# Critical Current Degradation in HTS Tapes for Superconducting Fault Current Limiter under Repeated Overcurrent

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## Abstract

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## 1. Introduction

_{C}.

- Generator or transformer feeder, busbar coupling, and power plant auxiliaries. It brings the following benefits: improvement in stability and circuit breakers, and switchgear components do not need to be replaced [21];

## 2. Characteristics of the Tested Materials

## 3. Measuring System, Method, and Scope of Research

#### 3.1. Measuring System

#### 3.2. Methods of Research

_{p}) is the current that would flow in the considered circuit if the SFCL did not limit it. On the other hand, due to the HTS tape leaving the superconducting state, the expected short-circuit current is limited. The highest possible instantaneous value of the short-circuit current is the surge current (I

_{0max}). When limiting the expected short-circuit current, due to the dynamics of the process of transition of the tape to the resistive state, the surge current (I

_{0max}) may significantly exceed the value of the critical current (I

_{C}). This process takes place in a few milliseconds. During the operation of the SFCL, there is a gradual increase in the voltage on the tape and a decrease in the current value due to the increase in temperature and, thus, the resistance of the tape. As a result of SFCL operation, the current is limited to the value I

_{lim}, and I

_{min}is the amplitude of the current limited at the end of the test pulse; U

_{max}is the maximum voltage on the HTS tape at the end of the test impulse. Figure 6 shows the principle of short-circuit containment by SFCL.

#### 3.2.1. Determination of the Critical Current of HTS Tapes

_{C}) values of HTS tapes provided by manufacturers are determined with direct current forcing [39]. The method of determining the critical current with a sinusoidal excitation with a frequency of 50 Hz is shown in Figure 7.

_{C}) of the tested HTS tape samples was assumed to be the minimum value of the test current amplitude initiating the sample’s exit from the superconducting state. The I

_{C}value was determined by gradually increasing the amplitude of the current I in the tested sample. For test currents (I) lower than the critical current (I

_{C}), the HTS current amplitude had a constant value, and the voltage on the sample had a negligible value related to the resistance of the junctions (Figure 7a). After the tape exited the superconducting state (I ≥ I

_{C}), the voltage on the sample increased and the current decreased (Figure 7b).

#### 3.2.2. Determination of the Value of Surge and Limited Current and Voltage on the HTS Tape

_{min}.

_{0max}, I

_{min}, U

_{max}, and the energy released in the belt for various values of the test pulse were determined:

#### 3.3. Scope of Research

- Determination of the values characterizing the HTS tapes in the process of limiting the prospective short-circuit current (I
_{0max}, I_{min}) and changes in the critical current (I_{C}) value occurring as a result of multiple transitions of the tapes from the superconducting state. These values are important from the point of view of cooperation between SFCL and system protection; - Determination of the voltage (U
_{max}) and energy E released in the HTS tapes during the operation of the test current pulse for different values of the prospective short-circuit current; - Testing changes in quantities that characterize HTS tapes in conditions of multiple exposures to test currents;
- Determination of the safe range of voltage drops per unit length for both tapes for which the degradation of HTS tapes does not occur or is small;
- The above issues are important for determining the required length of the HTS tape in SFCL, operating at a specific rated voltage, so that the voltage drops on the HTS tape do not exceed the permissible values.

- Microstructural tests showed changes in the HTS tape due to the current impulses test. The cross-sectional surfaces of the tapes were examined using an atomic force microscope (AFM) and an optical microscope (OM).

## 4. Experimental Results

_{0max}, I

_{min}, U

_{max}, and E were obtained and are presented in Table 3.

#### 4.1. Study of Changes in the Value of Surge Currents as a Function of the Prospective Short-Circuit Current

_{p}was limited due to the HTS tape transition from the superconducting state to the value of the surge current I

_{0max}. The values of the surge currents for the eight values of the prospective short-circuit current for the tested HTS tapes are shown in Figure 8. The green line indicates the values of the prospective short-circuit current (I

_{p}). With the increase in the value of the prospective short-circuit current, the value of the surge current increased. The surge current reached lower values for the SF12100-CF tape with a 4 μm silver layer (Figure 8).

