- Email: [email protected]
Stability of fault current limiter with conduction cooled Bi2223 screen
Cryogenics 42 (2002) 363–370 www.elsevier.com/locate/cryogenics
Stability of fault current limiter with conduction cooled Bi2223 screen K. Sasaki *, C. Nishizawa, T. Onishi Graduate School of Engineering, Hokkaido University, Kita-13, Nishi-8, Kita-ku, Sapporo 060-8628, Japan Received 26 November 2001; accepted 29 November 2001
Abstract We examined a stability of magnetic shield type fault current limiter (MSFCL) with Bi2223 screen cooled by cryocooler thermally. Conduction cooled MSFCL handles better and needs easier maintenance than that cooled by liquid cryogen. In addition, the cost of the MSFCL decreases by the decrease of the required volume of the superconductor with the increase of the critical current density. We made the small model of the MSFCL with Bi2223 ring, ac loss of one ring under a normal operating condition was measured at 30 K determined by the critical current density of Bi2223 short sample. The measured ac loss almost corresponded to the hysteresis loss calculated from Bean model. The ac loss of the MSFCL with the shielding body of the stacked Bi2223 rings for 6.6 kV–1 kA distribution power system was calculated from Bean model. From the relation between the required number of the rings and the critical current density, the design outlines of the shielding body of conduction cooled MSFCL was obtained. The MQE of one Bi2223 ring of the small model was measured, and we confirmed that the MSFCL using high Tc superconductor had high stability against a local heat disturbance even at 30 K. In the case of the MSFCL with the stacked rings for a distribution power system, the improvement of the stability due to the current sharing between rings was confirmed by the numerical calculation. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Fault current limiters; Conduction cool; Cryocooler; High Tc superconductors; Ac losses; Local heat disturbance
1. Introduction With increasing of the demand for electrical power, a fault current comes into problem of utmost importance. A superconducting fault current limiter (SFCL) is one of the solution for this problem. The advantages of SFCL is low nominal losses compared with other limiting apparatus and an automatic response to the fault. Several concepts of SFCL are proposed and developed [1–5], especially, SFCL applying high Tc superconductors (HTS) is developed actively as the performance of HTS are improved. A magnetic shield type fault current limiter (MSFCL) which we have been studying [6–8], is inductive SFCL, which consists of a superconducting magnetic shielding body, iron core and primary coil. Almost all HTS fault current limiters currently developed are cooled by liquid nitrogen. If SFCL can be cooled by cryocooler, it handles better and needs easier maintenance. In addition, the operating temperature can
*
Corresponding author. Tel.: +81-11-706-6167; fax: +81-11-7066516. E-mail address: [email protected] (K. Sasaki).
be reduced below liquid nitrogen temperature easily. The critical current density of the superconductor increases as the operating temperature reduces, therefore, it is possible to decrease the volume of superconductor, that is, the cost of SFCL. An important parameter for the MSFCL cooled by cryocooler is ac losses generated in the superconductor, because the heat is conducted into the cold stage of the cryocooler through the extra thermal resistance, such as the heat conduction plate and thermal contact resistance between MSFCL and the cryocooler, so that temperature of the superconductor is higher than that of the cooling by liquid nitrogen. From the bad cooling condition, it is also necessary to investigate the effect of the local heat disturbance on the behavior of the MSFCL. This paper discusses the stability of a conduction cooled MSFCL thermally. The ac loss is estimated from the measurement of the temperature rise using the small model, and the relation between the ac loss and required volume of the superconductor is discussed. We also present the test results of stability against a local heat disturbance, and the thermal stability of conduction cooled MSFCL for a distribution power system is discussed.
0011-2275/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 1 - 2 2 7 5 ( 0 2 ) 0 0 0 6 1 - 9
364
K. Sasaki et al. / Cryogenics 42 (2002) 363–370
2. Measurement using small model 2.1. Design of small model The schematic view of the small model of the conduction cooled MSFCL using Bi2223 ring is shown in Fig. 1, and the parameters are summarized in Table 1. The primary coil is wound around the iron core with 20 turns. The magnetic shielding body is one ring of Bi2223. The outer, inner diameter and thickness of the ring are 67, 47 and 1 mm, respectively. The reason why we chose not Bi2223 cylinder but a thick Bi2223 ring is for enhancing a surface area for cooling. The Bi2223 ring was fixed on CuZn heat conduction plate by epoxy resin containing 10 wt.% Ag powder [9], and the heat conduction plate was tightly contacted with cold stage in length of 27 mm at the end. In order to produce a measurable temperature rise due to ac loss, CuZn conduction plate with a low thermal conductivity was used for the small model. The conduction plate was divided into four plates as shown in the bottom of Fig. 1 for decreasing eddy current losses in the plate. The operating temperature of 30 K was determined from the measurement result of the critical current density of Bi2223 short sample. Fig. 2 shows the critical current density defined by 1 lV/cm criterion as a function of temperature. The short sample was 3 mm in width, 1.2 mm in thickness and 50 mm in length, and the length between voltage taps was 30 mm. The critical current density at 77 K of the short sample at was larger
Table 1 Parameters of the small model of the MSFCL Superconducting ring Material Jc Tc Outer diameter Inner diameter Thickness
Bi2223 750 A/cm2 at 77 K 105 K 67 mm 47 mm 1 mm
Primary coil Cu wire diameter Number of turns
1 mm 20
Iron core Cross-sectional area Magnetic path length
748 mm2 360 mm
Conduction plate Material Thickness Width Resistivity
CuZn 0.5 mm 10 mm 5:5 108 Xm at 300 K
Cryocooler Type Cooling capacity
Stirling cycle 15 W at 20K
Fig. 2. Measured critical current density of the Bi2223 short sample.
than that of the ring, because the size of the short sample was small and the composition of the short sample was more uniform than that of the ring. We can see from these results that the critical current density reaches plateau below about 30 K. Because a specific heat of Bi2223, that is, stability against heat disturbance, reduce as the decrease of temperature, we selected the operating temperature of 30 K. 2.2. Ac loss under a normal operating condition
Fig. 1. Schematic view of the small model of the conduction cooled MSFCL using Bi2223 ring.
