High-temperature superconducting (HTS) tapes currently used for the manufacture of resistive fault current limiters use metallic substrates upon which the HTS film is grown. Because the alloys used for these substrates, such as Hastelloy, have a rather high resistivity and low thermal conductivity, the HTS film must be protected by a more conducting metallic layer acting as a shunt to avoid burn out during a fault. This shunt layer limits severely the electric field generated during the fault to values smaller than 100 V/m. A long length of tape is then necessary to achieve the desired high voltage. We show here that by using a high thermal diffusivity dielectric substrate such as sapphire, it is possible to obtain much higher electric fields of up to several kilovolts per meter. Keywords High temperature superconductor · Fault current limiter · Dielectric substrate · Sapphire EFG ribbon · Thermal diffusivity 1 Introduction maximum power that can be dissipated per unit area of the tape without burn out can be increased by more than one Second-generation high-temperature superconducting order of magnitude. (HTS) tapes comprise a high-resistivity low thermal con- ductivity metallic substrate such as Hastelloy, buffer layers, a RBCO film and a stabilizing metallic layer acting as 2 Architecture and Operation a shunt. This architecture is well suited for applications of a Dielectric-Based SFCL Element such as superconducting cables, transformers, and high magnetic field coils. However, it is not well suited for We consider a tape architecture comprising a dielectric sub- superconducting fault current limiter (SFCL) applications. strate of thickness h, having a (high) thermal conductivity This is because the highly conductive shunt layer prevents K(T ) and a heat capacity C (T ), a thin buffer layer allow- the development of the desired high electric field when a ing an ideal thermal contact with the substrate, an HTS film fault triggers the return of the SFCL to the normal state. having a critical current per unit width I , and a thin shunt The electric field reached in state-of-the-art HTS tapes layer having a resistance per square R (T ), of negligible used for SFCL applications is then limited to 100 V/m. We thermal conductance and heat capacity. As will be shown show here that by replacing the low thermal conductivity below, a thin shunt later is sufficient when the substrate has substrate currently used by a high thermal conductivity, a high diffusivity. high-diffusivity dielectric substrate, it is possible to achieve When fault occurs, a current exceeding the critical electric fields of several kilovolts per meter, and that the current flows through the SFCL composite element as it returns to the normal state and the element starts to heat up. Empirical evidence shows that the time it takes to return to the normal state (τ ) is of the order of 1 ms. After about Guy Deutscher 100 ms, a mechanical device is activated and current stops firstname.lastname@example.org flowing through the SFCL element. We assume that on 1 these time scales, heating is adiabatic because heat exchange School of Physics and Astronomy, Tel Aviv University, between the SFCL element and the surrounding cryogen is Ramat Aviv, 69978 Tel Aviv, Israel 1962 J Supercond Nov Magn (2018) 31:1961–1963 negligible. In order to avoid damaging the HTS layer, the 4 Maximum Power temperature should not exceed a certain maximum value temperature (T ) of the order of 400 K, to be on the safe When a SFCL element is submitted to an applied ac voltage side . (V ) over a length scale equal to the width of the tape, the Because in the considered architecture the shunt layer power dissipated per unit area upon return to the normal is very thin, its thermal conductance and heat capacity state is given by: are negligible compared with those of the substrate. The P = V /R (T ) rms dissipated heat flows primarily to the substrate which controls the heating rate and therefore the maximum power The rate of temperature increase is given by: that can be dissipated without overshooting the allowed −1 dT /dt = p(C h) maximum temperature T within a set time. The shunt layer on the other hand controls through its resistance R (T ) where h is limited to the value of δ calculated above. The the maximum electric field that can develop before T is maximum power allowed will be: reached. p = C δ · (T /t ) M p m where T is the maximum allowed temperature increase 3 The Role of the Substrate Diﬀusivity and t is a time scale that can range from τ if immediate m s burn out is to be avoided to the time at which