Electrical conductors
Stefan Fassbinder
Deutsches Kupfer-Institut
January 2010
Practical applications
of electrical conductors
Electrical conductors
With a conductivity that is about 60% of that of copper, aluminium just
fails to make it onto the podium of the best three metallic conductors.
Silver takes gold, so to speak, with the silver medal going to copper, and
gold coming in third to take bronze. Aluminium follows a little behind
gold to take fourth place, but well ahead of the rest of the field of metal
conductors. Non-metallic conductors (carbon, electrolyte solutions,
conducting polymers, superconductors and nanotubes) have their role to
play – often in new applications - and rarely compete with metals.
Practical applications of electrical conductors
Practical applications of electrical conductors
1
Metals: familiar and versatile materials
1.1
Metallic conductors: the choice is limited
With a conductivity that is about 60% of that of copper, aluminium just fails to make it onto the podium of the best
three metallic conductors. Silver takes gold, so to speak, with the silver medal going to copper, and gold coming
in third to take bronze. Aluminium follows a little behind gold to take fourth place, but well ahead of the rest of the field
(see Table 1). The high prices of gold and silver makes their use in cables, wires, conductors and electrical machines
uneconomical, though they do find application as bond wires in integrated circuits where they are used in minute
quantities. All other known elements and compounds trail the top four metals in terms of electrical conductivity
by some way, with many materials not electrically conducting at all. Alloys, which are mixtures of different metals,
have much lower electrical conductivity than pure metals. The only two metals therefore offering high electrical
conductivity at economically viable prices are aluminium and copper, with the latter setting the benchmark for
all other materials. According to documents published by the German Copper Institute (DKI), the conductivity
of copper used for the conduction of electricity (Cu-ETP-1, Cu-OF-1 or Cu-OFE) is 58.58 MS/m1. The IEC standard
60028 was already quoting a value of 58.51 MS/m in 1925. This corresponds to 101 % of the value in the International
Annealed Copper Standard (IACS), which in 1913 set the standard electrical conductivity of engineering copper to be
58.00 MS/m2, 3 – the benchmark against which other electrically conducting materials must be measured.
Ω*m
(at 20°C)
Silver
Copper (99.95%)
Gold
Aluminium
CuCrZr alloy
Tungsten
Brass (CuZn37)
Iron
Stainless steel
Lead
Resistance wire (CuNi44Mn1)
Coal, graphite
Ω*m
from
-6
0.0160 * 10
0.0172 * 10-6
0.0220 * 10-6
0.0283 * 10-6
0.0375 * 10-6
0.0550 * 10-6
0.0645 * 10-6
0.1000 * 10-6
1.0000 * 10-6
0.2080 * 10-6
0.4900 * 10-6
40.0000 * 10-6
Sea water
Tap water
Distilled / demineralized water
Ice
Garten soil, top soil, peatland soils
Porous limestone
Wet concrete
Dry concrete
Sand
Gravel, crushed stone
Quartzite, weathered limestone
Rock
to
1
0,1
100
5
100000
2000
100000
10000
50
5
100
30
30
100
2000
10000
200
2500
2000
3000
300
1000
1000
10000
Table 1: Resistivity values of selected metallic materials compared to the resistivities of various types of water,
soils and rocks, which are often are treated as ‘conducting’ when discussing earthing systems
Aluminium is a light metal with a density of only about 30% that of copper. Furthermore, the day-to-day trading
price of aluminium, which is always quoted per unit weight (strictly, per unit mass), is usually slightly, and sometimes
significantly, lower than that of copper. However, the crucial quantity determining the amount of conducting material
required in a particular application is the conductor cross-section. What counts is therefore the volume and not
the mass (or weight) of material. Although the better conductivity of copper means that two litres of copper can
replace more than three litres of aluminium, copper as conductor material requires twice the mass of aluminium.
So why is it then that in Western Europe, for instance, aluminium is hardly ever used in the manufacture of electrical
machines? Or why are electrical machines using copper lighter and more compact that aluminium designs (for the
same efficiency)?