The ac loss under a normal operating condition was measured by calorimetric method. A power source was connected to the small model in series, a constant ac voltage of 50 Hz was applied for 280 s. The temperature rise of the Bi2223 ring was measured by the thermocouple attached on the ring as shown in Fig. 1. The data for converting from the temperature rise to ac loss was
K. Sasaki et al. / Cryogenics 42 (2002) 363–370
measured as follows; the heater wire was attached on the surface of the ring, and the relation between the dissipated power and the temperature was obtained from the heater power and measured temperature rise of the ring. The calibration curve shows in Fig. 3, and solid curve in this figure represents parabolic approximation. Fig. 4 shows examples of the temperature rises and currents in the primary coil, i1 . The power source voltage, Vps of 1.3 Vpeak at t ¼ 0 s was applied to the small model. The temperature of the ring increased slowly due to ac loss, and the final temperature reached to about 32.5 K as shown in Fig. 4(a), the reason why the temperature at t ¼ 0 s was not correspond to 30 K is the influence of the previous measurement. Such slow change of the temperature is caused by a low thermal diffusion time constant between the ring and cold stage. Because the flux flow resistance increases as the temperature increases, i1 decreased gradually from 28Apeak
Fig. 3. Relation between the temperature rise and the heater power.
365
to 25.6Apeak . At Vps ¼ 1:5Vpeak , the quench occurred, the temperature rose abruptly, and i1 decreased to 23.5Apeak as shown in Fig. 4(b). The resistance of the Bi2223 ring increases as the temperature, and the ohmic heating in the superconductor decreases, so that the heating and cooling value seem to be balanced at about 94 K. The ac losses converted from above results are shown in Fig. 5. The horizontal axis is the current which reaches finally during the measurement. The solid line represents the hysteresis loss of superconducting slab calculated from Bean model [10]. The equation for hysteresis loss by ac transport current, P (W) is given by P¼
2l0 d 2 Js3 fvsc ; 3Jc
ð1Þ
where d is the thickness of the slab, Js is the density of the transport current in the slab, Jc is the critical current
Fig. 5. Ac losses converted from temperature of Bi2223 ring and hysteresis loss calculated from Bean model.
Fig. 4. Examples of the temperature change due to ac loss and currents in the primary coil; (a) Vps ¼ 1:3Vpeak , (b) Vps ¼ 1:5Vpeak .
366
K. Sasaki et al. / Cryogenics 42 (2002) 363–370
density, f is the frequency of the ac transport current, and vsc is the volume of the superconductor. The solid curve in Fig. 5 represents calculated loss assuming the ring as the slab with 1 mm thickness, and Jc ¼ 5:4 107 A/m2 . Although the measured loss can not be compared with calculated one exactly because the critical current density changes according to the temperature rise of the ring, these results almost agree. 2.3. Stability of MSFCL against local heat disturbances Next, the behavior of MSFCL against local disturbances was measured. The heat disturbance was applied to the Bi2223 ring by a heating wire, and then, the temperature evolution around the heater was measured by the thermocouples. The arrangement of the heater and thermocouples is shown in Fig. 6. For simulating a thermal propagation only in the circumferential direction, the heating wire is wound around the Bi2223 and CuZn rings. The width of the heater is about 1.5 mm. Four thermocouples, T1–T4, are fixed on the ring at intervals of about 7 mm, and the distance between the heater and the nearest thermocouple, T1, is 3 mm. The heater and thermocouples are fixed by epoxy resin. After applying the constant ac voltage to MSFCL at t ¼ 0 s, the heater is fired at about t ¼ 200 s in order to minimize the effect of the temperature change due to ac loss. The time duration of heat pulse, td is 65 or 100 ms in this experiment owing to the limitation of the power source for the heater, although that of the actual local disturbance, for example epoxy crack, is expected about several hundreds ls. Examples of the evolution of temperature, temperature distribution and i1 are shown in Fig. 7 at td ¼ 100 ms. Fig. 7(a) illustrates the recovery process at Vps ¼
Fig. 6. The arrangement of the heater and thermocouples.
0:95Vpeak and the heat pulse of 8.05 J. The heater pulse started at t ¼ 199:7 s, and applying of Vps finished at t ¼ 280 s. The temperature rise at T1 was delayed 0.125 s from the rising of the heat pulse, it is thought that this delay caused by a high thermal conductivity of Bi2223. The temperature rises at other positions, T2–T4, were delayed 0.375, 0.775 and 1.175 s, respectively. The temperature at T1 reached to 54.0 K at 205.7 s, after that, it decreased slowly. The temperature diffusion process in the recovery process is also illustrated in Fig. 7(a). The temperature around the heater increased first, the temperature gradient became gentle after about 10 s, and then, the whole temperature decreases slowly. Although the measurement was finished at t ¼ 360 s, it is considered that the temperature of the ring recovers to the initial value after several hundred seconds. In the recovery process, i1 changed slightly. At t ¼ 200:35 s, i1 decreased to the minimum value of 18.1Apeak , from 20.1Apeak . This time seems to be when the total resistance of the Bi2223 ring reached a maximum. After that, i1 recovered to the initial value for about 4.5 s. Such change of i1 appeared clearly below Vps ¼ 1:3Vpeak . Above Vps ¼ 1:3Vpeak , the change of i1 was not observed at all. Examples of the quench process at Vps ¼ 0:95Vpeak and heat pulse of 8.19 J are shown in Fig. 7(b). The delay of the temperature rise at each position was the same as that in the recovery process. The temperature diffusion process was almost the same as that in the recovery process until t ¼ 205 s, too. The temperature gradient was kept during initial heating and even after the increasing rate of the temperature became small. From the figure of the temperature distribution, the temperature at opposite position to the heater was expected to be below 40 K. It is considered that the ring had the distribution of the heat generation accompanied with the temperature distribution in the circumferential direction. We see from the change of i1 that the total resistance of the ring decreased once after t ¼ 200:27 s because of the heat diffusion in the ring. Therefore, the ohmic heat in the ring reduced, and the ratio of the temperature rise reduced slightly from t ¼ 205 to 210 s. After that, the MSFCL went to the current limiting mode, and i1 decreased from 21Apeak to 16.2Apeak , because the ohmic heat was a little larger than the cooling by the heat diffusion and cryocooler. As same as in the recovery process, such transient recovery of i1 was not observed above Vps ¼ 1:3Vpeak . Fig. 8 shows the MQE at td ¼ 65 and 100 ms against the i1 =imax , where imax is the final current, 27.3Apeak , at Vps ¼ 1:5Vpeak , and i1 is the peak current in the primary coil just before the heat pulse. It is found that the MQE of Bi2223 ring were much larger than that of metal superconductor, for example NbTi with the MQE of several mJ [11], it indicates that MSFCL with Bi2223 screen has high stability against a local heat disturbance even at
K. Sasaki et al. / Cryogenics 42 (2002) 363–370
367
Fig. 7. Examples of the evolution of temperature, temperature distribution and i1 in (a) recovery process and (b) quench process.
