Renewable
Energy
Mehran Ahmadi, Ph. D., P. Eng.
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Objectives
▪ Understand the importance of renewable energy in relation to other energy
sources.
▪ Learn various solar energy applications including solar collectors, solar power
systems, and photovoltaic systems.
▪ Evaluate the performance of solar energy applications.
▪ Analyze wind turbines and discuss various factors affecting wind turbine
applications.
▪ Learn various hydraulic turbine types and evaluate performance of hydraulic
turbines.
▪ Introduce geothermal heating, cooling, and power production applications.
▪ Evaluate the performance of various type geothermal power plants.
Mehran Ahmadi, Ph. D., P. Eng.
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Are Electric Cars Zero Emission Vehicles?
Electric cars (and other electricity-driven equipment) are often touted as zero emission vehicles
and their widespread use is seen by some as the ultimate solution to the air pollution problem.
It should be remembered, however, that the electricity used by the electric cars is generated
somewhere else mostly by burning fuel and thus emitting pollution.
Therefore, each time an electric car consumes 1 kWh of electricity, it bears the responsibility for
the pollutants emitted as 1 kWh of electricity (plus the conversion and transmission losses
generated elsewhere).
The electric cars can be claimed to be zero emission vehicles only when the electricity they
consume is generated by emission-free renewable resources such as hydroelectric, solar, wind,
and geothermal energy.
Therefore, the use of renewable energy should be encouraged worldwide, with incentives, as
necessary, to make the earth a better place in which to live in.
Mehran Ahmadi, Ph. D., P. Eng.
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Introduction
Depletion of fossil fuels and pollutant and greenhouse gas emissions associated
with their combustion can be tackled by essentially two methods:
▪ Using renewable energy sources such as solar, wind, hydroelectric, biomass, and
geothermal to replace fossil fuels.
▪ Implementing energy efficiency practices in all aspects of energy production, distribution,
and consumption so that less fuel is used while obtaining the same useful output.
Note I: Energy efficiency is an expression for the most effective use of energy
resources, and it results in energy conservation, i.e., it can only reduce fossil fuel
use, while renewable energy can directly replace fossil fuels.
Note II: The main renewable energy sources include solar, wind, hydroelectric,
biomass, geothermal, biomass, wave, and tidal. The latter three are not
discussed here.
Mehran Ahmadi, Ph. D., P. Eng.
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Introduction
Renewable energy: An energy source is called
renewable if it can be renewed and sustained without
any depletion or any significant effect on the
environment.
Renewable energy is also called:
▪ Alternative energy
▪ Sustainable energy
▪ Green energy
Note: What we call renewable energy is usually nothing
more than the manifestation of solar energy in
different forms.
Mehran Ahmadi, Ph. D., P. Eng.
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Renewable Energy Sources
Solar: The best-known renewable source is solar energy. Although solar energy is sufficient to meet the entire
energy needs of the world.
Wind: The conversion of the kinetic energy of wind into electricity via wind turbines represents wind energy.
Hydro: The collection of river water into large dams at some elevation and directing the collected water into a
hydraulic turbine is the common method of converting water energy into electricity. Hydro or water energy
represents the greatest amount of electricity production, and it supplies most of the electricity needs of some
countries.
Geothermal: Geothermal energy refers to the heat of the earth. High temperature underground geothermal fluid
found in some locations is extracted and the energy of the geothermal fluid is converted to electricity or heat.
Geothermal energy conversion is one of the most mature renewable energy technologies and is mostly used for
electricity generation and district heating.
Biomass: Organic renewable energy is referred to as biomass and a variety of sources (agriculture, forest, residues,
crops, etc.) can be used to produce biomass energy.
Mehran Ahmadi, Ph. D., P. Eng.
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Solar Energy
The electromagnetic energy emitted by the sun is called solar radiation, solar energy, or solar
heat.
The amount of solar energy reaching the earth’s surface can easily meet the entire energy needs
of the world. However, capturing this energy is not easy due to its low concentration.
Main barrier to the extensive use of solar energy is intermittency.
The conversion of solar energy into other useful forms of energy can be accomplished by three
conversion processes:
▪ Heliochemical process: This is basically photosynthesis, and it is responsible for the production of fossil
fuel and biomass.
▪ Heliothermal process: Solar energy is collected and converted to thermal energy or heat. Flat-plate
collectors, concentrating collectors, and heliostats are common devices. Solar collectors are used for space
heating and cooling and for the production of hot water for buildings. Heliostats are mirrors that reflect
solar radiation into a single receiver.
▪ Helioelectrical process: The production of electricity by photovoltaic (solar cells).
Mehran Ahmadi, Ph. D., P. Eng.
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Solar Radiation
Solar Energy
The solar energy reaching the earth atmosphere is called the total solar
irradiance or solar constant, with the accepted value of 1,373 W/m2 (435.4
Btu/h·ft2), but its value changes by 3.5% from a maximum of 1,418 W/m2 on
January 3rd when the earth is closest to the sun, to a minimum of 1,325 W/m2 on
July 4th when the earth is farthest away from the sun.
The spectral distribution of solar radiation beyond the earth’s atmosphere
resembles the energy emitted by a blackbody (i.e., a perfect emitter and
absorber of radiation) at 5,780 K, with about 9% of the energy contained in the
ultraviolet region (at wavelengths between 0.29 to 0.4 μm), 39% in the visible
region (0.4 to 0.7 μm), and the remaining 52% in the near-infrared region (0.7 to
3.5 μm). The peak radiation occurs at a wavelength of about 0.48 μm, which
corresponds to the green color portion of the visible spectrum.
Mehran Ahmadi, Ph. D., P. Eng.
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Solar Radiation
Solar Energy
The solar radiation undergoes considerable attenuation
as it passes through the atmosphere as a result of
absorption and scattering.
Absorption by oxygen (O2) occurs in a narrow band
about λ = 0.76 μm. The ozone (O3) absorbs ultraviolet
radiation at wavelengths below 0.3 μm almost
completely, and radiation in the range 0.3–0.4 μm
considerably. Absorption in the infrared region is
dominated by water vapor (H2O) and carbon dioxide
(CO2).
The dust particles and other pollutants in the
atmosphere also absorb radiation at various
wavelengths. As a result of these absorptions, the solar
energy reaching the earth’s surface is weakened
considerably, to about 950 W/m2 on a clear day and
much less on cloudy or smoggy days.
Mehran Ahmadi, Ph. D., P. Eng.
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Solar Radiation
Solar Energy
When solar radiation strikes a surface, part of it is absorbed, part of it is reflected, and the remaining part, if any, is transmitted.
Conservation of energy requires that:
𝛼+𝜌+𝜏 =1
where τ is the transmissivity, ρ is the reflectivity, and α is the absorptivity of the surface for solar energy, which are the fractions
of incident solar radiation transmitted, reflected, and absorbed, respectively.
We can also define the emissivity ε of a surface as a measure of how closely a real surface approximates a blackbody, for which ε
= 1. Therefore, the emissivity of a surface varies between zero and one, 0 < ε < 1.
Mehran Ahmadi, Ph. D., P. Eng.
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Solar Radiation
Solar Energy
The surfaces are assumed to have two sets of properties: one for solar radiation (αs) and another for infrared
radiation (ε) at room temperature.
▪ Surfaces that are intended to collect solar energy, such as the absorber surfaces of solar collectors, should have high αs but low ε
values to maximize the absorption of solar radiation and to minimize the emission of radiation.
▪ Surfaces that are intended to remain cool under the sun, such as the outer surfaces of fuel tanks and refrigerator trucks, should
have just the opposite properties.
Surfaces are often given the desired properties by coating them with thin layers of selective materials. In practice,
engineers pay close attention to the ratio αs/ε when selecting materials:
▪ For heat collection, materials with large values of αs/ε (such as clean galvanized sheet metal with αs/ε = 5.0) are required.
