# Design and Numerical Study of Magnetic Energy Storage in Toroidal Superconducting Magnets Made of YBCO and BSCCO

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{c}(B, T). More precisely, the critical current density of a HTS material is influenced by parallel and perpendicular components of the magnetic fields, and also by the critical temperature. If one of these parameters exceeds critical values established by experimental measurements, the superconducting state disappears. Shi and Liang [11] present a comparative analysis of anisotropy both in its own field and in perpendicular and parallel magnetic fields. Therefore, in superconducting wires, the current densities are not uniformly distributed because of the screening currents that affect them. They present different methods for determining anisotropy. Determining the J(B) characteristics of superconducting materials is not easy task. In [12] Nugteren presents an empirical relationship for calculating the critical current.

_{2}Ca

_{3}Cu

_{4}O

_{10+δ}(Cu-1234) that has a relatively high superconducting transition temperature Tc of about 116 K at the ambient pressure, low crystallographic anisotropy and absence of toxic elements. It has a high value of the critical current density Jc of about 10

^{4}A/cm

^{2}at 77 K. The above features make the Cu-1234 a promising high-temperature superconductor (HTS) from a practical perspective. In a power grid, many problems occur, such as power outages, high power losses, voltage sags and low voltage stability, which are caused by the variable nature of renewable power generation and the large variations in load demand. In order to solve them, a distribution system has been designed in [15], using both short- and long-term energy storage systems composed of a super-conducting magnetic energy storage (SMES) and a pumped-hydro energy storage (PHES). The paper presents a metaheuristic-based optimization method to find the optimal size of a hybrid solar PV-biogas generator with SMES–PHES in the distribution system, and also a financial evaluation.

## 2. Toroidal Superconducting Coil

- -
- Coil geometry;
- -
- Stored energy.

- R—Major coil radius;
- r—Inner radius of a module;
- g—Thickness of a module;
- h—Height of a module.

_{c}. It can be expressed using the following parameters: stored magnetic energy ${\mathrm{W}}_{\mathrm{m}\mathrm{a}\mathrm{g}}$, peak value of the magnetic flux density ${\mathrm{B}}_{\mathrm{p}}$, internal radius r, I the operating current and ${\mu}_{0}$ the relative magnetic permeability of the vacuum. The following expression was obtained for the superconductor length L

_{c}[17]:

_{out}, respectively.

#### 2.1. Modularity of the Toroidal Magnet

_{2}Cu

_{3}O

_{3}, or YBCO-123 [18]. One of the most important constraint for the SMES design systems is the dimensions of the modular coils so they could be transported by conventional rail over the highways or integrated with other technological instruments. These short solenoids, must be assembled into a toroidal ring of a certain major diameter after they are delivered to the location. The most compact toroid is the most efficient. Considering the solenoid geometry, the current carrying capacity is reduced by the transverse field at the coil’s ends. This problem is avoided in a toroid. There is no edge effect and the B field is only longitudinal in a perfect torus [19,20,21].

#### 2.2. YBCO vs. BISCCO 2223 Superconductors

_{2}Cu

_{3}O

_{7−x}(also known as Y123). It is a second generation (2G) HTS materials based on thin films of an yttrium barium copper oxide YBa

_{2}Cu

_{3}O

_{3.}It was discovered in 1987 by Paul Chu at the University of Houston. It shows the highest critical temperature T

_{c}of 93 K. YBCO is highly studied as it is the cleanest and most ordered crystal and shows strong electron–electron interaction. At 77 K the 2G wire keeps its critical current density Jc at much higher magnetic fields than the 1G wire. The high-temperature superconductor YBCO is a promising candidate for high-field-magnet generation as it has high-critical temperature and an upper critical field over 100 T. The 2G wire has a significantly different architecture compared to the 1G wire. Unlike the 1G wire, the 2G wire did not employ noble metals like silver, which is still the main drawback for achieving a low-cost 1G wire. The main benefits of 2G wires are the perspective of two to three times cost reduction due to the higher critical current (Ic) and a lower manufacturing cost using automation [22]. In 2021, SuperOx, a Russian and Japanese company, developed a new manufacturing process for making YBCO wire for fusion reactors, drastically improving the production capacity. They used a plasma-laser deposition process on an electro polished substrate to make 12 mm width tape and then splice it into 3 mm tape [22].