applied heat pulse is written by one dimensional equation, o oT oT j ; ð2Þ S þ gS pcn ¼ SCp ox ox ot where S is the cross section area of the ring, j is the thermal conductivity, T is the temperature, g is the heat generation per unit volume, pcn is the heat conduction between the ring and conduction plate, and Cp is the specific heat. In this calculation, j and Cp are independent of a temperature, and they are 3 W/m K and 1 106 J/m3 K. The equivalent circuit of MSFCL is shown in Fig. 9, and the equivalent circuit equations are given by Fig. 8. Measured and calculated MQE, i1 =imax where imax is the final current at Vps ¼ 1:5Vpeak , 27.3Apeak , and i1 is the peak current in the primary coil just before the heat pulse.
30 K. In this measurement, the MQE is independent of the time duration of the heat pulse. It is considered that a thermal diffusion time constant of Bi2223 is larger than the heat pulse duration of the order of several tens to hundred ms. The calculated MQE of the Bi2223 ring in the small model is also plotted in Fig. 8. In this numerical calculation, the hysteresis loss under a normal operating condition is ignored in order to simplify the calculation. The thermal equilibrium equation of a ring
Vps ¼ L1
0 ¼ Mlk
N R þ1 X di1 dik þ M1k þ R1 i 1 ; dt dt k¼2 N R þ1 X k¼1
dik þ Rl il dt
ðl ¼ 2; . . . ; NR þ 1Þ;
ð3Þ
ð4Þ
where Mlk is the mutual inductance between coils l and k, Mlk at l ¼ k is the self inductance, and NR is the number of the Bi2223 rings, NR ¼ 1 for the small model. The resistance of the Bi2223 ring is obtained from the power law I–V characteristics [8], and it is a constant value of 9:1 106 Xm above Tc . Jc is assumed to
368
K. Sasaki et al. / Cryogenics 42 (2002) 363–370 Table 2 Parameters of MSFCL for a distribution power system Superconducting ring Material Tc Outer diameter Inner diameter Thickness
Bi2223 105 K 370 mm 350 mm 1 mm
Primary coil Number of turns
60
Iron core Cross-sectional area Magnetic path length Relative permeability
8:05 102 m2 5m 170
Fig. 9. Equivalent circuit of MSFCL with Bi2223 rings.
decrease linearly with the increase of the temperature. Jc for the calculation is assumed to 5400 A/m2 at 30 K from imax ¼ 27:3Apeak . The thermal equilibrium equation and the circuit equation are solved numerically. As shown in Fig. 8, the calculated results is smaller than the measured results. The reason for this seems to be the constitution of the heater. The heating wire was wound around the ring and CuZn plate for heating uniformly in the cross-section of the ring, and the wire covered with epoxy resin. Therefore, we consider that, in the experiment, CuZn plate and epoxy resin absorb the heat, and the extra heat needs to heat the ring.
3. Discussion This section presents that the ac loss under a normal operating condition and the transient stability against local heat disturbance of the MSFCL for 6.6 kV–1 kA distribution power system.
inner diameter of the Bi2223 ring, respectively, d is the thickness of the ring. Fig. 10 shows the calculated total ac loss and the required number of the rings as a function of n at Jc ¼ 7 107 A/m2 . The quadratic increase of total loss with n can be seen in this figure, whereas the required number of rings decreases with a increase of n. We can also see from this figure that the total loss decreases with a decrease of the critical current density. Since a lower loss is preferred to the MSFCL cooled by cryocooler, it is better to use many Bi2223 rings for the shielding body at low n than a few rings having high Jc from the viewpoint of loss. However, the value of n is limited by trigger current level of the MSFCL. For quenching the MSFCL at required trigger current, n needs to be a proper value, for example, n have to be larger than 0.5 when the trigger current level is twice nominal current. Other parameter for determining the number of the ring is Jc . Fig. 11 shows the total loss and the required number of rings as a function of Jc at n ¼ 0:8. The total loss increases linearly with Jc , and the number of rings is in inverse proportion to Jc . It seems from these result
3.1. AC loss under a normal operating condition It is found from the experimental results that ac loss in the MSFCL under a normal operating condition can be estimated roughly from hysteresis loss, Eq. (1). Using Eq. (1), the ac loss in MSFCL for 6.6 kV–1 kA distribution power system is estimated. The conceptual parameters of MSFCL are summarized in Table 2 from our latest work [8]. The magnetic shielding body is the stacked Bi2223 rings. The required number of Bi2223 rings for magnetic shielding, NR , is given by pffiffiffi Jc ðDo Di Þd ; ð5Þ N1 2In ¼ nNR 2 where N1 is the number of turns of the primary coil, In is the nominal current, Jc is the critical current density of Bi2223, n is the ratio of the current in the ring to the critical current of the ring, Do and Di are the outer and
Fig. 10. Calculated total ac loss and required number of rings as a function of n at Jc ¼ 7 107 A/m2 .
K. Sasaki et al. / Cryogenics 42 (2002) 363–370
369
Fig. 11. Total loss and required number of rings as a function of Jc at n ¼ 0:8.
