size for sintered RE PMs isreported to be in the range of 5–15 µm [52]. Assuming that only one surface layer isaffected by the cutting procedure, the approximate volumetric proportions of the regionswith a reduced coercivity in the studied samples in [52] were within 2.5–7.5% and 18–54% for the samples with S/V = 5 mm-1 and S/V = 36 mm-1, respectively. The larger PMshave a smaller S/V ratio. The results indicate that RE-based PM machine designs withthin magnets may have a notable proportion of magnetic phases with a reduced coercivity.In addition, the segmentation of RE PMs is a conventional way to reduce the possibleeddy-current-based loss in RE-based materials [35], [60]–[64]. Thus, the segmentedmagnetic pole of an electrical machine may have a higher hysteresis loss as a result of thecutting procedure, which produces a layer of damaged grains on the surface of PMs.

The behavior of the magnetic phases was studied in [53] for two NdFeB samples withmarkedly different magnetic properties. The hysteresis behavior measured by theVibrating Sample Magnetometer (VSM) revealed two types of magnetic phases with areduced coercivity. The first type of magnetic phase originates from the surface defectsof bulk samples as similar magnetic phases are absent in the x-ray diffraction images (byBL01C2 of the National Synchrotron Radiation Research Center, Taiwan) of the powdersthat were used for the preparation of the bulk samples. The second type of magnetic phasemay have a coercivity in the range of 0.03–0.4 of the expected coercivity of the bulksample. The magnetic phases of the second type may originate from -Fe and FeB phasesoccurring in the production process or may even be associated with the Nd-rich phase atthe grain boundaries. The Nd-rich phase is intentionally formed at the grain boundariesto enhance the coercivity of the NdFeB PMs. Therefore, part of the magnetic phases witha lower coercivity may be located in the volume of the PM.

The study reported in [46] addresses hysteresis loss in NdFeB PMs under the operatingconditions of electrical machines. The amount of hysteresis loss was not properlyassessed owing to the limited measurement data available. Nevertheless, the studyprovides discussion about the PM electrical machine design topologies that may be proneto hysteresis loss in a PM material. Another contribution of [46] is the Permagraphmeasurements (C-300 by Magnet-Physik), which clearly demonstrate the inapplicabilityof this measurement tool for studies of the hysteresis behavior of RE-based PMs; eddycurrents in the bulk PM material heavily corrupt the measurement output. The VSMmeasurement system (by Quantum design), however, showed a better ability to observethe magnetic behavior of hard magnetic materials with a low electrical resistivity, eventhough the measurement results were not treated appropriately.

1 Introduction18

At the time this doctoral dissertation started there was a clear contradiction between theexisting engineering practice and studies published. A convenient design procedure of anelectrical machine with PMs only included eddy-current-theory loss estimation in the PMmaterial, whereas the studies available reported a notable contribution of hysteresis lossin the total loss of a magnet [46], [54], [59]. There was no established practice of VSM-based measurements of high coercivity PMs with correct postprocessing of results interms of electrical machinery. Before this study, the hysteresis loss in PMs of electricalmachines has not been assessed with a reasonable accuracy in real operating conditionsof the PM material in rotating electrical machinery.

1.2 Outline of the doctoral dissertation

The objective of this doctoral dissertation is to evaluate the amount of hysteresis loss ina ferrite PM material during its operation in the magnetic circuit of a PM-excited rotatingelectrical machine.

The author of this doctoral dissertation is the principal author and investigator inPublications I and III–V, and is solely responsible for the scientific contributions of thepapers and the introductory part of the dissertation. In Publication II, the author isresponsible for the basic theoretical considerations of the measurement procedure andpostprocessing of the measured data.

Publication I focuses on the factors affecting the hysteresis loss in a PM material whenit is placed in the magnetic circuit of a rotating electrical machine. The magnetic field inthe PM region is estimated by the 2D FEA tool and a slotless analytical modelingapproach. A new equation is introduced for the radial component of the armature reactionfield inside the magnetic pole of a machine. The nonsinusoidal spatial distribution of thearmature current fundamental and the modulation of the field in the PM material by theslotting effect are found to be the major factors that cause the possible hysteresis loss inthe TCW RSM PMSM configuration. The inverter current time harmonics, local toothsaturation, and tooth tip leakage flux are less significant phenomena. The publicationcomplements the analytical slotless modeling approach, which offers a fast and relativelysimple tool for the initial step of an electrical machine design.

Publication II studies the hysteresis loss in three distinct PM grades (Ferrite, SmCo, andNdFeB) relevant to the electrical machine design. It introduces a new methodologyconcept to estimate the amount of hysteresis loss in the PM magnetic pole of a PMelectrical machine. The electrical machine design topologies prone to hysteresis loss arediscussed. Finally, the approximate amount of hysteresis loss in the PM material of twoessentially different electrical machine designs is calculated by combining the magneticflux density values in the PM region estimated by the 2D FEA and the hysteresis behaviorof the magnets measured by the VSM. The efforts to reduce the hysteresis loss in somecases are discussed.

19

Publication III estimates the hysteresis loss in the ferrite PM material of the RSM TCWPMSM used in a hybrid electrical vehicle. A VSM-based measurement system is used toobserve the hysteresis behavior of a sample that was cut from the PM pole of the machine.The methodology concept from Publication II is further developed to enable accurateestimation of the PM hysteresis behavior. A new equation is introduced for the history-dependent hysteresis model (HDHM) to enable accurate simulation of the ferrite PMmaterial, and other possible modeling options are also discussed. The reptation(accommodation) phenomenon is demonstrated for the ferrite PM material. The VSMmeasurements do not demonstrate a significant presence of magnetic phases with areduced coercivity in the studied sample. The calculated losses in the PM material arefound to be negligible under the operating conditions of the observed electrical machinedesign both for pure sinusoidal and frequency converter supplies. The paper provides auseful insight into advanced modeling of a PM material in rotating electrical machinery.The results are in perfect agreement with the prevailing engineering practice, where thehysteresis loss in a hard magnetic material is neglected if the magnet operates in the linearpart of the main BH demagnetization curve.

Publication IV extends the studies of hysteresis loss for three distinct commerciallyavailable ferrite PM grades, which are stock materials from a Chinese manufacturer. TheVSM measurements reveal a considerable presence of magnetic phases with a reducedcoercivity for all three samples under study. The hysteresis loss estimation is based onthe same methodology as in Publication III; however, a new modeling technique isintroduced to simulate the hysteresis behavior of the ferrite PM in rotating electricalmachinery when the bulk ferrite magnet manifests a simultaneous presence of magneticphases with significantly different magnetic properties. The proposed modeling principleis successfully verified by a total of six independent measurements. The hysteresis loss iscalculated for the RSM TCW PMSM topology used in Publication I, Publication II, andPublication III, and for the axial flux TCW PMSM design. The results clearly show aconsiderable contribution of the magnetic phases with a reduced coercivity to the totalhysteresis loss in the PM material, even though these losses are small in practice. Thecalculated hysteresis loss map clearly indicates that the amount of hysteresis loss in theferrite PM material can be considerable in unfortunate operating conditions.

Publication V addresses the linear-recoil-curve (LRC) modeling concept for the FEAsimulation of ferrite PMs in rotating electrical machinery. The LRC-concept-basedmodels in the present-day FEA software available for electrical machine design arediscussed. A new procedure is introduced for VSM-based measurements of the PMhysteresis behavior in the 2nd and 3rd quadrants of the intrinsic BH plane. The studies onthe general accuracy of the LRC concept provide a useful insight into the possible FEAcomputation error, which may result from an inappropriate choice of the model.

Chapter 1: The research topic and its practical importance are addressed in brief. Previousstudies are analyzed.

Chapter 2: The main findings and contributions of Publications I–V are presented in short.

1 Introduction20

Chapter 3: Conclusions are discussed and suggestions for future work are provided.

1.3 Scientific contribution

This doctoral dissertation investigates the amount of hysteresis loss in ferrite PMmaterials used in rotating electrical machinery. The scientific contributions of thedissertation are summarized as:

New analytical equation for the armature reaction field is introduced to the slotlessmodeling concept. The equation is able to estimate the radial magnetic fluxdensity component both in the air gap and magnet region of the machine. Theproposed equation simplifies the estimation of the magnetic field in the magnetsof radial-flux electrical machines and makes the slotless modeling concept moreappropriate for the study of the hysteresis loss phenomenon in magnets used inrotor-surface-magnet electrical machines. A similar equation for armaturereaction field can be derived for axial flux PMSMs.Methodology for the VSM-based measurements of PM intrinsic magneticproperties is established. The VSM measurement system enables high-precisionmeasurements of magnets with a high coercivity.The HDHM concept is developed further to enable the simulation of the hysteresisbehavior of ferrite magnets. The proposed new equation for the reversal curves isable to simulate with fair accuracy the ferrite PM material consisting of onemagnetic phase.A new concept is introduced to simulate the hysteresis behavior of ferrite PMs inthe region relevant to electrical machine design. The concept is able to simulatethe hysteresis response of the ferrite PM sample, which consists of multiplemagnetic phases with markedly different magnetic properties.The hysteresis losses are estimated in four distinct ferrite PM grades in conditionsrelevant to the actual use of the material in rotating electrical machinery.The proposed VSM-based measurement methodology enables detailed, accuratestudies of the LRC concept for the simulation of PMs in rotating electricalmachinery. The results clearly show that the LRC principle offers a simple andpowerful tool for FEA simulation in rotating electrical machinery, which,however, can be a source of considerable error in some cases.

21

2 PublicationsThis chapter provides an overview of the three journal and two conference papers.

2.1 Publication I

The phenomena affecting the hysteresis loss in the PM material of a PM electricalmachine are discussed in Publication I. A 50 kW ferrite PM synchronous machine withan external rotor topology, rotor-surface-magnets, and tooth coil winding configuration[65] is used as the study case. A sketch of the machine is depicted in Fig. 2. Theparameters and dimensions of the observed RSM TCW PMSM are provided inPublication I. The chosen electrical machine design can be exposed to large PM hysteresisloss because of the rotor-surface-mounted magnets, a high amount of permeanceharmonics caused by the current linkage spatial distribution, and relatively large slotopenings. The slotless analytical model [66]–[70] is refined for the task. The slotlessapproach is a reasonable compromise in terms of accuracy, implementation complexity,and calculation time compared with other possible analytical options, such as themagnetic equivalent circuit (MEC) method [71]–[75] and subdomain models [76]–[78].The field of a single coil is derived by a solution of the Laplacian equation in the air-gapregion. A new formulation for the armature reaction field for the slotless modelingconcept is presented. The derived analytical equation only needs the main parameters ofthe winding and the time-dependent values of the phase currents. On the contrary, theoriginal expression of the armature reaction field [67] requires a spectrum analysis of thephase current and winding-specific harmonics.

Figure 2: 2D sketch of the RSM TCW PMSM with the external rotor used in the study.

The analysis of the field distributions in the magnet region reveals that the nonsinusoidalarmature reaction spatial field distribution of the stator current linkage and the slottingeffect have the highest effect on the modulation of the PM operating point in the normal

2 Publications22

operating mode. The tooth saturation phenomenon cannot be taken into account by usingan analytical approach owing to the assumption of the constant relative permeability µrof steel. This contributes to the total error between the analytical and FEA calculation ofthe magnetic field in the PM region. The results calculated by the FEA show that toothsaturation may cause an additional fluctuation of the PM operating point and therebyincrease the total hysteresis loss. The influence of the inverter-caused current harmonicson the modulation of the PM operating point is found to be negligible.

The slotless modeling concept applies an idealized geometry of the slot, which neglectsthe tooth tip flux leakage. This contributes to a difference between the FEA and theanalytical results. Nevertheless, an analytical approach can be accurate enough toevaluate the possibility of hysteresis loss in PMs in the initial design stage of an electricalmachine. The presented analytical solution of the armature reaction field can be extendedto other winding configurations for electrical machines with internal, external, or axial-flux rotor topologies.

A comparison of the magnetic flux density distributions calculated by the FEA andsimulated by the model is depicted in Fig. 3 at the surface of the magnetic pole close tothe air-gap region. The modulation of the flux density by the discussed phenomena ishighest at the surface of the magnetic pole close to the air gap, and it is mitigatedconsiderably inside the magnet. Further details can be found in Publication I.

(a) (b)

Figure 3: Magnetic flux density on the surface of the magnetic pole of the machine close to theair gap: (a) FEA results, (b) model results. 1 – effect of slot opening, 2 – tooth saturation effect,3 – effect of tooth tip leakage flux, and 4 – effect of the current time harmonics caused by thenonsinusoidal converter supply. The analytical approach neglects the effects of the tooth tipleakage flux and the local tooth saturation. The studied electrical machine has ferrite PMs (BM9grade) with the remanence Br = 0.34 T and the relative permeability r = 1.26. The value of r

used in the FEA model is not supported by the experimental data from Publication III, where r 1.04 is calculated for a ferrite PM sample of BM9 grade at 83°C. This does not affect theconclusions in Publication I.

2.2 Publication II 23

2.2 Publication II

Three distinct PMs (NdFeB, SmCo and Ferrite) are studied for the possible hysteresis lossin Publication II. The test installation consists of a Physical-Properties-MeasurementSystem with up to 14 Tesla superconducting magnets by Quantum Design with a P525VSM option and a data collection system. The sensitivity of the measurement systemenables the detection of magnetization changes less than 10-6 emu at the data rate of 1 Hz.The measurement temperature can be set in the range of 1.9–350 K. The AC frequencyrange and the AC amplitude range are 10–10000 Hz and 2 × 10-3–15 Oe, respectively[79]. The magnetic field variation is programmed in compliance with the requiredmeasurement sequence. VSM measurements clearly indicate the contribution of differentmagnetic phases with a reduced coercivity to the total magnetic behavior of the sampleswhen the operating region of the magnet along its BH plane is relevant to the electricalmachine design. The amount of hysteresis loss in two essentially different machinedesigns is approximately estimated by several measured hysteresis loops, and themagnetic field distribution in the magnet region of the electrical machines is calculatedby the 2D FEA. The first machine design is represented by an RSM TCW permanentmagnet synchronous machine (PMSM) with an external rotor topology [65]. The PM polein such a design can be exposed to a significant variation in the magnetic field. Thevariation in the magnetic field is mostly caused by the highly nonsinusoidal armaturereaction field of the stator current linkage distribution and the slotting effect, as discussedin Publication I. The second machine design is a PM motor with a low number of poles.In such a design, the combination of the armature reaction field and the slotting effect canproduce considerable magnetic field strength variation in some regions of the magnet.The calculated hysteresis loss in the PM poles of the studied electrical machine designsis estimated to be up to 1.4% and 1.1% of the nominal efficiency of the motor for theRSM TCW PMSM and the low pole number PMSM, respectively.

The publication includes some misunderstandings, which are further explained inPublications III–V. In the study, the measurement temperature was set to 23°C, whichgenerally does not correspond to the actual thermal operating range of a PM material inrotating electrical machinery. The magnetic properties of the PMs are significantlyaffected by the temperature. The operating temperature in an electrical machine can benotably higher as a result of the losses generated in other parts of the machine and thecooling method. The measurement temperature was set to 80–83°C in Publications III–V, which is a reasonable thermal design consideration for some type of PMSM [2], [65],[80].

The open magnetic circuit measurement system of the VSM provides numerousadvantages over other options available (i.e., hysteresisgraph, pulsed field magnetometer,permagraph) [81], [82] when very accurate measurements of high coercivity materials areneeded. The system provides an opportunity of long-time measurements with apredefined temperature in high magnetic fields. The low speed of the field changemitigates eddy currents in the bulk material of the sample. The measurement data are notdistorted by eddy currents and hysteresis in the magnetic yoke of the measurement system

2 Publications24

[46]. The adverse effect of the open magnetic circuit measurement system is the highdemagnetizing field acting on the sample. Fig. 4 shows the field inside the magnet whenit is placed in an open and closed magnetic circuit. The VSM results represent polarizationversus applied field, where the applied field has to be corrected to the intrinsic field ofthe sample by the demagnetizing field. The inappropriate correction of the measuredresults by the demagnetizing field in this publication result in an overestimated totalhysteresis loss because the measured recoil loops are shifted to the second quadrant of theBH plane. The resulting hysteresis loss in the magnetic poles of the machine design understudy is calculated based on the maximum values of the magnetic flux density during theslot period, which leads to neglecting the additional field flux density variation caused bythe tooth saturation phenomenon. The measurement procedure and the loss calculationtechnique are further developed in Publications III–V.

(a) (b) (c)

Figure 4: Field inside a magnet. a) Closed magnetic circuit. The applied magnetic field strengthHa is in the direction of the polarization J. There is no demagnetizing field Hd occurring in themagnetic circuit without an air gap. The intrinsic magnetic field strength inside the magnet Hi isthe same as the applied field strength Ha. b) Magnetic circuit with an air gap; no external field isapplied. A demagnetizing field Hd occurs in the magnet, which is placed in the magnetic circuitwith an air gap. A demagnetizing field is directed opposite to J and always tries to demagnetizethe magnet. The field inside the magnet Hi is the same as the demagnetizing field Hd. c) Magneticcircuit with an air gap and Ha applied against the polarization direction. The field inside themagnet is the vector sum of Ha and Hd.

2.3 Publication III

In Publication III, the hysteresis loss is assessed in the magnetic poles of the RSM PMSMwith an external rotor topology and a TCW configuration [65]. The machine designtopology is the same as in Publication I and Publication II. The hysteresis behavior of thestudied sample is measured by the VSM at the temperature of 83°C. The VSM results areappropriately corrected by an analytically calculated magnetometric demagnetizing factor[83]. The hysteresis behavior of the studied sample is simulated by the History-Dependent

2.3 Publication III 25

Hysteresis Model (HDHM) concept [84] with a newly introduced equation for thehysteresis behavior of reversal curves.

The HDHM concept is not the only option to simulate the problem under study. There arenumerous hysteresis models available; another possible solution can apply for instancePreisach-type models [80], [85], general Positive-Feedback theory [86], [87], Magneto-Static Modeling Approach [88], Stop and Play models [89], [90], and others [87], [91].The choice of the HDHM concept is based on its implementation simplicity and flexibilitycompared with other options. A detailed literature review of suitable hysteresis modelingapproaches is provided in this publication.

The reptation (accommodation) phenomenon may affect the choice of the analyticalapproach used to simulate the hysteresis behavior of the material. Many hysteresis-modeling concepts available include implicitly or explicitly the return point memory ofreversal curves [22], [31], [36], [37], [50], [80], [82], [85]–[87], [89]–[92]. A detaileddiscussion can be found in this publication. The reptation (accommodation) phenomenonin ferrite magnets is demonstrated by measurements and discussed.

The measured data do not demonstrate hysteresis behavior similar to that reported inPublication II for the ferrite PM sample of the same BM9 grade. Instead, the hysteresisbehavior of the sample correspond to a magnet consisting primarily of a uniform hardmagnetic phase. The measured and calculated hysteresis loops are in good agreement.Fig. 5 depicts a comparison of the measured and the model-simulated reversal curves nearthe J-axis of the initially fully polarized PM. The total hysteresis loss in the magneticpoles of the studied electrical machine design is estimated by applying a

Figure 5: Comparison of the measured (solid lines) and model-simulated (circles) hysteresisbehavior of the PM (BM9 grade) at 83°C. The main JH curve of the initially fully polarized PM(solid-dot line) does not demonstrate a significant polarization decrease near the J-axis.

2 Publications26

combination of the commercial FEA tool Flux by Altair/CEDRAT and the HDHManalytical approach with the proposed equation for the reversal curves. The magnetic fieldvariation in each elemental volume of the magnetic pole of the machine calculated by the2D FEA is used as the input data for the HDHM. The hysteresis loss is determined to be0.0082% and 0.0084% of the machine nominal power for pure sinusoidal and frequencyconverter supplies, respectively. The results clearly indicate the relevance of theprevailing engineering practice to assess the loss in ferrite PMs if no magnetic phaseswith a reduced coercivity are present in the volume and at the surface of the ferrite PMmaterial.

2.4 Publication IV

The data measured by the VSM for the two distinct ferrite PMs from the same batchexhibit markedly different hysteresis behavior of the recoil curves, as it can be seen inPublications II and III. The PM sample in Publication II displays a knee in the hysteresisloops in low demagnetizing fields while the sample in Publication III shows an expectedhysteresis behavior of the bulk magnet with a homogeneous hard magnetic phase. In thispublication, the hysteresis behavior of three distinct commercially available ferrite PMgrades is studied. The batches are from a Chinese manufacturer. According to theproducer, the magnets were produced by a hydrothermal synthesis method. The VSMmeasurement data show a considerable polarization decrease near the J-axis for all thesamples under study, which indicates the presence of magnetic phases with a reducedcoercivity in the bulk sample material.

Studies available on the topic report on possible formation of iron oxide -Fe2O3 [47] andbarium oxide BaFe2O4 [48] as unwanted magnetic phases if the hydrothermal synthesismethod is used in the production of ferrite magnets. The coercivities of the undesirablemagnetic phases are considerably lower compared with the expected BaFe12O19 magneticphase of the hexagonal M-type ferrite PM. The measurement results from other studies[49], [51], [93] indicate that the coercivities of the magnetic phases with weaker magneticproperties can be in the range of knees observed in the samples. A detailed literaturereview is provided in this publication. The common electrical machine design practice isto use thick ferrite magnets in the PMSM magnetic poles because of the relatively weakmagnetic properties of this material compared with RE PMs. Therefore, it is assumed thatthe measured hysteresis behavior of the samples can be treated as a response of a bulksample that has evenly distributed volume regions with considerably weaker magneticproperties.

The measured hysteresis behavior of the samples is caused by a simultaneous contributionof numerous different magnetic phases in the volume of the sample. Available hysteresismodels are used to simulate the regions consisting of one magnetic phase, and cannot thusbe applied to the problem under study without modification. The newly introducedprocedure is used to reproduce the hysteresis behavior of the samples by a simultaneouscontribution of ‘soft’ and ‘hard’ magnetic phases. According to the standard No. 0100-

2.4 Publication IV 27

00 from the Magnetic Materials Producer Association, a magnetically hard material hasa coercivity higher than 120 Oersteds (9550 A/m) [94]; the ‘soft’ artificial magnetic phaseis hard by nature, and it is called ‘soft’ just because of the presence of the magnetic phasewith a considerably higher coercivity (which is referred to as a ‘hard’ magnetic phase).The introduced separation technique is not the only option available; the generalrequirement for the resulting main hysteresis loops is the absence of the nonphysicalbehavior, that is, J/ H > 0 must be true always. The model parameter identificationprocedure is performed simultaneously for both the artificial ‘hard’ and ‘soft’ magneticphases. The hysteresis behavior simulated by the model shows a very good agreementwith the experimentally obtained data for all three samples under study (a total of ninedistinct measurement sequences). Fig. 6 depicts the example comparison of the measuredand model-simulated hysteresis behavior of the PMs close to the J-axis of the initiallyfully polarized magnets.

Figure 6: Measured and model-simulated hysteresis behavior of the samples under study.

The hysteresis loss in the magnetic poles of two different electrical machine designs arestudied. The procedure is similar to the one used in Publication III. The values of themagnetic field strength calculated by the 2D FEA are used as the input data for theproposed hysteresis modeling approach. First, an electrical machine design with an

2 Publications28

external rotor topology and a TCW configuration is investigated. The estimated hysteresisloss is significantly higher compared with the original design with the BM9 grade inPublication III; nevertheless, the proportion of the loss does not exceed 0.056% of thenominal power of the machine. The second design is a 100 kW 1500 rpm axial fluxPMSM introduced in [35]. The original design of the motor with NdFeB magnets hadaround 15 kW of eddy current loss in the PM material. The eddy current loss is reducedby placing laminated iron stacks on top of the RE PMs, which are close to the air gap.Application of ferrite PMs does not require similar design efforts because of the highelectrical resistivity [11]. The original design [35] is updated for the study case: 1) theiron laminated stack is removed, 2) the RE PMs are substituted by the ferrite PM gradesunder study, and 3) the armature reaction field is reduced to avoid irreversibledemagnetization of the ferrite PMs. The analysis shows that the hysteresis loss in themagnetic pole of the machine is about 0.3% of the nominal power.

Another important contribution of this publication is the map of the energy stored in thehysteresis loops. Fig. 7 depicts the hysteresis loss map for the Y32H-2 grade at 80°C asan example. The calculated data demonstrate a small hysteresis loss if the operating pointof PM is located in the second quadrant of the intrinsic BH plane of the magnet, which isthe usual region of PM operation is rotating electrical machinery. The result is inagreement with the studies for the NdFeB magnet in [54]. There, the results were obtainedby a magnetically closed measurement system and a two-frequency method. The resultsin Publication IV and in [54] clearly show that hysteresis loss does not play a significantrole if the operating point of the magnet does not cross the B axis during the operationand remains in the region of the main BH demagnetization curve in the 2nd quadrant ofthe BH plane, where no irreversible demagnetization of the magnet is assumed. However,the contribution of the hysteresis loss in the total loss of a magnet can be notable if themagnetic field strength is able to modulate the PM operating point within the 2nd and the1st quadrant of the intrinsic BH plane of the magnet. The exact amount of hysteresis lossin the RE-based PM magnetic poles of an electrical machine has not been properlyassessed, and thus remains to be studied in more detail in further studies.