_{0max}) recorded on the samples reached values higher than the critical current of the tested HTS tape (which is related to the dynamics of the process of the tape transition from the superconducting state), which is shown in Figure 9a,b. The exit of the tape from the superconducting state was indicated by the appearance of a non-zero voltage value on the sample. The HTS tape transitioned to a resistive state, and the resistance of the tape gradually increased as a result of the heating of the sample due to the current flow (Figure 9). The prospective short-circuit current was limited and reached the value of the surge current I

_{0max}.

_{0max}value, the nucleate boiling phase begins. The temperature of the tape increases, but at the same time, a very intensive heat transfer from the HTS tape to nitrogen starts. A decrease in the current value and stabilization of the voltage value on the tape are observed, while the resistance of the tape increases very slightly. Then, in a very short period of time, there is a momentary increase in resistance (transition boiling). For both HTS tapes, the current and voltage values stabilization was observed from about 8 ms, corresponding to reaching the Leidenfrost point. The film boiling process begins with a linear relationship between the heat flow from the tape to liquid nitrogen.

#### 4.2. Study of Changes in the Value of the Minimum Currents Limited as a Function of the Prospective Short-Circuit Current

_{min}(Figure 11).

#### 4.3. Examination of Changes in Voltage Values and Energy Dissipated on HTS Tapes as a Function of the Prospective Short-Circuit Current

_{max}) is set on the sample. During the duration of the test impulse, energy (E) is released on the tape. The maximum values of voltage amplitudes (U

_{max}) on HTS tapes as a function of the prospective short-circuit current (I

_{p}) are shown in Figure 13. Slightly higher voltage values were recorded for the SF12100-CF tape with a 2 μm silver layer.

_{p}) are presented in Figure 14. The energy (E) values released on the samples of both HTS tapes are higher for the tape with a 4 µm silver layer.

_{max}). As the voltage on the samples increases, the amount of energy released increases. Due to the higher energy values and higher values of surge currents for the HTS tape with a 4 µm silver layer, worse working conditions of this tape in the resistive state can be expected. The tape heats up more as a result of the test current impulses, which may result in a change in the tape parameters.

#### 4.4. Examination of Changes in the Critical Current of HTS 2G Tapes as a Result of the Repeated Impact of Test Current Impulses

_{C}) of the HTS tapes for 8 different values of the prospective short-circuit current. Between the test current impulses, pauses allowed the system to return to thermal equilibrium and the state of superconductivity. The value of the critical current (I

_{C}) of the tested samples was measured for an unused sample (I

_{C}

_{0}) and then after 3 applications of the test current impulses and after applications 10 and 25. According to the manufacturer of HTS tapes, the values of the critical current (I

_{C}

_{0}) of new samples of HTS tapes may slightly differ, as was described in [33].

_{C}value dropped to 174 A.

_{C}drop below 3% for 3, 10, and 25 activations of the test current pulses). For the HTS tape with a 2 µm silver layer, similar I

_{C}changes were observed at energies of 90.73 J. For higher energy values, the degradation process was more noticeable. After 10 leads, the difference in the decrease in the critical current depending on the thickness of the silver layer was clearly marked. At the highest energies, after 10 leads, the 4 µm silver tape had a 7.55% decrease in I

_{C}and 4.08% for the 2 µm silver tape, and the 4 µm silver tape showed a 45.28% decrease in I

_{C}after 25 leads (it should be assumed that the tape has been damaged), while the 2 µm silver tape only decreased by 7.48%. For low values of prospective current (energy dissipated in the HTS tape), changes in the value of the critical current are negligible. This parameter degrades faster with the number of current test operations for higher energy values, which means the progressing process of thermal aging of the HTS tapes. The process is much more intensive for the HTS tape with a 4 µm silver layer due to the lower resistance value of the silver layer.

