energies

Article Electromagnetic Design of High-Power and High-Speed Permanent Considering Loss Characteristics

Wen Ji 1, Fei Ni 2,* , Dinggang Gao 2, Shihui Luo 1, Qichao Lv 3,4 and Dongyuan Lv 3,4

1 Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu 610031, China; [email protected] (W.J.); [email protected] (S.L.) 2 Maglev Transportation Engineering R&D Center, Tongji University, Shanghai 201804, China; [email protected] 3 Shanghai Aerospace Control Technology Institute, Shanghai 201109, China; [email protected] (Q.L.); [email protected] (D.L.) 4 Shanghai Space Intelligent Control Technology Key Laboratory, Shanghai 201109, China * Correspondence: [email protected]; Tel.: +86-21-6958-0338

Abstract: The motor is an important part of the flywheel energy storage system. The flywheel energy storage system realizes the absorption and release of electric energy through the motor, and the high- performance, low-loss, high-power, high-speed motors are key components to improve the energy conversion efficiency of energy storage flywheels. This paper analyzes the operating characteristics of the permanent magnet synchronous motor/generator (PMSG) used in the magnetically levitated

 flywheel energy storage system (FESS) and calculates the loss characteristics in the drive and power  generation modes. Based on this, the electromagnetic part of the motor is optimized in detail. Aiming at this design, this paper calculates the loss characteristics of driving and power generation modes Citation: Ji, W.; Ni, F.; Gao, D.; Luo, S.; Lv, Q.; Lv, D. Electromagnetic in detail, including its winding loss, core loss, eddy current loss and mechanical loss. The Design of High-Power and calculation results show that the design meets the loss requirements. It can reduce the no-load loss High-Speed Permanent Magnet of the permanent magnet synchronous motor at high speed and improve the energy conversion Synchronous Motor Considering Loss efficiency, which gives this system practical application prospects. Characteristics. Energies 2021, 14, 3622. https://doi.org/10.3390/ Keywords: magnetic levitation flywheel energy storage system; permanent magnet synchronous en14123622 motor; electromagnetic design; loss characteristics

Academic Editor: Jin-Woo Ahn

Received: 21 April 2021 1. Introduction Accepted: 15 June 2021 Published: 18 June 2021 The flywheel energy storage system is an energy storage device that converts electrical energy and mechanical energy with a high-speed rotating flywheel rotor as a carrier [1],

Publisher’s Note: MDPI stays neutral and it is one of the preferred solutions for short-term energy storage systems. The flywheel with regard to jurisdictional claims in energy storage system mainly has three working modes: charging, standby and discharging. published maps and institutional affil- When the flywheel energy storage system is charging, the motor runs electrically. It drives iations. the flywheel rotor to accelerate to a specified speed and converts electrical energy into flywheel kinetic energy for storage. When the flywheel energy storage system is in standby, the flywheel runs at a specified speed without load. When the flywheel energy storage system discharges, the flywheel decelerates and drives the motor to generate electricity. It uses the flywheel controller to convert the kinetic energy of the flywheel into electrical Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. energy and release it. This article is an open access article The motor is an important part of the flywheel energy storage system. The flywheel distributed under the terms and energy storage system realizes the absorption and release of electric energy through the conditions of the Creative Commons motor. The performance of the flywheel energy storage system obtained by using different Attribution (CC BY) license (https:// flywheel motors is also different. The requirements of the flywheel energy storage system creativecommons.org/licenses/by/ for the motor are: it can work in the state of electric and power generation; it has good 4.0/). high-speed performance, high efficiency, low no-load loss, small size, low noise, simple

Energies 2021, 14, 3622. https://doi.org/10.3390/en14123622 https://www.mdpi.com/journal/energies Energies 2021, 14, 3622 2 of 19

structure, easy maintenance, etc. The motors currently used in flywheel energy storage systems mainly include asynchronous motors, switched reluctance motors, permanent magnet brushless DC motors, and permanent magnet synchronous motors [2]. Each motor has its own structural characteristics. They have their own advantages and disadvantages in flywheel energy storage systems [3,4] Asynchronous motors (also called induction motors) are widely used. It has mature manufacturing technology, sturdiness and durability, small maintenance workload and low manufacturing cost. However, the motor has low efficiency, low power factor, and needs to absorb reactive power from the outside when generating electricity. Therefore, asynchronous motors are generally used in low-speed and large-capacity flywheel energy storage systems. Switched reluctance motors have the advantages of simple structure, sturdiness, high temperature resistance, low cost and reliable operation. However, the switched has large torque pulsation and high noise, and its operation must rely on sensors to obtain the rotor position signal, which increases the complexity of the system. Permanent magnet brushless DC motors have similar performance advantages as DC motors: easy to start, wide speed range, simple control and easy to achieve two-way power flow. However, permanent are easy to demagnetize and demagnetize at high temperatures, and the motor must rely on position sensors for current commutation. The square wave of current also makes its harmonic components high and torque ripple large. Comparing to above mentioned types, permanent magnet synchronous motors are widely used in high-speed flywheel energy storage systems [5,6]. It belongs to permanent magnet motors, just like the permanent magnet brushless DC motor. However, different waveforms of the counter electromotive force, the former counter electromotive force is a sine wave. The advantages of permanent magnet synchronous motors are: wide speed range, high power density, high efficiency, and high-power factor. However, the permanent magnet synchronous motor needs to install permanent magnets on the rotor. Therefore, the cost is relatively high. Improper use can easily cause permanent magnets to demagnetize and demagnetize. At the same time, the rotor structure is not as strong and durable as induction motors and reluctance motors. The operating speed of the motor of the flywheel energy storage system is often in the order of tens of thousands of rpm and is mostly supported by magnetic suspension bearings, which requires relatively high specific power and specific energy. The use of permanent magnet synchronous motors has higher power density and efficiency than permanent magnet brushless DC motors. Greater rotor stiffness is beneficial to increase the maximum speed of the flywheel [7]. The commonly used control strategies for permanent magnet synchronous motors include [8] and [9]. Direct torque control is the inde- pendent control of motor stator flux and motor torque in the stator stationary coordinate system. By integrating stator voltages, stator flux linkage can be estimated, and then, torque is estimated as a cross product of estimated stator flux linkage and measured motor current vector. By comparing the estimation with reference value, the controller can regulate the torque swiftly. The vector control technology transforms the three-phase AC current, expressed in the stator three-phase static coordinate system, into two DC components in the rotor synchronous rotational coordinate system using coordinate transformation. The two components are the excitation current component and the torque current component, respectively, which can be regulated separately, so that the flux linkage and torque control of the synchronous motor can be decoupled. By changing their combination, the required electromagnetic torque can be achieved [10]. Direct torque control has the advantage of fast dynamic response, but there is a large pulsation. Vector control technology is more mature and stable, and dynamic performance is better, and it is more widely used. Vector control is often used in flywheel energy storage systems driven by permanent magnet synchronous motors. In order to realize the continuous and stable operation of the flywheel energy storage system, low motor loss, high electromechanical conversion efficiency, high reliability and long life are required. This is also the general principle of this type of motor design [11]. Energies 2021, 14, 3622 3 of 19

Compared with ordinary motors, permanent magnet synchronous motors have smaller size, higher power density, higher switching frequencies and larger losses per unit volume. In addition, the rotor has poor heat dissipation conditions (usually in a vacuum chamber), and excessively high temperature will cause the performance of the motor to decrease and even cause the rotor to demagnetize, which limits the application of flywheel energy storage technology. The loss of a high-speed permanent magnet synchronous motor includes stator wind- ing loss, core loss, rotor eddy current loss and mechanical loss. Among them, due to the skin effect and proximity effect, the stator winding copper loss and core loss increase with the operating frequency, which account for the main sources of motor loss. Loss analysis and performance optimization under high-frequency conditions have always been key issues in the study of high-speed and high-power motors. The design of heat dissipation system, the improvement of reliability and the expansion of application fields are of great significance to the improvement of a high-speed permanent magnet synchronous motor structure and variable frequency drive scheme. Tao D. et al. [12] analyzed the electromag- netic characteristics of a two-pole 120 kW high-speed permanent magnet synchronous motor and the core loss characteristics of the stator and pointed out that the core loss in the stator yoke thickness accounted for the main part of the stator core loss; Zhang F. et al. [13] carried out electromagnetic design and loss calculation on a 1.12 MW high-speed perma- nent magnet motor. The iron loss, winding loss, eddy current loss and friction loss are calculated, considering factors such as the number of poles, the number of stator slots, the diameter of the rotor, the air gap, and the material. Li Y. et al. [14] convert the design of high-speed permanent magnet motors into a multi-objective optimization problem and comprehensively considers various losses in the design process. Du G. et al. [15] and Zhang Y. et al. [16] conducted thermal simulation and experimental analysis of the quasi-MW and MW-class motors studied and gave their respective cooling solutions based on the detailed calculation of the loss characteristics of the high-speed permanent magnet synchronous motor. In this paper, for the application of a flywheel energy storage system, low-loss design and optimization of high-speed motor under multiple constraints are carried out to reduce the steady-state power consumption of the motor and improve the energy conversion efficiency. The contents of this article are listed as follows: Chapter 2 gives a design and technical specifications of a 300 kW high-speed motor used in FESS and carries out electromagnetic design and finite element analysis of this design. Chapter 3 analyzes the operating characteristics of this high-speed motor design. Chapter 4 gives a detailed loss analysis of how the high-speed motor is used in FESS, including the high-frequency winding loss resulting from the skin effect and proximity effect; the high-frequency core loss includes eddy current loss and hysteresis loss, the rotor eddy current loss and other losses. Chapter 5 is the conclusion.

