# Electrical Circuits Simulator in Null-Flux Electrodynamic Suspension Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Unveiling the Inner Workings: Exploring the Principles and Model of an EDS System

#### 2.1. The Research Gap

#### Comparative Analysis of Related Studies

#### 2.2. The Basic Principles of an EDS System

#### 2.3. The Mathematical Model of an EDS System

#### 2.4. The Computational Algorithm

#### 2.5. The Calculation of Mutual Inductance between SC and 8-Shaped Coils

#### 2.6. The Implementation of the Analysis Using a Circuit Simulator

#### 2.7. The Electromagnetic Forces

#### 2.8. The Model Validation

#### 2.9. Three Superconducting Coils

## 3. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

8-shaped coil, 8C | Figure-eight-shaped coil |

DCT | Dynamic Circuit Theory |

EDS | Electrodynamic Suspension |

EMS | Electromagnetic Suspension |

FEM | Finite elements method |

HTS | High-temperature superconducting Suspension |

JR Central | Central Japan Railway Company |

JR-Maglev | Japan Railway Maglev system |

L0 Serie | Levitation 0 Serie |

Maglev | Magnetic levitation |

MLX01 | Magnetic Levitation Experimental 01 |

MS | Mechanical suspension |

PC | Propulsion coil |

RTRI | Railway Technical Research Institute |

SC | Superconducting coil |

## References

- Rote, D.M. Magnetic Levitation. In Encyclopedia of Energy; Cleveland, C.J., Ed.; Elsevier: New York, NY, USA, 2004; pp. 691–703. [Google Scholar] [CrossRef]
- Han, H.S.; Kim, D.S. Magnetic Levitation: Maglev Technology and Applications; Springer Tracts on Transportation and Traffic; Springer: New York, NY, USA, 2016; Volume 13. [Google Scholar]
- Deng, Z.; Zhang, W.; Zheng, J.; Wang, B.; Ren, Y.; Zheng, X.; Zhang, J. A High-Temperature Superconducting Maglev-Evacuated Tube Transport (HTS Maglev-ETT) Test System. IEEE Trans. Appl. Supercond.
**2017**, 27, 3602008. [Google Scholar] [CrossRef] - Stephan, R.M.; de Andrade Junior, R.; Ferreira, A.C.; Costa, F.S.; Machado, O.J. Maglev-cobra: An urban transportation system For highly populated cities. Transp. Syst. Technol.
**2015**, 1, 16–25. [Google Scholar] - Lim, J.; Kim, C.-H.; Lee, J.-M.; Han, H.-S.; Park, D.-Y. Design of magnetic levitation electromagnet for High-Speed Maglev train. In Proceedings of the 2013 International Conference on Electrical Machines and Systems (ICEMS), Busan, Republic of Korea, 26–29 October 2013; pp. 1975–1977. [Google Scholar] [CrossRef]
- Li, F.; Sun, Y.; Xu, J.; He, Z.; Lin, G. Control Methods for Levitation System of EMS-Type Maglev Vehicles: An Overview. Energies
**2023**, 16, 2995. [Google Scholar] [CrossRef] - Beauloye, L.; Dehez, B. Permanent Magnet Electrodynamic Suspensions Applied to MAGLEV Transportation Systems: A Review. IEEE Trans. Transp. Electrif.
**2023**, 9, 748–758. [Google Scholar] [CrossRef] - Ma, H.; Liu, L.; Xie, X.; Li, X. Study on Levitation Characteristics of the Superconducting EDS Maglev Vehicle. In Proceedings of the 2021 IEEE 4th International Electrical and Energy Conference (CIEEC), Wuhan, China, 28–30 May 2021; pp. 1–5. [Google Scholar] [CrossRef]
- Kitano, J. The Short History of the Superconducting Maglev: Changes in Null Flux Circuit and Pole Pitch. In Proceedings of the ISMB15: The 15th International Symposium on Magnetic Bearings, Kitakyushu, Japan, 3–6 August 2016. [Google Scholar]
- Stephan, R.M.; de Andrade, R., Jr.; Ferreira, A.C.; Sotelo, G.G. Superconducting Levitation Applied To Urban Transportation. In Wiley Encyclopedia of Electrical and Electronics Engineering; American Cancer Society: Atlanta, GA, USA, 2017; pp. 1–18. [Google Scholar]
- Johnson, L.R.; Rote, D.M.; Hull, J.R.; Coffey, H.T.; Daley, J.G.; Giese, R.F. Maglev Vehicles and Superconductor Technology: Integration of High-Speed Ground Transportation into the Air Travel System. Report, ANL/CNSV-67; Argonne National Laboratory: Argonne, IL, USA, 1989. Available online: https://www.osti.gov/biblio/6303324 (accessed on 1 December 2021).