_{C}degradation does not occur or occurs only slowly. Paper [41] presents a numerical model of the HTS tape SF12100, based on which the permissible value of voltage drops for a current pulse of 0.2 s duration is 0.47 V/cm. The permissible value of voltage drops is an important design parameter that determines, among other things, the minimum length of the tape used in the SFCL while ensuring the safe operation of the device. In the paper [42], from the point of view of design assumptions, the permissible value of the voltage drop was 1 V/cm.

#### 4.5. Testing the Cross-Sectional Area of HTS Tapes

## 5. Conclusions

- In HTS tapes subjected to multiple test current pulses (corresponding to the values of the prospective short-circuit current), the value of the critical current decreases depending on the number of transitions from the superconducting state.
- The value of the critical current of the HTS tapes decreases with the increase in the value of the test impulse.
- Measurements of the energy released in the sample during the operation of the test impulse allow us to determine the permissible range of energy and voltage drops that practically do not change the value of the critical current or do not exceed the permissible values from the point of view of cooperation between the SFCL and the system protection.
- HTS tape with a silver layer of 4 µm thickness degrades very quickly above a certain energy value; therefore, a safe voltage drop range of 0.55 V/cm can be assumed, at which the drop in the critical current value does not exceed 3%.
- Decrease in the value of the critical current of the HTS tape due to multiple occurrences of a short circuit in the SFCL system should be considered at the design stage. It should be controlled during the operation of the SFCL.
- Morphological studies reveal that HTS tapes subjected to test current impulses (corresponding to the values of the prospective short-circuit current), causing their exit from the superconducting state, and show microdamage occurring in the superconducting layer and the boundary layer between the superconductor and silver in the form of bubbles, which may cause degradation.
- The observed microstructural changes in HTS 2G tapes due to the effect of test currents on the parameters of HTS tapes require further research and analysis. Future research will include an extension of microstructural studies and statistical studies.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Fault Current Limiters, Raport on the CIGRE WG A3.10. In Proceedings of the CIGRE WG 13.10. Available online: https://www.ewh.ieee.org/soc/pes/switchgear/presentations/tp_files/2003-2_Lunch_1_A3-10.pdf (accessed on 27 March 2023).
- Sung, B.C.; Park, D.K.; Park, J.W.; Ko, T.K. Study on a series resistive SFCL to improve power system tranient stability: Modeling, simulation, and experimental verification. IEEE Trans. Ind. Electron.
**2009**, 26, 2412–2419. [Google Scholar] [CrossRef] - Rao, V.V.; Kar, S. Superconducting Fault Current Limiters—A Review. Indian J. Cryog.
**2011**, 36, 14–25. [Google Scholar] - Nagarathna, M.C.; Murthy, H.V.; Shashikumar, R. A Review on Super Conducting Fault Current Limiter (SFCL) in Power System. Int. J. Eng. Res. Gen. Sci.
**2015**, 3, 485–489. [Google Scholar] - Gupta, V.; Trivedi, U.; Buch, N.J. Solid State Electronic Fault Current Limiter to Limit the Fault Current in Power System. Physics
**2010**. [Google Scholar] - Nelson, A.; Masur, L.; Moriconi, F.; De La Rosa, F.; Kirsten, D. Saturated-Core Current Limiter Field Experience at a Distribution Substation. In Proceedings of the 21st International Conference on Electricity Distribution, Frankfurt, Germany, 6–9 June 2011. [Google Scholar]
- Yadav, S.; Bharati, K.; Tewari, V. Sperconducting Fault Current Limiter—A Review. Int. J. Appl. Eng. Res.