2
Practical applications of electrical conductors
Figure 1: Squirrel-cage rotors cast from copper were
exhibited to the public for the first time at the Hanover
Trade Fair in 2003
1.2
Figure 2: In high-voltage cables the insulating material
makes up a greater fraction of the total cross-sectional
area than the conductor material
Electrical machines
Consider an electric motor in which aluminium rather than copper is used for the motor windings. If this motor
is to be technically equivalent to one wound with copper (particularly with respect to efficiency), the current densities
have to be reduced by 40%, that is the cross-sectional area of the conductor will have to be increased by 64%, thus
increasing the size of the laminated core and all other mechanical components. However, the electrical sheet steel
used for the laminated core also has its price on the markets, which essentially cancels out the savings made by using
aluminium rather than copper in the windings. As a result, work has been underway for a number of years aimed
at casting the rotor cage from copper.4 A number of these new rotors are now commercially available and have already
been used in the first practical applications (Figure 1). The problem of casting the rotor cages from copper was the
much higher melting point of copper (1083 °C) compared to a much more convenient 660 °C for aluminium. This led
to a significantly higher rate of wear of the casting mould. Fortunately, these problems have now been solved and
moulds with economically feasible lifetimes are now available.5
Comparison of Dimensions
Cable diametre
13.2 mm
Typical fire resistant cable
3 * 1.5mm2 with protective earth
Cable comprises sheath and core insulation of organic insulant with glass fibre or mica filler and
flame protection foil
Cable diametre
7.2 mm
Mineral-insulated cable
2 * 1.5mm2 with copper sheath as protective earth
Cable comprises copper sheath and mineral insulant, optional outer sheath of LSF plastic
Figure 3: Mineral-insulated cables
1.3
Figure 4: The structure of ‘fireproof’ plastic-coated cable
and mineral-insulated cable
Cables and wiring
Space is really a critical criterion when discussing electrical cables and wires. In a low-voltage (LV) plastic-sheathed
cable with conductor cross-sections of up to 10 mm2 per conductor (Figure 5) or in high-voltage (HV) cables (Figure
2), the lion’s share of the cross-sectional area is occupied by the insulating material. If aluminium rather than copper is
used as the conductor material, the additional cross-sectional area required is more or less negligible in comparison.
3
Practical applications of electrical conductors
At least that is the situation for conventional plastic-coated cables. Mineral-insulated cables and wires (Figure 3) are
not only absolutely fireproof6, they also take up much less space (Figure 4) than conventional plastic-sheathed cables.
For a time, these mineral-insulated cables were even equipped with an aluminium sheath, but this never became
established and copper sheathing remains the norm.
Figure 5: Even in building installation and service cables,
the conductor material still makes a smaller contribution to
the total cross-sectional area than the insulating materials
Figure 6: Only in low-voltage high-current cables does the
conductor material make up most of the cable’s total crosssectional area
And in most European countries, copper is still used predominantly, if not exclusively, for electrical installation work
in buildings. So why is it that most European standards do not permit the use of aluminium conductors with crosssections up to 16 mm2 (or in some cases) up to 10 mm2?
There are three main reasons:
•
Although aluminium is quite ductile, it is not as ductile as copper. The ends of stiff wires laid in walls
e.g. as connections to flush-mounted sockets or wall outlets tend to break after being repeatedly bent back and
forth. This can be problematic if the imminent fracture point is located inside the insulating sheath and if the wire
continues to be used. In such cases the fault can remain undetected until the wire has to carry a sizeable current
(that is one close to its rated maximum current) and although it could be years before this situation arises, when
it does, the conductor material will melt at the fracture point and sustained arcing can occur. Aluminium also
tends to form these local constrictions more readily than copper and as it has a lower melting point and a lower
coefficient of thermal conductivity than copper, this sort of local melting will occur more readily in wires and
cables with aluminium conductors. In the worst case, this can cause the aluminium to catch fire and burn like
a fuse wire.
•
When exposed to air, the surface of aluminium rapidly becomes covered by a hard, durable oxide layer that does
not conduct electricity, thus making it harder to ensure electrical contact. The build up of oxide at points where
aluminium wires are terminated or connected, can increase the local electrical resistance of the conductor. The
increased resistance can cause elevated temperatures with the risk of heat damage to the insulating materials
and possibly fire. Copper also undergoes oxidation when exposed to air, but perhaps surprisingly, the oxide
layer does not inhibit electrical contact, even though the copper oxides (CuO and Cu2O) have conductivities
some 13 orders of magnitude less than elementary copper and can therefore hardly be described as electrical
conductors.
