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Journal articles on the topic 'Variable reluctance motor'

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Published: 4 June 2021
Last updated: 1 February 2022

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1

Manzer, D. G., M. Varghese, and J. S. Thorp. "Variable reluctance motor characterization." IEEE Transactions on Industrial Electronics 36, no. 1 (1989): 56–63. http://dx.doi.org/10.1109/41.20345.

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2

Zribi, Mohamed, and Muthana T. Alrifai. "Robust controllers for variable reluctance motors." Mathematical Problems in Engineering 2005, no. 2 (2005): 195–214. http://dx.doi.org/10.1155/mpe.2005.195.

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This paper investigates the control problem of variable reluctance motors (VRMs). VRMs are highly nonlinear motors; a model that takes magnetic saturation into account is adopted in this work. Two robust control schemes are developed for the speed control of a variable reluctance motor. The first control scheme guarantees the uniform ultimate boundedness of the closed loop system. The second control scheme guarantees the exponential stability of the closed loop system. Simulation results of the proposed controllers are presented to illustrate the theoretical developments. The simulations indicate that the proposed controllers work well, and they are robust to changes in the parameters of the motor and to changes in the load.
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3

Takahara, Kazuaki, Katsuhiro Hirata, Noboru Niguchi, and Akira Kohara. "Current superimposition variable flux reluctance motor with 8 salient poles." Open Physics 15, no. 1 (December 29, 2017): 857–61. http://dx.doi.org/10.1515/phys-2017-0102.

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AbstractWe propose a current superimposition variable flux reluctance motor for a traction motor of electric vehicles and hybrid electric vehicles, which consists of 10 salient poles in the rotor and 12 slots in the stator. However, iron losses of this motor in high rotation speed ranges is large because the number of salient poles is large. In this paper, we propose a current superimposition variable flux reluctance motor that consists of 8 salient poles and 12 slots. The characteristics of the 10-pole-12-slot and 8-pole-12-slot current superimposition variable flux reluctance motors are compared using finite element analysis under vector control.
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4

Kohara, Akira, Katsuhiro Hirata, Noboru Niguchi, and Yuki Ohno. "Current Superimposition Variable Flux Reluctance Motor." IEEJ Transactions on Industry Applications 135, no. 11 (2015): 1077–84. http://dx.doi.org/10.1541/ieejias.135.1077.

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5

Torrey, David A. "Excitation of Variable-Reluctance Motor Drives." Electric Machines & Power Systems 19, no. 6 (November 1991): 713–29. http://dx.doi.org/10.1080/07313569108909559.

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6

KOHARA, AKIRA, KATSUHIRO HIRATA, NOBORU NIGUCHI, and YUKI OHNO. "Current Superimposition Variable Flux Reluctance Motor." Electrical Engineering in Japan 200, no. 3 (April 24, 2017): 52–60. http://dx.doi.org/10.1002/eej.22894.

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7

Torrey, D. A., and J. H. Lang. "Modelling a nonlinear variable-reluctance motor drive." IEE Proceedings B Electric Power Applications 137, no. 5 (1990): 314. http://dx.doi.org/10.1049/ip-b.1990.0038.

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8

Torrey, D. A., and J. H. Lang. "Optimal-efficiency excitation of variable-reluctance motor drives." IEE Proceedings B Electric Power Applications 138, no. 1 (1991): 1. http://dx.doi.org/10.1049/ip-b.1991.0001.

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9

Li, Stephen Hsien-Yuan, Feng Liang, Yifan Zhao, and Thomas A. Lipo. "A Doubly Salient Doubly Excited Variable Reluctance Motor." IEEE Transactions on Industry Applications 31, no. 1 (January 1995): 99–106. http://dx.doi.org/10.1109/28.363044.

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10

Suriano, J. R., and Chee-Mun Ong. "Variable reluctance motor structures for low-speed operation." IEEE Transactions on Industry Applications 32, no. 2 (1996): 345–53. http://dx.doi.org/10.1109/28.491483.

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11

Tariq, Iqra, Raheel Muzzammel, Umar Alqasmi, and Ali Raza. "Artificial Neural Network-Based Control of Switched Reluctance Motor for Torque Ripple Reduction." Mathematical Problems in Engineering 2020 (November 30, 2020): 1–31. http://dx.doi.org/10.1155/2020/9812715.

