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Wound rotor synchronous machines are widely used because of their advantages, such as simple control, cost efficiency, and stable operation [1]. Because of these advantages, the wound rotor synchronous generator (WRSG) is used in large factories, aircraft, ships, and hydroelectric power generation that require a large power supply [2]. The WRSG does not have a rare earth magnet, and it forms a magnetic field through the rotor winding, as shown in Fig. 1(a). A magnetic field is formed by applying current to the rotor windings through an exciter, and the magnetic flux density can be controlled using the exciter to increase the power density. The core of many electrical machines is made of electrical steel with nonlinear characteristics, and the magnetic flux density must be adjusted to a level where the core is unsaturated to satisfy the user’s desired output power, efficiency, and voltage. Therefore, it is necessary to evaluate the electromagnetic characteristics through electromagnetic analysis during the initial design. Finite element analysis (FEA) software is commercially available because it can obtain accurate analysis results that reflect nonlinearity. However, FEA consumes significant analysis time in the initial design, in which the design parameters change frequently [3].&lt;br/&gt;Therefore, in this study, we propose a nonlinear magnetic equivalent circuit (MEC) to predict the electromagnetic and power generation characteristics of the WRSG. The magnetic equivalent area was divided according to the magnetic path of the WRSM (Fig. 1(b)). The paths through which the magnetic flux passes are divided into stator, rotor, air-gap, and interpolar regions. The magnetic flux inside the circuit could be calculated using the magnetomotive force(MMF) and reluctance, and the flux density in air gap could be calculated using the magnetic flux. Fig. 2(a) shows a comparison of the air gap flux density derived through the MEC and FEA when a field current is applied. The air flux density derived for the MEC represented the flux density waveform when the rotor position rotated, which could be used to derive the stator flux linkage waveform according to the rotor position. The derived flux linkage induced a back electromotive force (EMF) at no load (Fig. 2(b)). In the initial position, the rotor was positioned such that the flux linkage to the windings of one phase was maximized, and the back EMF through the flux that varied according to the rotation of one slot pitch was derived. The back EMF was influenced by the MMF of the rotor winding, and beyond the linearly increasing region, it became saturated because of the nonlinearity of the core material. The back EMF derived from the nonlinear MEC increased linearly and then nonlinearly, owing to saturation beyond a certain field current (Fig. 2(c)). The back EMF obtained using the nonlinear MEC was compared with those obtained through FEA and experimental measurements; the comparison validates the nonlinear MEC proposed in this study. It is necessary to determine the values of the back EMF, inductance, and phase resistance, which are equivalent circuit parameters, to predict the power generation characteristics of a WRSG. A MEC based on the rotor position must be constructed to reflect the inductance that varies with the rotor position, owing to the salient structure of the WRSG. Fig. 2(d) shows the prediction results of power generation characteristics using the inductance derived through the MEC, back EMF, and phase resistance. The FEA results indicated the power generation characteristics in the low-voltage regulation rate region, and the MEC results were in good agreement with the FEA results. Even when the rotational speed of the WRSG changed, the MEC results were in good agreement with the FEA results. By predicting power generation characteristics, the speed and power required by the designer can be predicted, which is useful in the initial design. The nonlinear MEC and analysis results of the WRSG will be presented in further detail in the main paper.

**References:**

[1] S. Nuzzo, M. Degano, M. Galea, et al, &lt;i&gt;IEEE Trans. Ind. Electron&lt;/i&gt;., vol. 64, no. 3, pp. 1958–1970, Mar. 2017.&lt;br/&gt;[2] A. Griffo, D. Drury, T. Sawata, et al, IEEE Trans. Ind. Electron, vol. 59, no. 9, pp. 3579–3587, Sep. 2012.&lt;br/&gt;[3] H.W. derbas, J.M. Williams, A.C. Koenig, et al, &lt;i&gt;IEEE Trans. Energy Convers., &lt;/i&gt;vol. 24, no. 2, pp. 388–396, Jun. 2009.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/30110081fcfd5756909893a64d2ecd83.jpg)
Fig 1. (a) WRSG analysis model and rotor core experimental model; (b) Construction of nonlinear MEC

![](https://assets.underline.io/uploads/markdown_image/1/image/0abfb2acf0d58abdf081b148aaeb8928.jpg)
Fig 2. Comparison of electromagnetic characteristics obtained using the FEA, MEC, and experimental methods: (a) Comparison of air-gap flux density obtained using FEA and MEC methods; (b) Waveform of back EMF at rated speed of 900 rpm; (c) Variation of back EMF with field current; (d) Power-voltage curve

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 Prediction of power generation performance of wound rotor synchronous generator using nonlinear magnetic equivalent circuit method

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Wound rotor synchronous machines are widely used because of their advantages, such as simple control, cost efficiency, and stable operation [1]. Because of these advantages, the wound rotor synchronous generator (WRSG) is used in large factories, aircraft, ships, and hydroelectric power generation that require a large power supply [2]. The WRSG does not have a rare earth magnet, and it forms a magnetic field through the rotor winding, as shown in Fig. 1(a). A magnetic field is formed by applying current to the rotor windings through an exciter, and the magnetic flux density can be controlled using the exciter to increase the power density. The core of many electrical machines is made of electrical steel with nonlinear characteristics, and the magnetic flux density must be adjusted to a level where the core is unsaturated to satisfy the user’s desired output power, efficiency, and voltage. Therefore, it is necessary to evaluate the electromagnetic characteristics through electromagnetic analysis during the initial design. Finite element analysis (FEA) software is commercially available because it can obtain accurate analysis results that reflect nonlinearity. However, FEA consumes significant analysis time in the initial design, in which the design parameters change frequently [3]. Therefore, in this study, we propose a nonlinear magnetic equivalent circuit (MEC) to predict the electromagnetic and power generation characteristics of the WRSG. The magnetic equivalent area was divided according to the magnetic path of the WRSM (Fig. 1(b)). The paths through which the magnetic flux passes are divided into stator, rotor, air-gap, and interpolar regions. The magnetic flux inside the circuit could be calculated using the magnetomotive force(MMF) and reluctance, and the flux density in air gap could be calculated using the magnetic flux. Fig. 2(a) shows a comparison of the air gap flux density derived through the MEC and FEA when a field current is applied. The air flux density derived for the MEC represented the flux density waveform when the rotor position rotated, which could be used to derive the stator flux linkage waveform according to the rotor position. The derived flux linkage induced a back electromotive force (EMF) at no load (Fig. 2(b)). In the initial position, the rotor was positioned such that the flux linkage to the windings of one phase was maximized, and the back EMF through the flux that varied according to the rotation of one slot pitch was derived. The back EMF was influenced by the MMF of the rotor winding, and beyond the linearly increasing region, it became saturated because of the nonlinearity of the core material. The back EMF derived from the nonlinear MEC increased linearly and then nonlinearly, owing to saturation beyond a certain field current (Fig. 2(c)). The back EMF obtained using the nonlinear MEC was compared with those obtained through FEA and experimental measurements; the comparison validates the nonlinear MEC proposed in this study. It is necessary to determine the values of the back EMF, inductance, and phase resistance, which are equivalent circuit parameters, to predict the power generation characteristics of a WRSG. A MEC based on the rotor position must be constructed to reflect the inductance that varies with the rotor position, owing to the salient structure of the WRSG. Fig. 2(d) shows the prediction results of power generation characteristics using the inductance derived through the MEC, back EMF, and phase resistance. The FEA results indicated the power generation characteristics in the low-voltage regulation rate region, and the MEC results were in good agreement with the FEA results. Even when the rotational speed of the WRSG changed, the MEC results were in good agreement with the FEA results. By predicting power generation characteristics, the speed and power required by the designer can be predicted, which is useful in the initial design. The nonlinear MEC and analysis results of the WRSG will be presented in further detail in the main paper.