that the ring having Jc of 3 107 to 5 107 A/m2 is proper for the MSFCL cooled by cryocooler. It is noticed that the total loss in Figs. 10 and 11 is a simple multiplication, NR times loss of one ring. If the stacked Bi2223 rings are considered as one cylinder owing to magnetic coupling, hysteresis loss may increase greatly. In order to reduce magnetic coupling, it is necessary to put the sufficient gap between Bi2223 rings. 3.2. Transient stability of MSFCL for a distribution power system From the comparison between calculated and measured MQE in the previous section, it is fond that the behavior of the MSFCL with the Bi2223 rings can be simulated using our simulation code. Using this simulation code, we calculated the behavior of MSFCL for a distribution power system, when a local heat disturbance was applied to a ring. The parameters in Table 2 is used for the calculation, and Jc , n and NR are assumed to 5 107 A/m2 at 30 K, 0.8 and 212, respectively. Fig. 12 shows the calculated results when the local heat disturbance over MQE of one ring is applied to a ring in the region of 3 mm at t ¼ 1 ms. The pulse width is 65 ms, and the input power is 9.75 J. Fig. 12(a) shows the temperature of the ring at x ¼ 0, 3, 10 mm, where x ¼ 0 is the heater position. After the heat pulse applies, the temperature at the heater position increases, however, it decreases as soon as the heat pulse finished. When the heated region of the ring transfers to the normal state, and the resistance of the ring increases as shown in Fig. 12(b), the current in the heated ring decreases to zero (Fig. 12(c)). That current transfers to the other rings coupled magnetically as shown in Fig. 12(d). In this calculation, since the coupling coefficient between the rings is the same everywhere, 0.98, the current in the heated ring is distributed among the other rings equally. When one ring quenches, the sharing current per one
Fig. 12. Calculated results of behavior of MSFCL for a distribution power system when the local heat disturbance over MQE of one ring is applied to a ring; (a) temperature evolutions in heated ring at x ¼ 0, 3 and 10 mm, (b) resistance in heated ring, (c) current in heated ring, (d) current in non-heated ring and (e) current in primary coil.
ring is 364.8/ðNR 1Þ ¼ 1:72Apeak . Because the critical current is 500 A, the non-heated rings do not quench. The ring applied the heat pulse is cooled because of the decrease of the heat generation, it recovers superconducting state at about t ¼ 0:46 s, and the current in its
370
K. Sasaki et al. / Cryogenics 42 (2002) 363–370
ring is restored. Total shielding current of the MSFCL does not change, therefore, i1 keeps a constant value. It is determined by the value of n whether the transient stability is improved by such current redistribution. When n is small, the rings that is not heated has a large margin to the quench, and the current can transfer from the heated ring without quench, therefore, the stability is improved, like a multi-strand cable [12]. Theoretically, even if the rings of the number of (1 nÞNR occur quench, the MSFCL is stable. In the practical MSFCL, when the rings below the theoretical number occur quench, the MSFCL would start the current limitation. Because there is the heat expansion between the heated and other rings, and the distribution of the coupling coefficient between rings prevent to share the current equally among the rings. Other interested problem related to the local heat disturbance is the influence of that on the performance of the Bi2223 ring. From the measurement results as shown in Fig. 7, there is the large temperature gradient in the ring during the quench occurred by a local heat disturbance. In the case of a large ring, it seems to appear clearly. The expands of the temperature distribution is very slow owing to a low thermal conductivity as shown in the measurement results, therefore, there is a possibility that a large thermal stress [5] is imposed on the ring for a long time. Because Bi2223 in itself is brittle, it is necessary to improve a mechanical strength, and add a heat conduction plate with a high thermal conductivity in order to promote a thermal expansion. However, that problem is not discussed here in detail.
4. Conclusions The temperature rise of the Bi2223 ring of small model we made was measured at 30 K, and the ac loss of a Bi2223 ring under a normal operating condition was estimated from these results. The obtained ac loss almost corresponded to the hysteresis loss by ac transport current. The ac loss and required number of the ring of the MSFCL for a distribution power system was calculated, and these results show that the ring with Jc of 3 107 to 5 107 A/m2 is proper for the shielding body of the MSFCL cooled by cryocooler. The MQE of the Bi2223 ring of the small model of the MSFCL was measured at 30 K. The measured MQE of the ring was several joule, which was much larger than that of the metal superconductor of the order of
several mJ, and it was found that one Bi2223 ring has a high stability even at 30 K. However, there is a large temperature gradient in the ring for a long time, therefore, the thermal stress accompanied with temperature gradient should be noted. We performed the numerical calculation of the behavior of the 6.6 kV–1 kA MSFCL with the magnetic shielding body which consists of the stacked rings. When one ring quenched, the current redistribution occurred between the rest of the rings, and the heated ring recovered to the superconducting state. From this result, it was confirmed that such redistribution of the shielding current improves the stability of the stacked rings in comparison with that of one ring in the MSFCL, like in the multi-strand cable. References [1] Tixador P, Porcar L, Floch E, Buzon D, Isfort D, Bourgault D, et al. Current limitation with bulk Y–Ba–Cu–O. IEEE Trans Appl Supercond 2001;11:2034–7. [2] Choi H-S, Kim H-R, Hyun O-B. Operating properties of superconducting fault current limiters based on YBCO thin films. Cryogenics 2001;41:163–7. [3] Nomura T, Yamaguchi M, Fukui S, Yokoyama K, Satoh T, Usui K. Single DC reactor type fault current limiter for 6.6 kV power system. IEEE Trans Appl Supercond 2001;11:2090–3. [4] Kaiho K, Yamaguchi H, Arai K, Umeda M, Yamaguchi M, Kataoka T. A current limiter with superconducting coil for magnetic field shielding. Physica C: Supercond 2001;354:115–9. [5] Cave JR, Willen WA, Nadi R, Zhu W, Paquette A, Boivin R, et al. Testing and modelling of inductive superconducting fault current limiters. IEEE Trans Appl Supercond 1997;7:832–5. [6] Onishi T, Nii A. Investigation on current limiting performances in magnetic shield type high-Tc superconducting fault current limiter. Cryogenics 1997;37:181–5. [7] Onishi T, Anii A, Yamazaki S. Development of magnetic shield type high-Tc superconducting fault current limiter with active trigger coil and its current limiting performances. In: Proceedings of the 15th International Conference on Magnet Technology, 1997. p. 514–7. [8] Onishi T, Sasaki K, Akimoto R. A proposal of fast self-acting and recovering limiter and the analyses of their characterisitcs. Cryogenics 2001;41:239–43. [9] Sasaki K, Yamagata A, Nii A, Onishi T, Shibuya M. Thermal design and performance tests of a current limiter with a conduction cooled Nb3 Sn screen. IEEE Trans Appl Supercond 2001; 11:2114–7. [10] Wilson MN. Superconducting magnets. Oxford: Clarendon Press; 1986. [11] Seo K, Morita M, Nakamura S, Yamada T, Jizo Y. Minimum quench energy measurement for superconducting wires. IEEE Trans Appl Supercond 1996;32:3089–93. [12] Amemiya N, Yonekawa H, Ogitsu T, Kobayashi E, Sasaki K, Ohuchi N, et al. Influence of current re-distribution on minimum quench energy of superconducting triplex cable against local disturbance. Cryogenics 1998;38:559–67.
