Session III
HYDROELECTRIC POWER GENERATION
Michael D. March
American University, Department of Physics,
4400 Massachusetts Ave. NW, Washington DC. 20016-8058, mm9135a@student.american.edu
Abstract — Hydroelectric power generation is a renewable
source of energy capable of contributing to the world’s
increasing energy demands.
Throughout history,
hydropower was used to generate mechanical energy to
factories near the source of water. Michael Faraday’s
discovery of the principles of electromagnetic induction led
to the invention of the electric generator and electric
transformer, and modernized the way hydropower is used
today. In the modern world, hydroelectric power can
contribute to the world’s ever increasing energy demands.
Currently, tidal and wave power are being researched as
modern sources of renewable energy. Hydroelectric power
generation will never meet our entire energy demands;
however, this source of renewable energy is overall
environmentally friendly, and extremely efficient. This
paper will address the basic physics concepts involved with
hydroelectric power generation.
not generate as much electricity as a large dam due to the
unpredictable nature of the oceans’ waves, and the time
between the changing of tides; however, these systems can
benefit smaller communities located near coastlines.
Generating electricity by harnessing the energy of the
oceans’ waves is similar to traditional power generation by a
dam. However, in the case of most wave-generated power,
the potential energy of a body of water can be ignored,
because the usable energy is contained in the form of a
longitudinal wave. Harnessing the power of a transverse
wave is a bit less feasible, but nonetheless has inspired a
small amount of research.
Hydroelectric power generation has served as a reliable
source of energy ever since early Greeks and Romans
discovered that the energy contained in moving water could
be used as a means to power mechanical machinery located
near a water source.
Index terms — Electromagnetic induction, energy, faraday’s
law, generator, hydroelectricity, tidal power, transformer.
HISTORY OF HYDROELECTRICITY
INTRODUCTION
Hydroelectricity is one of the earliest known sources of
renewable energy. This time tested generation of energy is
so appealing because the input energy is water provided by
the Earth’s hydrological cycle [1]. Nature’s hydrologic cycle
of rain and snow feed rivers that lead to the oceans. During
this migration, the water evaporates into clouds to once
again begin the same cycle [2]. This self-renewing cycle is
environmentally safe, efficient, and naturally renewable.
Following the advent of the electric generator in 1881, a
hydroelectric facility in Goldaming, England, produced
enough power to light three street lamps. The first fully
functional hydroelectric power plant in the United States
began operating in 1882 in Appleton, Wisconsin. This plant
generated 1 horsepower, or 746 Joules per second of usable
energy transformed into usable electricity for the areas grid.
Before the end of that decade, an additional 200 power
plants were built, some still functioning today such as the
Hoover Dam, and Roosevelt Dam [3]. During the middle of
the 20th century, hydroelectric power accounted for almost
40% of the United States electrical consumption [4].
Currently researchers are interested in harnessing the
power of the oceans’ generating electricity. Generating
electricity with waves is possible due to the large kinetic
energy contained in them. These small-scale operations do
April 26, 2013
Today more than 1,400 hydroelectric plants in the United
States of America supply 7 percent of the nation’s electricity
[5]. The early Greeks and Romans used the power of water
to turn wheels that would power mills to grind grain for
bread [6]. The water wheel would be placed near a source of
moving water to generate mechanical energy to be used in
their basic machines. As the wheel turned, the induced
motion provided a source of mechanical energy for many
applications. A series of belts, shafts, and ropes transferred
the energy to simple machines [7].
By the 1700s’ this application would be used to power
factories that used saws and looms to produce textiles and
furniture [8]. Such an application was popular until future
technological advancements.
Prior to the industrial revolution, water was the main
power source for milling lumber and grain, and powering
machinery [9]. The design improved over time and
eventually was able to produce electricity due to Michael
Faraday’s discovery of Electromagnetic Induction, and the
invention of the electric generator.