▪ For heat rejection, on the other hand, materials with small values of αs/ε (such as anodized aluminum with αs/ε = 0.17) are
desirable.
Mehran Ahmadi, Ph. D., P. Eng.
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Flat-Plate Solar Collector
Solar Energy
The objective of a solar collector is to produce useful heat from solar energy.
▪ Most solar collectors in operation today are used to produce hot water, normally used in
residential and commercial buildings for use in kitchens, bathrooms, showers, and other
areas.
▪ Another use of solar hot water is process heating in industrial facilities. Solar collectors
can also be used for space heating in winter.
Note: Solar heat is normally more available in summer when space heating is not
needed. Therefore, most solar collectors are used to produce hot water, and
they are very common in southern Europe and Asia, where solar energy is
available for more than 200 days a year.
Mehran Ahmadi, Ph. D., P. Eng.
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Flat-Plate Solar Collector
Solar Energy
There are two major types of flat-plate solar collectors:
▪ Thermosyphon solar water heater systems, which operate on
a natural circulation.
▪ Active, closed-loop solar water heater uses a pump for the
circulation of water containing antifreeze fluid.
Mehran Ahmadi, Ph. D., P. Eng.
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Flat-Plate Solar Collector
Solar Energy
A flat-plate collector consists of:
▪ A glazing (cover),
▪ An absorber plate,
▪ Flow tubes,
▪ Insulation,
▪ Glazing frame, and
▪ A box enclosure.
The absorber plate absorbs solar energy transmitted through the glazing, which
is a type of glass. Flow tubes are attached to the absorber plate and water is
heated as it flows in the tubes by absorbing heat from the absorber plate. The
sides and back are insulated to minimize heat losses.
Mehran Ahmadi, Ph. D., P. Eng.
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Flat-Plate Solar Collector
Solar Energy
The rate of solar heat absorbed by the absorber plate is:
𝑄ሶ abs = 𝜏𝛼𝐴𝐺
where τ is the transmissivity of the glazing, α is the absorptivity of the absorber plate, A is the area of the
collector surface, in m2, and G is the solar irradiation (solar radiation incident per unit surface area), in W/m2.
Heat is lost from the collector by convection to the surrounding air and by radiation to the surrounding surfaces
and sky, and it can be expressed as:
𝑄ሶ loss = 𝑈𝐴 𝑇𝑐 − 𝑇𝑎
where U is the overall heat transfer coefficient, in W/m2·°C, that accounts for the combined effects of convection
and radiation, Tc is the average collector temperature, and Ta is the ambient air temperature, both in °C.
Mehran Ahmadi, Ph. D., P. Eng.
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Flat-Plate Solar Collector
Solar Energy
The useful heat transferred to the water is the difference between the heat absorbed and the heat lost:
𝑄ሶ useful = 𝑄ሶ abs − 𝑄ሶ loss
𝑄ሶ useful = 𝐴 𝜏𝛼𝐺 − 𝑈 𝑇𝑐 − 𝑇𝑎
Note I: Useful heat is maximized when the difference between the collector temperature and the air temperature is minimized;
however, this also means that hot water is produced at a lower temperature due to the lower temperature of the absorber plate.
For known mass flow rate of water, ṁ:
𝑄ሶ useful = 𝑚𝑐
ሶ 𝑝 𝑇w, out − 𝑇w, in
where cp is the specific heat of water in J/kg·°C, and Tw,in and Tw,out are the inlet and outlet temperatures of water, respectively.
Note II: For the same useful heat, a higher mass flow rate would yield a lower temperature rise for water in the collector.
Mehran Ahmadi, Ph. D., P. Eng.
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Flat-Plate Solar Collector
Solar Energy
The efficiency of a solar collector may be defined as the ratio of the useful heat delivered to water to the radiation incident on
the collector:
𝑄ሶ useful
𝐴 𝜏𝛼𝐺 − 𝑈 𝑇𝑐 − 𝑇𝑎
𝑇𝑐 − 𝑇𝑎
𝜂𝑐 =
=
= 𝜏𝛼 − 𝑈
𝐴𝐺
𝐺
𝑄ሶ incident
Note I: The collector efficiency is maximized for maximum values of transmissivity of the glazing τ and the absorptivity α of the
absorber plate.
Note II: The smaller the difference between the collector and air temperatures Tc – Ta and the smaller the overall heat transfer
coefficient U, the greater the collector efficiency.
Mehran Ahmadi, Ph. D., P. Eng.
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Flat-Plate Solar Collector
Solar Energy
The introduced equation gives the collector efficiency as a function of average temperature of the collector; however, this temperature is usually not
available. Instead, water temperature at the collector inlet is usually available. The collector efficiency may be defined as a function of the water
inlet temperature as:
𝑇w, in − 𝑇𝑎
𝐺
where FR is the collector heat removal factor. This relation is known as the Hottel-Whillier-Bliss equation.
𝜂𝑐 = 𝐹𝑅 𝜏𝛼 − 𝐹𝑅 𝑈
Note I: The collector efficiency is maximized when the temperature difference and thus the term FRU(Tw,in – Ta) / G is zero. The maximum efficiency in
this case is equal to FRτα.
The solar collector is normally fixed in position. As the angle of solar incident radiation changes throughout the day, the product τα also changes.
This change can be accounted for by including an incident angle modifier Kτα as:
𝑇w, in − 𝑇𝑎
𝐺
where the value of Kτα is a function of the incident angle, and its value changes between 0 and 1.
𝜂𝑐 = 𝐹𝑅 𝐾𝜏𝛼 𝜏𝛼 − 𝐹𝑅 𝑈
Note II: The standard collector test data are normally based on a value of 1 for Kτα.
Mehran Ahmadi, Ph. D., P. Eng.
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Concentrating Solar Collector
Solar Energy
The concentration of solar energy is low, and as a result, the
temperature of hot water obtainable in a flat-plate collector
is low (usually under 80°C).
Hot fluid (water, steam, air, or another fluid) at much higher
temperatures can be produced using concentrating
collectors by concentrating solar radiation on a smaller area.
The most common type of concentrating solar collector is
the parabolic trough collector.
Mehran Ahmadi, Ph. D., P. Eng.
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Concentrating Solar Collector
Solar Energy
In a concentrating collector, solar radiation is incident on the collector surface, called aperture area Aa, and this radiation is
reflected or redirected into a smaller receiver area Ar.
The concentration ratio (factor) CR is then defined as:
𝐶𝑅 =
𝐴a
𝐴r
Note: The value of CR is greater than 1, and the greater the value of CR, the greater the hot fluid temperature.
The effectiveness of the aperture-to-receiver process is a function of the orientation of surfaces and their radiative properties
such as absorptivity and reflectivity and is expressed by an optical efficiency term ηar.
The net rate of solar radiation supplied to the receiver is:
𝑄ሶ r = ηar𝐴a 𝐺
where G is the solar irradiation, in W/m2.
Mehran Ahmadi, Ph. D., P. Eng.
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Concentrating Solar Collector
Solar Energy
The rate of heat loss from the collector is:
𝑄ሶ loss = 𝑈𝐴r 𝑇𝑐 − 𝑇𝑎
The useful heat transferred to the fluid is:
𝑄ሶ useful = 𝑄ሶ r − 𝑄ሶ loss = ηar𝐴a 𝐺 − 𝑈𝐴r 𝑇𝑐 − 𝑇𝑎
The efficiency of this solar collector is defined as the ratio of the useful heat delivered to the fluid to the radiation incident on the
collector:
𝜂𝑐 =
𝑄ሶ useful
ηar𝐴a 𝐺 − 𝑈𝐴r 𝑇𝑐 − 𝑇𝑎
𝐴r 𝑇𝑐 − 𝑇𝑎
𝑇𝑐 − 𝑇𝑎
=
= ηar − 𝑈
= ηar − 𝑈
𝐴a 𝐺
𝐴a 𝐺
𝐶𝑅 × 𝐺
𝑄ሶ incident
Note I: The collector efficiency is maximized for maximum values of the optical efficiency of the aperture-to-receiver process ηar
and the concentration factor CR. The efficiency of concentrating collectors is greater than that of flat-plate collectors.
