The document discusses wind turbines, including their basic components and functioning. It describes the two main types - horizontal axis wind turbines (HAWT) and vertical axis wind turbines (VAWT). HAWTs are the most common and can be upwind, downwind, or shrouded designs. VAWTs rotate around a vertical axis and include designs like anemometers and Savonious turbines. The document also covers topics like tip speed ratio, calculations for wind turbine power output, Betz's law establishing the maximum theoretical power coefficient of 0.59, and how the actual power coefficient varies by turbine and wind speed.

1. WIND TURBINE

2. Title and Content
Introduction
Wind turbine types
Horizontal axis wind turbines (HAWT)
Vertical axis wind turbines (VAWT)
The tip-speed ratio
Wind turbine power calculation
Betz Limit or Betz' Law
Power Coefficient (Cp)
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3. Introduction
Wind turbine:
A wind turbine is a device that converts the wind's
kinetic energy into electrical power.
OR
If the mechanical energy of wind is then converted into
electricity by a machine and then used, then the
machine is called wind turbine.
WIND TURBINE
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4. Wind turbine types:
Wind turbines can rotate about either a horizontal or a
vertical axis.
1. HORIZONTAL AXIS WIND TURBINES (HAWT)
2. VERTICAL AXIS WIND TURBINES (VAWT)
There are No. of available design for both and each has
certain advantages and disadvantages.
WIND TURBINE
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5. WIND TURBINE
HORIZONTAL AXIS WIND TURBINES (HAWT)
The horizontal wind turbine is a turbine in which the axis
of the rotor's rotation is parallel to the wind stream and
the ground.
It is the most common wind turbine designed in addition
being parallel to the ground. The axis of blade rotation is
parallel to the wind flow.
There are three types of HAWT.
 Up wind turbine
 Down wind turbine
 Shrouded wind turbine
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6. HORIZONTAL AXIS WIND TURBINES (HAWT)
Up wind turbine
Some wind turbines are designed to operate in an
up-wind mode. (with the blade up wind the tower).
Large wind turbines used a motor driven mechanism
that turns the machine in response to the wind
direction.
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7. Down wind turbine
Other wind turbines are operating in a downwind
mode. So, that the wind passes the tower before striking
the blades.
Shrouded wind turbine
Some turbines have an added structural design
feature called an augmenter. The augmenter is intended
to increase the amount of wind passing through the
blades.
HORIZONTAL AXIS WIND TURBINES (HAWT)
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8. VERTICAL AXIS WIND TURBINES (VAWT)
The rotor of the VAWT rotates vertically around its axis
instead of horizontally.
It is not as common as their horizontal counter parts. The
main reason for this is as that they do not take advantage
of higher wind speed at higher altitude above the ground.
The most common examples of VAWT are
 ANOMOMETRE
 SAVONIOUS WIND TURBINE
WIND TURBINE
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9. ANOMOMETRE
The anemometer is an instrument used for measuring the
speed of air flow.
Savonious wind turbine
It has “S” shaped if viewed from the above.
The drag type VAWT turns relatively slow but yield high
torque. It is useful for grinding grains, pumping water,
but it slow rotational speed make it unsuitable for
generating electricity on large scale.
VERTICAL AXIS WIND TURBINES (VAWT)
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10. Shrouded HAWT
Anemometer
VAWTSavonious
VAWT
HAWT
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11. The tip-speed ratio:
It is referred to the ratio between the wind speed and the speed of
the tips of the wind turbine blades.
TSR () = Tip speed of blades / wind speed
 = Lambda
If the rotor of the wind turbine turns too slowly, most of the
wind will pass undisturbed through the gap between the rotor
blades. Alternatively, if the rotor turns too quickly, the blades will
appear like a solid wall to the wind.
Also, rotor blades create turbulence as they spin through the air. If
the next blade arrives too quickly, it will hit that turbulent air
Therefore, wind turbines are designed with optimal tip speed
ratios to extract as much power out of the wind as possible.
WIND TURBINE
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12. WIND TURBINE
How to define tip speed
 Measure the rotor radius (length of the blade)
 Speed = distance / time
The distance travelled as the circumference = 2 r
Tip Speed = v= 2 r / t
The blade travelled one circumference “2 r” in a
rotation of time “t” seconds.
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13. WIND TURBINE POWER CALCULATION
WIND TURBINE
MATHEMATICAL MODEL
The following table shows the definition of various
variables used in this model:
E = Kinetic Energy (J) ρ = Density (kg/m3)
m = Mass (kg) A = Swept Area (m2)
v = Wind Speed (m/s) Cp = Power Coefficient
P = Power (W) r = Radius (m)
dm/ dt = Mass flow rate (kg/s) x = distance (m)
dE/ dt = Energy Flow Rate (J/s) t = time (s)
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14. Under constant acceleration, the kinetic energy of an object having
mass “m” and velocity “v” is equal to the work done ‘W” in
displacing that object from rest to a distance “S” under a force “F”,
i.e.:
E = W = FS
Per Newton’s Law, we have:
F = ma
Hence,
E = mas … (1)
Using the third equation of motion:
V² = U² + 2aS
we get:
a = (V²-U²) /2S
MATHEMATICAL MODEL
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15. MATHEMATICAL MODEL
Since the initial velocity of the object is zero, i.e. u = 0, we get:
a = V² / 2S
Substituting it in equation (1), we get that the kinetic energy of a
mass in motions is:
E = 1/2 mv² … (2)
The power in the wind is given by the rate of change of energy:
As mass flow rate is given by:
ρ = Density = m / V
= m / (area *distance) =m /A* X
⇒ m= ρ A X
So
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16. and the rate of change of distance is given by:
v = dt / dx
we get:
dm / dt = ρ Av
Hence, from equation (3), the power can be defined as:
MATHEMATICAL MODEL
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17. A German physicist Albert Betz concluded in 1919 that
no wind turbine can convert more than 16/27 (59.3%)
of the kinetic energy of the wind into mechanical
energy turning a rotor. To this day, this is known as the
Betz Limit or Betz' Law.
The theoretical maximum power efficiency of
any design of wind turbine is 0.59 (i.e. no more than
59% of the energy carried by the wind can be extracted
by a wind turbine). This is called the “power coefficient”
and is defined as:
Betz Limit or Betz' Law
MATHEMATICAL MODEL
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18. MATHEMATICAL MODEL
Also, wind turbines cannot operate at this maximum limit. The Cp
value is unique to each turbine type and is a function of wind
speed that the turbine is operating in. Once we incorporate
various engineering requirements of a wind turbine - strength
and durability in particular - the
real world limit is well below the Betz Limit.
That is normally 45% to 50 %.
Power available:
Power available = power × Cp
Betz Limit or Betz' Law
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19. Power Coefficient (Cp)
Power Coefficient (Cp) is a measure of wind turbine
efficiency often used by the wind power industry. Cp is
the ratio of actual electric power produced by a wind
turbine divided by the total wind power flowing into
the turbine blades at specific wind speed.
WIND TURBINE
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20. THANKS

21. ROOH UL AMIN
PIMSAT KARACHI
PAKISTAN