•
Aluminium has a propensity to undergo slow material creep. When subjected to high pressures, the material will
yield over time. One result of this is that originally tight connections may gradually become loose. Connection
technology is available that can deal with this problem and it is worth investing the extra cost and effort involved
for installations involving relatively few connection points (e.g. HV overhead transmission lines), but not for more
complex branched networks such as those found inside buildings.
Because of the second of the three problems listed above, connections involving the ends of aluminium conductors
should always be made as tight screw-fastened contacts. Unfortunately, the third problem discussed above means
that these joints are often not permanent. Spring contacts can be helpful, but they tend to suffer from the problems
associated with the insulating aluminium oxide layers. In both cases, the result is a slow rise in the contact resistance
4
Practical applications of electrical conductors
at the connection point and thus to an increased risk of fire. Grandfathering regulations continue to protect older
aluminium installations in Eastern Germany and in most countries in Eastern Europe, but the only real protection
being provided by this sort of regulation is protection from the threat of improvement! Fortunately, methods are
now available for ensuring proper electrical contact between these older ‘protected’ installations and newer electrical
systems. These connectors combine spring-loaded contacts with a special contact paste made from grease and sharp
metal particles. When the connection is made the particles penetrate the existing aluminium oxide layer while the
grease protects the contact area from renewed corrosion.7
Copper is also the preferred conductor material in high-voltage cables. Although the use of aluminium would result
in only a slight increase in the overall conductor cross-section, the insulating materials and the exterior shielding
required for HV cables are expensive and the greater total cross-sectional area of the cable would cancel out the
savings made by using the cheaper conductor material – in contrast to the situation with low-voltage power cables
(Figure 6). It is also worth remembering that the cable shielding is always made from copper, because it is the only
material suitable for the job. If aluminium is chosen as the conductor material, then processing the scrap cable at the
end of its (admittedly long) service life will involve the additional step of separating the two materials.
As a material, pure copper has a practically infinite lifetime. It can be reprocessed an indefinite number of times
without suffering any loss of quality. About 45 % of the copper required today is generated from scrap, and the
products for which it is used (cables, transformers, water pipes or roofing) will remain in use for a long time, on
average around forty years. However, forty years ago, the demand for copper was only about half of what it is today.
It follows that about 90 % of the copper used at that time is still in use today. This applies equally to aluminium and
other metals. Metals are not consumed, they are used.
1.4
Which metal for which job?
Apart from their electrical conductivity, the other technologically important properties of copper and aluminium
differ so significantly (density is an obvious example) that their areas of application are and have always been clearly
distinct (Figure 8). And not a lot has changed or is likely to change in that respect. The only really novel development
in recent years has been the introduction of cast copper rotor cages (Figure 1). There are really only three, now four,
areas in electrical engineering in which aluminium and copper are competing in the same market segments:
New!