_{2}Sr

_{2}Ca

_{n}

_{−1}Cu

_{n}O

_{2n+4+x}, the most studied compound being when n = 2. It was the first high-temperature superconductor that did not contain a rare earth element, and it is a type-II superconductor. BSCCO was a new class of superconductor discovered around 1988 by Hiroshi Maeda and colleagues at the National Research Institute for Metals in Japan [23]. It has a critical temperature of 108 K. Typical tapes of 4 mm width and 0.2 mm thickness support a current of 200 A at 77 K, reaching a critical current density in the Bi-2223 filaments of 5 kA/mm

^{2}. This value increases rapidly as the temperature is lower so that many applications are implemented at 30–35 K, even the critical temperature T

_{c}is 108 K. For BSSCO, the most commonly used method is to enclose the ceramic grains in a silver or silver-alloy matrix through a process called “Powder In Tube”. BSCCO powder is placed in silver or silver-alloy tubes. These tubes are then drawn to obtain small wires, which are stacked together and laminated to obtain a tape. The tape is then submitted to heat treatment for the BSCCO to obtain superconducting characteristics. Figure 2a,b show the structure of a tape for the two superconducting materials. The previously mentioned materials also present a disadvantage due to the presence of the magnetic anisotropy. More precisely, their superconducting state is strongly influenced by the direction of the generated magnetic field. When the field direction is perpendicular to the c-axis, the critical field reaches its peak value. As the angle between the field direction and the c axis is gradually reduced, the critical current drops. Figure 3 shows both the axes a, b and c as well as the vector representation of perpendicular and parallel magnetic field in a module of the modular torus [24]. Figure 4a,b illustrate the critical currents as functions of magnetic fields at a temperature of 20 K for previously described superconductors. Table 1 shows the critical values of the materials used in designing the energy storage coil. In practice, the effect of anisotropy must be considered when design the SMES coil. The superconducting wire is rotated at an angle of 360 degrees to create a torus module. Thus, when a current is passed through it, the direction of the magnetic field created by it changes from being parallel to the axis of the coil to perpendicular. Thus, the angle between the lines of the magnetic field and the axis is reduced from 90 degrees to 0 and vice versa. The values of the magnetic field must thus remain below the critical value, but very close to it for high efficiency operation [25].

## 3. SMES Design

#### 3.1. Algorithm Chart

_{c}) as a function of magnetic field (B) at different temperatures I

_{c}(B) for YBCO and BSCCO, the values for the maximum magnetic field and the supply current are obtained. These values must be chosen below the critical values of the respective material. In the present case, the maximum value of the 2T magnetic field is imposed for both materials, and the current values for YBCO is I = 400 A for BSCCO is 500 A. The next step consists of introducing the initial data into the problem (stored energy, radius of the modular coil, number of modules and the height of a module). With these data, and using the relationship for the magnetic energy (the imposed value of the stored magnetic energy W

_{mag}= 2.5 MJ), the value of the external radius of the toroidal coil module (R

_{out}) is obtained. This is composed of the inner radius r and the thickness of the module g (R

_{out}= r + g). Using the previous geometrical and electrical data, a numerical verification of the stored magnetic energy and of the perpendicular magnetic field is performed. The numerical verification means a Comsol simulation. If these numerical values, verify the condition (W

_{mag}≤ 2.5 MJ and B_⊥ < B

_{c}) then the next step is followed. It consists of a parametric analysis to choose the best possible performance of the coil. Otherwise, the external radius r of the coil module is increased. Regarding the parametric analysis, it is based on two parameters: r and g. Their variation is carried out over a range of 0–40 mm for g and 0–70 for r. These combinations of the two parameters are chosen so that the volume of the superconducting material remains constant and the stored magnetic energy is calculated for these values. If a lower energy value is obtained than the one imposed, the algorithm ends. Otherwise, the number of modules is reduced by one unit and the stored energy is calculated again until a value closed to the required one is reached. In this case, the algorithm provides the geometric data of the coil with the best efficiency.