- Hull, J.R. Magnetic Levitation and Transportation. In Applied Superconductivity: Handbook on Devices and Applications; Wiley-VCH: Weinheim, Germany, 2015; Chapter 4.8; Volume 1. [Google Scholar]
- Suzuki, E.; Fujiwara, S.; Sawada, K.; Nakamichi, Y. A Superconducting Transportation System. In Handbook of Applied Superconductivity; IOP Publishing Ltd.: Bristol, UK, 1998; Chapter G8; Volume 2. [Google Scholar]
- Thornton, R.D.; Perreault, D.; Clark, T. Linear Synchronous Motor for Maglev; Final Report. DOT/FAR/NMI-92/13; Laboratory for Electromagnetic and Electronic Systems, Massachusetts Institute of Technology: Cambridge, MA, USA, 1993. [Google Scholar]
- Talukdar, R.P.; Talukdar, S. Dynamic Analysis of High-Speed MAGLEV Vehicle-Guideway System: An Approach in Block Diagram Environment. Urban Rail Transit
**2016**, 2, 71–84. [Google Scholar] [CrossRef] [Green Version] - Nasar, S.A.; Boldea, I. Linear Motion Electric Machines, 1st ed.; John Wiley Sons: New York, NY, USA, 1976. [Google Scholar]
- Lv, G.; Liu, Y.; Zhou, T.; Zhang, Z. Analysis of Suspension and Guidance System of EDS Maglev Based on a Novel Magnetomotive Force Model. IEEE J. Emerg. Sel. Top. Power Electron.
**2022**, 10, 2923–2933. [Google Scholar] [CrossRef] - Sinha, P.K. Superconducting System. In Electromagnetic Suspension Dynamics Control; IEE Control Engineering Series; Peter Peregrinus Ltd.: London, UK, 1987; Volume 30, pp. 1–26. [Google Scholar]
- Reitz, J.R.; Davis, L.C. Force on a Rectangular Coil Moving above a Conducting Slab. J. Appl. Phys.
**1972**, 43, 1547–1553. [Google Scholar] - Chen, D.; Li, X.-F.; Huang, X.; Sheng, J.; Wu, W.; Hong, Z.; Jin, Z.; Ma, H.; Zhao, T. An FEM Model for Evaluation of Force Performance of High-Temperature Superconducting Null-Flux Electrodynamic Maglev System. IEEE Trans. Appl. Supercond.
**2021**, 31, 1–6. [Google Scholar] [CrossRef] - Gong, T.; Ma, G.; Wang, R.; Li, S.; Yao, C.; Xiao, L. 3-D FEM Modeling of the Superconducting EDS Train with Cross-Connected Figure-Eight-Shaped Suspension Coils. IEEE Trans. Appl. Supercond.
**2021**, 31, 1–13. [Google Scholar] [CrossRef] - He, J.L.; Rote, D.M.; Coffey, H.T. Applications of the dynamic circuit theory to Maglev suspension systems. IEEE Trans. Magn.
**1993**, 29, 4153–4164. [Google Scholar] [CrossRef] - He, J.L.; Coffey, H.T.; Rote, D.M. Analysis of the combined Maglev levitation, propulsion, and guidance system. IEEE Trans. Magn.
**1995**, 31, 981–987. [Google Scholar] [CrossRef] - Ohashi, S.; Ohsaki, H.; Masada, E. Equivalent Model of the Side Wall Electrodynamic Suspension System. IEEJ Trans. Ind. Appl.
**1997**, 117, 758–767. [Google Scholar] [CrossRef] [Green Version] - Murai, T.; Fujiwara, S. Design of Coil Specifications in EDS Maglev Using Optimization Program. IEEJ Trans. Ind. Appl.
**1997**, 117, 905–911. [Google Scholar] [CrossRef] [Green Version] - Knowles, R. Dynamic circuit and Fourier series methods for moment calculation in electrodynamic repulsive magnetic levitation systems. IEEE Trans. Magn.
**1982**, 18, 953–960. [Google Scholar] [CrossRef] - Maxwell, J.C. On the induction of electric currents in an infinite plane sheet of uniform conductivity. Proc. R. Soc.
**1872**, 20, 160–168. [Google Scholar] - Smythe, W.R. Static and Dynamic Electricity, 2nd ed.; McGraw-Hill Book Co.: New York, NY, USA, 1950; pp. 390–404. [Google Scholar]
- Paul, C.R. Inductance: Loop and Partial, 1st ed.; Wiley-IEEE Press: Hoboken, NJ, USA, 2009. [Google Scholar]
- Slemon, G.R. Magnetoelectric Devices: Transducers, Transformers, Machines, 1st ed.; John Wiley Sons: New York, NY, USA, 1966. [Google Scholar]
