Modes of heat transfer
Sonal K. Thengane, HRE-513, IIT Roorkee
1
Solar Energy
The Sun is the largest object in the Solar System, accounting for 99.86% of the mass. Solar energy is the radiation from
the sun capable of producing heat, causing chemical reactions, or generating electricity.
Characteristics of the sun:
Mass: 1.98892 x 1030 kg
Diameter: 1,391,000 kilometers
Surface gravity of the Sun: 274 m/s2
Volume of the Sun: 1.412 x 1018 km3
Density of the Sun: 1.622 x 105 kg/m3
Surface temperature, pressure: 5778 K, 0.0008 bar
Sun core temperature, pressure: 15 million K, 265 billion bar
2
Availability of solar energy
51% of the total incoming energy
from the sun’s radiation
penetrates the atmosphere and
reaches the earth. Of the 49%
that does not reach the earth,
30% is reflected back into space
and 19% is absorbed by the
atmosphere and clouds. So total
70% energy is absorbed by earth
which is further reradiated to the
space.
Total solar energy absorbed by
Earth's atmosphere, oceans and
land masses ~ 3,850,000 EJ per
year.
Earth's energy use by mankind ~
500 EJ per year. This is about
0.01% of the total yearly energy
coming from the sun.
1 EJ = 1018 J
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Solar Radiation, Irradiance, and Insolation
•
Radiation is usually short term for electromagnetic radiation and radiance is an instantaneous measurement at a distinct point in time.
Solar radiation "emits" from the sun equally in all directions at frequencies that are visible (wavelength 380 - 740 nm) and non-visible.
•
Solar irradiance is the power per unit area received from the sun in the form of electromagnetic radiation as measured in the
wavelength range of the measuring instrument. Unit: W/m2
•
Solar irradiance is often integrated over a given time period in order to report the radiant energy emitted into the surrounding
environment (Wh/m2 or J/m2) during that time period. This integrated solar irradiance is called solar irradiation, solar exposure, solar
insolation, or insolation.
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• “Insolation" is the amount of radiation "received" on a given surface (usually a square meter) on a plane perpendicular to
the sun in a given amount of time (usually a day). The name comes from a combination of the words "incident solar
radiation".
• Of the total solar radiation
that reaches Earth’s surface,
infrared radiation makes up
49-50%, visible light makes
up 42-43%, and ultraviolet
radiation makes up 7-8%.
• Infrared radiation is readily
absorbed by water and
carbon dioxide molecules
and converted to heat energy
• Absorbed solar radiation,
mainly infrared radiation is
responsible for warming
Earth’s surface
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• Peak Sun Hours is the number of hours in a day when the
Sun is at its maximum radiation. Average radiation from the
sun measured on the surface of the earth during a clear
day or noon is about 1000W/m2. (This value is standard for
all PV tests & measurements).
• 1 Sun Hour is equivalent to 1000 W/m2 of the sun’s
radiation collected in 1 hour.
Q. Solar power incident on a solar PV array averages 600 W/m2 for 12 hours. Calculate the total solar energy received.
For the same region, if average peak sun hours is 5, find the energy produced from a solar PV system of 2 kW AC
output at peak sun.
Ans. 600 x 12 = 7200 Wh/m2
Ans. 5 x 2 = 10 kWh
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Peak Sun Hours for Gujarat
Peak Sun Hours for Rajasthan
India comes in the Northern hemisphere with around 300 clear sunny days and solar insolation level ranges from 4 to 7
KWh/m2/day. India is rich in solar energy resource and is densely populated, which provides the right opportunity for solar
energy sector to proliferate. Top 5 states with highest solar insolation are Gujarat, Rajasthan, Madhya Pradesh,
Maharashtra, and Andhra Pradesh.
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The amount of solar radiation that reaches any one spot on the Earth's surface varies according to:
• the rotation of earth on its axis
• the angle of inclination of the sun’s rays (latitude)
• the length of the day
• the transparency of the atmosphere
• the configuration of land in terms of its aspect
Because the Earth is round, the sun strikes the surface at different angles, ranging from 0° (just above the horizon) to 90°
(directly overhead). When the sun's rays are vertical, the Earth's surface gets all the energy possible. The more slanted the
sun's rays are, the longer they travel through the atmosphere, becoming more scattered and diffuse. Solar irradiation may
reach a value of as much as 1100 W/m2 at noon on a clear day and may go down to 100 W/m2 or less during heavy cloud
cover. Sun-Earth distance is not fixed due to elliptical orbit of the Earth’s motion around sun. Hence, solar intensity in the
extraterrestrial region has been measured by NASA with the help of satellite.
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Solar Constant
• Solar constant is the total energy received from the sun, per unit time, on a
surface of unit area kept perpendicular to the radiation, in space, just outside the
earth’s atmosphere when the earth is at its mean distance from the sun.
R
r
Let the earth be moving in a circular path of radius r taking sun (Radius R) as its
centre.
Assuming sun as perfectly black body, the energy radiated per unit time from the
surface of the sun is given by
𝐻 = 𝐴𝜎𝑇 4
Earth
Sun
where A is the surface area of the sun and T is its absolute temperature
𝐻 = (4𝜋𝑅2 )𝜎𝑇 4 where R is radius of the sun
Energy received by earth’s unit area per second
𝑆=
(4𝜋𝑅2 )𝜎𝑇 4
4𝜋𝑟 2
=
𝑅 2
𝑟
𝜎𝑇 4
R = 6.963 x 108 m
r = 1.496 x 1011 m
T = 5777 K or 5778 K
σ = 5.67 x 10-8 W/m2K4 (Stefan-Boltzmann
Constant)
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• The current accepted value for this “solar constant” (now referred to as the total sky irradiance, TSI) is 1366 or
1367 W/m2. The solar constant actually varies by +/-3% because of the planet Earth's slightly elliptical orbit around the
star Sun.