All telecom wiring
Motors
HV and
EHV
underground
cables
Busbars
Transformers
Building wire
Copper
Figure 7: The underground cable in use at
Dietlikon power station in Switzerland: a
compromise solution that combines the
technological properties of copper and the
price of aluminium
All high and
medium voltage
overhead wiring
Cast squirrel cage rotors for
three-phase
induction motors
Low and medium voltage
underground cables
Aluminium
Figure 8: Practical uses of copper and aluminium in the electrical
engineering sector: areas in which both metals can be used are rare
5
Practical applications of electrical conductors
•
Low- and medium-voltage cables: The decision here is which is the lesser of two evils: a greater cable crosssection or a higher cable weight? Generally speaking, aluminium cable will be substantially cheaper. However,
it is still worth recalling that copper cable is more ductile and less susceptible to electrical contact problems and
thus offers a greater margin of safety than a corresponding aluminium cable. Due to its smaller cross-section,
the copper cable will also be easier to install as the stiffness of the cable depends on the square of the crosssectional area and thus on the fourth power of the diameter! It is also possible to get very small stranded copper
cable; stranded aluminium cable is only available at nominal cross-sectional areas of at least 10 mm2 and the
individual strands are still very thick compared to those in the equivalently sized copper cable. For technical
reasons, so-called ‘finely stranded’ and ‘extra finely stranded’ conductors are only available in copper.8 As a result,
the finest aluminium conductors available are significantly stiffer than the finest copper conductors and this
difference has on occasion led to some rather costly surprises. On paper, the aluminium conductor may well be
cheaper to buy, but that fails to take into account the extra cost and effort involved in installing the less pliable
aluminium cables.9 Recently, a combination Cu-Al cable has appeared as a compromise solution and is being
used at the Dietlikon power utility in Switzerland as an underground cable in low-voltage distribution networks
(Figure 7). A representative from the Swiss Dietlikon plant gave a presentation on the product and the underlying
concept after being invited to attend meetings of DKE Committee 712 ‘Safety of Information Technology
Installations including Equipotential Bonding and Earthing’ (DKE: German Commission for Electrical, Electronic
and Information Technologies). The Dietlikon electricity utility is the first known distribution network operator
that is systematically converting its distribution network to a five-wire TN-S system – work that it of course only
carries out during repairs, network expansions and new installations. In this new cable, the phase conductors
have the same cross-section as the neutral conductor, which helps to achieve a symmetrical cable structure. The
phase conductors are made of aluminium, while the same-diameter neutral conductor is of copper, enabling it to
carry a greater current and thus making the cable better suited to coping with the harmonic pollution problems
that are so commonly discussed today. The protective earth conductor is configured in this case as a surrounding
copper-wire shield, which offers far higher symmetry and EMC than a conventional fifth conductor.
•
Transformers: The problem of winding space is not as acute in transformers as it is in electric motors, which
is why the use of aluminium can at least be taken into consideration. In fact the main leakage channel, i.e. the
gap between the HV and LV windings, must have a certain size for the following three reasons: insulation, limiting
the short-circuit current, and cooling.10 However, a transformer with aluminium windings will be larger if power
losses and all other important operational data, such as the short-circuit voltage, are to be kept at the same level
as an equivalent transformer with copper windings (after all, this is what we mean when we say two transformers
are equivalent). However, the total weight of the marginally larger transformer with aluminium windings will
be slightly lower. Differences in manufacturing costs pretty much cancel each other out and in the opinion
of a number of well-respected manufacturing companies, the choice of conductor material is primarily a question
of company philosophy.
•
Busbars: In this application, spatial requirements weigh even less heavily in the decision-making process, but still
remain a factor. Secondly, busbar applications are characterized by a large amount of conducting material and
a small quantity of insulating material in a small space. This highlights the differences in material prices. Thirdly, the
large number of electrical connections within this small volume mean that the connectivity problems associated
with aluminium are more pronounced in such applications. When all these aspects are taken into consideration,
we are left with a stalemate and the question of which material to select becomes almost philosophical. However,
it is important to ensure that prices and costs are not being confused. If price is taken as the main criterion for
selection, aluminium generally tends to be preferred. But if all the costs (including operational costs) are taken
into account, it usually turns out that aluminium can learn a thing or two from copper.11 Copper it seems also has
the better appearance, because some of the aluminium busbars available are copper-coated – not to improve
electrical contact (because drilling, punching and screwing will anyway damage the copper coat), but simply for
aesthetic reasons (Figure 9, Figure 10).
6
Practical applications of electrical conductors
Figure 9: There are copper busbars, aluminium busbars …
•
Figure 10: …and copper busbars made of aluminium
One new area of application is copper rotor cages (Figure 1): In this application, the crucial factor is the greater
electrical conductivity per unit volume of copper. This factor alone made it worthwhile tackling all the technical
problems associated with the development of these devices. For more information, the reader is referred
to descriptions available elsewhere.4, 5
Aluminium’s undisputed domain is that of overhead high-voltage cables,12 where space requirements are of no
significance but where weight plays a critical role. The lower strength of aluminium means that the conductor cables
need to be reinforced with a steel core but this does not change the fact that the cables can be produced at low cost
and that the two materials can be readily separated from one another magnetically when scrapped.
2
Non-metallic conductors – a real alternative?
