Application of Superconductors in Surge Current Protection

What are Superconductors?

A superconductor is a material that achieves superconductivity, which is a state of matter that has no electrical resistance and does not allow magnetic fields to penetrate. An electric current in a superconductor can persist indefinitely. Superconductivity can only typically be achieved at very cold temperatures (Paul, 2021).

Combescot (2022) defined superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered even down to near absolute zero, a superconductor has a characteristic critical temperature below which the resistance drops abruptly to zero.

Historical Background on Superconductors

Superconductivity was discovered on April 8, 1911 by Heike Kamerlingh Onnes, who was studying the resistance of solid mercury at cryogenic temperatures using the recently produced liquid helium as a refrigerant. At the temperature of 4.2 K, he observed that the resistance abruptly disappeared. In the same experiment, he also observed the superfluid transition of helium at 2.2 K, without recognizing its significance. The precise date and circumstances of the discovery were only reconstructed a century later, when Onnes’s notebook was found. In subsequent decades, superconductivity was observed in several other materials. In 1913, lead was found to superconduct at 7 K, and in 1941 niobium nitride was found to superconduct at 16 K (Dirk & Peter, 2010).

Great efforts have been devoted to finding out how and why superconductivity works; the important step occurred in 1933, when Meissner and Ochsenfeld discovered that superconductors expelled applied magnetic fields, a phenomenon which has come to be known as the Meissner effect. In 1935, Fritz and Heinz London showed that the Meissner effect was a consequence of the minimization of the electromagnetic free energy carried by superconducting current (London  & London, 1935).

During the 1950s, theoretical condensed matter physicists arrived at an understanding of “conventional” superconductivity, through a pair of remarkable and important theories: the phenomenological Ginzburg–Landau theory (1950) and the microscopic BCS theory. In 1950, the phenomenological Ginzburg–Landau theory of superconductivity was devised by Landau and Ginzburg. This theory, which combined Landau’s theory of second-order phase transitions with a Schrödinger-like wave equation, had great success in explaining the macroscopic properties of superconductors. In particular, Abrikosov showed that Ginzburg–Landau theory predicts the division of superconductors into the two categories now referred to as Type I and Type II. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize for their work (Landau had received the 1962 Nobel Prize for other work, and died in 1968). The four-dimensional extension of the Ginzburg–Landau theory, the Coleman-Weinberg model, is important in quantum field theory and cosmology (Bardeen, Cooper & Schrieffer, 1957).

Also in 1950, Maxwell and Reynolds et al. found that the critical temperature of a superconductor depends on the isotopic mass of the constituent element. This important discovery pointed to the electron-phonon interaction as the microscopic mechanism responsible for superconductivity. The complete microscopic theory of superconductivity was finally proposed in 1957 by Bardeen, Cooper and Schrieffer. This BCS theory explained the superconducting current as a superfluid of Cooper pairs, pairs of electrons interacting through the exchange of phonons. For this work, the authors were awarded the Nobel Prize in 1972. The BCS theory was set on a firmer footing in 1958, when N. N. Bogolyubov showed that the BCS wavefunction, which had originally been derived from a variational argument, could be obtained using a canonical transformation of the electronic Hamiltonian. In 1959, Lev Gor’kov showed that the BCS theory reduced to the Ginzburg–Landau theory close to the critical temperature. Generalizations of BCS theory for conventional superconductors form the basis for the understanding of the phenomenon of superfluidity, because they fall into the lambda transition universality class. The extent to which such generalizations can be applied to unconventional superconductors is still controversial (Bardeen, Cooper & Schrieffer, 1957).

The first practical application of superconductivity was developed in 1954 with Dudley Allen Buck’s invention of the cryotron. Two superconductors with greatly different values of the critical magnetic field are combined to produce a fast, simple switch for computer elements. Soon after discovering superconductivity in 1911, Kamerlingh Onnes attempted to make an electromagnet with superconducting windings but found that relatively low magnetic fields destroyed superconductivity in the materials he investigated. Much later, in 1955, G. B. Yntema succeeded in constructing a small 0.7-tesla iron-core electromagnet with superconducting niobium wire windings. Then, in 1961, J. E. Kunzler, E. Buehler, F. S. L. Hsu, and J. H. Wernick made the startling discovery that, at 4.2 kelvin, niobium–tin, a compound consisting of three parts niobium and one part tin, was capable of supporting a current density of more than 100,000 amperes per square centimeter in a magnetic field of 8.8 tesla. Despite being brittle and difficult to fabricate, niobium–tin has since proved extremely useful in supermagnets generating magnetic fields as high as 20 tesla. In 1962, T. G. Berlincourt and R. R. Hake discovered that more ductile alloys of niobium and titanium are suitable for applications up to 10 tesla. Promptly thereafter, commercial production of niobium–titanium supermagnet wire commenced at Westinghouse Electric Corporation and at Wah Chang Corporation. Although niobium–titanium boasts less-impressive superconducting properties than those of niobium–tin, niobium–titanium has, nevertheless, become the most widely used “workhorse” supermagnet material, in large measure a consequence of its very high ductility and ease of fabrication. However, both niobium–tin and niobium–titanium find wide application in MRI medical imagers, bending and focusing magnets for enormous high-energy-particle accelerators, and a host of other applications. Conectus, a European superconductivity consortium, estimated that in 2014, global economic activity for which superconductivity was indispensable amounted to about five billion euros, with MRI systems accounting for about 80% of that total.