Eventually hydropower would be used as a source for
generating electricity. In 1881, engineers at Niagara Falls
harnessed the power of water to power two electric street
lamps [10]. Later in 1882, the first fully operating
hydroelectric power plant in the United Sates began
operation in Appleton, Wisconsin. This plant produced
around 746 watts of power [11]. Within the next twenty
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years, 40 percent of the nation’s power was generated
hydroelectrically [12]. Between 1905 and 1930, the Hoover
Dam, located on the border of Arizona and Nevada, and
Roosevelt Dam northeast of Phoenix, Arizona were
constructed to meet increasing power demands in the rapidly
developing West [13]. These dams are still operational
today; however, the largest hydroelectric dam is no longer
located in the United States. The largest dam in the world is
now the Three Gorges Dam, located on the Yangtze River in
China. The Three Gorges Dam generates 22,500 MW of
electricity (figure 1) [14].
Tidal Power
Tidal wave power plants are traditionally set up as tidal
dams or barrages along coastlines. Opening a sluice in the
dam when the tides go in and out generates electrical power.
When the water levels of the ocean and the reservoir behind
the dam are at different levels, the sluice is once again
opened to allow water to flow through. Electricity is
generated as the water flows through the sluice and turns the
hydro-turbines [19].
Unfortunately tidal barrages often wreak havoc on the
marine life ecosystem, most notably fish populations. New
designs have emerged in result of these negative
environmental consequences.
Under water tidal turbines that operate like wind
turbines appear to be the most promising [20]. Interestingly
enough, researchers contend that tidal turbines can produce
more electricity in a given area than wind turbines. Since
water is more dense than air the turbines are smaller, require
less space, and operate more efficiently than wind turbines
[21]. Although this technology is new, the physics involved
with the generation of electricity has remained the same.
FIGURE 1 [15]
THREE GORGES DAM: YANGTZE RIVER CHINA
BASIC CONCEPTS OF PHYSICS INVOLVED IN
Many other dams’ of similar size are located throughout
the world in areas such as South America, the United States,
Canada, and India.
Hydroelectric technology continues to advance.
Compared to older dams such as the Hoover Dam, the dams
being constructed are larger than ever with very large power
outputs. Although the size and output of modern day
hydroelectric projects are becoming larger the components
responsible for the generation of electricity have remained
largely unchanged, and the physics remains the same.
HYDROELECTRIC POWER GENERATION
MODERN APPLICATIONS
Wave and tidal energy are currently under development.
The technology is expensive at this point, but the potential of
future viable energy sources appears promising; however,
local geography will influence the potential for electricity
generation with this technology. Researchers are studying
“special buoys, turbines, and other technologies that can
capture the power of waves and tides, and convert it into
clean, pollution-free electricity” [16]. According to the
Renewable Northwest Project the “United States receives
2,100 terawatt-hours of incident wave energy along its
coastlines each year” [17]. Tapping into just one-quarter of
this massive amount of energy would produce “as much
energy as the entire U.S. hydropower system” [18]. The
Pacific Northwest appears to be the best region for tidal
power generation.
April 26, 2013
Hydroelectric power generation is traditionally generated by
dammed storage. The reservoir of water contained by a dam
stores potential energy:
PE = mgh
(1)
In the case of a hydroelectric power plant generated by
dammed storage of water, the mass is represented by the
mass of the stored water; the height is represented by the
height of the dam, and the acceleration of gravity:
g = 9.8
m
s2
(2)
The water moves through a network of piping through
the dam, while also overcoming a change in elevation due to
the acceleration of gravity. When the intake of the penstock
is opened, the water travels to the base of the dam. The
motion of the water now contains kinetic energy, or energy
of movement. The formula for kinetic energy is determined
by the product of mass of a moving object times the square
of its velocity and multiplied by one-half. The equation is
represented as:
1
𝐾𝐸 = 2 𝑚𝑣 2
(3)
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Since energy is conserved due to the law of
conservation of energy that states, “Energy cannot be created
nor destroyed; it may be transformed from one into another,
but the total amount of energy never changes” [22]. The
amount of kinetic energy is equal to the amount of potential
energy of the water contained by the dam:
KE = PE
(4)
The kinetic energy then provides usable energy to the
dam’s components that are responsible for generating
electricity.
BASIC COMPONENTS OF
HYDROELECTRIC POWER GENERATION
The most common structure used to convert the energy of
moving water into electrical energy is the dam.