2.5 Publication V

The PM material used in the magnetic circuit of an electrical machine can be irreversiblydemagnetized under high negative magnetic field strengths [2]. The irreversibledemagnetization of a PM magnetic pole can be a result of anomalous operating conditions[95]–[100] or an inappropriate cooling method [101]–[106]. The usual design procedureof the electrical machine with a PM material includes assessment of the PM irreversibledemagnetization. At the present time, an electrical machine design procedure often relieson FEA software, where various implementations of the Linear Recoil Curve (LRC)modeling concept are mostly used. Examples include Flux by CEDRAT/Altair [37],ANSYS Maxwell [31], COMSOL Multiphysics [36], and JMAG [22]. The studies in [36],[50], [82], [92] assume that the LRC-based demagnetization models provide a fairassessment of irreversible PM demagnetization if model-simulated and measured main

2.5 Publication V 29

Figure 7: Energy density [J/m3] stored in the hysteresis loop of the PM sample (Y32H-2 grade)studied when the internal magnetic field varies between Hmin and Hmax. The magnet is initiallyfully polarized. The measurement temperature is 80°C. The percentage values show a comparisonof the measured and model-simulated recoil loops where available. The difference is small in therelevant areas.

demagnetization curves are in good agreement. However, possible sources of inaccuracyof the LRC concept itself are usually out of consideration. At the same time, recent studiesof partial PM demagnetization report a significant difference between measured andFEA-simulated PM partial demagnetization both for electrical machine design [50],[107], [108] and general studies of irreversible demagnetization of the magnet [36],[109], [110].

Publication V provides an insight into the possible FEA computation error that originatesfrom the assumptions in the LRC concept itself. The proposed measurement algorithmenables VSM measurement of the minor loops within the 2nd and 3rd quadrant of theintrinsic magnet BH plane, which are the most interesting ones for an electrical machinedesigner. Fig. 8 demonstrates the principle of the proposed measurement procedure. Fig.

2 Publications30

9 provides a comparison of the studied LRC-based models in terms of accuracy. Themeasured data of the Y28H-2 ferrite PM grade at 80°C are used in the case study. TheNormalized Root Mean Square Deviation (NRMSD) is chosen as an adequatequantitative tool to compare the accuracy of the models [50], [91]. The comparison of themeasured and simulated macroscopic hysteresis behavior for the Y28H-2 ferrite PM

Figure 8: Principle of the measurement procedure applied in the study. The intrinsic recoil loopsA´ – B´ – A´ and C´ – D´ – C´ (dashed lines) in the 2nd and 3rd quadrants can be obtained from therespective VSM measured curves A – B – A and C – D – C (dash-dotted lines). The points B andD where the VSM field reverses are determined in real time with Ha Nm × J / 0. The value ofNm is calculated analytically assuming r = 1.

Figure 9: NRMSDs for the LRC-based demagnetization models under study (Y28H-2 grade at80°C). The figure differs from the version in Publication V. The error in Publication V is correctedhere.

2.5 Publication V 31

grade indicates that a universal LRC-based formulation does not exist. The linear slopedexponential and hyperbolic tangent function models show a comparable accuracy in thelinear region of the BH curve of the magnet in the 2nd quadrant. The linear sloped andexponential model have a better accuracy at the beginning of the knee region; however,at lower negative field strengths the error of these models becomes unacceptable. Thehyperbolic tangent function model manifests less erroneous results in the demagnetizingfields below the coercivity Hc of the magnet and should be preferred in thedemagnetization analysis after severe faults.

The spline-based models have the best accuracy compared with the previously discussedoptions, as the analytical and measured main demagnetization BH curves match exactly.Linear sloped, exponential and tangent function models can be easily made astemperature-dependent models based on a small number of coefficients. The spline-basedformulation of the LRC approach requires more memory space because the data for theBH curve at each temperature should be tabulated.

2 Publications32

3.1 Conclusions 33

3 Conclusions and future work

3.1 Conclusions

This doctoral dissertation investigated the hysteresis behavior of some commerciallyavailable PM grades for electrical machine design. The regions of phases with a reducedcoercivity were found to be an additional source of losses in a PM material under theoperating conditions of PM-excited electrical machines. The PMSM configurations withthe TCW topology and the RSM PM rotor structure were of the highest interest. The PMmaterials in such designs were exposed to a considerable variation in permeanceharmonics penetrating through the magnets. The estimated PM hysteresis loss in ferritePM-excited PMSMs did not significantly contribute to the total loss of the machine.Nevertheless, PM hysteresis loss represented a source of additional loss in a PM material.

The hysteresis loss may lead to an elevated temperature of a PM magnetic pole, whichmay change its magnetic properties. The amount of hysteresis loss in a ferrite PMmaterial may be high in unfortunate operating conditions, for instance, when the externalfield strength is able to modulate the magnetic state of the initially fully polarized magnetwithin the 2nd and the 1st quadrants of the BH plane with high enough positive values ofthe magnetic field strength. Such operating conditions are not the case for ferrite PM-excited PMSMs because of the presence of an air gap and the general designconsiderations to avoid partial irreversible demagnetization of PMs in the normaloperating mode.

The results of the research contribute to the hysteresis modeling theory and themeasurement methodology of hard magnetic materials. The introduced theory enables theHDHM concept to be used to simulate the hysteresis behavior of ferrite PMs consistingeither of one uniform or numerous markedly different magnetic phases in the regionrelevant to electrical machine design. The modeling theory can be adopted to otherhysteresis concepts that incorporate the return point memory property of reversal curves.The established VSM-based measurement methodology allows highly accuratemeasurements of high coercivity PM materials. The measurement data can be applied tothe further development of PM simulation approaches in electrical machine design.

A practical problem related to this work and the usage of permanent magnet materials inthe design of electrical machines is that the PM material to be used should be exactlymeasured a priori to model its hysteresis behavior. The difficulty can be seen whencomparing the results of Publications II and III. In principle, the same material displayeddifferent hysteresis behaviors in different measurement sessions. Obviously, the samplein Publication II had suffered from some kind of damage for instance when preparing thesample for the tests.

A general guideline to mitigate permanent magnet hysteresis losses in electrical machinesis to design the machine so that its permanent magnets always operate in the second

3 Conclusions and future work34

quadrant of the BH curve. Crossing the B-axis can be dangerous and cause significanthysteresis losses in PMs.

3.2 Suggestions for future work

The amount of hysteresis loss in RE PMs has not been assessed with a similar accuracyas it was done in the case of ferrite PMs. At the same time, the physical and geometricalproperties of RE-based magnets used in electrical machine design may result inconsiderably higher hysteresis losses compared with those of ferrite PM materials. Theintroduced modeling theory can also be extended to RE PM materials, which will providea relatively accurate analytical tool to estimate the amount of hysteresis loss in RE-basedPM magnetic poles of PM electrical machines. LRC-based models are widely used forthe simulation of RE-based PMs in electrical machinery. A study on the accuracy andlimitations of the LRC modeling concept can also be provided for RE PM materials,which are relevant to the electrical machine design.

35

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Publication I

Egorov, D., Uzhegov, N., Petrov, I., and Pyrhönen, J.Factors affecting hysteresis loss risk in rotor-surface-magnet PMSMs

Reprinted with permission fromXXII International Conference on Electrical Machines (ICEM)

pp. 1735–1741, 2016© 2016, IEEE Conferences

Abstract -- In early papers about Permanent Magnet Synchronous Machines (PMSMs) it was often stated that there are no rotor losses in PMSMs. Later, eddy current analyses for sintered permanent magnets (PMs) have been dominating the rotor loss analyses. However, in some designs also hysteresis losses can be possible in PMs. This paper uses 2D Finite Element Method (FEM) program and 2D slotless analytical model to show the main factors affecting the hysteresis loss emergence and the applicability limitations of the existing analytical approaches in evaluating the hysteresis loss. A Tooth Coil Winding PMSM prototype with external rotor topology is used in the analysis as a reference.

Index Terms--Hysteresis loss risk, permanent magnet losses, rotor-surface-magnet permanent magnet machines.

I. NOMENCLATURE Br Remanent flux density of permanent magnet, [T] b0 Stator slot opening, [m] rs Stator outer radius, [m] rr Rotor inner radius, [m] rm Permanent magnet inner radius, [m] m Number of phases n Rotational speed, [rpm] p Number of pole pairs Qs Number of stator slots N Number of series turns in the coil

PM Relative permanent magnet width ef Effective airgap, [m] μ0 Permeability of vacuum, 4 × 10 7 [H/m] μr Relative permeability of permanent magnet

II. INTRODUCTION

HE ability of PMs to provide excitation without an external source of energy allows avoiding Joule losses

in the excitation winding and, thus, increasing the efficiency of permanent magnet synchronous machines (PMSM) compared to the efficiencies of other machine types of similar power [1]. PMSMs are widely utilized in the industry [1], in wind power generation [2], in electrical vehicles [3]-[4], in marine propulsion, and in elevator drives [5].

Eddy current losses have been considered as the main source of losses in PMs during the normal operational mode of PMSMs. Eddy current loss models and analytical calculation of this phenomenon are widely discussed in research papers. Approaches for the eddy current loss calculation can be found, for example, in [6]-[8].

Papers [9], [10] state that in some cases a hysteresis loss is possible in PM material. The hysteresis loss mechanism is

D. Egorov, N. Uzhegov, I. Petrov and J. Pyrhönen are with the Department of Electrical Engineering, Lappeenranta University of Technology, FI-53851 Finland (e-mails: dmitry.egorov@lut.fi, nikita.uzhegov@lut.fi, ilya.petrov@lut.fi, juha.pyrhonen@lut.fi).

based on the hysteresis theory that is, in principle, the base theory for the PM materials. Structural defects in PM material can be considered as areas with soft magnetic properties. The presence of “soft” phases enables hysteresis loss under unfortunate operating conditions. Fig. 1 depicts the mechanism of the hysteresis loss in a PM material.

Fig. 1. Ideal PM behavior and real main hysteresis loop of a PM. The minor hysteresis loop is caused by the presence of some soft magnetic phases in the PM structure. The hysteresis risk can be considerable if the operating point of the PM is located close to the B-axis and the external field strength ( H) can move the operating point constantly from the 2nd quadrant to the 1st quadrant and back. Due to the presence of soft magnetic phases the actual movement of the operating point will be 1-2-3 and 3-4-1 when it moves from the 2nd quadrant to the 1st and back, respectively.

Hysteresis loss becomes possible if the magnetic field strength, which is acting on the PM material, changes its sign regularly under the machine operation [10]. In practice, the operating point of the magnet can vary between the first and the second quadrant in the BH-demagnetization curve of the magnet. The data in [10] shows the significant effect of the armature reaction on the possibility of hysteresis losses emerging in a Rotor-Surface-Magnet (RSM) PMSMs even during the normal operational mode. Hysteresis loss can take place if the armature reaction is capable of driving the operating point of the magnet to the first quadrant of the BH-curve and, e.g., permeance harmonics modulate the flux density below and over the remanent flux density in some regions of the magnet. This situation is possible e.g. in PMSM applications that require high torque/power density [1], [10], [11].

Existing analytical approaches are derived based on certain assumptions that can limit the application of models in hysteresis loss risk calculation. The assumptions can include, for example, infinite permeability of iron, neglecting of PM edge leakage flux, assuming sinusoidal phase currents. The aim of the paper is to show the main factors affecting the hysteresis loss risk emergence. FEM simulations and 2-D slotless analytical model with permeance function are used for calculation of the magnetic

Factors Affecting Hysteresis Loss Risk in Rotor-Surface-Magnet PMSMs

D. Egorov, N. Uzhegov, I. Petrov and J. Pyrhönen

T

field distribution in the PM region. Results are compared to observe possible sources of inaccuracies caused by assumptions in the model.

III. METHODS

A. Existing analytical approaches The present analytical methods can be divided into 3

main categories: 1) Equivalent Circuit Method (ECM), 2) Subdomain models, 3) 2-D slotless models.

ECM was successfully used for induction motors (IM) and electrically excited machines’ analysis [12]. In PM machines this method was applied in the prediction of cogging torque, unbalanced magnetic pull and some other basic performances [13], [14]. However, the relatively large effective air gap in PMSMs compared to IMs and other electrically excited machines results in a significant error in the prediction of the magnetic field distribution inside PM [12], [15].

Subdomain models are the most accurate existing analytical approaches available nowadays if the assumption of constant iron permeability is not critical [12]. The idea of the method is to solve directly 2-D Laplace’s and Poisson’s equations in polar coordinates for each subdomain and applying boundary conditions between subdomains. These models are used for the calculation of back-EMF, electromagnetic torque, cogging torque and unbalanced magnetic pull [12]. The main disadvantages of the subdomain models are the relative complexity of implementation, longer calculation time compared to ECM and 2-D slotless models and the assumption of infinite iron permeability.

Comparative analysis of the 2-D slotless model with equivalent circuit method (ECM) [1] and 2-D subdomain approaches [12], [16], [17] show that this type of model has the best accuracy taking into account the computational resources needed for the calculation of the field distribution in PMs and has a very straightforward implementation. In contrary to the subdomain model, the 2-D slotless model represents a set of ready solutions that can be easily programmed.

This study uses the 2-D slotless analytical model initially presented in [15], [18]-[20] and further improved in [21] to take into account relative permeability of PM μr other than unity. The solution for the armature reaction field is improved to make the analysis more applicable for hysteresis loss problem. Since the observed PMSM has radially magnetized PMs, the field calculation is provided only for the radial component of the flux density. It is assumed that due to the presence of domain orientation in the PM material, only the flux density component that is aligned with the magnetization direction of the magnet can affect the hysteresis loss emergence.

The theory provided in [15], [18]-[21] allows deriving the magnetic flux density distribution in the PM region based on solving the equations of scalar magnetic potential. Laplacian equations are solved in air region to get the radial component of the magnetic flux density created by a single

conductor. Quasi-Poissonian equation is used to get the field distribution inside PM. The following assumptions are made: 1) PM permeability is constant, 2) end-effects are neglected, 3) permeability of iron is infinite.

Taking into account the assumptions above, the radial component Brad of the magnetic field distribution in the PM region can be presented as a linear problem:

1,,,,,,,,, armPMrad trtrBtrBtrB

where BPM(r, , t), Barm(r , , t) are PM and armature reaction radial flux density components, (r, , t) is permeance function describing the slotting effect. The models for calculating of each component in (1) are depicted in Fig. 2.

a) b)

c)

Fig. 2. Models used in 2-D slotless model for calculation a) no-load magnetic flux density, b) armature reaction field, c) stator slotting effect

First, no-load flux density of PM and armature reaction field are calculated assuming slotless machine. Second, slotting effect is taken into account by multiplying the no-load flux density and armature reaction field by the slot permeance function, since the slotting effect has influence on these two components [19].

This paper studies Tooth Coil Winding (TCW) Rotor-Surface-Magnet (RSM) PMSM with external rotor topology and all equations provided are exactly for that topology. The analytical approach for other configurations of RSM PMSMs can be found in [18]-[21].

B. No-load flux density of PM Assuming linear second-quadrant demagnetization

characteristic and uniform magnetization throughout the cross section of the PM, the radial component of the magnetization vector can be calculated as follows:

2,...

cos

2

2sin

25,3,1 PM

PM

PM0

rr

pB

M

where =1,3,5… is the harmonic order. Solution of the Poissonian equation in the PM region gives (3) (see bottom

of page) as the expression for radial no-load flux density component in PM region for external rotor; the parameter A used in (3) is calculated as:

4.111

p

ppA

The main parameters, which are determining the PM flux

density, are the dimensions of PMSM and the magnetic properties of PM.

C. Armature reaction field Mostly, analysis of flux density is provided for the airgap

region, because the airgap magnetic field is mainly used to estimate the performance of the machine. However, due to the boundary conditions for two materials with different magnetic properties, the normal component of the flux density is not changing when it is passing from one region to another. In polar coordinate system, this property of flux density allows using the airgap solution for the radial flux density component also in the PM region. The model for the armature reaction proposed in this paper is based on a solution of Laplacian equation for single coil in the airgap region. The model for coil flux density calculation in case of an external rotor configuration is depicted in Fig. 2(b). Each coil conductor is represented as a thin current density sheet with width b0 at the surface of the slotless stator. The modification of the solution from [18] allows describing the radial flux density component of a coil in the PM region as follows:

5,cos12,,321

psoef

0radcoil,

...,,

NFKK

titrB

where =1,2,3…, N is the number of series winding turns in coil, slot opening factor Kso , coil span Kp can be described as:

6,

2

2sin

s

0

s

0

so

rb

rb

K

7,2

sin yp

aK

and the function dependent on the radius and harmonic order F in case of an external rotor:

8,

1

1

2

s

r

2r

sef

rr

rr

rr

rF

where rm r rr is radius where the magnetic flux density is calculated. The coefficient ay is determining actual coil span. In case of analyzed motor ay=2 /Qs mechanical radians. The effective airgap length ef will be defined in the next subsection.

Fig. 3. Winding configuration of TCW PMSM under observation. Due to symmetry, only half of winding is depicted.

The winding configuration of the observed machine is depicted in Fig. 3. Application of (5)-(8) to actual winding topology of machine under observation results in (9) (see bottom of next page), where 1=0,1,2, 2=0,1,2,3, 3=1,2 and ii(t) is instantaneous value of phase current in each phase. In case of sinusoidal phase currents:

10,322sin 1i

ftIti

Eq. (9) is appropriate only for winding configuration

depicted in Fig. 3. However, (6)-(9) allow creating the same model for other winding configurations. In contrary to mathematical approach used in [18] and [21], the proposed model for the armature reaction using a combination of (6)-

pxp

pAMpx

p

rr

p

pMpx

p

r

rp

r

rp

rr

p

r

rp

r

rp

r

r

p

r

rp

r

rA

p

r

rp

r

rA

p

pMrB

cos12r0cos

1

r12r0cos1

m1

r

m1

r

2

rm

2

m

s

r

1r2

r

s1r

1r

1

r

m

r

112

m

s

r

11

r

s1

m

s

r

11r

1

...5,3,1 12r0,PM

(3)

(9) do not need spectrum analysis of phase current and winding cased specific space harmonics to provide field distribution in airgap/PM regions. It is enough to know only the shape of phase currents; space harmonics created by the winding can be taken into account with using (9) without any complementary analysis.

D. Stator slotting effect Permeance function for the slotting effect is based on

conformal mapping technique that is applied to idealized single-slot model [19]:

11,cos6.1sin78125.0

5.04

6.111,

...3,2,1si2

i

2ii

t

0

c

i

xiQbb

bi

bK

rx

where i = 1,2,3…, i = (-1)i when the winding pitch is an odd integer of the slot pitch and 1 when winding pitch is an even integer of the slot pitch; bi = ib0/ t , t = 2 rs/Qs is stator tooth pitch, Kc = t/( t – · ef ) is Carter coefficient. The effective airgap ef in case of external rotor topology is:

12,r

mrsmef

rr

rr

and

13.2

1ln2

tan2

42

ef

0

ef

01

ef

0

bbb

Because of slotted stator, rse should be used further

instead of rs:

14.1 efcsse Krr

Coefficient is determined as following:

15,

12

1

1121

22

ef

0

b

is determined from solving equation:

16,2arctan2ln21

220

ef

0

ef22

22

0

abba

ab

y

17,212

0

ef

ba

18.efs rry

The model presented for the slot opening can be

appropriate for motors with relatively high ratio of the air gap length to the slot pitch [19].

E. Rotor reference frame In order to simplify further analysis, (1) is written in the

rotor reference frame. After modification, (1) becomes:

19,,,,,

,,,,,,

rrarm

rPMrad

ttrttrB

ttrtrBtrB

where r = 2 f/p is rotor mechanical angular velocity and is rotor position at time t = 0.

The usage of rotor reference frame is significantly simplify analysis, since fluctuation of operating point in each PM can be observed individually in different moments of time.

IV. RESULTS The analysis is provided for TCW RSM PMSM initially

presented in [22]. The prototype was designed as generator for hybrid vehicle application. The parameters of the observed machine are presented in Table I. The magnetic flux density of PMSM is calculated in the top (close to air gap), in the middle and in the bottom (close to rotor hub) of PM when machine runs with frequency converter.

TABLE I

PARAMETERS AND DIMENSIONS OF THE OBSERVED TCW RSM PMSM

Parameter Value Rated power P, [W] 50000 Rated torque T, [Nm] 159 Rated stator current Is, [Arms] 83.8 Rated speed n, [rpm] 3000 Permanent magnet remanence Br, [T] 0.34 Relative permeability of permanent magnet, μr 1.26 Number of stator slots Qs 24 Number of pole pairs p 10 Permanent magnet height, [m] 0.017 Stator outer radius rse, [m] 0.169 Rotor inner radius rr, [m] 0,187 Permanent magnet inner radius rm, [m] 0,170 Converter output frequency f, [Hz] 500 Number of turns in series per one coil N 10

2

2,1,0

3

...2,1,0

2

2,112

s3

spso

1

ef

1i0arm

1 2 3

23

3412cos112

Q

mQ

xFKKtNi

B (9)

The measured converter’s current waveforms are depicted in Fig. 4. The operation of a PMSM in frequency converter supply has a number of drawbacks, such as increasing of torque ripple, increased iron and PM losses. Permeance harmonics produced by slotting effect and nonsinusoidal distribution of windings in the stator have the highest effect on loss production in PM material when a PMSM operates with sinusoidal currents [2]. The simulation results in [2] clearly show that frequency converter caused current harmonics can dramatically increase eddy current losses in PMs and even lead to their partial permanent demagnetization. However, a high electrical resistance of Ferrite material makes eddy currents almost negligible [22]. In case of NdFeB and SmCo magnets, e.g. magnetic materials with relatively low electrical resistivity, the limitation of eddy current loss can be achieved by segmentation of PMs [2].

Fig. 4. Measured current waveforms when the PMSM observed is supplied with a frequency converter.

Figs. 5-8 depict the magnetic flux density distribution

calculated with FEM and analytical model during the time of one slot transition. The selected time clearly shows the main factors affecting hysteresis loss emergence.

A. Slotting effect Figs. 5-6 show that the slotting effect has the highest

Fig. 5. FEM-calculated magnetic flux density distribution at the surface of PM (close to airgap). 1 – slotting effect, 2 – tooth saturation effect.

Fig. 6. Model-calculated magnetic flux density distribution at the surface of PM (close to airgap). 1 – slotting effect, 2 – tooth saturation effect. influence on the permeance harmonics in TCW PMSMs. The reason for that is the relatively large distance between two adjacent teeth in TCW compared with Distributed Winding (DW) machines. Figs. 7-8 depicts the magnetic flux density distribution in the middle and on the bottom (close to rotor hub) of the PM, respectively. The remanent flux density of the PMs used in the PMSM observed is 0.34 T. Thus, it is seen from Figs. 5-8 that significant part of the PM has the magnetic flux density variation between the 2nd and the 1st quadrant, mainly due to stator slotting caused permeance harmonics.

Fig. 7. Magnetic flux density distribution in the middle of PM. a) FEM results, b) Model results.

Stator slotting has the strongest effect close to the airgap and the effect decreases significantly when approaching the rotor hub. This shows that the assumption about constant slotting effect within all height of PM will result in a higher value of hysteresis loss estimate.

Fig. 8. Magnetic flux density distribution at the bottom of PM (close to rotor hub). a) FEM results, b) Model results.

PM edge leakage flux phenomenon is also present in

PMs. It can be accurately calculated with using both 2-D slotless analytical and subdomain models, however, the application of ECM approach can result in inaccuracy. Moreover, ECM model requires knowing the flux paths to be able to create an equivalent circuit.

Measurement data in [23] shows that the amplitude of the flux density variation has the highest influence on the resulting emerging losses. Thus, the slotting effect causes the major part of possible hysteresis loss.

The 2-D slotless model presented in this paper is able to take into account the slotting effect with a separate multiplication function. However, the simplified slot geometry in (11)-(18) neglects the tooth tip leakage flux phenomenon. The analytical approach using complex relative permeance function [24] shows more accurate results for the slotting effect compared to (11)-(18). Nevertheless, it requires a numerical solution for each point and, thus, significantly increases the calculation time needed [12]. Subdomain models [12], [16] also demonstrate more accurate results for the slotting effect but the analysis is typically provided only for no-load magnetic flux density and is not suitable for the hysteresis loss evaluation. The

analytical approach in [16] demonstrates perfect agreement with FEM results for the armature reaction field when it is observed separately from the PM-generated field. Similar accuracy was obtained with the application of (9) during separate analysis of the armature reaction field. In fact, the accuracy of the analytical approaches is dramatically reduced by the presence of teeth saturation.

B. Teeth saturation The assumption about infinite permeability of iron in

ECM-based, slotless and subdomain models simplifies the analysis, but also leads to a lower accuracy compared to FEM results. It is clearly seen in Figs. 5-6 that the assumption of iron infinite permeability will cause losing additional fluctuations of magnetic flux density and, thus, result in a lower value of calculated hysteresis loss. However, the combination of 2-D slotless analytical model with EMC model [25] provided for axial flux PMSM has no assumption about infinite iron permeability and shows good agreement with FEM results. Figs. 5-8 show that the highest inaccuracy between the model and FEM results is possible in the part of PM that is closest to the airgap. The effects of teeth saturation and tooth tip leakage flux are decreasing when approaching the rotor yoke and the slotting effect together with supply current harmonics effect become dominating factors that cause the permeance harmonic modulation.

C. Inverter harmonics The effect of frequency converter on the magnetic flux

density can be seen (small flux density fluctuations) in Figs. 5-8. Experimentally measured current waveforms in Fig. 4 were used for simulation both in the model and in the FEM program. Current harmonics cause small ripples of the flux density compared to the slotting effect, and thus, create insignificant part of total hysteresis loss. The slotting effect caused fluctuations remains the dominating factor causing hysteresis loss in TCW PMSMs. However, the relatively small distance between adjacent teeth in DW PMSMs cause smaller fluctuations of magnetic flux density due to slotting. The effect of current harmonics can be larger in DW PMSMs compared to TCW PMSMs.