In 1962, Josephson made the important theoretical prediction that a supercurrent can flow between two pieces of superconductor separated by a thin layer of insulator. This phenomenon, now called the Josephson effect, is exploited by superconducting devices such as SQUIDs. It is used in the most accurate available measurements of the magnetic flux quantum Φ0 = h/(2e), where h is the Planck constant. Coupled with the quantum Hall resistivity, this leads to a precise measurement of the Planck constant. Josephson was awarded the Nobel Prize for this work in 1973. In 2008, it was proposed that the same mechanism that produces superconductivity could produce a superinsulator state in some materials, with almost infinite electrical resistance. The first development and study of superconducting Bose–Einstein condensate (BEC) in 2020 suggests that there is a “smooth transition between” BEC and Bardeen-Cooper-Shrieffer regimes (Josephson,1962).

Types of Superconductors

According to Elprocus (n.d.), superconductors are classified into two types namely type-I & type-II.

Type-I Superconductor

This kind of superconductor includes basic conductive parts and these are utilized in different fields from electrical cabling to microchips on the computer. These types of superconductors lose their superconductivity very simply when it is placed in the magnetic field at the critical magnetic field (Hc). After that, it will become like a conductor. These types of semiconductors are also named as soft superconductors due to the reason of loss of superconductivity. These superconductors obey the Meissner effect completely. These superconductor examples are Zinc and Aluminum (Elprocus, n.d.).

Type-II Superconductor

This kind of superconductor will lose their superconductivity slowly but not simply as it is arranged within the exterior magnetic field. When we observe the graphical representation between magnetization vs. the magnetic field, when the second type semiconductor is placed within a magnetic field, then it will lose its superconductivity slowly. This kind of semiconductors will start to lose their superconductivity on the less significant magnetic field and totally drop their superconductivity at the higher critical magnetic field. The condition between the slighter critical magnetic field and higher critical magnetic field is called an intermediate state otherwise vortex state.

This type of semiconductor is also named as hard superconductors due to the reason they lose their superconductivity slowly but not simply. These semiconductors will obey the effect of Meissner but not totally. The best examples of these are NbN and Babi3. These superconductors are applicable for strong field superconducting magnets (Elprocus, n.d.).

Properties of Superconductors

Electrical4U (2020) noted that the superconducting material shows some extraordinary properties which make them very important for modern technology. The research is still going on to understand and utilise these extraordinary properties of superconductors in various fields of technology. Such properties of superconductors are listed below-

  1. Zero Electric Resistance (Infinite Conductivity)
  2. Meissner Effect: Expulsion of magnetic field
  3. Critical Temperature/Transition Temperature
  4. Critical Magnetic Field
  5. Persistent Currents
  6. Josephson Currents
  7. Critical Current

Zero Electric Resistance or Infinite Conductivity

In Superconducting state, the superconducting material shows the zero electric resistance (infinite conductivity). When the sample of a superconducting material is cooled below its critical temperature/transition temperature, its resistance reduces suddenly to zero. For example Mercury shows zero resistance below 4k (Electrical4U, 2020).

Meissner Effect (Expulsion of Magnetic Field)

A Superconductor, when it is cooled below the critical temperature Tc), expel the magnetic field and doesn’t allow the magnetic field to penetrate inside it. This phenomenon in superconductors is called Meissner effect (Electrical4U, 2020).

Critical Temperature/Transition Temperature

Critical temperature of a superconducting material is the temperature at which the materials changes from normal conducting state to superconducting state. This transition from normal conducting state (phase) to superconducting state (phase) is sudden / sharp and complete (Electrical4U, 2020).

Critical Magnetic Field

The superconducting state / phase, of a superconducting material, breaks when the magnetic field (either external or produced by current flowing superconductor itself) increases beyond a certain value and sample starts behaving like an ordinary conductor. This certain value of magnetic field beyond which superconductor returns back to ordinary state, is called Critical magnetic field. The value of critical magnetic field depends on temperature. As the temperature (below the critical temperature) reduces the value of critical magnetic field increase (Electrical4U, 2020).