**2019**, 14, 2. [Google Scholar] - Ganev, G.I.; Hinov, K.; Karadzhov, N. Fault current limiters-Principiales and application. Siela
**2012**, 2012, 54–56. [Google Scholar] - Alam, M.S.; Abido, M.A.Y.; El-Amin, I. Fault Current Limiters in Power Systems: A Comprehensive Review. Energies
**2018**, 11, 1025. [Google Scholar] [CrossRef] - Yang, B.; Kang, J.; Lee, S.; Choi, C.; Moon, Y. Qualification test of a 80 kV 500 MW HTS DC cable for applying into real grid. IEEE Trans. Appl. Supercond.
**2015**, 25, 5402705. [Google Scholar] [CrossRef] - Lee, S.J.; Yang, H.S. Recent Progresand Design of Three-Phase Coaxial HTS Power Cable in Korea. IEEE Trans. Appl. Supercond.
**2019**, 29, 1–5. [Google Scholar] - Marian, A.; Hole, S.; Lallouet, N.; Marzahn, E. Development of Hightemperature Superconductivity Transformers for Railway Applications. IEEE Trans. Appl. Supercond.
**2003**, 13, 2325–2330. [Google Scholar] - Yazdani-Asrami, M.; Sadeghi, A.; Seyyedbarzegar, S.; Song, W. Role of Insulation Materials and Cryogenic Coolants on Fault Performance of MW-Scale Fault-Tolerant Current-Limiting Superconducting Transformers. IEEE Trans. Appl. Supercond.
**2023**, 33, 1–15. [Google Scholar] [CrossRef] - Schlosser, R.; Schmidt, H.; Leghissa, M.; Meinert, M.; Bruzek, C.E. Development of high temperature superconducting transformers for railway applications. IEEE Electr. Insul. Mag.
**2020**, 36, 30–40. [Google Scholar] [CrossRef] - Song, W.; Jiang, Z.; Staines, M.; Badcock, R.A.; Zhang, J. Design of a single-phase 6.5 MVA/25 kV Superconducting traction transformer for Chinese Fuxing high-speed train. Int. J. Elect. Power Energy Syst.
**2020**, 119, 105956. [Google Scholar] [CrossRef] - Haran, K.S.; Kalsi, S.; Arndt, T.; Karmaker, H.; Badcock, R.; Buckley, B.; Haugan, T.; Izumi, M.; Loder, D.; Bray, J.W.; et al. High power density superconducting rotating machines—Development status and technology roadmap. Supercond. Sci. Technol.
**2017**, 30, 123002. [Google Scholar] [CrossRef] - Song, X.; Buhrer, C.; Brutsaert, P.; Krause, J.; Ammar, A.; Wiezoreck, J.; Hansen, J.; Rebsdorf, A.V.; Dhalle, M.; Bergen, A.; et al. Designing and basic experimental validation of the world’s first MW-class direct-drive superconducting wind turbine generator. IEEE Trans. Energy Convers.
**2019**, 34, 2218–2225. [Google Scholar] [CrossRef] - Bock, J.; Bludau, M.; Dommerque, R.; Hobl, A.; Kraemer, S.; Rikel, M.O.; Elschner, S. HTS Fault Current Limiters—First Commercial Devices for Distribution Level Grid in Europe. IEEE Trans. Appl. Supercond.
**2011**, 21, 1202–1205. [Google Scholar] [CrossRef] - Lee, S.; Yoon, J.; Yang, B.; Moon, Y.; Lee, B. Analisis model development and specification proposal of 154 kV SFCL for the application to a live grid in South Korea. Phys. C Supercond. Appl.
**2014**, 504, 148–152. [Google Scholar] [CrossRef] - Doukas, D.I.; Blatsi, Z.D.; Milioudis, A.N.; Labridis, D.P.; Harnefors, L. Damping of electromagnetic transients in a superconducting VSC transmission system. In Proceedings of the 2015 IEEE Eindhoven PowerTech, Eindhoven, The Netherlands, 29 June–2 July 2015; pp. 1–6. [Google Scholar]
- Noe, M.; Steurer, M. High-temperature superconductor fault current limiters: Concepts, applications, and development statuts. Supercond. Sci. Technol.
**2007**, 20, R15. [Google Scholar] [CrossRef] - Elshiekh, M.E.; Mansour, D.-E.A.; Azmy, A.M. Improving Fault Ride-Through Capability of DFIG-Based Wind Turbine Using Superconducting Fault Current Limiter. IEEE Trans. Appl. Supercond.
**2013**, 23, 5601204. [Google Scholar] [CrossRef] - Zou, Z.C.; Chen, X.Y.; Li, C.S.; Xiao, X.Y.; Zhang, Y. Conceptual Design and Evaluation of a Resistive-Type SFCL for Efficient Fault Ride Through in a DFIG. IEEE Trans. Appl. Supercond.
**2016**, 26, 1–9. [Google Scholar] [CrossRef] - Chen, L.; Li, G.; Chen, H.; Ding, M.; Zhang, X.; Li, Y.; Xu, Y.; Ren, L.; Tang, Y. Investigation of a Modified Flux-Coupling-Type SFCL for Low-Voltage Ride-Through Fulfillment of a Virtual Synchronous Generator. IEEE Trans. Appl. Supercond.
**2020**, 30, 5601006. [Google Scholar] [CrossRef] - Lee, H.Y.; Asif, M.; Park, K.H.; Lee, B.W. Feasible Application Study of Several Types of Superconducting Fault Current Limiters in HVDC Grids. IEEE Trans. Appl. Supercond.