Stability of fault current limiter with conduction cooled Bi2223 screen K. Sasaki *, C. Nishizawa, T. Onishi Graduate School of Engineering, Hokkaido University, Kita-13, Nishi-8, Kita-ku, Sapporo 060-8628, Japan Received 26 November 2001; accepted 29 November 2001
Abstract We examined a stability of magnetic shield type fault current limiter (MSFCL) with Bi2223 screen cooled by cryocooler thermally. Conduction cooled MSFCL handles better and needs easier maintenance than that cooled by liquid cryogen. In addition, the cost of the MSFCL decreases by the decrease of the required volume of the superconductor with the increase of the critical current density. We made the small model of the MSFCL with Bi2223 ring, ac loss of one ring under a normal operating condition was measured at 30 K determined by the critical current density of Bi2223 short sample. The measured ac loss almost corresponded to the hysteresis loss calculated from Bean model. The ac loss of the MSFCL with the shielding body of the stacked Bi2223 rings for 6.6 kV–1 kA distribution power system was calculated from Bean model. From the relation between the required number of the rings and the critical current density, the design outlines of the shielding body of conduction cooled MSFCL was obtained. The MQE of one Bi2223 ring of the small model was measured, and we confirmed that the MSFCL using high Tc superconductor had high stability against a local heat disturbance even at 30 K. In the case of the MSFCL with the stacked rings for a distribution power system, the improvement of the stability due to the current sharing between rings was confirmed by the numerical calculation. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Fault current limiters; Conduction cool; Cryocooler; High Tc superconductors; Ac losses; Local heat disturbance
1. Introduction With increasing of the demand for electrical power, a fault current comes into problem of utmost importance. A superconducting fault current limiter (SFCL) is one of the solution for this problem. The advantages of SFCL is low nominal losses compared with other limiting apparatus and an automatic response to the fault. Several concepts of SFCL are proposed and developed [1–5], especially, SFCL applying high Tc superconductors (HTS) is developed actively as the performance of HTS are improved. A magnetic shield type fault current limiter (MSFCL) which we have been studying [6–8], is inductive SFCL, which consists of a superconducting magnetic shielding body, iron core and primary coil. Almost all HTS fault current limiters currently developed are cooled by liquid nitrogen. If SFCL can be cooled by cryocooler, it handles better and needs easier maintenance. In addition, the operating temperature can
*
Corresponding author. Tel.: +81-11-706-6167; fax: +81-11-7066516. E-mail address: [email protected] (K. Sasaki).
be reduced below liquid nitrogen temperature easily. The critical current density of the superconductor increases as the operating temperature reduces, therefore, it is possible to decrease the volume of superconductor, that is, the cost of SFCL. An important parameter for the MSFCL cooled by cryocooler is ac losses generated in the superconductor, because the heat is conducted into the cold stage of the cryocooler through the extra thermal resistance, such as the heat conduction plate and thermal contact resistance between MSFCL and the cryocooler, so that temperature of the superconductor is higher than that of the cooling by liquid nitrogen. From the bad cooling condition, it is also necessary to investigate the effect of the local heat disturbance on the behavior of the MSFCL. This paper discusses the stability of a conduction cooled MSFCL thermally. The ac loss is estimated from the measurement of the temperature rise using the small model, and the relation between the ac loss and required volume of the superconductor is discussed. We also present the test results of stability against a local heat disturbance, and the thermal stability of conduction cooled MSFCL for a distribution power system is discussed.
0011-2275/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 1 - 2 2 7 5 ( 0 2 ) 0 0 0 6 1 - 9
364
K. Sasaki et al. / Cryogenics 42 (2002) 363–370
2. Measurement using small model 2.1. Design of small model The schematic view of the small model of the conduction cooled MSFCL using Bi2223 ring is shown in Fig. 1, and the parameters are summarized in Table 1. The primary coil is wound around the iron core with 20 turns. The magnetic shielding body is one ring of Bi2223. The outer, inner diameter and thickness of the ring are 67, 47 and 1 mm, respectively. The reason why we chose not Bi2223 cylinder but a thick Bi2223 ring is for enhancing a surface area for cooling. The Bi2223 ring was fixed on CuZn heat conduction plate by epoxy resin containing 10 wt.% Ag powder [9], and the heat conduction plate was tightly contacted with cold stage in length of 27 mm at the end. In order to produce a measurable temperature rise due to ac loss, CuZn conduction plate with a low thermal conductivity was used for the small model. The conduction plate was divided into four plates as shown in the bottom of Fig. 1 for decreasing eddy current losses in the plate. The operating temperature of 30 K was determined from the measurement result of the critical current density of Bi2223 short sample. Fig. 2 shows the critical current density defined by 1 lV/cm criterion as a function of temperature. The short sample was 3 mm in width, 1.2 mm in thickness and 50 mm in length, and the length between voltage taps was 30 mm. The critical current density at 77 K of the short sample at was larger
Table 1 Parameters of the small model of the MSFCL Superconducting ring Material Jc Tc Outer diameter Inner diameter Thickness
Bi2223 750 A/cm2 at 77 K 105 K 67 mm 47 mm 1 mm
Primary coil Cu wire diameter Number of turns
1 mm 20
Iron core Cross-sectional area Magnetic path length
748 mm2 360 mm
Conduction plate Material Thickness Width Resistivity
CuZn 0.5 mm 10 mm 5:5 108 Xm at 300 K
Cryocooler Type Cooling capacity
Stirling cycle 15 W at 20K
Fig. 2. Measured critical current density of the Bi2223 short sample.
than that of the ring, because the size of the short sample was small and the composition of the short sample was more uniform than that of the ring. We can see from these results that the critical current density reaches plateau below about 30 K. Because a specific heat of Bi2223, that is, stability against heat disturbance, reduce as the decrease of temperature, we selected the operating temperature of 30 K. 2.2. Ac loss under a normal operating condition
Fig. 1. Schematic view of the small model of the conduction cooled MSFCL using Bi2223 ring.