• Solar radiation incident outside the earth's atmosphere is called extraterrestrial radiation. It is the solar radiation
striking the surface of the earth if there is no atmosphere present. On average the extraterrestrial irradiance is 1366
W/m2. For the nth day of the year the solar intensity on a
plane perpendicular to the direction of solar
radiation is calculated by
Iext = Isc [1 + 0.033 cos(360n/365)] (use radians unit in excel)
Iext = extraterrestrial radiation measured on the plane normal to the
radiation on the nth day of the year (W/m2).
Isc = solar constant (W/m2)
For June 22,
n=173 Iext= 1322 W/m2 for normal year
For December 21, n=355 Iext= 1411 W/m2 for normal year
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Air Mass (Am)
• A parameter that determines the solar irradiance under clear sky conditions is
the distance that the sunlight has to travel through the atmosphere.
• The distance is shortest when the sun is at the zenith, i.e. directly overhead.
• The ratio of an actual path length of the sunlight to this minimal distance is
known as the optical air mass or air mass.
• The air mass or atmospheric mass represents the proportion of atmosphere
z
that the light must pass through before striking the earth relative to its
overhead path length, and is equal to Y/X.
• When the Sun is at its zenith the optical air mass is unity, and the spectrum is
called the air mass 1 (AM1) spectrum.
• AM is commonly used to characterize the performance of solar cells under
standardized conditions.
1
𝐴𝑀 =
cos 𝑧
where z is the angle from the
vertical (zenith angle)
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• An easy method to determine the air mass is from the shadow of a vertical pole.
Air mass is the length of the hypotenuse divided by the object height h, and from
Pythagoras's theorem we get:
𝐴𝑀 =
𝑠
1+
ℎ
2
• Above expressions assume that the atmosphere is a flat horizontal layer, but because
of the curvature of the atmosphere, the air mass is not quite equal to the
atmospheric path length when the sun is close to the horizon.
• An equation (Kasten and Young, 1989) which incorporates the curvature of the earth is
12
Latitude and longitude
Coordinate system by means of which the position or location of any place on Earth’s surface can be determined and
described. The horizontal lines are latitude and the vertical lines are longitude.
Gps coordinates of Roorkee region: 29° 51' 15.3'' N and 77° 53' 16.8'' E
Latitude is a measurement on a globe or map of location north or south of the Equator. Longitude is a measurement of
location east or west of the prime meridian at Greenwich, the specially designated imaginary north-south line that
passes through both geographic poles and Greenwich, London.
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Declination angle (𝛿)
The declination angle is the angle made by the line joining the centres of the Sun and the Earth with the projection of
this line on the equatorial plane. The declination angle, denoted by δ, varies seasonally due to the tilt of the Earth on its
axis of rotation and the revolution of the Earth around the sun. The Earth is tilted by 23.45° and the declination angle
varies within plus or minus this amount. Only at the spring and fall equinoxes, the declination angle is equal to 0°.
14
Spring or
360
× 𝑛 + 10 )
365
360
𝛿 = 23.45° × sin (
× 𝑛 + 284 )
365
𝛿 = −23.45° × cos (
where n is the number of day with Jan 1 being n =1
Find the declination angle for today?
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Altitude angle (α)
The altitude angle or elevation angle is the angular height of the sun in the sky
measured from the horizontal. It is 0° at sunrise / sunset and 90° when the sun
is directly overhead.
Zenith angle (z)
The zenith angle is the angle between the sun and the vertical. It is similar to the
altitude angle but it is measured from the vertical rather than from the
horizontal, thus making z = 90° - α
Hour angle (HRA or ω)
Until the late 19th century most people used local solar time so that noon was when the sun was directly overhead, and
each town had its own definition. The Hour Angle converts the local solar time (LST) into the number of degrees which the
sun moves across the sky. By definition, the Hour Angle is 0° at solar noon. Since the Earth rotates 15° per hour, each hour
away from solar noon corresponds to an angular motion of the sun in the sky of 15°. In the morning the hour angle is
negative, in the afternoon the hour angle is positive.
ω = 15o (LST – 12)
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Solar azimuth angle (γ)
Solar azimuth angle is the azimuth (horizontal angle with respect to north)
of the Sun's position.
Most commonly accepted convention for analyzing solar irradiation, e.g. for
solar energy applications, is clockwise from due north, so east is 90°, south
is 180°, and west is 270°.
γ = 𝑐𝑜𝑠 −1
𝑠𝑖𝑛𝛿𝑐𝑜𝑠𝜑 − 𝑐𝑜𝑠𝛿𝑠𝑖𝑛𝜑cos ω
𝑐𝑜𝑠𝛼
where α is the altitude angle, φ is the latitude, δ is the declination angle, and ω is the hour angle.
The above equation only gives the correct azimuth in the solar morning so that:
Azimuth = γ , for LST < 12 or ω < 0
Azimuth = 360° - γ , for LST > 12 or ω > 0
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Sun path diagram
•
•
•
•
•
Obtain the chart of the correct Latitude.
Select the date/month line.
Select the hour line and mark its intersection
with the date line.
Read off from the concentric circles the
altitude angle (0 – 90o).