Note II: Temperatures in the receiver of a concentrating collector can reach 400°C. The heated fluid is usually water, and it can be
used for space and process heating and cooling or to drive a steam turbine for electricity production.
Mehran Ahmadi, Ph. D., P. Eng.
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Linear Concentrating Solar Power Collector
Solar Energy
Linear Concentrating Solar Power (CSP) collectors are used to capture and reflect solar radiation onto a linear receiver tube.
A common application is generating steam in the receiver tubes and running this steam through a turbine to generate electricity. Some
existing parabolic trough systems produce 80 MW of electricity.
If the parabolic trough collectors are oversized, excess heat can
be stored and this heat can be used during nighttime or cloudy
days to produce electricity (or it can be combined with conventional
power plants).
The efficiency of a solar system used to produce electricity may be
defined as the power produced divided by the total solar irradiation:
𝜂𝑐 = 𝑄ሶ
𝑊ሶ out
incident
𝑊ሶ
= 𝐴out
𝐺
c
where Ac is the collector surface area receiving solar irradiation and
G is the solar irradiation.
Mehran Ahmadi, Ph. D., P. Eng.
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Solar-Power-Tower Plant
Solar Energy
A solar-power-tower plant uses a large array of mirrors
called heliostats that track the sun and reflect solar radiation
into a receiver mounted on top of a tower.
An example of a solar-power-tower plant is Solar 1 located
in California, with capacity of 10 MW, and 91 m tower
height. The total cost of the Solar 1 plant was $14,000/kW,
which is 5 to 10 times greater than the cost of electric power
stations that run on fossil fuels and other renewables.
The other example is Gemasolar power plant located in
Seville, Spain, consists of 2,650 heliostats that focus 95% of
solar radiation onto a giant receiver. Temperatures as high as
900°C are obtained at the receiver. Molten salt tanks are
heated by concentrated solar heat, reaching a temperature
of above 500°C. Water runs through the molten salt tanks, in
which it is boiled and superheated. The resulting steam is
directed to turbines to produce power. Steam leaving the
turbine is condensed and pumped back to the molten salt
tanks to repeat the heat engine cycle.
Mehran Ahmadi, Ph. D., P. Eng.
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Solar Pond
Solar Energy
Another solar-based method of power generation involves collecting
and storing solar energy in large artificial lakes a few meters deep,
called solar ponds.
Solar energy is absorbed by all parts of the pond, and the water
temperature rises everywhere. The top part of the pond, however,
loses to the atmosphere much of the heat it absorbs, and as a
result, its temperature drops. This cool water serves as insulation for
the bottom part of the pond and helps trap the energy there.
Usually, salt is planted at the bottom of the pond to prevent the rise
of this hot water to the top.
A power plant that uses an organic fluid, such as alcohol, as the
working fluid can be operated between the top and the bottom
portions of the pond.
Mehran Ahmadi, Ph. D., P. Eng.
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Solar Pond
Solar Energy
The main disadvantage of a solar pond power plant is the
low thermal efficiency. For example, if the water
temperature is 35°C near the surface and 80°C near the
bottom of the pond, the maximum thermal efficiency can
be determined from the Carnot relation to be:
𝑇L
35 + 273 𝐾
𝜂th, max = 1 −
=1−
= 12.7%
𝑇H
80 + 273 𝐾
Note: An ocean thermal energy converter (OTEC) system
uses the same principle, but in this case the water at the
sea or ocean surface is warmer as a result of solar energy
absorption, and the water at a deeper location is cooler.
Experiments have been performed using the OTEC
principle, but the results have not been promising due to
high installation costs and low thermal efficiency.
Mehran Ahmadi, Ph. D., P. Eng.
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Photovoltaic Cell
Solar Energy
Direct conversion of solar radiation into electricity is possible by the use of photovoltaic cell systems, consist of
arrays of solar cells.
Understanding of the operation of solar cells requires physics of atomic theory and semiconductor theory.
Silicon which is commonly used as a semiconductor material in solar cells, is doped with phosphorus to produce
the n-type, or with boron to produce the p-type semiconductor.
Mehran Ahmadi, Ph. D., P. Eng.
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Photovoltaic Cell
Solar Energy
The current density J is defined as the current I over the cell surface area A.
The current density flow from n-type semiconductor to p-type semiconductor is denoted by Jr
and called the light-induced recombination current, and that from p-type to n-type is denoted by
Jo and called the dark current or reverse saturation current.
In an illuminated solar cell, the Jr is proportional to Jo according to the relation:
𝑒o 𝑉
𝐽r = 𝐽o exp
𝑘𝑇
where eo = 1.6 × 10-19 J/V is equal to charge of one electron, k = 1.381 × 10-23 J/K is Boltzmann’s
constant, V is voltage, and T is the cell temperature in Kelvin.
Mehran Ahmadi, Ph. D., P. Eng.
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Photovoltaic Cell
Solar Energy
The junction current density Jj is equal to the algebraic sum
of Jr and Jo:
𝑒o 𝑉
𝐽j = 𝐽r − 𝐽o = 𝐽o exp
−1
𝑘𝑇
The output current density Js flows through the junction or
load, so the load current density JL is given by:
𝐽L = 𝐽s − 𝐽j = 𝐽s − 𝐽o exp
𝑒o 𝑉
−1
𝑘𝑇
Note: The voltage, V is zero when the cell is short-circuited,
and thus Js = JL.
Mehran Ahmadi, Ph. D., P. Eng.
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Photovoltaic Cell
Solar Energy
The cell output is through the junction when the circuit is open and JL = 0. The
voltage in this case is called the open-circuit voltage, Voc:
𝑘𝑇
𝐽s
𝑉OC =
ln
+1
𝑒o
𝐽o
An expression for the ratio of the load current density JL to short-circuit current
density Js may be obtained:
𝐽L
𝐽o
𝑒o 𝑉
=1−
exp
−1
𝐽s
𝐽s
𝑘𝑇
Mehran Ahmadi, Ph. D., P. Eng.
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Photovoltaic Cell
Solar Energy
The power output delivered to the load is:
𝑊ሶ = 𝐽L 𝐴𝑉
where A is the cell area.
Substituting JL:
𝑊ሶ = 𝐽s 𝐴𝑉 − 𝐽o 𝐴𝑉 exp
𝑒o 𝑉
−1
𝑘𝑇
Differentiating with respect to voltage V and setting the derivative equal to zero gives the maximum load voltage
for the maximum power output:
𝐽s
1
+
𝑒o 𝑉max
𝐽o
exp
=
𝑒 𝑉
𝑘𝑇
1 + o max
𝑘𝑇
Note: The maximum voltage Vmax is implicit in this equation, and a trial-error approach is needed to solve for Vmax.
Mehran Ahmadi, Ph. D., P. Eng.
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Photovoltaic Cell
Solar Energy
The maximum power output of the cell is:
𝑊ሶ max =
𝐴𝑉max (𝐽s + 𝐽o )
𝑘𝑇
1+
𝑒o 𝑉max
The conversion efficiency of a solar cell can be expressed as the power output divided by the incident solar
radiation:
𝑊ሶ
𝜂cell =
𝐴𝐺
where G is the solar irradiation.