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Switched reluctance motor is acquiring major attention because of its simple design, economic development, and reduced dependability. These attributes make switched reluctance motors superior to other variable speed machines. The major challenge associated with the development of a switched reluctance motor is its high torque ripple. Torque ripple produces noise and vibration, resulting in degradation of its performance. Various techniques are developed to cope with torque ripples. Practically, there exists not a single mature technique for the minimization of torque ripples in switched reluctance motors. In this research, a switched reluctance motor is modelled and analysed. Its speed and current control are implemented through artificial neural networks. Artificial neural network is found to be a promising technique as compared with other techniques because of its accuracy, reduced complexity, stability, and generalization. The Levenberg–Marquardt algorithm is utilized in artificial neural networks due to its fast and stable convergence for training and testing. It is found from research that artificial neural network-based improved control shows better performance of the switched reluctance motor. Realization of this technique is further validated from its mean square error analysis. Operating parameters of the switched reluctance motor are improved significantly. Simulation environment is created in Matlab/Simulink.
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12

Takahara, Kazuaki, Katsuhiro Hirata, Noboru Niguchi, and Akira Kohara. "Performance of a Current Superimposition Variable Flux Reluctance Motor." IEEJ Transactions on Industry Applications 137, no. 8 (2017): 622–30. http://dx.doi.org/10.1541/ieejias.137.622.

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13

SINGH, BHIM, S. P. SRIVASTAVA, and S. K. BARAL. "LOAD COMMUTATED INVERTER FED VARIABLE SPEED RELUCTANCE MOTOR DRIVE." Electric Machines & Power Systems 18, no. 3 (May 1990): 277–82. http://dx.doi.org/10.1080/07313569008909472.

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14

Stepien, Slawomir, and Jakub Bernat. "Modeling and optimal control of variable reluctance stepper motor." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 30, no. 2 (March 8, 2011): 726–40. http://dx.doi.org/10.1108/03321641111101177.

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15

Shimomura, Shoji, Akira Ishizaki, and Kazutaka Saito. "Novel Variable Reluctance N-speed Synchro and its Application for Synchronous Reluctance Motor Drive." IEEJ Transactions on Industry Applications 116, no. 11 (1996): 1159–66. http://dx.doi.org/10.1541/ieejias.116.1159.

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16

Hanene, Hleli, Flah Aymen, and Tounsi Souhir. "Variable reluctance synchronous machines in saturated mode." International Journal of Power Electronics and Drive Systems (IJPEDS) 12, no. 2 (June 1, 2021): 662. http://dx.doi.org/10.11591/ijpeds.v12.i2.pp662-673.

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Electric vehicle seems largely based on electrical machines. Finding the best motor type seems be important for having more performances and a transport system robustness. In this work, we present an analytical model of the synchronous machine with variable reluctances in linear and saturated modes. The angular position of the rotor (θ) and the phase current (i) will beused as parameters. The analytical model of this machine will allow us to determinate its magnetic characteristics such inductors, magnetic flux and electromagnetic torque. The results obtained by the analytical model are compared with those obtained by the finite element method. So, basing on Matlab/Simulink tool and by working with finite element method, these results are depicted and the paper objective is illustrated.
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17

Kazakbaev, Vadim, Vladimir Prakht, Vladimir Dmitrievskii, Mohamed Ibrahim, Safarbek Oshurbekov, and Sergey Sarapulov. "Efficiency Analysis of Low Electric Power Drives Employing Induction and Synchronous Reluctance Motors in Pump Applications." Energies 12, no. 6 (March 24, 2019): 1144. http://dx.doi.org/10.3390/en12061144.

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Due to the rapid increase in the number of variable speed AC drives, the analysis of their energy efficiency has become highly essential. However, such an analysis requires consideration of a wide variety of factors. This includes considering the energy loss in the frequency converter, depending on the motor type. In this article, a computational comparison of the energy properties of variable frequency pump drive employing two types of electric machines, i.e. an induction and a synchronous reluctance motor, is presented. The effect of the motor type on the losses in a low-voltage two-stage frequency converter using analytical and numerical models, with a further comparison, is investigated. Furthermore, an alternative approach to determine the current magnitude and power factor of the load of the converter is suggested. Eventually, this study provides a quantitative estimate of the increase in losses in the converter caused by using the two different motor types. Several experimental tests are conducted on induction and synchronous 1.1 kW reluctance motors.
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18

A. Shanab, M., M. M. Khater, and A. H. Morsi. "OPERATION CHARACTERISTICS OF VARIABLE RELUCTANCE MOTOR SUPPLIED WITH BIPOLAR CURRENT." ERJ. Engineering Research Journal 32, no. 1 (January 1, 2009): 11–20. http://dx.doi.org/10.21608/erjm.2009.69384.