**2018**, 28, 5601205. [Google Scholar] [CrossRef] - Lee, H.-Y.; Asif, M.; Park, K.-H.; Lee, B.-W. Assessment of appropriate SFCL type considering DC fault interruption in full bridge modular multilevel converter HVDC system. Phys. C Supercond. Appl.
**2019**, 563, 1–6. [Google Scholar] [CrossRef] - Xi, J.; Pei, X.; Song, W.; Niu, L.; Liu, Y.; Zeng, X. Integration of superconducting fault current limiter with solid-state DC circuit breaker. Int. J. Electr. Power Energy Syst.
**2023**, 145, 108630. [Google Scholar] [CrossRef] - Reddy, S.R.P.; Kar, S.; Rajashekara, K. Resistive SFCL Integrated Ultra-Fast DC Hybrid Circuit Breaker for Subsea HVDC Transmission Systems. In Proceedings of the 2021 IEEE Industry Applications Society Annual Meeting (IAS), Vancouver, BC, Canada, 10–14 October 2021; pp. 1–6. [Google Scholar]
- Moon, W.-S.; Won, J.-N.; Huh, J.-S.; Kim, J.-C. A Study on the Application of a Superconducting Fault Current Limiter for Energy Storage Protection in a Power Distribution System. IEEE Trans. Appl. Supercond.
**2013**, 23, 5603404. [Google Scholar] [CrossRef] - Yehia, D.M.; Mansour, D.-E.A. Modeling and analysis of superconducting fault current limiter for system integration of battery banks. IEEE Trans. Appl. Supercond.
**2018**, 28, 5603006. [Google Scholar] [CrossRef] - Choudhary, N.K.; Mohanty, S.R.; Singh, R.K. Protection coordination of over current relays in distribution system with DG and superconducting fault current limiter. In Proceedings of the 2014 Eighteenth National Power Systems Conference (NPSC), Guwahati, India, 18–20 December 2014. [Google Scholar]
- Asgharigovar, S.; Seyedi, H.; Parchehbaf Dibazari, S. Optimal coorination of overcurrent protection in the presence of SFCL and distributed generation. Turk. J. Electr. Eng. Comput. Sci.
**2018**, 26, 31. [Google Scholar] - SuperPower
^{®}2G HTS Wier Specyfications. Available online: https://www.superpower-inc.com (accessed on 1 July 2022). - Amaro, N.; Šouc, J.; Vojenčiak, M.; Pina, J.M.; Martins, J.; Ceballos, J.M.; Gömöry, F. AC Losses and material degradation effects in a superconducting tape for SMES applications. In Proceedings of the 5th IFIP WG 5.5/SOCOLNET Doctoral Conference on Computing, Electrical and Industrial Systems, DoCEIS 2014, Costa de Caparica, Portugal, 7–9 April 2014. [Google Scholar]
- Yazaki, S.; Karasawa, A.; Kotoyori, T.; Ishiyama, A.; Miyahora, N. Critical Current Degradation in High-Temperature Supeperconducting Tapes Caused by Temperature Rise. IEEE Trans. Appl. Supercond.
**2013**, 23, 4602304. [Google Scholar] [CrossRef] - Ishiyama, A.; Nishio, Y.; Ueda, H.; Kashima, N.; Mori, M.; Watanabe, T.; Nagaya, S.; Yagi, M.; Mukoyama, S.; Machi, T.; et al. Degradation Characteristics of YBCO-Coated Conductors Subjected to Overcurrent Pulse. IEEE Trans. Appl. Supercond.
**2009**, 19, 3483–3486. [Google Scholar] [CrossRef] - Xiong, X.; Lenseth, K.P.; Reeves, J.L.; Oiao, Y.; Schmidt, R.M.; Chen, Y.; Li, Y.; Xie, Y.; Selvamanckam, V. High Throughput Processing of Long-Length IBA MgO and Epi-Buffer Templates at SuperPower. IEEE Trans. Appl. Supercond.
**2007**, 17, 3375–3378. [Google Scholar] [CrossRef] - Buchmuller, I. Influence of Pressure on Leidenfrost Effect; Technische Universität: Darmstadt, Germany, 2014. [Google Scholar]
- Kim, A.-R. Development of Critical Current Measurement System of HTS Tape Using Pulsed Current. IEEE Trans. Appl. Supercond.
**2016**, 26, 9001504. [Google Scholar] [CrossRef] - Zhu, J.; Chen, S.; Jin, Z. Progress on Second-Generation High-Temperature Superconductor Tape Targeting Resistive Fault Current Limiter Application. Electronics
**2022**, 11, 297. [Google Scholar] [CrossRef] - Majka, M.; Kozak, J.; Kozak, S. HTS Tapes Selection for Superconducting Current Limiters. IEEE Trans. Appl. Supercond.
**2017**, 27, 5601405. [Google Scholar] [CrossRef] - Kar, S.; Rao, V. Step-by-step design of a single phase 3.3 kV/200 A resistive type superconducting fault current limiter (R-SFCL) and cryostat. Phys. C Supercond. Appl.
**2018**, 550, 107–116. [Google Scholar] [CrossRef]

