Until the discovery of superconductivity, it was widely believed that all materials exhibited at least some electrical resistivity. For metals, resistivity decreases as a function of temperature due to the quieting of lattice vibrations which impede the flow of electrons. However, lattice impurities and other defects in the material prevent the material from ever reaching zero resistivity. This, of course, is not true in superconducting materials. A material’s resistance abruptly drops to zero when it is cooled below its critical temperature (TC), though not every material is known to be capable of superconducting. In BCS theory, which successfully describes most superconducting materials, two electrons condense into a bosonic state called a Cooper pair [1]. The result is that a current will persist within the material forever with no power dissipation, as long as the material stays superconducting.
There are two known classes of superconductors: Type I and Type II. Type I superconductors are explained perfectly by BCS theory. When superconducting, they exhibit zero resistivity and expel all magnetic fields. In contrast, Type II superconductors allow magnetic fields to penetrate a small distance into their interior below temperature TC2. Below temperature TC1, where TC1 is less than TC2, no flux can penetrate and the material acts as if it were a Type I superconductor. There is a direct analogue of this for both Type I and Type II superconductors with magnetic field. If a superconductor is placed in a field above its critical field it will return to its normal state, even if its temperature is below the critical temperature. The importance of the Type II superconductors is that not all can be explained by BCS theory. Where BCS theory predicts a maximum TC for any material as 30K, Type II superconductors have exhibited critical temperatures well above this. Recently, Type II superconductors with critical temperatures above 77K have been discovered [2]. The importance, of course, is that such a material can be cooled to below its critical temperature by liquid nitrogen (LN2), a relatively cheap and easy to handle cryogen rather than the more expensive and unwieldy liquid helium.
In any transmission line, valuable electrical energy is lost no matter how hard engineers and physicists work to minimize the losses. The most obvious loss (though not necessarily the largest) in conventional transmission lines comes from the resistance of the line. Power goes as the square of the current times the resistance, resulting in a fractional loss of power over any distance of cable. There are also losses in the sheath or metal surrounding the cable due to the alternating magnetic field of the EM wave traveling in the cable. The losses are proportional to the square of the current. The last major loss in transmission lines is loss to the insulating material surrounding the cable. Ideally, the cable would be surrounded by a perfect electrical insulator which admits no electromagnetic field. In real life, no such material exists, and the fields always penetrate somewhat into the surrounding insulators at a depth characterized by the skin depth. The dielectric breakdown field of the insulator limits the amount of power which can be run through the line, thus adding to the loss. For a standard 3-phase single-core cable run at 132kV full load, the total losses in a conventional transmission cable is estimated to be on the order of 30 to 40 W/m for each wire [3].
The obvious advantage of superconducting transmission lines is they have no resistive losses in the bulk. If superconducting transmission lines had no other sources of power dissipation, the choice between types of transmission lines would be easy. We would simply calculate the cost of conventional power lines and subtract the cost of the power that is dissipated in transporting the electricity. Then, we would compare it to the cost of making and cooling superconducting transmission lines.
Of course, real superconducting cables have other sources of loss which must also be factored in. There are a number of major sources of losses in superconducting transmission lines, many of them fundamentally different from those in conventional transmission lines. There are a number of relatively small losses due to need to cool the line. No cooling system is perfectly efficient, so there is some loss of liquid nitrogen needed to cool the line. Typical values for cooling efficiency are estimated to be on the order of 10% [3]. Furthermore, there are losses due to the imperfect efficiency of the liquid nitrogen pumping system itself, as well as hydraulic losses due to the flow friction in the circulating liquid nitrogen.
Similar to conventional transmission lines, superconducting transmission lines also have shield and dielectric losses, which can be calculated using the same physical models. Unlike conventional lines, superconducting transmission lines have conductor AC losses. There is no generally accepted physical model to describe these losses, so much of the data is empirical. There are also losses due to imperfect thermal insulation of the superconducting cable. The result is a thermal leak between the cold liquid nitrogen and the warm surroundings. The losses can be reduced but not eliminated by creating a vacuum between the superconducting cable and the thermal insulator. Finally, there are small losses due to joints and terminations of cables.
At full load, and dividing out cooling inefficiencies, superconducting transmission lines have been shown to exhibit total loss of about 15 W/m for each wire, less than half that of its conventional counterpart [3]. The load placed on the line is of particular importance. The majority of losses in superconducting transmission lines are independent of the load placed on the line, and so the total loss in the line is largely independent of the load, ranging from about 5 W/m at no load to 15 W/m at full load for each wire. The same is certainly not true of conventional transmission lines. A big reason for this is that power is dissipated as the square of the current run through the line. As the load is increased, the losses in the line increase quadratically. The break-even point of the two systems is around a 33% load [3].
At this point, superconducting lines could only possibly be a sensible alternative to conventional lines if they are placed in a high load setting. Large cities offer the perfect setting for superconducting lines, as they often demand large amounts of electrical power. American Superconductor and Consolidated Edison have agreed to build and test prototype superconducting transmission cables in the New York City infrastructure [4]. There have been talks about coupling the superconducting lines with a liquid hydrogen pipeline, thus reducing the money spent cooling the lines. Implementation of these plans is still decades away [5]. Superconducting transmission lines are difficult to implement since it often costs more to fund and maintain the lines that the power companies lose in electrical losses in conventional lines. However, in the right settings the energy saved presents one possible advantage to using superconducting lines rather than the traditional transmission lines.
© 2010 Matthew Yankowitz. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] L. N. Cooper, "Bound Electron Pairs in a Degenerate Fermi Gas," Phys. Rev. Lett. 104, 1189 (1956).
[2] M. K. Wu et al., "Superconductivity at 93 K in a Mew Mixed-Phase Y-Ba-Cu-O Compound System at Ambient Pressure," Phys. Rev. Lett. 58, 908 (1987).
[3] J. Oestergaard et. al., "Energy Losses of Superconducting Power Transmission Cables in the Grid," Applied Superconductivity, IEEE Transactions on 11, 2375 (2001).
[4] "Superconducting Power Line to Shore Up New York Grid," New Scientist, 22 May 07.
[5] P. M. Grant, C. Starr and T. J. Overbye, "A Power Grid for the Hydrogen Economy," Scientific American, 26 Jun 06.