2. Integrated Motor Design 2.1. High-Speed Motor Solutions and Technical Specifications The research object of this paper is the permanent magnet synchronous motor/generator (PMSG) used in the magnetic levitation flywheel energy storage system (FESS), which mainly aims at high efficiency, high speed and high output. The rated speed of the motor is 30 krpm. The rated power in power generation mode is 300 kW. The motor/generator structure of the flywheel energy storage system is shown in Figure1. The stator has a general AC motor stator shape. The rotor is made of a cylindrical permanent magnet wrapped with a metal sleeve and supported by radial and axial magnetic bearings. The rotor of the flywheel energy storage system operates in a near vacuum environment. The heat inside the shell is naturally transferred to the surface of the shell through the air between the shell and the rotor. Therefore, determining the amount of heat generated by the motor is crucial for choosing the cooling method of the flywheel energy storage system. When the flywheel energy storage system starts to operate, the flywheel energy storage system is driven by Energies 2021, 14, x FOR PEER REVIEW 4 of 21

heat inside the shell is naturally transferred to the surface of the shell through the air be- Energies 2021, 14, 3622 tween the shell and the rotor. Therefore, determining the amount of heat generated by4 ofthe 19 motor is crucial for choosing the cooling method of the flywheel energy storage system. When the flywheel energy storage system starts to operate, the flywheel energy storage system is driven by the inverter, and the flywheel speeds up to 30 krpm. At such a speed, eventhe inverter, in the absence and the of flywheel input power, speeds core up toloss 30 will krpm. still At occur such in a speed,the stator even due in to the the absence high- speedof input rotation power, of core the permanent loss will still magnet occur inrotor. the statorIn order due to toreduce the high-speed the loss of rotationthe stator, of the materialpermanent of magnetthe stator rotor. core In should order tobe reduceselected the reasonably loss of the and stator, the the geometry material of of the the motor stator shouldcore should be optimized. be selected For reasonably the design and of the permanent geometry magnet of the motor synchronous should be motors, optimized. several For feedbackthe design processes of permanent between magnet electromagn synchronousetic design motors, and several structural feedback design processes should betweenbe used toelectromagnetic determine whether design andthe design structural data design can shouldmeet the be requirements. used to determine What whether has been the designlisted hereinafterdata can meet is the the technical requirements. parameters What hasof the been flywheel listed hereinafter energy storage is the system. technical In parameters generator design,of the flywheel the most energy important storage thi system.ng is to In meet generator the requirements design, the most of efficiency important and thing output is to powermeet the at requirements30 krpm, and of the efficiency design should and output be carried power out at 30 within krpm, a and given the space design size should range. be carried out within a given space size range. Table1 listed the motor’s technical specifications Table 1 listed the motor’s technical specifications with its stator dimensions. with its stator dimensions.

Figure 1. Schematic diagram of flywheel energy storage system. Figure 1. Schematic diagram of flywheel energy storage system.

Table 1. Motor technical specifications. specifications. DescriptionDescription V Valuealue (Generation(Generation mode) mode) outputoutput power power 30 3000 k kWW (Electric(Electric driven driven mode) mode) inputinput power power 30~6 30~600 k kWW DC bus voltage 540 Vdc DC bus voltage 540 Vdc Synchronous speed 30,000 rpm EfficiencySynchronous at 30,000 speed rpm 30,00 98%0 rpm EfficiencyOuter diameter at 30,00 of stator0 rpm 25098% mm OuterStator diameter inner diameter of stator 25 1460 m mmm StatorStator inner core d lengthiameter 14 1806 m mmm Cooling method Stator natural air cooling Stator core length 180 mm Cooling method Stator natural air cooling Figure2 shows the electric driven mode and power generation mode of FESS. In the electricFigure driven 2 shows mode, the the electric AC power driven source mode AC and is converted power generation to DC by mode an AC/DC of FESS. converter. In the electricThe flywheel driven is mode, rotated the through AC power the source DC/AC AC inverter is converted to the to target DC by speed an AC/DC of 30 krpm. converter. After Thethat, flywheel only the is minimum rotated through power tothe maintain DC/AC inverter the speed to isthe continuously target speed provided, of 30 krpm. and After the that,shaft only that the reaches minimum 30 krpm power can to overcome maintain the the rotation speed is resistance continuously to maintain provided, this and speed. the shaftIn the that power reaches generation 30 krpm mode, can overcome it operates the in rotation the opposite resistance way to and maintain feeds thethis generated speed. In electrical energy back to the grid. In an emergency, a shaft rotating at 30 krpm transmits the power generation mode, it operates in the opposite way and feeds the generated elec- the generated energy to the grid. In the process of energy transfer, a reaction torque will be trical energy back to the grid. In an emergency, a shaft rotating at 30 krpm transmits the generated on the shaft, causing the speed to decrease rapidly. During the period when the generated energy to the grid. In the process of energy transfer, a reaction torque will be rotating shaft speed is reduced from 30 to 15 krpm within 15 s, it is necessary to be able to generated on the shaft, causing the speed to decrease rapidly. During the period when the output 300 kW of power. When the rotating shaft speed is 15 krpm, the voltage generated will drop by 50%, so the output current will be twice the original. The reduced voltage will be increased by a voltage boost device.

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rotating shaft speed is reduced from 30 to 15 krpm within 15 s, it is necessary to be able to output 300 kW of power. When the rotating shaft speed is 15 krpm, the voltage generated Energies 2021, 14, 3622 will drop by 50%, so the output current will be twice the original. The reduced voltage 5 of 19 will be increased by a voltage boost device.

Figure 2. Electric/powerFigure generation 2. Electric/power system. generation system.