**References:**

[1] S. Nuzzo, M. Degano, M. Galea, et al, IEEE Trans. Ind. Electron., vol. 64, no. 3, pp. 1958–1970, Mar. 2017. [2] A. Griffo, D. Drury, T. Sawata, et al, IEEE Trans. Ind. Electron, vol. 59, no. 9, pp. 3579–3587, Sep. 2012. [3] H.W. derbas, J.M. Williams, A.C. Koenig, et al, IEEE Trans. Energy Convers., vol. 24, no. 2, pp. 388–396, Jun. 2009.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/30110081fcfd5756909893a64d2ecd83.jpg)
Fig 1. (a) WRSG analysis model and rotor core experimental model; (b) Construction of nonlinear MEC

![](https://assets.underline.io/uploads/markdown_image/1/image/0abfb2acf0d58abdf081b148aaeb8928.jpg)
Fig 2. Comparison of electromagnetic characteristics obtained using the FEA, MEC, and experimental methods: (a) Comparison of air-gap flux density obtained using FEA and MEC methods; (b) Waveform of back EMF at rated speed of 900 rpm; (c) Variation of back EMF with field current; (d) Power-voltage curve

poster

1. Introduction The demand for low-speed and high-torque electrical machines is increasing in different industrial applications. Vernier permanent-magnet machines (VPM) and Pseudo-direct-drive machines (PDD) are especially suitable for this situation due to their magnetic gearing effect [1,2]. Generally, the power factor of the conventional VPM can be as low as 0.66 [3]. PDDs have the capability of high power factor as well as high torque density [2]. To output higher torque density compared with PDDs, a novel Vernier Pseudo-direct-drive machine (VPDD) is proposed in [4] as Fig. 1 (a) shows. In this paper, the subdomain analytical model is used to analyze and preoptimize a VPDD. After the preoptimization, a finite element model (FEM) is also used to optimize the slot opening and check the demagnetization. However, in this machine, the winding has not been optimized to reduce the size of end-winding, and as a result, the real torque density taking the end-winding into account is much lower. Our research focuses on further improving the torque density of the VPDD considering a structure that reduces the size of end-winding. A concentrated winding split-teeth VPDD topology (ST-VPDD), shown in Fig. 1 (b), is hence proposed. 2. Modeling and optimization The ST-VPDD can be regarded as a combination of a magnetic gear and a VPM. For the part that functions as a magnetic gear [4], the speed ratio can be expressed as Gtr=Ωt/Ωr=pr/pt=-Tr/Tt, where Ωt, Ωr are the rotational angular speed of the transmitter and of the low-speed (LS) rotor; pt, pr are the pole-pairs of permanent-magnets (PM) of the transmitter and of the LS rotor; Tt, Tr are the torque of the transmitter and of the LS rotor. The rotating magnetic field created by the armature winding drives the transmitter. The LS rotor will be driven by both the transmitter and by the field created by the armature winding. If the transmitter is removed, the ST-VPDD can be regarded as a VPM. According to [5], if Pf=nZ=pr±ps is satisfied, the rotating field of armature winding can drive the LS rotor. n is the number of split teeth per tooth, Z is the number of slots and ps is the pole-pairs of armature winding. The gear ratio can be expressed as Gsr=Ωs/Ωr=pr/(nZ-pr)=pr/ps, where Ωs is the rotational angular speed of the field created by the winding. We keep ps=pt so that Gsr=Gtr. Therefore, the part of the magnetic gear and the VPM will drive the low-speed rotor together at the same speed. The ST-VPDD is analyzed through a FEM. Its ferromagnetic material is made of M-45 steel. Fig. 2 (b) shows the proposed concentrated winding model. For comparison, the distributed winding model of the prototype VPDD is put in Fig. 2 (a). In the figure, lw is the length of the half-width of a slot, and ls depends on the winding material. According to the winding model, a mathematical model is built to calculate the torque density taking end-winding into account. The torque density of the ST-VPDD is optimized. The variable parameters are: 1. r1 is the radius of the transmitter iron; 2. hmt is the thickness of the transmitter PM; 3. hmr is the thickness of the rotor PM; 4. ls is the length of the split teeth; 5. c1=α1/α2; 6. c2=lt/ls; 7. c3=β1/β2. Once the optimization is done, we do the demagnetization check on the optimized ST-VPDD. 3. Results The following parameters of the ST-VPDD are assumed to be similar to the parameters of the VPDD [4]: Z=9, n=5, pt=ps=3 and pr=42, and its out radius ro is 90 mm and active length la is 75 mm. The optimized ST-VPDD can output 172.1 Nm of torque in theory. Without taking the end-winding into account, it provides 90.2 Nm/L of torque density, which is slightly lower than the torque density of 91.8 Nm/L of the VPDD in [4]. From the winding model of the VPDD and of the ST-VPDD, we get that the lengths of end-winding of VPDD and ST-VPDD are 96 mm and 49.6 mm, respectively. So, taking the end-winding into account, the torque density of VPDD and ST-VPDD are 40.3 Nm/L and 54.3 Nm/L. There is a 34.7% improvement in the torque density. The PM used for this design is VACODYM AP 776 [6]. When the temperature is 60 Celsius degree, its remanent flux density is 1.25 T and the demagnetization field is 1300 kA/m. No demagnetization occurs. 4. Conclusions With concentrated winding, the optimized ST-VPDD topology improves the torque density capability compared with the VPDD. And the concentrated winding is less complicated, which simplifies manufacture and hence decrease its cost. The split tooth allows more combinations of poles and slots, so the structure can be further optimized. 5. Acknowledgment This work was supported by the National Natural Science Foundation of China under Grant 51851110761. Corresponding author: P.-D. Pfister (e-mail: pierredaniel.pfister.public@gmail.com).

**References:**

 [1] A. Toba and T. A. Lipo, "Generic torque-maximizing design methodology of surface permanent-magnet vernier machine," in IEEE Transactions on Industry Applications, vol. 36, no. 6, pp. 1539-1546, Nov.-Dec. 2000, doi: 10.1109/28.887204. [2] K. Atallah, J. Rens, S. Mezani and D. Howe, "A Novel “Pseudo” Direct-Drive Brushless Permanent Magnet Machine," in IEEE Transactions on Magnetics, vol. 44, no. 11, pp. 4349-4352, Nov. 2008, doi: 10.1109/TMAG.2008.2001509. [3] D. Li, R. Qu and T. A. Lipo, "High-Power-Factor Vernier Permanent-Magnet Machines," in IEEE Transactions on Industry Applications, vol. 50, no. 6, pp. 3664-3674, Nov.-Dec. 2014, doi: 10.1109/TIA.2014.2315443. [4] X. Yin, Y. Fang, X. Huang and P. Pfister, "Analytical Modeling of a Novel Vernier Pseudo-Direct-Drive Permanent-Magnet Machine," in IEEE Transactions on Magnetics, vol. 53, no. 6, pp. 1-4, June 2017, Art no. 7207404, doi: 10.1109/TMAG.2017.2660241. [5] D. Li, T. Zou, R. Qu and D. Jiang, "Analysis of Fractional-Slot Concentrated Winding PM Vernier Machines With Regular Open-Slot Stators," in IEEE Transactions on Industry Applications, vol. 54, no. 2, pp. 1320-1330, March-April 2018, doi: 10.1109/TIA.2017.2778686. [6] VACUUMSCHMELZE. Rare Earth Permanent Magnets: VACODYM VACOMAX. Accessed: January 05, 2021. [Online]. Available: https://vacuumschmelze.de/Assets-Web/VACODYM-VACOMAX-PD002_2015_en.pdf.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bf5b96ee97deb34ae19d54612847229b.jpg)
Figure 1: (a) The structure of the VPDD [4]. (b) The structure of the proposed ST-VPDD.

![](https://assets.underline.io/uploads/markdown_image/1/image/14bd1a0ca6910cd527b238352b2c7e70.jpg)
Figure 2: (a) The distributed winding model of the prototype VPDD. (b) The concentrated winding model of the proposed ST-VPDD.