The so-called semiconductors like germanium and silicon, which in the periodic table of the elements are located
between the metals and the nonmetals and which are at the heart of the electronic systems that we know today, are
a subject in their own right and would go well beyond the scope of the present article. But semiconductors aside, we
can ask whether metals are the only other materials capable of carrying an electric current. Or are there other substances that could be usefully deployed as conductors?
2.1
A material for special purposes: Carbon
We are all familiar with the graphite electrodes in electric arc furnaces, and graphite electrodes were also used
in discharge lamps. In fact, the very first incandescent lamps were produced not with tungsten filaments but with
filaments made of carbon. Carbon brushes are still used today to establish electrical contact with the commutator
segments in DC machines. They are called brushes because their predecessors were in fact made from braided copper
and looked like tiny brushes. But graphite has better lubricating properties than copper. In applications in which the
significantly lower electrical conductivity of carbon is insufficient, sintered graphite-copper composites are available
(Figure 11). As sintered materials are not alloys they do not suffer from the reduction in conductivity that typically
accompanies the alloying process.
2.2
Important in electrochemistry: liquid conductors
Electrolyte solutions are typically made up of ionic salts dissolved in water in which the charge-carrying ions are
free to move. The dissociation of ionic salts in water to yield conducting fluids underlies such important processes
as electrolysis or the generation of electric power in a battery, and it gives soil its electrical conductivity, albeit one
that is very low and strongly weather dependent. In order to show compliance with some (often seemingly arbitrary)
soil resistance limit value, those in the know will carry out the requisite earth resistance measurements after a heavy
downpour of rain. It is worth emphasizing that the resistivity values shown on the left in Table 1 all have the factor
10-6 attached. The resistivity values of metals and those of what we commonly refer to as earth therefore differ by
between 6 and 12 orders of magnitude!
7
Practical applications of electrical conductors
2.3
Electrically conducting polymers: the material for a new generation of cables?
Plastic materials that are themselves able to conduct electricity (i.e. organic polymers that are ‘intrinsically conducting’)
are rare. Most electrically conducting polymers (so-called ‘conductive polymers’) are plastics that have been induced
to carry electrical current by adding fillers such as stainless steel flakes, steel fibres, silver-coated glass beads, graphite
or carbon black. The fraction of these additives is usually limited to a few percent by volume so as to be able to continue to exploit the properties of the organic polymer itself. As a result, the electrical conductivities of these materials
are at least four orders of magnitude lower than in metal conductors, in some cases the conductivity is reduced
by as much as 14 orders of magnitude. These relatively low conductivities are adequate or even desirable as these
materials are predominantly used to discharge or prevent static charging and to shield high-frequency electrical
or electromagnetic fields and waves. When it comes to potential applications for conductive polymers, power and
data transmission cables are hardly top of the list. Although one speaker at a discussion meeting13 on the subject
did present a demonstration model in which a torch bulb (estimated current: 50 mA) was connected to a battery via
an electrically conducting polymer rod (estimated cross-section: 10 mm2). The current density in the conductor was,
however, still about three orders of magnitude lower than would be found in copper or aluminium. If these sorts
of materials are going to replace metals in certain applications, they are likely to be used in the form of very thin
foils or extremely thin layers laid down by vapour deposition that are designed to provide shielding from electrical
fields. In fact, such applications are already well-established. If the plastic casing of a device that has to be protected
from emitting radiation or protected against the effects of incoming radiation is already (slightly) conducting, then
this type of antistatic coating can be dispensed with. It is of course perfectly justified to ask why one would want to
replace a metal casing with a plastic casing, when the metal was anyway better at providing the required screening
properties and when the plastic has first to be made conducting by incorporating metallic additives. The answer lies
in the extrudability of the plastic polymers and the greater scope they offer in terms of coloration and design. But who
knows? Perhaps metals will find a way to close the gap.