#### 3.2. Numerical Modelling

_{out}= r + g) are obtained

_{out}= 590 mm

_{out}= 560 mm

#### 3.3. Parametric Analysis

## 4. Results

#### Energy vs. Number of Modules

## 5. Discussions

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Lee, C.-C.; Hsin, Y.-M.; Dai, S.-C.; Kuo, C.-C. Optimal Modeling for Dynamic Response of Energy Storage Systems. Appl. Sci.
**2023**, 13, 4943. [Google Scholar] [CrossRef] - Chandel, T.A. Hybrid Energy Storage Systems for Renewable Energy Integration and Application. In AI Techniques for Renewable Source Integration and Battery Charging Methods in Electric Vehicle Applications; IGI Global: Hershey, PA, USA, 2023. [Google Scholar] [CrossRef]
- Park, M.J.; Kwak, S.Y.; Lee, S.W.; Kim, W.S.; Hahn, S.Y.; Choi, K.D.; Hand, J.H.; Lee, J.K.; Jung, H.K.; Seong, K.C.; et al. Designing of Superconducting Magnets for a 600 KJ SMES. Prog. Supercond.
**2006**, 8, 113–118. [Google Scholar] - Park, C.; Song, J.-B.; Lee, H.; Choi, K. Design of HTS magnets for a 2.5 MJ SMES. IEEE Trans. Appl. Supercond.
**2009**, 19, 1985–1988. [Google Scholar] - Jubleanu, R.; Cazacu, D.; Bizon, N. Hybrid energy storage–a brief overview. In Proceedings of the 13th International Conference on Electronics, Computers and Artificial Intelligence (ECAI), Pitesti, Romania, 1–3 July 2021; pp. 1–15. [Google Scholar]
- Xia, Y.; Song, M.; Ma, T. Electro-Magnetic Design of a 3MJ YBCO Magnet. IOP Conf. Ser. Mater. Sci. Eng.
**2020**, 768, 062096. [Google Scholar] [CrossRef] - Morandi, A.; Fabbri, M.; Gholizad, B.; Grilli, F.; Sirois, F.; Zermeno, V.M.R. Design and comparison of a 1-MW/5-s HTS SMES with toroidal and solenoidal geometry. IEEE Trans. Appl. Supercond.
**2016**, 26, 5700606. [Google Scholar] [CrossRef] - Mukherjee, P.; Rao, V.V. Optimization of HTS Superconducting Solenoid Magnet Dimensions for Maximum Energy Density. J. Supercond. Nov. Magn.
**2020**, 33, 2649–2656. [Google Scholar] [CrossRef] - Uglietti, D. A review on commercial HTS materials for large magnets: From wires and tapes to cables and conductors. Supercond. Sci. Technol.
**2019**, 32, 053001. [Google Scholar] [CrossRef] - Tsuchiya, K.; Kikuchi, A.; Terashima, A.; Norimoto, K.; Uchida, M.; Tawada, M.; Masuzawa, M.; Ohuchi, N.; Wang, X.; Takao, T.; et al. Critical current measurement of commercial REBCO conductors at 4.2 K. Cryogenics
**2017**, 85, 1–7. [Google Scholar] [CrossRef] - Shi, S.; Liang, R. Numerical Analysis of REBCO High-Temperature Superconducting (HTS) Coils Based on Screening Effect. J. Supercond. Nov. Magn.
**2022**, 35, 3487–3496. [Google Scholar] [CrossRef] - van Nugteren, J. High Temperature Superconductor Accelerator Magnets. Ph.D. Thesis, Universiteit Twente, Enschede, The Netherlands, 10 November 2016. [Google Scholar]
- Li, Y.; Pu, C.; Zhou, D. Structure, Stability, and Superconductivity of Two-Dimensional Janus NbSH Monolayers: A First-Principle Investigation. Molecules
**2023**, 28, 5522. [Google Scholar] [CrossRef] - Lynnyk, A.; Puzniak, R.; Shi, L.; Zhao, J.; Jin, C. Superconducting State Properties of CuBa
_{2}Ca_{3}Cu_{4}O_{10+δ}. Materials**2023**, 16, 5111. [Google Scholar] [CrossRef] [PubMed] - Agajie, T.F.; Fopah-Lele, A.; Ali, A.; Amoussou, I.; Khan, B.; Elsisi, M.; Nsanyuy, W.B.; Mahela, O.P.; Álvarez, R.M.; Tanyi, E. Integration of Superconducting Magnetic Energy Storage for Fast-Response Storage in a Hybrid Solar PV-Biogas with Pumped-Hydro Energy Storage Power Plant. Sustainability