D. Ways to limit PM hysteresis loss The measurement results provided in [23] show that the

hysteresis loops are non-symmetrical with respect to the B-axis and the BH-curve. The losses created by the same magnitude of flux density variation can differ significantly depending on the position of the operating point on the BH-curve. In fact, the hysteresis loss will be almost negligible when the magnetic flux density of PM is located in the second quadrant of the demagnetization curve [23].

Based on the analysis provided in this paper and measurement data in [23], the following design efforts will limit hysteresis loss: 1) select the dimensions of PMSM in such a way that the magnetic flux density in PM does not exceed Br during operation; 2) application of semi-magnetic wedges. The effectiveness of the proposed efforts requires further research.

V. CONCLUSION Factors affecting the hysteresis loss risk in rotor-surface-magnet PMSMs were studied by analytical means and finite element analysis. To get accurate results conventional 2-D slotless analytical models need to be complemented by iron saturation phenomenon modelling. This will allow creating fast and accurate tool for magnetic field calculation that further can be a part of reliable analytical hysteresis model.

Slotting effect is the dominant hysteresis causing phenomenon in TCW PMSMs. However, phase current harmonics can be a significant source of extra hysteresis loss in DW PMSMs. The assumption about constant relative permeability of PM limits the application of present FEM-based programs and analytical models for direct hysteresis loss calculation. The further research is needed to evaluate hysteresis loss.

VI. REFERENCES [1] J. Pyrhönen, T. Jokinen and V. Hrabovcova, Design of Rotating

Electrical Machines, John Wiley & Sons, Ltd, 2014. [2] D. Kowal, P. Sergeant, L. Dupre and H. Karmaker, “Comparison of

Frequency and Time-Domain Iron and Magnet Loss Modeling Including PWM Harmonics in a PMSG for a Wind Energy Application,” IEEE Trans. En. Conv., vol. 30, no. 2, pp. 476-486, June 2015.

[3] P. Lindh, J. Montonen, P. Immonen, J. A. Tapia and J. Pyrhönen, "Design of a Traction Motor With Tooth-Coil Windings and Embedded Magnets," IEEE Trans. Ind. Electron., vol. 61, no. 8, pp. 4306-4314, August 2014.

[4] J. Nerg, M. Rilla, V. Ruuskanen, J. Pyrhönen and S. Routsalainen, "Direct-Driven Interior Permanent-Magnet Synchronous Motors for a Full Electric Sports Car," IEEE Trans. Ind. Electron., vol. 61, no. 8, pp. 4286-4294, August 2014.

[5] C. Xia, B. Ji and Y. Yan, "Smooth Speed Control for Low-Speed High-Torque Permanent Magnet Synchronous Motor Using Proportional-Integral-Resonant Controller," IEEE Trans. Ind. Electron., vol. 62, no. 4, pp. 2123-2134, April 2015.

[6] A.Jassal, H. Polinder, D. Lahaye and J.A.Ferreira, "Analytical and FE Calculation of Eddy-current Losses in PM Concentrated Winding Machines for Wind Turbines," in IEEE International Electric Machines & Drives Conference (IEMDC), Niagara Falls, ON , 2011.

[7] J. Pyrhönen, H. Jussila, Y. Alexandrova, P. Rafajdus and J. Nerg, "Harmonic Loss Calculation in Rotor Surface Permanent Magnets—New Analytic Approach," IEEE Trans. Magn., vol. 48, no. 8, pp. 2358-2356, July 2012.

[8] A. Rahideh and F. Dubas, "Two-Dimensional Analytical Permanent-Magnet Eddy-Current Loss Calculations in Slotless PMSM Equipped With Surface-Inset Magnets," IEEE Trans. Magn., vol. 50, no. 3, March 2014.

[9] A. Fukuma, S. Kanazawa, D. Miyagi and N. Takahashi, "Investigation of AC Loss of Permanent Magnet of SPM Motor Considering Hysteresis and Eddy-Current Losses," IEEE Trans. Magn., vol. 41, no. 5, pp. 1964-1967, May 2005.

[10] J. Pyrhönen, S. Ruoho, J. Nerg, M. Paju, S. Tuominen, H. Kankaanpää, R. Stern, A. Boglietti and N. Uzhegov, "Hysteresis Losses in Sintered NdFeB Permanent Magnets in Rotating Electrical Machines," IEEE Trans. Ind. Electron., vol. 62, no. 2, pp. 857 - 865 , January 2014.

[11] S. Morimoto, S. Ooi, Y. Inoue and M. Sanada, "Experimental Evaluation of a Rare-Earth-Free PMASynRM With Ferrite Magnets for Automotive Applications," IEEE Trans. Ind. Electron., vol. 61, no. 10, pp. 5749 - 5756, January 2015.

[12] Z. Zhu, L. Wu and Z. Xia, "An Accurate Subdomain Model for Magnetic Field Computation in Slotted Surface-Mounted Permanent-Magnet Machines," IEEE Trans. Magn., vol. 46, no. 4, pp. 1100-1150, April 2010.

[13] S.-M. Hwang, J.-B. Eom, G.-B. Hwang, W.-B. Jeong and Y.-H. Jung, "Cogging torque and acoustic noise reduction in permanent magnet

motors by teeth pairing," IEEE Trans. Magn.,, vol. 36, no. 5, p. 3144–3146, September 2000.

[14] C. Bi, Q. Jiang and S. Lin, "Unbalanced-magnetic-pull induced by the EM structure of PM spindle motor," in Proc. Eighth Int. Conf. Electrical Machines and Systems, 2005.

[15] Z. Q. Zhu, D. Howe, E. Bolte and B. Ackermann, "Instantaneous Magnetic Field Distribution in Brushless Permanent dc Motors, Part I: Open-Circuit Field," IEEE Trans. Magn., vol. 29, no. 1, pp. 124-134, January 1993.

[16] T. Lubin, S. Mezani and A. Rezzoug, "2-D Exact Analytical Model for Surface-Mounted Permanent-Magnet," IEEE Trans. Magn., vol. 47, no. 2, pp. 479-492, February 2011.

[17] Y. Zhou, H. Li, G. Meng, S. Zhou and Q. Cao, "Analytical Calculation of Magnetic Field and Cogging Torque in Surface-Mounted Permanent-Magnet Machines Accounting for Any Eccentric Rotor Shape," IEEE Trans. Ind. Electron., vol. 62, no. 6, pp. 3438-3447, June 2015.

[18] Z. Q. Zhu and D. Howe, "Instantaneous magnetic field distribution in brushless permanent magnet DC motors. II. Armature-reaction field," IEEE Trans. Magn., vol. 29, no. 1, pp. 136-142, January 1993.

[19] Z. Q. Zhu and D. Howe, "Instantaneous Magnetic Filed Distribution in Brushless Permanent Magnetdc Motors, Part III: Effect of Stator Slotting," IEEE Trans. Magn., vol. 29, no. 1, pp. 143-151, January 1993.

[20] Z. Zhu and D. Howe, "Instantaneous Magnetic Field Distribution in Permanent Magnet Brushless dc Motors, Part IV: Magnetic Field on Load," IEEE Trans. Magn., vol. 29, no. 1, pp. 152-158, January 1993.

[21] Z. Q. Zhu, D. Howe and C. C. Chan, "Improved Analytical Model for Predicting the Magnetic Field Distribution in Brushless Permanent-Magnet Machines," IEEE Trans. Magn., vol. 38, no. 1, pp. 229-238, January 2002.

[22] I. Petrov, M. Polikarpova and J. Pyrhönen, "Rotor surface ferrite magnet synchronous machine for generator use in a hybrid application — Electro-magnetic and thermal analysis," in 39th Annual Conference of the IEEE Industrial Electronics Society, IECON 2013 , Vienna, 2013.

[23] I. Petrov, D. Egorov, J. Link, R. Stern, S. Ruoho and J. Pyrhonen, "Hysteresis losses in different types of permanent magnets used in PMSMs," IEEE Trans. Ind. Electron., vol. PP, March 2016.

[24] D. Zarko, D. Ban and T. Lipo, "Analytical Calculation of Magnetic Field Distribution in the Slotted Air Gap of a Surface Permanent-Magnet Motor Using Complex Relative Air-Gap Permeance," IEEE Trans. Magn., vol. 42, no. 7, pp. 1828-1837, July 2006.

[25] A. Hemeida and P. Sergeant, "Analytical Modeling of Surface PMSM Using a Combined Solution of Maxwell’s Equations and Magnetic Equivalent Circuit," IEEE Trans. Magn., vol. 50, no. 12, December 2014.

VII. BIOGRAPHIES

Dmitry Egorov received the B.Sc. degree from Moscow Power Engineering Institute (MPEI), Moscow, Russia, in 2013 and the M.Sc. degree in Electrical Engineering from Lappeenranta University of Technology (LUT), Lappeenranta, Finland, in 2015. He is currently a Doctoral Student in the Department of Electrical Engineering, LUT. Nikita Uzhegov (M’14) received D.Sc. degree in 2016 from Lappeenranta University of Technology (LUT), Finland. He is currently a fellow researcher in the Department of Electrical Engineering, LUT. Ilya Petrov received D.Sc. degree in 2015 from Lappeenranta University of Technology (LUT), Finland. He is currently a fellow researcher in the Department of Electrical Engineering, LUT. Juha J. Pyrhönen (M’06) born in 1957 in Kuusankoski, Finland, received the Doctor of Science (D.Sc.) degree from Lappeenranta University of Technology (LUT), Finland in 1991. He became Professor of Electrical Machines and Drives in 1997 at LUT. He is engaged in research and development of electric motors and power-electronic-controlled drives. Prof. Pyrhönen has wide experience in the research and development of special electric drives for distributed power production, traction drives and high-speed applications. Permanent magnet materials and applying them in machines have an important role in his research. Currently he is also researching new carbon-based materials for electrical machines.

Publication II

Petrov, I., Egorov, D., Link, J., Stern, R., Ruoho, S., and Pyrhönen, J.Hysteresis losses in different types of permanent magnets used in PMSMs

Reprinted with permission fromIEEE Transactions on Industrial Electronics

vol. 64(3), pp. 2502–2510, 2017© 2017, IEEE Journals & Magazines

2502 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 64, NO. 3, MARCH 2017

Hysteresis Losses in Different Types ofPermanent Magnets Used in PMSMs

Ilya Petrov, Dmitry Egorov, Joosep Link, Raivo Stern, Sami Ruoho, Member, IEEE,and Juha Pyrhonen, Member, IEEE

Abstract—In permanent magnet synchronous machines(PMSM), depending on the machine application, differ-ent types of permanent magnets (PM) can be used.The most common PMs are ferrite magnets, neodymiumiron boron magnets (NdFeB), and samarium cobalt mag-nets (SmCo). The selection of a suitable magnet fora particular machine design depends on the magnetproperties: remanence, conductivity, mechanical rigidity,losses, and demagnetization characteristics. Usually, thepossibility of hysteresis losses in PM materials is neglected.In this paper, however, it is demonstrated that possible hys-teresis losses have to be evaluated in the machine design.It is shown by measurements and simulations that in somemachine designs, hysteresis losses in NdFeB, SmCo, andferrite magnets can be a source of significant additional aclosses that may lead to too high PM operating temperaturesand a reduction in the machine efficiency.

Index Terms—Ferrite magnets, hysteresis losses,neodymium magnets, permanent-magnet machines, samar-ium cobalt magnets.

I. INTRODUCTION

P ERMANENT magnets (PMs) have been used in electri-cal machines since the first half of the 20th century [1].

Until samarium cobalt magnets and neodymium magnets wereinvented, only ferrite magnets and AlNiCo were available in themarket. The energy densities of these magnets were relativelylow, and their demagnetization risk was high. Therefore, ferriteand AlNiCo magnets were not used widely in high-power (tensof kW) industrial applications. However, the penetration of PMtechnology into the field of high-power high-torque electricalmachines was boosted by the invention of samarium cobalt mag-nets [2] and neodymium magnets [3]. The high energy producttogether with satisfactory demagnetization properties allowed

Manuscript received December 2, 2015; revised February 8, 2016;accepted February 24, 2016. Date of publication March 30, 2016; dateof current version February 9, 2017.

I. Petrov, D. Egorov, and J. Pyrhonen are with the Department ofElectrical Engineering, LUT Energy, School of Technology, Lappeen-ranta University of Technology, 53851 Lappeenranta, Finland (e-mail:ilya.petrov@lut.fi; dmitry.egorov@lut.fi; juha.pyrhonen@lut.fi).

J. Link and R. Stern are with the Department of Chemical Physics,National Institute of Chemical Physics and Biophysics, 12618 Tallinn,Estonia (e-mail: jooseplink@gmail.com; raivo.stern@gmail.com).

S. Ruoho is with Nordmag Oy, 28600 Pori, Finland (e-mail:samiruoho@hotmail.com).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2016.2548440

the use of PMs even in challenging applications such as direct-drive wind power generators [4], [5] and propulsion motor drivesin hybrid vehicles [6], [7].

In principle, the implementation of PM technology in electri-cal machines eliminates the losses related to the excitation fieldgeneration. Thus, it can be expected that the efficiency of an ap-propriately designed permanent-magnet synchronous machine(PMSM) should be higher compared with electrical machines ofthe same size without PMs (e.g., induction motor, synchronousmachine, switched reluctance machine, synchronous reluctancemachine, dc machine) [8]–[10]. Therefore, application of PMtechnology is constantly increasing in electrical machines fordifferent purposes.

Recently, in some electrical machine designs, a phenomenonrelated to PMs hysteresis losses was observed. The origin ofthe phenomenon was explained in [11]. The machine operat-ing point at which the hysteresis losses in PMs occur was alsoshown in [11]. However, no clear picture of the amount of hys-teresis losses in the magnets has been given (e.g., the energyof hysteresis loops at different magnetic field strengths), andno method for the estimation of hysteresis losses in a PMSMhas been shown so far. This paper should fill this gap. Threedifferent PM types (NdFeB, SmCo, and ferrite magnets) areanalyzed in terms of hysteresis losses, and the possible PMSMefficiency reduction resulting from the hysteresis losses is as-sessed. Parameters of the PMs analyzed in this paper are listedin Table I.

The paper is organized as follows. In Section II, the originof hysteresis losses in PMs is described and the measured re-sults are introduced. In Section III, the influence of a PMSMconstruction on hysteresis losses in different PM types is eval-uated. A comparison between the hysteresis losses in differentPM types applied in similar PMSMs is provided. Section IVconcludes the paper.

II. HYSTERESIS LOSSES IN PMS

A. Reasons for Hysteresis Losses

PMs with a relative permeability of μr > 1 are prone to hys-teresis losses, if the PM flux density varies over and under theremanent flux density because of the armature reaction and per-meance modulation in the operating point [11]. For the sake ofcompleteness, the reasons for this phenomenon are described inbrief in this section. Fig. 1 shows the idealized hysteresis loopof the PM (in the first and the second quadrants) including the

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PETROV et al.: HYSTERESIS LOSSES IN DIFFERENT TYPES OF PERMANENT MAGNETS USED IN PMSMS 2503

TABLE IPERMANENT MAGNETS

Parameter NdFeB Sm2 Co1 7 Ferrite magnet

Br [T] 1.1 1.11 0.38H c B [kA/m] 830 822 280H c J [kA/m] 1950 1600 290(BH )m a x [kJ/m3] 225 230 29μr 1.07 1.09 1.15

Fig. 1. Idealized hysteresis loop of the PM (in the first and the secondquadrants). It includes two small hysteresis loops of magnetically softmagnet areas. However, in an actual PM, the number of hysteresis loopsmay be large (depending on the number or type of magnetically softPM material areas), and the total hysteresis loop of the PM would besomewhat smoother.

hysteresis loops of the magnetically soft magnet areas. In thefigure, two hysteresis loops for the magnetically soft magnet ar-eas are illustrated with different BH curves. However, in reality,there may be numerous types of magnetically soft magnet areaswith different hysteresis loops. It means that the actual resultanthysteresis loop of the magnetically soft magnet areas can besmooth rather than discrete as it is shown in Fig. 1.

In Fig. 1 it can be seen that if the PM flux density exceedsthe magnet remanent flux density (1 → 2), some of the mag-netically soft magnet areas are magnetized and the total PMmagnetization increases (2 → 3). If the PM flux density is fur-ther increased (3 → 4), other magnetically soft magnet areas aremagnetized and the PM magnetization reaches its maximumvalue (4 → 5). However, if the PM flux density returns back tothe operating point in the second quadrant (5 → 6 → 7 → 8 →1), the magnetically soft magnet areas are demagnetized and thetotal PM magnetization reduces. This explains the appearanceof hysteresis loops in the PMs when the PM flux density exceedsthe remanent magnet flux density.

B. Hysteresis Specific Energy of PMs

The actual magnetic losses caused by these hysteresis loopsof the magnetically soft magnet areas are determined by the

Fig. 2. Estimation of the energy in one hysteresis loop (hysteresis area)of a PM.

Fig. 3. (a) Test bench for measurement of magnets BH curves consistsof a physical properties measurement system with up to 14 Tesla super-conducting magnet from Quantum Design with a P525 VSM and dataacquisition system. (b) Sample size of the PM used for the measurementprocedure.

amplitude of the variable field strength applied to the magnets,the quantity of the magnetically soft magnet areas, and the be-havior of these magnetically soft magnet areas. These character-istics depend on the quality of magnets and may vary in differentmagnets (magnet type, magnet grade, manufacturer). When thehysteresis loop is measured, it is possible to find the energy thatthis loop includes, as it is shown in Fig. 2. If the hysteresis loopis known, it is possible to integrate its lower and upper linesover the applied field strength (e.g., −380 to 380 kA/m). Afterthat, the total hysteresis specific energy [J/m3] can be found as

Ehyst =∫ Hm a x

Hm in

Bup(H)dH −∫ Hm a x

Hm in

Blow (H)dH (1)

where Bup represents the upper line and Blow represents thelower line of the hysteresis loop.

In order to observe the possible difference in hysteresis loopsof the PMs with different structures, it was decided to measurethe actual hysteresis loops of samples of most common PMtypes and estimate the possible hysteresis losses for ferrite PM,NdFeB, and SmCo. The photograph of the test bench used formeasurements of the PMs BH curves in a wide field strengthrange (while keeping the measurement precision in acceptablelevel) is shown in Fig. 3(a). Approximate size of the samplesused for the measurements is shown in Fig. 3(b).

The measurement procedure includes field strength variationwith recording of the PM magnetization in a similar manner asit was done in [11]. The field strength variation was applied with

2504 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 64, NO. 3, MARCH 2017

Fig. 4. (a) Self-demagnetization field in open magnetic circuit. (b) Ap-plied field in the same direction as the self-demagnetization field. (c)Applied field in the opposite direction as the self-demagnetization field.

different extreme values to investigate the influence of hysteresislosses on the external field strength. Further, the influence of thefield strength alternation only in one (second) quadrant on thehysteresis losses was observed. No irreversible demagnetizationpoint was reached during the measurements of the hysteresisloops. It means that the hysteresis losses do not include energy,which would be required for irreversible demagnetization ormagnetization of the magnets.

The vibrating sample magnetometer (VSM) shown inFig. 3(a) used an open-circuit measurement system. This meansthat there is a self-demagnetization field (Hd ) in a PM as it isshown in Fig. 4(a). The self-demagnetization field contributesto the total magnet field as shown in Fig. 4(b) and (c). There-fore, the self-demagnetization field of the open circuit should betaken into account and a proper correction of the applied field(Happ ) should be made to find the actual internal magnet field(Hint).

The value of self-demagnetization field can be estimated ifthe permeance coefficient is known, whereas the permeancecoefficient of a magnet sample with rectangular shape can beestimated by [12]

kΛ = 1.77h

lw

√h (l + w) + lw (2)

where h is the height of magnet (the height is along the mag-netization direction), l is the length of the magnet, and w is thewidth of the magnet.

Fig. 5. Neodymium magnet hysteresis loop. Hysteresis loops of themagnet that do not exceed the remanent flux density contain far lessenergy than those which exceed the remanent flux density. The mea-surements were implemented at room temperature (T = +23 °C).

Based on the permeance coefficient, the demagnetization fac-tor can be estimated by

Nd = 1/ (kΛ + 1) (3)

and finally the self demagnetization field can be found for eachmagnet sample by

Hd = −JNd

μ0(4)

where J is the magnetic polarization of the magnet and μ0 is thepermeability of vacuum.

The actual internal field in the magnet during the open-circuitmeasurement procedure should be found by correction of the ap-plied field with the demagnetization field. The illustrated figuresshown hereafter with magnets hysteresis loops already includethis correction. Thereby, they comprise only internal magnetfield.

C. Hysteresis Loop Shapes of PMs at Different FieldStrengths

Fig. 5 shows the hysteresis loops in a neodymium magnet sim-ilar to the one analyzed in [11]. The hysteresis loops shown inthe figure with different field strength amplitudes differ signifi-cantly from each other with regard to the magnetic energy value.The highest energy losses can be found in the hysteresis loopthat exceeds the remanent flux density and which has the highestfield strength variation, as it was expected earlier. However, anadditional phenomenon can be observed in Fig. 5, which is thedifferent slope angles of the hysteresis loops with different ap-plied field strengths. The different slopes of the hysteresis loopswith a higher applied field strength can be explained by irre-versible demagnetization of the magnetically soft magnet areasat higher negative field strengths, whereas the magnetizationof these magnetically soft magnet areas occurs only partiallybecause no strong enough positive magnetic field is applied.Therefore, the remanent flux density decreases when a highernegative field strength is applied starting from the initial com-plete magnetization of the magnet as it is shown in Fig. 6. Thisfigure comprises the following procedure: after complete mag-netization of the neodymium magnet (where all magneticallysoft areas are magnetized), a fairly high negative field strength

PETROV et al.: HYSTERESIS LOSSES IN DIFFERENT TYPES OF PERMANENT MAGNETS USED IN PMSMS 2505

Fig. 6. BH curve of the neodymium magnet: 1 − BH curve after com-plete magnetization applying −650 kA/m magnetic field strength, 2 −Hysteresis loops with field strength variation from −250 to −50 kA/m, 3− Hysteresis loops with field strength variation from −470 to 100 kA/m.

Fig. 7. Hysteresis loop of the samarium cobalt magnet. The hysteresisloops of the magnet that do not exceed the remanent flux density containless energy than those which exceed the remanent flux density. Themeasurements are implemented at room temperature (T = +23 °C).

of −650 kA/m corresponding to opening of the PM circuit isapplied. At this negative field strength, the magnetically soft ar-eas are demagnetized (curve 1) and the magnet has, in principle,attained its operating performance. The next step is to vary thefield strength between −250 and −50 kA/m (curve 2) describ-ing a possible hysteresis behavior under armature reaction andmodulation by permeance harmonics. With this field strengthnone of the magnetically soft areas are magnetized or demagne-tized. Finally, the field strength varies between −470 and +100kA/m (curve 3). In this curve, we can clearly see the magnetiza-tion and demagnetization of the part of magnetically soft areas,which represents the actual possibility of having considerablehysteresis losses in PMs if the flux density in the magnet repeat-edly exceeds the critical flux density. This critical flux densityfor different types of PMs can vary, but it is usually found closeto zero magnetic field strength. The similar phenomenon wasalso observed in [13].

The BH curves of the SmCo magnet at different applied fieldstrengths are shown in Fig. 7. The figure shows that the hystere-sis loops that are closer to H-axis (especially those that crossH-axis) contain higher energy.

Ferrite magnets analyzed in the paper are prone to partialirreversible demagnetization already at relatively small negativefield strengths. It means that in order to exclude the possible

Fig. 8. Hysteresis loop of the ferrite magnet. Hysteresis loops of themagnet that do not exceed the remanent flux density contain far lessenergy than those which exceed the remanent flux density. The ferritemagnet is not fully magnetized in order to exclude the possible partialirreversible demagnetization in the hysteresis loops at a high applied fieldstrength (normally magnetized remanent flux density, at T = +23 °C isBrem = 0.38 T).

effects of irreversible demagnetization on the hysteresisloop, it is necessary to analyze the magnet in only a slightlydemagnetized condition, as it is shown in Fig. 8. The hysteresisloop produced by the magnetically soft magnet areas is clearlyseen in the figure.

When a machine with ferrite magnets is designed, it is usuallyassumed that no losses take place in the PMs, because ferritemagnets have a very high electric resistivity, which preventsany practical eddy current losses [14]. However, if the armaturereaction is strong enough, the hysteresis losses can be significantin some machine design. This can have a negative effect onthe motor efficiency. Therefore, the influence of the describedphenomenon on the actual PM losses and consequently, on themachine efficiency should be estimated. The estimation methodsand the results are described in the following section.

III. FEA-BASED EVALUATION OF ADDITIONAL AC LOSSES

CAUSED BY PM HYSTERESIS LOSSES IN A PMSM

A. Influence of the PM type on the Motor Parameters,Including PM Hysteresis Losses

At the beginning of a PMSM design process, a suitable PMtype should be selected. The selection is based on the magnetproperties required for a certain PMSM design. For example, inrotor surface magnet PMSMs, the no-load air gap flux density isdetermined by the remanent flux density and the magnetic cir-cuit reluctance. As a result of the magnetic flux density, the polecross-sectional surface, and the number of effective stator wind-ing turns, a suitable back electromotive force (EMF) is induced.The number of turns and the pole pair number have an influenceon the synchronous inductance (Ls ≈ N 2 , Ls ≈ 1/p2) of themachine [15]. The synchronous inductance indicates how muchmagnetic flux linkage is produced by a certain armature phasecurrent. This magnetic flux linkage (armature reaction) may sig-nificantly contribute to the resultant magnetic condition of themachine, which at no load is only affected by the PM flux. If thelow air-gap flux density effects in a PMSM with ferrite magnetsare compensated by a higher electrical loading (linear current

2506 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 64, NO. 3, MARCH 2017

density) to achieve a tangential stress even close to the levels ofPMSMs with neodymium magnets, the armature reaction can bemuch more essential than in a machine construction with strong(neodymium) magnets. Knowing the actual air gap flux densityand the required tangential stress, the linear current density Acan be estimated by

A =2σF tan

Bδcosϕ(5)

where σF tan is the tangential stress, Bδ is the peak air gap fluxdensity of the working harmonic, and ϕ is the phase shift anglebetween the linear current density and the air gap flux density.

