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Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
Renewable Energy
Systems11
Dr. Caroline Dong
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11Energy from Water
11-1 ENERGY IN MOVING WATER
11-2 HYDROELECTRIC DAM OPERATION
11-3 WATER TURBINES
11-4 TIDAL POWER GENERATION
11-5 WAVE POWER GENERATION
Chapter Outline
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-1 Energy in Moving Water
Hydroelectric energy is a useful renewable energy source.
Most hydropower comes from converting falling water to electricity.
Some power comes from moving streams, rivers, and ocean tides.
Worldwide, it accounts for over 6% of all energy and 17% of electricity production.
3
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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Moving water has kinetic energy that can be converted to useful work directly or by using it to generate electricity.
Hydroelectric is the most efficient method of large-scale power generation; it has and efficiency of 80% to 95% for large installation with high flow rates but less in installations with a low flow rate.
11-1 Energy in Moving Water
© nstanev/Fotolia
4
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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11-1 Energy in Moving Water
The amount of kinetic energy in a moving substance was given by the equation:
5
21
2KEW mv
WKE = kinetic energy in J
m = mass in kg
v = velocity in m/s.
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
Water behind a dam or any object above a reference point posses potential energy, which is the energy of position. Potential energy is given by the equation:
11-1 Energy in Moving Water
PEW mgh
What is the potential energy in joules of the car
and driver? The car and driver weigh 1400 lbs.
40 feet
1 lb = 0.454 kg; 1 ft = 0.305 m
2
1400 lb0.454 kg 9.8 m 0.305 m
40 ft 76 kJlb s ft
PEW mgh
6
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-1 Energy in Moving Water
What is the speed of the car in the previous example if 70% of
the energy is transformed to kinetic energy? The car had a
potential energy of 76 kJ and a mass of 636 kg.
0.70 0.70 76 kJ 53.2 kJKE PEW W
21
2
2 53.2 kJ212.9 m/s (29 mi/h)
636 kg
KE
KE
mvW
Wv
m
When energy is transformed from potential to kinetic energy, some will be lost to friction (heat).
7
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-1 Energy in Moving Water
Water behind a dam posses potential energy which is converted to kinetic energy as it falls. Each cubic meter weighs 1000 kg and the distance it falls relative to a reference is called the head.
Head is a height of water created by a vertical difference in elevation.
A 1 m drop corresponds to 9794 Pa.
In hydropower applications, the head is measured from the top of the water level to the inlet at the turbine.
8
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-1 Energy in Moving Water
The distance is considered the gross head. The net head is the equivalent height after equivalent friction losses in piping are subtracted.
To calculate the gross energy stored in a pond or reservoir, the volume and the average height are used.
9
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-1 Energy in Moving Water
Assume the head on a dam is 30 m.
(a)What is the WPE for one m3 of water at the top of the reservoir?
(b)If this passes a turbine in 1 s, what total power does it
represent? (Ignore friction).
2
9.8 m1000 kg 30 m 294 kJ
sPEW mgh
(a)
294 kJ 294 kW
1 sP
W
t (b)
10
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-1 Energy in Moving Water
2
2eq
vh
g
ph
h = height in meters,
p = pressure in N/m2,
= specific weight of water (9807 N/m3)
v = velocity in m/s
g = gravitational constant (m/s2)
The energy in moving water can be thought of as potential energy plus the kinetic energy, Summarizing:
1) potential energy due to elevation,
2) potential energy due to pressure and
3) kinetic energy due to motion.
The equivalent head, heq is:
11
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-1 Energy in Moving Water
12
2
2eq
vh
g
ph
ℎ𝑝 =𝑝
𝛾
ℎ𝑘𝑒 =𝑣2
2𝑔ℎ𝑒𝑞 = ℎ + ℎ𝑝 + ℎ𝑘𝑒
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-1 Energy in Moving Water
The volumetric flow rate, Qv, is measured in m3/s or ft3/s. The product of specific weight, , and Qv is the weight passing the turbine per time, which is mg/t.
eq
eq
mghW mgP h
t t t
Power is energy per time, so the power in moving water
can be written in terms of equivalent head:
By substitution:
v eqP Q h
© r
eb
/Fo
tolia
13
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-1 Energy in Moving Water
Example:
A small stream has a head of 8 m from the diverter to the turbine. The volumetric flow rate is determined to be 0.05 m3/s.