 A novel split-teeth Vernier pseudo-direct-drive permanent-magnet machine with concentrated winding

I. Introduction Vernier permanent-magnet (VPM) machine takes advantage of high torque density and low rotational speed, which makes it a promising candidate in direct-drive applications. The industrial application prospect makes it a research interest in recent years. A fault-tolerant structure is proposed in [1], which can decouple the interaction between different phases and hence improve the fault-tolerant ability. However, as the fractional slot concentrated winding (FSCW) configuration is adopted, the torque capability is consequently reduced [2]. This paper proposes a split-pole fault-tolerant (SPFT) VPM machine as is shown in Fig. 1(a). The consequent-pole PM structure is adopted to improve the torque density with less magnet usage [3]. Meanwhile the stator affiliated PMs are employed to further enhance the torque capability. Last but not least, the inner stator is composed of alternately arranged modular teeth and fault-tolerant teeth. The modular tooth consists of root part and split-pole structure, and the split-pole structure plays the role of flux modulation poles (FMPs). The concentrated windings are wound around the modular teeth, so the fault-tolerant teeth can segregate the adjoining phases. The stator only has one modular tooth for each phase, and the winding pole pair is set to one. Thus, the coils can link nearly 120 mechanical degree of the flux linkage even if the FSCW configuration is adopted. In this way the torque capability can be maximized. In this paper the operation principle and working mechanism of proposed machine are described. The influences of the key parameters on electromagnetic performances are investigated by finite element analysis (FEA) method. A comparison between conventional FTVPM machine and proposed machine is discussed. Besides, the analytical model of proposed machine is illustrated and analyzed. The prototype is manufactured and tested which verifies the feasibility of calculation results. The analytical model and experiment results are not shown in the digest for space limitation, and will be added in the full paper. II. Parameter Optimization and Electromagnetic Performance Comparison The influences of the key parameters on electromagnetic performances are investigated to optimize the proposed structure. As can be seen in Fig. 1(b), the optimal stator modular tooth width is 18mm. It is because the proposed structure only has 3 stator teeth for windings. When the d-axis and the modular tooth coincide, all the flux linkage will pass through one of the modular teeth, so that the saturation problem is heavier. Therefore the modular teeth have to be wide enough. When the width is larger than 18mm the area for armature winding is reduced, thus the torque decreases instead. When the fault-tolerant tooth width increases, there is a small drop at first as is shown in Fig. 1(c). The reason is when fault-tolerant teeth is very thin, the split-pole occupies larger air-gap angle, so there will be more flux linkage passes through the coils. The stator and rotor PM thickness are also confined by the winding area since the outer diameter is fixed. The rotor yoke thickness has to be large enough to prevent the saturation problem, which is concluded in Fig. 1(e). It should be noted that when the rotor yoke thickness is large, the air-gap volume which stores the magnetic field energy is reduced as well as the winding area. The comparison between proposed machine and conventional FTVPM machine is discussed. The same main parameters are shown in Fig. 2(a). The proposed machine is 18/17-pole with one-pole-pair winding and the conventional topology is 18/13-pole with five-pole-pair winding. The no-load flux density at the air-gap is investigated to find out the harmonic characteristic of proposed machine. As can be seen in Fig. 2(c), the 5th and 13th harmonic of FTVPM are both larger that the fundamental and 17th harmonic of proposed machine. But as a VPM machine, the rotor with 17 pole-pair has larger pole ratio, which means the modulated magnetic field rotates faster. Meanwhile the proposed topology makes phase coil link more flux linkage, so the open circuit back-EMF is 2.45 times that of the conventional one. Moreover, according to Fig. 2(e), the proposed structure can provide larger average torque while maintain a low torque ripple. It is because the magnitude of torque ripple is inversely proportional to the lowest common multiple (LCM) of the number of stator and rotor pole pairs. III. Conclusion The split-pole fault-tolerant VPM machine is proposed in this paper. The topology and operation principle are presented. The FEA results show that the proposed structure takes advantage of large torque, low torque ripple, short end turn length and fault-tolerant capability. Compared with conventional FTVPM machine, the proposed machine can produce 145% higher output torque under the same copper loss. The analytical analysis and experiment results will be added in the full paper.

**References:**

[1] G. Liu, J. Yang and W. Zhao, IEEE Trans. on Magn., vol. 48, no. 11 (2012) [2] L. Xu, G. Liu and W. Zhao, IEEE Trans. on Energy Conversion, vol. 30, no. 4 (2015) [3] D. Li, R. Qu and J. Li, 2014 IEEE Energy Conversion Congr. and Expo., (2014)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e430a86c7bc6ac3985a6b6ff99d41d37.jpg)
Fig. 1. (a) Topologies of both machines. (b) Influence of modular tooth width on torque. (c) Influence of fault-tolerant tooth width on torque. (d) Influence of stator and rotor PM thickness on torque. (e) Influence of rotor yoke thickness on torque. (f) Influence of stator and rotor PM ratio on torque.

![](https://assets.underline.io/uploads/markdown_image/1/image/a159a16b049e0040224d3c011ce46c4a.jpg)
Fig. 2. (a) Main parameters of both topologies. (b) Flux density waveforms at the air-gap. (c) Flux density spectra at the air-gap. (d) Open-circuit back-EMF. (e) Torque performances

 Design and Analysis of Novel Split-Pole Fault-Tolerant Vernier Permanent Magneic Machine

—A novel dual permanent magnet (PM) dual three phase vernier machine is proposed for electric vehicles in this paper. Compared with conventional dual PM vernier machines, a dual three-phase winding connection is adopted to reduce sub-harmonics and improve working harmonics at the same time. The dual three-phase windings supplied by two separate converters can improve the reliability of the machine driving systems, which is an important issue in electric vehicles. Therefore, this proposed machine exhibits higher torque density, higher reliability, lower force ripple, and lower unbalanced force. The simulation result shows that with the proposed dual three phase winding, the torque is improved by 3.9% while the torque ripple and unbalanced force are reduced about 50% and 72.5%, respectively. Index Terms—Concentrate winding, permanent magnet, torque density, vernier machine. Introduction With the emergence and widespread use of automobiles, people's lives have been highly improved. However, while the cars bring convenience in our lives, they also cause excessive consumption of non-renewable energies and the emission of greenhouse gasses at the same time, which have aggravated environmental pollution. To solve these problems, electric vehicles are a potential solution. Therefore, the motors, which are the key components in the electric vehicles' driving system, have attracted a lot of attention in recent years. The induction motor and permanent magnet (PM) motor are the two main types of motors used in electric vehicles. Compared to the induction motor, the PM motor has higher power density, lower copper loss and smaller volume; hence it has become the mainstream in academia and commercial applications. However, there are only limited pole and slot combinations which have been investigated due to the high iron loss and unbalanced force under high-speed operation in electric vehicles. In this paper a novel dual three phase dual PM vernier machine with high torque density and low unbalanced force is proposed. Its structure will be presented first. Then the operation principle is illustrated, and the performance of the motor is shown. Structure, Operation Principle and Performance The structure of the proposed motor is shown in Fig. 1. The outer diameter is 220mm and the rated speed is 3980rpm. It has 12 slots and 10 poles; PMs are employed on both the rotor and stator. The windings on the stator are fractional slot concentrated windings (FSCWs). All the armature windings can be divided into two sets of 3 phases windings which are supplied by two separate converters. The two converters supply phase A1, B1 and C1, and phase A2, B2 and C2, which has π/6 shift. This arrangement can improve the fault tolerance capability since the motor can operate under one set of winding when a failure occurs in the other one. Referring to [1], the MMF of armature windings adopting dual three structure can be given as Ft(t,θ)=∑k=1,-5,7...∝(12NI/kπ)sin(kπ/12)sin((k-1)π/12)sin(kθ-ωt-(k-1)π/12) According to the equation, it is obvious that by adopting dual three structure, the subharmonic can be eliminated, and the 5th, 7th, 17th and 19th harmonics can be increased. Considering the modulation effect, the working harmonics of the proposed motor can be obtained which are 5th, 7th and 17th. Therefore, the output torque of the proposed motor is increased, and the torque ripple reduced. The analytical result is verified by 2-D FE analysis. Fig. 2 shows the torque comparison between the conventional dual PM vernier machine and the proposed one. It can be seen that the output torque increases 3.9% from 148Nm to 154Nm and the torque ripple reduces about 50% from 2.75% to 1.4%. The proposed machine not only improves the torque performances, but also the core loss and unbalanced force. After applying this structure, the unbalanced force is reduced a lot, which is from 1158.2N to 318.54N. The efficiency and torque density are also improved a little bit from 96.63% to 96.77% and 3.54*10-5 Nm/mm3 to 3.68*10-5 Nm/mm3. Conclusion A novel dual three phase dual PM machine is proposed in this paper. The structure, operation principle and the performance are analyzed. The simulation result shows that adopting this novel structure can reduce the subharmonics and improve the working harmonics. It increases the output torque, reduces the torque ripple and unbalanced force. It is a very effective way to improve the performance and more detailed characteristics will be reported in full paper.

