1. Introduction

Superconducting materials have the potential to revolutionize various industries due to their ability to carry significantly higher current densities than traditional conductors, enabling the development of compact and efficient devices. Furthermore, the absence of electrical resistance in superconductors reduces energy loss, leading to substantial cost savings during long-term operations. The evolution of high-temperature superconducting (HTS) tapes has seen the emergence of first-generation (1G) HTS tapes, which primarily consist of Bismuth compounds (Bi-2223 or Bi-2212) in a silver matrix, and second-generation (2G) HTS tapes, predominantly featuring Yttrium Barium Copper Oxide (YBCO) or Rare Earth Barium Copper Oxide (REBCO) compounds that are deposited as thin films on a flexible metal substrate^[1]. The superior characteristics of 2G HTS tapes, such as increased critical current density, enhanced performance under the influence of magnetic fields and strain, and more efficient, scalable manufacturing processes, have led to their growing popularity for various applications, including power transmission and medical superconducting accelerators. For example, a resistive 220kV high-temperature superconducting fault current limiter (HTSFCL) has been industrialized and opeational at Russia's Mnevniki substation since 2019, and a resistive 154kV HTSFCL has been undergoing field tests in Gochang, South Korea since 2016^{[2, 3]}. In addition, commercialization of 23kV distribution HTS cables between the Shingal and Heungduk substations has already taken place^{[4, 5]}.

In superconducting power equipment, research on the electrical breakdown characteristics of liquid nitrogen (LN2) is crucial, as high voltage is required for its operation. Larger scale superconducting apparatuses require larger LN2 gaps of electrical insulation. However, previous research has only analyzed the electrical breakdown characteristics of under small LN2 gap conditions^{[6, 7]}. Research on the electrical breakdown characteristics of LN2 in long gap conditions is lacking. Therefore, this study aimed to analyze the electrical breakdown characteristics of LN2 in long gap conditions.

2. Experimental Set-up

To analyze the dielectric characteristics of LN2, electrical breakdown experiments were conducted at an environmental pressure of 0.1MPa. A sphere-to-plane electrode system was utilized to create several long gap conditions, which were then submerged in LN2. To reduce errors, the experiment was replicated five times under identical conditions.

The sphere electrode was connected to a high voltage power supply (AC or lightning impulse), while the plane electrode was grounded. The electrode system was installed vertically to prevent bubbles from occurring between the sphere and plane electrode. In order to minimize bubble formation, the system had a stabilization time of 15 minutes. The AC voltage gradually increased at a ramp rate of 1kV/s until electrical breakdown occurred in the system. The experimental specifications are presented in Table 1., Fig. 1 illustrates the experimental schematic diagram.

Fig. 1. Schematic diagram of electrical breakdown experiment

3. Experimental Result

The breakdown voltage (VBD) measurements conducted under alternating current (AC) conditions at varying gap distances are presented in Fig. 2. The red data points correspond to measurements obtained from previous research, which covered gap distances ranging from 1 to 4mm^[7]. As depicted in Fig. 2, the VBD saturates at 140kV and does not increase further even when the gap is increased.

Fig. 3 presents the relationship between the VBD and gap distance under lightning impulse voltage (Imp.) conditions. It is evident from the graph that the breakdown voltage remains dependent on the gap distance. To analyze and calculate the electrical breakdown characteristics of LN2, the Weibull distribution is employed^[8]. The Weibull distribution is commonly used in reliability studies of equipment because of its capability to identify random and wear-out failures using scale and shape parameters. Equation (1) illustrates the formula for a two-parameter cumulative distribution function (CDF), where α and β represent the scale and shape parameters, respectively.

In the case where the electrical breakdown probability follows an exponential distribution with a constant distribution that is not influenced by the duration of operation, the shape parameter β takes on a value of 1. When the time and scale parameters are equal, as in (2), the resulting value is 0.632, indicating that the probability of electrical breakdown is 63.2%.

This characteristic is employed as a lifetime parameter in the industry.

Fig. 2. VBD according to gap under AC voltage

Fig. 3. VBD according to gap under Imp. voltage

4. Analysis

Simulation using Ansys Maxwell software was conducted to calculate the mean (Emean,1kV) and maximum (Emax,1kV) electric field intensities with a input voltage of 1kV. To obtain the electric field intensity at electrical breakdown, the acquired electric field intensity calculated from the simulation was multiplied by the experimental breakdown voltage, as illustrated in (3) ^[9].

To determine the reference electric field for insulation design, a simulation of an electrode system with varying electric field concentrations is necessary. Due to differences in electrode shapes, the concentrated electric field also varies. By considering the electric field utilization factor, which represents the degree of an average electric field with the concentrated electric field, the reference electric field can be derived.

Fig. 4 displays the dependence of the mean electric field intensity at sparkover with a probability of 63.2% (Emean,63.2%) at the applied gap distance. For the long gap configuration in AC condition, a significant decrease in Emean,63.2% was observed due to the presence of a large area with very low electric field intensity between the two electrodes. On the other hand, Fig. 5 demonstrates that the correlation between Emean,63.2% and the field utilization factor. Additionally, as depicted in Fig. 6 and 7, the Emean,63.2% was found to be independent of both the gap distance and the field utilization factor under the lightning impulse voltage.

In previous studies, the AC long gap condition showed a relatively low Emean,63.2% and field utilization factor range in comparison to the small gap condition, as illustrated in Fig. 8 ^[10]. Additionally, Fig. 9 and 10 present the maximum electric field intensity (Emax,63.2%) at sparkover with a probability of 63.2% as a function of the field utilization factor.

As shown in Fig. 9, Emax,63.2% was observed to be higher than 50kV/mm under AC voltage and decreased as the field utilization factor increased. Similarly, Emax,63.2% for the lightning impulse voltage was greater than 60kV/mm if the range of the field utilization factor less than 0.2 and had an exponential function similar to that of AC voltage.

Table 2 shows the empirical formulae to calculate Emax,63.2% according to the field utilization factor.

Fig. 4. Emean,63.2% according to gap under AC voltage

Fig. 5. Emean,63.2% according to utilization factor under AC voltage

Fig. 6. Emean,63.2% according to gap under lightning impulse voltage

Fig. 7. Emean,63.2% according to utilization factor under lightning impulse voltage

Fig. 8. Emean,63.2% comparison with previous research under AC voltage

Fig. 9. Emean,63.2% according to utilization factor under AC condition

Fig. 10. Emean,63.2% according to utilization factor under lighting impulse voltage

5. Conclusion

In this study, the elelctrical breakdown voltage characteristics of LN2 under long gap conditions was investigated. Experimental results show that under AC voltage, the electrical breakdown voltage of LN2 saturates at 140kV, even with increasing gap, up to 350mm. On the other hand, under lightning impulse voltage, the electrical breakdown voltage increases linearly up to 300kV for gaps below 18mm. Electrical breakdown characteristics of LN2 were analyzed under AC and lightning impulse voltages by examining the functional relationship between Emax,63.2% and Emean,63.2% with respect to the field utilization factor and gap distance.

As a result, experimental formulas for the Emax,63.2% and Emean,63.2% were derived for each voltage type. The empirical formulae predict the electrical field value using the utilization factor value. For future designs, the utilization factor can be detemined once design is complete. That value to can be used to predict whether the design is safe or if it may experience an electrical breakdown.

Further investigation on the electrical breakdown voltage characteristics of LN2 under various impulse voltage magnitudes is planned.