Calculate the total power available to the turbine (ignore the pipe friction).
Answer:
Gamma = 1000 kg /m3 * 9.807 m/s2 =9807 N/m3
P = 9.807 N/m3 * 0.05 m3/s * 8m = 3.92 kW
14
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-2 Hydroelectric Dam Operation
Compared to thermal plants, hydroelectric plants are more efficient in converting energy to electricity.
Most hydroelectricity, by far, is generated in conventional hydroelectric dams.
Other types of power dam:
• Run-of-the-river
• Microhydroelectric dams
• Pumped storage system
15
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-2 Hydroelectric Dam Operation
In a conventional hydroelectric generating system,
stored water is allowed to flow through a penstock and
used to spin a turbine/generator, generating electricity.
Large dams will have multiple penstocks and turbines.
16
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-2 Hydroelectric Dam Operation
The process in Conventional Hydroelectric Dam:
• A large screen is located in front of the inlet gate to keep debris from damaging the turbine.
• The inlet gate controls the amount of water that flows through a penstock.
• Penstock directs the water to the turbine blades to spin the shaft at a high speed
• The shaft is connected to a generator.
• After giving up most of its energy, the water passes through a channel called the tailrace to a relatively shallow storage area called the afterbay.
17
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-2 Hydroelectric Dam Operation
Water is stored behind the dam.
As more water is stored, its level becomes higher, and its ability to produce electrical energy increases.
The dam has spillways that are built into it to allow water to be released and to avoid overfilling the reservoir during rainy periods.
Water in the spillway does not go through the penstock and past the turbine, so its energy is lost.
It is important that the water level is not allowed to increase to the point where water runs over the dam because this can damage the dam.
18
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-2 Hydroelectric Dam Operation
A very useful concept for renewable energy systems in
mountainous areas is pumped storage.
A pumped storage system is a system of two dams,
each with a reservoir. One is located at a much higher
elevation than the other.
If the idea is applied to renewable systems, the storage
water can be used when the resource is not available.
Currently it is mostly used to help power companies
level loads.
So
urc
e: c
ou
rte
sy o
f X
CEL
En
erg
y
19
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-2 Hydroelectric Dam Operation
• During low-peak electrical hours, water is pumped from the lower reservoir into the higher reservoir.
• During the highest peak times, when electrical energy is needed on the grid, water is released from the upper reservoir, where it flows down through penstocks to turbines, as in a traditional hydroelectric dam, producing electricity.
20
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-2 Hydroelectric Dam Operation
Raccoon Mountain pumped storage plant in Tennessee:
21
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-2 Hydroelectric Dam Operation
The Cabin Creek pumped storage power plant is located in Colorado and consists of two reservoirs connected by a tunnel. It has a total installed generating capacity of 320 megawatts in two reversible pump-turbine units.
22
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-2 Hydroelectric Dam Operation
A very large pumped storage plant is the Helms
Pumped Storage Plant, located high in a remote area
of the Sierra Nevada Mountains. This is the largest
hydroelectric and pumped storage facility in the
California electric system and consists of three units. The
rotors alone weigh 1 million pounds and are 20 feet in
diameter and 10 feet high.
Helms produces 1,212 MW by
moving water from the upper
reservoir, which is CourtrightLake to a reservoir that is 1700
feet below at Lake Wishon.
Ph
oto
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urt
esy
o
f P
ac
ific
Ga
s a
nd
Ele
ctr
ic C
o.
23
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-2 Hydroelectric Dam Operation
• The generator in a pumped storage facility can act as a motor. Technically, it is called a motor/generator.
• When water from the lower reservoir is to be pumped to the higher reservoir, power from the grid is applied to the motor generator rather than just an ac generator or alternator.
• The pump generating system is used to provide extra electrical power at the peak times when it is needed.