**Figure 1.**The layer structure of HTS-2G SF12100-CF tapes [33].

**Figure 3.**The intensity of heat dissipation in liquid nitrogen as a function of the temperature difference between the sample and liquid nitrogen [38].

**Figure 7.**Waveforms of current and voltage for the HTS tape: (

**a**) sample in the superconducting state; (

**b**) sample in the resistive state.

**Figure 8.**The value of the surge current (I

_{0max}) as a function of the expected short-circuit current (I

_{p}) for the tested HTS tapes.

**Figure 9.**Example waveforms for the first period of test current pulses (ΔT = 20 ms) for HTS tapes: (

**a**) with a silver layer of 4 μm thickness and (

**b**) with a silver layer of 2 μm thickness.

**Figure 11.**The value of the minimum limited current (I

_{min}) as a function of the expected short-circuit current (I

_{p}) for the tested HTS tapes.

**Figure 12.**Increase in resistance (R) during the operation of the current impulse for the tested HTS tapes.

**Figure 13.**The voltage value (U

_{max}) on HTS tapes as a function of prospective short-circuit current (I

_{p}).

**Figure 14.**The values of energy (E) dissipated on HTS tapes as a function of the prospective short-circuit current (I

_{p}).

**Figure 15.**The dependence of the energy released in the tape as a function of the voltage set on the HTS tape (U

_{max}).

**Figure 16.**Dependences of the critical current value of the SF12100-CF tape with 4 µm silver as a function of the number of test current pulse activations for 3, 10, and 25 transitions from the superconducting state.

**Figure 17.**Dependences of the critical current value of the SF12100-CF tape with 2 µm silver as a function of the number of test current pulse activations for 3, 10, and 25 transitions from the superconducting state.

**Figure 18.**Decrease in the value of the critical current of the HTS 2G tape due to its transition from the superconducting state with test current impulses after 3, 10, and 25 transitions for the HTS tape SF12100-CF (4 µm silver) without electrical insulation.

**Figure 19.**Decrease in the value of the critical current of the HTS 2G tape due to its transition from the superconducting state with test current impulses after 3, 10, and 25 transitions for the HTS tape SF12100-CF (2 µm silver) without electrical insulation.