**References:**

[1] A. S. Abdel-Khalik, S. Ahmed and A. M. Massoud, IEEE Trans. Magn., Vol. 51, p. 1-10 (2015). [2] Q. Wang, S. Niu and L. Yang, IEEE Trans. Ind. Electron., Vol. 64, p. 9924-9933 (2017).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bf5f772e696b4639e00ea3daa4addbc4.jpg)
Fig.1. Structure of the proposed motor.

![](https://assets.underline.io/uploads/markdown_image/1/image/85e8edc3a6931d4de9baf4ac75941535.jpg)
Fig. 2. Output torque comparison.

 Analysis of a Novel Dual-PM Vernier Machine with High Torque Density and Low Torque Ripple and Unbalanced Force

—This paper proposes and compares two different 12 slots DC-biased dual-PM vernier machines. Both machines have tangentially magnetized magnets located in the slot openings, and an integrated winding is adopted to produce the armature field and excitation field at the same time. The slot-opening PMs not only improve the machine torque performance but also relieve the saturation caused by the DC-biased. The results show that both structures exhibit high torque density and slot-opening PMs in machine 1 contribute more to torque improvement while PMs in machine 2 are more for dc-saturation relief. Index Terms—DC-bias, dual PM, finite-element method, vernier machine. Introduction With the emergence of the magnetic gear and the proposal of a unified theory of flux modulation, vernier machine has attracted people's attention. Due to its high torque density and wide operation range, vernier machine becomes the potential candidate for many applications such as electric vehicles and wind power generation. To further increase the torque density under the constrain dimension, dual-PM vernier machine is proposed, and several structures have been investigated. In order to achieve a more compact structure and wider flux weakening range, the integrated winding with DC-biased structures have also been studied. In this paper, two novel DC-biased dual-PM vernier machines with slot-opening PM are proposed and investigated. To showcase the effectiveness of the slot-opening PMs, the conventional DC-biased dual PM vernier machines will be presented first. Then the operation principle of proposed novel machines will be presented, and the comparison between different structures will be conducted. Structure, Operation Principle and Performance The structure of the proposed motors and their conventional structures are shown in Fig.1. To make a relatively fair comparison, the main dimensions of all the structures are the same. The outer diameter is 90mm, the air gap is 0.5mm, and the stack length is 80mm. As shown in Fig. 1, PMs are located on both the rotor and stator. The PMs in the rotor and stator tooth are both radially magnetized, while the slot-opening PMs are tangentially magnetized. The main difference between the two novel machines is the PMs in the stator teeth region, which is directly attached to the teeth surface in machine 1 while embedded in the teeth in machine 2. The phase windings are arranged as follows. Ia1=Iaccos(2πft)+Idc Ib1=Iaccos(2πft-2π/3)+Idc Ic1=Iaccos(2πft+2π/3)+Idc Ia2=Iaccos(2πft)-Idc Ib2=Iaccos(2πft-2π/3)-Idc Ic2=Iaccos(2πft+2π/3)-Idc The machines can achieve different operation mode by simply adjust the DC-bias. The magnetic field can be strengthened by applying the positive DC biased, while negative DC biased can weaken the magnetic field. The 2-D FE analysis is conducted to analyze the machine performances. Fig. 2 shows the torque comparison between the conventional and novel structures. It is obvious that both conventional and novel structures of machine 1 have better torque performances than machine 2. They have higher output torque and lower torque ripple. The output torque of conventional and novel machine 1 are11.44 Nm and 13.25Nm while machine 2 are 10.75Nm and 11.77Nm, respectively. The output torque of novel machine 1 improves 12.57% compares to novel machine 2. It also can be found that structures of machine 2 have better flux regulated capability. By injecting different direction of DC biased, the output torque can increase 6.68% and decrease 14.6% in conventional machine 1 while output increases 10.98% and decreases 22.98% in conventional machine 2. It also can be seen that the slot-opening PMs are more effectively in torque improvement in machine 1 and saturation relief in machine 2. The output torque increases by 15.82% after adopting the slot-opening PMs in machine 1, while machine 2 only increases by 9.49%. Furthermore, the torque improvement percentage with DC biased have a different degree of increase. After applying the slot-opening PMs, the percentage increases from 6.68% to 9.81% in machine 1 while 10.98% to 24.47% in machine 2. Conclusion Two novel DC-biased dual PM machine with slot-opening PM are proposed and compared in this paper. The structure, operation principle and performance are analyzed. The simulation result shows that the machine 1 has better torque performance while machine 2 has better flux regulation capability. More detailed characteristics will be reported in the full paper.

**References:**

[1] X. Zhao, S. Niu and W. Fu, IEEE Trans. Magn., vol. 55, p. 1-5 (2019) [2] Q. Wang, S. Niu and X. Luo, IEEE Trans. Ind. Electron., vol. 64, p. 6908-6919 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b81421f215e772db5c7a5ab9cfd6e63a.jpg)
Fig. 1. Structure of the proposed motors. (a) Conventional machine1. (b) Novel machine1. (c) Conventional machine2. (d) Novel machine2

![](https://assets.underline.io/uploads/markdown_image/1/image/cecc19a943460a3549e06acd090e80d2.jpg)
Fig. 2. Output torque comparison. (a) Machine 1 (b) Machine 2

 Analysis of 12 Slots Novel DC-Biased Dual-PM Vernier Machines with Slot-Opening PMs

