Current distribution mapping in insulated (Gd,Y)BCO based stabilizer-free coated conductor after AC over-current test for R-SFCL application

Uniformity of critical current (Ic) over long lengths of (GdY)-Ba-Cu-O ((Gd,Y)BCO)-based high temperature superconducting (HTS) tapes after long periods of AC current excitation is an important criterion in their selection for resistive type superconducting fault current limiter (R-SFCL). The present work describes such critical current (Ic) uniformity measurements performed over 1m long, stabilizer-free (SF), 12 mm wide, 2nd generation (2G) (Gd,Y)BCO based HTS tape. A non-destructive method using a static hall probe (Tapestar®) with moving HTS tape configuration was employed for estimation of Ic uniformity. Scanning Hall probe microscopy (SHPM) was then used to examine the weak superconducting regions (i.e. less Ic) with a static HTS tape. Remanent field distribution on the HTS tape was measured to yield the critical current density distribution. Except for small degradation of Ic at some locations, these studies confirmed near-uniform critical current distribution over meter-long (Gd,Y)BCO tapes, both in virgin state and after exposure to AC over current.


Introduction
R-SFCLs based on HTS tapes have the ability to reduce fault current levels (5-10 times higher than its critical current, Ic) within the first cycle. The first cycle suppression of fault current by R-SFCL can lead to an increased transient stability of the power system. The first limited peak current of the R-SFCL is much higher than its Ic value and termed as over-current. Stabilizer free (SF) (Gd,Y)BCO based coated conductors (CCs) are being used for R-SFCL, as they have the required normal state resistance without current sharing in the stabilizer layers and low AC losses as well as sufficient mechanical strength and thermal capacity [1]. Uniformity of Ic over long lengths of HTS tapes for use over long periods of AC operation is an important criterion in their selection for R-SFCL. Heat generation occurs in HTS tapes due to non-uniform current flow in the conductor even though it is partially superconductive. Hence, it is necessary to investigate the local degradation of Ic of the HTS tape, if any, after its exposure to AC over-current operations. These studies are useful in predicting the reliable and reproducible performance of R-SFCL based on SF (Gd,Y)BCO tapes. In the present work, such critical current (Ic) uniformity measurements are carried over 1m of stabilizer free 12 mm wide 2nd generation (2G) SF (Gd,Y)BCO based HTS tape, before and after AC over-current operation. For this, we employed a non-destructive method using a static hall probe (Tapestar ® ) with moving HTS tape configuration [2]. Scanning Hall Probe Microscopy (SHPM) was then used to closely examine at the degraded zones by mapping the two dimensional (2D) current density (Jc) distributions [3]. Roth et al. and Shiohara et al. [4,5] reported that SHPM can be used to obtain Jc from the magnetic field mapping of CCs. 2D current in a superconducting tape generates magnetic field which can be measured by a scanning Hall probe. From the measured magnetic field map, the 2D Jc distribution can be obtained by mathematical models (using Biot-Savart law). Magnetic field mapping using scanning Hall probe microscopy (SHPM) of (Gd,Y)BCO CC is conducted at a fully penetrated state (0.5 T applied perpendicular field). In Tapestar measurement, z-axis (vertical distance between hall sensor array and sample) is fixed but in SHPM technique, z-axis can be changed for better resolution.

2.
Non-destructive critical current measurement approach

Distribution of Ic over long length of virgin 2G (Gd,Y)BCO CC
The specification of the SF 2G (Gd,Y)BCO tape as provided by the manufacturer is given in Table 1.
The critical current of the virgin tape was measured using Tapestar.
The calibration of the Hall array is done based on the geometry of the sensor array, its distance and alignment relative to the tape. The calibration is done by measuring a tape with known Ic and the calibration factor cf derived from the following equation [6].
where, N is the number of sensors and Bi is the field at sensor i. The values of B for the virgin tape can be calculated from the measurements performed by a Hall sensor array across the width of the tape. From these B measurements, local Ic of the tape is then calculated using eqn. (1).  The measured non-destructive Ic values (with suitable cf) over 1m length of the virgin SF (Gd,Y)BCO CC is given in figure 1.The figure 1 shows almost uniform Ic over 1m length with an average Ic of 471 A, maximum Ic of 486 A and a minimum Ic of 437 A with a standard deviation (STDEV) of about 1.98% in the measurement.