- Reitz, J.R. Forces on Moving Magnets due to Eddy Currents. J. Appl. Phys.
**1970**, 41, 2067–2071. [Google Scholar] - Hill, R.J. Teaching Electrodynamic Levitation Theory. IEEE Trans. Educ.
**1990**, 33, 346–354. [Google Scholar] - Guderjahn, C.A.; Wipf, S.L.; Fink, H.J.; Boom, R.W.; MacKenzie, K.E.; Williams, D.; Downey, T. Magnetic Suspension and Guidance for High Speed Rockets by Superconducting Magnets. J. Appl. Phys.
**1969**, 40, 2133–2140. [Google Scholar] - Hao, L.; Huang, Z.; Dong, F.; Qiu, D.; Shen, B.; Jin, Z. Study on Electrodynamic Suspension System with High-Temperature Superconducting Magnets for a High-Speed Maglev Train. IEEE Trans. Appl. Supercond.
**2019**, 29, 3600105. [Google Scholar] - Guo, Z.; Li, J.; Zhou, D. Study of a Null-Flux Coil Electrodynamic Suspension Structure for Evacuated Tube Transportation. Symmetry
**2019**, 11, 1239. [Google Scholar] - He, J.L.; Rote, D.M.; Coffey, H.T. Study of Japanese Electrodynamic-Suspension Maglev Systems; Report, ANL/ESD-20; Argonne National Laboratory: Argonne, IL, USA, 1994. [Google Scholar]
- Nonaka, S.; Hirosaki, T.; Kawakami, E. Analysis of characteristics of repulsive magnetic levitated train using a space harmonic technique. Electr. Eng. Jpn.
**1980**, 100, 80–88. [Google Scholar] [CrossRef] - Fujimoto, T.; Aiba, M.; Suzuki, H.; Umeki, T.; Nakamura, S. Characteristics of Electromagnetic Force of Ground Coil for Levitation and Guidance at the Yamanashi Maglev Test Line. Q. Rep. RTRI
**2000**, 41, 63–67. [Google Scholar] [CrossRef] - Song, M.; Zhou, D.; Yu, P.; Zhao, Y.; Wang, Y.; Tan, Y.; Li, J. Analytical Calculation and Experimental Verification of Superconducting Electrodynamic Suspension System Using Null-Flux Ground Coils. IEEE Trans. Intell. Transp. Syst.
**2022**, 23, 14978–14989. [Google Scholar] [CrossRef] - Powell, J.R.; Danby, G.T. Dynamically Stable Cryogenic Magnetic Suspensions for Vehicles in Very High Velocity Transport Systems. In Proceedings of the 6th Annual Meeting of Society of Engineering Science, Princeton, NJ, USA, 11–13 November 1968. [Google Scholar]
- Franca, T.N. Study of Electrodynamic Levitation Applied to Maglev Vehicles. Master’s Thesis, The Alberto Luiz Coimbra Institute for Graduate Studies and Research in Engineering (COPPE), Federal University of Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil, March 2019. Available online: http://www.pee.ufrj.br/index.php/pt/producaoacademica/dissertacoes-de-mestrado/2019-1/2016033359–172/file (accessed on 10 January 2020).
- Grover, F.W. Inductance Calculations: Working Formulas and Tables; Instrument Society of America: Research Triangle Park, NC, USA, 1973. [Google Scholar]
- Machado, K.D. Teoria do Eletromagnetismo 3 [Theory of Electromagnetism 3]; UEPG Publisher: Ponta Grossa, Brazil, 2002. [Google Scholar]
- Zhu, H.; Huang, H.; Zheng, J.; Shi, H.; Xiang, Y.; Li, K. A Numerical Calculation Model of Multi-Magnet-Array and 8-Shaped Null-Flux Coil for Permanent Magnet EDS Vehicle System. IEEE Trans. Magn.
**2022**, 58, 8300311. [Google Scholar] - Cai, Y.; Ma, G.; Wang, Y.; Gong, T.; Liu, K.; Yao, C.; Yang, W.; Zeng, J. Semianalytical Calculation of Superconducting Electrodynamic Suspension Train Using Figure-Eight-Shaped Ground Coil. IEEE Trans. Appl. Supercond.
**2020**, 30, 3602509. [Google Scholar] [CrossRef] - Li, H.; Zhu, H.; Huang, H.; Li, H.; Deng, Z.; Zheng, J. A new suppression strategy of pitching vibration based on the magnetic-electric-mechanical coupling dynamic model for superconducting EDS transport system. Mech. Syst. Signal Process.
**2023**, 188, 110039. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Diagram of the main components of the JR–Maglev, Yamanashi test track. PC: propulsion coil. MS: mechanical suspension. SC: superconducting coil. 8C: figure-eight-shaped coil. (