2.2. Electromagnetic2.2. Electromagnetic Design Design The rated powerThe rated of the power motor of studied the motor in this studied paper inis this300 k paperw. Considering is 300 kw. the Considering re- the quirements requirementsof motor weight, of motor no-load weight, loss no-loadand back loss electromotive and back electromotive force, the number force, theof number of poles and slotspoles and and the slots winding and the method winding of the method motor of should the motor be reasonably should be reasonablyselected. The selected. The number of polesnumber of high of poles-speed of motors high-speed is generally motors issmall generally and its small combination and its combination with the slot with the slot structure design greatly affects the overall performance of the motor [17,18]. The available structure design greatly affects the overall performance of the motor [17,18]. The available option is either two poles or four poles, and each has its advantages and disadvantages. option is either two poles or four poles, and each has its advantages and disadvantages. The advantage of a two-pole motor is that the permanent magnets of the rotor can be The advantage of a two-pole motor is that the permanent magnets of the rotor can be integrated into a compact structure. It ensures that the rotor’s mechanical structure is integrated into a compact structure. It ensures that the rotor’s mechanical structure is iso- isotropic in the radial direction, which is beneficial to the dynamic balance of the rotor. tropic in the radial direction, which is beneficial to the dynamic balance of the rotor. At At the same time, it can reduce the alternating frequency of the stator winding current the same time, it can reduce the alternating frequency of the stator winding current and and the magnetic field in the iron core, which lead to reduced high-frequency additional the in the iron core, which lead to reduced high-frequency additional loss. loss. The disadvantage of a two-pole motor is that the stator winding ends are longer and The disadvantage of a two-pole motor is that the stator winding ends are longer and the the core yoke is thicker. On the contrary, the advantage of a four-pole motor is that the core yoke is thicker. On the contrary, the advantage of a four-pole motor is that the stator stator winding ends are shorter and the core yoke is thinner; while the disadvantage is that winding ends are shorter and the core yoke is thinner; while the disadvantage is that the the permanent magnet rotor requires multiple permanent magnets to be spliced, which permanent magnetreduces rotor the rigidity requires of themultiple rotor. permanent At the same magnets time, the to alternating be spliced, frequency which re- of the stator duces the rigiditywinding of currentthe rotor. and At the the magnetic same time, field the in thealternating iron core frequency is higher, whichof the increasesstator the iron winding currentloss. Fromand the the magnetic perspective field of in electromagnetic the iron core is and higher, mechanical which increases considerations, the iron especially the loss. From themechanical perspective strength of electromagnetic and rigidity of theand rotor, mechanical it is more considerations, advantageous especially to adopt the two-pole the mechanicalsolution. strength After and the rigidity number of of the poles rotor, is determined,it is more advantageous the number ofto correspondingadopt the slots is two-pole solution.easier toAfter determine. the number Usually of poles a stator is determined, with a 24-slot the number structure of corresponding is used, and the winding slots is easiermethod to determine. is a double-layer Usually a distributedstator with winding.a 24-slot structure The appropriate is used, pitch and the is selected wind- to improve ing methodthe is a electromotive double-layer force distributed and magnetomotive winding. The force appropriate waveform. pitch is selected to improve the electromotivThe maine sizeforce of and the PMSMmagnetomotive can be determined force waveform. by the required electromagnetic power The mainrequirements size of the and PMSM the preselected can be determined electromagnetic by the requiredload value. electromagnetic The size is given by the power requirementsfollowing and equation the preselected [19]: electromagnetic load value. The size is given by π the following equation [19]: P = α K K D 2L nA B (1) 60 i B dp i1 1 1 δ  2 P i K B K dp D i1 L 1 nA 1 B (1) where P is the electromagnetic60 power; αi is the calculated pole arc coefficient; KB is the air gap magnetic field waveform coefficient; K is the winding coefficient; D is the stator where P is the electromagnetic power; αi is the calculateddp pole arc coefficient; KB is the airi1 inner diameter; L is the iron core length; n is the motor speed; A is the electric load; B is gap magnetic field waveform1 coefficient; Kdp is the winding coefficient; Di1 is the stator δ the air gap magnetic density. inner diameter; L1 is the iron core length; n is the motor speed; A1 is the electric load; Bδ is According to the requirements of the motor layout and the space limitation of the the air gap magnetic density. flywheel cavity, the effective length of the stator is initially selected to be 150 mm, and the According to the requirements of the motor layout and the space limitation of the electrical load generally ranges from 150 to 500 A/mm. According to the heat dissipation flywheel cavity, the effective length of the stator is initially selected to be 150 mm, and the condition of the motor, which is natural cooling, the load is set as 377 A/mm, while the electrical load generally ranges from 150 to 500 A/mm. According to the heat dissipation magnetic load of the motor is 0.8 T, K and K are, respectively, 1.1 and 0.96. The length of condition of the motor, which is natural cooling,B the loaddp is set as 377 A/mm, while the the motor air gap has a great influence on the performance of the motor. Properly increasing magnetic load of the motor is 0.8 T,KB and Kdp are, respectively, 1.1 and 0.96. The length the air gap length can reduce torque ripple and harmonic components and can also reduce the eddy current loss in the permanent magnet and reduce the risk of permanent magnet demagnetization. From the perspective of installation, appropriately increasing the air gap can facilitate the installation of the flywheel rotor. However, increasing the air gap can also cause the raise of reluctance and consequently the decrease in power factor. Energies 2021, 14, 3622 6 of 19

In the stator shape design, the following content needs to be considered: (a) design the magnetic circuit to make the magnetic flux energy conversion smooth; (b) design the winding to generate the required three-phase voltage; (c) determine the slot shape to locate the winding. At this time, the following items should be estimated: (a) Conductors of each phase: estimate the number of serials turns based on the driven voltage and the generation voltage; (b) Number of slots: estimate the number of slots in the stator by determining the number of slots for each pole; (c) Slot area: estimate the required slot section based on the current density. Under open circuit conditions, through equivalent circuit analysis or finite element analysis, it is necessary to modify the shape of the stator many times. In open circuit analysis, a magnetic flux path must be established so that magnetic flux saturation does not occur. The magnet material plays a vital role in the allowed magnetic flux. The rotor studied here uses samarium–cobalt (SmCo) magnets, which is a strong rare-earth permanent magnet made of samarium and cobalt alloy. SmCo magnets generally have a higher temperature rating and higher coercivity, and they are the only viable material with an operating temperature above 250 ◦C[20]. In particular, the maximum energy range 3 of the Sm2Co17 products of these alloys is 20~32 MGOe, which is about 160~260 kJ/m . These alloys have the best reversible temperature coefficient of all rare earth alloys, usually −0.03%/◦C. However, they are very brittle and can easily crack and chip. Table2 lists the typical range of properties of Sm2Co17 materials.

Table 2. Typical range of Sm2Co17 (2:17 alloy) properties.

Br Hc (Hcb) Hci (Hcj) BHmax Material T kG kA/m kOe kA/m kOe kJ/m3 MGOe SmCo24H 0.95–1.02 9.5–10.2 700–750 8.7–9.4 >1990 >25 175–191 22–24 SmCo26H 1.02–1.05 10.2–10.5 750–780 9.4–9.8 >1990 >25 191–207 24–26 SmCo28H 1.03–1.08 10.3–10.8 756–796 9.5–10.0 >1990 >25 207–220 26–28 SmCo30H 1.08–1.10 10.8–11.0 788–835 9.9–10.5 >1990 >25 220–240 28–30

In Figure3, the magnetic flux shown by the designed stator is consistent with the designed magnetic flux. Figure3a is the magnetic line of force distribution in the stator when there is no load. Figure3b shows the magnetic flux density distribution of the stator cross-section. The local magnetic flux density saturation does not exceed 1.6 T. Figure4 is a graph of the magnetic flux distribution along the semicircular curve of the contour of the yoke and slot teeth in the stator. It can be determined that the magnetic flux density does not exceed 1.6 T. Using a two-pole, 24-slot motor structure, the three-phase winding arrangement under Y-connection is shown in Figure5. Figure6 is the axial and radial cross-sectional view of the permanent magnet synchronous motor, including the stator core, stator laminated fixed layer, end coils, sheath and permanent magnets (Sm2Co17-26H). The length, outer diameter of the stator, outer diameter of the permanent magnet and thickness of the sheath are all determined according to the characteristics and rigidity of the rotating structure. This is the starting point for determining the volume in the design. The thickness of the sheath and length of the shaft are the most important factors in the structural design. The rotating shaft with permanent magnets generates electromotive force at the stator coil terminals according to the rotation speed. The electromotive force increases with the increase in length, speed and magnetic flux density, as shown in Equation (2).

eph = kw Nphec = kw Nph(NcBωmDL) (2)

Combining the finite element model and the simulation calculation of the circuit to calculate the electromotive force (EMF), the circuit is shown in Figure7. Energies 2021, 14, x FOR PEER REVIEW 7 of 21 Energies 2021, 14, 3622 7 of 19

Energies 2021, 14, x FOR PEER REVIEW 7 of 21

(a) (b) (a) (b) Figure 3. a b FigureFigure 3. Stator3. StatorStator magnetic magnetic magnetic flux flux flux distribution distribution distribution underunder no nono load: load:load: ( (a )() aThe The) The magnetic magnetic magnetic flux flux flux line line linedistribution. distribution. distribution. ( (b)) The The (b magnetic) magnetic The magnetic flux flux flux densitydensitydensity distribution distribution distribution.. .

1.81.8 Dia=160mmDia=160mm 1.61.6 Dia.=220mmDia.=220mm 1.41.4 1.21.2 11 0.8 0.8 0.6 0.6 0.4 0.4

Magnet Magnet Flux Density [T] 0.2

Magnet Magnet Flux Density [T] 0.20 0 0 30 60 90 120 150 180 Energies 2021, 14, x FOR PEER REVIEW Revolute Angle [deg] 8 of 21 0 30 60 90 120 150 180 Revolute Angle [deg] FigureFigure 4. 4. TheThe magnetic magnetic flux flux density density on on the the inner inner contour contour of of the the stator stator under under no no load. load. Figure 4. The magnetic flux density on the inner contour of the stator under no load. Using a two-pole, 24-slot motor structure, the three-phase winding arrangement un- der Y-connection is shown in Figure 5. Figure 6 is the axial and radial cross-sectional view of theUsing permanent a two -magnetpole, 24 synchronous-slot motor motor,structure, including the three the -statorphase core, winding stator arrangemenlaminated t un- derfixed Y- layer,connection end coils, is shown sheath in and Figure permanent 5. Figure magnets 6 is the (Sm2Co17 axial and-26H). radial The cross length,-sectional outer view ofdiameter the permanent of the stator, magnet outer synchronous diameter of motor, the permanent including magnet the stator and thicknesscore, stator of laminated the fixedsheath layer, are all end determined coils, sheath according and topermanent the characteristics magnets and (Sm2Co17 rigidity of- 26H).the rotating The length, struc- outer diameterture. This ofis the the starting stator, point outer for diameter determining of the volume permanent in the magnetdesign. The and thickness thickness of of the sheaththe sheath are alland determined length of the according shaft are the to themost characteristics important factors and in rigidity the structural of the design.rotating struc- ture. This is the starting point for determining the volume in the design. The thickness of the sheath and length of the shaft are the most important factors in the structural design.