Persistent Current

If a ring made of a superconductor is placed in a magnetic field above its critical temperature, now cool the ring of superconductor below its critical temperature and now if we remove the magnetic field a current is induced in ring due to its self-inductance. By Lenz law the direction of this induced current is such that it opposes the change in flux passing through the ring. As the ring is in superconducting state (zero resistance), the current induced is ring will be continue to flow this current is called the persistent current. This persistent current produce a magnetic flux which makes the magnetic flux passing through the ring constant (Electrical4U, 2020).

Josephson Current

If two superconductors are separated by a thin film of insulating material, which forms a low resistance junction, it is found that the cooper pairs (formed by phonon interaction) of electrons, can tunnel from one side of junction to the other side. The current, due to flow of such cooper pairs, is called Josephson Current (Electrical4U, 2020).

Critical Current

When a current is passed through a conductor under superconducting state, a magnetic field is developed. If the current increase beyond certain value the magnetic field increased up to critical value at which conductor returns to its normal state. This value of current is called critical current (Electrical4U, 2020).

Application of Superconductors in Surge Current Protection

Superconductor-based fault current limiters offer an alternative solution to controlling fault levels on the network. A superconducting fault current limiter (SFCL), unlike reactors or high-impedance transformers, will limit fault current without adding impedance to the circuit during normal operation. Most SFCLs are based on the “superconducting and normal” (SN) transition property. Superconductors are the only materials that change their resistance automatically from zero to a high value when a certain ‘critical current’ is surpassed. Early superconducting fault current limiters were too expensive for wide application in electrical utilities, since they were based on superconducting materials, which can only operate under extremely low temperatures (-269°C). With the discovery of high temperature superconductors (HTSs) twenty five years ago, the cooling problem has been greatly reduced. These new materials can be operated at much higher temperatures (-196°C) and can be cooled simply by using liquid nitrogen (Xueguang, Joseph, Nick & Goran, 2003). There are various types of SFCLs as earlier mentioned, but in this paper, a resistive SFCL is considered.

Resistive SFCL

A resistive SFCL utilizes resistance increase upon quench of a superconductor. It has advantages such as simpler structure, smaller size, and possibly lower capital cost than other types. During normal operation, the superconducting element is in its superconducting state and the normal load current passes with theoretically no loss. In the case of a short circuit, the circuit current rises sharply and the superconductor undergoes a transition to its normal state, so a certain value of nonlinear resistance is created by selfsensing and self-triggering, thus limiting the fault current level (Firouzi et al., 2012). The fault current pushes the superconductor into a resistive state directly and a resistance appears in the circuit. The advantage of the resistive SFCL is that the superconductor absorbs the energy of the fault current directly (Xueguang et al., 2003).

References

Bardeen, J., Cooper, L.N. & Schrieffer, J.R. (1957). “Microscopic Theory of Superconductivity”. Physical Review. 106 (1): 162–164.

Combescot, R. (2022). Superconductivity. Cambridge University Press. pp. 1–2.

Dirk, V. & Peter, K. (2010). “The Discovery of Superconductivity”. Physics Today. 63 (9): 38–43.

Electrical4U (2020). Properties of Superconductors. Retrieved on 8th October, 2022 from https://www.electrical4u.com/properties-of-superconductors/

Elprocus (n.d.). What is Superconductor : Types, Materials & Properties. Retrieved on 3rd October, 2022 from https://www.elprocus.com/what-is-superconductor-types-materials-properties/

Firouzi M., Aslani S., Gharehpetian G. B. and Jalilvand A. (2012). Effect of Superconducting Fault Current Limiters on Successful Interruption of Circuit Breakers: European Association for the Development of Renewable Energies, Environment and Power Quality (EA4EPQ). International Conference on Renewable Energies and Power Quality

Josephson, B.D. (1962). “Possible new effects in superconductive tunnelling”. Physics Letters. 1 (7): 251–253.

London, F.  & London, H. (1935). “The Electromagnetic Equations of the Supraconductor”. Proceedings of the Royal Society of London A. 149 (866): 71–88

Paul, S. (2021). What is a superconductor? Retrieved on 2nd September, 2022 from https://www.livescience.com/superconductor#section-how-do-superconductors-work

Xueguang W., Joseph M., Nick J. and Goran S. ( 2003). An investigation of Network Splitting for Fault Level Reduction: Tyndall Centre for Climate Change Research. Vol . 25(1). pp. 6-10.

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