Rare-earth PMs should be used in machines in which it isadvantageous to have a high air gap flux density with the lowestpossible machine weight. Otherwise, if the cost of the machineis an important factor, ferrite magnets could be used [14]. How-ever, because of the low air gap flux density when rotor surfaceferrite magnets are the only source of the excitation field, ahigher number of stator winding turns is required to induce thesame back EMF as in the case of stronger PMs. This means thatif the current density is kept unchanged, the phase resistanceincreases proportionally with the number of turns (length of theconductor), and consequently, the copper Joule losses increase.Therefore, it is expected that a machine with weaker PMs shouldhave a lower efficiency than its counterpart with stronger mag-nets. However, according to the above, an additional negativeeffect of using weaker magnets may appear; that is, hysteresislosses. This means that when low-cost and weaker magnets areused instead of stronger magnets, the efficiency degradation isnot only due to the stator copper losses, but also to the higherhysteresis losses in the magnets, which should be taken intoaccount when the PM type is selected as it will be shown below.

B. Description of PMSMs Used as an Example toDetermine the PM Hysteresis Losses

For a fair comparison of the hysteresis losses of three dif-ferent PM types (ferrite PM, NdFeB, SmCo), the same PMSMconstruction was used in all three cases; an outer rotor tooth coilwinding (TCW) PMSM with rotor surface PMs with the samegeometry dimensions. The only part that was modified for eachcase is the stator tooth width to keep the peak flux density in theteeth at 1.6 T. This particular PMSM construction with an outerrotor and rotor surface PMs is based on an actual machine proto-type with ferrite magnets, which was developed and constructedas a generator for a hybrid electrical bus [16]. In the tests of theTCW PMSM, it was found that its efficiency at the nominal loadis lower than expected. This is partly explained by additionalac losses in the stator windings produced by strand-level andbunch-level circulating currents [17], [18]. However, a sourceof a large proportion of the losses has thus far been unknown.Therefore, it was decided to analyze whether the ferrite magnetsare prone to hysteresis losses, because during the machine de-sign it was assumed that no losses take place in the magnets asa result of their high resistivity, which, however, does not havean impact on the possible hysteresis losses.

Fig. 9. (a) Construction of the PMSM with neodymium magnets. (b)Construction of the PMSM with samarium-cobalt magnets. (c) Construc-tion of the PMSM with ferrite magnets. The flux density distribution in amagnet at the time instant when it is subjected to the maximum armaturereaction at the nominal load is illustrated for each design solution (Flux2-D software by Cedrat).

The simplified constructions of the machines with differentmagnets are illustrated in Fig. 9. The main parameters of thePMSMs are listed in Table II. In Fig. 9, we can see that in thecase of rare-earth magnets, the PM flux density does not exceedthe remanence at the nominal load. In the case of ferrite mag-nets instead, the armature reaction is sufficient to increase thePM flux density beyond its remanence. It can be assumed thatno significant hysteresis losses take place in this PMSM con-struction type if rare-earth magnets are used. This assumptionis, however, not valid for the case of the PMSM with ferritemagnets, which can be prone to PM hysteresis losses.

C. Evaluation and Comparison of Hysteresis Losses inDifferent PM Types Applied in a PMSM

It was assumed (during the FEM simulations) that the perme-ability of the PMs is constant (the one which is in the second

PETROV et al.: HYSTERESIS LOSSES IN DIFFERENT TYPES OF PERMANENT MAGNETS USED IN PMSMS 2507

TABLE IITCW PMSM PARAMETERS WITH DIFFERENT PM TYPES APPLIED

Parameter NdFeB SmCo Ferrite magnet

Nominal torque T [Nm] 180 198 122Nominal speed n [rpm] 3000 3000 3000Number of slots Q 24 24 24Number of pole pairs p 10 10 10Current density J [A/mm2] 3.6 3.6 3.6Number of winding turns Np h 288 336 864Linear current density A [kA/m] 27 34.5 61.7Stator tooth width bd [mm] 22.4 19.4 8.4Stator core outer diam. Ds [mm] 340 340 340PM remanence B r e m [T] 1.15 1.0 0.37PM relative permeability μr 1.05 1.05 1.15PM height hP M [mm] 8 8 8Air gap length δ [mm] 1 1 1Back EMF Ep h [Vrms] 230 230 230Phase current Ip h [Arms] 8.3 9.1 6.3

quadrant) and the FEM results were used only to achieve fluxdensity distribution in the magnet at the nominal load, whereasthis flux density distribution was post processed and used forcomputations of potential hysteresis losses. The computed ex-treme values of the flux density variation in a certain PM areaswere compared with the measured values of the magnet sam-ples. It was assumed that if the computed extreme values exceedmeasured values then this computed area has the same loss dis-tribution as the measured sample.

The effects of armature reaction on the flux density distri-bution in the air gap of the PMSMs analyzed with differentmagnets are shown in Fig. 10, where the flux density distribu-tions curves are illustrated in the air gap along the PM, whichis subjected to the maximum armature reaction at the nominalload. In the figure, we can see that in the case of ferrite magnetsthere is a local region where the air gap flux density exceedsthe ferrite magnet remanence because of the armature reaction.This local region of the PM is expected to be prone to hystere-sis losses at the nominal load. The rest of the PM (right part inFig. 10) instead remains in the second quadrant of the BH curve,which means that no practical hysteresis losses take place in thisregion.

As it is shown in Figs. 9 and 10, not the whole ferrite magnetis prone to hysteresis losses but only the part where the PMflux density exceeds the remanent flux density and, on the otherhand, is modulated by permeance or current linkage harmonics.

In order to estimate an exact PM region that can be proneto hysteresis losses, the PM was divided into several regions.Each region is analyzed separately as it is shown in Fig. 11. Theflux density in each point shown in Fig. 11 can be estimated asfunction of time (or as function of PM region position duringthe rotor movement) at the nominal load.

The actual PM shown in Fig. 9(c) was divided into 4200regions (seven layers along the PM height and 600 layers alongthe PM width). The high number of regions is used to reduce themargin of error resulting from the discrete nature of the analysis.When the flux density variation in each region is known afterthe simulation during one slot period, it is possible to evaluatehow these regions are exposed to hysteresis losses. The PMSM

Fig. 10. Normal component curves of the flux densities on the magnetsurface of the PMSMs with different PMs and their remanent flux densi-ties (dashed lines). The only magnet the flux density of which exceedsits remanence on the left half of the magnet is the ferrite magnet. Nopractical hysteresis losses should be expected in this PMSM construc-tion with rare-earth PMs, but the ferrite magnet version will suffer fromhysteresis losses as the armature reaction and the slot opening mod-ulate the flux below and above Brem . αPM is the electrical pole angle(i.e., 180° represents one pole pitch).

Fig. 11. Division of a PM into several equal regions. The flux densityin one point of each region represents the flux density in this region.

with ferrite magnets shown in Fig. 9(c) was used for evaluationof the hysteresis losses at the nominal load. The ferrite magnetused in the PMSM is the same to the one whose hysteresis losseswere measured, Fig. 8.

Because only two BH curves were measured during the fer-rite magnet hysteresis loss measurements in Fig. 8 (with 2229

2508 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 64, NO. 3, MARCH 2017

Fig. 12. Ferrite magnet regions that can be prone to hysteresis losses.The PM is used in the PMSM shown in Fig. 9(c) at the nominal load. ThePM surface close to the air gap is found at the bottom of the figure. Only7 mm (out of 8 mm) PM height is illustrated.

and 606 J/m3), it was decided to use only these values for thePM regions that are prone to hysteresis losses (if the simulatedextreme values exceed measured ones shown in Fig. 8). Theresultant regions of the ferrite magnet that can be prone to hys-teresis losses are shown in Fig. 12. In the figure, we can see thatthe PM regions that are prone to hysteresis losses are locatedonly on one side of the PM as it was expected above.

In order to determine the total hysteresis loss during oneperiod of flux density variation in the PM, it is necessary to sumup all volumes of the regions that have a particular hysteresisloss (e.g., 2229 J/m3) and multiply the total volume by this valueof hysteresis loss as

Etot.hyst = EhystVhyst (6)

where Vhyst is the total PM volume that has Ehyst hysteresislosses in one electrical cycle.

In the PMSM shown in Fig. 9(c), the resultant energy dissipa-tion resulting from the hysteresis losses during one flux densityperiod in one magnet is Ehys = 22.6 mJ. Knowing the numberof slots Qs , the number of PMs NPM and the rotational speedn, the total hysteresis losses can be estimated by

Phys = Etot.hystQNPMn (7)

where n is the rotational speed [s−1]. If it is assumed that therotational speed is 3000 r/min, with the number of stator slotsQ = 24 and the number of PMs NPM = 2p = 20, the total PMhysteresis losses in the PMSM shown in Fig. 9(c) is Phys = 543W, which is 1.4% of the nominal power of the analyzed PMSM(see Table II).

The original PMSM with ferrite magnets designed as a gen-erator for a hybrid bus has a similar structure to the one inFig. 9(c). However, to prevent the demagnetization risk at thenominal load, the PM height in the original PMSM was selectedto be hPM = 17 mm. The PM height in a PMSM with the samelinear current density should have a direct influence on the PMhysteresis loss because of the different magnetic circuit reluc-tance and the larger amount of PM material. Fig. 13 shows the

Fig. 13. Ferrite magnet regions of the original PMSM that can be proneto hysteresis losses. The PM surface close to the air gap is found at thebottom of the figure. Only 14 mm (out of 17 mm) PM height is illustrated.

regions in the PM of the original PMSM that can be prone tohysteresis losses at the nominal load. Fig. 13 resembles Fig. 12with the only difference that the PM regions which are prone tohysteresis losses in Fig. 13 do not penetrate through the wholePM height. This is due to the fact that with the larger PM height,the effect of the armature reaction is reduced as a result of thelow PM permeability. The resultant total hysteresis losses ofthe original PMSM at 3000 r/min are Phys = 278 W, which isapproximately half of that in the PMSM with hPM = 8 mm.Thus, it can be said that it is possible to reduce the hysteresislosses in the PM if its height is increased.

D. PM Hysteresis Losses in PMSMs With Low Numberof Poles

It was found earlier that the rare-earth PMs are not likelyto be affected by hysteresis losses if the number of pole pairsis high (e.g., 10). However, if the number of poles is low (as,e.g., in high-speed machines), the synchronous inductance canbe large enough so that the armature reaction may shift thePM flux density above its remanence in some magnet regions.In order to analyze the possible hysteresis losses in rare-earthPMs that can be used in PMSMs with a small pole number, twosimilar PMSMs were designed with neodymium and samariumcobalt magnets. The main parameters of the PMSMs are listedin Table III.

The effect of the armature reaction on the PM flux densityin the PMSM with neodymium magnets at the nominal load isshown in Fig. 14. The figure shows that one half of the PMhas the same magnetization direction as the armature reaction,whereas another half of the PM opposes the armature reaction.Therefore, we are interested in the magnet region whose mag-netization coincides with the armature reaction, because thisregion can be prone to hysteresis losses. As in the case withferrite magnets, only two major hysteresis loops are used forthe estimation of the hysteresis losses in rare-earth magnets.For neodymium magnets they are with 2868 and 923 J/m3 (seeFig. 5), and for samarium cobalt magnets they are 6001 and2172 J/m3 (see Fig. 7).

PETROV et al.: HYSTERESIS LOSSES IN DIFFERENT TYPES OF PERMANENT MAGNETS USED IN PMSMS 2509

TABLE IIIDW PMSMS PARAMETERS WITH DIFFERENT PM TYPES

Parameter NdFeB SmCo

Nominal torque T [Nm] 117 106Nominal speed n [rpm] 1500 1500Number of slots Q 24 24Number of pole pairs p 1 1Current density J [A/mm2] 3.6 3.6Number of winding turns Np h 48 52Linear current density A [kA/m] 31.3 31.3Stator tooth width bd [mm] 16 16Stator core outer diam. Ds [mm] 250 250PM remanence B r e m [T] 1.15 1.0PM relative permeability μr 1.05 1.05PM height hP M [mm] 7 7Air gap length δ [mm] 1 1Back EMF Ep h [Vrms] 143 143Phase current Ip h [Arms] 8.3 9.1

Fig. 14. PM flux density distribution at the nominal load of the PMSMwith neodymium magnets (parameters of which are listed in Table III).Id = 0 control is applied.

The total hysteresis losses at the nominal load in the PMSMwith neodymium magnets are Phys = 96 W, which is 0.52%of the nominal power, and in the PMSM with samarium cobaltmagnets, the total hysteresis losses are Phys = 187 W, which is1.1% of the nominal power. Therefore, we may conclude thateven rare-earth PMs can be prone to hysteresis losses if thearmature reaction is strong enough to shift the permanent fluxdensity above the remanent flux density, and at the same time,there is a phenomenon that modulates the flux density belowand above the remanent magnet flux density.

IV. CONCLUSION

The actual hysteresis losses in PMs were found by the FEMbased on the measurements of the hysteresis losses of differ-ent PM types: ferrite magnets, samarium cobalt magnets, andneodymium magnets. It was found that ferrite magnets are moreprone to hysteresis losses than rare-earth PMs if the same cur-rent density in the slot and flux density in the stator tooth areapplied. Therefore, in the PMSM design, when selecting the PMmaterial, one should also consider possible hysteresis losses inthe PMs.

When comparing neodymium magnets with samarium cobaltmagnets, it was also found that samarium cobalt magnets havelarger hysteresis losses at a smaller field strength variation. How-ever, to be able to claim a possible trend in these magnets,different PMs grades from different manufactures should betested, which is out of the scope of this paper and remains to bestudied.

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[15] P. Ponomarev, Y. Alexandrova, I. Petrov, P. Lindh, E. Lomonova, andJ. Pyrhonen, “Inductance calculation of tooth-coil permanent-magnetsynchronous machines,” IEEE Trans. Ind. Electron., vol. 61, no. 11,pp. 5966–5973, Nov. 2014.

[16] I. Petrov, M. Polikarpova, and J. Pyrhonen, “Rotor surface ferrite magnetsynchronous machine for generator use in a hybrid application electr-magnetic and thermal analysis,” in Proc. 39th Annu. Conf. IEEE Ind.Electron. Soc., Nov. 2013, pp. 3090–3095.

[17] P. Reddy and T. Jahns, “Scalability investigation of proximity losses infractional-slot concentrated winding surface PM machines during high-speed operation,” in Proc. IEE Energy Convers. Congr. Expo., Sep. 2011,pp. 1670–1675.

[18] M. van der Geest, H. Polinder, J. Ferreira, and D. Zeilstra, “Current sharinganalysis of parallel strands in low-voltage high-speed machines,” IEEETrans. Ind. Electron., vol. 61, no. 6, pp. 3064–3070, Jun. 2014.

2510 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 64, NO. 3, MARCH 2017

Ilya Petrov received the D.Sc. degree from theLappeenranta University of Technology (LUT),Lappeenranta, Finland, in 2015.

He is currently a Fellow Researcher in theDepartment of Electrical Engineering, LUT.

Dmitry Egorov received the B.Sc. degreefrom the Moscow Power Engineering Institute,Moscow, Russia, in 2013, and the M.Sc. degreein electrical engineering from the LappeenrantaUniversity of Technology (LUT), Lappeenranta,Finland, in 2015. He is currently a Doctoral stu-dent in the Department of Electrical Engineering,LUT.

His research mainly concerns electrical ma-chines and drives, in particular, short circuits an-alytical modeling.

Joosep Link received the Bachelor’s degree inengineering physics from the Tallinn Universityof Technology, Tallinn, Estonia, in 2013, wherehe is currently a Master’s student.

He is also an Engineer in the Department ofChemical Physics, National Institute of Chemi-cal Physics and Biophysics, Tallinn, Estonia. Hisresearch interests include permanent magnets,multiferroics, and memristive materials.

Raivo Stern received the M.Sc. degree incondensed matter physics from Tartu Univer-sity, Tartu, Estonia, and the Ph.D. (Solid StatePhysics) degree from Zurich University, Zurich,Switzerland, in 1987 and 1995, respectively.

He is currently a Research Professor inthe Department of Chemical Physics, NationalInstitute of Chemical Physics and Biophysics(NICPB), Tallinn, Estonia, and has served, since2006, as the Director of the whole NICPB. Hisresearch interests include the field of various

modern materials, in particular, quantum magnets, strong permanentmagnets, memristive materials, and unconventional superconductors.

Sami Ruoho (M’10) received the M.Sc. degreein applied physics from the University of Turku,Turku, Finland, in 1997, and the D.Sc. (Tech-nology) degree from Aalto University, Helsinki,Finland, in 2011.

He has been workig in the permanent mag-net industry since 2002. He is currently a Man-aging Director of Nordmag Oy, Pori, Finland,a company offering consulting and engineeringservices concerning permanent magnets andPM machines. His research interests include the

properties of rare earth magnets and electromagnetic and thermal mod-eling of electromagnetic devices.

Juha Pyrhonen (M’10) was born in Kuu-sankoski, Finland, in 1957. He received the Doc-tor of Science (D.Sc.) degree from the Lappeen-ranta University of Technology (LUT), Lappeen-ranta, Finland, in 1991.

He became an Associate Professor of electri-cal engineering at LUT in 1993 and a Professorof electrical machines and drives in 1997. He isengaged in research and development of elec-tric motors and electric drives. His current re-search interests include different synchronous

machines and drives, induction motors and drives, and solid-rotor high-speed induction machines and drives.

Publication III

Egorov, D., Petrov, I.; Link, J., Stern, R., and Pyrhönen, J. J.Model-based hysteresis loss assessment in PMSMs with ferrite magnets

Reprinted with permission fromIEEE Transactions on Industrial Electronics

vol. 65(1), pp. 179–188, 2018© 2018, IEEE Journals & Magazines

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 1, JANUARY 2018 179

Model-Based Hysteresis Loss Assessment inPMSMs With Ferrite Magnets

Dmitry Egorov , Ilya Petrov , Joosep Link, Raivo Stern, Member, IEEE,and Juha J. Pyrhonen , Member, IEEE

Abstract—Hysteresis losses in ferrite permanent mag-nets (PMs) of a rotor-surface-magnet (RSM) PM syn-chronous machine (PMSM) were studied by means ofvibrating sample magnetometer (VSM) measurements, up-dated static history dependent hysteresis model (HDHM)and finite element analysis (FEA). Open magnetic circuitVSM measurement results were applied to determine themagnet intrinsic properties. The HDHM developed originallyfor electrical steel hysteresis modeling is adopted for ferritePM material. FEA-based results for magnetic field strengthin PMs of a tooth coil winding RSM PMSM under ideal si-nusoidal and frequency converter supplies were used asinput data for the HDHM and the hysteresis losses were cal-culated in the machine’s magnets. Differently from NdFeBand SmCo PMs ferrite PMs do not seem to demonstrate sig-nificant hysteresis behavior. It was found that the hystere-sis loss could be neglected in ferrite PMs in most PMSMdesigns if the magnet is fully polarized.

Index Terms—Ferrite magnets, hysteresis loss, per-manent magnet (PM) losses, rotor-surface-magnet (RSM)permanent magnet machines.

I. INTRODUCTION

THE property of permanent magnet (PM) material to pro-duce a magnetic field without a continuous external source

of energy has led to a wide usage of PMs in electrical machinesdesigned for various purposes.

In theory, the application of PMs allows us avoiding the exci-tation Joule loss and, thus, increasing the efficiency of an electri-cal machine compared with similar speed and power machineswithout PM material. However, in practice, the PM material inan electrical machine can be prone to both eddy-current and hys-teresis losses [1]. The eddy current losses of sintered rare-earthmagnets are widely discussed in research papers and can becalculated both by analytical and finite element analysis (FEA)based means [2]–[4].

Manuscript received November 22, 2016; revised March 3, 2017 andApril 24, 2017; accepted May 17, 2017. Date of publication June 9, 2017;date of current version November 16, 2017. (Corresponding Author:Dmitry Egorov.)

D. Egorov, I. Petrov, and J. J. Pyrhonen are with the Department ofElectrical Engineering, LUT Energy, School of Technology, Lappeen-ranta University of Technology, Lappeenranta 53851, Finland (e-mail:dmitry.egorov@lut.fi; ilya.petrov@lut.fi; juha.pyrhonen@lut.fi).

J. Link and R. Stern are with the Department of Chemical Physics,National Institute of Chemical Physics and Biophysics, Tallinn 12618,Estonia (e-mail: jooseplink@gmail.com; raivo.stern@gmail.com).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2017.2714121

The hysteresis loss possibility in electrical machine PM ap-plications is a relatively lately studied phenomenon, which hasattracted attention with the increasing penetration of perma-nent magnet synchronous machines (PMSMs) on the marketand general demands of electrical machine effectiveness. Thehysteresis losses in NdFeB magnets were separated from eddycurrent losses by a two-frequency method and applied to theanalysis of a rotor surface magnet (RSM) PMSM in [5]. Thetesting procedure in [5] uses magnetically short-circuited PMsthat is not a normal situation in a rotating machine, which hasan air gap. Therefore, the method results in overestimated hys-teresis loss. The possibility of hysteresis loss was analyticallyobserved for a traction motor and a high-speed motor in [6]and for a tooth coil winding (TCW) RSM PMSM in [7]. Fi-nally, some hysteresis loops for NdFeB, SmCo, and ferrite PMswere measured in [1] at ambient temperature and the hysteresislosses themselves were roughly determined for an RSM PMSMbased on a couple of measured loops. The measurement resultsfor SmCo and NdFeB in [1] are provided for fully magnetizedsamples and clearly depict the possibility of SmCo and NdFeBPM materials having hysteresis loss during the normal operationmode of the machine in an unfortunate design case. However,the results for the ferrite PM grade were obtained for a partiallydemagnetized sample that is not typical for the actual usage ofPMs in electrical machinery and, because of this, a mislead-ing conclusion regarding the observed ferrite PM material wasmade. Thus, no appropriate investigation has been provided yetabout the possible contribution of ferrite PM’s hysteresis loss inthe total loss of an electrical machine during its normal operationmode.

Recently, ferrite PMs were used in high-speed electrical ma-chines [8]. The high electrical resistivity of ferrite PM materialssignificantly damps possible eddy currents in this material andmakes it attractive, e.g., for high-speed applications. The resultsin [8] depict a significant reduction of high-speed PMSM costwith very small degrading of efficiency when comparing the useof SmCo or ferrite in PMSMs. The much lower remanence offerrite PMs compared to typical remanences of rare-earth mag-nets requires using a smaller airgap and despite this, a low airgap flux density will be still observed in an RSM PMSM. Thelow air gap flux density can be compensated by a higher linearcurrent density in the stator. However, this leads to a higherarmature reaction field. Thus, the necessary conditions for thehysteresis loss are more likely created in PMSMs with ferritePMs than with rare-earth PMSMs [6], [9].

0278-0046 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

180 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 1, JANUARY 2018

Fig. 1. Typical NdFeB JH-loop behavior. Due to the presence of struc-tural defects, i.e., some soft magnetic material in PM the JH-curvechanges its slope when crossing the J-axis. If the external field strengthΔH is high enough to move the operating point of the PM from the sec-ond quadrant to the first and back, the hysteresis loop A-B-C-D-A isformed.

This paper studies the hysteresis loss in the ferrite PMs ofa TCW RSM PMSM designed to work as a generator in a hy-brid vehicle application [9]. High accuracy measurements, FEAsimulations, and analytical modeling are used in the study. Theparameters of the observed PMSM are provided in [9] and forthe sake of completeness, repeated in this paper (see Section III).The paper is organized as follows. The measurements and an-alytical model principle are presented in Section II. Section IIIcontains the model calculation results accounting the lossesin ferrite PMs. Discussion of the results and conclusions areprovided in Sections IV and V.

II. METHODS

A. Hysteresis Loss Mechanism and Measurements

The presence of soft magnetic regions in PM material enableshysteresis loss in some PMSM designs [1]. As an indicationof the existence of these soft magnetic regions is the relativepermeability μr value of the material higher than one [6]. Inpresent day, ferrites μr ≈ 1.05 − 1.1 [10], [11]. Fig. 1 depictsa typical hysteresis loop of an NdFeB magnet found by mea-surements provided in [1] and [6]. The measurement results forfully polarized NdFeB and SmCo PMs show that the possibilityof hysteresis losses in a PM material can be detected with thesteepness change of the main loop when it is crossing the J-axis.

The test bench is the same as was used in [1] and containsa physical properties measurement system with up to 14 T su-perconducting magnet developed by Quantum Design with aP525 vibrating sample magnetometer (VSM) and data acquisi-tion system. The testing sample (BM9 ferrite PM) was cut fromthe magnetic pole of the PMSM observed. It has the dimensionsof 3 × 3.6 × 4 mm3 with the direction of magnetization Maligned along the longest edge (M↑↑) and mass of 0.1689 g.In this case, the sample was heated up to 83 °C that approx-imately corresponds to the actual working temperature of theobserved PMSM [9]. The choice of the measurement system ismade based on the report that the hysteresisgraph-based mea-surements with closed magnetic circuit can have insufficientaccuracy in this very case [6].

The measurement results in Fig. 2 depict small loops that areformed by varying the magnitude and sign of the external field

Fig. 2. VSM output for BM9 sample at 83 °C obtained during onemeasurement. Both main and minor loops do not change the steepnessof slope when passing from the second quadrant to the first and back.Some intermediate loops were excluded to make the data more readable.