Lay a straight edge from the center of the
chart through the marked time point to the
perimeter scale and read off the azimuth
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angle (0 – 360o) from the North clockwise.
19
Sun path diagram
Find azimuth and altitude
angles at 5 pm in December
255 deg and 10 deg
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Types of solar radiation
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Types of solar radiation
• Direct radiation (beam radiation): describes solar radiation traveling in a straight line from the sun down to the surface
of the earth. These radiations are received from the sun without change of direction
• Diffuse radiation: describes the sunlight that has been scattered by molecules and particles in the atmosphere but that
has still made it down to the surface of the earth.
• Reflected radiation: describes sunlight that has been reflected off of non-atmospheric things such as the ground and
clouds. Negligible for a horizontal surface. Asphalt reflects about 4% of the light that strikes it and a lawn about 25%.
• Total solar radiation or global solar radiation is all solar radiation incident on a surface, including scattered, reflected and
direct.
• For a horizontal surface on earth, total solar radiation is mostly considered as addition of beam and diffuse radiations as
the reflected portion is relatively much lower.
Sonal K. Thengane, HRE-513, IIT Roorkee
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Solar radiation on clear day
▪ Hourly global, beam and diffuse radiation on a horizontal surface
𝜃 - angle of incidence
𝐼𝑔 = 𝐼𝑏 + 𝐼𝑑
𝐼𝑏 = 𝐼𝑏𝑛 𝑐𝑜𝑠𝜃𝑧
𝜃𝑧
𝐼𝑏
𝐼𝑏𝑇
𝐼𝑔 = 𝐼𝑏𝑛 cos𝜃𝑧 + 𝐼𝑑
Tilt Angle (β) is the angle between the horizontal plane and the solar panel which can be set or adjusted to maximize
seasonal or annual energy collection.
Note: The optimum tilt angle is calculated by adding 15 degrees to your latitude during winter, and subtracting 15
degrees from your latitude during summer. For instance, if your latitude is 34°, the optimum tilt angle for your solar
panels during winter will be 34 + 15 = 49°. The summer optimum tilt angle on the other hand will be 34 – 15 = 19°.
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Solar radiation on tilted surfaces
• Ratio of beam radiation flux falling on a tilted surface to that falling on
a horizontal surface is called the tilt factor for the beam radiation
𝐼𝑏𝑇
cos 𝜃 sin 𝛿 sin( 𝜑 − 𝛽) + cos 𝛿 cos 𝜛 cos( 𝜑 − 𝛽)
𝑟𝑏 =
=
=
𝐼𝑏
𝑐𝑜𝑠𝜃𝑧
sin 𝜑 sin 𝛿 + cos 𝜑 cos 𝛿 cos 𝜛
• Ratio of diffuse radiation flux falling on a tilted surface to that falling
on a horizontal surface is called the tilt factor for the diffuse
radiation
1 + cos 𝛽
𝑟𝑑 =
2
• If the surroundings have a diffuse reflectance of ρg for the
total solar radiation, the reflected radiation from the
surroundings on the surface will be 𝐼𝜌𝑔
𝑟𝑟 =
1 − cos 𝛽
2
• Flux on tilted surface:
𝐼𝑇 = 𝐼𝑏 × 𝑟𝑏 + 𝐼𝑑 × 𝑟𝑑 + (𝐼𝑏 + 𝐼𝑑 ) 𝜌𝑔 × 𝑟𝑟
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Steps to find solar radiation on a given day (n) for a given latitude (φ) and LST/hour angle (ω)
Step I-
Find the declination
𝛿 = 23.45 sin
Step II-
Average beam radiation tilt factor
𝑅𝑏 =
Step III-
Tilt factor for diffuse radiation
𝑅𝑑 =
1 + cos 𝛽
2
Step IV-
Tilt factor for reflected radiation
𝑅𝑟 =
1 − cos 𝛽
2
Step V-
Total solar radiation intensity falling on surface
𝐻𝑡 = 𝐻𝑏 𝑅𝑏 + 𝐻𝑑
360
(284 + 𝑛)
365
sin( 𝜑 − 𝛽) sin 𝛿 + cos( 𝜑 − 𝛽) cos 𝛿 cos 𝜔
sin 𝜑 sin 𝛿 + cos 𝜑 cos 𝛿 cos 𝜔
𝐻𝑡 = 𝐻𝑏 𝑅𝑏 + 𝐻𝑑 𝑅𝑑 + 𝐻𝜌𝑔 𝑅𝑟
1 + cos 𝛽
1 − cos 𝛽
+ 𝐻𝜌𝑔
2
2
I – instantaneous / hourly
H – daily radiation
𝐻 - daily average radiation
β = 0 for horizontal surface
ρg : diffuse reflectance of
surroundings for the total
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solar radiation
Solar radiation measuring instruments
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Pyranometer (a) measures global solar radiation and works on thermoelectric detection principle. The radiation from the surrounding
atmosphere passes through the glass dome and falls onto the blackbody situated at the center of the instrument. This raises the
temperature of the module with one side of the module getting hot and another cold because of the heat sink. As temperature difference is
related to radiation absorbed by the black body, we can say the output voltage is linearly proportional to the radiation. The value of total
radiation can be easily obtained from this voltage value. Also by using the shade (shading ring) and following the same procedure, we can
also obtain the diffuse radiation. PV pyranometer works on photoelectric effect principle (current).
