2.1 Theory

In terms of energy, the unit of work can be expressed in units such as calorific value. This can be confirmed by 식(1) and 식(2). The amount of work is determined by the relationship between the strength of the magnetic field and the magnetic flux density. Therefore, the amount of heat generated is proportional to the intensity and magnetic flux density of the magnetic field generated in the coil. In the case of superconductors, the closer the magnetic field strength is, the closer the critical field is. At this time, the impedance is generated as the superconductor transitions to the phase conduction state with the quench phenomenon. Depending on the winding types, the generation of magnetic field and the increase of magnetic flux density of the superconductor can induce fast quench characteristics. Therefore, in this paper, spiral and helical types, which are general winding methods, were designed using Maxwell program. The difference between the lengths of the superconductor and the magnetic field is generated by two winding types. As the quench speed of the superconductor is shortened, it is possible to secure the fast breaking characteristic of the DC circuit breaker that constrains and blocks the fault current.

$W_{s}$: magnetic energy of superconducting coil,

$H$ : magnetic field strength of superconducting coil,

$B$ : magnetic flux density of superconducting coil,

$Q_{s}$: calorific value,

$V_{s}$: voltage flowing in the superconducting coil,

$I_{s}$: current flowing in the superconducting coil

2.2 Modeling and magnetic field distribution using the Maxwell program

표 1 shows the coil design of the superconducting current-limiting part. 그림 1(a) and (b) show the results of the analysis of each wire type’s magnetic field characteristics using Maxwell simulation. In Maxwell simulation, the magnetic flux density can be expressed as shown in 식 (3). The simulation analysis results showed that the magnetic flux density of the spiral wire type was 0.850 T, and its magnetic field intensity was 67.680$\times 10^{4}$ A/m. For the helical wire type, on the other hand, the magnetic flux density was 0.813 T, and the magnetic field intensity was 64.769$\times 10^{4}$ A/m. The spiral wire type had an approximately 0.037 T higher magnetic flux density and a 2.911$\times 10^{4}$ A/m higher magnetic field intensity. As mentioned earlier, increases in the magnetic flux density and magnetic field intensity can increase the blocking speed of the DC circuit breaker as they increase the calorific value generated during the quench of the superconductor. Finally, the inductance of the spiral wire type can be calculated using 식(4) and 식(5) while that of the helical type can be calculated using 식 (6) ^(9-10).

$D_{i.n}$: Innermost diameter of the spiral coil,

W : Width of the superconductor,

S : Pitch of the superconducting wire,

N : Number of turns of the superconducting wire,

H : Height of the helical coil

2.3 Circuit design and parameters using PSCAD/ EMTDC

그림 2 shows the circuit diagram, which includes the superconducting current-limiting part that limits the fault current, and the mechanical DC circuit breaker that blocks the fault current, using PSCAD/EMTDC. The superconductor for limiting the fault current was designed using 식 (7) ⁽¹¹⁾. In addition, an applied voltage of 100 kV and a steady-state current of 400 A were selected for the simulation, and the maximum fault current was set to 70 kA. As for the superconductor, (maximum impedance) was set to 5 Ω, and (quench time constant of the superconductor) was set to less than 2 ms. The L and C for generating resonance were 0.01 mH and 100 uF, respectively. Finally, the surge arrest (SA) for absorbing the residual current after blocking the fault current was set to 80 kV. Simulation analysis was conducted by selecting the same inductance of 0.007 mH for the two wire types.

$R_{m}$: superconductor maximum shunt resistance,

$t_{SC}$: superconductor time constant

2.4 PSCAD/EMTDC simulation results

그림 3 shows the experimental results of each wire type that used the same inductance. The spiral wire type performed blocking approximately 0.0008 ms later than the helical wire type, but its blocking completion time of 0.133 ms was similar to that of the helical wire type. The resonance frequencies can be expressed using 식(8) and 식(9) through the oscillation of LC ⁽¹²⁾. Therefore, the helical wire type has a lower resonance frequency than the spiral wire type as the number of turns increases. As a result, the fault current by LC oscillation was increased by approximately 34 kA for the spiral wire type and by 28 kA for the helical wire type. If the length of the superconducting wire is analyzed instead of the same inductance, the inductance of the helical wire type increases. This further delays the blocking of the fault current.

3.1 Experimental conditions

Experiments for each wire type were carried out under the conditions shown in Tables 2 and 3. The configuration of the equipment for the experiment can be seen in 그림 4(a). Up to 80 batteries are connected in series to simulate a DC environment. In addition, the fault situation can be simulated using the accident generating device. The superconductor can maintain superconductivity by the cooling system, and the experiment was constructed so that the limited current can be cut off using a circuit breaker. Also, the circuit diagram configuration for the blocking test is shown in 그림 4(b). For the comparison of the two wire types, the applied voltage was increased from 400 to 550 V by 50 V increments. In addition, the normal load was set to 23.4 Ω, and the fault load was set to 1 Ω..

3.2 Experimental results

그림 5(a) shows the current characteristics according to the voltage. As the voltage increased, the fault current limitation rates of the spiral wire type were found to be 9.39, 8.62, 8.52 and 11.63%. For the helical wire type, the fault current limitation rates were found to be 5.69, 5.24, 6.01 and 7.62%. 그림 5(b) shows the impedance characteristics according to the voltage. As the voltage increased, the impedance of the spiral wire type increased by 0.028, 0.045, 0.073 and 0.096 Ω. The impedance of the helical type, on the other hand, increased by 0.022, 0.028, 0.045, and 0.065 Ω. Based on the results shown in 그림 5(a) and (b), it was found that the fault current limitation ra tes of the spiral wire type were 3.70, 3.38, 2.51 and 4.01% higher than those of the helical wire type as the impedance of the spiral wire type was 0.006-0.031 Ω higher. Finally, the blocking time according to the voltage was analyzed using the power applied to the circuit breaker in 그림 5(c). The breaker opening times due to the introduction of the fault current were found to be 11.01, 10.11, 9.66 and 9.15 ms for the spiral wire type, and 11.13, 10.30, 9.81 and 9.24 ms for the helical wire type. The breaker opening time of the spiral wire type was approximately 0.09-0.19 ms faster than that of the helical wire type. Moreover, the breaker operation completion times were found to be 12.87, 12.01, 11.56 and 11.45 ms for the spiral wire type, and 12.95, 12.26 and 11.67 ms for the helical wire type. The spiral wire type exhibited approximately 0.06-0.25 ms faster blocking speed. 표 4 shows the experimental results of the spiral wire type, and 표 5 shows those of the helical wire type.