Using the maximum power output expression, the maximum conversion efficiency of a solar cell can be written
as:
𝑊ሶ max
𝑉max (𝐽s + 𝐽o )
𝜂cell, max =
=
𝑘𝑇
𝐴𝐺
𝐺 1+
𝑒o 𝑉max
Mehran Ahmadi, Ph. D., P. Eng.
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Photovoltaic Cell
Solar Energy
We can plot the current density ratio
JL/Js and normalized power as a
function of load voltage for a specified
value of open-circuit voltage Voc (0.55V
in this case).
Note: A high-quality silicon solar cell
can produce an open-circuit voltage of
about 0.6V.
Mehran Ahmadi, Ph. D., P. Eng.
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Wind Energy
Small windmills have been used to generate electricity since
1900, but the development of modern wind turbines
occurred only recently in response to the energy crises in
the early 1970s.
Note the distinction between the terms windmill used for
mechanical power generation (grinding grain, pumping
water, etc.) and wind turbine used for electrical power
generation, although technically both devices are turbines
since they extract energy from the fluid.
The rotation speed of rotors of wind turbines is usually
under 40 rpm (under 20 rpm for large turbines).
Mehran Ahmadi, Ph. D., P. Eng.
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Wind Energy
The cost of wind power has dropped an order of magnitude
from about $0.50/kWh in the early 1980s to about
$0.05/kWh in the mid-1990s, which is about the price of
electricity generated at coal-fired power plants.
Areas with an average wind speed of 6 m/s (or 14 mph) or
higher are potential sites for economical wind power
generation.
Commercial wind turbines generate from 100 kW to 8 MW
of electric power each at peak design conditions.
The blade span (or rotor) diameter of the 3.2 MW wind
turbine built by Boeing Engineering is 320 ft (97.5 m).
Mehran Ahmadi, Ph. D., P. Eng.
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Wind Turbine Types, Power Performance Curve
Wind Energy
We generally categorize wind turbines by the orientation of their axis of rotation:
horizontal axis wind turbines (HAWTs) and vertical axis wind turbines (VAWTs).
An alternative way to categorize them is by the mechanism that provides torque
to the rotating shaft: lift or drag.
So far, none of the VAWT designs or drag-type designs has achieved the
efficiency or success of the lift-type HAWT; therefore, the vast majority of wind
turbines being built around the world are of this type.
Mehran Ahmadi, Ph. D., P. Eng.
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Horizontal Axis Wind Turbines (HAWTs)
Wind Energy
Mehran Ahmadi, Ph. D., P. Eng.
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Vertical Axis Wind Turbines (VAWTs)
Wind Energy
Mehran Ahmadi, Ph. D., P. Eng.
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Combined and Other Types of Wind Turbines
Wind Energy
Mehran Ahmadi, Ph. D., P. Eng.
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Wind Turbine Types, Power Performance Curve
Wind Energy
Every wind turbine has a characteristic power
performance curve, in which electrical power
output is plotted as a function of wind speed V at
the height of the turbine’s axis.
There are three key wind-speeds:
▪ Cut-in speed is the minimum wind speed at which
useful power can be generated.
▪ Rated speed is the wind speed that delivers the
rated power, usually the maximum power.
▪ Cut-out speed is the maximum wind speed at
which the wind turbine is designed to produce
power. At wind speeds greater than the cut-out
speed, the turbine blades are stopped by some
type of braking mechanism to avoid damage and
for safety issues.
Mehran Ahmadi, Ph. D., P. Eng.
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Wind Power Potential
Wind Energy
Reminder: Mechanical energy can be defined as the form of energy that can be converted to mechanical work
completely and directly by an ideal mechanical device such as an ideal turbine.
The mechanical energy of a flowing fluid can be expressed as:
𝑃 𝑉2
𝐸ሶ mech = 𝑚ሶ
+
+ 𝑔𝑧
𝜌
2
where P/ρ is the flow energy, V2/2 is the kinetic energy, and gz is the potential energy of the fluid, all per unit
mass, and ṁ is the mass flow rate of the fluid.
The pressures at the inlet and exit of a wind turbine are both equal to the atmospheric pressure, and the elevation
does not change across a wind turbine, so a wind turbine converts the kinetic energy of the fluid into power. For
the wind velocity of V, the available wind power (maximum power) is expressed as:
1
𝑊ሶ available = 𝑚𝑉
ሶ 2
2
Mehran Ahmadi, Ph. D., P. Eng.
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Wind Power Potential
Wind Energy
Mass flow rate is given by:
𝑚ሶ = 𝜌𝑉𝐴
where ρ is the density and A is the disk area of a wind turbine
(the circular area swept out by the turbine blades as they
rotate);
1
𝑊ሶ available = 𝜌𝐴𝑉 3
2
Air density can be determined from the ideal gas relation (P =
ρRT), when pressure P and temperature T of air are generally
known, R is the gas constant (0.287 kPa·m3/kg·K), and A is the
disk area (πD2/4), with D being the blade diameter;
𝜋𝑃𝐷2 𝑉 3
𝑊ሶ available =
8𝑅𝑇
Mehran Ahmadi, Ph. D., P. Eng.
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Wind Power Density
Wind Energy
For comparison of various wind turbines and
locations, it is more useful to think in terms of the
available wind power per unit area, called wind
power density in W/m2;
𝑊ሶ available 1 3
= 𝜌𝑉
𝐴
2
Wind speed varies greatly throughout the day and
throughout the year; so, it is useful to define the
average wind power density in terms of annual
ത based on hourly averages as:
average wind speed 𝑉,
ഥሶ
𝑊
1 3
available
= 𝜌𝑉ത
𝐴
2
Mehran Ahmadi, Ph. D., P. Eng.
| 43
Wind Turbine Efficiency
Wind Energy
An actual wind turbine can convert only a percentage of available power potential into actual
shaft power, called the wind turbine efficiency, and is determined from:
𝑊ሶ shaft
𝑊ሶ shaft
𝜂wt =
=
ሶ
𝑊available 1 𝐴𝜌𝑉 3
2
where Ẇshaft refers to rotor shaft power output.
A gearbox/generator connected to the turbine converts shaft power into electrical power output
Ẇelectric, and they are related to each other by:
𝑊ሶ electric = 𝜂gearbox/generator 𝑊ሶ shaft
where ηgearbox/generator is the gearbox/generator combined efficiency and is typically above 80%.
Mehran Ahmadi, Ph. D., P. Eng.
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Wind Turbine Efficiency
Wind Energy
We may also define an overall wind turbine efficiency as the electrical power output divided by the available wind power as:
𝑊ሶ electric
𝑊ሶ electric
𝜂wt, overall =
=
1
𝑊ሶ available
𝐴𝜌𝑉 3
2
Note I: A given wind turbine efficiency sometimes refers to overall wind turbine efficiency, and the context usually makes it clear.
The overall wind turbine efficiency is related to wind turbine efficiency by:
𝑊ሶ shaft
𝑊ሶ electric
𝑊ሶ electric
𝜂wt, overall = 𝜂wt × 𝜂gearbox/generator =
×
=
𝑊ሶ available
𝑊ሶ shaft
𝑊ሶ available
Note II: The efficiency of a wind turbine is usually referred to as the power coefficient Cp, usually ranges between 30% and 40%.