Fig. 3. Influence of the demagnetizing field Hd on the field inside PM.The demagnetizing field Hd arises in the PM sample in a partly or totallyopened magnetic circuit and always tries to demagnetize the PM. Thefield strength inside PM Hi is equal to the vector sum of Ha and Hd .(a) VSM measurements in case where the direction of the external ap-plied field strength Ha coincides with the direction of magnetization Mof the PM. (b) Simplified magnetic circuit of a PMSM. The armature re-action field is represented by the applied field Ha that is opposite to M,which is the usual but not the only possible case in rotating machinery.

strength acting on the initially fully polarized sample. It is seenthat both the main loop and the minor loops do not experienceany clear change of the slope steepness when crossing the J-axis.The result, however, indicates that there exist hysteresis loops,and therefore a possibility for hysteresis loss but the behaviorof the present ferrite PM grade is different compared to thebehavior of rare-earth magnets illustrated in Fig. 1.

The open circuit measurement system of VSM creates a de-magnetizing field problem that will be discussed in the followingsection. It makes the interpretation of the measurement resultssomewhat complicated because the conditions of the magnetstrongly differ from the conditions in a real machine and a cor-rection in the analysis must be made.

B. Demagnetizing Field

The obtained polarization measurements J versus the appliedfield Ha represent the characteristics of a ferrite sample in atotally open magnetic circuit. The demagnetizing field emergesin a PM if an airgap is present in the PM’s magnetic circuit[10]. This field is directed against the magnetization and triesto demagnetize the PM as shown in Fig. 3. The presence of thedemagnetizing field Hd results in a different shape in a VSM-measured JH-curve compared to the real or intrinsic hysteresis

EGOROV et al.: MODEL-BASED HYSTERESIS LOSS ASSESSMENT IN PMSMS WITH FERRITE MAGNETS 181

curve of the PM material that is represented as polarizationversus internal field Hi and can be measured when the sampleis magnetically short circuited. A magnetometric demagnetizingfactor Nm can be used to convert the VSM measurement resultsinto the intrinsic hysteresis curve of the material [10]:

Hi,i = Ha,i − Nm

μ0Ji (1)

where Hi, i are the field strength values inside the PM, (Ha,i , Ji)are the measurement results from VSM, and μ0 = 4π ×10−7 H/m is vacuum permeability. Assuming that the materialsusceptibility χ = μr − 1 is constant and close to zero, Nm iscalculated analytically for a parallelepiped formed sample with2x × 2y × 2z (M↑↑) being the dimensions of the sample asfollows [12]:

Nm =2π

arctan

(xy

z√

x2 + y2 + z2

)+

13πxyz

(F2 + F3)

+1

2πxyz(Fm (x, y, z) + Fm (y, x, z) − Fm (z, x, y)

− Fm (z, y, x)) (2)

where

F2 = x3 + y3 − 2z3 +(x2 + y2 − 2z2) √

x2 + y2 + z2 (3)

F3 =(2z2 − x2) √

x2 + z2 − (2z2 − y2) √

y2 + z2

− (x2 + y2)3/2

(4)

Fm (u, v, w) =

u2v log

(u2 + w2

) (u2 + 2v2 + 2v

√u2 + v2

)u2

(u2 + 2v2 + w2 + 2v

√u2 + v2 + w2

) . (5)

For the observed sample χ = 1.26 – 1 = 0.26 results inNm = 0.29. Comparison with FEA-based calculation data pro-vided in [13] for χ = 0.26 demonstrates (0.29 – 0.2899) ×100%/0.29 = 0.03% of inaccuracy. Thus, the usage of (2)–(5)for the calculation of Nm is acceptable for practical purposes.

The measured and actual JH- and respective BH-curves of theferrite sample are depicted in Fig. 4. The intrinsic polarizationcurve of the PM has a clearly steeper slope than in case ofthe VSM open circuit measurement system. Thus, neglectingthe effect of the demagnetizing field Hd during VSM results’treatment will result in incorrect determination of material’sintrinsic properties.

A demagnetizing field is present inside a PM when it is placedin a magnetic circuit of an electrical machine because of thepresence of an airgap and slot openings. This field is taken intoaccount with FEA-based program that is used in the paper for thecalculation of the magnetic field strength inside the PM regionduring the PMSM operation.

C. History Dependent Hysteresis Model (HDHM)

The variation of the magnetic field strength in each elemen-tary volume of a PM in a PMSM under operation is not symmet-rical with respect to the H-axis of its BH-plane and depends on

Fig. 4. Second quadrant JH- (left group) and BH-curves (right group)of the ferrite sample according to VSM open circuit measurements (red)and transferred results of a corresponding closed magnetic circuit (blue).The intrinsic JH-curve of the ferrite sample has a steeper slope comparedto the VSM measurement result.

the magnetic circuit configuration of the PMSM, local teeth sat-uration, permeance, and inverter caused harmonics. This makesthe measurements of symmetrical hysteresis loops similar tothat in Fig. 2, and [1] insufficient for the determination of thehysteresis loss with acceptable accuracy during actual PMSMnormal operational mode.

The modeling of PMs in FEA software for electrical machinedesign has been provided in different ways balancing betweensimplicity and accuracy of models. The linearized models [14],[15] can be a good option in case of combined thermal and mag-netic analysis but they neglect the hysteresis loss, in principle.The Preisach-type models are able to simulate the hysteresisbehavior of a PM but are known for some considerable draw-backs, such as congruency problem, complex procedure of themodel identification method, and sensitivity to measurementerrors [16]–[18]. For example, the classical Preisach model (C-PM) used for the FEA simulation of NdFeB magnets in a PMSM[17] exhibit vertical congruency of minor loops, which can beabsent in real magnetic materials and, therefore, can lead toan overestimation of hysteresis loss [16]. An FEM-based soft-ware using vector potential A requires magnetic field strengthH as function of flux density B or J whereas C-PM output isB(H) or J(H). Extensive research has been carried out to over-come or at least to suppress the aforementioned drawbacks ofthe Preisach modeling concept [16]. As an alternative to thePreisach-type models, the phenomenological HDHM was pro-posed in [18] for the simulation of quasi-static H(B) curves ofelectrical steels. The mathematics of the HDHM is able to repro-duce exactly a measured main loop and incorporates the mostrelevant Madelung’s empirical rules, i.e., return point memory(RPM) and wiping out property [18]. The HDHM does not suf-fer from a congruence problem and the direct generation of H(B)or H(J) dependencies without any model modifications makes itattractive for implementation in transient simulators [19]–[21].

The parameters of the HDHM are defined based on the as-sumption that an adjustment of the model to agree with the mea-sured major loop and a set of first-order recoil curves (FORCs),i.e., curves that start from the main loop and end at its tip,enables the simulation of high-order recoil curves with accept-able accuracy. Similar approach was followed to identify the

182 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 1, JANUARY 2018

Fig. 5. Reversal curves measured for the tested ferrite material at am-bient temperature for an initially fully polarized sample. Similarly to thedata in Fig. 2 the loops do not steeply change their slope when cross-ing the J-axis. Due to the presence of accommodation phenomenon,the reversal curves do not return exactly to previous reversal point and,therefore, move in parallel with the main JH-loop but do not match withit exactly after a recoil loop is formed. The effect of accommodation,however, seems to be negligible close to the J-axis that is the region ofinterest in the study.

parameters of some Preisach-type models [17], [22] andphysics-based analytical general positive-feedback (G-PFB)model [16], [23] for the simulation of semihard and hard mag-netic materials. In particular, the G-PFB model demonstratedfair accuracy between model-simulated and measured reversalcurves for materials with coercivities of 1.35 × 106 – 18 A/m,including ferrite magnet grade [24]. The hysteresis loss canchange the shape of the main loop as shown in Fig. 1. The abil-ity of the G-PFB model to reproduce exactly the measured mainloop is severely limited in the mathematics employed. This cansignificantly degrade the model’s accuracy close to the J-axis ofan initially fully polarized PM, and that is the region of interestin the study. Therefore, it is expected that the HDHM will bea reasonable compromise between implementation complexity,dataset needed for model’s identification and accuracy com-pared with the Preisach-type and G-PFB models in this verycase.

The key assumption in the HDHM is that in the absence ofaccommodation (reptation) phenomenon the reversal curves ofa material obey the RPM effect, i.e., any reversal curve fromcurrent arbitrary reversal point always returns to the previousreversal point. The comprehensive literature review provided in[23] demonstrates the physical and theoretical evidence that theRPM effect is normally the expected feature of hysteresis in PMmaterials. Fig. 5 depicts arbitrary measured recoil loops of thestudied sample at ambient temperature. The reversal curve tendsto travel close to the main loop after any recoil loop is formed.Such a behavior to some extent demonstrates both the RPMeffect and the wiping out memory property of hysteresis used inthe mathematics of the HDHM. However, detailed investigation

Fig. 6. Illustration of the HDHM principle. The outer loop for the FORCB-K-P-N is the main loop (blue line) since B-K-P-N starts from mainloop’s branch and is fully enclosed by the main loop (main loop is not fullyshown). The outer loop for the SORC P-D-B is formed by using B-K-P-N(red dashed line) and part of the main descending loop N-B. The curvesB1 − K1 − P1 − B1 (green dashed line) and B1 − K1 − P1 − B ′

1 − P ′1

(magenta dashed line) demonstrate a possible difference between themodeled and the actual magnet behavior due to the accommodationphenomenon when the magnetic field strength iterates between HB 1and HP 1 . Accommodation displaces the ends of recoil loops along J-axisby drifts Δ1 and Δ2 whose values and directions depend on the width ofthe minor loop, its location on the main loop and the number of iterationsbetween HB 1 and HP 1 . Figs. 2 and 5 show that the accommodationeffect can be neglected close to the J-axis of an initially fully polarizedmagnet.

of the measurement results in Fig. 5 reveals the presence of theaccommodation phenomenon since the reversal curve does notmatch the main loop exactly but moves in parallel with it afterthe recoil loop was formed [25]. The phenomenon observed canlimit the accuracy of the models incorporating the RPM effect,e.g., the HDHM used in this study, some Preisach-type mod-els, linearized, and G-PFB models. Nevertheless, the measuredloops near the J-axis in Figs. 2 and 5 show that the effect ofaccommodation is negligible when the magnet operates close toits fully polarized state. Similar behavior of the recoil loops weredemonstrated for electrical steels [26], [27] and NdFeB magnet[6]. Some of the results in [6] (see Fig. 6 in [6]), however, areheavily corrupted by eddy currents in the tested material causedby measurement system used. As the consequence of the find-ings in [6], [26], and [27], and the data in Figs. 2 and 5, theaccommodation phenomenon is neglected in the model used inthis study. However, the effect of accommodation can be inte-grated into the HDHM concept as it was demonstrated in [27]with the early version of the HDHM.

The principle of the HDHM is shown in Fig. 6. For example,if for some reason the external field at point P, that lies at curveB-K-P-N in Fig. 6, is reversed and goes negative then the re-versal curve P-D-B ends at the previous reversal point B. Thisillustrates the RPM effect described earlier. The constructionof the ascending FORC B-K-P-N and the descending second-order reversal curve (SORC) P-D-B are depicted in Fig. 6 inorder to clarify the mathematics used by the HDHM. The con-struction of any reversal curve is based on its outer loop–theloop that envelopes the reversal curve. For any FORC the outerloop matches with the main loop. The modeling principle canbe applied for any order reversal curve, so the term outer loop

EGOROV et al.: MODEL-BASED HYSTERESIS LOSS ASSESSMENT IN PMSMS WITH FERRITE MAGNETS 183

is used further also for the FORC case. The outer loop is alwaysknown from previous magnetization and stored in the model’smemory. The ascending reversal curve B-K-P-N begins fromthe descending branch of the outer loop at point B and ends atpoint N where ascending and descending branches of the outerloop merge. The width of the outer loop at the starting point ofa constructed FORC ΔHrev is determined as follows:

ΔHrev = Hacs (JRC) − Hdes (JRC) (6)

where Hacs(J) and Hdes(J) represent the ascending and de-scending branches of the current outer loop, respectively, JRCis the polarization value at the starting point of the reversal curve(for B-K-P-N JRC = JB ). The H-value for an arbitrary point Kwith polarization value JK of the FORC B-K-P-N is determinedas distance ΔH from point C that lies on the ascending branchof the outer loop and has the same J-coordinate as point K:

HK (JK ) = Hacs (JK ) − ΔH (JK ) (7)

where ΔH(J) is the term that determines the behavior of thereversal curves, i.e., the shape of the hatched zone in Fig. 6 thatdecreases from ΔHrev to zero in a nonmonotonic way as theJ-values of the reversal curve approaches from the reversal pointto the tip of the outer loop. The original expression is providedin [18] for ΔH(B) of electric steels and insufficiently accuratelyrepresents the hysteretic behavior of a ferrite PM. The FORCB-K-P-N in Fig. 6 shows the typical behavior of FORCs thatwere observed for the ferrite sample. First, the FORC quicklyapproaches about horizontally the ascending branch of the outerloop, then climbs almost parallel to it for a certain range ofJ-values and finally, decreasing its rise rate in a monotonic wayapproaches the fully polarized state of the PM. The describedbehavior approximately takes place along the B-K, K-P, and P-N segments of B-K-P-N. The following expression is proposedin this paper for ΔH(J) for the ferrite PM’s reversal curves:

ΔH (JK ) =

ΔHrev (JRC) · [1 − ((b − d) · ξ (JK ) + d)] ξ (JK )

· e−a ·ΔJr e v ·(1−ξ(JK )) + (Hacs (JK ) − Hdes (JK ))

· ((b − d) · ξ (JK ) + d) (8)

where

ξ (JK ) =Jh − JK

Jh − JRC(9)

ΔJrev = Jh − JRC (10)

ξ is dimensionless quantity that decreases from 1 to 0 as a re-versal curve approaches the outer loop tip, Jh is the polarizationvalue at the tip of the outer loop (for B-K-P-N Jh = JN ). Co-efficients a > 0, 0 � b � 1, 0 � d � 1 in (8) determine the shapeof the hatched zone in Fig. 6 and are obtained by fitting of themodel with experimentally obtained FORCs during the model’sparameter identification procedure. Fig. 7 shows the influenceof a, b, and d coefficients on the shape of the reversal curves.Similarly to the original model [18] the choice of a, b, and din the provided ranges guaranties that any reversal curve willalways be inside its outer loop. Fig. 7 depicts the possibility

Fig. 7. The influence of the coefficients a, b, and d on the behavior ofthe reversal curves that are generated with an HDHM. Curve 5d depictsthe possibility of nonphysical behavior (dB/dH < 0) of the model if thecoefficient d is chosen inappropriately.

of nonphysical behavior of the model if coefficient d is choseninappropriately. This can be avoided with careful balancing ofall coefficients during the fitting of the model with experimentalFORCs. It is seen in Fig. 5 that the shape of the FORCs dependson their starting point at the main loop. Thus, the coefficientsa, b, and d are characterized by a dimensionless ratio β that isdetermined for any ascending reversal curve as follows:

β =Jh − JRC

ΔJ(11)

where ΔJ is the peak-to-peak polarization value of an currentouter loop.

When the FORC B-K-P-N in Fig. 6 is constructed, it formsa new outer loop that is used for further computations. Nowthe ascending and descending branches of the outer loop areformed by B-K-P-N and N-B, respectively. The constructionof the SORC P-D-B is performed in a similar way with somecorrections of (6)–(11). The value of the field strength corre-sponding to the polarization value at an arbitrary point D thatbelongs to P-D-B is obtained as follows:

HD (JD ) = Hdes (JD ) + ΔH (JD ) . (12)

The term ΔH(J) is also determined by (8). However, thefollowing coefficients have to be used instead of (9)–(11) forany descending reversal curve:

ξ (JD ) =JD − Jl

JRC − Jl(13)

ΔJrev = JRC − Jl (14)

β =JRC − Jl

ΔJ(15)

where JRC and Jl are the polarization values of the reversal pointand the lowest point, respectively, of the current outer loop.In the observed example of P-D-B construction JRC = JP ,Jl = JB , and ΔJ = JN − JB . The new outer loop B-K-P-D-B is formed. This loop can be used further if some arbitrary pointD of the curve P-D-B will become the newest reversal point.According to the wiping out property, if the reversal curve P-D-B propagates further than B, it will continue to propagate alongthe descending branch of the previous outer loop, i.e., along themain loop in the observed case, as if the loop B-K-P-D-B hadnever existed. Similarly, if an ascending reversal curve D-S-P

184 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 1, JANUARY 2018

Fig. 8. Coefficients used in the model. Similarly to the major loops thecoefficients can be inserted in the model by using interpolation tools thatare available in most commercial software.

Fig. 9. Comparison of measurement data (blue solid lines) and HDHMresults (red dashed lines).

Fig. 10. Comparison of measurement data (blue solid lines) and theHDHM results (red dashed lines) in the regions that are actually usedduring the PMSM operation.

propagates further than P, it moves along the segment P–N of theprevious outer loop ascending branch. The described methodsfor the FORC B-K-P-N and the SORC P-D-B are applicable forany higher-order (third, fourth etc., order curves starting fromthe previous order curve) ascending and descending reversalcurves, respectively [18].

Fig. 8 depicts the coefficients obtained by sequential fittingof measured and model-calculated FORCs during the identifica-tion procedure of a model’s parameters for the observed ferritesample. The HDHM concept assumes that trajectories of themajor and minor loops are similar [18], and therefore the de-pendences of a(β), b(β), and d(β) are used for the constructionof any ascending or descending reversal curve for which β iscalculated by (11) and (15), respectively. Figs. 9 and 10 show

Fig. 11. Comparison of the experimentally obtained hysteresis loops(blue solid lines) with the model results (red solid lines).

TABLE IPARAMETERS AND DIMENSIONS OF THE OBSERVED TCW RSM PMSM

Parameter Value

Rated power P, [W] 50 000Rated torque T, [Nm] 159Rated stator current Is , [Arms] 83.8Rated speed n, [rpm] 3000Relative width of magnet on a machine’s pole αp 0.95Permanent magnet remanence Br , [T] 0.34Relative permeability of the permanent magnet μr 1.26Number of stator slots Qs 24Number of pole pairs p 10Permanent magnet height hP M , [m] 0.017Permanent magnet length l, [m] 0.102Stator outer radius rs , [m] 0.169Rotor inner radius rr , [m] 0.187Width of slot opening b0 , [m] 0.0075Converter frequency, [Hz] 500Number of series turns per one coil 10

the accuracy of (8) accounting the modeling of FORCs, andFig. 11 depicts the comparison of the model-calculated resultswith some hysteresis loops in Fig. 2 corrected by (1)–(5).

The slope of the major loop is not changing when it is crossingthe J-axis. Such a behavior of the major loop is different fromwhat was observed in the case of NdFeB and SmCo PMs [1].The absence of a strong hysteretic behavior of the ferrite samplemakes it possible to use the presented HDHM for the hysteresisloss evaluation in the PM material.

III. RESULTS

A TCW RSM PMSM that was originally presented in [9] isobserved in this paper. The PMSM has external rotor topologywith radially magnetized ferrite PMs. The parameters of thePMSM are provided in Table I and a sketch of the machine isdepicted in Fig. 12. The topology of the observed PMSM hasseveral advantages: short end-turns in TCW PMSMs reduce theamount of copper material needed and the application of the ex-ternal rotor design allows using more magnetic material with thesame overall dimensions of the machine. The main drawbacks ofthe TCW configuration are increased rotor core and PM lossesbecause of significant amount of space harmonics, especiallyin case of high-speed machines [28]. Rotor core losses can be

EGOROV et al.: MODEL-BASED HYSTERESIS LOSS ASSESSMENT IN PMSMS WITH FERRITE MAGNETS 185

Fig. 12. Magnetic circuit of the studied TCW PMSM. The mesh of themodel contains 91 256 nodes. The PM is divided in 11 layers with 200points in each layer. The PM division is depicted at the rightmost part ofthe figure by yellow lines.

Fig. 13. Measured current waveforms when the PMSM observed issupplied with a frequency converter.

minimized by keeping a low flux density in the core during thedesign process. The high resistivity of ferrite PMs significantlyreduces the eddy-current loss [29]. However, the usage of ferritePMs can also result in a variation of the magnetic field strengthbetween the second and the first quadrant of the BH-curve insome parts of PM as a result of strong armature reaction. Thisis because the relatively low PM’s remanence requires using ahigh linear current density to provide torque/power density atthe same level as in machines with NdFeB/SmCo PMs.

This study uses commercially available FEA software Flux2D by CEDRAT for the simulation of the observed PMSM dur-ing the normal operation. The linearized models for the magnetutilized in the software chosen neglect the variation of polariza-tion that can occur at the linear part of main loop as depictedin Fig. 11. Thus, the usage of the magnetic field strength val-ues provide less error for the hysteresis loss calculation withthe procedure applied. The magnetic field strength values canbe easily transferred to the correct flux density values for theHDHM since the structure of the model ensures that the be-havior of a reversal curve starting from any arbitrary reversalpoint is known in advance until the next reversal point takesplace [18].

The FEA simulations were performed with step 10–5 s fora full mechanical period of the PMSM (0.02 s) for two cases:supplying the motor with ideal sinusoidal current with rated rmsvalue from Table I and the experimentally measured currentwaveform depicted in Fig. 13. The full mechanical period ischosen as the optimal time period to be used in the calculationsas a compromise between the speed and the accuracy of the

Fig. 14. Hysteresis loss distribution in the PM. (a) Ideal sinusoidalcurrent supply. (b) Frequency converter supply. The outer rotor PMs arerotating counter clockwise.

FEA-simulation. In such a case every elemental volume of thePMSM’s magnetic pole experiences all possible air-gap spaceharmonics created by the drive system. The PM was dividedin k = 11 × 200 = 2200 elementary volumes as shown inFig. 12. The magnetic field strength values were calculated ineach elementary volume of the PM and used then as input forthe HDHM. The hysteresis loss in the whole volume of thePMSM’s pole magnet for one mechanical period Ehyst (Jouleper 0.02 s in the studied case) is calculated as the average ofthe calculated losses in each ith elementary volume of the PMPhyst,i multiplied by the volume of the PM as follows:

Ehyst =l · αp · π ·

(r2r − (rr − hPM)2

)

2p · kk∑

i=1

Physt,i (16)

whose parameters can be found in Table I. The total hysteresisloss in the whole PM material of the machine per second dependson its number of poles 2p and the machine’s rated speed n:

Physt =n · p · Ehyst

30. (17)

The distribution of the loss in the volume of the PM is depictedin Fig. 14. The total losses calculated by (16) and (17) in themagnets of the observed PMSM are only 4.1 and 4.2 W forsinusoidal and frequency converter supply, respectively.

IV. DISCUSSION

The FEA calculated values of the field strength variation usedin the calculation of the hysteresis loss in the PMSM under fre-quency converter supply are depicted in Fig. 15 for time period0.001 s that is chosen as appropriate to demonstrate the mainphenomena affecting the hysteresis loss. The variation of thefield strength is the highest in the part of PM that is closestto the airgap and decreases considerably when approaching therotor yoke. It is seen in Fig. 15 that the slotting creates the domi-nant effect on the magnetic field strength variation. The invertercaused current harmonics produce small fluctuations of the field

186 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 1, JANUARY 2018

Fig. 15. Field strength variation in the PM within the time period of0.001 s under frequency converter supply. (a) Top of PM (close toair gap), (b) Middle of PM. (c) Bottom of PM (close to rotor yoke).1–slotting effect, 2–tooth tip leakage flux effect, 3–effect of local toothsaturation. The effect of converter caused current harmonics can beseen as small ripples of the magnetic field strength in any part of the PMwithin the time.

strength that can be observed as small ripples in Fig. 15. Themodel computational results show that the current harmonicsproduce (4.2–4.1)/4.2 = 2.4% of total calculated hysteresis lossand, thus, the FEA calculation under sinusoidal supply seemsgood enough to calculate the hysteresis loss for practical meansfor TCW PMSMs with ferrite magnets. The situation, however,can be different in case of distributed winding (DW) PMSMssince these machines have relatively small slot openings com-pared to TCW PMSMs, i.e., the share of hysteresis loss causedby frequency converter time harmonics is expected to be higherin DW PMSMs [29].

The variation of the field strength in the PM is additionallyenhanced by the armature field spatial harmonics caused by thecurrent fundamental, the tooth tip leakage flux effect and localtooth saturation. The phenomena have the highest influence inthe parts of the PM that are closest to the airgap. Figs. 10, 11,and 15 show that the variation of the magnetic field strengthof the observed machine is located on the part of the JH-curvethat is traditionally considered a part with constant polarizationvalue and linear behavior of the BH-curve, i.e., no irreversibledemagnetization takes place under the field variation. The mea-surement results, however, show that the ferrite PM materialforms minor loops that contain very little energy density. Fig. 11shows that the magnitude of the magnetic field strength varia-tion is the most dominant factor that affects the value of thehysteresis loss at the parts of the JH-curve that are actually usedduring the PMSM normal operation.

The loss distribution depicted in Fig. 14 is analyzed withthe magnetic field variation in Fig. 15. The loss distribution re-veals the highest losses at the air-gap surface of the PM. Thehighest losses are caused by the highest magnitudes of the mag-netic field strength variation that take place in the part of thePM that is closest to the airgap due to the combined effect ofthe armature and PM fields modulated by the permeance har-monics and tooth tip leakage flux. The armature-reaction-fieldand permeance-variation-caused harmonics are significantly re-duced when approaching from the airgap towards the rotor yokeas it can be seen in Fig. 15(a)–(c) [30], [31]. The local toothsaturation phenomenon produces additional field variation atthe top of PM and, thus, increases the hysteresis loss. Fig. 15demonstrates that the effect of tooth saturation has its highestinfluence at the top of PM and become negligible when ap-proaching the rotor yoke. The hysteresis loss in other parts ofthe PM is significantly less compared to the air-gap surface ofthe PM. The average magnitudes of the magnetic field strengthvariations in Fig. 15(b), (c) are about one fourth in the middleand bottom of the PM compared to the parts of the PM thatare closest to the airgap. The reason for that is the significantlyreduced slotting effect, decreased armature field caused spatialharmonics and negligible tooth tip leakage flux effect deeper inthe magnet [30], [31].