The ac loss under a normal operating condition was measured by calorimetric method. A power source was connected to the small model in series, a constant ac voltage of 50 Hz was applied for 280 s. The temperature rise of the Bi2223 ring was measured by the thermocouple attached on the ring as shown in Fig. 1. The data for converting from the temperature rise to ac loss was
K. Sasaki et al. / Cryogenics 42 (2002) 363–370
measured as follows; the heater wire was attached on the surface of the ring, and the relation between the dissipated power and the temperature was obtained from the heater power and measured temperature rise of the ring. The calibration curve shows in Fig. 3, and solid curve in this figure represents parabolic approximation. Fig. 4 shows examples of the temperature rises and currents in the primary coil, i1 . The power source voltage, Vps of 1.3 Vpeak at t ¼ 0 s was applied to the small model. The temperature of the ring increased slowly due to ac loss, and the final temperature reached to about 32.5 K as shown in Fig. 4(a), the reason why the temperature at t ¼ 0 s was not correspond to 30 K is the influence of the previous measurement. Such slow change of the temperature is caused by a low thermal diffusion time constant between the ring and cold stage. Because the flux flow resistance increases as the temperature increases, i1 decreased gradually from 28Apeak
Fig. 3. Relation between the temperature rise and the heater power.
365
to 25.6Apeak . At Vps ¼ 1:5Vpeak , the quench occurred, the temperature rose abruptly, and i1 decreased to 23.5Apeak as shown in Fig. 4(b). The resistance of the Bi2223 ring increases as the temperature, and the ohmic heating in the superconductor decreases, so that the heating and cooling value seem to be balanced at about 94 K. The ac losses converted from above results are shown in Fig. 5. The horizontal axis is the current which reaches finally during the measurement. The solid line represents the hysteresis loss of superconducting slab calculated from Bean model [10]. The equation for hysteresis loss by ac transport current, P (W) is given by P¼
2l0 d 2 Js3 fvsc ; 3Jc
ð1Þ
where d is the thickness of the slab, Js is the density of the transport current in the slab, Jc is the critical current
Fig. 5. Ac losses converted from temperature of Bi2223 ring and hysteresis loss calculated from Bean model.
Fig. 4. Examples of the temperature change due to ac loss and currents in the primary coil; (a) Vps ¼ 1:3Vpeak , (b) Vps ¼ 1:5Vpeak .
366
K. Sasaki et al. / Cryogenics 42 (2002) 363–370
density, f is the frequency of the ac transport current, and vsc is the volume of the superconductor. The solid curve in Fig. 5 represents calculated loss assuming the ring as the slab with 1 mm thickness, and Jc ¼ 5:4 107 A/m2 . Although the measured loss can not be compared with calculated one exactly because the critical current density changes according to the temperature rise of the ring, these results almost agree. 2.3. Stability of MSFCL against local heat disturbances Next, the behavior of MSFCL against local disturbances was measured. The heat disturbance was applied to the Bi2223 ring by a heating wire, and then, the temperature evolution around the heater was measured by the thermocouples. The arrangement of the heater and thermocouples is shown in Fig. 6. For simulating a thermal propagation only in the circumferential direction, the heating wire is wound around the Bi2223 and CuZn rings. The width of the heater is about 1.5 mm. Four thermocouples, T1–T4, are fixed on the ring at intervals of about 7 mm, and the distance between the heater and the nearest thermocouple, T1, is 3 mm. The heater and thermocouples are fixed by epoxy resin. After applying the constant ac voltage to MSFCL at t ¼ 0 s, the heater is fired at about t ¼ 200 s in order to minimize the effect of the temperature change due to ac loss. The time duration of heat pulse, td is 65 or 100 ms in this experiment owing to the limitation of the power source for the heater, although that of the actual local disturbance, for example epoxy crack, is expected about several hundreds ls. Examples of the evolution of temperature, temperature distribution and i1 are shown in Fig. 7 at td ¼ 100 ms. Fig. 7(a) illustrates the recovery process at Vps ¼
Fig. 6. The arrangement of the heater and thermocouples.
0:95Vpeak and the heat pulse of 8.05 J. The heater pulse started at t ¼ 199:7 s, and applying of Vps finished at t ¼ 280 s. The temperature rise at T1 was delayed 0.125 s from the rising of the heat pulse, it is thought that this delay caused by a high thermal conductivity of Bi2223. The temperature rises at other positions, T2–T4, were delayed 0.375, 0.775 and 1.175 s, respectively. The temperature at T1 reached to 54.0 K at 205.7 s, after that, it decreased slowly. The temperature diffusion process in the recovery process is also illustrated in Fig. 7(a). The temperature around the heater increased first, the temperature gradient became gentle after about 10 s, and then, the whole temperature decreases slowly. Although the measurement was finished at t ¼ 360 s, it is considered that the temperature of the ring recovers to the initial value after several hundred seconds. In the recovery process, i1 changed slightly. At t ¼ 200:35 s, i1 decreased to the minimum value of 18.1Apeak , from 20.1Apeak . This time seems to be when the total resistance of the Bi2223 ring reached a maximum. After that, i1 recovered to the initial value for about 4.5 s. Such change of i1 appeared clearly below Vps ¼ 1:3Vpeak . Above Vps ¼ 1:3Vpeak , the change of i1 was not observed at all. Examples of the quench process at Vps ¼ 0:95Vpeak and heat pulse of 8.19 J are shown in Fig. 7(b). The delay of the temperature rise at each position was the same as that in the recovery process. The temperature diffusion process was almost the same as that in the recovery process until t ¼ 205 s, too. The temperature gradient was kept during initial heating and even after the increasing rate of the temperature became small. From the figure of the temperature distribution, the temperature at opposite position to the heater was expected to be below 40 K. It is considered that the ring had the distribution of the heat generation accompanied with the temperature distribution in the circumferential direction. We see from the change of i1 that the total resistance of the ring decreased once after t ¼ 200:27 s because of the heat diffusion in the ring. Therefore, the ohmic heat in the ring reduced, and the ratio of the temperature rise reduced slightly from t ¼ 205 to 210 s. After that, the MSFCL went to the current limiting mode, and i1 decreased from 21Apeak to 16.2Apeak , because the ohmic heat was a little larger than the cooling by the heat diffusion and cryocooler. As same as in the recovery process, such transient recovery of i1 was not observed above Vps ¼ 1:3Vpeak . Fig. 8 shows the MQE at td ¼ 65 and 100 ms against the i1 =imax , where imax is the final current, 27.3Apeak , at Vps ¼ 1:5Vpeak , and i1 is the peak current in the primary coil just before the heat pulse. It is found that the MQE of Bi2223 ring were much larger than that of metal superconductor, for example NbTi with the MQE of several mJ [11], it indicates that MSFCL with Bi2223 screen has high stability against a local heat disturbance even at
K. Sasaki et al. / Cryogenics 42 (2002) 363–370
367
Fig. 7. Examples of the evolution of temperature, temperature distribution and i1 in (a) recovery process and (b) quench process.
