Noncontact measurement of transient potential distribution in superconducting cable

PII: S0011-2275(98)00082-4

Cryogenics 38 (1998) 977–982  1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0011-2275/98/$ - see front matter

Noncontact measurement of transient potential distribution in superconducting cable H. Shimizu*, K. Taketa, Y. Yokomizu and T. Matsumura Department of Electrical Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan

Received 25 May 1998 To measure transient potential distribution in a superconducting wire or cable after quench, some voltage taps are usually soldered with the sample conductor. However, the thermal and electromagnetic environment in the sample may be disturbed by the soldering of the voltage taps. As a method which can solve such problems, a noncontact measurement system with capacitance dividers is devised. It is experimentally found that our proposed method enables us to detect the quench initiation point and measure the propagation velocity of normal zone without any disturbances.  1998 Elsevier Science Ltd. All rights reserved Keywords: noncontact measurement; superconducting cable; potential distribution

A generating process of a normal resistance in a superconducting wire or cable after quench have been investigated by many researchers1–3, because it is one of the most important factors related to the performance of the superconducting equipment such as superconducting current limiter. The transient behavior of the normal resistance generation depends on the position of quench initiation and the propagation velocity of normal zone. To measure the quench initiation point and the propagation velocity, the transient potential distribution along the sample conductor is usually observed by attaching of the voltage taps soldered with the sample. The voltage taps may, however, disturb the thermal and electromagnetic environment in the sample. In the case of the superconducting wire or cable having high resistive matrix, a part of current may run through the solder after quench and the joule heat generated in the normal zone may partially flow out through the taps because of the low thermal conductivity of the matrix. As a result, the propagation velocity of normal zone may apparently be slower than the prospective one without the voltage taps. The quench current level and a.c. loss may also be affected by the change of the electrical coupling between strands due to soldering of voltage taps. In this paper, we describe a noncontact system to measure the potential distribution in the superconductor after quench. The system is devised to avoid the problems caused in the voltage tap method. The noncontact measurement system is constructed with capacitance dividers and *To whom correspondence should be addressed. Tel.: + 81-52789-3635; Fax:. + 81-52-789-3149

its performance is evaluated on the basis of the electric circuit theory. It is experimentally confirmed that the quench initiation point and the propagation velocity of normal resistive zone can be measured by the noncontact method. Finally, by comparison the capacitance method with the measurement by the voltage taps, we point out the feasibility of the method proposed.

Principle of noncontact measurement In the noncontact measurement system, the capacitance dividers consisting of a pair of capacitors C1 and C2 are used. Figure 1 illustrates the structure of the capacitance divider. A metal sheet is connected through a dielectric material with superconducting wire or cable in order to compose C1.

Figure 1 Structure of capacitance divider in noncontact measurement

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Noncontact measurement of potential distribution: H. Shimizu et al. The superconductor and the metal sheet are inner and outer electrodes of C1, respectively. The capacitor C2 is connected in series with C1. We can derive the real voltage at the position of C1 on the sample conductor by measuring the voltage V⬘ across C2 as follows. We now discuss how V⬘ appears on C2 when the normal zone propagates along the sample conductor on the basis of the electric circuit theory. It is assumed that the length of C1 is L and both the sample current Is and the normal resistance per unit length R are constant. The voltage is thus distributed with a constant gradient along the sample conductor as shown in Figure 2. In this discussion, the left edge of C1 is considered as the position of z = 0 and it is assumed that there is the normal front at z = zf. In the case of zf ⬍ L, i.e., the normal front exists inside C1, C1 can be divided into two parts of 0 ⱕ z ⬍ zf and zf ⱕ z ⬍ L from the viewpoint whether the sample conductor

is in the normal or superconducting state. For the normal state area (0 ⱕ z ⬍ zf ), the electric charge dQ1 on a small area dz of C1 at z = z is expressed by dQ1 = (v(z) − V⬘)C1

冉

冊

dz dz zf − z = v(0) − V⬘ C1 L zf L

(1)

where C1 is the capacitance of C1, v(z) and v(0) are the voltage on the sample conductor at z = z and z = 0, respectively. Since v(0) is equal to IsRzf, dQ1 = (IsRzf − IsRz − V⬘)C1

dz L

(2)

From Equation (2), the total electric charge Q1 on the region of 0 ⱕ z ⬍ zf is obtained as follows.