Pyrheliometer (b) measures direct solar irradiance and is used with a tracking mechanism to follow the sun continuously. Its outer structure
looks like a long tube projecting the image of a telescope and we have to point the lens to the sun to measure the radiance. The black body
absorbs the radiation falling from the lens causing temperature rise and difference between two thermocouples at two points. Deviation
because of galvanometer is proportional to current, which in turn is proportional to temperature difference at junctions. Keep adjusting the
rheostat until the galvanometer deviation becomes completely void. Once this happens we can obtain voltage and current readings from
the meters and do a simple calculation to determine the heat absorbed by the black body.
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A sunshine recorder is a device that records the amount of sunshine at a given
location or region at any time. Most common is Campbell-Stokes sunshine recorder,
the original instrument was invented by Campbell in 1858 but the later card-
holding version was a development by Stokes in 1879. A Campbell-Stokes sunshine
recorder concentrates sunlight through a glass sphere onto a recording card placed
at its focal point. The length of the burn trace left on the card represents the
sunshine duration. Card is replaced on a daily basis.
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Month-wise hourly and daily average global radiation (kWh/m2) for Goa
Monthly average global
radiation (kWh/m2)
Annual average global radiation (kWh/m2) = ?
30
The availability of solar energy varies with geographical location of site and is the highest in regions closest to the equator.
Average annual global radiation impinging on a horizontal surface which amounts to approx. 1000 kWh/m2 in Central
Europe, Central Asia, and Canada reach approx. 1700 kWh/m2 in the Mediterranian and to approx. 2200 kWh/m2 in most
equatorial regions in African, Oriental, and Australian desert areas.
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Routes of Solar Energy Utilization
• By converting solar energy to thermal energy through solar thermal conversion
• By converting solar energy directly to electricity through photovoltaic approach
32
Solar Thermal
Sonal K. Thengane, HRE-513, IIT Roorkee
33
The Rankine cycle is the fundamental operating cycle of all power
plants where an operating fluid is continuously evaporated and
condensed. Efficiency is the ratio of net work done by the steam
turbine power plant Wnet and heat supplied to the boiler Qs.
Process 0-1: Isentropic compression in Pump.
Process 1-2: Constant pressure heat addition in the Boiler.
Process 2-3: Isentropic expansion in Turbine.
Process 3-4: Constant pressure heat rejection in Condenser.
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Central receiver solar thermal power plant with storage
Solar thermal power plants are ideal for locations that offer high direct normal irradiance (DNI), preferably in the range of
35
2000 kWh/m2 to 2500 kWh/m2.
A central receiver solar thermal power plant mainly includes
Design parameters of the central receiver plant
three sub systems: Heliostat field, the central receiver, and
power conversion system. Central receiver plants use point
focus technology where a heliostat field consisting of a
number of flat movable mirrors focuses the sunlight on to a
receiver mounted on top of a tower. The heat transfer fluid
(HTF) circulated in the central receiver absorbs the heat
from the solar rays reflected by the heliostats. By using
appropriate HTFs, a working temperature of even 1000°C
can be achieved by solar tower-based technology, improving
power cycle efficiency. A power conversion system
employing the Rankine cycle then converts the thermal
energy absorbed by HTF into electrical energy.
Ref.: Praveen RP. Sustainability 2020, 12(1), 127
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35 acres land
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Components of Solar Thermal Power Plant
Although there are several different concentrating solar power (CSP) technologies, they all essentially involve reflecting
sunlight to a focal point where a heat-transfer material absorbs the sun's concentrated energy which is used to create steam
that powers conventional generators.
Main components
A CSP plant has the following major solar systems components:
- Solar Field and Collector/Mirror System
- HTF (Heat transfer fluid) System
- Heat Exchanger
- Thermal Energy Storage (TES)
- Controls System
In addition to the solar components listed above, CSP plants have other elements that represent standard technology for
generating electricity. These include natural gas boilers, steam turbine, steam generator, condenser, cooling tower, pump,
and auxiliary systems.
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Solar collectors
Solar thermal energy is utilized by capturing the heat of the sun in devices, generally known as solar collectors, designed to
maximize the heat absorption through their surfaces exposed to the sun. The heat that is absorbed on the surfaces of such
solar collectors is then transferred through a heat transfer media, generally liquid in nature, which takes the collected heat
to the point of use. In most of the concentrating solar power plants, sun’s heat is captured by a receiver, transferred to a
thermo fluid – also known as heat transfer fluid; and this heat from the thermo fluid is then used in a heat exchanger to
convert water to steam.
Based on the temperatures range, solar thermal collectors are classified as Low-, Medium- or High-temperature
collectors. Low temperature collectors (60°C - 100°C) are flat-plates generally used to heat swimming pools. Mediumtemperature collectors (100°C - 300°C) are also usually flat-plates but are used for heating water or air for residential and
commercial use. High-temperature collectors (>300℃) concentrate sunlight using mirrors or lenses, are focusing type, and
are generally used for electric power production.
Based on the design, solar collectors can be classified into two general categories: (i) non-concentrating and (ii)
concentrating
39
40
In the non-concentrating type, the collector area (the area that intercepts the solar radiation) is the same as the absorber
area (the area that absorbs the radiation). Aperture area is the area over which the solar radiation enters the collector.
For flat plate collectors the aperture area and the absorber area are the same. Flat plate collectors (FPC) and evacuated
tube collectors (ETC) are non-concentrating type collectors. These collectors are mainly designed for solar hot water and
industrial process heat applications which require energy delivery at temperatures in the range of 60-250℃. These
collectors use both diffuse and beam solar radiation and do not require tracking of the sun. They are mechanically
simpler than concentrating collectors and require less maintenance.