**2023**, 15, 10736. [Google Scholar] [CrossRef] - Dimitrov, I.K.; Zhang, X.; Solovyov, V.F.; Chubar, O.; Li, Q. Rapid and Semi-analytical Design and Simulation of a Toroidal Magnet Made with YBCO and MgB
_{2}Superconductors. IEEE Trans. Appl. Supercond.**2015**, 25, 5701208. [Google Scholar] [CrossRef] - Lieurance, D.W. Global cost optimization of 1–10 MWh toroidal SMES. IEEE Trans. Appl. Supercond.
**1997**, 7, 14–17. [Google Scholar] [CrossRef] - Sunwong, P.; Higgins, J.S.; Tsui, Y.; Raine, M.J.; Hampshire, D.P. The critical current density of grain boundary channels in polycrystalline HTS and LTS superconductors in magnetic fields. Supercond. Sci. Technol.
**2013**, 26, 095006. [Google Scholar] [CrossRef] - Hassenzahl, W.V.; Hazelton, D.W.; Johnson, B.K.; Komarek, P.; Noe, M.; Reis, C.T. Electric power applications of superconductivity. Proc. IEEE
**2004**, 92, 1655–1674. [Google Scholar] [CrossRef] - Noguchi, S.; Ishiyama, A.; Akita, S.; Kasahara, H.; Tatsuta, Y.; Kouso, S. An optimal configuration design method for HTS-SMES coils. IEEE Trans. Appl. Supercond.
**2005**, 15, 1927–1930. [Google Scholar] [CrossRef] - Tixador, P. Superconducting magnetic energy storage: Status and perspective. In Proceedings of the IEEE/CSC & ESAS European Superconductivity News Forum, 2008. Available online: https://snf.ieeecsc.org/abstracts/cr5-superconducting-magnetic-energy-storage-status-and-perspective (accessed on 10 July 2023).
- Molodyk, A.; Samoilenkov, S.; Markelov, A.; Degtyarenko, P.; Lee, S.; Petrykin, V.; Gaifullin, M.; Mankevich, A.; Vavilov, A.; Sorbom, B.; et al. Development and large volume production of extremely high current density YBa
_{2}Cu_{3}O_{7}superconducting wires for fusion. Sci. Rep.**2021**, 11, 2084. [Google Scholar] [CrossRef] [PubMed] - Maeda, H.; Tanaka, Y.; Fukutomi, M.; Asano, T. A New High-Tc Oxide Superconductor without a Rare Earth Element. Jpn. J. Appl. Phys.
**1988**, 27, L209. [Google Scholar] [CrossRef] - Zimmermann, A.W. Design of a High Temperature Superconducting Coil for Energy Storage Applications; Faculty of Engineering and Physical Sciences: Southampton, UK, 2021. [Google Scholar]
- Strickland, N.M.; Wimbush, S.C. The Magnetic-Field Dependence of Critical Current: What We Really Need to Know. In IEEE Transactions on Applied Superconductivity; IEEE: Southampton, UK, 2017; Volume 27, pp. 1–5. [Google Scholar] [CrossRef]
- Turrioni, D.; Barzi, E.; Lamm, M.J.; Yamada, R.; Zlobin, A.V.; Kikuchi, A. Study of HTS Wires at High Magnetic Fields. Appl. Supercond. IEEE Trans.
**2009**, 19, 3057–3060. [Google Scholar] [CrossRef] - Osamura, K. Standardization of Test Methods for Practical Superconducting Wires. In Proceedings of the IEEE/CSC & ESAS European Superconductivity News Forum, No. 33, January 2015. Available online: https://snf.ieeecsc.org/abstracts/st446-standardization-test-methods-practical-superconducting-wires (accessed on 10 July 2023).
- Zheng, J.; Peng, S.S.; Li, W.Y.; Dai, Y.J. Magnet design of 10MJ multiple solenoids SMES. IOP Conf. Ser. Earth Environ. Sci.