1. Introduction Vernier permanent magnet machines(VPMM) have a simple structure and high torque density due to the so-called magnetic-gear effect and are very suitable for direct drive applications, such as wind power turbines and electric vehicles [1]. In addition, the VPMM has low pulsing torque due to its more sinusoidal back-EMF, compared with traditional designs of PM machines [2]. However, the power factor of the VPMM is relatively low (sometimes even below 0.3), which requires a converter with a larger capacity for the fixed output power [1]. Many researchers have been carried out to address this problem and some improvements in structure have also been studied in recent decades. Vernier structure was proposed in the early 19th century and then applied to stepping motors [3]. The VPMM as a unique electromechanical device is firstly derived from the earlier Vernier reluctance machine [4-5]. Further, dual-excitation VPMM is invented with a dual stator and toroidal winding, which not only has high torque density at low speed but also improves space utilization [6]. In [7-8], dual-excitation VPMM is further investigated. A generic torque maximizing design methodology for the motor is proposed to improve the torque density in the machine in [6], and a new structure constructed with interior PM, spoke-array rotor, and dual-stator with a displacement of half slot is proposed to improve the power factor and the pole shoe was also investigated to further improve the torque performance [7-8]. In this paper, a novel effective, and convenient method aiming to improve the torque density and power factor of DS-VPMM is proposed. The key is to rotate the inset-type PMs in the rotor with a certain electrical angle as well as the excitation direction and it is found that the flux leakage is significantly reduced in the air-gaps and the flux distribution in the inner and outer stator windings can be compensated with each other. Hence not only the back-EMF and torque are boosted but also the power factor is greatly improved. The paper is organized as follows. The operation principles including the structure and magnetic field analyses are introduced first. In the third section, the electromagnetic characteristics of this machine are evaluated based on FEM analyses, including flux density in the two air gaps and their harmonic investigation to find the effective components of the flux density. Besides, back-EMF, cogging torque, and on-load torque, as well as torque density and power factor will be analyzed. Machines with different rotation angles are studied and compared. The power factor improving method proposed in this paper can also be extended to other machines to improve the torque density within a limited peripheral. 2. Machine Topology The original design of DS-VPMM is as shown in Fig.1 (a). A flux concentrating structure using spoke-array magnets rotor to increase the useful magnet flux and decrease the flux leakage between adjacent PMs is adopted. The stator has a tooth-pole structure, which functions as modulation pieces in a flux modulate machine. The windings with yellow, green, and red color refer to phase A, B, C respectively. Fig. 1 (b) shows the DS-VPMM that adopts the proposed method to rotate the inserted PMs as well as their excitation directions with a certain angle. The other parts of DS-VPMM are kept the same. Windings of inner and outer stators can be connected independently or series according to the applications. In order to investigate more explicitly, the windings of two stators are connected independently in this paper. This machine follows the following rule [7]: Z2 =Z1-p or Z1+p (1) where p, Z1, Z2 are the pole-pair number (PPN) of winding, stator teeth, and rotor, respectively. According to the modulation effect of magnet gear, the main effective harmonic order will be 1st and 11th order harmonics. 3. Initial Investigation Results Fig. 2 shows the variations of torque and power factor when changing the rotation angle of the inset-type PMs in the rotor iron core. It can be found that the highest torque density is 24.275 KN/m3, whereas the power factor is 0.726. Since a rotation angle of 15 degrees exhibits a more preferable power factor, the torque of the machine with a 15-degree rotation angle versus the current control angle is investigated and shown in Fig. 12. It is found that when the current control angle is 55 degrees, the power factor can reach nearly 0.8. The torque reaches the highest value when the current control angle is nearly 30 degrees and the power factor is around 0.7 at this control angle. In this abstract, only one machine topologies and its investigation results are shown. More machines applied with this method will be investigated in the full paper. 4. Conclusion A novel method to improve the power factor of VPMM machine is proposed in this paper and the analyses are strongly proved that this method is efficient and the power factor can be improved nearly to 0.8 which is significantly higher than the traditional VPMM. In addition, through the rotation of PMs, the machine can get more space for PMs, thus obtaining higher torque density within the limited volume.

**References:**

[1] G. Eason, B. Noble, and I. N. Sneddon, Phil. Trans. Roy. Soc. London, vol. A247, pp. 529-551(1955) [2] A. Ishizaki, T. Tanaka, K. Takasaki, Electrical Machines and Drives Seventh International Conference(2002) [3] C. H. Lee, IEEE Trans. Power App. And Syst., vol.82, no. 66, pp. 343-349(2007) [4] T. Toba, T. A. Lipo, Conference Record of the 1999 IEEE Industry App. Conference, vol.4, pp.2539-2544(2002) [5] A. Toba, T. A. Lipo, IEEE Trans. Indus. Appl., vol. 36, no. 6, pp. 1539-1546(2002) [6] Dawei Lin, Ronghai Qu, Thomas A. Lipo, IEEE Trans. Indus. Appl., vol.50, no.6, pp. 3664-3674(2014) [7] Dawei Li, Ronghai Qu, Jian Li, IEEE Energy Conversion Congress and Exposition, pp. 1885-1891(2015) [8] Ronghia Qu, Dawei Li, Jin Wang, 2011 International Conference on Electrical Machines and Systems, pp. 1-6(2011)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/afa91c099179c87a719ab4a8bb270ff7.jpg)
Fig. 1. The topology of the DS-VPMM. (a) Initial machine structure. (b) Machine with the rotated PMs.

![](https://assets.underline.io/uploads/markdown_image/1/image/293e2aaa11b0471adf5d1f87a9e9aff9.jpg)
Fig. 2. Power factor and torque versus rotor-PM rotation angle.

 A Novel Approach for Power Factor Improvement in Dual-Stator Vernier Permanent Magnet Machines

I. INTRODUCTION Nowadays, the demands of high torque/power rating in critical industrial applications usually lead to bulky size and excessive material consumption in the conventional permanent magnet (PM) machines [1]. Thus, torque density improvement is widely recognized as a challenging issue for traditional PM machines [1]. As a common practice, doubling the stator is normally employed to increase the torque density within a limited overall dimension, namely, the dual-stator (DS) machines [2]-[4]. For the DS machines, the thermal management and protection issues associated with the PMs tend to be problematic issues with the cantilever cupped rotor. The stator-PM DS machines [4] can well facilitate the PM heat dissipation, but also have a simple and robust rotor which is preferable for high-speed critical-safety operation. Nevertheless, the inner and outer stators in the preceding stator-PM DS structures are structurally duplicated, the geometric conflicts between the PM excitations and windings on the stator still exist similar to those single stator counterparts. Therefore, this paper aims to propose novel DS biased PM machines (DS-BPMM) only having biased PM excitations in the inner stator. Different from the existing DS machines having two identical stators, the developed DS-BPMMs combines the advantages of the design concept of “partitioned stator (PS) [5]” and the conventional DS machines. In the perspective of the geometry, the proposed machines can be considered as the synergies of an outer-rotor stator PM machine plus a separate outer stator similar to traditional fractional-slot machines. As a result, the space tradeoff between PM and copper areas, as well as severe magnetic saturation are significantly alleviated compared to the traditional DS counterparts. In this paper, the electromagnetic characteristics of the DS-BPMMs with different PM arrangements in the inner stator are investigated and compared. The machine topology and operating principle based on interior PM (IPM) and surface-mounted PM (SPM) structures will be addressed. Finally, an IPM-DS-BPMM prototype is manufactured and tested to verify the theoretical analyses. II. MACHINE TOPOLOGIES AND STATOR/ROTOR POLE COMBINATION Figs. 1 (a) and (b) show the proposed machine topologies, which can be regarded as IPM and SPM types, respectively. It should be noted that the total PM usage, outer stator, stack length, and rated current are kept the same for the two designs to offer a fair comparison. Meanwhile, the two machines are both characterized by a 6/11/6 outer-stator-pole/rotor-segment/inner-stator-pole configuration. Since the two machines comply with the variable reluctance principle, their stator/rotor pole combinations can be governed by [6] Ns/GCD(Ns, Nr)=km (1) where GCD signifies the Greatest Common Divisor between the stator pole number Ns and rotor pole number Nr, m is the number of phases, and k is a positive integer. It should be emphasized that the outer stator pole number is identical to that of the inner stator pole in these two machines. Besides, the flux linkage of single-coil is bipolar for SF machine, while unipolar for VR machine. However, the resultant phase flux linkage of VR topology is bipolar, which is mainly attributed to the opposite connection of armature windings in the same phase, as evidenced by the coil and phase flux linkages in the outer stator windings in Figs. 1 and (c) and (d), respectively. III. ELECTROMAGNETIC PERFORMANCE COMPARISON The open-circuit back-EMFs of the two machines are shown in Fig. 2(a). The significantly high EMF magnitudes can be observed in the IPM case. This is mainly attributed to the higher resultant phase flux linkage of the IPM machine due to its bipolar coil flux linkage. Accordingly, the SPM machine exhibits relatively lower torque capability compared to the IPM counterpart as reflected in the rated-load steady torque in Fig. 2(b). Meanwhile, it can be observed that the IPM one shows ~higher torque ripple ratio than the SPM one, which is undesired for the applications requiring smooth torque performance. IV. EXPERIMENTAL VALIDATION Based on the analysis abovementioned, the IPM configuration is selected and manufactured as shown in Fig. 2(c). The finite element (FE) and measured back-EMF waveforms are shown in Fig. 2(d), in which the good agreement between FE predictions and test results are achieved. The detailed characteristics analysis, comparison results, and experimental validation will be presented in the full paper.