In the concentrating type solar collector, various types of mirrors, reflectors or concentrators are used to concentrate the
solar energy and they provide higher temperatures (i.e., 250–2000℃) than non-concentrating type collectors.
Compound parabolic concentrator (CPC), central receiver or solar tower, parabolic trough collector and parabolic dish
collectors are concentrating type collectors and are known as concentrated solar power (CSP) systems. The concentration
ratio CR (i.e., the ratio of solar radiation entering the collector to solar radiation received by the receiver, or ratio of the
area of aperture to the area of the receiver (geometrical interpretation) ) varies from less than unity to high values of the
order of 105. CR represents the system's ability to concentrate solar energy.
Most common types of collectors:
• Flat plate
• Focusing type
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Flat plate collector
A flat plate collector has area of interception equal to the
area of absorption for solar radiations.
Components:
1. Absorber
2. Transparent cover
3. Heat Transfer Medium
4. Insulation
5. Housing / Collector box
• has low initial and maintenance cost
• uses both beam and diffuse radiations
• does not require continuous orientation
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Focusing type solar collector
It is constructed by introducing a reflecting surface between the solar
radiation and receiving surface. Maximum temperature of the order of
few thousands can be obtained though this collector. Various components
of a focusing type solar collector are show in the figure.
The combinations of the receivers and the reflectors are representatives
of the concentration ratio (the ratio of solar radiation entering the
collector to solar radiation received by the receiver) of the system which
in turn indicates the quality of output energy that could be achieved with
a certain system.
43
44
Absorptivity, Reflectivity, Transmissivity
Radiation impinging on the surface of a body may be partly absorbed, partly
transmitted and partly reflected. The fraction of the incident radiation absorbed is
called the absorptivity α. Similarly, the fraction of the incident radiation reflected is
called as the reflectivity, ρ and the fraction transmitted is called as transmissivity, τ.
If I denotes the total incident radiation per unit time per unit area of surface, and Iα,
Iρ and Iτ, represent respectively the amount of radiation absorbed, reflected and
transmitted then,
Iα + Iρ + Iτ = I
α+ρ+τ=1
The equation hold for surfaces or for layers of finite thickness. The following points are to be noted:
•
Values of α, ρ, τ are always positive and lie between the limits 0 and 1
•
ρ =0 (i.e. α+τ =1) represents a non-reflecting surface, ρ =1 (i.e τ = α =0) represents perfect reflector.
•
τ =0 (i.e. ρ+α =1) represents an opaque surface, τ =1 (i.e. ρ = α =0) represents a perfectly transparent surface.
•
α =0 (i.e. ρ+τ =1) represents non absorbing surface, α =1 (i.e ρ = τ =0) represents perfectly absorbing surface.
45
Absorption of solar radiation by absorber plate under a cover
system:
The transmittance-absorptance product (τα) should be
thought of as a property of a cover-absorber combination
rather than the product of two properties
Reasonable approximation for most practical solar collectors:
Of the radiation passing through the cover system and incident on the plate, some is reflected back to the cover system.
However, all this radiation is not lost since some of it is, in turn, reflected back to the plate. τ is the transmittance of the
cover system at the desired angle and α is the angular absorptance of the absorber plate. Of the incident energy, τα is
absorbed by the absorber plate and (1 − α)τ is reflected back to the cover system. The reflection from the absorber
plate is assumed to be diffuse (and unpolarized) so the fraction (1 − α)τ that strikes the cover system is diffuse radiation
and (1 − α)τρd is reflected back to the absorber plate. The quantity ρd refers to the reflectance of the cover system for
diffuse radiation incident from the bottom side.
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Flat-plate collector energy balance equation and efficiency
In steady state, the performance of a solar collector is described by an energy balance that indicates the distribution
of incident solar energy into useful energy gain Qu (J/s), thermal losses, and optical losses.
𝑄𝑢 = 𝐴𝑐 𝐼 − 𝑈𝐿 (𝑇𝑎𝑝 − 𝑇0 )
I (or H): solar radiation absorbed by a collector per unit area of absorber (which is equal to the difference between the
incident solar radiation and the optical losses) (W/m2); ap: absorber plate
Using
𝐻𝑡 = 𝐻𝑏 𝑅𝑏 + 𝐻𝑑
𝐻𝑡 = 𝐻𝑏 𝑅𝑏 (𝜏𝛼)𝑏 +𝐻𝑑
1 + cos 𝛽
1 − cos 𝛽
+ 𝐻𝜌𝑔
2
2
1+cos 𝛽
2
(𝜏𝛼)𝑑 +𝐻𝜌𝑔
1−cos 𝛽
2
(𝜏𝛼)𝑔
Second term in RHS: thermal energy lost from the collector to the surroundings by conduction, convection, and infrared
radiation represented as the product of a heat transfer coefficient UL (W / m2K) times the difference between the mean
absorber plate temperature Tap and the ambient temperature T0.
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A measure of collector performance is the collection efficiency, defined as the ratio of
the useful gain (Qu) over some specified time period to the incident solar energy over
the same time period.
I
If conditions are constant over a time period:
Q. In absence of atmosphere or any hindrance to sun rays on their way to earth’s
surface, if the useful gain of flat-plate collector is 1000 W, then (i) what is its
area at 50% collection efficiency and (ii) what is its efficiency at 10 m2 area ?
𝑄𝑢 = 𝐴𝑐 𝐼 − 𝑈𝐿 (𝑇𝑎𝑝 − 𝑇0 )
Answers: IT = 1366 W/m2 ; 1.4 m2 ; 7.3%
48
Q. Calculate the temperature rise of water in 100-litre capacity solar thermal water heating system during a typical day of
operation. Find the electricity saved because of solar water heater and a corresponding reduction in monthly electricity
bill.