Intrinsically conducting polymers were discovered about 25 years ago, with one such polymer having an electrical
conductivity similar to that of a metallic conductor. The problem with these materials, however, is that they are all
infusible, non-formable and insoluble – making them practically impossible to process. They are also susceptible
to attack by oxygen and when exposed to air they fairly rapidly lose their conductivity, which it turns out is not
only directionally dependent but also varies strongly depending on the manufacturing process used. It is obvious
that materials with these properties will never be selected in favour of metal conductors, which exhibit far superior
processability and stability. In a number of instances it has proved possible to improve the properties of intrinsically
conductive polymers, but this has always resulted in a reduction in the material’s electrical conductivity by several
orders of magnitude. These materials are used in the same limited areas as the conductive filled polymers, namely in
the prevention of static charge build-up. One such material is polyethylene dioxythiophene (PEDT), which is used to
provide antistatic coatings for photographic film. Without the PEDT coating, the film would accumulate static charge
during the photographic development process. If allowed to build up, the charge can discharge as a flash of light
that would re-expose the film and ruin the original image. The final image would then look like it had been taken in
a thunderstorm.
It should be mentioned that electrically conducting polymers have been used for some time in power transmission
systems, specifically in HV cables, where so-called ‘semiconducting layers’ are introduced once around the conductor
and once between the inner insulation and the outer cable coat, the latter serving to provide ‘field-strength control’.
This enables the electric field to be kept as homogeneous as possible and prevents local spikes in the electric field that
would cause partial discharging and the gradual destruction of the cable’s insulation.
Despite the currently rather limited applications of conductive polymers, one visionary at Kabelwerk Brugg was
not deterred from publishing an article in an IEC information leaflet in which he describes a scenario for ‘Power
Networks 2050’ where each network is composed exclusively of cables that are made from conductive polymers
and that can therefore be manufactured in a single extrusion process. The exceptionally high insulating capacity
of the insulating material (around 100 kV/mm) would apparently also enable high-voltages to be used in living
areas. Working electricians will no doubt shudder at the thought. The high capacitance of such cables certainly
helps to reduce EMC problems, but the calculations on which this vision of the future is based completely ignore
the tripping conditions in these cables and fail to take a number of other important factors into account. The
company’s website14 makes no mention of such flights of fancy and an enquiry as to what had become of the idea
yielded the information that no one knows anything about it and the author of the original article left the company
some time ago.
8
Practical applications of electrical conductors
Figure 11: Brushes made from a sintered graphite-copper
composite are an alternative to pure carbon brushes
2.4
Figure 12: The structure of a superconductor: Copper is an
essential component of superconducting cables
Superconductors
Superconductivity is a physical phenomenon exhibited by certain materials in which at temperatures below a materialspecific critical temperature the materials lose their ohmic resistance making them in principle able to conduct electric
current without loss. The discovery of high-temperature superconductors a little more than 20 years ago resulted in
an astonishing increase in the critical temperature from around 4 K before the discovery to around 100 K afterwards.
In other words, the distance from the critical temperature to absolute zero increased by a factor of 25. Roughly put,
one could say that the use of superconductors in applications suddenly became about 25 times easier. For instance,
for so-called high-temperature superconductors, the refrigerant medium is liquid nitrogen, which is far cheaper to
produce than the liquid helium previously required. But 100 K is still -173 °C and the effort required to maintain this
temperature is large. But this effort may well be worthwhile, particularly in applications that exploit another beneficial property of superconductors – their ability to carry current densities approximately one hundred times greater
than those in metals, where current densities are limited by thermal effects. Semiconductors are used to generate
extremely powerful magnetic fields for research in nuclear physics and for medical diagnostics. They are also used in
the construction of lighter machines for applications in which volume or weight are of crucial importance. For a long
time many of these highly specialized applications delivered behind-the-scenes benefits that remained generally
unknown to the wider public. An industry association15 has now been established in Germany that is working to
promote superconducting applications and improve public recognition of these technical developments. Applications
include a drive system for a naval vessel and an 8 MW wind turbine. Superconducting short-circuit current limiters
also look set to revolutionize power network engineering. Until recently the demands for a vanishingly small network
impedance during normal operations and for a sufficiently large impedance in the event of a short-circuit appeared
incompatible and a compromise solution was needed. It now seems that it is possible in principle to meet both
demands and a number of systems are currently undergoing practical testing. In addition to the critical temperature
another important parameter of any superconductor is its saturation current density, called quench, that is the
current density at which superconductivity suddenly collapses just as suddenly in fact as it appears. The remarkably
simple solution to this problem involves a conventional metallic conductor (usually made of copper) that surrounds
the superconductor and that carries the current for the very short period until the short-circuit has ceased with the
current limited by the ohmic resistance of the metallic conductor.