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19

A. Al-Sabbagh, Taha, and Kamil G. Salih. "Sequence Generator To Derive 8-Phase Variable Reluctance Stepper Motor." AL-Rafdain Engineering Journal (AREJ) 18, no. 5 (October 28, 2010): 73–87. http://dx.doi.org/10.33899/rengj.2010.32893.

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20

NIGUCHI, Noboru, Katsuhiro HIRATA, and Akira KOHARA. "Current Harmonics of a Current Superimposition Variable Flux Reluctance Motor." Journal of the Japan Society of Applied Electromagnetics and Mechanics 25, no. 2 (2017): 70–75. http://dx.doi.org/10.14243/jsaem.25.70.

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21

NIGUCHI, Noboru, Katsuhiro HIRATA, Akira KOHARA, and Kazuaki TAKAHARA. "Vector Control of a Current Superimposition Variable Flux Reluctance Motor." Journal of the Japan Society of Applied Electromagnetics and Mechanics 27, no. 1 (2019): 140–45. http://dx.doi.org/10.14243/jsaem.27.140.

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22

Feng Liang, Yuefeng Liao, and T. A. Lipo. "A new variable reluctance motor utilizing an auxiliary commutation winding." IEEE Transactions on Industry Applications 30, no. 2 (1994): 423–32. http://dx.doi.org/10.1109/28.287514.

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23

Ehsani, Mehrdad, James T. Bass, Timothy J. E. Miller, and Robert L. Steigerwald. "Development of a Unipolar Converter for Variable Reluctance Motor Drives." IEEE Transactions on Industry Applications IA-23, no. 3 (May 1987): 545–53. http://dx.doi.org/10.1109/tia.1987.4504944.

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24

Shimomura, Shoji, Akira Ishizaki, and Kazutaka Saito. "A novel variable-reluctance N-speed synchro and its application for synchronous reluctance motor drive." Electrical Engineering in Japan 120, no. 3 (August 1997): 54–63. http://dx.doi.org/10.1002/(sici)1520-6416(199708)120:3<54::aid-eej6>3.0.co;2-q.

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25

Kruthika, Tumma. "Sensor less Control of Switched Reluctance Motor." International Journal for Research in Applied Science and Engineering Technology 9, no. VII (July 31, 2021): 3707–9. http://dx.doi.org/10.22214/ijraset.2021.36398.

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Switched reluctance motor is considered for variable speed applications. It is a power device which can be manufactured easily and inexpensively and relatively high reliable. A sensor less control of SRM is proposed. Here, the communication of SRM is done without use of position detector. It is ensured that the switching of each phase winding takes place during positive slope of inductance profile. Simulation is carried out using MATLAB. A 6/4 SRM is used for this purpose.
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26

Morón, Carlos, Enrique Tremps, Angel Gomez, Alfonso Garcia, and Jose Andrés Somolinos. "Switched Reluctance Motors Control." Key Engineering Materials 605 (April 2014): 247–50. http://dx.doi.org/10.4028/www.scientific.net/kem.605.247.

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A current controlled switched reluctance motor (SRM) drive for variable speed applications with efficiency optimization is presented. A robust, modular and flexible prototyping SRM drives is proposed. It is composed of a power electronic block, a driver board, a measurement and interface board and a DSP controller board. Firing angles are computed online, the turn-on is calculated by means of the Boses rule, and the turn-off is calculated using the general theory of the optimal turn-off angle proposed by Gribble. In steady state operation, tie initial selection of firing angles is fine-tuned by means of an algorithm that minimizes the input power of the drive. A 6/4 switched reluctance motor drive prototype was tested and the experimental results show an improvement in online efficiency, a good steady-state performance and no deterioration in the dynamic response. An efficiency comparison with a commercial vector-controlled induction motor drive of the same size is also included.
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27

Li, Chunyan, Fei Guo, Baoquan Kou, and Tao Meng. "Research on the Non-Magnetic Conductor of a PMSM Based on the Principle of Variable Exciting Magnetic Reluctance." Energies 14, no. 2 (January 8, 2021): 318. http://dx.doi.org/10.3390/en14020318.