FigureFigure 5. 5. ThreeThree-phase-phase winding winding distribution. distribution.

Figure 6. Cross-section of permanent magnet synchronous motor.

The rotating shaft with permanent magnets generates electromotive force at the sta- tor coil terminals according to the rotation speed. The electromotive force increases with the increase in length, speed and magnetic flux density, as shown in Equation (2).

eph k wphc N e  k wph N() N c B m DL (2)

Combining the finite element model and the simulation calculation of the circuit to calculate the electromotive force (EMF), the circuit is shown in Figure 7.

Probe Va

PhasePhase AA Rcoil Lleak

Probe Vb

PhasePhase BB Rcoil Lleak

Probe Vc

PhasePhase CC Rcoil Lleak

Figure 7. Back-EMF simulation circuit.

In Figure 8, the back-EMF diagrams are obtained through simulation calculations at 15 and 30 krpm, respectively. Figure 9 is a graph of the electromotive force as the speed increases, and the back electromotive force coefficient is 0.012 [V/rpm].

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Figure 5. Three-phase winding distribution.

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Figure 5. Three-phase winding distribution.

Figure 6. Cross-section of permanent magnet synchronous motor.

The rotating shaft with permanent magnets generates electromotive force at the sta- tor coil terminals according to the rotation speed. The electromotive force increases with the increase in length, speed and magnetic flux density, as shown in Equation (2).

eph k wphc N e  k wph N() N c B m DL (2)

Combining the finite element model and the simulation calculation of the circuit to FigureFigurecalculate 6. 6. CrossCross-section the-section electromotive of of permanent permanent magnetforce magnet synchronous(EMF), synchronous the motor. circuit motor. is shown in Figure 7.

The rotating shaft with permanent magnets generates electromotiveProbe Va force at the sta- tor coil terminals according to the rotation speed. The electromotive force increases with the increase inPhasePhase length, AA speed and magneticRcoil fluxLleak density, as shown in Equation (2).

eph k wphc N e  k wph N() N c B m DL (2) Probe Vb Combining the finite element model and the simulation calculation of the circuit to PhasePhase BB Rcoil Lleak calculate the electromotive force (EMF), the circuit is shown in Figure 7.

Probe Vc Probe Va PhasePhasePhasePhase AA CC Rcoil RcoilLleak Lleak

Probe Vb FigureFigure 7. 7.Back-EMF Back-EMF simulation simulation circuit. circuit. PhasePhase BB Rcoil Lleak Energies 2021, 14, x FOR PEER REVIEW In Figure8, the back-EMF diagrams are obtained through simulation calculations at9 of 21

15 and 30 krpm, respectively. Figure9 is a graph of the electromotive force as the speed In Figure 8, the back-EMF diagrams are obtainedProbe Vc through simulation calculations at increases,15 and 3 and0 k therpm, back respectively. electromotive forceFigure coefficient 9 is a isgraph 0.012 [V/rpm]. of the electromotive force as the speed PhasePhase CC Rcoil Lleak increases, and the back electromotive force coefficient is 0.012 [V/rpm]. Va Vab Vb Vc Va Vab Vb Vc 600 600 Figure 7. Back-EMF simulation circuit. 500 500 400 400 300 In Figure 8, the back-EMF diagrams300 are obtained through simulation calculations at 200 15 and 30 krpm, respectively. Figure200 9 is a graph of the electromotive force as the speed 100 increases, and the back electromotive100 force coefficient is 0.012 [V/rpm]. 0 0

etromotive [V] -100 -100 -200 -200 -300 -300 -400

Counter Counter El -400 -500 Counter Electromotive [V] -500

-600 -600 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Time [ms] Time [ms] (a) (b)

FigureFigure 8. Back 8. Back-EMF-EMF when when open open circuit. ((aa)) 15 15 krpm. krpm. (b ()b 30) 3 krpm.0 krpm.

400 350 300 250 200 150 100 50

Counter Counter Electromotive [Vrms] 0 0 5 10 15 20 25 30 Rotor Speed [krpm]

Figure 9. The change in Back-EMF versus rotor speed.

3. Analysis of Operating Characteristics of High-Speed Motors 3.1. Electric Driven Mode At startup, FESS accelerates to 30 krpm in the electric driven mode. The applied power is determined by the acceleration time and the moment of inertia in the simulation process, assuming that the input power is 30 and 60 kW, respectively. At a constant speed, the iron loss changes, whereas the power stays basically unchanged. Table 3 list the oper- ational characteristics of the motor at 30 krpm electric driven mode. Figures 10 and 11 depict the input voltage, input current, input power and loss characteristics of the motor at 30 krpm with an input power of 30 and 60 kW, respectively.

Table 3. Characteristics of 30 krpm electric driven mode.

Power [kW] Speed [krpm] Voltage [V] Current [A] Core loss [kW] 30 30 364 56 1.6 60 30 370 100 1.6

Energies 2021, 14, x FOR PEER REVIEW 9 of 21

Va Vab Vb Vc Va Vab Vb Vc 600 600 500 500 400 400 300 300 200 200 100 100 0 0 etromotive etromotive [V] -100 -100 -200 -200 -300 -300 -400

Counter Counter El -400 -500 Counter Electromotive [V] -500 -600 -600 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Time [ms] Time [ms] Energies 2021, 14, 3622 (a) (b) 9 of 19 Figure 8. Back-EMF when open circuit. (a) 15 krpm. (b) 30 krpm.

400 350 300 250 200 150 100 50

Counter Counter Electromotive [Vrms] 0 0 5 10 15 20 25 30 Rotor Speed [krpm]

FigureFigure 9. 9. TheThe change change in in Back Back-EMF-EMF versus versus rotor rotor speed.

3.3. Analysis Analysis of of Operating Operating Characteristics Characteristics of of High High-Speed-Speed Motors 3.1. Electric Driven Mode 3.1. Electric Driven Mode At startup, FESS accelerates to 30 krpm in the electric driven mode. The applied power At startup, FESS accelerates to 30 krpm in the electric driven mode. The applied is determined by the acceleration time and the moment of inertia in the simulation process, power is determined by the acceleration time and the moment of inertia in the simulation assuming that the input power is 30 and 60 kW, respectively. At a constant speed, the iron process, assuming that the input power is 30 and 60 kW, respectively. At a constant speed, loss changes, whereas the power stays basically unchanged. Table3 list the operational the iron loss changes, whereas the power stays basically unchanged. Table 3 list the oper- characteristics of the motor at 30 krpm electric driven mode. Figures 10 and 11 depict the ationalinput voltage, characteristics input current, of the inputmotor power at 30 andkrpm loss electric characteristics driven mode. of the Figure motors at10 30 and krpm 11 depictwith an the input input power voltage, of 30 input and 60current, kW, respectively. input power and loss characteristics of the motor at 30 krpm with an input power of 30 and 60 kW, respectively. Table 3. Characteristics of 30 krpm electric driven mode. Table 3. Characteristics of 30 krpm electric driven mode. Power [kW] Speed [krpm] Voltage [V] Current [A] Core loss [kW] Power [kW] Speed [krpm] Voltage [V] Current [A] Core loss [kW] 3030 30 30 364 364 56 56 1.6 1.6 60 30 370 100 1.6 60 30 370 100 1.6

3.2. Rated Load (Generation Mode) The power control system (PCS) is added to the actual power generation system, but the load library is assumed in the finite element analysis for simulation. Figure 12 shows the coupling circuit diagram used in simulation. When the FESS rotates at 30 krpm, the output is changed by adjusting the Rload value, so that the output power is 300 kW when the load circuit is turned on. When decelerating to 15 krpm, R should be changed to load output 300 kW. When the speed slows down, the generated voltage decreases proportionally. There- fore, in order to obtain a constant output power, the current needs to be increased. The simulation results show this characteristic, as shown in Table4. Figures 13 and 14 depicts the output voltage, output current, output power and loss characteristics of the motor in 300 kW power generation mode at 30 and 15 krpm, respectively.