applied heat pulse is written by one dimensional equation, o oT oT j ; ð2Þ S þ gS pcn ¼ SCp ox ox ot where S is the cross section area of the ring, j is the thermal conductivity, T is the temperature, g is the heat generation per unit volume, pcn is the heat conduction between the ring and conduction plate, and Cp is the specific heat. In this calculation, j and Cp are independent of a temperature, and they are 3 W/m K and 1 106 J/m3 K. The equivalent circuit of MSFCL is shown in Fig. 9, and the equivalent circuit equations are given by Fig. 8. Measured and calculated MQE, i1 =imax where imax is the final current at Vps ¼ 1:5Vpeak , 27.3Apeak , and i1 is the peak current in the primary coil just before the heat pulse.
30 K. In this measurement, the MQE is independent of the time duration of the heat pulse. It is considered that a thermal diffusion time constant of Bi2223 is larger than the heat pulse duration of the order of several tens to hundred ms. The calculated MQE of the Bi2223 ring in the small model is also plotted in Fig. 8. In this numerical calculation, the hysteresis loss under a normal operating condition is ignored in order to simplify the calculation. The thermal equilibrium equation of a ring
Vps ¼ L1
0 ¼ Mlk
N R þ1 X di1 dik þ M1k þ R1 i 1 ; dt dt k¼2 N R þ1 X k¼1
dik þ Rl il dt
ðl ¼ 2; . . . ; NR þ 1Þ;
ð3Þ
ð4Þ
where Mlk is the mutual inductance between coils l and k, Mlk at l ¼ k is the self inductance, and NR is the number of the Bi2223 rings, NR ¼ 1 for the small model. The resistance of the Bi2223 ring is obtained from the power law I–V characteristics [8], and it is a constant value of 9:1 106 Xm above Tc . Jc is assumed to
368
K. Sasaki et al. / Cryogenics 42 (2002) 363–370 Table 2 Parameters of MSFCL for a distribution power system Superconducting ring Material Tc Outer diameter Inner diameter Thickness
Bi2223 105 K 370 mm 350 mm 1 mm
Primary coil Number of turns
60
Iron core Cross-sectional area Magnetic path length Relative permeability
8:05 102 m2 5m 170
Fig. 9. Equivalent circuit of MSFCL with Bi2223 rings.
decrease linearly with the increase of the temperature. Jc for the calculation is assumed to 5400 A/m2 at 30 K from imax ¼ 27:3Apeak . The thermal equilibrium equation and the circuit equation are solved numerically. As shown in Fig. 8, the calculated results is smaller than the measured results. The reason for this seems to be the constitution of the heater. The heating wire was wound around the ring and CuZn plate for heating uniformly in the cross-section of the ring, and the wire covered with epoxy resin. Therefore, we consider that, in the experiment, CuZn plate and epoxy resin absorb the heat, and the extra heat needs to heat the ring.
3. Discussion This section presents that the ac loss under a normal operating condition and the transient stability against local heat disturbance of the MSFCL for 6.6 kV–1 kA distribution power system.
inner diameter of the Bi2223 ring, respectively, d is the thickness of the ring. Fig. 10 shows the calculated total ac loss and the required number of the rings as a function of n at Jc ¼ 7 107 A/m2 . The quadratic increase of total loss with n can be seen in this figure, whereas the required number of rings decreases with a increase of n. We can also see from this figure that the total loss decreases with a decrease of the critical current density. Since a lower loss is preferred to the MSFCL cooled by cryocooler, it is better to use many Bi2223 rings for the shielding body at low n than a few rings having high Jc from the viewpoint of loss. However, the value of n is limited by trigger current level of the MSFCL. For quenching the MSFCL at required trigger current, n needs to be a proper value, for example, n have to be larger than 0.5 when the trigger current level is twice nominal current. Other parameter for determining the number of the ring is Jc . Fig. 11 shows the total loss and the required number of rings as a function of Jc at n ¼ 0:8. The total loss increases linearly with Jc , and the number of rings is in inverse proportion to Jc . It seems from these result
3.1. AC loss under a normal operating condition It is found from the experimental results that ac loss in the MSFCL under a normal operating condition can be estimated roughly from hysteresis loss, Eq. (1). Using Eq. (1), the ac loss in MSFCL for 6.6 kV–1 kA distribution power system is estimated. The conceptual parameters of MSFCL are summarized in Table 2 from our latest work [8]. The magnetic shielding body is the stacked Bi2223 rings. The required number of Bi2223 rings for magnetic shielding, NR , is given by pffiffiffi Jc ðDo Di Þd ; ð5Þ N1 2In ¼ nNR 2 where N1 is the number of turns of the primary coil, In is the nominal current, Jc is the critical current density of Bi2223, n is the ratio of the current in the ring to the critical current of the ring, Do and Di are the outer and
Fig. 10. Calculated total ac loss and required number of rings as a function of n at Jc ¼ 7 107 A/m2 .
K. Sasaki et al. / Cryogenics 42 (2002) 363–370
369
Fig. 11. Total loss and required number of rings as a function of Jc at n ¼ 0:8.