Data: collector with absorber plate area = 2 m2;
Solar radiation falling = 5 kWh/m2
collector efficiency =50%
specific heat of water = 4.2 kJ/kg°C
geyser efficiency = 95%
Cost of electricity per unit = Rs 5.50
initial temperature of water = 20°C
49
Temp rise of water:
Energy absorbed by collector = Enthalpy change in water
Solar radiation incident on collector/day x collector area x collector efficiency = m Cp ΔT
(5 x 3600) x 2 x 0.5 = 100 x 4.2 x (Tf – 20)
=> Tf = 63 C
Tf
Sun rays
Storage
tank
Hot water
Cold water
Collector
Electrical energy saved:
Ti
Geyser Efficiency = Output (enthalpy change in water) / Input (electrical energy to geyser)
0.95 = 5 x 2 x 0.5 (kWh) / Input (kWh)
 Input = 5.26 kWh
 Electricity cost per day = 5.26 x 3.5 = Rs. 18.42
 Cost for 1 mont = 18.42 x 30 = Rs. 553
50
Solar PV
Sonal K. Thengane, HRE-513, IIT Roorkee
51
52
Working Principle
Conversion of light energy in electrical energy is based on a
phenomenon called photovoltaic effect. Solar cells convert
the energy in sunlight to electrical energy. Solar cells
contain a material such as silicon (semiconductor) that
absorbs light energy. A single photovoltaic cell consists of pconducting base material and an n-conducting layer on the
top side. The energy knocks electrons loose so they can
flow freely and produce a difference in electric potential
energy, or voltage. The flow of electrons or negative charge
creates electric current. Solar cells have positive and
negative contacts, like the terminals in a battery. If the
contacts are connected with a conductive wire, current
flows from the negative to positive contact.
Why Silicon?
The generation of electric current happens inside the depletion zone of the
PN junction where the electrons from the N-type silicon, have diffused into
the holes of the P-type material. When a photon of light is absorbed by one of
these atoms in the N-Type silicon it will dislodge an electron, creating a free
electron and a hole. The free electron and hole have sufficient energy to jump
out of the depletion zone. If a wire is connected from the cathode (N-type
silicon) to the anode (P-type silicon) electrons will flow through the wire. The
electron is attracted to the positive charge of the P-type material and travels
through the external load (meter) creating a flow of electric current. The hole
created by the dislodged electron is attracted to the negative charge of Ntype material and migrates to the back electrical contact. As the electron
enters the P-type silicon from the back electrical contact it combines with the
hole restoring the electrical neutrality.
Si is the 2nd most abundant element in the earth crust (26% of the earth crust)
Si processing technology is mature due to the development in Si ICs
53
A solar cell can produce about 1 to 2 watts of
electricity. This energy is too less for use in
any household or for a commercial purpose.
In order to increase the output of electricity,
several photovoltaic cells are electrically
connected together to form a photovoltaic
module and these modules are further
electrically connected to form a photovoltaic
panel. The panels are connected together to
form a photovoltaic array. This array is then
used in a typical solar PV system along with
other components.
The performance of PV modules and arrays are generally rated according to their maximum DC power output (watts)
under Standard Test Conditions (STC). Standard Test Conditions are defined by a module (cell) operating temperature of
25oC, and incident solar irradiance level of 1000 W/m2 and under Air Mass 1.5 spectral distribution.
54
Classification of materials
Conductor: Conducting materials are those in which
plenty of free electrons are available for electric
conduction. In terms of energy bands, it means that
electrical conductors are those which have
overlapping in valence and conduction bands. These
elements (metals) mostly have 1 valence electron in
its outermost orbit with some having 2 to 3
electrons. Their resistance is very low.
Semiconductor: These are characterized by a very
narrow energy gap (0.7-1.2 eV) between the valence
band and conduction band. These are solids whose
electrical conductivity lies between high conductivity
of conductors and low conductivity of insulators. Their
resistance is medium or high. Ex: Ge, Si, GaAs. Band
gap in Ge, Si and GaAs are 0.7eV, 1.1eV and 1.43eV
respectively.
Insulator: Solids having a wide energy gap (10 eV) between a
filled valence band and empty conduction band are
insulators because valence electrons can not acquire so
much energy from an applied field that they could cross the
gap and enter the conduction band hence conduction is
impossible in them. Their resistance is very high.
55
Types of PV Systems
• Directly connected systems
PV
Panel
➢ Simplest possible PV systems that require no
batteries, charge controllers, or inverters.
DC
Load
➢ Panels directly connect to the appliance
➢ Example: DC fan, water pumping system, etc.
• Systems with battery storage
➢ Battery used vary widely as a storage medium
➢ Battery regulated voltage, suppresses transients,
PV
Panel
Charge
controller
DC
Load
can provide higher current than PV array capability
➢ Charge controller is required to protect
Battery
overcharging or over-discharging of battery
56
• Systems with both AC and DC loads
DC-AC
Converter
AC
Load
Charge
V
controller
DC
Load
➢ Inverter (DC-AC converter) is required to
convert DC into AC current
➢ Inverter efficiency is in the range of 85-95%
PV
Panel
Battery
• Systems connected with grid / generator
➢ Back-up or additional energy source can be used
Utility
grid
DC-AC
Converter
AC
Load
Charge
Controller
DC
Load
with a PV system
➢ A back-up can be a DG (Diesel Generator) set
➢ PV system can also take or give power to utility
PV
Panel
Generator
Battery
57
58
Solar Cell I-V Characteristic Curve
Solar Cell I-V Characteristic Curves are graphs of output voltage versus current for different levels of irradiation and
temperature and can explain a PV cell or panel’s ability to convert sunlight into electricity.