The provided measurements reveal the absence of high hys-teresis losses when ferrite PM material is placed in the operatingconditions of an actual PMSM including the effects of operatingtemperature. The hysteresis losses are calculated with the modeland are equal to 0.0082% and 0.0084% of the machine nominalpower [9] for pure sinusoidal and frequency converter supply,respectively. Such results clearly show that the hysteresis losscan be neglected during the design process in case of fully polar-ized ferrite magnets. This should be actual, also for high-speedmachines, if the operational point of the PM is designed on thelinear part of the BH-demagnetizing curve.

Inverter caused current harmonics can significantly increasethe eddy currents in rare-earth PM material and even lead to itspartial demagnetization if an electrical machine does not havevery efficient cooling [32]. The model calculation results forthe ferrite PM hysteresis loss show that small magnetic fieldstrength fluctuations created by the inverter current harmonics

EGOROV et al.: MODEL-BASED HYSTERESIS LOSS ASSESSMENT IN PMSMS WITH FERRITE MAGNETS 187

cause only very small share of the total hysteresis loss in ferritePMs in case of TCW PMSM topology.

V. CONCLUSION

The hysteresis loss was studied in a ferrite PM by meansof VSM measurements, FEA simulation, and analytical modelfor the real operating conditions of an electrical machine. Inthis case, the ferrite PM did not demonstrate similar hysteresisbehavior in contrary to NdFeB and SmCo PMs. Some hystere-sis loss is present in the ferrite material. However, it can beneglected in most practical cases even if the PMSM is underfrequency converter supply. Slotting effect together with phe-nomena of tooth tip leakage flux, local teeth saturation, andarmature reaction space harmonics caused by the current fun-damental has the dominant contribution to the magnetic fieldstrength variation in a TCW PMSM and, thus, produce thelargest part of the total hysteresis loss, whereas the influenceof phase current harmonics is insignificant.

VSM is able to provide an accurate data for the analy-sis of PM allowing continuously and slow enough to varythe magnetic field at a fixed temperature; however, re-quires the correction of measured results with demagne-tizing field to get the intrinsic properties of the materialthat are of the most interest for the machine designer. Theanalytical model, which is used, has a relatively simpleimplementation algorithm and parameter identification proce-dure. It can be potentially implemented in an FEA software forelectrical machine design resulting in a complementary possibleoption for simulation of ferrite PMs.

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Dmitry Egorov received the B.Sc. degreefrom the Moscow Power Engineering Institute,Moscow, Russia, in 2013, and the M.Sc. degreein electrical engineering from the LappeenrantaUniversity of Technology (LUT), Lappeenranta,Finland, in 2015. He is currently working towardthe Doctoral degree in the Department of Elec-trical Engineering, LUT.

His research interests include electrical ma-chines and drives, in particular, the applicationswith the permanent magnets.

Ilya Petrov received the D.Sc. degree fromLappeenranta University of Technology (LUT),Lappeenranta, Finland in 2015.

He is currently a Fellow Researcher in theDepartment of Electrical Engineering, LUT.

Joosep Link received the Master’s degree inengineering physics from Tallinn University ofTechnology (TUT), Tallinn, Estonia, in 2016. Heis currently working toward the Doctoral degreeat TUT and an early-stage Researcher in theDepartment of Chemical Physics, National Insti-tute of Chemical Physics and Biophysics, Tallinn,Estonia.

His research interests include permanentmagnets, multiferroics, and memristive materi-als.

Raivo Stern (M’16) received the M. Sc. Degreein condensed matter physics from Tartu Univer-sity, Tartu, Estonia, and the Ph. D. degree in solidstate physics from Zurich Universitym, Zurich,Switzerland, in 1987, and 1995, respectively.

He is currently a Research Professor in theDepartment of Chemical Physics, National Insti-tute of Chemical Physics and Biophysics, Tallinn,Estonia. His research interests include the fieldof various modern materials, especially quan-tum magnets, strong permanent magnets, and

unconventional superconductors.

Juha J. Pyrhonen (M’06) born in Kuusankoski,Finland, in 1957. He received the D.Sc. de-gree from Lappeenranta University of Technol-ogy (LUT), Lappeenranta, Finland in 1991.

He became Professor of electrical machinesand drives in LUT, in 1997. He is engaged in re-search and development of electric motors andpower-electronic-controlled drives. He has wideexperience in the research and development ofspecial electric drives for distributed power pro-duction, traction, and high-speed applications.

Permanent magnet materials and applying them in machines have animportant role in his research. He is currently researching new carbon-based materials for electrical machines.

Publication IV

Egorov, D., Petrov, I., Pyrhönen, J. J., Link, J., and Stern, R.Hysteresis loss in ferrite permanent magnets in rotating electrical machinery

Reprinted with permission fromIEEE Transactions on Industrial Electronics

vol. 65(12), pp. 9280–9290, 2018© 2018, IEEE Journals & Magazines

9280 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 12, DECEMBER 2018

Hysteresis Loss in Ferrite Permanent Magnets inRotating Electrical Machinery

Dmitry Egorov , Ilya Petrov , Juha Pyrhonen, Senior Member, IEEE, Joosep Link,and Raivo Stern , Member, IEEE

Abstract—In this paper, hysteresis loss in magnetic polesof electrical machines with ferrite permanent magnets isstudied. A vibrating sample magnetometer is used to ob-serve the hysteresis behavior of three distinct commercialferrite magnet grades. The measurement results indicatethe presence of additional magnetic phases with reducedcoercivity in the samples under study. These phases canact as an additional source of loss in ferrite magnets. Anew modeling concept is introduced to simulate the hys-teresis behavior of the ferrite magnet grades in the secondand first quadrants of the intrinsic BH plane. Finite-element-calculated magnetic field distribution is used as an inputfor the analytical model to determine the hysteresis lossin the magnets of two distinct permanent magnet machinedesigns. The results indicate that some hysteresis loss inthe ferrite permanent magnet magnetic poles of electricalmachines may occur, but it plays a minor role in practice.

Index Terms—Electric machines, ferrites, loss measure-ment, magnetic field measurement, magnetic hysteresis,magnetic losses, magnetic materials, permanent magnet(PM) machines, permanent magnets.

NOMENCLATURE

a First coefficient in (16) determining the behavior ofthe constructed reversal curves.

asc Spline determining the ascending branch of the respec-tive main JH curve.

a1 Fitting parameter determining the maximum height ofthe main JH curve of the “soft” magnetic phase in (7)and (8) [T].

B Magnetic flux density [T].Br Remanent magnetic flux density [T].b1 Fitting parameter determining the slope change of the

main JH curve of the “soft” magnetic phase in (7)and (8).

bst Ratio of slot opening to tooth tip width.

Manuscript received October 17, 2017; revised January 17, 2018 andFebruary 20, 2018; accepted March 12, 2018. Date of publication April2, 2018; date of current version July 30, 2018. (Corresponding author:Dmitry Egorov.)

D. Egorov, I. Petrov, and J. Pyrhonen are with the Department of Elec-trical Engineering, LUT Energy, School of Technology, LappeenrantaUniversity of Technology, 53851 Lappeenranta, Finland (e-mail: dmitry.egorov@lut.fi; ilya.petrov@lut.fi; juha.pyrhonen@lut.fi).

J. Link and R. Stern are with the Department of Chemical Physics,National Institute of Chemical Physics and Biophysics, 12618 Tallinn,Estonia (e-mail: jooseplink@gmail.com; raivo.stern@gmail.com).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2018.2822619

c1 Fitting parameter in (7) determining the intrinsic coer-civity of the descending branch of the main JH curveof the “soft” magnetic phase [A/m].

c2 Fitting parameter in (8) determining the intrinsic co-ercivity of the ascending branch of the main JH curveof the “soft” magnetic phase [A/m].

d Second coefficient in (16) determining the behavior ofthe constructed reversal curves.

desc Spline determining the descending branch of the re-spective main JH curve.

Ehyst Hysteresis loss in the magnetic pole of the machine[W].

f Electrical frequency [Hz].H Magnetic field strength [A/m].H1 Lower value of magnetic field strength used in (6)

[A/m].H2 Higher value of magnetic field strength used in (6)

[A/m].Ha Applied magnetic field strength [A/m].Hasc Spline describing the ascending branch of the current

outer loop.HcB Normal coercivity [A/m].HcJ Intrinsic coercivity [A/m].Hdes Spline describing the descending branch of the current

outer loop.Hi Internal magnetic field strength [A/m].Hmax Maximum value of the magnetic field strength in the

magnet when the magnetic field strength varies be-tween Hmin and Hmax [A/m].

Hmin Minimum value of the magnetic field strength in themagnet when the magnetic field strength varies be-tween Hmin and Hmax [A/m].

hPM Permanent magnet height [m].Is Rated stator current [Arms].J Magnetic polarization [T].JRC Value of polarization at reversal point [T].k Number of elemental volumes in a magnetic pole.l Machine length in the axial direction [m].M Magnetization [A/m].N Number of turns in series turns in the stator phase.Nm Magnetometric demagnetizing factor.n Order of the respective reversal curve.nrated Rated speed [r/min].Physt, i Calculated hysteresis energy in the i-elemental volume

of the magnetic pole [J/m3].

0278-0046 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

EGOROV et al.: HYSTERESIS LOSS IN FERRITE PERMANENT MAGNETS IN ROTATING ELECTRICAL MACHINERY 9281

p Number of pole pairs.Qs Number of slots per stator.rri Rotor internal radius [m].rse Stator external radius [m].rsi Stator internal radius [m].S/V Surface-to-volume ratio of a magnet sample [m–1].Smeas Measured area of recoil loop [J/m3].Smod Model-simulated area of recoil loop [J/m3].tν Period when the magnetic field values at each magnet

point are repeated tν [s].VPMpole Volume of one magnetic pole [m3].x Half-width of a parallelepiped sample along the x-axis

[m].y Half-length of a parallelepiped sample along the y-axis

[m].z Half-height of a parallelepiped sample along the z-axis

[m].αp Relative width of a magnet on a pole of the machine.β Relation between the height of the constructed reversal

curve and the height of the current outer loop along theJ-axis.

δ Air-gap length [m].ζ Parameter in (6) to smooth the descending branch of

the main JH curve of the “hard” magnetic phase.μ0 Vacuum permeability 4π × 10 –7 [ H/m] .μr Relative permeability (of permanent magnet).ΔB Parameter to determine the descending branch of the

main JH curve of the “hard” magnetic phase [T].ΔH Distance along the H-axis between a point on the con-

structed reversal curve and a point with the same polar-ization coordinate belonging to the current outer loop[A/m].

ΔHrev Distance along the H-axis between the constructed re-versal curve and the current outer loop at the polariza-tion coordinate of the reversal point [A/m].

ΔJ Distance along the J-axis between the current point ofthe constructed reversal curve and the tip of the currentouter loop where the reversal curve ends [T].

ΔJout Height of the current outer loop [T].ΔJrev Distance along the J-axis between the reversal point of

the constructed reversal curve and the tip of the currentouter loop where the reversal curve ends [T].

I. INTRODUCTION

P ERMANENT magnet synchronous motors (PMSMs) withrare-earth (RE)-based magnets offer the highest efficiency

and power/torque density solutions compared with other motordesigns of similar power and speed. Nevertheless, the high cost,price volatility, unsustainable production process, and possiblesupply chain threats of RE materials used in permanent mag-net (PM) production have boosted intensive research aiming atfinding alternatives to RE PMs in electrical machinery [1]–[3].Ferrite PM-based electrical machine designs are a viable optionto overcome the RE-related mass production problems in somecases [1], [4]. The much weaker magnetic properties of fer-rite magnets compared with RE PMs (e.g., SmCo and NdFeB)

require special design efforts for ferrite PM machines to achieveperformances comparable with the level of RE magnet machinedesigns [4]. The growing number of applications of electricalmachines with ferrite magnets clearly reflects the increasinginterest in this type of PM material [1], [4]–[6].

Any material used in the magnetic circuit of an electrical ma-chine is usually investigated for losses that may be generatedduring a specific operating mode. The present-day electrical ma-chine design relies predominantly on the finite-element method(FEM), which enables a detailed analysis of a prototyped ma-chine. Present-day calculations of PM losses in commercialFEM software follow the eddy current loss theory [7]–[9] andthe hysteresis models that consider a magnet as a material con-sisting of a uniform hard magnetic phase [10]–[12]. However,the latest studies clearly show the possibility of some initiallyfully polarized PM materials to be the source of an additionalhysteresis loss, the magnitude of which can even be at the levelof the eddy current loss in the worst cases [13]–[15]. Eventhough sufficient conditions for the hysteresis loss in PMs havebeen demonstrated for both RE and ferrite PM-based electricalmachines, for instance, in [16], this loss is mostly neglected inthe analysis.

The hysteresis loss was determined from the total magneticac losses in Nd-based PM by a two-frequency method andapplied to the analysis of a rotor-surface-magnet PMSM in[13]. The experimental procedure in [13] estimates the lossesof a magnetically short-circuited sample. This situation is notvalid for PM machines, which have an air gap. Therefore, themethod in [13] is prone to overestimate the PM hysteresis lossin actual PMSMs. Three commercially available PM grades(NdFeB, SmCo, and ferrite) were studied with respect to hys-teresis loss at ambient temperature in [16] using a high accuracyvibrating sample magnetometer (VSM) measurement system.The measured data were used further for the calculation ofthe hysteresis loss in the magnetic poles of some PMSM de-signs. Nevertheless, inappropriate treatment of the VSM outputin [16] caused a shift of the measured hysteresis loops of thesamples in the second quadrant of the JH plane, and the cal-culated hysteresis loss was overestimated in the magnets of themachine designs under study. Furthermore, the ferrite PM sam-ple in [16] was partially demagnetized before the measurementtest, which is not a normal situation in the actual usage of PMmaterial in electrical machinery and may lead to an increasedPM hysteresis loss [12], [14]. Moreover, both the postprocess-ing methods used in [13] and [16] neglect the contribution ofsmall field fluctuations, caused for instance by local tooth sat-uration or tooth tip leakage flux, to the total PM hysteresisloss. Detailed VSM-based investigations of the hysteresis be-havior were conducted in [17] for ferrite PM samples (BM9grade) at the temperature of 83 °C and applied to the analy-sis of a tooth coil winding PMSM [17], including the effect offrequency converter current harmonics. The hysteresis loss inthe PM poles of the electrical machine in [17] was determinedby the combination of FEM-calculated magnetic field strengthvalues and the history-dependent hysteresis model (HDHM).The results in [17] show that the total PM hysteresis loss canbe neglected in ferrite PM motors in practice. However, the

9282 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 12, DECEMBER 2018

investigations in [17] are limited to the ferrite PM grade understudy.

The results available in the literature indicate that the totalmagnetic losses in PM materials used in electrical machinerycannot be understood with the eddy current theory and hysteresisloss in the main magnetic phase of the magnet only because ofthe possibility of extra hysteresis loss; however, this loss isusually neglected in the conventional efficiency analysis of PMmachines. The magnitude of PM hysteresis loss in PM poles isstill unclear both for RE- and ferrite-based PM machine designs.This paper studies the hysteresis loss phenomenon in the ferritePM magnetic poles of PMSMs. The hysteresis behavior of threecommercially available ferrite PM grades is investigated by ahigh accuracy VSM-based measurement system. A combinationof FEM-based calculations and a newly introduced analyticalmodeling concept is used to determine the total hysteresis lossin the magnetic poles of a tooth coil winding PMSM with anexternal rotor topology [4] and an axial flux PMSM design withan open slot structure [18].

This paper is organized as follows. Section II presents the de-tails of the measurement tests and the analytical model principle.Calculated results taking into account the hysteresis loss in PMsof the studied PMSM topologies are presented in Section III.Discussion of the results is provided in Section IV. Section Vconcludes the paper.

II. METHODS

A. Measurement Equipment and Procedure

A physical-properties-measurement system with up to 14Tesla superconducting magnets developed by Quantum Designwith a P525 VSM option and a data acquisition system is usedin the study. The VSM-based measurement system enables con-tinuous and slow enough variation of the magnetic field actingon the sample. The open magnetic circuit of the VSM elimi-nates the distortion of the measured results caused by the extrahysteresis loss and eddy currents that may occur in the yokesof the devices with a closed magnetic circuit, for instance, thehysteresis graph and installations used in [13] and [14]. Thedrawback of the VSM is the demagnetizing field in the samplehaving an air gap in its magnetic circuit. The output of the VSM,that is, the polarization J versus the applied field Ha, does notdirectly correspond to the intrinsic properties of the material,which are represented as J with respect to the internal field Hi.The postprocessing of the VSM data requires correction of eachmeasured point (Ji , Ha,i) as follows [19]:

Hi,i = Ha,i − Nm

μ 0Ji (1)

where Nm is the magnetometric demagnetizing factor and μ0 =4π × 10 –7 [H/m] is vacuum permeability. Assuming that therelative permeability of the ferrite PM μr is close to one [19],[20], Nm can be determined analytically for a parallelepiped-shape sample with the dimensions 2x × 2y × 2z (M↑↑) and the

Fig. 1. Ferrite PM samples under test. (a) C8 grade (0.0589 g, 2 ×2 × 3(M ↑↑) mm3 ). (b) Y28H-2 (0.0574 g, 2 × 2 × 3.1(M ↑↑) mm3 ). (c)Y32H-2 (0.0562 g, 2 × 2 × 3(M ↑↑) mm3 ).

magnetization M along the z-axis as follows [21]:

Nm =2π

arctan

(xy

z√

x2 + y2 + z2

)+

13πxyz

(F2 + F3)

+1

2πxyz(Fm (x, y, z) + Fm (y, x, z) − Fm (z, x, y)

−Fm (z, y, x)) (2)

where

F2 = x3 + y3− 2z3 +(x2 + y2 − 2z2)√x2 + y2 + z2 , (3)

F3 =(2z2 − x2)√x2 + z2 +

(2z2 − y2)√y2 + z2

− (x2 + y2)3/2, (4)

Fm(u, v, w) = u2v log

(u2 + w2

) (u2 + 2v2 + 2v

√u2 + v2

)u2(u2 + 2v2 + w2 + 2v

√u2 + v2 + w2

) .(5)

The FEM-calculated values of Nm [22] show a close matchto the analytically calculated values in the case of PMs, andtherefore, the use of (2)–(5) is acceptable for practical purposeswhen magnets of a parallelepiped shape are measured.

Fig. 1 depicts the three samples of different ferrite PM gradesused in the study. The sample of each grade was randomly se-lected from a batch ordered from a manufacturer. Based on theinformation provided by the manufacturer, the magnets to bestudied were produced by a hydrothermal synthesis method.The temperature of the measurements was selected to be 80 °C,which corresponds to the normal operating temperatures of fer-rite PM machines [4], [6]. The samples were fixed in the VSMsample holder with glass and nonmagnetic glue.

The measurement procedure was comprised of three separatetests for each sample. In the first test, the main JH curve andsets of first-order reversal curves (FORCs) were measured. Thestarting points of the FORCs were selected within an intervalfrom an initially fully polarized state to the normal coerciv-ity HcB of the respective sample. This region corresponds tothe second and first quadrants of the BH plane of the magnet,which are of the highest interest for a convenient loss analysisof magnetic components in rotating electrical machinery [23].The second test included observation of the sample behaviorwithin the second quadrant of the intrinsic JH plane. The de-tails of the measurement sequence can be found in [12]. In thethird test, several arbitrary reversal curves up to the fourth order

EGOROV et al.: HYSTERESIS LOSS IN FERRITE PERMANENT MAGNETS IN ROTATING ELECTRICAL MACHINERY 9283

Fig. 2. Main intrinsic JH curves for the PM samples under study andsome results according to the described measurement tests: a set ofFORCs for the C8 grade, recoil loops within the second quadrant of theintrinsic JH plane for the Y32H-2 grade, and variation of the magneticfield between the second and first quadrants of the intrinsic JH plane forthe Y28H-2 grade. All samples were fully polarized before each test.

were measured when the applied magnetic field strength wasstrong enough to move the operating point of the magnet fromthe second quadrant of the JH plane to the first and back. Fig. 2depicts the main JH curves of the samples together with somemeasurement results according to the test procedures describedin the paper.

The unusual behavior of the measured curves is clearly ob-servable for all the samples. The main JH curves show a consid-erable change in the slope at the external magnetic field strengthvalues around –120 kA/m when passing through the secondquadrant of the JH plane of the initially fully polarized PM. TheFORCs starting from magnetic field strength values lower than–120 kA/m also exhibit an unexpected behavior when reachingmagnetic field strength values around 40–80 kA/m for all thetested samples. The results of the second test for the Y32H-2 grade show no wide loops when the internal magnetic fieldstrength is varied in the second quadrant of the JH plane. How-ever, the data of the third test for the Y28H-2 grade reveal thatconsiderable loops can occur if the magnetic field strength isstrong enough to move the operating point of the PM from thesecond quadrant to the first quadrant and back. The possibilityof the magnetic field strength in PMs to vary between the secondand first quadrants of the intrinsic JH plane has been reportedfor rotor-surface-magnet PMSMs with a tooth coil winding [17]and a distributed winding in [13] and [16], for traction motors[15] in their normal operating modes. Therefore, the hystere-sis loops of the PMs depicted in Fig. 2 can result in additionallosses in the PMs of PMSMs, yet these losses are neglected inthe present-day analysis of PM electrical machines.

B. Origin of Hysteresis Loss

The VSM output indicates the average response of all mag-netic phases in the sample volume to the highly homogeneous

applied field. The sample may have structural defects that can belocated in the sample volume or generated at the surface duringthe machining (or cutting) of the magnet. Ferrite magnets pro-duced by the hydrothermal synthesis method can have unwantedphases of iron oxide α-Fe2O3 [24] and orthorhombic bariumiron oxide BaFe2O4 [25] as impurities in addition to the majorphase of the hexagonal barium M-type ferrite BaFe12O19 . Thecoercivities of both these undesirable phases at ambient tem-perature can be in the range of the anomaly in Fig. 2 [26]–[28],which supports the assumption about the volumetric origin ofthe hysteresis loss in ferrite PMs.

The studies of Nd-based magnets mostly assume that thehysteresis loss originates from the reduced coercivity of thedamaged grains on the sample surface [14], [29]. The resultsin [29] show that the heat treatment of a thin NdFeB PM sam-ple with the surface-to-volume ratio S/V = 21.9 mm–1 in tem-peratures exceeding the melting point of the Nd-rich phaseresults in a considerable reduction in the unexpected slopechange near the J-axis, but does not fully eliminate it. TheJH curve of the sample in [29] still indicates an unexpecteddecrease in polarization at magnetic field strength values belowthe intrinsic coercivity |HcJ|. The NdFeB sample with a rela-tively small S/V = 1.82 mm−1 (3.1 × 2.9 × 4.1 (M↑↑) mm3)in [16] demonstrates a considerable slope change near the J-axis while the ferrite sample of the BM9 grade in [17] withS/V = 1.72 mm−1 (3 × 3.6 × 4 (M↑↑) mm3) does not exhibita similar behavior of the recoil curves. The pulse field mag-netometer measurement results in [30] show the possibility ofhysteresis loss in Nd- and SmCo-based PM samples even withvalues of S/V = 0.4–0.6 mm−1 . The recent research [31] pro-vides convincing evidence that the hysteresis loss can partlybe an intrinsic property of the Nd-based magnet material, gen-erated in the PM manufacturing as a negative consequence ofenhanced coercivity.

Based on the observations available about the possible ori-gin of the hysteresis loss in PMs, it was concluded that bothvolume- and surface-caused defects can be present in ferritePMs simultaneously. Thin RE PMs used in electrical machineryobviously contain a considerable proportion of damaged grainson the magnet surface. This damage is caused by the machiningphase in the production process if no other surface treatmentis applied. However, the relatively weak magnetic propertiesof the ferrite PMs facilitate the designs of PMSMs with thickmagnets to avoid possible irreversible demagnetization of fer-rite magnet material [4]. Therefore, the hysteresis loss in ferritemagnets with dimensions relevant to the actual machine designwill mostly be associated with volumetric defects. This studyassumes that the behavior of the recoil curves in Fig. 2 is causedby the presence of unwanted magnetic phases, which are equallydistributed in the PM volume.

C. Modeling of Hysteresis Loss

The measured hysteresis behavior of the samples in Fig. 2is caused by a combination of multiple phases with markedlydifferent magnetic properties compared with the main phaseproperties. Most of the hysteresis models have been devel-oped for materials consisting of one magnetic phase, and thus,

9284 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 12, DECEMBER 2018

require modification to the case under study. Some conceptsbased on closed-form operators, such as Preisach, Stop, andPlay models, make an exception. They, however, may sufferfrom certain drawbacks such as the congruency problem, sensi-tivity to measurement errors, a complex procedure of parame-ter identification, which can be highly computer intensive, andthe inverse problem [32]–[35]. These drawbacks have partlybeen resolved in various studies, but simulation of a materialconsisting of multiple phases requires a lot of measurementdata for model identification, and unpredictable errors are stillpossible [36].