• Energy can be stored in various ways, but pumped water storage is one of the most effective.
24
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-2 Hydroelectric Dam Operation
Run-of-the-River systems (ROR) are hydroelectric systems that primarily use the kinetic energy in flowing rivers to generate electricity.
When a dam is part of the system, storage area behind it is called pondage.
Two types of ROR:
• Without pondage; no storage of water and subject to seasonal river flows
• With pondage; can provide regular water flow.
25
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-2 Hydroelectric Dam Operation
The photo shows a small
run-of-the-river system in
King Cove, AK, which
helped offset expensive
power from diesel
generators.
This plant generates only 800 kW of power. Very
small systems like this are
useful in remote villages
and in developing countries.
So
urc
e: N
REL
26
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-2 Hydroelectric Dam Operation
Compared to conventional dams, ROR dams are considered environmental friendly, as they have onya small effect on river flow, and they do not have large reservoirs with their accompanying environmental impact.
Even with its smaller capacity, an ROR system with pondage can help with flood control to a limited extent.
27
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-2 Hydroelectric Dam Operation
Micro- and small hydroelectric dams
• Small hydroelectric dams generate between 100 kW and 10 MW.
• Small hydroelectric systems can be connected directly to the grid, or they can be used to provide electrical power to a building or business with grid power backup when the water level is not high enough to produce all the power that is needed.
• Microhydroelectric system: <100 kW
28
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-2 Hydroelectric Dam Operation
Microhydroelectric system is designed to prevent harm to fish or other wildlife in the system.
It is now being used in developing countries to provide small amounts of electrical power for refrigeration or pumping and purifying water.
Picohydroelectric system: < 5 kW
Picohydroelectric systems typically operate the same as larger ROR systems but without pondage.
It is inexpensive and it can be installed around the world, in developing countries.
29
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-3 Water Turbines
Turbine: A rotary engine that extracts energy from a fluid and converts it to useful work.
Water turbine is to transfer the kinetic energy in moving water into turning the shaft.
The key to high efficiency is to minimize losses such as those resulting from turbulence, vibration, or heat.
The minimize the turbulence, the turbine blades must be smooth and the turbine must be well balanced with low friction bearings.
30
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-3 Water Turbines
Water turbines are defined by the form of energy they convert to mechanical motion.
Turbines are classified to:
• Impulse turbine
• Reaction turbine
Most turbines are a mixture of both.
31
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-3 Water Turbines
1. An impulse turbine is a rotary engine that changes
the direction of a high velocity fluid, thus converting
kinetic energy into mechanical rotating energy.
Impulse turbines are primarily
used in applications with high
pressure heads and relatively
lower flow rates.
32
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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11-3 Water Turbines
Pelton and Turgo turbines are examples of impulse
turbines. Notice the double cups on these Pelton
turbines, a innovation by William Doble, an employee of
Pelton.
The double cups split the
water flow in half, which transfers most of the
momentum of the water to
the wheel.
co
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Vo
ith
Hyd
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mb
H &
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y
33
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-3 Water Turbines
2. Reaction turbines are the second type; they develop
torque from the pressure of water and are
submerged at all times. It primarily converts potential
energy into mechanical rotating energy.
In a reaction turbine, the rotating blades are
completely encased in a pressure encasement and the
fluid flows through a fixed guide mechanism onto
rotating both potential energy due to its pressure and
kinetic energy due to its motion, but the primary mover
is the pressure drop, which creates the reaction force.
34
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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11-3 Water Turbines
Impulse and reaction turbines are further divided into specific types of turbines:
• Fourneyron Turbine
• Francis Turbine
• Kaplan Turbine
• Pelton Turbine
• Turgo Turbine
• Crossflow water turbines
35
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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11-3 Water Turbines
Fourneyron turbine
The reaction turbine was built by Benoit Fourneyron; from 1827 onwards he designed the first water turbines with good efficiency. From 1834 to 1883 this turbine was used to drive the machines in a Black Forest cotton mill.
The turbine was connected to a pressure pipe with a 108 m head which gave it an unusually high speed.