Table 4. Characteristics in power generation mode.

Power [kW] Speed [krpm] Voltage [V] Current [A] Core Loss [kW] 300 30 360 495 1.6 300 15 178 993 0.6 Energies 2021, 14, x FOR PEER REVIEW 10 of 21 Energies 2021, 14, 3622 10 of 19

Energies 2021, 14, x FOR PEER REVIEW 10 of 21 Va Vb Vc Ia Ib Ic 400 200 300 150 Ia Ib Ic 200 Va Vb Vc 100 400 200 100 50 300 150 oltage [V] 0 200 100 0 -100 100 50-50 Input Current [A] Input V -200oltage [V] 0 -1000 -300-100 -50-150 Input Current [A] Input V -400-200 -100-200 -30090 91 92 93 94 95 96 97 98 99 100 -150 90 91 92 93 94 95 96 97 98 99 100 -400 Time [ms] -200 Time [ms] 90 91 92 93 94 95 96 97 98 99 100 90 91 92 93 94 95 96 97 98 99 100 Time(a) [ms] Time( b[ms])

60 (a) 1.8 (b) 1.6 50 60 1.8 1.61.4 40 50 1.2 [kW] 1.4 40 1.2 1 30[kW] 10.8 Power Power 30

0.8 Loss [kW] 20 Power 0.6

20 Loss [kW] Input 0.60.4

10Input 0.4 10 0.2 0.2 0 0 0 0 10 20 30 40 50 60 70 80 90 100 0 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Time [ms] Time [ms] Time [ms] Time [ms]

(c)( c) (d) (d) FigureFigureFigure 10.10.Characteristics Characteristics 10. Characteristics atat 30at30 3 krpmk0rpm krpm (30(3 (300 kWk kWW electric electricelectric drivendriven mode): mode):mode): (a ()(a aInput)) InputInput voltage. voltage.voltage. (b) Input ((b)) InputInput current. current.current. (c) Input (c) power. InputInput power. ((dd)) Loss.Loss.(d) Loss.

VaVa VbVb Vc Ia Ia Ib Ib Ic Ic 400 200 400 200 300 150 300 150 200 100 200 100 100 50 50 100 0 0 0-100 -50 0 Input Voltage [V] -100-200 Input Current [A] -100-50 Input Voltage [V] -200-300 -150Input Current [A] -100 -300-400 -200-150 90 91 92 93 94 95 96 97 98 99 100 90 91 92 93 94 95 96 97 98 99 100 -400 -200 Time [ms] Time [ms] 90 91 92 93 94 95 96 97 98 99 100 90 91 92 93 94 95 96 97 98 99 100 Time(a) [ms] (b) Time [ms]

Cont (a) Figure 11. . (b)

Energies 2021, 14, x FOR PEER REVIEW 11 of 21

140 1.8 120 1.6 1.4 EnergiesEnergies2021, 142021100, 3622, 14, x FOR PEER REVIEW 11 of 21 11 of 19 1.2 80 1 60 0.8 Loss Loss [kW] ut ut [kW]Power 140 0.6 1.8 40 Inp 120 0.4 1.6 20 0.2 1.4 100 0 0 1.2 0 10 20 30 40 50 60 70 80 90 100 80 01 10 20 30 40 50 60 70 80 90 100 Time [ms] Time [ms] 60 0.8 Loss Loss [kW] ut ut [kW]Power (c) 0.6 (d) 40 FigureInp 11. Characteristics at 30 krpm (60 kW electric driven mode): (a) Input0.4 voltage. (b) Input current. (c) Input power. (d) Loss.20 0.2 0 3.2. Rated Load (Generation Mode) 0 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 The power control system (PCS) is added to the actual power generation system, but Time [ms] Time [ms] the load library is assumed in the finite element analysis for simulation. Figure 12 shows the(c) coupling circuit diagram used in simulation. When the FESS(d )rotates at 30 krpm, the output is changed by adjusting the Rload value, so that the output power is 300 kW when Figure 11. Characteristics at 30 krpm (60 kW electric driven mode): (a) Input voltage. (b) Input current. (c) Input power. Figure 11. Characteristics at 30 krpmthe (60load kW circuit electric is turned driven on. mode): When ( adecelerating) Input voltage. to 15 ( bk)rpm, Input Rload current. should ( cbe) Input changed power. to (d) Loss. (d) Loss. output 300 kW. 3.2. Rated Load (Generation Mode) The power control system (PCS) is added to the actual power generation system, but the load library is assumed in the finite element analysis for simulation. Figure 12 shows the coupling circuit diagram used in simulation. When the FESS rotates at 30 krpm, the output is changed by adjusting the Rload value, so that the output power is 300 kW when the load circuit is turned on. When decelerating to 15 krpm, Rload should be changed to output 300 kW.

Energies 2021, 14, x FOR PEER REVIEW 12 of 21

FigureFigure 12. CouplingCoupling circuit circuit diagram. diagram.

Va WhenVab the speedVb slowsVc down, the generated voltage decreasesIa proportionally.Ib Ic There- 600 fore, in order to obtain a constant output800 power, the current needs to be increased. The simulation results show this characteristic,600 as shown in Table 4. Figures 13 and 14 depicts 400 the output voltage, output current, output400 power and loss characteristics of the motor in 200 300 kW power generation mode at 30 and200 15 krpm, respectively. 0

oltage [V] 0 Table 4. Characteristics in power generation mode. -200 -200 Figure 12. Coupling circuit diagram.

Power [kW] Speed [krpm] VoltageInput Current [A] -400 [V] Current [A] Core Loss [kW] Input V -400 When300 the speed slows30 down, the-600 generated360 voltage495 decreases proportionally.1.6 There- -600 fore, in300 order to obtain15 a constant output-800178 power, the current993 needs to be0.6 increased. The 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3simulation 4 5 6 results7 8 show9 10 this characteristic, as shown in Table 4. Figures 13 and 14 depicts Time [ms] Time [ms] the output voltage, output current, output power and loss characteristics of the motor in 300( ak)W power generation mode at 30 and 15 krpm, respectively.(b) 350 1.8 Table 4. Characteristics in power generation mode. 300 1.6 Power [kW] Speed [krpm] 1.4Voltage [V] Current [A] Core Loss [kW] 250 1.2 [kW] 200 300 30 1 360 495 1.6 300 15 178 993 0.6 ower 150 0.8 Loss [kW] 0.6 100 0.4 Input P 50 0.2 0 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Time [ms] Time [ms]

(c) (d) Figure 13. CharacteristicsFigure 13. Characteristics at 30 krpm at 30 k (300rpm (30 kW0 k powerW power generation generation state): state): (a) (Outputa) Output voltage. voltage. (b) Output (b) current. Output (c) current. Output (c) Output power. (d) Loss. power. (d) Loss.

Va Vab Vb Vc Ia Ib Ic 600 1600

] 1200

[V 400 800 200 400 0 0

-200 -400 Output Output Voltage Output Output Current [A] -800 -400 -1200 -600 -1600 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Time [ms] Time [ms]

(a) (b)

Energies 2021, 14, x FOR PEER REVIEW 12 of 21

Va Vab Vb Vc Ia Ib Ic 600 800 600 400 400 200 200 0

oltage [V] 0 -200 -200

Input Current [A] -400 Input V -400 -600 -600 -800 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Time [ms] Time [ms]

(a) (b) 350 1.8 300 1.6 1.4 250 1.2 [kW] 200 1

ower 150 0.8 Loss Loss [kW] 0.6 100 0.4 Input P 50 0.2 0 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Time [ms] Time [ms]

(c) (d) EnergiesFigure2021, 1413., 3622Characteristics at 30 krpm (300 kW power generation state): (a) Output voltage. (b) Output current. (c) Output12 of 19 power. (d) Loss.

Va Vab Vb Vc Ia Ib Ic 600 1600

] 1200

[V 400 800 200 400 0 0

-200 -400 Output Output Voltage Output Output Current [A] -800 -400 -1200 -600 Energies 2021, 14, x FOR PEER REVIEW -1600 13 of 21 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Time [ms] Time [ms]

(a) (b) 350 700 300 600 250 500

200 [kW] 400 150 300 Loss t Power [kW] 100 200

Outpu 50 100 0 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Time [ms] Time [ms]

(c) (d)

FigureFigure 14.14. CharacteristicsCharacteristics atat 1515 krpmkrpm (300(300 kWkW powerpower generationgeneration state):state): ((aa)) OutputOutput voltage.voltage. ((bb)) OutputOutput current.current. ((cc)) OutputOutput power. (d) Loss. power. (d) Loss.