Dams are constructed in rivers and feature a large drop
in elevation. The purpose of a dam is to create a reservoir of
water that contains a large amount of potential energy due to
the change in head elevation. The height difference between
the water contained in the reservoir behind the dam and that
of the water released below the dam, or change in elevation
[23]. As a result of the change in elevation created by the
dam, the reservoir of water contains gravitational potential
energy. The reservoir of water travels through a penstock in
the dam, converting gravitational energy into kinetic energy
[24]. Penstocks’ are large metal pipes that serve as the
pathway for the water to travel from a high to an area of low
elevation at the base of the dam.
The penstock is responsible for the conversion of
potential energy into kinetic energy. At the end of the
penstock is a turbine connected to a generator. The force of
the water causes the turbine to rotate. The energy of the
turbine’s rotation is the source of the mechanical energy to
be transferred to the generator (figure 2) [25].
The shaft of the generator rotates coils of copper wire
surrounded by a ring of magnets [26]. This setup creates an
electromagnetic (EM) field capable of producing electricity,
which can be stored in batteries or sent to a transformer prior
to traveling through the electrical grid [27].
The entire process is in accordance with conservation of
energy laws. In order for the mechanical energy produced
by the turbine to become usable electricity, an electric
generator is necessary.
THE ELECTRIC GENERATOR
The physics involved in an alternating current generator
includes electromagnetic induction, Faraday’s Law of
Induction and magnetic force on current-carrying wires. An
understanding of DC motors also further clarifies the physics
of the electric generator. Beginning with a discussion on the
electromagnetic induction and the magnetic force on currentcarrying wires will provide a clear understanding to the stepby-step process of electrical generation, and the physics
involved in each of those steps.
Magnetic Force on Current Carrying Wires
With previous understanding of some basic physics
concepts, we know that “a charged particle when moving
through a magnetic field experiences a deflecting force, then
a current of charged particles moving through a magnetic
field also experiences a deflecting force” [29]. When the
current is reversed, the deflection will occur in the opposite
direction. The force is a sideways force or a vector force
that is perpendicular to both the magnetic field lines and the
direction of the current carrying wire (figure 4) [30].
FIGURE 4 [31]
DEFLECTION OF A CURRENT CARRYING WIRE
INFLUENCED BY MAGNETIC FIELD
This discovery led to a better understanding between
electricity and magnetism, therefore ushering great
experiments with electric meters and motors.
Electric Motors
An electric motor builds on the understanding of the
magnetic force on a current carrying wire. The main
difference however is that the deflection of the wire makes a
full rotation instead of a partial one (figure 5) [32].
FIGURE 3 [28]
HYDROELECTRIC DAM COMPONENTS
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Voltage increases proportionately by the number of
loops of wire moving within a magnetic field. For example,
a coil with 3 times the amount of loops produces 3 times the
voltage (figure 7) [39].
FIGURE 5 [33]
SIMPLE MOTOR
FIGURE 7 [40]
This is possible because the current through the wire
changes its direction each half-rotation. Following the initial
half turn the coil continues in motion where again, the
current is reserved, and as a result the coil is forced to
continue rotating in the same direction instead of being
reversed by the magnetic field [34]. Rotation is continuous
as long as an alternating current is applied.
The energy output of a simple motor and generators can
be determined with the physics represented in Michael
Faraday’s Law of Induction. However, an understanding of
the physics involved in Electromagnetic Induction is
necessary before proceeding to Faraday’s Law.
Electromagnetic Induction
Michael Faraday and Joseph Henry discovered that an
electrical current could be produced in a wire simply by
moving a magnet in and out of loops of wire without an
additional voltage source [35].
The phenomenon of
inducing voltage by changing the magnetic field in loops of
wire is known as electromagnetic induction [36].
Paul
Hewitt explains that, “Voltage is caused, or induced, by the
relative motion between a wire and a magnetic field-that is,
whether the magnetic field of a magnet moves near a
stationary conductor or the conductor moves in a stationary
magnetic field” (figure 6) [37].