The water flows in from above through a vessel. The distributor at the bottom of the vessel deflects the water outwardly into the runner.
36
http://www.deutsches-
museum.de/en/collections/machines/power-
engines/water-turbines/fourneyron-turbine-1834/
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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11-3 Water Turbines
Francis Turbine
The Francis turbine is the most widely used reaction turbine and is used in moderate-head, high-volume applications.
Water from behind a dam flows through the guide vanes on the side of the turbine, spins the runner, and exits through the bottom tailrace tube.
37
Runner for the Francis Turbine
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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11-3 Water Turbines
38
The Kaplan turbine is a propeller type reaction turbine used in low-head applications such as run-of-the river systems.
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-3 Water Turbines
A typical installation of Kaplan
Turbine:
• There is pressure on the
upstream side of the turbine
runner and suction on the
downstream side.
• On the outlet side of the
turbine is the draft tube, which connects the turbine
to the tailrace.
• The tailrace is the channel
leading away from the turbine.
39
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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11-3 Water Turbines
Pelton turbine
The runner has a number of cup-shape containers connected around its circumference.
40
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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11-3 Water Turbines
A cross-flow turbine is an impulse turbine used in smaller
hydro plants with relatively large flow. They can operate
effectively with a low head.
Source: OSSBERGER GmbH + Co.
41
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-3 Water Turbines
Reaction Turbines Impulse turbines
Fourneyron Pelton
Francis Turgo
Kaplan Crossflow
42
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-4 Tidal Power Generation
There is a huge amount of power in ocean tides, which move
primarily by the influence of the moon, so are quite predictable
and occur every 12 h and 25 min.
The moon’s gravity produces a tidal bulge on one side of the earth
and centrifugal force causes a second tidal bulge at the same
time on the opposite side.
43
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
When the sun, moon, and earth all align, a stronger gravitational pull occurs on the oceans, and higher and lower tides called spring tides are produced.
Spring tide: it occurs at new moon and again at full moon (twice a lunar month).
Neap tide: at first and third quarter, the net gravitational force of the sun and the moon is not as pronounced, so lesser tides than normal.
The currents associated with the tides depend on the particular location on earth.
Currents from tides can vary from 0 to over 2 m/s.
44
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-4 Tidal Power Generation
A few locations in the world can take advantage of a
natural estuary, harbor or river by trapping water
behind a barrage dam and taking advantage of the
inflowing and/or outflowing water to generate power.
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Po
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r
The Annapolis Tidal Power Station is located
in the Bay of Fundy and
is the only such station
in North America. It is
rated at 20 MW; power
varies depending on
the tides. It has been in operation since 1984.
45
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-4 Tidal Power Generation
The turbines at Annapolis Tidal Power Station use a
unique but older design called a Straflo turbine. It is
similar to a Kaplan turbine but with larger blades. The
Straflo is a rim generator, in which the rotor is attached
to the periphery of the blades of the runner. At the end
of the rotor rim is a water seal.
46
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-4 Tidal Power Generation
The energy in the water behind a barrage can be
calculated from considering gravitational potential energy. Recall that WPE is given by PEW mgh
Substituting rAh for mass, and using ½ the maximum
height of the tidal basin to account for average height,
we obtain: 21 1
2 2PEW Ah gh Aghr r
WPE is the energy stored in J
h is the maximum height of the vertical tide in m
A is the horizontal area of the barrage basin in m2
ρ is the density of seawater = 1025 kg/m3
(Fresh water density = 1000 kg/m3)g is the gravitational constant = 9.8 m/s2.
47
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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Example:
Determine the theoretical energy stored in a barrage if the height of the tide is 3 m in a barrage with an area of 300,000 m2.
Answer:
Density: 1025 kg/m3; A = 300,000 m2; h = 3 m
Wpe = ½ (1025 kg/m3)(300,000 m2)(9.8 m/s2)(3 m)^2
= 1.36 E10 J = 13,600 MJ
48
21 1
2 2PEW Ah gh Aghr r
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
11-4 Tidal Power Generation
Another method for generating power from the tides is
a tidal stream generator, which is anchored to the
bottom. The generator can generate power from
incoming (flood) or outgoing (ebb) tide.
