hydroelectric power generation

Session III

HYDROELECTRIC POWER GENERATION

Michael D. MarchAmerican University, Department of Physics,

4400 Massachusetts Ave. NW, Washington DC. 20016-8058, [email protected]

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.

Index terms — Electromagnetic induction, energy, faraday’s law, generator, hydroelectricity, tidal power, transformer.

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

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.

HISTORY OF HYDROELECTRICITY

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

April 26, 2013 American University, Washington, DC13th Annual New Millennium Conference

51

Session III

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].

FIGURE 1 [15]THREE GORGES DAM: YANGTZE RIVER CHINA

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.

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.

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.

BASIC CONCEPTS OF PHYSICS INVOLVED IN HYDROELECTRIC POWER GENERATION

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:

KE=12

m v2 (3)


52

Session III

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 OFHYDROELECTRIC 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].

FIGURE 3 [28]HYDROELECTRIC DAM COMPONENTS

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 current-carrying wires will provide a clear understanding to the step-by-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].


53

Session III

FIGURE 5 [33]SIMPLE MOTOR

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

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 7 [40]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=

−NΔϕ β

Δt (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


54

Session III

of the alternating voltage drop that is induced equals the 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.

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]SIMPLE GENERATOR. VOLTAGE IS INDUCED IN THE LOOP WHEN ROTATED

IN THE MAGNETIC FIELD

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 the result of the law of induction (current as a result of motion) (figure 9) [55].

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.

TRANSPORTING ELECTRICITY

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,


55

Session III

known as the current, flows through the conductor [59]. The 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, non-traditional 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.

REFERENCES

[1] “Harnessing Hydropower: The Earth’s Natural Resource.” Western Area Power Administration. April 2011. http://ww2.wapa.gov/sites/western/newsroom/pubs/Documents/HarnessingHydropower.pdf

[2] Ref. 1[3] Ref. 1[4] Ref. 1


56

Session III

[5] Ref. 1[6] “Renewable Energy: Hydropower.” Kennesaw State University

Physics.http://www.esa21.kennesaw.edu/activities/hydroelectric/hydroactivity.pdf

[7] Ref. 6[8] Ref. 6[9] Ref. 6[10] Ref. 1[11] Ref. 1[12] Ref. 1[13] Ref. 6[14] “China Three Gorges Dam Completed.” Engineering & Technology

Magazine. 4 July 2012. http://eandt.theiet.org/news/2012/jul/china-hydropower.cfm

[15] Ref. 14[16] “Wave & Tidal Energy Technology.” Renewable Northwest Project.

April 4, 2007. http://www.rnp.org/node/wave-tidal-energy-technology

[17] Ref. 16[18] Ref. 16[19] Ref. 16[20] Ref. 16[21] Ref. 16[22] Hewitt, Paul G. “Conceptual Physics.” 11th ed. 2010. 425-451. Print.[23] “Hydro Technology: Conventional Hydropower.” National

Hydropower Association. 2013. http://www.hydro.org/tech-and-policy/technology/conventional/

[24] Ref. 23[25] Ref. 23[26] Ref. 23[27] Ref. 23[28] Ref. 23[29] “Hydroelectric.” Next Era Energy Resources. 2013.

http://www.nexteraenergyresources.com/what/hydro.shtml. [30] Ref. 22[31] Ref. 22[32] Ref. 22[33] Ref. 22[34] Ref. 22[35] Ref. 22[36] Ref. 22[37] Ref. 22[38] Ref. 22[39] Ref. 22[40] Ref. 22[41] Ref. 22[42] Ref. 22[43] “Faraday’s Law of Induction.” McGraw-Hill Encyclopedia of Science

& Technology. 10th ed. Vol. 8. 2007. 780-783. Print.[44] Ref. 43[45] Ref. 22[46] Ref. 22[47] Ref. 22[48] Ref. 22[49] Ref. 22[50] Ref. 22[51] Ref. 22[52] Ref. 22[53] Ref. 22[54] Ref. 22[55] Ref. 22[56] Ref. 22[57] Ref. 22[58] Ref. 22[59] Ref. 22[60] Ref. 22[61] Ref. 22[62] Ref. 22

[63] Ref. 22[64] Ref. 22[65] Ref. 22[66] Ref. 22[67] Ref. 22[68] Ref. 22


57