**References:**

[1] G. A. Capolino and A. Cavagnino, “New trends in electrical machines technology,” IEEE Trans. Ind. Electron., vol. 61, no. 8, pp. 4281-4285, Aug. 2014. [2] M. Abbasian, M. Moallem, and B. Fahimi, “Double-stator switched reluctance machines (DSSRM): fundamentals and magnetic force analysis,” IEEE Trans. Energy Convers., vol. 25, no. 3, pp. 589-597, Sep. 2010. [3] S. Niu, K. T. Chau, J. Z. Jiang, and C. Liu. “Design and control of a new double-stator cup-rotor permanent-magnet machine for wind power generation,” IEEE Trans. Magn., vol. 43, no. 6, pp. 2501-2503, Jun. 2007. [4] D. Kim, H. Hwang, S. Bae, and C. Lee.” Analysis and design of a double-stator flux-switching permanent magnet machine using ferrite magnet in hybrid electric vehicles,” IEEE Trans. Magn., vo. 52, no. 7, pp. 1-4, Jul. 2016. [5] D. Evans and Z. Q. Zhu, “Novel partitioned stator switched flux permanent magnet machines,” IEEE Trans. Magn., vol. 51, no. 1, Art. no. 8100114, Jan. 2015. [6] J. T. Chen, and Z. Q. Zhu, “Winding configurations and optimal stator and rotor pole combination of flux-switching PM brushless AC machines,” IEEE Trans. Energy Convers., vol. 25, no. 2, pp. 293 - 302, Jun. 2010.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/aedc4c0d896721af698b5502619d7a66.jpg)
Fig. 1. Topologies and flux linkage waveforms of the DS-BPMMs.

![](https://assets.underline.io/uploads/markdown_image/1/image/2ea5c842c25e8e95ad6c73004ee52f0f.jpg)
Fig. 2. Electromagnetic performance comparison and test result. (a) Back-EMFs. (b) Rated-load steady torque waveforms. (c) Prototype. (d). FE predicted and measured phase EMF waveforms.

 Comparative Study of Novel Dual Stator Machines Having Different Biased PM Configurations

I.Introduction The inter-turn short-circuit (ITSC) faults can cause excessively high short-circuit current in PM motors. This elevated current level will increase the temperature of the faulty windings and further melt the insulation of the nearby turns. As a result, some more serious faults can be induced, such as the interphase short-circuit fault, phase-to-ground short-circuit fault, and PM demagnetization [1]. The axial split phase permanent magnet synchronous motor (ASP-PMSM) has better isolation performance between phases compared to traditional circumferential split phase permanent magnet synchronous motor (CSP-PMSM) [2], which is benefit in preventing the spread of fault between phases. In this paper the behavior difference of ITSC fault between ASP-PMSM and CSP-PMSM has been investigated. Through theoretical analysis, finite element analysis (FEA) and experimental verification, it is found that compared to the CSP-PMSM, the ASP-PMSM has inherently advantages in mitigating the severity of ITSC fault. II.Modeling And Analysis of ITSC Fault A. Topology and advantages. As shown in Fig.1 (a), the phase-stators of ASP-PMSM are independently distributed along axial direction, which realized excellent magnetic, physical and thermal isolation between phases. These features are benefit in preventing the spread of fault between phases. There is only one phase in the circumferential direction of ASP-PMSM, and therefore the number of turn in series per phase of the ASP-PMSM is closed to three times that of CSP-PMSM. B. The behavior of fault current. This section build the electrical model of PMSM with ITSC fault, as is shown in Fig.1(b). For an incipient fault, the contact resistance is not ideal zero. Therefore, the contact resister rf is included in this model to consider the degradation process of insulation materials. Based on this model, the expression of fault current if is derived. |if|=|Vf|/(Rf+Rs+jωLaNs/N1) Vf=ea-Rf+jωLa(N1-Ns)/N1ia Rf=Nrf/Ns In above equation, N, N1 and Ns represent number of turns in series, number of turns per coil and number of shorted turns; respectively; and represent the phase back-EMF vector and current vector, respectively; La represents the self-inductance of phase A; Rs represents the phase resistance. The vector diagram of Vf for CSP-PMSM and ASP-PMSM is shown in Fig.1 (c) and (d), respectively, the blue line and black line represents the vector at low speed and high speed, respectively. Because the number of turns in series of ASP-PMSM is triple that of CSP-PMSM, therefore the Rf for ASP-PMSM is triple that of CSP-PMSM. At low speed, the amplitude of vector Vf-ls in Fig 1(d) is three times larger than that in Fig.1 (c). Thus the fault current of ASP-PMSM is larger than that of CSP-PMSM. However, for an incipient fault, the fault current of ASP-PMSM and CSP-PMSM are both small at low speed. At high speed, the amplitude of vector Vf-hs in Fig.1 (d) is smaller than that in Fig.1 (c). Thus the fault current of ASP-PMSM is smaller than that of CSP-PMSM. It can also be seen from Fig.1 (c) and (d) that the higher the fault resistance, the higher the speed to obtain the minimum short circuit current, that is, for an incipient fault, the ASP-PMSM can obtain lower fault current than CSP-PMSM at relative high operating speed. III.Simulation Analysis The fault current of ASP-PMSM and CSP-PMSM at different contact resistance and operating speed combinations is calculated by FEA and shown in Fig.1 (e) and (f). It can be seen that when the fault resistance is relatively large, the fault current of ASP-PMSM is small in the full speed range. This point is very benefit in limiting the further deterioration of fault and expanding the span life of the faulty motor. The simulation results are consistent with the theoretical analysis results in section II. The variation of fault current with the number of shorted turns at different contact resistance conditions is also investigated. The losses of two types of motors under healthy and different fault conditions are compared. It is verified that the copper loss of ASP-PMSM at different ITSC fault conditions is much lower than that of CSP-PMSM, which proved that the ASP-PMSM itself can mitigating the fault severity of ITSC fault compared to that of CSP-PMSM. IV.Experimental Test A 6.3kW prototype is manufactured, and the test platform is shown in Fig.2(a). The variation of one-turn short-circuit current with the operating speed at different contact resistance conditions is tested, and shown in Fig.2(b) and (c), which proved the accuracy of the above analysis. V.Conclusion 1) For an incipient fault, the ASP-PMSM can achieve small fault current at much wider speed range than that of CSP-PMSM, and the ASP-PMSM investigated in this paper has realized low fault current within full speed range. This is very useful to limit the further deterioration of fault and expanding the span life of the faulty motor. 2) With the same number of shorted turns, the loss of ASP-PMSM are much smaller than that of CSP-PMSM, it is proved that the ASP-PMSM itself can mitigating the fault severity of ITSC compared to that of CSP-PMSM. 3) The experimental test verified the accuracy of the theoretical analysis and the FEA.

**References:**

[1] N. Leboeuf, T. Boileau, B. Nahid-Mobarakeh, F. Meibody-Tabar, and G. Clerc, “Real-time detection of inter-turn faults in PM drives using back EMF estimation and residual analysis, ” IEEE Trans. Industry Applications, vol. 47, no. 6, pp. 2402-2412, 2011. [2] Feng Chai, Lina Geng, Yulong Pei,“A novel fault tolerant motor with integral slot non-overlapping concentrated Winding,” IEEE Access, vol.7, PP. 99462 – 99469, Jul. 2019.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d7bf3ea3d54fb2244b7850515ad0103a.jpg)
Fig.1 (a)Motor topology (b) Electrical circuit model. Vector diagram of (c) CSP-PMSM and (d) ASP-PMSM at different speed. The one-turn fault current varies with speed when rf is (e) 5mΩ and (f) 10mΩ.

![](https://assets.underline.io/uploads/markdown_image/1/image/b629ca0b5935825e7e8a30b58562c801.jpg)
Fig.2 (a) The test platform. The one-turn ITSC fault current varies with speed at (b) zero contact resistance condition and (b) non-zero contact resistance condition.