**Figure 21.**The images show cross-sections of tape samples obtained with an optical microscope: (

**a**) control sample (Lens: E500: ×1500) and (

**b**) sample subjected to surge currents (Lens: E500: ×700). The corresponding topographic maps are presented below (

**c**,

**d**).

**Figure 22.**AFM image of the HTS tape sample subjected to surge currents along with the cross-section in the place marked with red lines 1 and 2.

**Table 1.**Parameters of the tested tapes [33].

Tape | SF12100-CF | SF12100-CF |
---|---|---|

the thickness of the silver layer | 4 μm | 2 μm |

width | 12 mm | 12 mm |

thickness | 0.105 mm | 0.105 mm |

substrate thickness (Hastelloy) | 0.1 mm | 0.1 mm |

minimum critical current I_{Cmin} _{(77 K)} | 312 A | 281 A |

**Table 2.**Structure of buffer layers in tapes SF12100-CF [33].

Buffer Layers | Layer Thickness |
---|---|

alumina (Al_{2}O_{3}) | ~80 nm |

yttria YSZ | ~7 nm |

IBAD MgO | ~10 nm |

homo-epi MgO | ~20 nm |

LMO (LaMnO_{3}) | ~30 nm |

**Table 3.**The value of the surge current I

_{0ma}

_{x}, the minimum value of the limited current I

_{min}, the maximum value of the voltage on the sample U

_{max}, and energy E for HTS tapes SF12100-CF (4 μm and 2 μm silver).

Prospective Short-Circuit Current | SF12100—4 µm Silver I _{Cmin} _{(77 K)} = 312 A | SF12100—2 µm Silver I _{Cmin} _{(77 K)} = 281 A | ||||||
---|---|---|---|---|---|---|---|---|

I_{p} (A) | I_{0max} (A) | I_{min} (A) | U_{max} (V) | E (J) | I_{0max} (A) | I_{min} (A) | U_{max} (V) | E (J) |

675 | 527.2 | 195.7 | 4.1 | 83.3 | 504.6 | 154.5 | 4.4 | 74.1 |

810 | 577.8 | 203.7 | 5.1 | 112.8 | 517.4 | 160.0 | 5.5 | 97.4 |

945 | 617.4 | 212.5 | 6.1 | 145.7 | 535.7 | 162.2 | 6.5 | 119.0 |

990 | 636.7 | 222.2 | 6.4 | 158.5 | 545.3 | 163.7 | 6.8 | 129.1 |

1035 | 646.2 | 222.2 | 6.8 | 169.8 | 552.3 | 167.8 | 7.2 | 137.4 |

1080 | 662.6 | 223.5 | 7.1 | 181.5 | 555.9 | 169.5 | 7.4 | 145.1 |

1125 | 667.9 | 228.1 | 7.4 | 193.3 | 562.7 | 172.2 | 7.8 | 154.3 |

1170 | 683.3 | 230.2 | 7.7 | 207.0 | 565.3 | 172.2 | 8.1 | 163.6 |

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**MDPI and ACS Style**

Hajdasz, S.; Kempski, A.; Solak, K.; Marc, M.; Rusinski, J.; Szczesniak, P. Critical Current Degradation in HTS Tapes for Superconducting Fault Current Limiter under Repeated Overcurrent. *Appl. Sci.* **2023**, *13*, 4323.
https://doi.org/10.3390/app13074323

**AMA Style**

Hajdasz S, Kempski A, Solak K, Marc M, Rusinski J, Szczesniak P. Critical Current Degradation in HTS Tapes for Superconducting Fault Current Limiter under Repeated Overcurrent. *Applied Sciences*. 2023; 13(7):4323.
https://doi.org/10.3390/app13074323

**Chicago/Turabian Style**

Hajdasz, Sylwia, Adam Kempski, Krzysztof Solak, Maciej Marc, Jacek Rusinski, and Pawel Szczesniak. 2023. "Critical Current Degradation in HTS Tapes for Superconducting Fault Current Limiter under Repeated Overcurrent" *Applied Sciences* 13, no. 7: 4323.
https://doi.org/10.3390/app13074323