Photo courtesy AEM.
All modern countries are crisscrossed with high-voltage
transmission lines, which
transport electrical power from generators at power plants to substations and
ultimately consumers. Why are high voltages used? What are the advantages of
alternating current (AC) versus direct current (DC)? How much energy is lost
in transmitting electrical power over long distances? The main physics principle
this topic addresses is electrical resistance.
Electrical current, the flow of charge, has a sort of friction
associated with it,
which is called resistance. Good conductors, like most metals,
allow current to flow
without much loss. Poor conductors, like most non-metals, impede the flow of
current to a great extent. Superconductors like very cold
niobium-tin, are special substances that allow
current to flow with essentially zero loss; semiconductors,
like silicon, are either good or poor conductors depending on certain conditions.
You get current to flow through a conductor by applying a voltage across
it. The amount of current that flows is measured in
amperes, or amps,
named after a 19th-century French physicist and abbreviated
A. An ampere is a fairly large amount of current: 0.1 A flowing between
your hands across your heart will kill you. (Fortunately, your body
has fairly high resistance so it takes a substantial voltage to drive
that much current.) Voltage, or electric potential, is measured
in volts, named after a
physicist named Volta, and abbreviated V.
Most small batteries (size AAA, AA, C, D) are 1.5 V; there is the
familiar box-like 'transistor' 9 V
battery, and car batteries are 12 V. In contrast, high-voltage lines
have many thousands of volts between them.
Resistance quantifies how much current you get across something per
volt applied. Namely, if you apply a voltage V across a
wire and measure current I, the resistance R is
R = V/I
Resistance therefore has units of V/A, which get another name, ohms,
represented by the Greek letter .
We are all aware that electric current can transport energy from
one place to another: the energy given off by a 100 Watt light
bulb in your bedroom originated by burning coal or slowing down
falling water or releasing nuclear energy at a power plant, for
example. The expression for electric power comes from
the definitions of electric potential (volts) and electric
The MKS unit of energy is the joule (J) and the
MKS unit of electric charge is the coulomb (C), which is the
amount of charge that flows by in one second if the current is
one amp. The volt is therefore defined by saying that if a
charge of 1 C moves across a potential drop of 1 V it picks up
energy 1 J:
1 V = 1 J/C
In general, then, a charge Q picks up energy
U = QV
when it moves across a
potential drop V.
Electric power is the rate at which energy is
transported. Since current is the rate of transport of charge,
electric power is given by the above expression, but using
current I instead of charge Q:
P = IV
This is a very handy formula. For example, you may see written
on your hair dryer that it draws 10 A current on the hot setting
from a standard US 110 V outlet. This means that the power
drawn by the hair dryer is 10x110=1100 W, or 1.1 kW. That's
about as high a power as home appliances go,
and this is not too far from tripping a 15 A
circuit breaker, standard in modern US houses. For very high
power appliances, like a clothes washer or dryer, you may need a special
outlet and dedicated circuit breaker. (Note: even though house
current is alternating, or AC, at 60 cycles/sec (50 in Europe),
this formula works because the
average or RMS current and voltage are quoted and you
therefore get the average power.)
Another handy version of the power formula replaces voltage
V with resistance and current: V=IR:
P = I²R
High-Voltage Transmission Lines
So we now finally come to the topic of this page: the transport
of large amounts of electrical power over long distances. This
is done with high-voltage transmission lines, and the question
is: why high voltage? It certainly has a negative safety aspect,
since a low voltage line wouldn't be harmful (you can put your
hands on a 12 V car battery, for example, you won't even feel
it; but make sure you don't put metal across the
terminals, you'll get a huge current and a nasty spark!).
Electric energy is transported across the countryside with
high-voltage lines because the line losses are much
smaller than with low-voltage lines.
All wires currently used have some resistance (the development
of high-temperature superconductors will probably change this
some day). Let's call the total resistance of the transmission
line leading from a power station to your local substation
R. Let's also say the local community demands a
power P=IV from that substation. This means the
current drawn by the substation is I=P/V and the
higher the transmission line voltage, the smaller the current.
The line loss is given by Ploss=I²R,
or, substituting for I,
Ploss = P²R/V²
Since P is fixed by community demand, and
R is as small as you can make it (using big fat
copper cable, for example),
line loss decreases strongly with increasing voltage.
The reason is simply that you want the smallest amount of
current that you can use to deliver the power P.
Another important note: the loss fraction
Ploss/P = PR/V²
increases with increasing load
P: power transmission is less efficient at times of
higher demand. Again, this is because power is proportional to
current but line loss is proportional to current squared. Line
loss can be quite large over long distances, up to 30% or so.
By the way, line loss power goes into heating the transmission
line cable which, per meter length, isn't very much heat.
Alternating (AC) vs. Direct Current (DC)
Given that we want to reduce line loss by using high voltage,
the choice between AC and DC becomes straightforward. It is
quite difficult to reduce a DC high voltage to low voltage
without additional loss; it is easy to reduce an AC high voltage
to low voltage using a step-down transformer. You see
lots of these when you walk by a substation. An ideal
transformer reduces V and increases I so
that the power IV is constant. A neighborhood
substation typically reduces the voltage to a reasonable value
for street lines, say 330 V, and then a small transformer
outside and/or inside your house reduces it to 110 V (220 in
Europe). Since the current and voltage are alternating with
sine waves, the power delivered to, say, a toaster also
oscillates. The current or voltage oscillation frequency is 60
cycles/sec (60 Hz) in the US and 50 Hz in Europe. The figure
below shows how the current, voltage and power look as a
function of time along with the average (RMS) values for a load
drawing 10 A in the US.
Voltage, current and power for a resistive appliance that draws
10 amps (like a toaster). The average (RMS) values are shown
with dotted lines. This appliance draws 1100 watts RMS.
- electric resistance: R = V/I
- electric power: P = IV = I²R
- Resistance quantifies the amount of current that
will flow in a wire per volt.
- Power loss due to wire resistance increases as the
square of the current and therefore decreases as the square of
the voltage at fixed total power. The loss fraction in a
transmission line increases with demand.