FIGURE 6 [38]
VOLTAGE IS INDUCED IS RELATIVE TO MOTION OF
THE MAGNETIC FIELD AND ITS CONDUCTOR
April 26, 2013
VOLTAGE INCREASES PROPORTIONALLY WITH
ADITTIONAL COILS OF WIRE
However, increasing the amount of loops also increases
the tendency of the magnetic field to resist rotation, and as a
result requires a stronger applied force to induct voltage.
Interrupting a magnetic field quickly induces a greater
amount of voltage.
Faraday’s Law is a mathematical explanation of the
amount of energy produced during electromagnetic
induction.
Michael Faraday’s Law of Induction
In 1831, Michael Faraday with the aide of Joseph Henry
discovered that when a magnet is moved into a loop of
wires, electric current was induced in them. Therefore, a
faster moving magnet creates more voltage to induce
electrical current [41]. Faraday’s Law states that the
induced voltage in a coil is proportional to the product of its
number of loops, the cross-sectional area of each loop, and
the rate at which the magnetic field changes within those
loops [42]. Faraday’s law presents the output voltage and
can be represented in equation form:
E=
-NDfb
Dt
(5)
N is equal to the number of turns in the coil, Ø the
equals the magnetic flux of wire through a loop, and t is the
time in seconds of one full rotation [43]. Michael Faraday’s
Law of Induction provides an understanding of the physics
involved in the operation of hydroelectric generators and the
amounts of energy capable of being produced. It has been
discovered that when moving a magnet in and out of a coil
the direction of induced voltage alternates [44]. Induced
voltage is directed one way as the strength of a magnetic coil
increases, and is directed in the opposite direction when the
strength of the magnetic coil decreases [45]. The frequency
of the alternating voltage drop that is induced equals the
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frequency of the changing magnetic field within the loop.
Inducing voltage by moving a magnet is rather difficult;
therefore it is more practical to induce voltage by moving a
coil [46]. The hydroelectric turbo generator operates by
rotating a coil, or the iron frame of the rotor, inside a
stationary field of magnetic coils contained in the generator.
the result of the law of induction (current as a result of
motion) (figure 9) [55].
Electric Generators
Voltage is induced when a magnet is repeatedly moved in
and out of a coil of wire. The movement of the magnet
causes the voltage to alternate [47]. “As the magnetic
strength inside the coil is increased (as the magnet enters the
coil), the induced voltage in the coil is directed one way.
When the magnetic field strength diminishes (as the magnet
leaves the coil), the voltage is induced in the opposite
direction. The frequency of the alternating voltage that is
induced equals the frequency of the changing magnetic field
within the loop” [48]. This process requires great amounts
of force when the amount of loops in a coil of wire is rather
significant.
As a result, it is more practical to induce a voltage by
moving the coil rather than moving the magnet [49]. This
method of inducing voltage is possible by rotating the coil in
or about a stationary magnetic field. Paul Hewitt defines
this arrangement as a generator (figure 8) [50].
FIGURE 8 [51]
FIGURE 9 [56]
(A) REPRESENTS THE MOTOR EFFECT
(B) REPRESENTS THE GENERATOR EFFECT
APPLYING PHYSICS TO THE OPERATION OF
HYDROELECTRIC GENERATORS
Hydroelectric turbo generators’ generate usable electricity
with concepts of physics including: the magnetic force on
current carrying wires, electromagnetic induction, Michael
Faraday’s Law, and the generator effect. These large turbo
generators convert mechanical energy into electrical energy.
The electrical energy can then be stored in batteries or used
immediately.
The turbine is set into motion when running water pass
through the inlets. The shaft of the turbine is magnetized,
and rotates inside of a stationary coil of wires. The constant
rotation inside the B field creates an alternating current that
is then directed through wiring to either be stored in batteries
near the power plant, or to be transported through the
electrical grid. It if important to remember that generators
don’t produce energy, they merely convert energy from one
source to another [57]. The transportation of electricity is
possible due to familiar concepts of physics such as
electromagnetic induction.
