Download Transmission of electrical power

Topic 12: Electromagnetic induction
12.3 Transmission of electrical power
12.3.1 Outline the reasons for power losses in
transmission lines and real transformers.
12.3.2 Explain the use of high-voltage step-up
and step-down transformers in the
transmission of electrical power.
12.3.3 Solve problems on the operation of real
transformers and power transmission.
12.3.4 Suggest how extra-low-frequency
electromagnetic fields, such as those created
by electrical appliances and power lines,
induce currents in the human body.
12.3.5 Discuss some of the possible risks
involved in living and working near highvoltage power lines.
Topic 12: Electromagnetic induction
12.3 Transmission of electrical power
Outline the reasons for power losses in
transmission lines and real transformers.
Observe the simplified electrical grid:
FYI
Power is lost as heat during transformer step-up
and -down of the voltage due to eddy currents.
Power is lost as heat in the lines during the
current transmission due to internal resistance.
Topic 12: Electromagnetic induction
12.3 Transmission of electrical power
Outline the reasons for power losses in
transmission lines and real transformers.
For transmission lines, the gauge of
wire is determined in trade-off between
cost of large-diameter (low resistance)
wire, and cost of power lost due to lowdiameter (high resistance) wire.
P = I2R
heat loss in transmission lines
EXAMPLE: Many transmission lines are made of
aluminum (having a resistivity of 5.210-8  m)
reinforced with steel (see picture).
(a)What is the cross-sectional area of the cable?
SOLUTION: The diameter is
d = (4 in )(2.54 cm in-1) = 10 cm = 0.1 m.
The area is then
A = d2/4 = (0.1)2/4 = 0.008 m2.
Topic 12: Electromagnetic induction
12.3 Transmission of electrical power
Outline the reasons for power losses in
transmission lines and real transformers.
For transmission lines, the gauge of
wire is determined in trade-off between
cost of large-diameter (low resistance)
wire, and cost of power lost due to lowdiameter (high resistance) wire.
P = I2R
heat loss in transmission lines
EXAMPLE: Many transmission lines are made of
aluminum (having a resistivity of 5.210-8  m)
reinforced with steel (see picture).
(b)Assuming the cable is all aluminum, find the
resistance of a 150 km section.
SOLUTION: Use R = L/A:
R = L/A
= (5.210-8)150000/0.008 = 1 .
Topic 12: Electromagnetic induction
12.3 Transmission of electrical power
Outline the reasons for power losses in
transmission lines and real transformers.
For real transformers, there are eddy currents
(Ieddy  f2 )and hysteresis currents (Ihyst  f)
both of which are set up by Faraday’s law due to
the magnetic flux change that is part of AC
circuits. Both of these currents produce I2R heat
loss.
Hysteresis losses are less
significant than eddy
losses. Recall from Topic
12.2 that eddy currents can
be minimized by lamination
of the transformer core.
There is also the I2R heat loss simply due to the
resistance of the length of wire in the windings
in the primary and secondary coils.
Topic 12: Electromagnetic induction
12.3 Transmission of electrical power
Explain the use of high-voltage step-up and stepdown transformers in the transmission of
electrical power.
Recall that heat loss is determined by P = I2R.
Since the resistance R of the transmission cable
is fixed once its diameter has been chosen, the
only other way to reduce power loss is to reduce
the current I going through the cable.
Since P = VI, if we want to minimize I we
can do so if we increase V, thus maintaining
the power P that is to
be delivered.
This is the idea behind
the use of the step-up
transformer at the
generation side of the
power grid.
Topic 12: Electromagnetic induction
12.3 Transmission of electrical power
Explain the use of high-voltage step-up and stepdown transformers in the transmission of
electrical power.
Since the high voltage used for transmission is
very dangerous, at the end of the transmission it
is brought back down to a safer level through the
use of a step-down transformer.
Topic 12: Electromagnetic induction
12.3 Transmission of electrical power
Solve problems on the operation of real
transformers and power transmission.
PRACTICE: The 150 km cable whose resistance was
calculated previously to be 1  is designed to
deliver 270 MW to a community.
(a) If the transmission occurs at 138 kV, what is
the current and the heat loss?
(b) If the transmission occurs at 765 kV, what is
the current and the heat loss?
SOLUTION: Use P = VI ( or I = P/V ) and P = I2R.
(a) I = P/V = 270106/138103 = 2000 A (1957 A).
P = I2R = 19572(1) = 3.8106 W = 4 MW.
This is a 4/270 = 0.01 = 1% heat loss.
(b) I = P/V = 270106/765103 = 350 A (353 A).
P = I2R = 3532(1) = 1.2105 W = 0.1 MW.
This is 0.1/270 = 0.0004 = 0.04% heat loss.
Topic 12: Electromagnetic induction
12.3 Transmission of electrical power
Solve problems on the operation of real
transformers and power transmission.
Topic 12: Electromagnetic induction
12.3 Transmission of electrical power
Suggest how extra-low-frequency electromagnetic
fields, such as those created by electrical
appliances and power lines, induce currents in
the human body.
The frequency of transmitted and home-used power
is about 60 Hz, which is considered to be an
extremely low frequency (ELF).
The photons emitted by such ELF radiation are not
energetic enough to ionize living cells, and thus
cannot harm cells via ionization as alpha, beta
and gamma rays can.
The alternating field, however, can set up small
alternating currents in the body. This is because
there are both ions and polarized molecules in
cellular structures which can respond to
alternating electromagnetic fields according to
Faraday’s law.
Topic 12: Electromagnetic induction
12.3 Transmission of electrical power
Discuss some of the possible risks involved in
living and working near high-voltage power lines.
Many studies have shown that ELF fields do not
harm genetic material.
Studies on the effect of ELF-induced currents in
living cells are inconclusive, however.
Read the article
Power lines link to cancer
to see evidence that induced
currents do increase the
incidence of childhood leukemia.
Other obvious risks are danger
of electrocution.