4. Loss Analysis 4.1. Composition of High-SpeedHigh-Speed Motor Loss Motor lossloss includesincludes windingwinding loss, corecore loss,loss, rotorrotor eddyeddy currentcurrent lossloss andand mechanicalmechanical loss.loss. SinceSince thethe motor motor in in this this article article uses uses a magnetic a magnetic suspension suspension bearing bearing to support to support the rotor, the thererotor, is there almost is almost no mechanical no mechanical friction friction loss. On loss. the electricOn the ele side,ctric the side, high-frequency the high-frequency current ofcurrent high-speed of high motors-speed will motors cause will the cause skin effect, the skin proximity effect, proximity effect and high-ordereffect and high harmonics-order toharmonics become obvious,to become resulting obvious, in resulting increased in motorincreased losses. motor At losses. the same At the time, same the time, changes the inchanges the proportion in the proportion of different of different types of lossestypes areof losses also obvious. are also Dueobvious. to the Due high to speedthe high of thespeed high-speed of the high motor-speed and motor the high and frequencythe high frequency of the winding of the current,winding thecurrent, iron lossthe andiron copperloss and loss copper per unit loss volume per unit of volume the stator, of the high-frequencystator, the high- eddyfrequency current eddy loss current of the rotor loss andof the the rotor surface and airthe friction surface loss air frictio are muchn loss larger are much than thoselarger of than ordinary those motorsof ordinary of the motors same powerof the same level. power level. During thethe operationoperation of of high-speed high-speed motors, motors, the the above-mentioned above-mentioned losses losses can can generally gener- beally divided be divided into theinto following the following categories: categories: (1)(1) Stator loss, which is divided into iron loss andand coppercopper loss.loss. Stator iron lossloss refersrefers toto thethe loss caused byby thethe changechange in in the the main main magnetic magnetic field field in in the the iron iron core. core. Whether Whether it isit alternating magnetization or rotating magnetization, it will cause hysteresis loss and is alternating magnetization or rotating magnetization, it will cause hysteresis loss eddy current loss in the core. The stator copper loss is composed of basic copper loss and eddy current loss in the core. The stator copper loss is composed of basic copper and additional copper loss. Basic copper loss refers to the loss caused by the working loss and additional copper loss. Basic copper loss refers to the loss caused by the current in the copper winding. Additional copper loss refers to the high-frequency working current in the copper winding. Additional copper loss refers to the high- additional loss in the winding due to the skin effect of the alternating magnetic field. frequency additional loss in the winding due to the skin effect of the alternating mag- netic field. The high-frequency additional loss of the winding is related to many fac- tors such as the working frequency of the motor, the size of the winding conductor and the arrangement position in the slot. (2) Rotor loss, which is divided into air friction loss on the rotor surface and rotor eddy current loss. The air friction loss on the rotor surface refers to the loss caused by the friction between the rotor and the surrounding air when the rotor is running at high speed. It is related to the speed, air flow rate and the roughness of the rotor surface. The eddy current loss of the rotor refers to the eddy current loss generated in the rotor sheath and permanent magnet by the space and time harmonics of the air gap magnetic field. Among the above losses, the basic copper loss of the stator winding can be obtained by the winding current value and the resistance value. Although it is difficult to obtain the high-frequency additional copper loss of the winding accurately through analytical methods, the high-speed electrical circuit coupled transient finite element analysis can

Energies 2021, 14, 3622 13 of 19

The high-frequency additional loss of the winding is related to many factors such as the working frequency of the motor, the size of the winding conductor and the arrangement position in the slot. (2) Rotor loss, which is divided into air friction loss on the rotor surface and rotor eddy current loss. The air friction loss on the rotor surface refers to the loss caused by the friction between the rotor and the surrounding air when the rotor is running at high speed. It is related to the speed, air flow rate and the roughness of the rotor surface. The eddy current loss of the rotor refers to the eddy current loss generated in the rotor sheath and permanent magnet by the space and time harmonics of the air gap magnetic field. Among the above losses, the basic copper loss of the stator winding can be obtained by the winding current value and the resistance value. Although it is difficult to obtain the high-frequency additional copper loss of the winding accurately through analytical methods, the high-speed electrical circuit coupled transient finite element analysis can obtain a more accurate calculation result of the high-frequency loss of the stator winding. To calculate stator iron loss, the current more classic calculation method is to establish a discrete Bertotti’s iron loss model, which means the iron loss is divided into three parts, namely hysteresis loss, classic eddy current loss and abnormal eddy current loss [21]. The accuracy of iron loss calculation depends on two conditions. One is that the loss coefficient of the iron core material should be selected correctly; the other is that the magnetic flux density of each part of the iron core should be calculated correctly. For high-speed motors, due to the relatively high speed of the rotor, the air friction loss on the surface of the rotor is much greater than that of ordinary motors. At the same time, in order to avoid high-frequency electromagnetic waves from causing hysteresis loss and eddy current loss in the permanent magnet, a metal shielding sleeve is usually installed on the surface of the permanent magnet. However, how to calculate the eddy current loss in the sheath still needs to establish a model for analysis.

4.2. High-Frequency Winding Loss The skin effect and proximity effect caused by the will increase the copper loss of the motor winding, especially for a high-speed motor with a relatively high fundamental frequency of the current. The additional copper loss caused by the skin effect and proximity effect will greatly increase. In the stator slots of a high-speed permanent magnet synchronous motor, in addition to the fundamental wave leakage flux, there is also the leakage flux generated by the stator slot and the inverter PWM modulation current harmonics. The frequency of these leakage fluxes is relatively high, which will cause large AC losses in the stator windings. The AC loss of the motor winding is not only related to the diameter of the conductor, but also related to many factors such as the slot size, the location of the conductor and the frequency of the current harmonics. The AC loss of the winding is closely related to the diameter of the conductor. When the frequency and amplitude of the current is constant, the AC loss of the winding has a minimum value as the diameter of the conductor varies. The higher the frequency, the larger the minimum value can achieve, where conductor diameter can also achieve an optimal minimal value. Meanwhile, the magnetic field at the conductor closest to the slot notch directly affects the magnitude of the AC loss of the winding. As the height of the notch increases and the width of the notch decreases, the AC loss of the winding will increase accordingly, and the influence of the notch width is greater than the influence of the notch height. When the windings are placed in an offset slot, the AC loss is obviously greater than the AC loss in the middle and offset slot bottom placement, but it is closer to the AC loss when the winding is placed evenly. The current harmonics caused by inverter PWM modulation also have a great influence on the AC loss of the winding. As the PWM carrier ratio of the inverter increases, the AC loss of the winding decreases. However, the rate of decrease gradually slows down as the carrier ratio increases. High-speed motors will cause high-frequency additional eddy current copper loss in the windings due to the Energies 2021, 14, 3622 14 of 19

skin effect and proximity effect. This part of the loss is defined as eddy current loss, and DC loss is collectively called AC loss. In order to suppress the generation of eddy currents, high-speed permanent magnet synchronous motor windings usually use multiple thin copper wires in parallel. As the energization frequency increases, the penetration depth of the copper wire decreases monotonously, the skin effect becomes more pronounced, and the Joule loss increases. In order to reduce the Joule loss of the current flowing outside the wire, the diameter of the copper wire should be less than twice the penetration depth. However, eddy currents caused by a time-varying external magnetic field still exist in the wire at this time, and the ratio of diameter to penetration depth needs to be further reduced. In this paper, 70 wires with a diameter of 0.64 mm are used in the motor to reduce the eddy current loss and the winding process when winding, and the eddy current loss can be further reduced by placing the wires as close to the bottom of the groove as possible. The input power while charging the energy storage flywheel motor is 30~60 kW, and the copper consumption is 30~90 W. The standby current is smaller than the charging current, and the copper consumption of the energy storage flywheel is relatively large during high-power discharge. The output current of the motor at 30,000 and 15,000 r/min and the discharge power of 300 kW correspond to the copper consumption of 2.1 and 8.6 kW, respectively.