Using the wind turbine efficiency, the actual shaft power output from a wind turbine can be expressed as:
1
𝑊ሶ shaft = 𝜂wt 𝜌𝐴𝑉 3
2
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Wind Turbine Efficiency
Wind Energy
Neglecting frictional effects in a wind turbine and taking the wind velocity as the average velocity of air at the turbine inlet, the
portion of incoming kinetic energy not converted to shaft power, can be assumed to leaves the wind turbine as outgoing kinetic
energy:
𝑉12
𝑉22
𝑚ሶ
= 𝑊ሶ shaft + 𝑚ሶ
2
2
The efficiency is also expressed as:
Replace:
𝑊ሶ shaft
𝜂wt =
𝑉1 𝑉12
𝑚ሶ
𝑉2 2
𝑉22
𝑉12
𝑉1
𝑚ሶ
= 𝑚ሶ
1 − 𝜂wt
2
2
𝑉2
Solving for the exit velocity, we obtain:
𝑉2 = 𝑉1 1 −
𝑉1
𝜂
𝑉2 wt
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Betz Limit for Wind Turbine Efficiency
Wind Energy
The perfect conversion of kinetic energy to work occurs only
when the velocity of air at the turbine exit is zero, which is not
possible because air must be taken away at the turbine exit to
maintain the mass flow through the turbine.
So, there is a maximum possible efficiency for a wind turbine,
first calculated by Albert Betz in the mid-1920s:
▪ We consider two control volumes surrounding the disk area, a large
control volume and a small one, with upstream wind speed V taken
as V1.
▪ The axisymmetric stream tube (enclosed by streamlines) can be
thought of as forming an imaginary “duct” for the flow of air
through the turbine.
▪ Since locations 1 and 2 are sufficiently far from the turbine, take
P1=P2= Patm, yielding no net pressure force on the control volume.
▪ Approximate the velocities at the inlet 1 and outlet 2 to be uniform
at V1 and V2, respectively.
Mehran Ahmadi, Ph. D., P. Eng.
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Betz Limit for Wind Turbine Efficiency
Wind Energy
In this ideal analysis:
▪ The pressure starts at atmospheric pressure far upstream (P1 = Patm),
▪ Pressure rises smoothly from P1 to P3,
▪ Pressure drops suddenly from P3 to P4 across the turbine disk, and
▪ Pressure rises smoothly from P4 to P2, reaching atmospheric pressure far downstream (P2
= Patm).
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Betz Limit for Wind Turbine Efficiency
Wind Energy
The momentum equation is written as:
𝐹𝑅 = 𝑚ሶ 𝑉2 − 𝑉1
where FR is the reaction force on the turbine.
Approximating the turbine as a disk, the smaller control volume that encloses the turbine, is infinitesimally thin (A3 =A4=A); so,
since air is incompressible here, V3=V4. However, the wind turbine extracts energy from the air, causing a pressure drop, P3≠P4.
Apply the streamwise component of the momentum equation on the small CV:
𝐹𝑅 + 𝑃3 𝐴 − 𝑃4 𝐴 = 0
⇒
𝐹𝑅 = 𝐴 𝑃4 − 𝑃3
The Bernoulli equation is certainly not applicable across the turbine, since it is extracting energy from the air; however, it is a
reasonable approximation between locations 1 and 3 and between locations 4 and 2:
𝑃1 𝑉12
𝑃3 𝑉32
+
+ 𝑧1 =
+
+ 𝑧3
𝜌𝑔 2𝑔
𝜌𝑔 2𝑔
and
𝑃4 𝑉42
𝑃2 𝑉22
+
+ 𝑧4 =
+
+ 𝑧2
𝜌𝑔 2𝑔
𝜌𝑔 2𝑔
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Betz Limit for Wind Turbine Efficiency
Wind Energy
Setting P1=P2=Patm and V3=V4, and since the wind turbine is horizontal, z1=z2=z3=z4
(gravitational effects are negligible in air anyway):
𝑉12 − 𝑉22 𝑃3 − 𝑃4
=
2
𝜌
Substituting ṁ = ρV3A:
𝑉1 + 𝑉2
𝑉3 =
2
Thus, we conclude that the average velocity of the air through an ideal wind turbine is
the arithmetic average of the far upstream and far downstream velocities.
Note: Validity of this result is limited by the applicability of the Bernoulli equation.
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Betz Limit for Wind Turbine Efficiency
Wind Energy
Define a new variable a as the fractional loss of velocity from far upstream to the turbine disk as:
𝑉1 − 𝑉3
𝑉1
The velocity through the turbine thus becomes V3 = V1(1 – a), and the mass flow rate through the turbine
becomes ṁ = ρV3A=ρAV1(1 – a):
𝑉2 = 𝑉1 1 − 2𝑎
For an ideal wind turbine without irreversible losses such as friction, the power generated by the turbine is simply
the difference between the incoming and outgoing kinetic energies:
𝑎=
𝑉12 − 𝑉22
𝑉12 − 𝑉12 1 − 2𝑎 2
𝑊ሶ ideal = 𝑚ሶ
= 𝜌𝐴𝑉1 1 − 𝑎
= 2𝜌𝐴𝑉13 𝑎(1 − 𝑎)2
2
2
Assuming no irreversible losses in transferring power from the turbine to the turbine shaft, the efficiency of the
wind turbine is expressed as:
𝑊ሶ shaft
𝑊ሶ ideal
2𝜌𝐴𝑉13 𝑎(1 − 𝑎)2
𝜂wt, max =
=
=
= 4𝑎(1 − 𝑎)2
1 3
1 3
1 3
𝜌𝑉1 𝐴
𝜌𝑉1 𝐴
𝜌𝑉 𝐴
2
2
2 1
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Betz Limit for Wind Turbine Efficiency
Wind Energy
Finally, as any good engineer knows, to calculate the
maximum value of ηwt, set dηwt/da =0 and solving for
a. This yields a = 1 or 1/3. Since a=1 is the trivial case
(no power generated), a must equal 1/3 for
maximum possible power coefficient:
1
1
𝜂wt, max = 4𝑎(1 − 𝑎)2 = 4 1 −
3
3
2
=
16
= 0.5926
27
This value of ηwt, max represents the maximum
possible efficiency of any wind turbine and is known
as the Betz limit. All real wind turbines have a
maximum achievable efficiency less than this due to
irreversible losses which have been ignored in this
ideal analysis.
Wind turbine efficiency ηwt as a function of the ratio of turbine blade
tip speed Vtip=ωR to wind speed V for several types of wind turbines,
where ω is angular velocity of the wind turbine blades and R is their
radius. Angular velocity of rotating machinery is typically expressed in
rpm (number of revolutions per minute) and denoted by ṅ.
ω = 2πṅ rad/min or ω = 2πṅ/60 rad/s
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Hydropower
Large dams are built in the flow path of rivers to collect water. The
water, having potential energy, is run through turbines to produce
electricity. Such an installation is called a hydroelectric power plant.
Turbines have been used for centuries to convert freely available
mechanical energy from rivers and water bodies into useful
mechanical work, usually through a rotating shaft.
When the working fluid is water, the turbomachines are called
hydraulic turbines or hydroturbines. The rotating part of a
hydroturbine is called the runner.
Some dams are also used for irrigation of farms and flood control. The
large dam takes a long time and a large capital investment to build,
but the cost of producing electricity by hydropower is much lower
than the cost of electricity production by fossil fuels.
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Analysis of Hydroelectric Power Plant
Hydropower
The mechanical energy of a flowing fluid can be expressed on a unit mass basis as:
𝑃 𝑉2
𝑒mech = +
+ 𝑔𝑧
𝜌
2
where P/ρ is the flow energy, V2/2 is the kinetic energy, and gz is the potential energy of the fluid, all per unit
mass.
The mechanical energy change of a fluid during incompressible flow becomes:
𝑃2 − 𝑃1 𝑉12 − 𝑉22
∆𝑒mech =
+
+ 𝑔 𝑧2 − 𝑧1
𝜌
2
In the absence of any irreversible losses, the mechanical energy change represents the mechanical work supplied
to the fluid (if Δemech>0) or extracted from the fluid (if Δemech<0).
The maximum (ideal) power generated by a turbine, for example, is Ẇmax = ṁΔemech, and ṁ is the mass flow rate
of the fluid.