the mechanical The rate at which a heat front progresses is governed by the switch is operated. In fact, the shortest time scale at which thermal diffusivity D = K/C : the ac power is defined is half a cycle or 10 ms. In what follows, we will use this time scale and take T = 300 K. X = Dt In the case of sapphire, the heat capacity is strongly temperature dependent, ranging from 0.4 J/cm around 90 K 3 3 to 2.8 J/cm at room temperature. Taking a value of 1 J/cm , Over the switching time scale (τ ), the heat front moves a and δ = 0.3 cm, we get a maximum power of 9,000 W/cm . distance: For comparison for a Hastelloy substrate, using a room temperature heat capacity value of 2.7 J/cm and δ = 50μm, 1/2 δ = (Dτ ) we get a maximum power of 400 W/cm . These values compare reasonably well with published Sapphire is a specific example of a dielectric substrate data. For sapphire, Kraemer et al. gives a maximum power having a high diffusivity. At 65 K, below the critical 2 2 of 1200 W/cm , Yamasaki et al. at 1700 W/cm , temperature of the HTS layer, its value is about 100 cm /s. If while for Hastelloy-based tapes, reported values are of the a hot spot develops because of the presence of some defect 2 order of 100 W/cm . in the HTS layer, within 1 ms, the temperature increase of the substrate is smoothed out over the length scale δ = 3 mm, which is of the order of a typical tape width. The 5 Shunt Optimization for Achieving Highest heat front also penetrates to that depth into the substrate. Possible Electric Field By comparison, the thermal diffusivity of Hastelloy is only 0.03 cm /s and δ = 50 μm. While the maximum power is basically a property of the The heat penetration depth (δ) determines the maximum substrate, the maximum electric field that can be achieved effective thermal thickness of the SFCL element, and hence is also determined by the shunt resistance. The critical the maximum effective heat capacity and the lowest possible current of the HTS layer needs also to be taken into rate of temperature increase for a given power (p).The account. larger δ, the thicker the substrate one can use and the slower For a given value of the maximum power, the voltage this rate can be. A SFCL element based on sapphire will over a length equal to the width of the tape is given by: heat up less at a given time than one based on Hastelloy, 1/2 V = (R (T )p ) and as a result will be able to withstand a larger power. We rms M note that δ is not strongly time dependent. This is because at However, we have to take into account that when a fault long times, the element heats up and the diffusivity reduces. occurs, the current that flows through the shunt is at least For sapphire, δ remains close to 3 mm from 1 ms, the time equal to the critical current and the voltage that develops is scale that characterizes the transition to the normal state, to at least equal to R (T )I .Wehavetomakesurethat: 100 ms which is the time at which a mechanical device will R (T )I <p cut the fault current and heating will stop. c J Supercond Nov Magn (2018) 31:1961–1963 1963 The highest value of R (T ) that is allowed is p /I ,and Acknowledgments Useful discussions with Mishael Azoulay and Amir Saraf are gratefully acknowledged. This work has received the maximum electric field that can be reached without funding from the European Union’s Horizon 2020 research and damaging the tape is: innovation programme under grant agreement No 721019 and from the Israel Ministry of Energy. E = p /I max M c Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http:// creativecommons.org/licenses/by/4.0/), which permits unrestricted For a critical current of 300 A/cm-w, the maximum electric use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a field that can be achieved will be 3 kV/m for a sapphire- link to the Creative Commons license, and indicate if changes were made. based tape and 130 V/m for a Hastelloy-based tape. References 6 Conclusions 1. Tixador, P. In: Tixador, P. (ed.): Superconducting fault limiters. World Scientific, Singapore (2018). (to appear) By using thick dielectric substrates of high thermal diffu- 2. Kraemer, H.P. et al.: IEEE Trans. Appl. Supercond. 13, 1988 sivity, such as sapphire, it is possible to make relatively short (2003) SFCL elements that can sustain high-power dissipation and 3. Yamasaki, H. et al.: Appl. Phys. Lett. 85, 4427 (2004) high voltage. 4. Hobl, A. et al.: IEEE Trans. Appl. Supercond. 23, 5601804 (2013)
Journal of Superconductivity and Novel Magnetism – Springer Journals
Published: Jun 1, 2018
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