Figure shows the current-voltage ( I-V ) characteristics of a typical silicon PV cell operating under normal conditions.
VOC = open-circuit voltage – This is the maximum
voltage that the array provides when the terminals are
not connected to any load (an open circuit condition).
This value is much higher than Vmp which relates to the
operation of the PV array which is fixed by the load.
This value depends upon the number of PV panels
connected together in series.
ISC = short-circuit current – The maximum current
provided by the PV array when the output connectors
are shorted together (a short circuit condition). This
value is much higher than Imp which relates to the
normal operating circuit current.
MPP = maximum power point – This relates to the
point where the power supplied by the array that is
connected to the load (batteries, inverters) is at its
maximum value, where MPP = Imp x Vmp. MPP of a PV
array is measured in Watts (W) or peak Watts (Wp).
59
Fill factor (FF) – The fill factor is the relationship between the maximum
power that the array can actually provide under normal operating
conditions and the product of the open-circuit voltage multiplied by the
short-circuit current, ( VOC x ISC ). This fill factor value gives an idea of the
quality of the array and the closer the fill factor is to 1 (unity), the more
power the array can provide. Typical values are between 0.7 and 0.8.
Efficiency – The efficiency of a photovoltaic array is the ratio between
the maximum electrical power that the array can produce compared to
the amount of solar irradiance hitting the array. The efficiency of a
typical solar array is normally low at around 10-15%, depending on the
photovoltaic type (monocrystalline, polycrystalline, amorphous or thin
film) of cell being used.
Photovoltaic panels can be wired or connected together in
either series or parallel combinations, or both to increase the
voltage or current capacity of the solar array. If the array
panels are connected together in a series combination, then
the voltage increases and if connected together in parallel
then the current increases.
60
Effect of irradiation and temperature
As the temperature increases, due to environmental changes or heat generated by internal power dissipation during energy production, the
open circuit voltage (Voc) decreases. This in turn reduces the power output. The design of a solar PV system must take into account the PV
module temperature coefficient, comparing the expected average cell temperature in its operational environment, against the STC data
used to calculate the module output. In the same way, irradiance will also affect module performance, with a reduction of sunlight resulting
primarily in a reduction in current and consequentially a reduced power output.
61
Types of Solar PV Panels
Three types of solar panels that are widely
available for use in photovoltaic systems:
(1) Monocrystalline
(2) Polycrystalline
(3) Amorphous thin-film
Each type of panel has its advantages and
disadvantages. The primary differences between
these panel types are their cost and efficiency.
•
•
•
Monocrystalline panels have a uniform crystal structure across the entire panel. Monocrystalline solar panels have the highest efficiency
ratings to date and perform better than other types of panels in low-light conditions. The efficiency also decreases more slowly over time.
Monocrystalline solar panels are produced from silicon ingots and are expensive to manufacture.
Polycrystalline silicon solar panels have a unique speckled blue color that varies in shade with different areas of the panel. The silicon
used in these panels is not homogenous; which means that the crystal structure can be different in various areas of the panel. As a result,
polycrystalline solar panels are less efficient and less expensive than monocrystalline solar panels.
Thin-film solar panels are less efficient than monocrystalline or polycrystalline solar panels and have a shorter lifetime. However, their
costs are much lower due to the simple manufacturing methods in comparison with crystalline solar panels. Thin-film solar panels can
also be made flexible, whereas crystalline solar panels are much more brittle and will crack if they are bent.
62
Components of Solar PV Module / Panel
•
•
•
•
•
•
•
•
Solar cells are the building blocks of solar panels. Thousands of cells
come together to form a solar panel. These Solar Cells are stringed
together to make Solar Panels which involves soldering, encapsulating,
mounting them on a metal frame, testing, etc.
The main function of tempered glass (3-4 mm thick) is to protect the
solar cells from harsh weather, dirt, and dust.
EVA sheet or the ‘ethylene vinyl acetate’ is a highly transparent (plastic)
layer used to encapsulate the cells. It provides laminated layering on top
of the cells to hold them together.
Backsheet is the rear-most layer of the panel providing both mechanical
protection and electrical insulation. It is essentially a protective layer.
Frame provides structural strength to the panel. It is recommended to
use a frame made of strong but lightweight material.
A junction box is fixed at the backside of the panel. It is the central point
where cables interconnect with the panels.
A busbar is a thin strip of aluminum or copper found between cells in a
solar panel. Its job is to separate solar cells and conduct the direct
current the solar cells collect from solar photons to the solar inverter.
Inter or cross connectors help solar panels connect with one another.
Silicon glue creates strong bonds and is resistant to chemicals, moisture,
and weather conditions.
Most common residential panels still use the standard 6”
(156mm) square 60-cell panels while commercial systems
use the larger format 72 cell panels.
63
Average Cost of Solar Panel Installation for Home in India (2023)
Government Solar Subsidy Scheme (MNRE)
Companies: Sprng Agnitra, Ayana Solar, SB Energy Solar,
ACME, Azure, NTPC, Tata Power Ren Energy Ltd, Renew
Power, FRV Ltd, Fortum Finnsurya Energy Pvt Ltd., PSEPL,
Adani Green Energy, JSW Energy, etc.