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Analysis of Hydroelectric Power Plant
Hydropower
Mechanical energy of an ideal hydraulic turbine coupled with an ideal generator. In the absence
of irreversible losses, the maximum produced power is proportional to (a) the change in water
surface elevation from the upstream to the downstream reservoir or (b) (close-up view) the drop
in water pressure from just upstream to just downstream of the turbine.
Mehran Ahmadi, Ph. D., P. Eng.
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Analysis of Hydroelectric Power Plant
Hydropower
In fluid systems, we are usually interested in the process of extracting mechanical energy from a fluid by a turbine
and producing mechanical power in the form of a rotating shaft that can drive a generator or any other rotary
device.
The degree of perfection of the conversion process between the mechanical work extracted and the mechanical
energy change of the fluid is expressed by the turbine efficiency. In rate form, it is defined as:
𝑊ሶ shaft
𝑊ሶ shaft 𝑊ሶ shaft
𝜂turbine =
=
=
𝑚𝑔ℎ
ሶ
∆𝐸ሶ mech, fluid
𝑊ሶ max
where Ẇshaft is the shaft power output from the turbine and ṁΔemech is the rate of decrease in the mechanical
energy of the fluid, which is equal to maximum power Ẇmax=ṁgh, based on the notation in previous slide figure.
Note: A turbine efficiency of 100% indicates perfect conversion between the mechanical energy of the fluid and
the shaft work, and this value can be approached (but never attained) as the frictional effects are minimized.
Mehran Ahmadi, Ph. D., P. Eng.
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Analysis of Hydroelectric Power Plant
Hydropower
The mechanical efficiency of a turbine should not be confused with the generator
efficiency, which is defined as:
𝑊ሶ electric
𝜂generator =
𝑊ሶ shaft
where Ẇelectric is the electrical power output from the generator.
A turbine is usually packaged together with its generator; therefore, we are
usually interested in the combined or overall efficiency of a turbine-generator
combination:
𝑊ሶ shaft 𝑊ሶ electric 𝑊ሶ electric
𝜂turbine−generator = 𝜂turbine 𝜂generator =
=
𝑊ሶ max 𝑊ሶ shaft
𝑊ሶ max
Note: Most turbines have efficiencies approaching 90%. Large hydroturbines
achieve overall efficiencies above 95%.
Mehran Ahmadi, Ph. D., P. Eng.
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Analysis of Hydroelectric Power Plant
Hydropower
The analysis of a hydroelectric power plant involves that of the turbine and the
penstock, which is the piping system between the upper and lower water levels:
𝑃1 𝑉12
𝑃2 𝑉22
+
+ 𝑔𝑧1 =
+
+ 𝑔𝑧2 + 𝑤turbine + 𝑒mech, loss
𝜌1
2
𝜌2
2
When the flow is incompressible, either absolute or gage pressure can be used
for P since Patm/ρ would appear on both sides and would cancel out:
𝑃1 𝑉12
𝑃2 𝑉22
𝑚ሶ
+
+ 𝑔𝑧1 = 𝑚ሶ
+
+ 𝑔𝑧2 + 𝑊ሶ turbine + 𝐸ሶ mech, loss
𝜌1
2
𝜌2
2
where Ẇturbine is the shaft power output through the turbine’s shaft, and Ėmech,
loss, total is the total mechanical power loss, which consists of turbine losses as
well as the frictional losses in the piping network (penstock).
𝐸ሶ mech, loss = 𝐸ሶ mech, loss, turbine + 𝐸ሶ mech, loss, piping
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Analysis of Hydroelectric Power Plant
Hydropower
By convention, irreversible turbine losses are treated separately from irreversible losses due to other components of the piping
system; thus, the energy equation is expressed in its most common form in terms of heads by dividing each term by ṁg:
𝑃1
𝑉12
𝑃2
𝑉22
+
+ 𝑧1 =
+
+ 𝑧2 + ℎturbine,e + ℎL
𝜌1 𝑔 2𝑔
𝜌2 𝑔 2𝑔
The term hturbine,e is the extracted head removed from the fluid by the turbine. Because of irreversible losses in the turbine,
hturbine,e is greater than Ẇturbine/ ṁg by the factor ηturbine.
The term hL is the irreversible head loss between 1 and 2 due to all components of the piping system other than the turbine.
𝐿 𝑉2
𝑉2
𝐿
𝑉2
ℎL = ℎL,major + ℎL,minor = 𝑓
+ ෍ 𝐾L
= 𝑓 + ෍ 𝐾L
𝐷 2𝑔
2𝑔
𝐷
2𝑔
where f is the Darcy friction factor. It can be determined from the Moody chart (or Colebrook equation) for turbulent flow, and f =
64/Re for laminar flow, L is the length of the penstock, D is the diameter of the penstock, V is the velocity of water in the
penstock, and KL is the loss coefficient for minor losses in the piping system.
Mehran Ahmadi, Ph. D., P. Eng.
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Analysis of Hydroelectric Power Plant
Hydropower
Consider a typical hydroelectric dam as shown in the figure:
The overall or gross head, Hgross, is defined as the elevation difference between the
reservoir surface upstream of the dam and the surface of the water exiting the dam.
𝐻gross = 𝑧A − 𝑧E
If there were no irreversible losses anywhere in the system, the maximum amount of
power that could be generated per turbine would be:
ሶ gross
𝑊ሶ max = 𝜌𝑔𝑉𝐻
If we were to insert a Pitot probe at point B at the end of the penstock just before the turbine, the water in the tube would rise to a column height
equal to the energy grade line EGLin at the inlet of the turbine.
Note: The energy grade line (EGL) represents the total head of the fluid:
EGL = Pressure head + Velocity head + Elevation head =
P V2
+
+z
ρg 2g
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Analysis of Hydroelectric Power Plant
Hydropower
This column height is lower than the water level at point A, due to
irreversible losses in the penstock and its inlet.
After passing through the turbine runner, the exiting fluid (point C)
still has appreciable kinetic energy (velocity head), and perhaps swirl.
To recover some of this kinetic energy (which would otherwise be
wasted), the flow enters an expanding area diffuser called a draft
tube, which turns the flow horizontally and slows down the flow
speed, while increasing the pressure prior to discharge into the
downstream water, called the tailrace.
If we were to imagine another Pitot probe at point D (the exit of the draft tube),
the water in the tube would rise to a column height equal to the energy grade
line labeled EGLout:
𝐻net = EGLin − EGLout
Note: Due to its pressure recovery, the draft tube prevents the pressure at the outlet of the runner (point C) to decrease below
atmospheric pressure, thereby lowering the chance of sub-atmospheric pressures that causes cavitation.
Mehran Ahmadi, Ph. D., P. Eng.
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Analysis of Hydroelectric Power Plant
Hydropower
The overall efficiency of the entire hydroelectric plant, including penstock flow, is the ratio of actual electric power
produced to maximum power, based on gross head:
𝑊ሶ electric
𝑊ሶ electric
𝜂plant =
=
ሶ gross
𝑊ሶ max
𝜌𝑔𝑉𝐻
However, by convention, turbine efficiency ηturbine should be based on net head Hnet rather than gross head Hgross.