49
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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11-4 Tidal Power Generation
A crossflow turbine is another form of tidal stream
generator with the advantage of moving in the same
direction regardless of the direction of the tidal currents.
The generator (in center) can generate power from
incoming (flood) or outgoing (ebb) tides.
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50
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
Advantages to tidal stream power include predictability and the generates are located under water – no visual impact and no sound. There are many sites around the world that can benefit from tidal stream generators.
Disadvantage:
• Initial expense
• Fish, seals, marine life
• Changing sediments
51
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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11-5 Wave Power Generation
Water waves are created by wind moving across
large stretches of water, creating waves that are a
combination of transverse and longitudal so
individual waves move in an elliptical pattern. some
definitions for waves are:
52
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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11-5 Wave Power Generation
Energy converters are classified into three basic
types.
Point absorbers that have an upper and lower section that move relative to each other.
Attenuators that have relative motion between large floating sections.
Terminating devices that can trap the up and down motion to generate winds in a tube.
Source: NREL Source:Pelamis Wave Power Ltd.
53
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11-5 Wave Power Generation
54
Mass per unit length of a half of a sinusoid is:𝑚
𝑙=𝜌𝐴𝜆
𝜋Height of the center of gravity is:
ℎ =𝜋𝐴
8
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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11-5 Wave Power Generation
The potential energy per unit length is 𝐸
𝑙=𝑚
𝑙𝑔Δℎ =
𝜌𝐴𝜆𝑔
𝜋
𝜋𝐴
4=1
4𝜌𝐴2𝜆𝑔
The wave’s kinetic energy is equal to its potential energy, so the total energy is:
𝐸
𝑙=𝜌𝐴2𝜆𝑔
2
The wavelength is related to its period:
𝜆 =𝑔𝑇2
2𝜋
Thus the wave energy is :𝐸
𝑙=𝐴2𝑔2𝜌𝑇2
4𝜋55
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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11-5 Wave Power Generation
The power per unit length is given as:𝑃
𝑙=𝐴2𝑔2𝜌𝑇
4𝜋
Substituting A = H/2 into the above equation, giving𝑃
𝑙=𝐻2𝑔2𝜌𝑇
16𝜋
Substituting the values of density, gravitational constant, giving
𝑃
𝑙= 1.96 𝑘𝑊/(𝑚3/𝑠)𝐻2𝑇
56
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
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Selected Key Terms
Attenuator
Francis turbine
Impulse turbine
Kaplan turbine
With respect to wave energy devices, it is a
device that extracts energy from wave power by
converting relative motion between large semi-
submerged cylindrical sections to electricity.
A reaction type water turbine that directs water from the outer circumference towards the center
of a runner. Water flows through a scroll case
which is a curved tube that diminishes in size with
a shape similar to a snail shell.
A reaction type water turbine that uses propellers
with adjustable blades. The turbine is usually
placed in a spiral casing called a volute.
A rotary engine that changes the direction of a
high velocity fluid, thus converting kinetic energy
into mechanical rotating energy.
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
Selected Key Terms
Oscillating water column
Pelton turbine
Point absorber
Reaction turbine
A fixed device for producing electrical power
from waves. It consists of a large tube that
extends over a cliff and into the ocean. Wave action causes water to rise in the tube and
displace air, which rotates a wind turbine.
An impulse turbine in which water moves under it
(impulse) rather than water falling over it. It is
among the most efficient types of water turbines.
A rotary engine that develops torque by reacting
to the pressure of a fluid moving through the
turbine, thus primarily converting potential energy
into mechanical rotating energy.
A floating wave energy converter that is in a
fixed in position. It bobs up and down from wave motion. The motion with respect to a fixed
reference is captured and the energy converted
to electricity.
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
Selected Key Terms
Run-of-the-river (ROR)
Tidal barrage system
Tidal stream generator (TSG)
A hydroelectric system that uses river flow to
generate electricity. The system may include a
small dam with storage for water but many do not.