Distribution of Ic over 1m length of AC over-current treated 2G YBCO CC
The HTS tape described in Figure 1 was used for over-current (2 kAPeak) testing. At the time of exposure to 2kAPeak for 100ms, the tape showed current limiting behavior within 2ms and the 1 st limited peak was at 888APeak as shown in figure 2. Figure 3 shows the measured Ic of the HTS tape after AC over-current test. The tape shows an average Ic of 460 A, maximum Ic of 495 A and minimum Ic of 391A with a standard deviation (STDEV) of about 2%. The result shows nearly uniform Ic over the length after exposure to AC over-current. Some minor Ic degradation observed after over-current exposure may be attributed to conductor vibration (due to huge Lorentz force acting on it for short duration) during AC over-current test. The two red circles marked in figure 3 show the sections with reduced Ic. These weaker tape sections were cut for further analysis using SHPM.

Mathematical approach to current density
The relation between current and magnetic field (Ampere's circuital law) in the Fourier space from the convolution theorem is used to reconstruct the 2D sheet current density Jn = xy J x J y   from the measured ẑ component of magnetic field Bz (at levitation height z) and the details are given below [4,7,8]. (2) The 2D current density for closed loop condition is given by Using (2) and (3) we have (4) Here, k cannot be 0, required by (3), since when kx = ky = 0, j is unpredictable and the magnetic field generated by a homogeneous in-plane current does not have a ẑ component.

SHPM for current distribution in SF (Gd,Y)BCO CC after AC over-current test
Two pieces of 12mm wide and 14 mm long HTS tape from two weak sections (locations are shown in fig. 3) were studied using Scanning Hall Probe Microscopy. In a rectangular aluminium sample holder of 15cm × 5cm, the sample was fixed using adhesive kapton tape and cooled to 77.3 K in liquid nitrogen, and then the sample was magnetized using an NdFeB permanent magnet with a flux density above 0.5 T at its surface. The 0.5 T magnetic field is more than double the penetration field and hence the persistent current, which is the Jc of the sample at fully saturated condition, can be obtained. The SHPM measurement was initiated 10 minutes after the removal of the external magnetic field to measure the remanent field related to local Jc. The Hall probe (Arepoc AXIS-3) of 50 μm effective area, was excited by 10 mArms AC current at 20 kHz. The scan was done continuously and the data pick-up frequency corresponds to one data point per 50 μm without much noise. The Hall voltage created by the AC current and DC magnetic field is measured by a Signal Recovery 7280 Lock-in amplifier. The time constant is chosen as high as 10 ms for this measurement to reduce the noise. During the scan, the Hall probe is placed as close as possible to the sample in vertical direction and scanned in the horizontal plane. Remanent field was measured and Jc distribution was calculated according to the measured field map. Our sample showed a 2D Jc of 385 A/cm (using average Ic of 460 A) and the penetration field [9] Bp = μ0Jc/π(1+ln(w/t)) is 160 mT, where w is the width of the tape (12 mm) and t is the thickness of the superconducting region (estimated to be 1 μm).

Conclusion
A meter-long HTS tape (SF (Gd,Y)BCO CC) has been examined by non-destructive Ic measurements to evaluate its Ic uniformity before and after AC over current test. Before AC over current test, an average Ic of 471 A, maximum Ic of 486 A and minimum Ic of 437 A were measured by Tapestar. After AC over-current test, a similar uniform Ic was measured over the 1meter length except for two weak sections. The two sections of HTS tape where Ic degradation is observed were further investigated using SHPM technique to locate the defective region. In one of the sections (section 2), a defect at (x, y) = (-4, 0) with 15% lower Jc than its surroundings was identified by SHPM. The minor current density reduction at a few locations of the meter-long SF 2G (Gd,Y)BCO CC tape was not found to affect R-SFCL performance due to over-current operation of short duration pulse.