The modeling concept introduced in this study is based on thecoexistence of multiple magnetic phases in the PM volume. Thehysteresis behavior of the recoil loops in Fig. 2 is suggested tobe represented as a combination of artificial “hard” and “soft”magnetic phases acting simultaneously (the “soft” phase is ac-tually hard in nature, but it is called soft because of the presenceof the main phase with much harder magnetic properties). Theartificial phases are assumed not to show an unnatural hysteresisbehavior of reversal curves similar to that observed in Fig. 2,in other words, they consist predominantly of one magneticphase. Therefore, the measured behavior of the samples canbe simulated by a combination of two hysteresis models rep-resenting “hard” and “soft” artificial phases. This study usestwo HDHMs [33] to simulate the measured hysteresis behav-ior of the samples illustrated in Fig. 2. The advantages of theHDHM modeling concept include the absence of congruency ofthe recoil curves, a straightforward parameter identification al-gorithm, and an ability to reproduce the major loop of any shapeowing to the splines used. The spline technique also enables theHDHM to have H or B(J) data as the model input. The mathe-matics of the HDHM incorporates the most relevant empiricalrules of hysteresis observed by Madelung, in other words, inthe absence of the reptation phenomenon, the reversal curves ofthe material obey the return point memory effect and the wip-ing out property rule [33]. The HDHM principle assumes thatfitting of the model-simulated results with the measured mainloop and the sets of FORCs enables simulation of other reversalcurves with a sufficient accuracy. Similar empirical rules andparameter identification procedures are implemented in othermodels, for instance, in some Preisach-type models [10], [37],physics-based general-positive feedback theory [32], [36], andthe behavioral magneto-static modeling approach [38]. Recentmeasurement results demonstrate that a reptation (accommoda-tion) phenomenon is actually present in real PMs [12], [15], [17];however, it has a negligible effect on the hysteresis behavior ofrecoil curves when a PM operates close to its fully polarizedstate, that is, in the region of interest in this study [17], [23],[32]. The modeling concepts [32], [34]–[38] can also be used asan alternative to the HDHM in the case under study. However,the mathematical instruments of the models [32], [34]–[38] offera relatively limited option to adjust the measured and simulatedmain loop and the set of FORCs compared with the HDHM.This can lead to a higher error of the model-simulated results bydefault. The output of the HDHM can be H(J) or H(B) values,which promotes the use of the model in transient simulators [33],

Fig. 3. Identification of the major loops for artificial “soft” and “hard”magnetic phases for the Y28H-2 PM grade sample.

[39]–[42]. This feature may be absent in the Preisach model andthe Play model [34], [43].

The mathematical structure and parameter identification pro-cedure of the HDHM makes it possible to simulate part of the JHcurve of a material, which considerably reduces the amount ofmeasurement data required. In the case under study, the HDHMapproach is applied according to the following new procedurewith the Y28H-2 grade PM sample as example.

Step 1: Creation of the major loops for artificial “hard”and “soft” magnetic phases.

The simulation region is limited by the part of the main JHloop desc(H) and the FORC asc(H) starting from the value of themagnetic field strength close to HcB as depicted in Fig. 3. The de-scending main curve of the “hard” magnetic phase deschard(H)is generated by the summation of desc(H) with the parameterΔB, which provides the acceptable smoothness of the resultingcurve

ΔB =

⎧⎨⎩

desc(H1 )−desc(H2 )ζ H < H1

−(

desc(H1 )−desc(H2 )ζ

)H > H2

(6)

where the values of H1 , H2 , and ζ are determined manually andthe data in deschard(H) in the range of H1 < H < H2 are wipedout. The correct adjustment of the H1 , H2 , and ζ results in adescending main loop of the artificial “soft” phase descsoft(H) =desc(H) – deschard(H), which will not experience a nonphysicalbehavior dB/dH < 0 and can be described as follows:

descsoft(H) = a1 tanh (b1 × (H + c1)) (7)

where a1 , b1 , and c1 are fitting parameters. After a1 , b1 , and c1have been defined, the ascending main loop for the artificially“soft” magnetic phase aschard(H) is determined as follows:

ascsoft(H) = a1 tanh (b1 × (H + c2)) (8)

where c2 is selected in a way that eliminates, as much as possi-ble, the steep slope change of the ascending main curve of the

EGOROV et al.: HYSTERESIS LOSS IN FERRITE PERMANENT MAGNETS IN ROTATING ELECTRICAL MACHINERY 9285

TABLE ICOEFFICIENTS USED IN (6)–(8) FOR ARTIFICIAL “SOFT” MAGNETIC PHASES

artificial hard magnetic phase. The values of H1 , H2 , ζ, a1 , b1 ,c1 , and c2 in (6)–(8) for the samples are presented in Table I.

Step 2: Simultaneous parameter identification of HDHMfor artificial “soft” and “hard” magnetic phases.

The details of HDHM are exhaustively explained in [33] withan example of ferrite PM modeling in [17], and therefore, theyare discussed only in brief in this paper. The HDHM conceptuses the gap ΔH(J) that determines the distance between theconstructed reversal curve and the current outer loop. The outerloop is the loop that envelopes the constructed curve, and it isalways known in advance from the previous magnetization his-tory. In general, the reversal curve of the nth order is constructedby using the n – 2 and n – 1 previous reversal curves (the mainloop of the material is considered a zero-order reversal curve).This paper introduces a modified expression for ΔH(J) from[17] with a reduced number of parameters needed for the modelidentification:

ΔH(J) = ΔHrev(JRC) · (1− d) ·ΔJ (J)ΔJrev

· e−a ·ΔJ rev·(1−Δ J (J )Δ J rev )

+ d · (Hasc (J) − Hdes (J)) (9)

where JRC is the polarization coordinate of the reversal point,Hasc(J) and Hdes(J) represent the ascending and descend-ing branches of the current outer loop, and ΔHrev(JRC) =Hasc(JRC) – Hdes(JRC). The values of ΔJ(J) and ΔJrev are deter-mined as shown in Fig. 4 with a third ORC n = 3 as an example.The behavior of the reversal curve depends on its starting pointat the current outer loop, and is described by a set of coefficientsa(β) > 0, 0 � d(β)� 1. The values of a(β) and d(β) are deter-mined by fitting the model-simulated results with the measuredsets of FORCs in the parameter identification procedure of themodel. The parameter β is defined as follows:

β =ΔJrev

ΔJout(10)

where ΔJout is the height of the current outer loop. The use of (8)instead of the original expression in [17] simplifies the procedureof the model identification yet maintaining an adequate accuracyof the model-simulated results in the region under study. Thecoefficients a(β) and d(β) are determined simultaneously to getthe sum of FORCs of two artificial phases corresponding to theresulting measured FORCs. Fig. 5 depicts the coefficients forthree grades obtained in the fitting procedure. Fig. 6 shows acomparison of the simulated and measured results.

Fig. 4. Illustration of the HDHM principle. The descending Hdes(J )and ascending Hacs(J ) branches of the outer loop for the third ORCS-D-Q (n = 3, dashed line) are formed by the second ORC Q-S-P (n– 1, dash-dotted line) and part P-K-C-Q of FORC P-K-C-Q-N (n – 2,dotted line), which are known from the previous magnetization history.The value of the magnetic field strength for the arbitrary point D withthe polarization value JD belonging to the constructed third ORC S-D-Qcan be obtained from the respective point C with JC = JD belonging toHacs(J ) with a correction by ΔH (JD) (8). According to the return pointmemory effect, any reversal curve of the nth order ends at the reversalpoint of the n – 1 reversal curve, e.g., any third ORC starting from thesecond ORC Q-S-P will end at point Q from which the second ORC Q-S-P originates. Following the wiping out property of reversal curves, if theexternal magnetic field strength is strong enough to move the operatingpoint lying at the third ORC S-D-Q further than Q, then it continues topropagate along the n – 2 reversal curve (Q-N part of FORC P-K-C-Q-N)as if the n – 1 and n reversal curves (i.e., the second ORC Q-S-P andthe third ORC S-D-Q) had never existed. The curves P1 – K1 – Q1 –P1 and P1 – K1 – Q1 – P′

1 – Q′1 demonstrate the possible difference

between the simulated and real behavior of the reversal curves in thePM material as a result of the reptation (accommodation) phenomenonwhen the magnetic field is varied between HP 1 and HQ 1 . Reptationshifts the ends of the reversal curves along the J-axis for the values Δ1and Δ2 , whose magnitudes and directions depend on the width of thecurrent recoil loop, its location within the main JH loop, and the numberof magnetic field strength variations between HP 1 and HQ 1 [17]. Thereptation phenomenon can be practically ignored when the PM operatesclose to its fully polarized state [17], [23], [32].

Fig. 5. Coefficients determined for the artificial “soft” (a(β1 )) and “hard”(a(β2 )) magnetic phases of C8 (dotted lines), Y32H-2 (dashed lines),and Y28H-2 (solid lines) grades.

9286 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 12, DECEMBER 2018

Fig. 6. Comparison of the measured and model-simulated results. (a)Measured FORCs of the Y28H-2 grade, results of test 2 for the C8 grade,and results of test 3 for the Y32H-2 grade. (b) Measured FORCs of theY32H-2 grade, results of test 2 for the Y28H-2 grade, and results of test3 for the C8 grade.

III. RESULTS

Fig. 7 presents the model-simulated areas of recoil loops[J/m3] for the Y32H-2 grade at the selected measurement tem-perature when the internal field strength is varied between Hmin

and Hmax values of an initially fully polarized sample. The re-sults in Fig. 7 follow the idea of measurements provided in [13]and [14], but allow getting an extended representation of pos-sible values of the hysteresis loss at the linear part of the mainBH curve. A comparison with experimental data from the sec-ond and third measurement tests is provided where available.The model-simulated and measured areas of the recoil loopsSmod and Smeas are compared by a relative inaccuracy method(Smeas – Smod) × 100%/Smeas.

Fig. 7. Energy stored in the hysteresis loop of an initially fully polarizedPM (Y32H-2 grade) when the internal magnetic field strength is variedbetween Hmin and Hmax. A comparison with the measured loops is pro-vided where available (percentage values). A relatively high inaccuracyis possible in areas with a small loss, but the value of such a loss isinsignificant.

Rotor-surface-magnet PMSM designs have the highest riskfor the hysteresis loss because the air gap magnetic field harmon-ics penetrate directly into the magnets without being damped inthe rotor steel as, for example, in the PMSMs with embeddedmagnetic poles [16], [23], [44]. The tooth coil winding config-uration offers significant manufacturing advantages such as asimple winding process and short end windings. The drawbackof the tooth coil winding arrangement is the higher number ofmagnetic field harmonics compared with distributed windingmachine designs. Variation of the magnetic field in the mag-netic poles of the machine is also increased by the slottingeffect, which is typically more severe in tooth coil windingthan in distributed winding designs of similar power and speed[45]. Therefore, ferrite rotor-surface-magnet tooth coil windingPMSM with an external rotor topology [4], [45] and doublestator tooth coil winding axial flux PMSM [18] designs are cho-sen in this study. The rotor-surface-magnet tooth coil windingPMSM was investigated for the PM loss in [17], and the hys-teresis losses were calculated to be negligible in practice. Themeasured data of the BM9 PM grade in [17] do not show sig-nificant hysteresis loops similar to those observed in Figs. 2 and6 for the grades under study. Therefore, the value of the hys-teresis loss is of interest when the original BM9 grade in [17] isreplaced by the PM grades investigated in this paper.

The initial design of the 100 kW 1500 r/min axial flux PMSMwith NdFeB PMs in [18] showed about 15 kW of PM loss(with nonsegmented magnets) caused by the eddy current phe-nomenon. The high variation of the magnetic field in the PMpoles is due to the combined effect of the open slot stator struc-ture together with the armature reaction spatial harmonics pro-duced by the phase current fundamental. The PMs of the axialflux PMSM in [18] were segmented and covered by steel lam-inations to reduce the influence of undesired field harmonicstravelling through the magnetic poles. The high electrical re-sistivity of ferrite PMs allows to neglect the eddy current lossphenomenon in ferrite magnets in the electrical machine de-sign [45]. Therefore, the focus of analysis is usually on the PM

EGOROV et al.: HYSTERESIS LOSS IN FERRITE PERMANENT MAGNETS IN ROTATING ELECTRICAL MACHINERY 9287

TABLE IIPARAMETERS AND DIMENSIONS OF THE OBSERVED PMSMS

Fig. 8. Two-dimensional FEA sketches of the studied PMSMs. (a) Toothcoil winding rotor-surface-magnet PMSM. (b) Tooth coil winding axial fluxPMSM.

demagnetization when investigating the PM material in a ferritemagnet electrical machine [4]. Thus, the final design of the ax-ial flux PMSM in [18] was modified for this study: the NdFeBmagnets were replaced by ferrite magnets with the same di-mensions, the iron covers at the PM surface were removed, andthe magnitude of the phase current was reduced to avoid partialdemagnetization of the machine poles in the normal operatingmode. The parameters and sketches of the machines are given inTable II and Fig. 8, respectively. The magnetic properties of thestudied PM samples are approximated by the linear model withtwo parameters (remanence Br, relative permeability μr), andthey are used for the two-dimensional simulation of the observedelectrical machine designs with the commercially available soft-ware FLUX by Altair/CEDRAT. The linear modeling concepttakes into account the change in the PM polarization as follows:

J (Hi) = Br + (μr − 1) · Hi (11)

which is a reasonable compromise between the implementationcomplexity of the model, computation cost, and accuracy in thecase of the chosen procedure of the hysteresis loss calculation[17]. The PM poles of the electrical machines were divided into

Fig. 9. Model-calculated hysteresis loss and FEM-simulated magneticfield strength variation (Y28H-2 grade). The machine rotates counter-clockwise in the motoring mode. (a) Hysteresis loss distribution in thepole of the tooth coil winding PMSM with an external rotor topology. (b)Minimum and maximum values of the magnetic field strength in the nor-mal operating mode at the surface (close to the air gap, solid line), middle(cross-dashed line), and bottom (close to the rotor hub, circle-dotted line)in the PM pole.

11 layers with 200 points at each layer, that is, k = 11 × 200 =2200 elemental volumes. The magnetic field strength values ineach volume were determined under sinusoidal supply at thetime tν , corresponding to the period when each point of the PMhas been exposed to all possible values of the field in the specificoperating mode. The value of tν in the case under study dependson the electrical frequency f, the number of pole pairs p, and thenumber of slots per stator Qs of the machine

tν =1f· 2p

Qs. (12)

The FEM results for the magnetic field strength in each vol-ume were used as the input for the HDHMs, and the hysteresisloss in the machine was calculated as follows:

Ehyst =2 · p · VPMpole

k · tνk∑

i=1

Physt, i (13)

where VPMpole is the volume of one PM pole, and Physt, i isthe model-calculated loss in the i-elemental volume of the PMfor the time period tν . Figs. 9 and 10 show the distribution ofthe hysteresis loss and the maximum/minimum values of themagnetic field strength in the magnetic poles of the machinedesigns. The parameters used for the linear PM model in theFEM software are defined from the data in Fig. 2: Br = 0.334 T,μr = 1.094 for the Y28H-2 grade, Br = 0.349 T, μr = 1.101for the Y32H-2 grade, and Br = 0.358 T, μr = 1.099 for theC8 grade. The values of the calculated hysteresis loss for allPM material in the magnetic poles of the investigated toothcoil winding PMSM topology with an external rotor are 28.37(0.056% of the machine output power Pout), 21.73 (0.041%Pout), and 24.24 W (0.045% Pout) for the Y28H-2, Y32H-2,and C8 PM grades, respectively. The calculated values of thehysteresis loss for the double stator tooth coil winding axialflux PMSM design are 14.2 (0.32% Pout), 11.5 (0.25% Pout),

9288 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 12, DECEMBER 2018

Fig. 10. Model-calculated hysteresis loss and FEM-simulated mag-netic field strength variation (Y28H-2 grade). The machine rotates coun-terclockwise in the motoring mode. (a) Hysteresis loss distribution in thepole of the double stator axial flux PMSM. (b) Minimum and maximumvalues of the magnetic field strength in the PM pole in the normal oper-ating mode at the surface (close to the air gap, solid line), 2/11 of hPMfrom the surface (cross-dashed line), and middle (circle-dotted line) ofthe PM.

and 11.8 W (0.25% Pout) for the Y28H-2, Y32H-2, and C8 PMgrades, respectively.

IV. DISCUSSION

The model-simulated losses in Fig. 7 are negligible when thePM operates at the second quadrant of the BH plane. Theseresults are consistent with the data of test 3 in Figs. 2 and 6.Some small hysteresis losses are possible if Hmin approachesHcB while Hmax remains in the second quadrant. However, suchmagnetic field variation is practically avoided in the machinedesign procedure to enable PM poles to withstand short-circuitfaults [4]. The hysteresis loss in Fig. 7 is still low when Hmin> –120 kA/m and stays in the second quadrant of the BH plane, andHmax propagates further in the first quadrant of the BH plane.The data for the Y32H-2 grade from Figs. 2 and 6, and Table Ishow that the artificial “soft” magnetic phase has intrinsic coer-civity of about 120 kA/m. The material under observation doesnot produce wide minor loops if the maximum negative mag-netic field strength applied to the initially fully polarized sampledoes not exceed this value. Wide hysteresis recoil loops may oc-cur when the magnetic field strength is varied from the secondquadrant to the first and back with the values of magnetic fieldstrength exceeding the intrinsic coercivity of the “soft” magneticphase. Fig. 9(a) depicts a typical distribution of the hysteresisloss calculated in the magnets of the tooth coil winding rotor-surface-magnet PMSM with an external rotor topology. Thehighest proportion of the hysteresis loss is concentrated on thesurface of the PM close to the air gap of the machine. The mag-netic field strength variation at the surface of PM is a resultof the combined effect of slotting, tooth tip leakage flux, andarmature reaction harmonics caused by the current fundamental[17]. Fig. 9(a) and (b) shows that a relatively high magnitude ofmagnetic field strength variation at the surface of the PM poledecreases rapidly deeper in the magnet. The calculated hystere-sis loss in the same PMSM design with the BM9 ferrite gradein [17] shows around 4 W of total hysteresis loss in the wholemagnet material. Thus, magnetic phases with reduced coercivity

may increase the magnetic loss in the ferrite PM material usedin electrical machinery. Nevertheless, the calculations in thispaper and in [17] both demonstrate that the hysteresis lossesin the PM poles of a ferrite magnet tooth coil winding rotor-surface-magnet PMSM [4] are very small and can be neglectedin practice.

The investigated ten-pole double stator axial flux PMSM isin synchronism with the fifth harmonic. The fundamental isasynchronous with the rotor of the machine, has a relativelyhigh magnitude, and penetrates deep in the volume of the PMpole [18]. This could require additional design efforts to preventoverheating of the RE PMs having a relatively low electrical re-sistivity. The open slot configuration produces a considerablechange in permeance thereby increasing the variation of themagnetic field inside the PM. The influence of undesirable spa-tial harmonics at the magnetic poles of an electrical machine canbe significantly reduced with special design efforts, for instance,by using semimagnetic wedges in the slot openings, coveringthe PMs with iron covers, and segmentation of the magneticpole. These options complicate the production process of themachine. However, the conventional understanding of ferritePMs as a hard magnetic material with high electrical resistiv-ity makes it possible to use bulk poles in the machine, andthey are expected not to produce any loss. A rotor constructioncombining fiber glass and ferrite magnets allows, in principle,manufacturing a rotor with a negligible amount of magnetic-field-caused losses. However, the results in Figs. 7 and 10 showthe possibility of unexpected loss in the PM material resultingfrom the presence of magnetic phases with reduced coercivity.

The results in [17] and in Figs. 9 and 10 clearly show that thelargest proportion of hysteresis loss occurs at the surface of thePM pole close to the air gap. This is a consequence of the highestmagnetic field strength variation compared with other parts ofthe magnetic pole. The high coercivity of RE PMs comparedwith ferrite magnets enables a higher armature reaction field,which can result in increased variation of the magnetic fieldstrength in the magnetic pole of the machine. The height of theRE PM pole could be in the range of a couple of millimeters,in other words, all the volume of the RE magnet material in theelectrical machine can be exposed to a considerable variation ofthe magnetic field as it can be seen in Figs. 9 and 10. The resultsfound in the literature [14], [29] provide convincing evidencethat the cutting of the magnet can create phases with reducedcoercivity at the sample surface. These phases can significantlyincrease the total hysteresis loss of RE magnets. Thus, the REPM poles of electrical machines in some designs are expected tohave markedly higher hysteresis losses, which are often missedin the present-day loss analysis of electrical machines.

V. CONCLUSION

In this paper, three commercial ferrite PM grades were mea-sured by the VSM in the region of the JH curve correspondingto the normal operation of PM material in electrical machinery.The studied samples showed an unexpected hysteresis behaviorcaused by the presence of magnetic phases with markedly softermagnetic properties compared with the expected hard magneticphase of hexagonal barium M-type ferrite. Unwanted magnetic

EGOROV et al.: HYSTERESIS LOSS IN FERRITE PERMANENT MAGNETS IN ROTATING ELECTRICAL MACHINERY 9289

phases in ferrite PMs can originate both from impurities in theraw materials and surface damages induced in the final magnetmachining stage; however, in ferrite magnets with dimensionsrelevant to the actual machine design, the former phenomenonis expected to be more significant than the latter. Magneticphases with reduced coercivity can result in additional loss inferrite PMs.

The hysteresis behavior of the initially fully polarized sam-ples in the first quadrant and in the linear part of the secondquadrant of the BH plane was modeled by the combination oftwo HDHMs. The applied modeling concept is able to simulatethe hysteresis behavior of a PM within a desired region of themain JH curve only, which significantly reduces the amountof measurement data required for the parameter identificationof the model. The proposed simulation method can be furtherimproved to be applied to studies of the hysteresis loss phe-nomenon in RE PMs used in rotating electrical machinery.

The hysteresis loss in the magnetic poles of two ferrite PMmachine designs under sinusoidal supply was determined by thecombination of the FEM-calculated magnetic field distributionin the PM regions of the machines and the proposed modelingconcept. The calculation results indicate that the actual hystere-sis loss in ferrite PM poles of the studied PMSMs is small inpractice. However, in some cases, it can be a source of consider-able additional loss in the ferrite magnet material. The currentlyavailable commercial FEM software tools for electrical machinedesign usually ignore the contribution of the observed hystere-sis loss phenomenon to the total loss in the PM material. Theamount of hysteresis loss in the magnetic poles of RE PM-basedmotors has still not been assessed properly and remains to bestudied.

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Dmitry Egorov received the B.Sc. degree inelectrical engineering from Moscow Power En-gineering Institute, Moscow, Russia, in 2013,and the M.Sc. degree in electrical engineeringfrom the Lappeenranta University of Technology(LUT), Lappeenranta, Finland, in 2015. He iscurrently working toward the Doctoral degree inelectrical drives at the Department of ElectricalEngineering, LUT.

His research interests include electrical ma-chines and drives, in particular, the applications

with the permanent magnets.

Ilya Petrov received the D.Sc. degree in electri-cal drives from Lappeenranta University of Tech-nology (LUT), Lappeenranta, Finland, in 2015.

He is currently a Research Fellow with theDepartment of Electrical Engineering, LUT.

Juha Pyrhonen (M’06–SM’17) born in 1957 inKuusankoski, Finland. He received the D.Sc.degree in electrical engineering from Lappeen-ranta University of Technology (LUT), Lappeen-ranta, Finland, in 1991.

In 1997, he became a Professor of Electri-cal Machines and Drives with LUT. He is en-gaged in research and development of electricmotors and power-electronic-controlled drives.He has wide experience in the research anddevelopment of special electric drives for dis-

tributed power production, traction and high-speed applications. Perma-nent magnet materials and applying them in machines have an importantrole in his research. Currently, he is also researching new carbon-basedmaterials for electrical machines.

Joosep Link received the Master’s degree inengineering physics from Tallinn University ofTechnology (TUT), Tallinn, Estonia, in 2016. Heis currently working toward the Doctoral degreein engineering physics with TUT.

He is an early-stage Researcher with the De-partment of Chemical Physics, National Instituteof Chemical Physics and Biophysics, Tallinn. Hisresearch interests include permanent magnets,multiferroics, and memristive materials.

Raivo Stern (M’16) received the M.Sc. degreein condensed matter physics from Tartu Uni-versity, Tartu, Estonia, in 1987, and the Ph.D.degree in solid-state physics from Zurich Uni-versity, Zurich, Switzerland, in 1995.

He is currently a Research Professor with theDepartment of Chemical Physics, National Insti-tute of Chemical Physics and Biophysics, Tallinn,Estonia. His research interests include the fieldof various modern materials, especially quan-tum magnets, strong permanent magnets, and

unconventional superconductors.

Publication V

Egorov, D., Petrov, I., Pyrhönen, J., Link, J., and Stern, R.Linear recoil curve demagnetization models for ferrite magnets in rotating

machinery

Reprinted with permission fromIECON 2017 - 43rd Annual Conference of the IEEE Industrial Electronics Society

pp. 2046–2052, 2017© 2017, IEEE Conferences

Linear Recoil Curve Demagnetization Models forFerrite Magnets in Rotating Machinery

Dmitry Egorov, Ilya Petrov, Juha PyrhönenDepartment of Electrical Engineering,

Lappeenranta University of TechnologyLappeenranta, Finland

dmitry.egorov@lut.fi, ilya.petrov@lut.fi,juha.pyrhonen@lut.fi

Joosep Link, and Raivo SternLaboratory of Chemical Physics,

National Institute of Chemical Physics and BiophysicsTallinn, Estonia

joosep.link@kbfi.ee, raivo.stern@kbfi.ee

Abstract—Electrical motors with ferrite Permanent Magnets(PM) are a possible solution when avoiding the usage of rareearth materials in rotating machinery. Irreversibledemagnetization of the ferrite PMs is the one of the keychallenges that needs to be analyzed in such designs. Nowadayselectrical machine design is increasingly relying on FiniteElement Analysis (FEA) software that require having accurateand easy-to-implement models for a magnet. Linear Recoil Curve(LRC) models are among the best candidates. This paper studiesthe LRC models for FEA simulation of ferrite PMs in rotatingmachinery. Comparison of the model-based results with highaccuracy Vibrating Sample Magnetometer (VSM) measured datafor a commercially available ferrite magnet grade show that noneof the existing temperature dependent LRC models is universal.However, the further development of the studied modellingconcept can offer an accurate tool for FEA simulation of ferritePMs in electrical machines.