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A permanent magnet synchronous motor (PMSM) based on the principle of variable exciting magnetic reluctance (VMRPMSM) is presented. The motor is equipped with symmetrical non-magnetic conductors on both sides of the tangential magnetized permanent magnets (PMs). By placing the non-magnetic conductor (NMC), the magnetic reluctance in the exciting circuit is adjusted, and the flux weakening (FW) of the motor is realized. Hence, the NMC is studied comprehensively. On the basis of introducing the motor structure, the FW principle of this PMSM is described. The shape of the NMC is determined by analyzing and calculating the electromagnetic force (EF) acting on the PMs. We calculate the magnetic reluctance of the NMC and research on the effects of the NMC on electromagnetic force, d-axis and q-axis inductance and FW performance. The critical speeds from the test of the no-load back electromotive force (EMF) verify the correctness of the NMC design. The analysis is corresponding to the test result which lays the foundation of design for this kind of new PMSM.
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28

Li, Chunyan, Fei Guo, Baoquan Kou, and Tao Meng. "Research on the Non-Magnetic Conductor of a PMSM Based on the Principle of Variable Exciting Magnetic Reluctance." Energies 14, no. 2 (January 8, 2021): 318. http://dx.doi.org/10.3390/en14020318.

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A permanent magnet synchronous motor (PMSM) based on the principle of variable exciting magnetic reluctance (VMRPMSM) is presented. The motor is equipped with symmetrical non-magnetic conductors on both sides of the tangential magnetized permanent magnets (PMs). By placing the non-magnetic conductor (NMC), the magnetic reluctance in the exciting circuit is adjusted, and the flux weakening (FW) of the motor is realized. Hence, the NMC is studied comprehensively. On the basis of introducing the motor structure, the FW principle of this PMSM is described. The shape of the NMC is determined by analyzing and calculating the electromagnetic force (EF) acting on the PMs. We calculate the magnetic reluctance of the NMC and research on the effects of the NMC on electromagnetic force, d-axis and q-axis inductance and FW performance. The critical speeds from the test of the no-load back electromotive force (EMF) verify the correctness of the NMC design. The analysis is corresponding to the test result which lays the foundation of design for this kind of new PMSM.
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29

Kolluru, Ashok Kumar, and Malligunta Kiran Kumar. "Closed-loop speed control of switched reluctance motor drive fed from novel converter with reduced number of switches." International Journal of Power Electronics and Drive Systems (IJPEDS) 11, no. 1 (March 1, 2020): 189. http://dx.doi.org/10.11591/ijpeds.v11.i1.pp189-199.

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This paper presents a novel converter configuration with fewer for switched reluctance motor (SRM) drive. The proposed novel converter insists for less number of switches compared to conventional asymmetrical type of converter configuration for switched reluctance motor. Switch count reduction in converter reduces the losses, volume of heat sink, and number of gate drive circuits and thereby the performance of the system. Closed loop speed control of switched reluctance motor fed from proposed novel converter topology was presented in this paper. Performance of closed loop operation is compared to open loop system. Further the proposed converter for SRMT is evaluated with loaded condition and comparative analysis of no-load and loaded SRM is presented. The model presented is developed and the results are analyzed using MATLAB/SIMULINK software. Closed loop performance of proposed novel converter fed switched reluctance motor drive is verified at fixed speed and variable speed conditions.
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30

Namazi, Mohammad Masoud, Amir Rashidi, Hamidreza Koofigar, Seyed Morteza Saghaiannejad, and Jin-Woo Ahn. "Adaptive Control of Switched Reluctance Motor Drives under Variable Torque Applications." Journal of Electrical Engineering and Technology 12, no. 1 (January 2, 2017): 134–44. http://dx.doi.org/10.5370/jeet.2017.12.1.134.

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31

Zhao, Xianchao, Aide Xu, and Wen Zhang. "Research on DTC system with variable flux for switched reluctance motor." CES Transactions on Electrical Machines and Systems 1, no. 2 (2017): 199–206. http://dx.doi.org/10.23919/tems.2017.7961342.