4.3. High-Frequency Core Loss The most classic method to calculate the iron loss of a motor is the ratio loss method. This method scales the iron loss of the stator material under a certain frequency and magnetic density to the working frequency and magnetic density of the motor according to a certain rule and, then, uses empirical coefficients to modify the results. Because of the small amount of data required and the fast calculation speed, it has been widely used in traditional motor design. For general motors, the iron loss can be calculated according to the loss curve and empirical formula of the iron core steel sheet under the excitation of the power frequency sine wave power supply. However, for special motors, especially high- speed permanent magnet motors, the speed is tens of thousands of revolutions per minute, and the power supply frequency can reach thousands of hertz. In such high-frequency, high-speed conditions, if still using the silicon loss curve and the empirical formula of the sinusoidal frequency, iron loss computing power would bring great error. The iron loss error will have a direct impact on the accurate design of high-speed permanent magnet motors, which limits practical applications. Core loss includes eddy current loss and hysteresis loss. Among them, the eddy current loss is closely related to the thickness of the silicon steel sheet used. The penetration depth of the silicon steel sheet is small at high frequencies. The magnetically dense skin effect and eddy current density skin effect of silicon steel sheet is significant, and the Joule loss is large. In order to suppress the generation of eddy currents, the core of high-speed permanent magnet synchronous motors is usually laminated with multiple thin silicon steel sheets. In addition, when the magnetically permeable material is repeatedly magnetized in an alternating magnetic field, the magnetic induction and magnetic field strength inside the material present a hysteresis loop. At this time, energy loss will be caused in the magnetic material, which is called core loss. Silicon steel sheets in a time-varying magnetic field will produce hysteresis losses. The hysteresis loss of the silicon steel sheet is proportional to the alternating frequency of the magnetic field and the area enclosed by the hysteresis loop. The area of the hysteresis loop is approximately proportional to the square of the magnetic induction intensity. For high-speed motors, the alternating frequency of the magnetic field in the stator core is relatively high, resulting in relatively large stator iron loss, which accounts for the main part of the motor loss. Therefore, reducing iron loss is a major measure to improve motor efficiency. As the frequency increases, the ratio of stator eddy current loss to iron loss gradually increases. In summary, we should choose a silicon steel sheet with low core Energies 2021, 14, 3622 15 of 19

loss (core eddy current loss and core hysteresis loss) at high frequencies. For traditional non-oriented electrical steel, the thinnest grade is designed for high frequency applications. In this work, the motor design in this paper adopts 20PNF1500 electrical steel with low core loss under high frequency to design the high-speed motor stator. Figure 15 is the BH curve of 20PNF1500. The core loss data of steel suppliers are almost all sine wave data, which can be characterized by the Steinmetz Equation (3) of hysteresis and eddy current loss [22]:

n 2 2 P = Ch f Bpk + Ce f Bpk (3)

where Bpk is the peak flux density in T; f is the frequency in Hz; Ch is the hysteretic return loss coefficient; Ce is the eddy current loss coefficient. The index n is usually assumed to be Energies 2021, 14, x FOR PEER REVIEW 16 of 21 1.6~1.8, but changes with Bpk. Since n = a + bBpk, wherein a and b are both positive values, n has a certain change. The unit of P is usually W/kg.

2 1.8 1.6 1.4 1.2 1 0.8 0.6

Magnetic Magnetic Induction [Tesla] 0.4 0.2 0 1 10 100 1,000 10,000 100,000 Magnetic Field Intensity [A/m]

FigureFigure 15. 15. BHBH curve curve of of20PNF1500. 20PNF1500.

TheThe core magnetic loss data flux of steel density suppliers in the are motor almost laminations all sine wave may data, be which far from can sinusoidal. be char- acterizedTherefore, by the modifiedSteinmetz Steinmetz Equation Equation(3) of hysteresis (4) is used, and eddy which current has the loss following [22]: form: n 2 2 2 P Ch fa B+ pkbB  C e f B pkdB (3) P = C f B pk + C (4) h pk e dt where Bpk is the peak flux density in T; f is the frequency in Hz; Ch is the hysteretic return loss coefficient;The hysteresis Ce is the loss eddy component current loss is unchanged, coefficient. The but theindex eddy n is currentusually componentassumed to is beproportional 1.6~1.8, but changes to the meanwith B squarepk. Since value n = a + of bBdBpk,/ whereindt in the a and fundamental b are both frequencypositive values, period. n has a certain change. The unit of P is usually W/kg. Eddy current loss coefficient Ce1 can be modified from the sine wave coefficient Ce. If 2 2 2 2 2 B =TheBpk sin(2 magneticπft), then fluxdB density/dt = 2 π infB thepkcos(2 motorπft) and laminations (dB/dt) = may 4π f beB pk farcos from(2π ft sinusoidal.), and mean Therefore, the modified2 2 2Steinmetz2 Equation (4) is used, which has the following form: value (dB/dt) = 2π f Bpk . For the sine wave magnetic flux density, the same result is given as Equation (5): 2 a bBpk dB  P Ch f B pk C Ce e   (4) Ce1 = dt  (5) 2π2 TheUsing hysteresis the above loss component equations, is the unchanged, relationship but betweenthe eddy corecurrent loss component and frequency is pro- of portional20PNF1500 to the can mean be obtained, square value which of is dB depicted/dt in the in Figurefundamental 16. frequency period. Eddy currentEven loss when coefficient the permanent Ce1 can be magnet modified rotor from of a permanent the sine wave magnet coefficient synchronous Ce. If motorB = Bpkrotatessin(2πft freely,), then it dB will/dt cause = 2πfB corepkcos(2 lossπ inft) the and stator (dB/dt core.)2 = 4 Theπ2f2 changeBpk2cos2(2 inπ coreft), and loss mean with speedvalue is (dBshown/dt)2 = in2π Figure2f2Bpk2. 17For, and the thesine value wave of magnetic loss is listed flux in density, Table5. the same result is given as Equation (5):

C e C e1  2 (5) 2 Using the above equations, the relationship between core loss and frequency of 20PNF1500 can be obtained, which is depicted in Figure 16.

Energies 2021, 14, 3622 16 of 19

4.4. Rotor Eddy Current Loss High-speed permanent magnet synchronous motor stator slotting caused by air gap permeability changes, magnetic space harmonics caused by non-sinusoidal windings and current time harmonics generated by PWM power supply will produce large eddy current losses in the rotor. Due to the poor heat dissipation conditions of the rotor, excessive rotor eddy current loss will cause the rotor temperature rise to be too high. Excessive temperature causes the performance of the motor to decrease and even causes the permanent magnets to demagnetize. Therefore, the accurate calculation of rotor eddy current loss is of great significance to the improvement of motor performance and reliability. Usually, there are two calculation methods for permanent magnet synchronous motor rotor eddy current loss: analytical calculation method and finite element method. The analytical method can quickly and intuitively reveal the essence of the problem and can well estimate the eddy current loss of the rotor in the motor design stage. The physical Energies 2021, 14, x FOR PEER REVIEWmodel established by the finite element method is closer to reality than17 theof 21 analytical Energies 2021, 14, x FOR PEER REVIEW 17 of 21 method. The calculation accuracy is higher than the analytical method. Figure 18 shows the finite element simulation results of rotor eddy current loss. 1000 100Hz 1000 200Hz 100Hz 100 400Hz 200Hz 100 1000Hz400Hz 10 2000Hz1000Hz 10 1 2000Hz Loss Loss [W/kg]

1 Loss Loss [W/kg] 0.1

0.010.1 0.01 0.1 1 10 Magnetic Induction [Tesla]

0.01 Figure 16. The relationship between core loss and frequency of 20PNF1500. 0.01 0.1 1 10 Magnetic Induction [Tesla] Even when the permanent magnet rotor of a permanent magnet synchronous motor FigurerotatesFigure 16. freely, 16. TheThe relationshipit relationshipwill cause betweencore between loss corein core the loss lossstator and and core. frequency frequency The change of of 20PNF1500. 20PNF1500. in core loss with speed is shown in Figure 17, and the value of loss is listed in Table 5. Even when the permanent magnet rotor of a permanent magnet synchronous motor 1.8 rotates freely, it will cause core loss in the stator core. The change in core loss with speed is shown1.6 in Figure 17, and the value of loss is listed in Table 5. 1.4 1.8 1.2 1.61.0 1.40.8

Core loss [kW] loss Core 1.20.6 1.00.4 0.80.2

Core loss [kW] loss Core 0.60 0 5 10 15 20 25 30 0.4 Motor Speed [krpm] FigureFigure0.2 17. 17. CoreCore loss loss vs. vs.speed speed change change graph. graph. Table 5.0 Core loss and speed change. krpm0 5 5 1010 15 2020 2525 3030 kW 0.18 0.39 Motor Speed0.63 [krpm] 0.91 1.22 1.57 Figure 17. Core loss vs. speed change graph. 4.4. Rotor Eddy Current Loss TableHigh 5. Core-speed loss permanentand speed change.magnet synchronous motor stator slotting caused by air gap permeability changes, magnetic space harmonics caused by non-sinusoidal windings and currentkrpm time harmonics5 generated10 by PWM power15 supply will20 produce large25 eddy current 30 losseskW in the rotor. 0.18Due to the poor0.39 heat dissipation0.63 conditions0.91 of the rotor, excessive1.22 rotor1.57