 Analysis of Inter-turn Short-Circuit Faults of Axial Split Phase Permanent Magnet Synchronous Motors

I. Introduction Direct drive wave energy conversion (DDWEC) device using permanent magnet linear generator (PMLG) eliminates the inefficient transmission device and achieves simpler mechanical structure. However, due to the direct connection between buoy and translator, the low-speed linear reciprocating wave motion will be directly transmitted to the translator. So PMLG needs to adopt a low-speed design [1]. It is necessary to increase the number of pole pairs of the generator or use power electronic devices to increase the output voltage and power density. But this will increase the loss and reduce the efficiency of the whole system. The linear-rotating axial flux permanent magnet generator (AFPMG) is proposed to improve the output voltage and power density of the DDWEC. By employing the magnet screw (MS) and AFPMG, it combines the merits of MS and AFPMG and realizes the soft connection between the buoy and generator rotor. The nut and screw of MS are directly connected to the buoy and generator rotor, respectively. When approximately 0.5m/s reciprocating wave motion comes, the movement can be accelerated by MS and magnetic field modulation and finally the speed of the rotor will reach 1200 rpm/min, which can improve the output voltage and power density consequently. While this structure brings advantages, at the same time, due to the use of a large number of rare-earth PMs, it will increase power generation costs and reduce practical competitiveness. Therefore, a hybrid excitation axial flux permanent magnet generator (HE-AFPMG) is proposed to reduce the amount of PMs and become a candidate for DDWEC. Not only that, because the wave conditions (typically 3-20s) are constantly changing, the corresponding wave excitation forces of the same buoy vary widely. By using hybrid excitation, the excitation current can easily adjusted to regulate the magnetic field of the air gap [2], which make generator suitable for different working conditions in wave energy conversion. II. Machine Configuration and Operation Principle In the proposed topology, as shown in Fig. 1, the armature winding and field winding are placed in upper stator and lower stator of AFPMG, respectively. PMs are placed at the slots of the upper stator and work as parallel excitation source. There is no risk of irreversible demagnetization in PMs with this configuration, meanwhile, it can reduce flux linkage and back electromotive force (EMF) harmonics. The operation principle of AFPMG based on modulation effect is similar to a magnetic gear and a magnetically geared machine when the rotor is consists of modulation teeth. The magnetic field will be accelerated due to the magnetic gear effect, when the excitation magnetic field passes through the air gap and modulation teeth. Eventually, potentials are induced in the armature windings. The number of pole pairs and speed of armature magnetic field are expressed as follow: paw = | pfw ± pmt | Ωaw = ( pfwΩfw ± pmtΩmt ) / ( pfw ± pmt ) where paw, Ωaw, pfw, Ωfw are the number of pole pairs and rotational speed of magnetic field in armature winding and field winding, respectively. pmt and Ωmt are the number and rotational speed of modulation teeth, respectively. In proposed AFPMG, the upper stator pole number Nus = 12, hence the number of pole pairs of magnetic field in armature winding paw = 2 or paw = 1 when the number of modulation teeth satisfies pmt = Nus ±2 or pmt = Nus ±1. Fig.1 III. Results Fig.2 The output power versus excitation current in proposed HE-AFPMG with armature winding having different load current is shown in Fig.2. IV. Conclusion The application of hybrid excitation in AFPMG used in DDWEC can eliminate risk of irreversible demagnetization in PMs and reduce flux linkage and back electromotive force harmonics. Meanwhile, it can adjust the air gap magnetic field to suit different sea conditions.

**References:**

[1] W. Li, K. T. Chau and J. Z. Jiang, "Application of Linear Magnetic Gears for Pseudo-Direct-Drive Oceanic Wave Energy Harvesting," in IEEE Transactions on Magnetics, vol. 47, no. 10, pp. 2624-2627, Oct. 2011. [2] C. Ye, Y. Du, J. Yang, X. Liang, F. Xiong and W. Xu, "Research of an Axial Flux Stator Partition Hybrid Excitation Brushless Synchronous Generator," in IEEE Transactions on Magnetics, vol. 54, no. 11, pp. 1-4, Nov. 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/951d474bb6205f855448b547badaaa7c.jpg)
Fig. 1

![](https://assets.underline.io/uploads/markdown_image/1/image/53fb22268e717a1e38e511372a0a531b.jpg)
Fig. 2

 A Hybrid Excitation Axial Flux Permanent Magnet Generator for Direct Drive Wave Energy Conversion

Due to the widespread concern of the greenhouse effect, people's requirements for energy saving and emission reduction of drive systems are becoming higher. The electrification of drive systems seems to be an irresistible trend. As the core of electric drive system, electric motor has been widely mentioned. The Permanent Magnet Synchronous Machine (PMSM) proved to be better in energy conversion which efficiency is higher than conventional Induction Machines [1-2]. In the application field of commercial logistics vehicles, the trend of electrification is increasing and the space occupied by the electric drive system is limited. As a result, a higher demand for density is required. Conventional electric motors applied in this platform are mainly Radial Flux Permanent Machines (RFPM). In particular, the application of the logistics EV traction motor requires low maximum speed but high output torque. The conventional design developed on this platform is a PMSM using traditional round copper wire as winding part and the rotor adopts “delta” shape topology. The “flux barrier” structure was added to increase the reluctance torque ratio, which was aimed to increase torque density of the whole system. However, due to the further reduction in already limited space, it will be difficult to meet the requirements using RFPM. Since the topological structure of the disc motor was proposed in last 70s [3-4], many researches have been done, especially on AFPM’s topological structures. Among them, some classic structures are: the TORUS (double-rotor-one-stator) structure, whose stator part is composed of copper winding and iron core, and the rotor part is composed of the surface mounted PMs and back iron; the AFIR (double-stator-one-rotor) structure, whose stator part is the same, but rotor part is composed only of the fan-shaped PMs [5-6]. As there is no back iron structure in the rotor part for AFIR, its rotational inertia is quite low and resulting the starting torque is low [7-8]. This advantage attracts us because the size requirements are more stringent for our platform. Based on this consideration, the optimal structure of the traction motor is selected as the AFIR structure with two stators and one rotor. In AFPM design, the rotor Permanent Magnets (PM) are directly in contact with the air gap, and the complex magnetic field has rich harmonic content, resulting in a higher proportion of eddy current losses in rotor PMs. Which can cause higher temperature rise in the rotor of an AFIR structure AFPM. Reducing PM eddy current loss is significantly important to the PM topology design, rotor temperature rise and overall performance. The AFPM in this paper adopts an AFIR 24s/20p design. The rotor PMs are segmented with identical radial distance, in order to reduce the length of the eddy current path in each PM and reduce the eddy-current loss, thereby reducing the risk of PM demagnetization caused by high temperature. In this paper the main body is divided in three parts, in part II, the design problems will be presented, which mainly includes: 1) Stator and rotor design, 2) The influence of the rotor support material on the motor, 3) The magnetic field measurement on the surface of the segmented magnet, 4) difference analysis between simulation and test. Part III will mainly introduce the problems encountered and the corresponding solutions during the manufacturing process, which includes: 1) assembly problem due to strong magnetic force, 2) air-gap width balance before and after test and in part IV we conclude. This application research is aimed to have a positive guiding significance for the AFPM production. We hope that our description of prototype developing process and the solutions we took to deal with the manufacturing problems can have a positive influence for future research.