A system designed to convert tidal power into
electricity by trapping water behind a dam,
called a tidal barrage dam, and generating
power from the inflow and/or the release of
water.
An electrical generating system that uses a water
turbine to turn a generator and produce
electrical power when a stream of water caused
by tides or a river flow past it.
Renewable Energy SystemsDavid Buchla | Thomas Kissell | Thomas Floyd
Copyright © 2015 by Pearson Education, Inc.All Rights Reserved
true/false quiz
1. In the equation, P = Qvheq, the
stands for the volumetric flow rate.
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true/false quiz
2. The potential energy in water behind
a dam is converted to kinetic energy
to spin a turbine and generator.
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3. Run-of-the-River systems primarily use
the kinetic energy in flowing rivers to
generate electricity.
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true/false quiz
4. Impulse turbines are primarily used in
applications with low heads and
relatively high flow rates.
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true/false quiz
5. The turbine pictured
here is a Kaplan
turbine.
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true/false quiz
6. A cross-flow turbine can work in low
head hydro plants or in tidal streams.
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7. The tides are primarily caused by the
gravitational pull of the sun on the
earth.
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true/false quiz
8. A barrage dam is used to trap tidal
waters and use the flow to generate
electricity.
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true/false quiz
9. The vertical distance from the trough
of a wave to the crest is called the
amplitude.
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true/false quiz
10. One type of wave energy converter
is called an attenuator.
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true/false quiz
Answers:
1.F
2.T
3.T
4.F
5.F
6.T
7.F
8.T
9.F
10. T
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Multiple Choice Quiz
1. Water stored behind a hydroelectric dam is an example of
A. Kinetic energy
B. Potential energy
C. Electrical energy
D. All of these
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2. A good turbine for a ROR system is:
A. Pelton
B. Kaplan
C. Crossflow
D. Francis
72
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3. The unit for torque in the SI system is the
A. kilogram-meter
B. Kilogram-meter/second
C. Newton
D. Newton-meter
73
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4. A pumped storage system has
A. A single reservoir that allows water to flow through a penstock to turn a turbine
B. Two reservoirs; water is pumped from the lower one to the higher one during low usage times
C. Two reservoirs; power is generated when pumped from the lower one to the higher one
D. A single reservoir that has its water pumped past a turbine, which turns a generator
74
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5. An oscillating water column uses
A. A tube or chamber and waves that cause air to compress and flow past a turbine blade that rotates and turns a generator
B. Water from a reservoir to flow through a penstock and turn a turbine and generator
C. Hydraulic cylinders to pump oil through hydraulic motors to turn generators
D. A barrage to produce electrical power
75
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6. Total equivalent head includes
A. Head due to elevation
B. Pressure equivalent head
C. Kinetic energy equivalent head
D. All of the above
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1. B
2. B
3. D
4. B
5. A
6. D
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Example:
A small river, 40 m wide and 6 m deep, flows at a velocity of 2 m/s. If 20% of the flow of the river is diverted through a run-of-the river hydroelectric system that generates electricity at an efficiency of 90%, what is the output in power?
Answer:
Q = 2 m/s * 40 m * 6 m = 480 m3/s
20% Q = 96 m3/s
P = ½ (m/t)v2 = ½ (ρQ)v2 = ½ (1000 kg/m3 * 96 m3/s) * (2m/s)^2 = 192,000 W
90% efficiency considered, the output is 173 kW 78
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Example:
What is the equivalent head if the velocity of a river is 3 m/s?
Answer:
hke = v2/2g = (3 m/s)^2 / 2 / 9.8 m/s2 = 0.45 m
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Example:
What is power generated if the elevation head of a dam is 20 m, the velocity of the flow in reservoir is 4 m/s, the sectional area is 600 m2, and the efficiency of power generation is 85% ?
Answer:
h = 20 m; hke = v2/2g = (4 m/s)^2 / 2 / 9.8 m/s2 = 0.816 m
heq = 20+0.816 = 20.816 m
P = (1000 kg /m3) * (9.8 m/s2) * (4 m/s) * (600 m2) * 20.816 m * 85% = 416 MW
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