**b**) Sketch of the null-flux coils. (

**c**) Equivalent electrical circuit. The numbers 1 and 2 refer to the upper and lower loops of the coil, respectively [41].

**Figure 2.**(

**a**) Conventional notation used in Maglev systems. Sketch of SC and 8-shaped coils. (

**b**) Dimensional drawing of the current 8-shaped and SC coils from the Yamanashi test track.

**Figure 4.**(

**a**) Specifications of the hardware used for numerical calculation, a desktop computer. (

**b**) Specifications of the hardware used for the simulation of the EDS circuit, a laptop.

**Figure 5.**The mutual inductance between the SC and 8-shaped coils depends on their relative positions.

**Figure 6.**Circuit implemented in Ansys${}^{\circledR}$ Twin Builder software. The indices 1, 2, and sc refer to the upper and lower loops of the 8-shaped and the SC coil, respectively. Data: data tables with mutual inductances ${M}_{s1}$ and ${M}_{s2}$.

**Figure 7.**Electric current induced in the 8-shaped coil fed by one SC coil for five different speeds.

**Figure 8.**The electrical circuit implemented in the Ansys${}^{\circledR}$ Twin Builder software, along with the respective force curves generated as a function of time for a cruising speed of v = 600 km/h. The red, green, and blue lines represent drag, lift, and guidance forces, respectively.

**Figure 12.**The electric current induced in one 8-shaped coil fed by one SC coil for six different air gaps.

**Figure 16.**Levitation and drag forces as a function of displacement speed. A comparison between the model utilizing the circuit simulator and experimental measurements conducted on the Yamanashi test line. The configuration consists of four SC coils onboard and twenty 8-shaped coils on the guideway.

**Figure 17.**Guiding force as a function of train travel speed. A comparison between the model using the circuit simulator and experimental measurements obtained from the Yamanashi test line. The setup includes four SC coils onboard and twenty 8-shaped coils on the guideway.

**Figure 18.**The electrical equivalent circuit of an 8-shaped coil powered by three SC coils, forming a null-flux EDS system at a cruising speed of v = 600 km/h, was implemented in the Ansys${}^{\circledR}$ Twin Builder software, which also displays the respective force curves generated as a function of time. The red, green, and blue lines represent drag, lift, and guidance forces, respectively.

Physical Parameter | Value | Unit |
---|---|---|

Width × height, 8-shaped coil | $0.35\times 0.34$ | m × m |

Number of turns, 8-shaped coil | 24 | units |

Resistance, 8-shaped coil (1 loop) | $8.99$ ^{1} | m$\Omega $ |

Inductance, 8-shaped coil (1 loop) | $287.26$ ^{1} | $\mathsf{\mu}$H |

Mutual inductances ^{2} | $21.22$ ^{1} | $\mathsf{\mu}$H |

Distance between centers ^{2} | $0.42$ | m |

Pole pitch, 8-shaped coil | $0.45$ | m |

Air gap between SC and 8-shaped coil | $0.185$ | m |

${z}_{0}$ equilibrium position | $0.0366$ | m |

Width × height, SC coil | $0.963\times 0.5$ | m × m |

Magnetomotive force, SC coil | 700 | kAturn |

Inductance, SC coil | $2.7$ | H |

Pole pitch, SC coil | $1.35$ | m |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

França, T.N.; Li, H.; Zhu, H.; Shi, H.; Liang, L.; Deng, Z.
Electrical Circuits Simulator in Null-Flux Electrodynamic Suspension Analysis. *Appl. Sci.* **2023**, *13*, 6666.
https://doi.org/10.3390/app13116666

**AMA Style**

França TN, Li H, Zhu H, Shi H, Liang L, Deng Z.
Electrical Circuits Simulator in Null-Flux Electrodynamic Suspension Analysis. *Applied Sciences*. 2023; 13(11):6666.
https://doi.org/10.3390/app13116666

**Chicago/Turabian Style**

França, Thaís N., Hengda Li, Hanlin Zhu, Hongfu Shi, Le Liang, and Zigang Deng.
2023. "Electrical Circuits Simulator in Null-Flux Electrodynamic Suspension Analysis" *Applied Sciences* 13, no. 11: 6666.
https://doi.org/10.3390/app13116666