**References:**

 [1] Edward, Iman, Said Wahsh, and M. A. Badr. "Analysis of PMSM drives for electric vehicles." Proceedings of the 37th SICE Annual Conference. International Session Papers. IEEE, 1998. [2] Situ, Lixin. "Electric vehicle development: the past, present & future." 2009 3rd International Conference on Power Electronics Systems and Applications (PESA). IEEE, 2009. [3] P. Campbell, "Principles of a permanent-magnet axial-field d.c. machine," in Proceedings of the Institution of Electrical Engineers, vol. 121, no. 12, pp. 1489-1494, December 1974. [4] P. Campbell, “The magnetic circuit of an axial-field DC electrical machine”, IEEE Transactions on Magnetics, Vol.Mag11, No.5, Sept. 1975, pp.1541-1543. [5] E. Spooner and B. J. Chalmers, “TORUS, a slotless, toroidal stator, permanent magnet generator”, Proc. IEE, Part-B, Vol.139, No. 6, Nov. 1992, pp. 497-506. [6] F. Caricchi, F. Crescimbini and E. Santini, “Basic principles and design criteria of axial-flux PM machines having counterrotating rotors”, IEEE Transactions on Industry Applications, Vol.31, No. 5, Sept/Oct 1995, pp.1062-1068. [7] Aydin. M, Huang. S and Lipo, T.A. (2004). Axial flux permanent magnet disc machines: A review. Conf. Record of SPEEDAM. [8] Akatsu, K. and Wakui, S. , “A comparison between axial and radial flux PM motor by optimum design method from the required output NT characteristics”, in international journal for computation and mathematics in electrical and electronic engineering, Vol. 25 No. 2, pp. 496-509.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8d70807489b42e8db65cc0ef3398b370.jpg)
Impact of PM Segment Number on Rotor PM Eddy Current Loss

![](https://assets.underline.io/uploads/markdown_image/1/image/d5d466e7ccd06071dfca97e53692f578.jpg)
Rotor magnetic flux density distribution

 Axial-flux Permanent Magnet Machine Application Research with Strap-wire Technique and Difference Analysis of Rotor Eddy-current Loss between Simulation and Test

I. INTRODUCTION With the increasingly serious problems of energy shortage and environmental pollution, the development of electric vehicles has become the focus of the world. Electric motors and their drive systems are one of the largest electrical energy consumptions, consuming more than twice as much as lighting, the next largest end-use, accounting for about between 43% and 46% of all global electricity consumption [1]. Therefore, it is necessary to further improve the overall efficiency of electric motors, especially for New European Driving Cycle (NEDC). More and more scholars improve motor efficiency by changing motor materials [2-6]. Grain-Oriented electrical steel materials (GO materials) are mainly used in the core manufacturing of transformers, reactors and large generators. In recent years, GO materials are gradually introduced into motors. Compared with the non-oriented electrical steel materials (NO materials) commonly used in motors, the GO material has the advantages of lower core loss characteristic and higher saturation magnetic flux density. However, the GO material has different permeability and core loss in different directions, so it is difficult to design an axial-flux permanent magnet (AFPM) motor with yoke to take advantage of the GO material. The main flux of the AFPM motor with yokeless stator studied in this paper only passes through the stator in one direction, eliminating the disadvantages of AFPM motor with stator yoke. This paper discusses the application of GO materials in AFPM motors with yokeless stator, compares the basic characteristics of the GO material and NO material used in AFPM motor, analyses the difference between two axial-flux topologies in the use of materials and verifies through finite-element analysis (FEA). II. DESCRIPTION OF THE AFPM MACHINE AND GRAIN-ORIENTED ELECTRICAL STEEL SHEET The GO material has electromagnetic anisotropy: the electromagnetic properties in different directions are different, as is shown in Fig.1(a). In the easy magnetization direction of GO material, it can be seen from Fig.1(b-e) that it is easier to magnetize than NO material, with higher saturation point and lower core loss. However, in the direction of hard magnetization, the GO material is harder to magnetize and has higher core loss. So reasonable use of the easy magnetization direction can provide better torque output ability and less core loss for motors. The explosive view of the AFPM machine investigated in the paper with 48-slot /8-pole is shown in Fig.2, which belongs to the axial-flux topology with a single-stator double-rotor. Main parameters of the motor are shown in Tab. I. Due to the arrangement of the PMs, the main magnetic flux paths only pass through the stator in one direction, which can be set as easy magnetization direction, without passing through the stator yoke tangentially, as shown in Fig.3. III. FEA AND PERFORMANCE Due to AFPM machine’s particular 3-D configuration, 3-D FEA is carried out. Fig.4 shows the stator flux distributions and flux density under no load, showing that the main flux paths go through the easy magnetization direction. It should be noted that even if the GO material is easier to magnetize, the air-gap flux density and back-EMF are not greatly improved under no-load condition due to the large air-gap and PM reluctance. With the increase of armature current, the advantages of GO material are gradually manifested. The torque output capacity of the AFPM machine with GO material and NO material obtained by 3-D FEA is shown in Fig.5, reflecting that the motor with GO material has better torque output capacity than that of NO material. Taking Irms=530A as an example, the torque of GO material is about 15 N.m higher than that of NO material, increased by about 3%. Fig.6 shows the efficiency map of the motor with different materials. The GO material not only improves the torque, but also improves the efficiency. Tab. II compares torque, core loss and efficiency of motors with yokeless stator using different materials under typical working conditions. Similarly, this paper also tried the application of GO material in AFPM machine with stator yoke. As is shown in Fig.7, since a tangential magnetic circuit passes the stator yoke, it is hard to avoid the different magnetization direction when using the easy magnetization direction. Tab. III compares the torque and efficiency of the AFPM machine with yoke under several working conditions. With the stator using GO material, the torque output capacity is lower than that with NO material, and core loss is also increased. Hence, it is not recommended to use GO material in this AFPM topology. IV. CONCLUSION By introducing GO material to yokeless stator, an attempt is made in this paper to use its electromagnetic anisotropy to make the main magnetic flux paths of the motor passing through its easy magnetization direction, without crossing hard magnetization direction, so as to improve torque performance and reduce core loss as well as efficiency. Base on the 3-D FEA model of 48-slot /8-pole AFPM machine, the field distributions, flux density, torque output capacity and efficiency map have been compared between GO and NO material. Benefitting from GO material and yokeless structure, the torque output capacity of AFPM machine is increased by about 5%, the core loss is also reduced by 10%, and the efficiency is improved by 2%. Furthermore, the inapplicability of GO material in the AFPM with stator yoke is also discussed and verified in this paper.

**References:**

[1] P. Waide and C. U. Brunner, “Energy-efficiency policy opportunities for electric motor-driven systems,” International Energy Agency (IEA), 2011. [2] W. Geng, Z. Zhang and Q. Li, "High Torque Density Fractional-Slot Concentrated-Winding Axial-Flux Permanent-Magnet Machine With Modular SMC Stator," IEEE Transactions on Industry Applications, vol. 56, no. 4, pp. 3691-3699, July-Aug. 2020. [3] D. Kowal, P. Sergeant, L. Dupre and A. Van den Bossche, "Comparison of Nonoriented and Grain-Oriented Material in an Axial Flux Permanent-Magnet Machine," IEEE Transactions on Magnetics, vol. 46, no. 2, pp. 279-285, Feb. 2010. [4] J. Ma et al., "Optimal Design of an Axial-Flux Switched Reluctance Motor With Grain-Oriented Electrical Steel," IEEE Transactions on Industry Applications, vol. 53, no. 6, pp. 5327-5337, Nov.-Dec. 2017. [5] Y. Tsuchiya and K. Akatsu, "A Study of the Switched Reluctance Motor using Grain-Oriented Electrical Steel Sheets," 2020 IEEE Energy Conversion Congress and Exposition (ECCE), Detroit, MI, USA, 2020, pp. 3623-3628. [6] S. Javadi, M. Mirsalim and J. Sabzivand, "3-D FEM analysis of a novel structure for axial-flux homopolar generators using a grain-oriented silicon steel stator core," 2008 International Conference on Electrical Machines and Systems, Wuhan, 2008, pp. 3640-3643.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2e470724e420eb5e24f1d276f4bcb0de.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/9c74136a3b306c49ec4636f896a67e57.jpg)

 Electromagnetic Analysis and Efficiency Improvement of Axial-Flux Permanent Magnet Motor with Yokeless Stator by using Grain-oriented Silicon Steel Material

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