**2019**, 233, 032026. [Google Scholar] [CrossRef] - Yi, K.-P.; Ro, J.-S.; Lee, S.; Lee, J.-K.; Seong, K.-C.; Choi, K.; Jung, H.-K.; Hahn, S. A Design Methodology for Toroid-Type SMES Using Analytical and Finite-Element Method. IEEE Trans. Appl. Supercond.
**2013**, 23, 4900404. [Google Scholar] [CrossRef] - Cazacu, D.; Jubleanu, R. Superconducting Magnetic Energy Storage in Power Grids-Chapter 2 Overview of SMES Technology; The Institution of Engineering and Technology: London, UK, 2022; ISBN 978-1-83953-500-0. e-ISBN 978-1-83953-501-7. [Google Scholar] [CrossRef]
- Cazacu, D.; Jubleanu, R.; Bizon, N.; Monea, C. Comparative numerical analysis of the stored magnetic energy in cylindrical and toroidal superconducting magnetic coils. In Proceedings of the 11th International Conference on Electronics, Computers and Artificial Intelligence (ECAI), Pitesti, Romania, 27–29 June 2019; pp. 1–5. [Google Scholar]
- Jubleanu, R.; Cazacu, D.; Bizon, N. Theoretical and Numerical Aspects Concerning the Stress in a Superconducting Solenoid. In Proceedings of the 2020 IEEE 26th International Symposium for Design and Technology in Electronic Packaging (SIITME), Pitesti, Romania, 21–24 December 2020; pp. 430–433. [Google Scholar] [CrossRef]
- Jubleanu, R.; Cazacu, D.; Bizon, N. Stress in cylindrical and toroidal superconducting coils. In Proceedings of the 2020 12th International Conference on Electronics, Computers and Artificial Intelligence (ECAI), Bucharest, Romania, 25–27 June 2020; pp. 1–6. [Google Scholar] [CrossRef]
- Sirois, F.; Grilli, F. Potential and limits of numerical modelling for supporting the development of HTS devices. arXiv
**2017**, arXiv:1412.2312v3. [Google Scholar] [CrossRef] - Dutoit, B.; Grilli, F.; Sirois, F. Numerical Modeling of Superconducting Applications; World Scientific Series in Applications of Superconductivity and Related Phenomena; World Scientific Publishing Company: Singapore, 2023. [Google Scholar]
- Berrospe-Juarez, E.; Trillaud, F.; Zermeño, V.M.R.; Grilli, F. Advanced electromagnetic modeling of large-scale high-temperature superconductor systems based on H and T-A formulations. Supercond. Sci. Technol.
**2021**, 34, 044002. [Google Scholar] [CrossRef] - Huber, F.; Song, W.; Zhang, M.; Grilli, F. The T-A formulation: An efficient approach to model the macroscopic electromagnetic behaviour of HTS coated conductor applications. Supercond. Sci. Technol.
**2022**, 35, 043003. [Google Scholar] [CrossRef] - Kapolka, M.; Zermeno, V.M.R.; Zou, S.; Morandi, A.; Ribani, P.L.; Pardo, E.; Grilli, F. 3D Modeling of the Magnetization of Superconducting Rectangular-Based Bulks and Tape Stacks. arXiv
**2017**, arXiv:1709.09548v2. [Google Scholar] - Usoskin, A.; Betz, U.; Gnilsen, J.; Noll-Baumann, S.; Schlenga, K. Long-length YBCO coated conductors for ultra-high field applications: Gaining engineering current density via pulsed laser deposition/alternating beam-assisted deposition route. Supercond. Sci. Technol.
**2019**, 32, 094005. [Google Scholar] [CrossRef] - Kagiyama, T.; Kobayashi, S.-I.; Yamazaki, K.; Kikuchi, M.; Yamade, S.; Nakashima, T.; Hayashi, K.; Sato, K.-I.; Shimoyama, J.-I.; Kitaguchi, H. Recent R&D progress on DI-BSCCO wires with high critical current properties. Phys. Procedia
**2012**, 27, 256–259. [Google Scholar]