4.4. Rotor Eddy Current Loss High-speed permanent magnet synchronous motor stator slotting caused by air gap

permeability changes, magnetic space harmonics caused by non-sinusoidal windings and current time harmonics generated by PWM power supply will produce large eddy current losses in the rotor. Due to the poor heat dissipation conditions of the rotor, excessive rotor

Energies 2021, 14, x FOR PEER REVIEW 18 of 21

eddy current loss will cause the rotor temperature rise to be too high. Excessive tempera- ture causes the performance of the motor to decrease and even causes the permanent mag-

Energies 2021, 14, 3622 nets to demagnetize. Therefore, the accurate calculation of rotor eddy current loss17 is of 19of great significance to the improvement of motor performance and reliability. Usually, there are two calculation methods for permanent magnet synchronous mo- tor rotor eddy current loss: analytical calculation method and finite element method. The Tableanalytical 5. Core method loss and can speed quickly change. and intuitively reveal the essence of the problem and can well estimate the eddy current loss of the rotor in the motor design stage. The physical krpm 5 10 15 20 25 30 model established by the finite element method is closer to reality than the analytical method.kW The calculation 0.18 accuracy 0.39 is higher 0.63 than the analytical 0.91 method. 1.22 Figure 18 1.57 shows the finite element simulation results of rotor eddy current loss.

22.50 Curve Info Solid Loss 20.00 Setup1:Transient 17.50 15.00 ] W [ 12.50 10.00 7.50 SolidLoss 5.00 2.50 0.00 0.00 20.00 40.00 60.00 80.00 100.00 Time [ms] Figure 18. Rotor eddy current loss.

4.5. Other Losses Other losses mainly include airair frictionfriction losseslosses andand straystray losses.losses. Air frictionfriction lossloss isis mainly causedcaused byby thethe mutual mutual friction friction between between the the rotor rotor and and the the surrounding surrounding air. air. Air Air friction fric- losstion isloss related is related to the to rotorthe rotor surface surface structure, structure, surface surface roughness, roughness, motor motor speed, speed, air density,air den- airsity, velocity, air velocity, air radial air radial pressure pressure and other and factors.other factors. Without Without the derivation the derivation process, process, it can be it expressed as [23]: can be expressed as [23]: 3 4 Pair = k Cf π ρ ω r l (6) 3 4 Pair kC f   r l (6) in which k is the surface roughness coefficient of the rotor (smooth rotor surface k = 1); ρinis which the air k is density; the surfaceCf is theroughness coefficient coefficient of air friction; of the rotorω, r and(smoothl are rotor the angular surface velocity,k = 1); ρ radiusis the air and density; axial length Cf is ofthe the coefficient rotor, respectively. of air friction; Using ω Equation, r and l (6), are the the steady-state angular velocity, power Energies 2021, 14, x FOR PEER REVIEW 19 of 21 consumptionradius and axial curve length under of air the and rotor, rough respectively. vacuum can Using be calculated, Equation which (6), the is illustrated steady-state as thepower green consumption and blue line curve in Figure under 19 air, respectively.and rough vacuum can be calculated, which is illus- trated as the green and blue line in Figure 19, respectively. 30

25 ) W

( 20 Loss at 100Pa Loss at air pressure 15 state Loss Loss state - 10

Steady 5

0 0 5 10 15 20 25 30 Flywheel Speed (krpm)

FigureFigure 19. 19. SteadySteady-state-state power power consumption consumption curve curve under under air air and and rough rough vacuum. vacuum.

The most effective way to reduce air friction loss is to increase the degree of vacuum in the flywheel housing. As shown in Figure 19, it is found that as the rotation speed in- creases, increasing the vacuum degree effectively reduces the steady-state power con- sumption of the motor. Generally, the method to reduce friction loss is to use high vacuum sealing means to prevent air leakage, control the distance between the outer circle of the flywheel rotor and the inner wall of the cavity to improve the pressure in the cavity and minimize the surface roughness as much as possible to make the rotor surface smooth. The research results show that through the analysis of the , me- chanical and loss of the motor, the output power of the motor reaches more than 300 kW, and the specific power reaches 5000 W/kg. Additionally, through a series of measures to reduce the core loss, the simulation results show that the core loss at the rated speed is only 1.57 kW. The current of the motor running at no load is very small, and the resistance is not large. Therefore, copper consumption only accounts for a small percentage. There- fore, the no-load loss of the motor does not exceed 2 kW, which can satisfy the long-term stable operation of the flywheel.

5. Conclusions This paper takes the low-loss, high-power, high-speed permanent magnet synchro- nous motor used in the magnetically levitation flywheel energy storage system as the re- search object and conducts research on the electromagnetic design, mechanical design, loss analysis and other key technologies of high-speed permanent magnet synchronous motor. The winding loss, core loss, rotor eddy current loss and mechanical loss of the high-speed permanent magnet synchronous motor are analyzed and optimized. By opti- mizing the design of the windings and placing the wires as close to the bottom of the slot as possible, the winding loss caused by the skin effect and proximity effect of the high- speed motor in the windings is reduced. The paper analyzes the influencing factors and calculation methods of core loss and reduces core loss by adopting Pohang Steel’s 20PNF1500 with good core loss performance under high frequency and multi-layer thin silicon steel sheet lamination. This paper analyzes the eddy current loss of the permanent magnets of the rotor and verifies the feasibility of designing the whole permanent magnet excitation for high-speed operation. The use of magnetic bearing technology almost elim- inates mechanical friction loss. The main factor of mechanical loss during high-speed op- eration—the influencing factor of air friction loss—is analyzed, and the loss is limited by increasing the vacuum degree in the flywheel housing. Finally, through the above series of analysis and design, the loss of the high-speed permanent magnet synchronous motor was reduced, and the loss reached the expected goal.

Energies 2021, 14, 3622 18 of 19

The most effective way to reduce air friction loss is to increase the degree of vacuum in the flywheel housing. As shown in Figure 19, it is found that as the rotation speed increases, increasing the vacuum degree effectively reduces the steady-state power consumption of the motor. Generally, the method to reduce friction loss is to use high vacuum sealing means to prevent air leakage, control the distance between the outer circle of the flywheel rotor and the inner wall of the cavity to improve the pressure in the cavity and minimize the surface roughness as much as possible to make the rotor surface smooth. The research results show that through the analysis of the electromagnetism, me- chanical and loss of the motor, the output power of the motor reaches more than 300 kW, and the specific power reaches 5000 W/kg. Additionally, through a series of measures to reduce the core loss, the simulation results show that the core loss at the rated speed is only 1.57 kW. The current of the motor running at no load is very small, and the resistance is not large. Therefore, copper consumption only accounts for a small percentage. Therefore, the no-load loss of the motor does not exceed 2 kW, which can satisfy the long-term stable operation of the flywheel.

5. Conclusions This paper takes the low-loss, high-power, high-speed permanent magnet synchronous motor used in the magnetically levitation flywheel energy storage system as the research object and conducts research on the electromagnetic design, mechanical design, loss analy- sis and other key technologies of high-speed permanent magnet synchronous motor. The winding loss, core loss, rotor eddy current loss and mechanical loss of the high-speed per- manent magnet synchronous motor are analyzed and optimized. By optimizing the design of the windings and placing the wires as close to the bottom of the slot as possible, the winding loss caused by the skin effect and proximity effect of the high-speed motor in the windings is reduced. The paper analyzes the influencing factors and calculation methods of core loss and reduces core loss by adopting Pohang Steel’s 20PNF1500 with good core loss performance under high frequency and multi-layer thin silicon steel sheet lamination. This paper analyzes the eddy current loss of the permanent magnets of the rotor and verifies the feasibility of designing the whole permanent magnet excitation for high-speed operation. The use of magnetic bearing technology almost eliminates mechanical friction loss. The main factor of mechanical loss during high-speed operation—the influencing factor of air friction loss—is analyzed, and the loss is limited by increasing the vacuum degree in the flywheel housing. Finally, through the above series of analysis and design, the loss of the high-speed permanent magnet synchronous motor was reduced, and the loss reached the expected goal.

Author Contributions: Conceptualization, W.J.; methodology, F.N.; software, D.G.; validation, W.J.; formal analysis, F.N.; investigation, Q.L.; resources, D.L.; data curation, Q.L.; writing—original draft, W.J.; writing—review and editing, F.N.; visualization, D.G.; supervision, S.L.; project administra- tion, D.G.; funding acquisition, F.N. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundations of China under Grant 51907143, 52072269. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. Energies 2021, 14, 3622 19 of 19

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