冕

冉

zf

Q1 = (IsRzf − IsRz⬘ − V⬘)C1

dz⬘ C1zf IsRzf = − V⬘ L L 2

0

冊

(3)

The superconducting state region of zf ⱕ z ⬍ L is equivalently connected with C2 in parallel because the sample conductor is kept at ground potential. Thus, the total electric charge Q1 is distributed on the region of zf ⱕ z ⬍ L of C1 and C2 as follows. Q1 = Q1⬘ + Q2 =

冉

冊

L − zf L − zf C1V⬘ + C2V⬘ = C1 + C2 V⬘ L L (4)

where Q⬘1 is the electric charge on the region of zf ⱕ z ⬍ L and C2 is the capacitance of C2. Substitution of Equation (3) for Equation (4) yield V⬘ IsRz2f 2L

(5)

C1 C1 + C2

(6)

V⬘ = K· where K=

On the other hand, in the case of zf ⱖ L, the electric charge Q1 on C1 is expressed by

冕 L

Q1 = (IsRzf − IsRz⬘ − V⬘)C1 0

冉

dz⬘ IsRL − C1 IsRzf − − V⬘ L 2

冊 (7)

Since C2 is connected with C1 in series, the same charge is stored on C2, thus, Q1 = C2V⬘

(8)

From Equation (7) and Equation (8), we get, Figure 2 Distributions of normal zone and voltage along the superconductor; (a) for zf ⬍ L and (b) for zf ⱖ L

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冉

V⬘ = K· IsRzf −

冊

IsRL = K·v(L/2) = K·V 2

(9)

Noncontact measurement of potential distribution: H. Shimizu et al.

Figure 4 Cross-section of sample conductor with capacitor C1

Figure 3 Voltage V⬘ as a function of position of normal front zf

where V is the voltage at the center of C1 (z = L/2). Figure 3 illustrates V⬘ as a function of the position of the normal front zf. The voltage V⬘ begins to increase slightly just after the normal zone reaches the edge of C1 at z = 0. As seen from Equation (9), for zf ⱖ L, V⬘ is proportional to the voltage V at the center of C1. Hence, V can be derived from V⬘ using Equation (9) although this value contains some error for zf ⬍ L. In this method, the sample conductor is insulated thermally by the dielectric material of C1 and there are no shortcircuit between the strands. Thus, the problems mentioned in the preceding section may be avoided. Figure 5 Measured results of capacitance C1

Experimental set-up and procedure The measurement of the transient potential distribution along a superconducting cable was carried out using the noncontact method mentioned above. The specifications of the superconducting cable adopted are listed in Table 1. Figure 4 illustrates the cross section of the sample conductor with the capacitor C1. Since this sample is coated by electrical insulating varnish, we can form C1 by directly covering the sample with an aluminum sheet. In this case, the electrical insulation of the sample can be regarded as the dielectric of C1. To avoid the eddy current generated by the self field in the Al sheet, we provided a slit of 1.5 mm in width. Figure 5 shows measured results of the capacitance C1 as a function of the length L. These results were obtained Table 1 Specifications of superconducting cable adopted Strand

Subcable Cable

Diameter Matrix Nb-Ti : Cu-10%Ni Filament diameter Filament number Twist pitch Electric insulation Diameter Twist pitch Diameter (bare) Twist pitch SC strand number Electric insulation

⭋ 0.193 mm Cu-10%Ni 1:2 ⭋ 0.744 ␮m 23 749 1.83 mm (S-twisted) None ⭋ 0.580 mm 6.7 mm (S-twisted) ⭋ 1.852 mm (⭋ 1.740 mm) 15.7 mm (S-twisted) 12 Epoxy

both at liquid helium and at room temperature. As seen in this figure, the capacitances C1 measured in liquid helium almost agreed with those at room temperature. The capacitance C1 increases in proportion to L and the proportionality constant is 1.3 pF/mm. The length L is preferred to be short to realize high spatial resolution. On the other hand, the large C1 may be required to obtain the large V⬘. To make C1 large, the capacitor C1 must be long. In the experiments, we adopted C1 of 50 mm in length whose capacitance was 65 pF. The capacitance C2 is preferred to be as small as possible to obtain large V⬘ within the limit that the impedance of C2 must be sufficient smaller than the input impedance of the data recorder. The capacitor C2 of 105 pF was connected with C1 outside the cryostat. From Equation (6), K was calculated to be 6.5 × 10−4, i.e., V⬘ being 6.5 × 10−4 times as large as the real voltage V is measured. Figure 6 shows the sketch of the sample superconducting cable with the capacitance dividers and heating coils. The

