Download Magnetic Field and High-Voltage Power Lines

Student’s Guide
Magnetic Field and High-Voltage
Power Lines
Alexandre April
Olivier Tardif-Paradis
Mathieu Riopel
Cégep Garneau
Source : Alexandre April
High-Voltage Power Lines: Is There Cause for Concern?
Context
Dear Electricity and Magnetism Student,
I am looking for a new home, and I think I found my dream house. It seems perfect, but there is
something bothering me: the house is located right beside a high-voltage power transmission line. I have
heard that electric wires that carry these currents create a magnetic field. So I am worried. Will these
high-voltage lines near my future home have harmful effects on my health? Am I right to worry about the
presence of high-voltage lines around the home I want to buy? Before I make the purchase, I would like
to be reassured and have a clear mind.
I already checked the Hydro-Québec website about the health effects of the magnetic fields generated by
their network, and there seems to be no danger, but I would like to hear the opinion of an disinterested
party. I thought I would call on your expertise, as I understand that you are studying the production of
magnetic fields around wires that carry electric currents. Can you help me and calculate the typical
maximum magnetic field that exists around high-voltage lines? I would like to know whether the value of
the magnetic field produced by these lines is lower or higher than the standards in effect.
There is a good chance that you will need the value of the electric current that flows through electric
transmission lines like the one near my future home. To this end, I emailed Hydro-Québec and here is
their reply:
Hello,
Thank you for your interest in Hydro-Québec. In response to your question, we can confirm that the
amplitude of the electric current on the electric energy transmission lines varies considerably based on
electricity demand. On high-voltage lines, it may range from 1500 to 3000 A. On low-voltage lines, the
maximum amplitude of the electric current is 1200 A.
We hope this information will be useful to you. Please feel free to contact us with other questions or to
share your comments.
Sincerely,
Hydro-Québec employee
Thanks in advance for your answer to my question. I hope to hear from you soon.
Pierre Deschamps,
Hoping to be reassured for once and for all
PBL/Student’s Guide: Magnetic Field and High-Voltage Power Lines
2
Magnetic field produced by a long, straight wire
Transmission lines carry the electric energy generated by power stations to cities, where the people live.
In general, the current in these transmission lines is not direct, that is, it does not flow in just one
direction; the current is alternating at a frequency of 60 Hz. That means that the current flows in one
direction for 1/120 of a second and in the other direction for 1/120 of a second and so on. The alternating
current generated by power plants is divided into three parts, called “phases,” so we speak of “threephase current.”
The electric pylons scattered across Québec carry high-voltage
electric energy (735 kV). They support three groups of conducting
wires, one for each phase of current (see photo to the left). Each of
these groups (called bundles) is composed of four wires separated by
spacers (see photo to the right), which ensure constant spacing
between the wires. In practice, four wires are used instead of one to
optimize the transmission of electric energy: for example, four wires
that are 3 cm in diameter are as effective as a single wire that is 46
cm in diameter… and of course such a
wire would be much heavier!1 To
simplify this problem, however, we will
assume
each bundle has a single
Fig. 1
conducting wire of negligible diameter.
Source : Alexandre April
Furthermore, although conducting wires
are somewhat curved due to their weight,
we will assume that they are straight and horizontal. We should also
Fig. 2
mention the presence of two ground wires at the top of the pylon that do
not transmit electric energy. They are there as protection against lightning;
Source : Alexandre April
these grounded wires attract lightning so it will not strike the three-phase
transmission lines.
HYDRO-QUÉBEC, Comprendre l’électricité, [online], [http://www.hydroquebec.com/comprendre/transport/lignespylones.html] (Viewed November 30, 2015).
1
PBL/Student’s Guide: Magnetic Field and High-Voltage Power Lines
3
Figure 3 shows a diagram of a high-voltage pylon like the one behind Mr. Deschamps’s future
home.
8m
8m
I1(t)
I2(t)
I3(t)
25 m
P
Fig. 3 – Electric pylon supporting three conducting wires at a height of 25m above the ground; the three sets of wires
are separated by a horizontal distance of 8m.
