3.1.3. Temperature

When the short-circuit current is large, a large amount of joule heat generated by winding will result in a significant temperature rise, affecting the electromagnetic properties of the tape. Taking the simulation result voltage magnitude of 30 V as an example, the rising temperature curve of primary and secondary windings is shown in Figure 10. Since the rising temperatures of different turns are different in the same winding, the averages of temperature rise of the primary and secondary sides are used. As shown in Figure 10, the average temperature of the primary winding increases from the initial 77 K to 85.8 K, and that of the secondary winding increases from 77 K to 81.1 K. Figure 6 shows that the primary current is greater than the secondary current, so the primary temperature rise should

be greater than the secondary, but because the primary side resistivity is less than the secondary side, the combined action causes a minor difference in temperature rise.

**Figure 10.** Rising temperature of primary and secondary windings under voltage magnitude of 30 V.

In order to further analyze the internal operation of the SFCL, Figure 11 shows the temperature distribution of the primary and secondary windings at 0.02 s, 0.04 s, 0.06 s, and 0.08 s (only the upper half of the winding is drawn because it is symmetric).

**Figure 11.** Temperature distribution of primary and secondary windings at (**a**) 0.02 s, (**b**) 0.04 s, (**c**) 0.06 s, and (**d**) 0.08 s.

As shown in Figure 11, the portion with the greatest temperature rise is at the end of the primary innermost winding. Since it is affected by the largest magnetic field (especially the magnetic field perpendicular to the tape), the critical current there is minimized. A large amount of joule heat causes the greatest temperature rise. In the space between the primary and secondary windings, due to the opposite direction of the current, the generated magnetic fields are superimposed and enlarged, but the magnetic field direction is parallel to the strip, so the field has little effect on the critical current. It can be seen that the temperature rises more inside the primary winding than outside. Similarly, in the secondary winding, the temperature rises the most at the end. Since the structure of all-metal and no-insulation layers makes it possible to exchange heat with liquid nitrogen directly, the heat conduction speed is fast. So overall, the temperature rises significantly less in the secondary winding than in the primary winding.

As shown in Figure 11, compared with the secondary winding, the temperature of the primary winding rises more greatly in the current-limiting state of the HTS FCL. In order to speed up the recovery time after the fault current is cut o ff, the heat dissipation problem should be considered in the actual design and manufacture of the primary winding structure. While ensuring support strength, the contact area between the winding and the liquid nitrogen is increased as much as possible.

## *3.2. Short-Circuit Test*

In order to simulate the fault conditions in an actual grid, a SFCL prototype with the same simulation structure is fabricated and connected to the short-circuit test platform. The primary winding is an insulation superconducting winding with insulating material of KAPTON, and the secondary winding is a no-insulation superconducting winding. In this paper, superconducting winding is wound with second-generation high temperature superconducting material—YBCO tapes with stainless-steel package, which are produced by Shanghai Superconductor.

HTS coated conductor (CC) tapes were used in this paper is 4.8 mm wide and critical current is 40 A (77 K, self-field). Superconducting tapes are with a 1.5 μm thick YBCO layer, a 50 μm thick Hastelloy substrate, a 2 μm thick silver cap layer, and a 10 μm + 10 μm thick copper stabilization layer. The structure diagram of YBCO tape is shown in Figure 12. Then, the outermost is packaged in 75 m thick stainless steel.

**Figure 12.** Structure diagram of YBCO tape.

The primary winding and secondary winding consist of four double-pancake coils, respectively. A pancake coil is a coil with a flat spiral form, and a double-pancake coil is two pancake coils made by a superconducting tape. Double-pancake coils are connected in series by soldering, and resistance is 1.5 μΩ. Specifications of the SFCL prototype is shown in Table 1, same with the SFCL model, and the inductive SFCL prototype is shown in Figure 13.

Critical current of primary winding and secondary winding is 28 A and 30 A (77 K), respectively. Self-inductance of primary winding and secondary winding is 0.237 mH and 0.206 mH. The mutual inductance between the primary and the secondary is 0.196 mH, and the coupling coe fficient is 0.887.

The short-circuit test platform is shown in Figure 14; voltage source consists of voltage regulator (input: 400 V, output: 0~400 V) and step-down transformer (ratio is 20:1 or 10:1). Di fferent voltage can be obtained by changing output voltage of voltage regulator. A load resistor connected in parallel with IGBT fast switching is in series with the SFCL prototype, and the IGBT controlled by the host computer is used to generate a short-circuit voltage for a specified duration.

**Figure 13.** Superconducting inductive SFCL prototype: (**a**) Schematic diagram, (**b**) secondary winding, (**c**) SFCL prototype.

**Figure 14.** Short-circuit test platform.

The step-down transformer is used as a voltage source and the turn-off time is controlled to provide a short-circuit current with a fixed time for the SFCL. In this experiment, the short-circuit time is 5 cycles of 100 ms.

Considering the difficulty of measuring and simulating the internal impedance of voltage regulator, the experimental voltage value is directly input into the transient model for calculation. Figure 15 shows the comparison of the experimental waveform (left) and the simulated waveform (right) at different voltages (waveforms in two cycles after the short-circuit current becomes steady state).

**Figure 15.** Comparison of experimental (left) and simulation (right) results of voltage and current curves. (**a**) Comparison of primary current curve between experimental and simulation under voltage magnitude of 2.6 V, (**b**) overall simulation current under voltage magnitude of 2.6 V, (**c**) comparison of primary current curve between experimental and simulation under voltage magnitude of 4.5 V, (**d**) overall simulation current under voltage magnitude of 4.5 V, (**e**) comparison of primary current curve between experimental and simulation under voltage magnitude of 19.5 V, and (**f**) overall simulation current under voltage magnitude of 19.5 V.

As shown in Figure 15, the simulated current waveform is basically consistent with the experimental waveform, which proves that the simulation can well simulate the operating characteristics of the air core current limiter under short-circuit current, which lays a foundation for future SFCL design.

The error between the experiment and the simulation may be caused by the measurement error of the strip electrical and thermal parameters, or by nonuniform electrical and thermal parameters of the strip in the longitudinal direction. The primary current waveform is related to the secondary current waveform, especially when the secondary current begins to shunt in the HTS and metal layers, the secondary side impedance increases, and the instantaneous current value begins to decrease compared with the standard sine wave. At the same time, the primary current is distorted, and the overall distortion is less than the secondary winding.