that the ring having Jc of 3 107 to 5 107 A/m2 is proper for the MSFCL cooled by cryocooler. It is noticed that the total loss in Figs. 10 and 11 is a simple multiplication, NR times loss of one ring. If the stacked Bi2223 rings are considered as one cylinder owing to magnetic coupling, hysteresis loss may increase greatly. In order to reduce magnetic coupling, it is necessary to put the sufficient gap between Bi2223 rings. 3.2. Transient stability of MSFCL for a distribution power system From the comparison between calculated and measured MQE in the previous section, it is fond that the behavior of the MSFCL with the Bi2223 rings can be simulated using our simulation code. Using this simulation code, we calculated the behavior of MSFCL for a distribution power system, when a local heat disturbance was applied to a ring. The parameters in Table 2 is used for the calculation, and Jc , n and NR are assumed to 5 107 A/m2 at 30 K, 0.8 and 212, respectively. Fig. 12 shows the calculated results when the local heat disturbance over MQE of one ring is applied to a ring in the region of 3 mm at t ¼ 1 ms. The pulse width is 65 ms, and the input power is 9.75 J. Fig. 12(a) shows the temperature of the ring at x ¼ 0, 3, 10 mm, where x ¼ 0 is the heater position. After the heat pulse applies, the temperature at the heater position increases, however, it decreases as soon as the heat pulse finished. When the heated region of the ring transfers to the normal state, and the resistance of the ring increases as shown in Fig. 12(b), the current in the heated ring decreases to zero (Fig. 12(c)). That current transfers to the other rings coupled magnetically as shown in Fig. 12(d). In this calculation, since the coupling coefficient between the rings is the same everywhere, 0.98, the current in the heated ring is distributed among the other rings equally. When one ring quenches, the sharing current per one
Fig. 12. Calculated results of behavior of MSFCL for a distribution power system when the local heat disturbance over MQE of one ring is applied to a ring; (a) temperature evolutions in heated ring at x ¼ 0, 3 and 10 mm, (b) resistance in heated ring, (c) current in heated ring, (d) current in non-heated ring and (e) current in primary coil.
ring is 364.8/ðNR 1Þ ¼ 1:72Apeak . Because the critical current is 500 A, the non-heated rings do not quench. The ring applied the heat pulse is cooled because of the decrease of the heat generation, it recovers superconducting state at about t ¼ 0:46 s, and the current in its
370
K. Sasaki et al. / Cryogenics 42 (2002) 363–370
ring is restored. Total shielding current of the MSFCL does not change, therefore, i1 keeps a constant value. It is determined by the value of n whether the transient stability is improved by such current redistribution. When n is small, the rings that is not heated has a large margin to the quench, and the current can transfer from the heated ring without quench, therefore, the stability is improved, like a multi-strand cable [12]. Theoretically, even if the rings of the number of (1 nÞNR occur quench, the MSFCL is stable. In the practical MSFCL, when the rings below the theoretical number occur quench, the MSFCL would start the current limitation. Because there is the heat expansion between the heated and other rings, and the distribution of the coupling coefficient between rings prevent to share the current equally among the rings. Other interested problem related to the local heat disturbance is the influence of that on the performance of the Bi2223 ring. From the measurement results as shown in Fig. 7, there is the large temperature gradient in the ring during the quench occurred by a local heat disturbance. In the case of a large ring, it seems to appear clearly. The expands of the temperature distribution is very slow owing to a low thermal conductivity as shown in the measurement results, therefore, there is a possibility that a large thermal stress [5] is imposed on the ring for a long time. Because Bi2223 in itself is brittle, it is necessary to improve a mechanical strength, and add a heat conduction plate with a high thermal conductivity in order to promote a thermal expansion. However, that problem is not discussed here in detail.
4. Conclusions The temperature rise of the Bi2223 ring of small model we made was measured at 30 K, and the ac loss of a Bi2223 ring under a normal operating condition was estimated from these results. The obtained ac loss almost corresponded to the hysteresis loss by ac transport current. The ac loss and required number of the ring of the MSFCL for a distribution power system was calculated, and these results show that the ring with Jc of 3 107 to 5 107 A/m2 is proper for the shielding body of the MSFCL cooled by cryocooler. The MQE of the Bi2223 ring of the small model of the MSFCL was measured at 30 K. The measured MQE of the ring was several joule, which was much larger than that of the metal superconductor of the order of
several mJ, and it was found that one Bi2223 ring has a high stability even at 30 K. However, there is a large temperature gradient in the ring for a long time, therefore, the thermal stress accompanied with temperature gradient should be noted. We performed the numerical calculation of the behavior of the 6.6 kV–1 kA MSFCL with the magnetic shielding body which consists of the stacked rings. When one ring quenched, the current redistribution occurred between the rest of the rings, and the heated ring recovered to the superconducting state. From this result, it was confirmed that such redistribution of the shielding current improves the stability of the stacked rings in comparison with that of one ring in the MSFCL, like in the multi-strand cable. References [1] Tixador P, Porcar L, Floch E, Buzon D, Isfort D, Bourgault D, et al. Current limitation with bulk Y–Ba–Cu–O. IEEE Trans Appl Supercond 2001;11:2034–7. [2] Choi H-S, Kim H-R, Hyun O-B. Operating properties of superconducting fault current limiters based on YBCO thin films. Cryogenics 2001;41:163–7. [3] Nomura T, Yamaguchi M, Fukui S, Yokoyama K, Satoh T, Usui K. Single DC reactor type fault current limiter for 6.6 kV power system. IEEE Trans Appl Supercond 2001;11:2090–3. [4] Kaiho K, Yamaguchi H, Arai K, Umeda M, Yamaguchi M, Kataoka T. A current limiter with superconducting coil for magnetic field shielding. Physica C: Supercond 2001;354:115–9. [5] Cave JR, Willen WA, Nadi R, Zhu W, Paquette A, Boivin R, et al. Testing and modelling of inductive superconducting fault current limiters. IEEE Trans Appl Supercond 1997;7:832–5. [6] Onishi T, Nii A. Investigation on current limiting performances in magnetic shield type high-Tc superconducting fault current limiter. Cryogenics 1997;37:181–5. [7] Onishi T, Anii A, Yamazaki S. Development of magnetic shield type high-Tc superconducting fault current limiter with active trigger coil and its current limiting performances. In: Proceedings of the 15th International Conference on Magnet Technology, 1997. p. 514–7. [8] Onishi T, Sasaki K, Akimoto R. A proposal of fast self-acting and recovering limiter and the analyses of their characterisitcs. Cryogenics 2001;41:239–43. [9] Sasaki K, Yamagata A, Nii A, Onishi T, Shibuya M. Thermal design and performance tests of a current limiter with a conduction cooled Nb3 Sn screen. IEEE Trans Appl Supercond 2001; 11:2114–7. [10] Wilson MN. Superconducting magnets. Oxford: Clarendon Press; 1986. [11] Seo K, Morita M, Nakamura S, Yamada T, Jizo Y. Minimum quench energy measurement for superconducting wires. IEEE Trans Appl Supercond 1996;32:3089–93. [12] Amemiya N, Yonekawa H, Ogitsu T, Kobayashi E, Sasaki K, Ohuchi N, et al. Influence of current re-distribution on minimum quench energy of superconducting triplex cable against local disturbance. Cryogenics 1998;38:559–67.