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32

OGURI, Kazuya, Sanshirou OGINO, Akihiro MIZUTANI, Naoki YAMAGUCHI, Nobuhiro UCHIDA, Yasuzumi OCHIAI, and Yoshitake NISHI. "Properties of hybrid variable reluctance magnet using new high-torque motor." Proceedings of the JSME annual meeting 2002.2 (2002): 479–80. http://dx.doi.org/10.1299/jsmemecjo.2002.2.0_479.

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33

Zhang, Chao, Kun Wang, Shuhui Zhang, Xiaoyong Zhu, and Li Quan. "Analysis of Variable Voltage Gain Power Converter for Switched Reluctance Motor." IEEE Transactions on Applied Superconductivity 26, no. 7 (October 2016): 1–5. http://dx.doi.org/10.1109/tasc.2016.2594861.

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34

ROSSI, C., and A. TONIELLI. "Feedback linearizing and sliding mode control of a variable reluctance motor." International Journal of Control 60, no. 4 (October 1994): 543–68. http://dx.doi.org/10.1080/00207179408921480.

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35

Clarkson, P. J., and P. P. Acarnley. "Stability limits for dynamic operation of variable reluctance stepping motor systems." IEE Proceedings B Electric Power Applications 135, no. 6 (1988): 308. http://dx.doi.org/10.1049/ip-b.1988.0033.

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36

Milman, R., and S. A. Bortoff. "Observer-based adaptive control of a variable reluctance motor: Experimental results." IEEE Transactions on Control Systems Technology 7, no. 5 (1999): 613–21. http://dx.doi.org/10.1109/87.784425.

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37

Filicori, F., C. G. Lo Bianco, and A. Tonielli. "Modeling and control strategies for a variable reluctance direct-drive motor." IEEE Transactions on Industrial Electronics 40, no. 1 (1993): 105–15. http://dx.doi.org/10.1109/41.184827.

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38

Materu, P. N., and R. Krishnan. "Steady-state analysis of the variable-speed switched-reluctance motor drive." IEEE Transactions on Industrial Electronics 36, no. 4 (1989): 523–29. http://dx.doi.org/10.1109/41.43012.

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39

Tounsi, Souhir. "Finite element validation of the analytical model of variable reluctance motor." International Journal of Power and Energy Conversion 11, no. 3 (2020): 248. http://dx.doi.org/10.1504/ijpec.2020.10027377.

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40

Tounsi, Souhir. "Finite element validation of the analytical model of variable reluctance motor." International Journal of Power and Energy Conversion 11, no. 3 (2020): 248. http://dx.doi.org/10.1504/ijpec.2020.107948.

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41

Sudhoff, S. D. "Multiple reference frame analysis of a multistack: variable-reluctance stepper motor." IEEE Transactions on Energy Conversion 8, no. 3 (1993): 418–24. http://dx.doi.org/10.1109/60.257054.

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42

Roth, R. B., and Kok-Meng Lee. "Design Optimization of a Three Degrees-of-Freedom Variable-Reluctance Spherical Wrist Motor." Journal of Engineering for Industry 117, no. 3 (August 1, 1995): 378–88. http://dx.doi.org/10.1115/1.2804344.

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This paper presents the basis for optimizing the design of a three degrees-of-freedom (DOF) variable reluctance (VR) spherical motor which offers some attractive features by combining pitch, roll, and yaw motion in a single joint. The spherical wrist motor offers a major performance advantage in trajectory planning and control as compared to the popular three-consecutive-rotational joint wrist. Since an improved performance estimate is required, a method for optimizing the VR spherical motor’s magnetics was developed. This paper begins with a presentation of the geometrical independent and dependent variables which fully described the design of a VR spherical motor. These variables are derived from examination of the torque prediction model. Next, a complete set of constraint equations governing geometry, thermal limitations, amplifier specifications, iron saturation, and leakage flux are derived. Finally, an example problem is presented where the motor’s geometry is determined by maximizing the output torque at one rotor position. The concept of developing a spherical motor with uniform torque characteristics is discussed with respect to the optimization methodology. It is expected that the resulting analysis will improve the analytical torque prediction model by the inclusion of constraint equations, aid in developing future VR spherical motor designs, improve estimates of performance, and therefore will offer better insight into potential applications.
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43

Sudhoff, S. D., and P. C. Krause. "Analysis of steady-state operation of a multistack variable-reluctance stepper motor using qd0 variables." IEEE Transactions on Energy Conversion 6, no. 4 (1991): 693–99. http://dx.doi.org/10.1109/60.103643.