Figure 6 Sketch of sample superconducting cable with capacitance dividers and heating coils

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Noncontact measurement of potential distribution: H. Shimizu et al. judged that the quench occurred at t = 2.50 ms because va appeared at this point. In this paper, we define the instantaneous value of is at this point as the quench current level Iq. For this example, Iq was measured to be 480 A. Figure 9 indicates details of the waveforms before and after the quench in Figure 8. This figure shows the sample current is and voltages received at a, b and c. The voltage vb⬘ and vc⬘ were received by the capacitance dividers. Note that the range of the vertical axis for va is different from that for vb⬘ and vc⬘. Figure 7 Experimental circuit diagram

Detection of quench initiation point by capacitance method

sample conductor was 1 m in length. Two capacitance dividers were installed at positions marked b and c and the voltage taps were soldered at the left and right edges marked a and d. The separation lengths from a to b, b to c and c to d were 100 mm, 600 mm and 300 mm, respectively. The heater was located in each section to cause the quench. In the section a–b and c–b, the heaters were put at the distance of 50 mm from b and d, respectively. In b– c, the heater was installed at the center of the section. The sample conductor was fixed on a GFRP bobbin without epoxy resins. Figure 7 shows the experimental circuit diagram. The frequency of the power source is 60 Hz. The output of the voltage regulator was adjusted to a particular magnitude and the sample current is was supplied by turn-on of a pair of thyristors. The turn-on phase angle was controlled to be 0° in order to contain no DC transient component in is. By controlling the output of the voltage regulator, we can adjust the prospective current Ip or the current increasing rate dis/dt. We can change the quench initiation point and the quench current level by changing the heater used and its turn-on time, respectively.

Dividing vb⬘ and vc⬘ by K ( = 6.5 × 10−4 ) allows us to obtain the real voltages vb and vc, respectively. From va, vb and vc, the voltages across the section a–b, b–c and c–d can be derived. Figure 10(a) illustrates is, vab, vbc and vcd for the case of Figure 9. As seen in Figure 10(a), the voltages begin to appear in the order of vab, vbc and vcd. This indicates that the quench was initiated in the section a–b and the normal zone propagated toward d. Figure 10(b) and (c) illustrate the sample currents and the voltages for the cases that the heaters turned on in the sections b–c and c–d, respectively. These results were also obtained under the condition of Iq = 480 A and Ip = 600 Apeak. In the case of Figure 10(b), after vbc was generated, vab and vcd appeared simultaneously. This fact means that the normal zone was originated in the section b–c and propagated in both directions of b and c. From the order of voltage generation shown in Figure 10(c), it is found that the normal zone propagated from the section c–d to a–b through b–c. Consequently, it was experimentally confirmed that the quench initiation point can successfully be detected by our noncontact system.

Results and discussion Measured waveforms Figure 8 shows the measured waveforms of the heater current ih, the sample current is and the whole voltage of the sample va. In this example, the prospective current Ip was 600 Apeak and the quench was caused by the heater between a and b. The sample current is began to be supplied at t = 0 ms and the heater was turned on at t = 1.53 ms. It was

Figure 8 Measured waveforms of heater current ih, sample current is and sample voltage va

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Measurement of apparent propagation velocity of normal zone The apparent propagation velocity vp of the normal zone can be estimated from Figure 10. In the multi-strand cable, there are the propagation mechanisms of the normal zone with the current commutation among strands and those are quite different from the case of single superconducting

Figure 9 Time variations of sample current is and voltage at each point. vb and vc were measured by capacitance dividers

Noncontact measurement of potential distribution: H. Shimizu et al.