Source: Alexandre April
The three currents (one for each phase) flowing through these conducting wires vary as a function of time
t and are expressed, as they are in Figure 1, as I1(t), I2(t) and I3(t). The equations for these currents
are:
I1 (t) = I 0 sin(w t)
I 2 (t) = I 0 sin(w t + 2p 3)
I 3 (t) = I 0 sin(w t + 4p 3)
where I0 is the amplitude of the current (its maximum value) and ω is a constant called the “angular
frequency”; in this case, since the current oscillates at a frequency of 60 Hz, the angular frequency is
w = 120p rad s. If the current is negative, that means it is flowing in the opposite direction from the
direction shown in Figure 3. Figure 4 shows these currents as a function of ωt. Note that although the
three currents all have the same maximum value I0, they do not all reach it at the same time (we say that
these currents are “out of phase” because they each have a different phase).
I1 (t)
I2 (t)
I3 (t)
I0
p 2
w t (rad)
Fig. 4 – The three currents flowing in the high-voltage line as a function of time.
Source: Alexandre April
PBL/Student’s Guide: Magnetic Field and High-Voltage Power Lines
4
Three-Step Cycle
List all the relevant information you have gathered from the problem. Based on this information,
state what you need to know to solve the problem. As new information comes in, you will want to
summarize and update the relevant information you have gathered and ask new questions.
List the following:
What we know
What we need to know
Summary
PBL/Student’s Guide: Magnetic Field and High-Voltage Power Lines
5
Questions
We are going to calculate the magnetic field at point P (see Figure 1) at two different moments to
check whether the value obtained is lower or higher than the standards in effect (see box below).
Exposure standards for 60 Hz magnetic fields2
There is no Québec or Canadian standard for public or worker exposure to 60 Hz electromagnetic
fields. Internationally, there is an influential non-governmental scientific organization, the
International Commission on Non-Ionizing Radiation Protection (ICNIRP), that issues
recommendations concerning exposure limits to 60 Hz electromagnetic fields. According to this
organization, the exposure limit is 200 μT.
First consider the moment that corresponds to
one is at its maximum (see Figure 4).
ωt = π/2 rad, when all three currents are not at zero and
1) Determine the value of the electric current flowing through each wire, taking into account the signs
(which tell you the direction of the current). To estimate the magnetic field in the worst conditions,
take the biggest amplitude provided by Hydro-Québec.
2) On a diagram that accurately shows the three currents (including their directions), draw the magnetic
fieldlines, passing through point P, that are generated by the three currents. Then show the magnetic
field vectors produced by these currents. Hint: The right-hand rule will be useful for determining the
direction of each magnetic field.
3) What is the mathematical relationship that allows you to calculate the magnetic field generated by a
long, straight wire with an electric current running through it? Once you have determined it, calculate
the magnitude of the magnetic field generated at point P by each of the three wires.
2
HYDRO-QUÉBEC, Le réseau électrique et la santé : les champs électriques et magnétiques, [online],
[http://www.hydroquebec.com/champs/pdf/pop_23_01.pdf], p.18, (Viewed November 30, 2015).
PBL/Student’s Guide: Magnetic Field and High-Voltage Power Lines
6
4) The magnetic field generated at point P by the three wires is the resultant of the three
magnetic fields (principle of superposition). Calculate the module of the resultant magnetic
field at point P attributable to the three currents.
5) An optimization calculation (like the ones you learn to do for differential calculus) allows you to
determine that the magnetic field attains its maximum magnitude at point P when ωt = 0.35π rad.
Repeat questions 1 to 4 now for the moment corresponding to ωt = 0.35π rad.
6) Draw your conclusion. Is the magnetic field generated by the currents in the transmission line lower
or higher than the standards in effect? Compare with the values of the magnetic fields that you
calculated with the terrestrial magnetic field modulus.
PBL/Student’s Guide: Magnetic Field and High-Voltage Power Lines
7