𝑊ሶ shaft
𝜂turbine =
ሶ net
𝜌𝑔𝑉𝐻
When the total irreversible head loss hL in the piping is known, the corresponding power loss is determined from:
ሶ 𝐿
𝐸ሶ mech,loss,piping = 𝜌𝑔𝑉ℎ
The turbine efficiency is then expressed as:
𝜂turbine =
𝑊ሶ shaft
𝑊ሶ shaft
𝑊ሶ shaft
=
=
ሶ 𝐿
ሶ gross −𝜌𝑔Ѵℎ
𝑊ሶ max −𝐸ሶ mech,loss,piping
𝜌𝑔𝑉𝐻
𝜌𝑔𝑉ሶ 𝐻gross −ℎL
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Analysis of Hydroelectric Power Plant
Hydropower
The effect of irreversible head losses in the piping system can be accounted for using an efficiency term ηpiping as:
𝐸ሶ mech,loss,piping
𝜂piping = 1 −
𝑊ሶ max
The generator efficiency is ηgenerator = Ẇelectric/Ẇshaft, the overall efficiency of a hydroelectric power plant can be expressed as:
𝜂plant = ηgenerator ηturbine ηpiping
𝜂plant =
𝑊ሶ electric
𝑊ሶ shaft
𝑊ሶ electric
𝜂plant =
𝑊ሶ shaft
𝑊ሶ shaft
𝑊ሶ max − Eሶ mech,loss,piping
𝑊ሶ max
𝑊ሶ shaft
𝐸ሶ mech,loss,piping
1−
𝑊ሶ max
1−
𝐸ሶ mech,loss,piping
𝑊ሶ max
𝐸ሶ mech,loss,piping
1−
𝑊ሶ max
𝑊ሶ electric
𝜂plant =
𝑊ሶ max
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Turbine Types
Hydropower
In hydroelectric power plants, large dynamic turbines are used
to produce electricity. There are two basic types of dynamic
turbine—impulse and reaction.
In an impulse turbine, the fluid is sent through a nozzle so that
most of its available mechanical energy is converted into kinetic
energy. The high-speed jet then impinges on bucket-shaped
vanes that transfer energy to the turbine shaft.
The modern and most efficient type of impulse turbine is Pelton
turbine, and the rotating wheel is now called a Pelton wheel.
Note: Impulse turbines require a higher head but can operate
with a smaller volume flow rate.
Mehran Ahmadi, Ph. D., P. Eng.
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Turbine Types
Hydropower
Reaction turbine, consists of fixed guide vanes called stay vanes,
adjustable guide vanes called wicket gates, and rotating blades
called runner blades.
Flow enters tangentially at high pressure, is turned toward the
runner by the stay vanes as it moves along the spiral casing or
volute, and then passes through the wicket gates with a large
tangential velocity component.
There are two main types of reaction turbine; Francis and Kaplan:
▪ The Francis turbine is somewhat similar in geometry to a
centrifugal or mixed-flow pump, but with the flow in the
opposite direction.
▪ The Kaplan turbine is somewhat like an axial-flow fan running
backward.
The runner of a Francis mixed-flow with 17 runner
blades of outer diameter 20.3 ft (6.19 m), rotation
speed of 100 rpm power generation rate of
194MW at a volume flow rate of 375 m3/s from a
net head of 54.9 m.
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Turbine Types
Hydropower
The five-bladed propeller turbine with outer diameter 12.7 ft
(3.87 m), rotation speed of 100 rpm and power generation rate
of 5.37 MW at a volume flow rate of 63.7 m3/s from a net head
of 9.75 m.
Runner of a Francis radial-flow turbine with 17 runner blades
of outer diameter 11.8 ft (3.60 m), rotation speed of 180 rpm
and power generation rete of 119 MW at volume flow rate of
127 m3/s from a net head of 105 m.
Mehran Ahmadi, Ph. D., P. Eng.
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Turbine Types
Hydropower
Note I: We classify reaction turbines according to the angle that the flow enters
the runner. If the flow enters the runner radially, the turbine is called a Francis
radial-flow turbine.
Note II: Reaction turbines can operate with much less head but require a higher
volume flow rate.
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| 67
Geothermal Energy
Geothermal energy is the thermal energy within the earth’s interior.
It is a renewable energy source because heat is continuously transferred
from within the earth to the water recycled by rainfall or reinjected back
to the ground after use.
The origin of geothermal energy is earth’s core. The core includes the inner
core, iron center, and outer core made up of very hot magma.
The temperature in the magma remains very high due to decay of
radioactive particles. The outer core is surrounded by the mantle whose
thickness is about 3000 km. The mantle is made of magma and rock.
The layer of the earth housing continents and ocean floors is called the
crust. The thickness of the crust is 25 to 55 km on the continents and 5 to
8 km under the oceans. The crust is made up of tectonic plates. Volcanoes
occur near the edges of these plates due to magma getting close to it.
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| 68
Geothermal Energy
At some reasonable depths, the rocks and water absorb heat from magma. These sites are
characterized as geothermal resources. By digging wells and pumping the hot water to the surface, we
make use of geothermal energy.
Geothermal resources can be classified based on their thermal and compositional characteristics:
▪ Hydrothermal: These are known geothermal fields containing high temperature water in vapor, mixture, or
liquid phases.
▪ Geopressurized: These resources contain hot liquid water at 150°C to 180°C at very high pressures (up to 600
bar). The fluid in these deposit-filled reservoirs also contains methane and high levels of dissolved solids. The
fluid is highly corrosive and thus very difficult to harvest and handle.
▪ Magma: They are also called molten rock, and typically contained under active volcanoes at temperatures above
650°C.
▪ Enhanced: They are also called hot, dry rock geothermal systems. These are not natural geothermal resources.
The idea is injecting water into hot rock formation at high pressure and bringing the resulting hot water to the
surface.
Note I: Only hydrothermal resources are being exploited. Other three are estimated to have
enormous energy potentials but current technologies do not allow feasible energy production from
these resources.
Note II: The quality and life of a hydrothermal resource can be prolonged by reinjecting the waste
fluid back to the ground.
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Geothermal Energy
A geothermal resource contains geothermal water at a temperature higher than that of the
environment. One common classification of geothermal resources is based on the resource
temperature:
▪ High temperature resource; T > 150°C
▪ Medium temperature resource; 90°C < T < 150°C
▪ Low temperature resource; T < 90°C
The state of geothermal water in the reservoir may
be superheated or saturated steam (dry steam),
saturated steam-liquid mixture, or liquid (usually
compressed liquid).
Steam-dominated resources are of the higher quality
than liquid-dominated resources due to their higher
enthalpy values.
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Geothermal Energy
There are several options for utilizing the thermal energy produced from
geothermal energy systems.
▪ Electricity production: Geothermal energy is most commonly used for base-load electric
power generation. The technology for producing power from geothermal resources is
well-established and there are numerous geothermal power plants operating worldwide.
The temperature of geothermal resource should be about 150°C or higher for economic
power production.
▪ Space heating: Many residential and commercial districts are effectively heated in winter
by low-cost geothermal heat in many parts of the world. Some of the largest district
heating installations are in China, Sweden, Iceland, Turkey, and USA. Almost 90% of
buildings in Iceland (a small country) are heated in winter by geothermal heat. The annual
amount of space heating supplied in the world by geothermal is estimated to be about
60,000 TJ (1 terajoule – TJ = 1012 J).
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Geothermal Energy
Geothermal heat is used for space heating mostly in a district heating scheme. Normally,
hot geothermal water is not directly circulated to the district due to undesirable
chemical composition and characteristics of geothermal brine. Heat exchangers are
used to transfer the heat of geothermal water to fresh water and this heated fresh
water is sent to the district. This heat is supplied to the buildings through individual heat
exchangers.
Note: Geothermal energy is more effective when
used directly than when converted to electricity,
particularly for moderate- and low-temperature
geothermal resources, since the direct use of
geothermal heat for heating and cooling would
replace greater amounts of fossil fuels from
which electricity is generated much more
efficiently.
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Geothermal Applications
Geothermal Energy
Cogeneration: A cogeneration system utilizing a geothermal resource and producing electricity and heat allows an
enhanced use of the resource. This is a cascaded application in which the used geothermal water leaving the
power plant is used for heating before being reinjected back to the ground. Geothermal brine is reinjected back to
the ground at much lower temperatures in cogeneration applications in comparison to single power production.