Figure 10 Time variations of sample current is and voltage at each section under the condition of heater turn-on; (a) in a – b, (b) in b – c and (c) in c – d (measurements by capacitor)

wire2,3. Thus, the estimated propagation velocity is the apparent value. In the case of Figure 10(a), the voltage vcd was observed 39 ␮s after the appearance of vbc. This interval is regarded as the time which the normal zone takes to propagate from b to c. Since the length between b and c is 600 mm, vp was calculated as follows. vp =

600 × 10−3 m = 1.54 × 104 m/s = 15.4 km/s 39 × 10−6 s

(10)

Figure 11 shows vp measured under the condition of Ip = 600 Apeak as a function of Iq. In Figure 11, the measured results due to the noncontact method are indicated by 䊊. The propagation velocity vp increases with Iq. We carried out the experiments three times for each Iq. As seen in Figure 11, the noncontact method has reproducibility for the measurements of vp. Furthermore, we have confirmed that vps measured for the other sample having the same specifications almost agree with the results in Figure 11. It has been reported that the abnormal quench process with enormously high propagation velocity of normal zone (fast quench) occurs in multi-strand superconducting cable2,3. From the measured vps, it is confirmed that the fast quench processes were observed in our sample conductor.

Figure 11 Measured propagation velocity vps as a function of Iq ( Ip = 600 A)

Comparison of capacitance method with measurement by voltage taps Figure 12 indicates the processes of the generation of normal resistance in the whole sample, which were estimated

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Noncontact measurement of potential distribution: H. Shimizu et al.

Figure 12 Difference of normal resistance generating process

from is and va measured under the condition that the quench initiation point was a–b and Iq was 480 A. In this figure, the dashed line curve corresponds to the case without any voltage sensors at positions b and c on the sample. The solid line curve and dash-dotted line curve are the results derived with capacitance dividers and voltage taps at b and c, respectively. The resistance generation behavior measured by the noncontact measurement system agrees with that without voltage sensors. The derivative of the resistance generation determined by voltage taps is slower than those by the noncontact measurement and no voltage sensors. These results mean that the propagation characteristics of normal zone are not influenced by capacitance dividers while they are disturbed by the voltage taps. Figure 13 shows time variations of vab, vbc and vcd measured by voltage taps. The experimental conditions such as the quench initiation section, Iq and Ip were the same as the case of Figure 10(a). In Figure 13, the results obtained by the capacitance dividers are also illustrated. In the case of the voltage tap method, the interval between the origination of vbc and vcd was 79 ␮s and the apparent propagation velocity vp was calculated to be 7.6 km/s. This value was equal to half of that obtained by the noncontact measurement system. The propagation velocities observed by voltage taps are also plotted in Figure 11 by 쐌. From these results, the voltage tap method also has the reproducibility for the measurements of vp. It has been confirmed that similar results can be received in the experiments for the other sample with the same specifications. Although the propagation velocities measured by voltage taps have the same tendency for Iq as those by the noncontact measurement, the magni-

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Figure 13 Waveforms of sample current is and voltages measured by voltage taps and capacitance dividers

tudes obtained by voltage taps are about half of those by the noncontact measurement.

Conclusion We devised a noncontact measurement method of the transient potential distribution along superconducting wire or cable after quench. It is experimentally confirmed that the quench initiation point can be detected and the propagation velocity of normal zone can be measured by our proposed method. Furthermore, we pointed out that the propagation process may be disturbed by the voltage tap method and such a problem can be avoided in the noncontact measurement system.

References 1. Ten Kate, H. H. J., Boschman, H. and Van De Klundert, L. J. M., Normal zone propagation velocities in superconducting wires having a high-resistivity matrix. Advances in Cryogenic Engineering, 1988, 34, 1049–1056. 2. Iwakuma, M., et al., Abnormal quench process with very fast elongation of normal zone in multi-strand superconducting cables. Cryogenics, 1990, 30, 686–692. 3. Vysotsky, V. S., Tsikhon, V. N. and Mulder, G. B. J., Quench development in superconducting cable having insulated strands with high resistive matrix (part 1, Experiment). IEEE Trans Magnetics, 1992, 28, 735–742.