SIMPLE GENERATOR. VOLTAGE IS INDUCED IN THE LOOP WHEN ROTATED
IN THE MAGNETIC FIELD
TRANSPORTING ELECTRICITY
Generators and motors share the same construction, and
their roles in power generation are essentially the same in
principle. Their main difference is that the roles of input and
output are reversed [52]. In a motor, electrical energy is the
input source and the output source is mechanical energy. In
contrast, a generators input source is mechanical energy, and
its output energy source is electrical energy [53].
Motors and generators also provide the same function:
transforming energy states. Their underlying principle is the
same, “moving electrons experience a force that is mutually
perpendicular to both their velocity and the magnetic field
they traverse” [54]. The motor effect is the deflection of the
wire (motion as a result of current) and the generator effect
Most hydroelectric power plants are located in remote areas
removed from society, where the majority of the power is
needed. Because hydroelectric turbo generators produce
alternating currents of very high voltage, the product is
desirable for long transport from the power plant to
civilization. A high-voltage wire carrying a relatively small
charge will also provide higher levels of energy.
Given that our V or voltage is equal to energy measured
in joules divided by charge measured in Coulombs. Power
with high voltage (greater pressure of electrical current) is
needed to transmit power efficiently across long distances
[58]. However, heat losses occur as the electrical charge,
known as the current, flows through the conductor [59]. The
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energy is transmitted from one system of conducting wires
to another by electromagnetic induction [60]. Energy is
transmitted from location to location with the aid of
transformers.
Transformers
Transformers allow electrical energy to be carried across an
empty space. Paul Hewitt defines a transformer as “A
device for transferring electric power from one coil of wire
to another, by means of electromagnetic induction, for the
purpose of transforming one value of voltage to another”
[61]. This is achieved by arranging two coils of wire in line
with the conduit carrying the energy source (figure 10).
FIGURE 10 [62]
BASIC TRANSFORMER
The primary coil’s magnetic field builds up whenever
current begins to flow through the coil. This changing field
in the primary coil will grow and extend to the nearby
secondary coil. Voltage is induced in the secondary coil
without any direct contact. When alternating current is used
to power the primary, the frequency of periodic changes in
the magnetic field is equal to the frequency of the alternating
current [63]. Transformers are used to transport electricity
long distances because of their ability to step up or step
down voltages. This is achieved by varying the number of
turns of wire in both the primary and secondary coils.
If the secondary coil has more turns than the primary,
the alternating voltage produced in the secondary coil will be
greater than that produced in the primary. In this instance,
voltage is said to be stepped up. If the secondary coil has
less turns than the primary, then the alternating voltage
produced in the secondary will be lower than that produced
in the primary. Voltage is stepped down [64]. This process
allows for electrical energy to be “fed into the primary at a
given alternating voltage and taken from the secondary at a
greater or lower alternating voltage, depending on the
number of turns in the primary and secondary coil windings”
(figure 11) [65].
FIGURE 11 [66]
VOLTAGE STEPPED UP IN A TRANSFORMER
Keep in mind that conservation of energy laws regulate
this process. Whenever a voltage is stepped up with a
transformer, conservation of energy laws regulate the
relationship between current and voltage. If voltage is
stepped up in a secondary coil, the current in the secondary
is less than in the primary [67]. Energy cannot be stepped
up or down, therefore the power or rate at which energy is
transferred will be equal in each coil as long as minor losses
as heat are neglected [68].
Hydroelectric power generation is extremely efficient.
Transporting electricity poses a challenge because of heat
losses, and the long distances electricity must travel. In the
future, improved transformer technology must be developed
in order to take advantage of sustainable electrical sources.
At this point, the principles of electromagnetic induction can
only be improved on.
CONCLUSION
As the World’s energy demands continue to increase, nontraditional sources of energy are becoming more popular.
Investing in this technology and other renewable energies
will decrease the demand for fossil fuels in effort of moving
in a sustainable direction.
Fossil-fuels and other
conventional sources, such as coal and nuclear, can not be
abandoned entirely; however, by investing in more
hydroelectric solutions we can reduce their frequency of use
and concentrate on conserving precious resources for future
generations. Although the technology involved with tidal
power is relatively new, our understanding of the physics
involved remains the same.
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