•
Bhadla Solar Park is a solar PV power plant located in the Thar Desert of Rajasthan. After its completion in 2019, the solar park
achieved a total installed capacity of 2.24 GW (area req 5600 hec), making it the largest solar park in the world as of 2023.
•
Pavagada Solar Park is a solar park (area 5300 hec) in Pavagada taluk, Tumkur district, Karnataka. Completed in 2019, the park has
a capacity of 2.05 GW.
•
Other major solar pv parks in India: Kurnool Ultra Mega Solar Park (1 GW), NP Kunta Ultra Mega Solar Park (1 GW), Rewa Ultra
Mega Solar (0.75 GW), etc.
64
Components of a typical SPV system
• PV generator (PV cell,
PV module, PV array)
• Charge Controller /
MPPT
• Battery system
• Inverter
• Grid / Auxiliary
Connection
• Load / Load Center
A charge controller or charge regulator is basically a voltage
and/or current regulator to protect batteries from
overcharging/over-discharging. An MPPT, or maximum power
point tracker is an electronic DC to DC converter that optimizes
the match between the solar array (PV panels), and the battery
bank or utility grid. They convert a higher voltage DC output
from solar panels down to the lower voltage needed to charge
batteries. Inverters are used to convert the 12V, 24V or 48 Volts
direct current (DC) power from the solar array and batteries into
an alternating current (AC) electricity and power of either 120 V
AC or 240 V AC for use in the home to power AC mains
appliances. For minimizing losses, voltages of battery bank, pv
65
array and inverter are kept nearly equal.
PV System Design
• Specifying ratings, numbers and arrangements of all components of a PV system
- Approximate design
- Precise design
For designing a PV systems, each component in the path of energy flow should be considered.
Consideration for specifications, efficiency, rating , autonomy etc.
The choice of the system configuration mainly depends on the following parameters:
•
Load requirements
•
Resource availability
•
Performance of the system
•
Reliability of the system
•
Cost of the system
66
How to design a standalone PV system
Standalone PV system: not connected to
any source other than PV
Follow demand to source approach in design
Steps:
1) Determine the power load (AC/DC) (demand)
2) Determine the size of inverter
3) Determine the size of battery
4) Determine the size of power controller
5) Determine the size of PV panel/array based on solar
radiations for a given region (source)
From Step 2, efficiency of each component must be considered when deciding the energy input to that component
67
Q. Design a standalone PV system for the following load in Roorkee (radiation: 6 kWh/m2-day; latitude 30o):
Items
Number
Rating (W)
Usage (h/day)
TV
1
100
2
Fans
2
50
8
Lights
3
18
5
Inverter: 85 % efficiency
Battery: 24 V, DOD 50%, 80% efficiency, Autonomy = 2 (12V, 100 Ah available in market)
Charge Controller: 100% efficiency
PV modules: 24 V (60 Wp, 12 V available in market)
Daily energy consumed = watts x usage/day
Efficiency = energy output / energy input
Depth of Discharge (DOD): how much charge can we take from the battery. 100% DOD means we can drain the
battery completely
Autonomy: number of days system should supply load without sunlight. If autonomy is 3, charge storage will be 3
+ 1 = 4 days (for today plus 3 extra days with no sun)
PV module rating = PV module output / (peak sun hours per day)
68
Light
Fan
TV
Total load
No.
3
2
1
Watt
18
50
100
Usage (h/day)
5
8
2
Wh/day
270
800
200
1270
Total load= 1.27 kWh/day
Inverter: Total power needed to supply from inverter = 3x18 + 2x50 + 1x100
= 254 W = 254 VA
So, we need an inverter of rating 260 W.
Energy input to inverter (η=85%) = 1270 / 0.85 = 1494 Wh/day = 1494 VAh/day
Battery: 24 V battery bank is to be installed as given in question
Hence, battery system should supply = 1494 / 24 = 62.2 Ah/day
Had this number be 473.2 Ah, you
would calculate 5 batteries but will
need 6 batteries to maintain desired
voltage of system
Market has 12 V, 100 Ah battery.
Battery system capacity = 62.2/DOD = 62.2 / 0.5 = 124.4 Ah/day
Autonomy = 2, charge storage for 2+1=3 days.
Battery system charge capacity for 3 days = 124 x 3 = 373.2 Ah
System voltage required = 24 V
System energy required= 373.2 Ah
Hence, number of battery required = 373.2/100
= 3.73 = 4 batteries (approx.)
69
Battery configuration
Energy Input to battery =
(Ƞ = 80%)
1494
0.8
= 1867.5 VAh / day or Wh/day
B1
B3
24V, 400Ah
Charge controller :
Ƞ = 100%
B2
1 battery:
E = 12 (V) x 100 (A) = 1200 Wh
Battery Bank:
E = 24 (V) x 200 (A) = 4800 Wh
B4
PV Module :
PV module must supply 1867.5 Wh/day
Roorkee : 6 kWh/m2-day
radiation
= 6000 Wh/m2-day
= 6 hrs of 1000 Wh/m2-day
Peak sun hours
PV module rating =
1867.5 𝑊ℎ/𝑑𝑎𝑦
6 ℎ/𝑑𝑎𝑦
PV module design basis
= = 311.25 Wp
P1
P3
P5
Market has 60 Wp modules of 12V.
We need =
311.25
60
P2
= 5.18 ≃ 6 modules
For 24 V system, configuration will be:
Had this number be 5
module, we will still need
6 to maintain desired
voltage of system
P4
P6
24V
360Wp