9
Practical applications of electrical conductors
The numerous reports in recent years of the potential of superconductors to save energy should, however, be viewed
with a healthy degree of scepticism. The power network components that we have been discussing such as extrahigh-voltage underground cables and large transformers already have efficiencies significantly above 99 %, in fact
a high-power transformer (≈800 MVA) exhibits an efficiency of 99.75 % at full load and 99.8 % at half load. In grids
such as those in Germany, Austria and Switzerland no more than 5 % of the electrical energy is lost along the path
between the power generating station and the domestic outlet socket – and most of that 5 % is lost in the heavily
branched low-voltage distribution network. Distribution transformers have efficiencies of ‘only’ 98.5 % at full load
and 99.0 % when operating at half load.16 Even if copper losses at half load are a quarter of their value under full load
conditions, the energy needed to cool the transformer down to the cryogenic temperatures of a superconductor
remains unchanged. A (relatively large) distribution transformer with a rated output of, say, 1 MVA and losses of 15 kW
(or significantly less than 5 kW when operating at half-load) would have to be maintained at a temperature of 100 K in
order for any sort of energy savings to be made. And even then, only the copper losses would be eliminated, not the
iron losses that actually contribute substantially to the transformer’s life-cycle costs.
Calculations have shown that for an extra-high-voltage underground cable a positive energy balance would be achieved
at transmission powers of 5 GW and above. That corresponds to the total power output from four nuclear power plant
blocks. But a cable of this type does not exist as there is simply no demand for it at present and there is unlikely to be any
demand in the future. The model calculation is thus purely academic and of no real practical utility.
There have also been reports of energy savings of ‘up to 50 %’ if the wind turbine mentioned above is fitted with
a superconducting generator. First of all, the expression ‘up to’ is usually of no practical worth as it only ever specifies one
extremum, while the other extremum in the opposite direction and the average value are never mentioned. Secondly, what
is meant here is, of course, a reduction in the losses, which translates to an energy saving of about 1 % of the energy generated.
Wind turbines typically operate at full load for only a relatively few number of hours per year. It is all the more important
then to recall that the copper losses increase with the square of the load, but that the cooling for the superconducting
material is a permanent requirement and has to be maintained even during windless periods as the duration of such
periods is unpredictable. It is also worth noting that one could also save about 90 % of the power losses using conventional
copper conductors were these conductors cooled from the usual operating temperature to cryogenic temperatures. The
temperature dependence of the ohmic resistance of copper would effectively allow us to create a ‘90 % superconductor’
– but nobody would ever do this, because it is simply not worth it. Finally, we note that superconductivity functions only
fully with direct electric current, and is only partially present with alternating currents. Attempts to use superconductors
directly to avoid ohmic losses and thus save energy are well suited to newspaper reports or political sound bites, but they
tend to be compromised by practical realities. Superconductors do though offer extremely interesting applications in areas
where copper and silver conductors cannot be used. Returning to the wind turbine discussed above, the generator can be
made smaller and lighter by using superconducting materials and this opens up new performance categories that would
unattainable with a conventional electric generator, as a conventional generator would be so heavy that no crane is currently
available that could lift it into place. A fact that is generally not mentioned too prominently in the relevant press releases.
2.5
Carbon again: Nanotubes
Some years ago the national papers started to report on something called ‘nanotubes’. As the name suggests,
nanotubes are tiny tubes of rolled-up graphite with diameters of around 1 nm. According to these reports, these novel
tubules have all sorts of beneficial properties among them ‘high electrical conductivity’. But what’s ‘high’? The lowest
resistivity value measured so far is 0.34 Ω·mm2/m – exactly 20 times higher than that for copper.