This represents a much higher utilization rate for a given resource corresponding to higher potential revenues.
Cooling: Geothermal heat may be supplied to an absorption refrigeration system for space cooling applications.
The temperature of geothermal water should be above 95°C for absorption cooling for reasonable coefficient of
performance values. A district cooling system utilizing geothermal heat may be feasible depending on the annual
cooling load of the district. The use of geothermal heat for cooling is not common. A geothermal cooling system
installed in Oregon Institute of Technology was estimated to pay for itself in about 15 years.
Heat pump: Ground-source heat pumps represent perhaps the most common use of geothermal energy in terms
of the number of units installed. These heat pumps are called geothermal heat pumps as they utilize the heat of
the earth. Ground-source heat pumps provide higher values of coefficient performance (COP) compared to airsource units. The ground at a few meters depth is at a higher temperature than the ambient air in winter and it is
at a lower temperature than the ambient in summer. These systems use higher ground temperatures in winter for
heat absorption (heating mode) and cooler ground temperatures in summer for heat rejection (cooling mode),
and this is the reason for higher COPs.
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Geothermal Power Production
Geothermal Energy
Only a fraction of geothermal resources have relatively high temperatures
making them suitable for electricity production. Geothermal power plants have
been in operation for decades in many parts of the world.
The first geothermal power plant was built in
Italy in 1904. There is currently no electricity
being generated from geothermal sources in
Canada although substantial potential exists
in the Canadian Cordillera. The most advanced
project exists as a test geothermal-electrical
site at the Mount Meager massif in BC, where
a 100 MW facility could be developed.
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Geothermal Power Production
Geothermal Energy
The simplest geothermal cycle is the direct steam cycle.
Steam from the geothermal well is passed through a
turbine and exhausted to the atmosphere or to a
condenser.
Flash steam plants are used to generate power from
liquid-dominated resources that are hot enough to flash
a significant proportion of the water to steam in surface
equipment, either at one or two pressure stages.
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Geothermal Power Production
Geothermal Energy
The flashing process in a flash plant is
essentially a constant-enthalpy process as
shown in the temperature–enthalpy
diagram below.
Saturated (or compressed) liquid
geothermal water (state 1) enters the flash
chamber in which its pressure and
temperature are decreased. The enthalpy
of the fluid stream remains constant since
the chamber is adiabatic and there is no
work interaction. The fluid is a saturated
liquid–vapor mixture at the exit of the
chamber (state 2). Water vapor (state 3) is
separated from the liquid (state 6) in the
separator. The water vapor is directed to
the turbine while the liquid is sent to a
reinjection well.
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Geothermal Power Production
Geothermal Energy
Thermodynamic analysis of a single-flash geothermal power plant:
𝑊ሶ out = 𝑚ሶ 3 ℎ3 − ℎ4
𝜂th =
𝑊ሶ out
𝐸ሶ in
𝐸ሶ in = 𝑚1 ℎ1 − ℎ0
where h0 is the enthalpy at the environmental state and it can be approximated as saturated liquid at 1 atm
and 25°C. That is, h0 ≌ hf @ 25°C.
𝜂th =
𝑊ሶ out 𝑚ሶ 3 ℎ3 − ℎ4
=
𝑚ሶ 1 ℎ1 − ℎ0
𝐸ሶ in
Using the energy rejected from the plant:
𝜂th =
𝑊ሶ out
𝐸ሶ out
=1−
𝐸ሶ in
𝐸ሶ in
𝐸ሶ out = 𝑚ሶ 6 ℎ6 − ℎ0 + 𝑚ሶ 4 ℎ4 − ℎ0
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Geothermal Power Production
Geothermal Energy
In a double-flash plant, the liquid water leaving the
separator after the first flashing process is further
expanded in a second flash chamber. Additional water
vapor resulting from this process is separated and sent
to a lower pressure stage of the turbine for additional
power production. The rest of the operation is the
same as the single-flash plant.
Thermal efficiency of a double-flash geothermal power
plant:
𝑊ሶ out 𝑚ሶ 3 ℎ3 − ℎ4 + 𝑚ሶ 8 ℎ8 − ℎ4
𝜂th =
=
ሶ
𝑚ሶ 1 ℎ1 − ℎ0
𝐸in
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Geothermal Power Production
Geothermal Energy
Binary cycle plants use the geothermal brine
from liquid-dominated resources at relatively
low temperatures (e.g., 57°C). These plants
operate on a Rankine cycle with a binary
working fluid (isobutane, pentane, isopentane,
R-114, etc.) that has a low boiling temperature.
Thermal efficiency of a binary cycle plant:
𝑊ሶ net,out 𝑊ሶ turbine − 𝑊ሶ pump − 𝑊ሶ fan
𝜂th =
=
ሶEin
𝐸ሶ i
n
𝐸ሶ in − 𝑚ሶ 5 ℎ5 − ℎ0
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Geothermal Power Production
Geothermal Energy
Thermodynamic analysis of a binary cycle
plant:
𝑊ሶ turbine = 𝑚ሶ 3 ℎ3 − ℎ4
𝑊ሶ pump = 𝑚ሶ 1 ℎ2 − ℎ1
𝑊ሶ net,out
𝜂th =
𝑄ሶ in
𝑄ሶ in = 𝑚ሶ 6 ℎ6 − ℎ7 = 𝑚ሶ 2 ℎ3 − ℎ2
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Geothermal Power Production
Geothermal Energy
Binary fluid should be vaporized completely (state 2a to 2b)
and superheated by the geothermal water (state 2b to 3) as
the water temperature is decreased from T6 to T6a. Binary
fluid is heated from T2 to T2a as the temperature of
geothermal water is decreased from T6a to T7.
To achieve this heat exchange, there must be a
temperature difference between the vaporization
temperature of the binary fluid (state 2a) and the
temperature of geothermal water at state 6a. This
temperature difference is called pinch-point temperature
difference ΔTpp. The value of ΔTpp is usually between 5°C
and 10°C.
The state 6a is called the pinch point of geothermal water.
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Geothermal Power Production
Geothermal Energy
An application of the conservation of energy
principle on this adiabatic heat exchanger gives
the following two equations:
𝑚ሶ geo ℎ6 − ℎ6𝑎 = 𝑚ሶ binary ℎ3 − ℎ2𝑎
𝑚ሶ geo ℎ6𝑎 − ℎ7 = 𝑚ሶ binary ℎ2𝑎 − ℎ2
ℎ2a = ℎf@Tvap
ℎ2𝑏 = ℎg@Tvap
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Geothermal Power Production
Geothermal Energy
A combined flash/binary plant incorporates a binary unit and a
flashing unit to exploit the advantages associated with both
systems. The liquid portion of the geothermal mixture serves as
the input heat for the binary cycle while the steam portion
drives a steam turbine to produce power. Power is obtained
from both the steam turbine and the binary turbine. The
geothermal liquid water is reinjected to the ground at a lower
temperature (state 7) compared to a single-flash plant.
Thermal efficiency of a combined flash/binary geothermal
power plant:
𝑊ሶ net,out 𝑊ሶ turbine − 𝑊ሶ pump − 𝑊ሶ fan
𝜂th =
=
ሶ
𝐸in
𝐸ሶ in
𝑚ሶ 3 ℎ3 − ℎ4 + 𝑚ሶ 8 ℎ8 − ℎ9 − 𝑊ሶ pump − 𝑊ሶ fan
=
𝑚ሶ 1 ℎ1 − ℎ0
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Summary
▪ Introduction
▪ Solar energy
▪ Wind energy
▪ Hydropower
▪ Geothermal energy
Mehran Ahmadi, Ph. D., P. Eng.