Keywords—demagnetization models; ferrite magnets; finite-element analysis; permanent magnet machines

I. INTRODUCTION

Electrical machines with Permanent Magnet (PM)excitation may offer higher efficiency and power densitysolutions compared with other electrical machine types ofsimilar power and speed having electrical excitation. RareEarth (RE) magnets have a high energy density and, therefore,are preferable in applications with limited physical space, suchas electrical vehicles [1]. However, the limited availability andsignificant price volatility of RE metals has led to an extensiveresearch for alternative designs of electrical machines withreduced amount of RE PMs or totally without them [1], [2]. Ifmachine’s volume is not a limiting factor, electrical machinedesigns with ferrite magnet material can be a viable option.Ferrite magnets demonstrate stable pricing over decades and issignificantly cheaper compared to RE magnets [2]. Nowadays,ferrite PMs are widely used in designs of Permanent MagnetSynchronous Machines (PMSM) [3], [4], DC motors [5], [6],PM assisted Synchronous Reluctance (PMaSynR) [1], [2] andsome switched reluctance machine types [7].

Ferrite magnets have considerably lower values ofremanence Br and coercivity Hc compared to typical RE PMgrades (i.e. NdFeB and SmCo). The low coercivity HcJ of

ferrite PM, and therefore its weak capability to withstandirreversible demagnetization makes it important to performPM’s partial demagnetization analysis during the designprocess of a machine with ferrite magnet material [2]-[7].

The Finite Element Analysis (FEA) is a conventional toolfor electrical machine design since it enables relatively simpleand detailed analysis of each component’s influence on theoverall machine performance. The permanent magnet materialin FEA has been modelled in different ways using e.g. variablemagnetization and Stoner-Wohlfarth model methods [8], [9],Preisach-type models [10], [11], non-Preisach HistoryDependent Hysteresis Model (HDHM) or Linear Recoil Curve(LRC) models [12]-[14].

Variable magnetization and Stoner-Wohlfarth modelmethods are appropriate for magnetization processes ratherthan simulation of permanent magnet material in an electricalmachine and are limited by a possibly complex shape ofPMSM’s magnetic pole [6], [9]. Classical Preisach model hasbeen considered in [10] for the simulation of NdFeB PM insynchronous motor and it demonstrated adequate accuracywithin the 2nd and 3rd quadrants of the magnet’s BH-plane.Nevertheless, the drawbacks of the Preisach models arerelatively complicated implementation algorithm, sensitivity tomeasurement errors and identification method problems [15].HDHM was used in [13] for the simulation of NdFeB PM andit demonstrated slightly optimistic back-EMF calculationresults after partial demagnetization of NdFeB magnet. Theimplementation of HDHM provided in [13] requires using arelatively complicated transplantation method.

LRC models are widely used tools for PM’sdemagnetization analysis using FEA software due to an easyimplementation algorithm and a lower amount of inputparameters. The parameters can be made temperaturedependent and, thus, enable coupled thermal and magneticsimulation of an electrical machine [12], [13]. LRC models areconsidered to be appropriate for any type of PMs anddemonstrate adequate accuracy for some NdFeB magnets [13],[16]. However, very little attention has been paid to theexperimental verification of the ability of the LRC models todescribe the macroscopic behavior of ferrite PMs despite thatthey are widely used in FEA softwares during design ofelectrical machines with ferrite magnet material [3], [7].

Therefore, the aim of this study is to observe the accuracy ofthe LRC models in FEA-based simulation of ferrite PMs inrotating machinery.

II. METHODS

A. Measurement Equipment and procedureThe measurement installation is depicted in Fig. 1(a) and

contains a Physical Properties Measurement System with up to14 Tesla superconducting magnet developed by QuantumDesign with a P525 Vibrating Sample Magnetometer (VSM)option and data acquisition system. The test sample (Y28H-2grade ferrite magnet) is depicted in Fig. 1(b). The sample hasthe dimensions of 2 2 3.1 mm3 with the direction ofmagnetization M along the longest axis (M ) and mass of0.0574 g.

Machines excited with ferrite magnet material have to betested at the lowest possible operating temperature in order todetermine the capability of withstanding the maximum drivingcurrent or a short-circuit fault [2], [3]. However, the LRCmodels are expected to be appropriate for any thermal regimeof a magnet relevant to a machine’s operation [12]. Therefore,the temperature of the sample was selected to be 80 degreesCelsius that corresponds to the normal operating temperature ofsome PMSMs [10], [17]. The second and the third quadrants ofthe BH-curve are chosen as the regions of interest since theoperating point of a PM for most electrical machine’s designswill be somewhere in these two regions both in normal anddemagnetized states of a PM. The operating point of a magnetduring the normal operational mode of a PMSM can also crossthe B-axis from the second quadrant to the first one in somehigh power density machines [18], [19]. Nevertheless, thisstudy assumes that the operating point of a magnet is selectedto be close to the maximum energy product (BH)max of the PMin the second quadrant of its BH-plane and cannot cross the B-axis. Such magnetic circuit design is the traditional way toprovide the most efficient usage of PM material in rotatingmachinery [20].

The open circuit measurement system of a VSM creates ademagnetizing field in the sample [21]. The output of a VSM isthe polarization J with respect to the applied field Ha. It doesnot directly correspond to the intrinsic properties of themeasured material of which a machine designer is interested in.The intrinsic properties of the material, i.e. J with respect to thefield inside the sample Hi, could be measured from amagnetically short-circuited sample with a hysteresisgraph. Inprinciple, measurements with a hysteresisgraph delivering thecorrect BH-curve directly should be preferred. However,according to the experience of the authors the extremelyaccurate measurements needed in case of searching thehysteresis behavior of permanent magnet materials cannot bedone with such devices as extra hysteresis and eddy currents inthe magnetic yoke of the measurement device easily corruptthe measurement results. In [18] a most probably eddy-current-corrupted result of a hysteresisgraph measurement is seen.Therefore, the VSM is used even though the interpretation ofthe results becomes more difficult, since VSM open circuitmeasurement results need to be corrected for eachmeasurement point (Ji, Ha, i) as:

iii JN

HH0

m,a,i , (1)

where Nm is a magnetometric demagnetizing factor, μ0 = 410-7 H/m is the permeability of vacuum and the demagnetizingfield is assumed to be proportional to the polarization [21].

Assuming that the magnetic susceptibility of the ferritemagnet is close to zero Nm can be calculated analytically for theparallelepiped shape sample with the dimensions 2a 2b2c(M ) as follows [22]:

abcFbacFcabFcbaFabc

FFabccbac

abN

,,,,,,,,2

1

31arctan2

mmmm

32222m, (2)

where

2222223332 22 cbacbacbaF , (3)

2/322222222223 22 bacbbccaacF , (4)

2222222

222222

2m

22

22log,,

wvuvwvuu

vuvvuwuvuwvuF . (5)

The measurement procedure included two separate tests atthe chosen temperature. During the first test, the main JH-loopand the First Order Reversal Curves (FORCs) were measured.FORCs are the curves that start at some point of the main JH-

a)

b)Fig. 1. The measurement setup. a) VSM measurement system, b) the samplethat is placed in the VSM sample holder and fixed with glass andnonmagnetic glue.

sample holder glass

sample

loop and end at the fully polarized state of the magnet. Duringthe second test, recoil loops of the ferrite magnet in the 2nd and3rd quadrants of the intrinsic JH-plane were obtained byimplementing an additional script in the VSM’s software. Thescript’s principle is shown in Fig. 2. The results of the VSM

measurements are depicted in Fig. 3 along with intrinsic curvesof the observed sample. The intrinsic curves were found byapplying (1)-(5) to the VSM measured results.

Fig. 3(b) demonstrates that the intrinsic JH-curve of thematerial has a clearly steeper slope than the output of the VSM.Thus, neglecting the use of (1)-(5), i.e. building the modelbased on the VSM output, would result in a misunderstandingof the actual magnetic properties of the material. Thecomparison of the measured main JH-loop delivered by thefirst test with the data from the second test in Fig. 3(b)demonstrate the processes of reversible demagnetizationexperienced by each recoil loop. The JH-curve from the secondtest does not exactly match with the main JH-loop but movessomewhat parallel to it after the recoil loops were formed. Thiscan be explained by the presence of the accommodation(reptation) effect in the observed material that leads to adifference in the magnet’s hysteresis behavior depending on itsprevious demagnetization history [23]. The results obtainedwith analogous measurement procedure for five different hardmagnetic materials in [24] show that with an acceptable marginof error the accommodation effect can be neglected in the casestudied. Therefore, the J(Hi) data in Fig. 3(b) are converted toB(Hi) as [21]:

iii HJB ,i0 , (6)

and are treated in the way that every recoil loop is assumed toexhibit a perfect return point memory feature, i.e. its startingpoint matches with the ending point.

B. LRC modelsLRC models use straight lines to model the recoil loops of a

magnet both for fully magnetized and partially demagnetizedcases. These models are the coercivity limit model, the linearvertical [25] and the linear sloped [14] models or exponential[13] and hyperbolic tangent function [12] models. Thecoercivity limit and the linear vertical models were excludedfrom this study due to limited ability to simulate postdemagnetization performances of PM compared with othermodels [13], [14].

Despite different possible implementation algorithms, thegeneral principle of the studied LRC models in FEA is thesame and is depicted in Fig. 4. Actual PM flux density isdescribed as a line whose slope and value at zero field strengthare determined by the recoil permeability μrec and remanenceBr, respectively. The demagnetization BH-curve of the magnet(blue line in Fig. 4) has a linear region that corresponds to themagnetic field strength values from fully polarized state of thePM in the 1st quadrant up to point (Hlim, Blim) where the kneeregion starts. In the linear region of the BH-curve thepolarization value is assumed to be a constant where noirreversible processes of the PM’s demagnetization take place.At the field values below Hlim the magnet starts to lose itspolarization irreversibly and, therefore, its magnetic propertiesneed to be updated. It is seen in Fig. 4 that the new B new (H) incase of partial PM demagnetization can be found from thecurrent worst operating point of the PM P (Bp, Hp) as [26]:

Fig. 2. The principle of the script for the second test. PM sample is initiallyfully polarized. The intrinsic recoil loops A – B – A and C – D – C (blacksolid lines) represent the hysteretic behavior of PM in closed magnetic circuitwhen Hi varies from some negative value at the main JH-loop to zero andback, i.e. only in the 2nd and 3rd quadrants of the JH-plane. The loops areobtained from the respective VSM measured loops A – B – A and C – D – C(red solid lines) corrected by (1)-(5). The points B and D of the measuredloops, where Ha generated by the VSM is reversed, are determined in realtime from (1) as Ha Nm J/μ0 in order to take the demagnetizing field intoaccount.

a)

b)

Fig. 3. Measurement results from VSM (red line) and intrinsic curves of thesample – black and blue lines depict recoil and main JH- curves of the PM,respectively. a) Intrinsic main JH-loop and the set of FORCs. b) J(Ha) andJ(Hi) in the first, second and third quadrant of the JH-plane according to thesecond test procedure. The recoil loops were measured one after anotherduring one measurement session. The enlarged area in Fig. 3(b) demonstratesthe possible effect of accommodation (reptation) phenomenon.

HHBHB rec0prec0pnew )()( , (7)

where μrec is determined from the linear part of the PM’sdemagnetization curve [13]. The obtained B new (H) be willvalid until the operating point goes further negative. If astronger than Hp negative magnetic field strength is achievedthen B(H) is recalculated again by (7) according to the newworst operating point. The recoil permeability can bedetermined for any recoil loop as [21]:

HB

0rec , (8)

where B and H characterize the mean slope of a given recoilloop as shown in Fig. 4.

The difference between the studied models is in themathematical tools used for the modelling of the PM’sdemagnetization BH-curve. One of the ways that can be usedfor the linear sloped model is the following:

t000rect0r

trec0r

HHHKKHB

HHHB , (9)

where K0 determines the slope of the line when the values ofthe internal field strength go further negative than Ht. Thevalues of μrec, Ht and K0 are determined in the way to obtain thebest possible fitting of the modelled and measureddemagnetization curves. The exponential model proposed in[13] describes the demagnetization curve of a PM as:

HKKeBHBB 21Erec0r , (10)

where K1 determines the sharpness of the knee, BE = 1 T is aconstant for unit conversion and K2 is found as follows:

cJ1

EcJ0recr

2

11lnH

KB

HB

K . (11)

The parameters K1 and μrec in (10)-(11) are optimized to get(10) correspond to the measured main BH-loop. The hyperbolictangent function model describes the BH-curve as:

Hh

HHb

hHH

bHB 01

cJ1

0

cJ0 tanhtanh , (12)

where parameters b0, b1, h0 and h1 are the subjects ofoptimization [12].

Fig. 5 depicts the demagnetization BH- and JH- curves withthe recoil loops in the second and third quadrants of the BH-plane obtained from the VSM output data in Fig. 3(b) by (1)-(6) neglecting the accommodation phenomenon. The measuredrecoil loops in the BH-plane are very narrow and, thus, can bemodelled by lines in the similar way that is applied in the LRCmodels under consideration.

The observed models assume that the value of μrec isconstant and, thus, can be used to describe the mean slope ofany loop of the PM after its partial demagnetization. The datain Fig. 5 show that μrec can be determined individually for eachrecoil loop by (8) as a function of the maximum negativeintrinsic magnetic field strength applied to the initially fullypolarized magnet Hmax. Fig. 6 depicts the values of μrec (Hmax)determined from the datasets in Fig. 3 converted to the BH-plane by (6).

The analysis of Figs. (4)-(6) shows that the accuracy of themodels under consideration depends on μrec and themathematical means used for the description of the PM’sdemagnetization curve. The influence of the assumption about

Fig. 4. The principle of the models. PM is modelled by B(H) = Br + μ0μrecH. Ifthe operating point P (Bp, Hp) in any part of a PM falls below the linear part ofthe BH-curve the Br for that element is updated with Br

new and the time step inFEA is recalculated. The red line shows a recoil loop in the BH-plane similarto the intrinsic loops depicted in the JH-plane in Fig. 3(b).

Fig. 5. Demagnetization BH- (blue line) and JH- (red line) curves of thestudied PM grade and recoil loops (black lines). The recoil permeability μrec

can be determined for each recoil loop individually. HcJ and HcB denote thecoercive field strengths of the zero magnetic polarization and of the zeromagnetic flux density, respectively.

the constant value of μrec and (9)-(12) to the predictive abilityof the LRC models is investigated in the following section.

III. RESULTS AND ANALYSIS

In order to verify the predictive ability of the consideredLRC models and the general accuracy of such a modellingconcept in case of ferrite magnets further two additionalmodels with the same principle were included into the study: 1)a spline model with constant permeability where thedemagnetization curve exactly matches with the measured oneand the value of μrec used in (7) is constant, being the object ofoptimization, and 2) a spline model with non-constantpermeability that also uses the exact main BH-curve. However,the value of μrec in (7) is dependent on the maximum negativeintrinsic magnetic field experienced by the magnet. The valuesof μrec(Hmax) used in the model were determined from the datain Fig. 3(a) and are depicted in Fig. 6. For a fair comparison,the linear sloped, the exponential and the hyperbolic tangentfunction models were fitted with the measured BH-curve at themagnetic field strength values within (HcJ, 0) as the magneticproperties of PMs are typically provided by manufacturers inthis range [21], [27]. Table I depicts the parameters of themodels determined by optimization technics. The linear slopedand the exponential models include μrec in (9)-(11) ascoefficient determined during the fitting while the value of μrecin the hyperbolic tangent function model (12) is always equalto one [12], [13]. For all the models Br = 0.335 T and HcJ = –322 kA/m were used if applicable.

Fig. 7 depicts the differences between the measured and thedemagnetization curves modelled by (9)-(12) with theparameters of Table I. The comparison of results in Fig. 7 forthe linear sloped and exponential models show that in the casestudied the latter demonstrates a better ability to fit the

experimentally measured demagnetization curve at themagnetic field strength values (HcJ, 0). This is controversial tothe results provided in [16] for NdFeB magnet where the linearslope model has the best fitting. Fig. 7 shows that both thelinear sloped and exponential models cannot be used to modelthe demagnetization curve at the magnetic field strength valuesbelow HcJ as the difference between measured and model-based demagnetization curves become too large. Themathematical means (12) used by the hyperbolic tangentfunction model demonstrate a better fitting to the experimentaldemagnetization curve compared with (9)-(11) for almost allnegative magnetic field strength values as it can be seen in Fig.7. The relatively close matching of the modelled and themeasured demagnetization curves is the good prerequisite butnot a guarantee of the model’s accuracy as μrec in (7) can alsocontribute to the model’s possible error. Therefore, the data inFig. 5 are used further to investigate the accuracy of the LRCmodels studied here.

Normalized Root Mean Square Deviation (NRMSD) wasused in [28] to compare the accuracy of some models forelectrical steel hysteresis and is chosen to be used also in thispaper as an adequate quantitative tool to assess the predictiveability of the observed LRC models. The NRMSD isdetermined for every recoil loop in Fig. 5 as:

%1001NRMSD 1

2calc,meas,

minmax n

BB

BB

n

tnn

, (12)

where Bmax and Bmin are maximum and minimum flux densityvalues of a loop, Bmeas, n represents measured values of recoilloop, Bcalc,n is calculated by (7) and respective mathematicaltools used by the models with the coefficients from Table I, n isthe number of the measured points in the recoil loop. Theresults calculated by (12) can be slightly different depending onmachine’s magnetic circuit configuration that determines theslope of load line. For clarity, this study investigates theaccuracy of the LRC models to predict the intrinsic properties

Fig. 6. Calculated μrec(Hmax) for the parts of intrinsic FORCs in 2nd and 3rd

quadrants of BH-plane from data in Fig. 3 (a) (blue dashed line) and for theintrinsic recoil loops in Fig. 5 (red dashed line). The μrec(Hmax) can be used in(7) instead of μrec = const.

TABLE I. MODELS USED IN THE STUDY

Model Coefficients for BH-curveRecoil

permeability,μrec

Linear sloped K0 = 38.1, Ht = 316 kA/m 1.11

Exponential K1= 1.8 10 4 1.10

Hyperbolictangent function

b0 = 0.24, b1 = 0.09, h0 = 3.9 103, h1 = 8.7 104

1.00

Spline, μrec = const - 1.05

Spline, μrec const - Fig. 6

Fig. 7. Differences between the measured and modelled demagnetizationcurves for the linear sloped, exponential and tangent function models. Thevalues of Bmeas – Bmodel for the linear sloped and exponential models increasedramatically at the magnetic field strength values below HcJ due to themathematical means (9)-(11) used by the models (not fully shown).

of a material, i.e. Hi = Ha. Fig. 8 shows the NRMSDs for thestudied models accounting the examined ferrite grade.

The comparison of the linear sloped, exponential andtangent function models is performed first as they require asmall amount of input parameters to become temperaturedependent. Figs. (6)-(8) show that the accuracy of thehyperbolic tangent function model, at the linear region ofdemagnetization curve caused by the better fitting, reducesconsiderably when approaching the knee region as the result ofthe actual μrec is increasing. All the three models have closevalues of residuals at the beginning of the knee region,however, the value of μrec used by the hyperbolic tangentmodel leads to a worse prediction ability compared to the linearsloped and the exponential models. The accuracy of thehyperbolic tangent function model is better when movingfurther to the negative magnetic field strength values. This iscaused by a better fitting to the demagnetization curve anddecreasing value of μrec as it can be observed from Figs. (6)-(7). The difference in the prediction ability of the linear slopedand exponential model in the case studied is caused mainly byfitting to experimental demagnetization curve as it can be seenin Figs. (7)-(8) and in the values of μrec in Table I. The data inFigs. (7)-(8) indicate that the sharpness of the knee region cancause significant errors in the output of the model as the fluxdensity of the magnet can change dramatically within arelatively small range of magnetic field strength. Thecomparison of the total accuracy of the models depicted in Fig.8 shows that the linear sloped and exponential models shouldbe preferable if the magnet operates close to the knee regionand if there is a risk of partial PM’s demagnetization in normaloperational mode of a machine. It can be missed by some PMdemagnetization models. The hyperbolic tangent model will bemore reliable to analyze the performances of the machine aftersevere faults, e.g. short circuit.

Fig. 9 depicts a comparison of the measured recoil loopswith the results from spline-based models defined withparameters from Table I. The data in Fig. 9 clearly show thatthe LRC model with the experimentally measureddemagnetization curve could have adequate accuracy

accounting PM’s hysteretic behavior within the 2nd and the 3rd

quadrant of the BH-plane if the magnet is initially fullypolarized. The NRMSD does not exceed 17% and 5% for thespline models with μrec = const and μrec const, respectively asit can be seen from Fig. 8.

Comparison of the spline models with the measured resultsdemonstrates the best accuracy within the models studied. Themeasured recoil loops in the second and in the third quadrantsare very narrow and, thus, the modelling concept used by theLRC models is accurate enough if the mathematical toolsdescribing the demagnetization curve show a good agreementwith the measured curve and the value of μrec is selectedaccordingly. The observed behavior of the recoil loops in thesecond and the third quadrant of the BH-plane in Fig. 5 and thedata in Fig. 6 show that the μrec(Hstart) can be determined alsofrom the FORCs. This simplifies the measurement procedureneeded for the model’s parameter identification.

IV. CONCLUSION

The concept of the LRC models for the PM simulation inelectrical machinery was investigated for a commerciallyavailable ferrite magnet material. VSM-obtained open circuitmeasurement data were used to determine the intrinsicproperties of the studied ferrite sample. The results are clearlyindicating that there is no universal LRC model existing. Thedifference between the actual and modelled demagnetizationcurves leads to significant inaccuracies in the prediction of themagnet’s hysteretic behavior, especially at the knee region of aPM. The assumption about a constant μrec is acceptable if theLRC model is able to describe the main BH-loop exactly andthe value of μrec is appropriately selected.

Linear sloped and exponential models are not appropriatefor the simulation of PM’s hysteretic behavior at the magneticfield strength values below HcJ, nevertheless, demonstratebetter accuracy compared with the hyperbolic tangent functionmodel close to the beginning of knee region of the BH-curve.The linear sloped and exponential models can be a good toolduring combined thermal and electromagnetic machine’sanalysis in order to determine the possibility of partial PM’s

Fig. 8. Comparison of the NRMSDs for the studied LRC demagnetizationmodels.

Fig. 9 Comparison of the measured and spline-based models results for theobserved ferrite grade behavior in the 2nd and 3rd quadrant of the BH-plane.

demagnetization but can be not accurate enough to track post-demagnetizing performances of a magnet after severe faultswhen the operating point can fall close to HcJ and furthernegative values.

The LRC models based on exact experimentally measureddemagnetizing BH-curve can simulate quite accurately theactual ferrite PM’s behavior within the 2nd and the 3rd quadrantseven if μrec is assumed to be constant. Such models, however,are built at fixed operating temperature of the magnet andcannot be easily made temperature-dependent based on acouple of parameters. The LRC model based on measured BH-loop and set of FORCs offer accurate tool with simpleimplementation and parameter identification procedures for thesimulation of a ferrite magnet’s hysteretic behavior in rotatingmachinery.

ACKNOWLEDGMENT

J.L. and R.S. acknowledge support from Estonian Ministryof Education and Research grant IUT23-7, and the EuropeanRegional Development Fund project TK134.

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860. SOKOLOV, ALEXANDER. Pulsed corona discharge for wastewater treatment andmodification of organic materials. 2019. Diss.

861. DOSHI, BHAIRAVI. Towards a sustainable valorisation of spilled oil by establishing agreen chemistry between a surface active moiety of chitosan and oils. 2019. Diss.

862. KHADIJEH, NEKOUEIAN. Modification of carbon-based electrodes using metalnanostructures: Application to voltammetric determination of some pharmaceutical andbiological compounds. 2019. Diss.

863. HANSKI, JYRI. Supporting strategic asset management in complex and uncertaindecision contexts. 2019. Diss.

864. OTRA-AHO, VILLE. A project management office as a project organization’sstrategizing tool. 2019. Diss.

865. HILTUNEN, SALLA. Hydrothermal stability of microfibrillated cellulose. 2019. Diss.

866. GURUNG, KHUM. Membrane bioreactor for the removal of emerging contaminantsfrom municipal wastewater and its viability of integrating advanced oxidation processes.2019. Diss.

867. AWAN, USAMA. Inter-firm relationship leading towards social sustainability in exportmanufacturing firms. 2019. Diss.

868. SAVCHENKO, DMITRII. Testing microservice applications. 2019. Diss.

869. KARHU, MIIKKA. On weldability of thick section austenitic stainless steel using laserprocesses. 2019. Diss.

870. KUPARINEN, KATJA. Transforming the chemical pulp industry – From an emitter to asource of negative CO2 emissions. 2019. Diss.

871. HUJALA, ELINA. Quantification of large steam bubble oscillations and chugging usingimage analysis. 2019. Diss.

872. ZHIDCHENKO, VICTOR. Methods for lifecycle support of hydraulically actuated mobileworking machines using IoT and digital twin concepts. 2019. Diss.

ISBN 978-952-335-428-9ISBN 978-952-335-429-6 (PDF)

ISSN-L 1456-4491ISSN 1456-4491

Lappeenranta 2019