**Figure 7.**(

**a**) Perpendicular magnetic field for both materials; (

**b**) Parallel magnetic field for both materials.

Parameter | Superconducting Material | |
---|---|---|

YBCO | BSCCO | |

Critical temperature [K] | 20 | 20 |

Operating current [A] | 420 | 510 |

Peak value magnetic field [T] | 2 | 2 |

Critical tensile strength [MPa] | 600 | 130 |

**Table 2.**Toroidal coil parameters [16].

Parameter | Value |
---|---|

Stored energy | ${\mathrm{W}}_{\mathrm{m}\mathrm{a}\mathrm{g}}$ = 2.5 MJ |

Major radius of the torus | R = 1000 mm |

Module internal radius | r = 200 mm |

Number of modules | N_{m} = 16 |

The height of a module | h = 96 mm |

Coil Material | Stored Magnetic Energy [MJ] | Length of Conductor [Km] | Specific Energy [J/m] |
---|---|---|---|

YBCO | 2.48 | 36.19 | 68.5 |

BSCCO | 2.53 | 28.14 | 89.9 |

Materials | No.of Modules | Configuration | Stored Energy [MJ] | Conductor Length [km] |
---|---|---|---|---|

YBCO | 16 | r = 200/g = 390 | 2.48 | 36.19 |

r= 265.14/g = 350 | 3.23 | 36.19 | ||

15 | r = 265.14/g =350 | 2.88 | 33.93 | |

14 | r = 265.14/g = 350 | 2.55 | 31.67 | |

BSCCO | 16 | r = 200/g = 360 | 2.53 | 28.14 |

r = 267.5/g = 320 | 3.36 | 28.14 | ||

15 | r = 267.5/g = 320 | 2.94 | 26.39 | |

14 | r = 267.5/g = 320 | 2.66 | 34.64 |

Material | Design | r [mm] | g [mm] | No. of Modules | Stored Energy [MJ] | Superconductor Length [Km] | Analytical Length Equation (4) [Km] | Relative Error [%] |
---|---|---|---|---|---|---|---|---|

YBCO | Initial | 200 | 390 | 16 | 2.48 | 36.19 | 27.87 | 29.85 |

Final | 265.14 | 350 | 14 | 2.55 | 31.67 | 27.87 | 13.63 | |

BSCCO | Initial | 200 | 360 | 16 | 2.53 | 28.14 | 22.92 | 22.7 |

Final | 267.5 | 320 | 14 | 2.66 | 24.64 | 22.92 | 7.5 |

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**MDPI and ACS Style**

Jubleanu, R.; Cazacu, D.
Design and Numerical Study of Magnetic Energy Storage in Toroidal Superconducting Magnets Made of YBCO and BSCCO. *Magnetochemistry* **2023**, *9*, 216.
https://doi.org/10.3390/magnetochemistry9100216

**AMA Style**

Jubleanu R, Cazacu D.
Design and Numerical Study of Magnetic Energy Storage in Toroidal Superconducting Magnets Made of YBCO and BSCCO. *Magnetochemistry*. 2023; 9(10):216.
https://doi.org/10.3390/magnetochemistry9100216

**Chicago/Turabian Style**

Jubleanu, Radu, and Dumitru Cazacu.
2023. "Design and Numerical Study of Magnetic Energy Storage in Toroidal Superconducting Magnets Made of YBCO and BSCCO" *Magnetochemistry* 9, no. 10: 216.
https://doi.org/10.3390/magnetochemistry9100216