Physicists have also apparently measured extremely high current carrying capacities for these nanotubes, with some
measurements claiming ampacities of 1011 A/mm2. How is that possible? The answer lies in the minute size of these
tubules, whose diameters are six orders of magnitudes smaller than the wires in a typical electrical installation cable,
meaning that their cross-sectional areas are twelve orders of magnitude smaller. Relative to the cross-sectional area,
a nanotube therefore has 106 times more surface area available than a conventional copper wire over which it can
dissipate heat – a similar ratio to that found between small and large transformers.17 However, if the nanotubes are
bundled together to produce a conductor with a cross-section of 1 mm2, the bundle will not have much more surface
area available than a conventional wire, as the following calculation shows: A cube of ‘nanotube material’ with an
edge length of 1 m has a resistance of 0.34·10-6 Ω. If it could be made, a ‘nanowire’ 1 m long and with a cross-sectional
area of 1 mm2 would have a resistance of 0.34 Ω. At the current density of 1011 A/mm2 mentioned above, the ‘nanowire’
would have to carry a current of 1011 A. The power loss in this one-metre-long ‘nanowire’ would therefore be:
V
P = I 2 R =1022 A2 ⋅0.34 = 3.4⋅1021W .
A
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Practical applications of electrical conductors
It goes without saying that the nanotubes would be destroyed within a nanosecond. But so far this question has no
real practical relevance because firstly, no one is seriously thinking about using these materials as electrical conductors
(information on possible future uses of nanotubes can be found on a dedicated website18) and secondly, the longest
nanotube created thus far is only 1 mm. While that may sound pretty modest on its own, relatively speaking it
corresponds to a length of 1 km in a conventional wire with a diameter of 1 mm. And we all know how important it is
for physicists to see things relatively.
(Endnotes)
1 Information leaflet i4 ‘Kupfer / Vorkommen, Gewinnung, Eigenschaften, Verarbeitung, Verwendung’ [‘Copper: Deposits, extraction, properties, processing,
use’, available from the German Copper Institute (DKI), Düsseldorf, Germany or at: www.kupferinstitut.de
2 www.burde-metall.at/iacs.htm
3 www.copper.org/applications/electrical/building/wire_systems.html
4 www.copper.motor.rotor.org
5 Stefan Fassbinder: ‘Eine runde Sache: Kupferrotoren’ [‘Turning to efficiency: Copper rotors’] in de, 20/2004, p. 68
6 Stefan Fassbinder: ‘Brandsichere Kabel und Leitungen’ [‘Fireproof cables’] in etz, 1-2/1997, p. 48
7 Fritz Hengelhaupt: ‘Kontaktverbessernde Wirkung von Kontaktpasten für die Elektro-Installation’ [‘The use of contact pastes in electrical installation work’]
in de, vol. 15-16/2001, p. 38
8 EN 60228 (VDE 0295):2005-09
9 Stefan Fassbinder: ‘Rationalisierungsmaßnahmen in kommunalen Stromnetzen’ [‘Rationalization strategies in local electric power networks’] in de, 5/2001, p. 40
10 Stefan Fassbinder: ‘Verteiltransformatoren – Teil 3: Betriebsverhalten’ [‘Distribution transformers – Part 3: Operational behaviour’] in Schweizer Zeitschrift
für angewandte Elektrotechnik, 4/2005
11 alumno: Spanish for student or pupil
12 Stefan Fassbinder: ‘Erdkabel kontra Freileitung?’ [‘Underground cable vs. overhead cable?’], in de, 9/2001, appears in DKI reprint ‘Drehstrom, Gleichstrom,
Supraleitung – Energie-Übertragung heute und morgen’ [‘Three-phase AC, DC and superconducting systems – Power transmission now and in the future’]
from the German Copper Institute (DKI), Düsseldorf
13 www.otti.de
14 www.brugg.ch
15 www.ivsupra.de
16 Stefan Fassbinder: ‘Verteiltransformatoren – Teil 5: Wirkungsgrad von Verteiltransformatoren’ [‘Distribution transformers – Part 5: Efficiencies of distribution
transformers’] in Schweizer Zeitschrift für angewandte Elektrotechnik, 6/2005
17 Stefan Fassbinder: ‘Verteiltransformatoren – Teil 1: Warum überhaupt Transformatoren in Versorgungsnetzen?’ [‘Distribution transformers – Part 1: Why
have transformers in distribution networks?’] in Schweizer Zeitschrift für angewandte Elektrotechnik, 1/2005, p. 79
18 http://www.pa.msu.edu/cmp/csc/nanotube.html
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Practical applications of electrical conductors
12