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44

Lee, Kok-Meng, Ronald B. Roth, and Zhi Zhou. "Dynamic Modeling and Control of a Ball-Joint-Like Variable-Reluctance Spherical Motor." Journal of Dynamic Systems, Measurement, and Control 118, no. 1 (March 1, 1996): 29–40. http://dx.doi.org/10.1115/1.2801148.

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Examination of existing joint designs for robot wrist applications has indicated that a spherical wrist motor offers a major performance advantage in trajectory planning and control as compared to the popular three-consecutive-rotational joint wrist. The tradeoff, however, is the complexity of the dynamic modeling and control. This paper presents the dynamic modeling and the control strategy of a three degree-of-freedom (DOF) variable-reluctance (VR) spherical motor which presents some attractive possibilities by combining pitch, roll, and yaw motion in a single joint. The spherical motor dynamics consist of the rotor dynamics and a torque model. The torque model is described as a function of coil excitations and a permeance model in terms of the relative position between the rotor and the stator. Both the forward dynamics which determine the rotor motion as a result of activating the electromagnetic coils and the inverse model which determines the coil excitations required to generate the desired torque are derived in this paper. The solution to the forward dynamics of the spherical motor is unique, but the inverse model has many solutions and therefore an optimization is desired. Experimental results verifying the dynamic model are presented. The control of a VR spherical motor consists of two parts; namely, the control of the rotor dynamics with the actuating torque as system input, and the determination of the optimal electrical inputs for a specified actuating torque. The simulation results and implementation issues in determining the optimal control input vectors are addressed. It is expected that the resulting analysis will serve as a basis for dynamic modeling, motion control development, and design optimization of the VR spherical motor.
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45

Hu, Wei Chao, Yan Chao Li, Ze Bin Yang, and Huang Qiu Zhu. "Direct Torque Control of Bearingless Synchronous Reluctance Motor." Applied Mechanics and Materials 150 (January 2012): 36–39. http://dx.doi.org/10.4028/www.scientific.net/amm.150.36.

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The bearingless synchronous reluctance motor (BSynRM) is a multi-variable, nonlinear and strong-coupled system. To solve the difficult problem of precise decoupling in electric torque and radial suspension force control, the theory of direct torque control of traditional synchronous reluctance motor are applied to the torque control of a BSynRM in this paper. Based on mathematical models of the BSynRM, A direct torque control algorithm based on space vector pulse width modulation (SVM-DTC) is deduced. The SVM-DTC control system is designed and simulated. The simulation results show the control algorithm of SVM-DTC realizes decoupling in electric torque and radial suspension force control. The static and dynamic performance of electric torque, speed and radial suspension force of the BSynRM is excellent.
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46

Miranda, B. B., J. R. Camacho, and A. C. F. Mamede. "Design, Simulation and Performance of a Four Phases Linear Variable Reluctance Motor." Renewable Energy and Power Quality Journal 1, no. 15 (April 2017): 443–48. http://dx.doi.org/10.24084/repqj15.349.

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47

Nelson, A. L., and M. Y. Chow. "Characterization of Coil Faults in an Axial Flux Variable Reluctance PM Motor." IEEE Power Engineering Review 22, no. 7 (2002): 50. http://dx.doi.org/10.1109/mper.2002.4312358.

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48

LIANG, FENG, LONGYA XU, and T. A. LIPO. "d-q ANALYSIS OF A VARIABLE SPEED DOUBLY AC EXCITED RELUCTANCE MOTOR." Electric Machines & Power Systems 19, no. 2 (March 1991): 125–38. http://dx.doi.org/10.1080/07313569108909511.

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49

Tolikas, M., J. H. Lang, and J. L. Kirtley. "Algebraic dual-energy magnetic analysis with application to variable reluctance motor design." IEEE Transactions on Energy Conversion 14, no. 3 (1999): 270–76. http://dx.doi.org/10.1109/60.790869.

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50

NIGUCHI, Noboru, Katsuhiro HIRATA, and Akira KOHARA. "Current Superimposition Variable Flux Reluctance Motor Using the 5th-Order Magnetic Flux." Journal of the Japan Society of Applied Electromagnetics and Mechanics 26, no. 1 (2018): 8–14. http://dx.doi.org/10.14243/jsaem.26.8.

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