Download ECE 7800: Renewable Energy Systems

ECE 7800: Renewable Energy
Systems
Topic 10: Wind Power Fundamentals
Spring 2010
© Pritpal Singh, 2010
Types of Wind Turbines
Two types: Horizontal and Vertical
Axis types
There are two types of horizontal axis
wind turbines – upwind and downwind machines.
Types of Wind Turbines (cont’d)
The vertical axis wind turbine has three
distinct advantages over horizontal axis
wind turbines:
1) No yaw control required to keep them
facing in the direction of the wind.
2) Heavy machinery in the nacelle (the
housing around the generator, gearbox,
etc.) is located on the ground and not on
top of the tower – thus, the tower requires
less structural support.
3) The blades are always in tension =>
blades can be relatively lightweight and
therefore inexpensive.
Types of Wind Turbines (cont’d)
On the other hand, the vertical axis wind
turbines have several disadvantages
over horizontal axis ones:
1) Blades are close to ground where wind
speed is lower => limits output power
that can be generated.
2) The wind near the ground is also more
turbulent, increasing stress on the
blades.
3) Control at low and high wind speeds
not as good as for horizontal axis wind
turbines.
Most wind turbines are horizontal axis.
Types of Wind Turbines (cont’d)
A downwind turbine has the advantage of
the wind itself controlling the yaw (leftright motion) of the blade. However, the
wind shadowing of the tower can cause
excessive blade stress (when the blade
swings behind the tower) which can lead
to blade failure. Furthermore, it also
increases blade noise and reduces output
power.
Upwind turbines, on the other hand,
require complex yaw control systems to
keep the blades facing into the wind.
However, they behave more smoothly and
produce more power.
Most wind turbines are of the upwind type.
Types of Wind Turbines (cont’d)
Another issue with wind turbines is the
number of blades that should be used.
Water pumping windmills have many
blades because this increases the
torque available to start the pump.
However, for electricity generation,
fewer blades are preferred since this
allows the turbine to operate at higher
rotational speed. With fewer blades,
turbulence caused by one blade to the
next blade is also reduced. Higher
rotational speed allows the wind turbine
to smaller in size.
Types of Wind Turbines (cont’d)
Most modern European wind turbines
have three blades whereas American
wind turbines have two. Three-blade
turbines operate more smoothly with
respect to tower interference and
wind speed variation. However, the
third blade does add considerably to
the cost and weight of the turbine.
Construction of a three-blade turbine
is also generally more difficult than a
two-blade turbine.
Power in the Wind
The power in the wind Pw is related to
wind speed by:
1
3
Pw 
Av
2
where ρ = density of air,
A = cross-sectional area through
which the wind passes, and
v = wind speed
In SI units, Pw is in Watts, ρ is in kgm-3, A
is in m2 and v is in m/s (1m/s = 2.237mph)
Power in the Wind (cont’d)
Note: Pw increases as cube of wind speed.
Thus energy in 1 hr. of 20 mph wind is
same as 8 hrs. of 10 mph wind or 2½ days
of 5 mph wind!
Power in the Wind (cont’d)
Also, the wind power is proportional to
the swept area of the turbine blades.
For a horizontal axis wind turbine,
A=(π/4)D2, so wind power is
proportional to the square of the blade
diameter.
The cost of a turbine increases in
proportion to the blade diameter but
the power output increases by the
square of the blade diameter. Thus,
larger systems are more cost-effective.
Power in the Wind (cont’d)
For a vertical axis wind turbine, the
effective area of the blades is
approximately given by A≈⅔D.H as
shown in the figure below:
Power in the Wind (cont’d)
Example 6.1
Temperature Correction for Air Density
The density of air decreases with
increase in air temperature. The
density of air at absolute temp., T is
given by:
ρ=
P x mol. wt. x 10-3
RT
where R = ideal gas constant
(8.2056 x 10-5 m3.atm.K-1.mol-1)
and P = absolute pressure (atm.)
Temperature Correction for Air Density
(cont’d)
Example 6.2
Altitude Correction for Air Density
Air density also depends on atmospheric
pressure and therefore changes with
altitude.
Atmospheric pressure changes with
altitude in that more pressure is exerted
from the air above on a lower section of
air (see figure below).
Altitude Correction for Air Density (cont’d)
Thus, the pressure at height z is given by:
P(z) = P(z+dz) + gρAdz
A
where g = 9.806m/s2 is the
acceleration due to gravity
Thus, dP = - ρg
dz
Since ρ itself is a function of P, we can
write:
3
 gmol.wt.x10
dP
 
dz
RT


.P

Altitude Correction for Air Density (cont’d)
There is another complication – air
temperature varies with altitude (at a
rate of 6.5ºC/km.) Neglecting this
effect, we can put in the values of the
variables into the previous equation
and at a temperature of 15ºC, we get:
dP = -1.185 x 10-4.P
dz
Thus, P=P0e-1.185x10-4H where P0 is the
reference pressure (1 atm.) and H is
the height in meters.
Altitude Correction for Air Density (cont’d)
Example 6.3
Altitude Correction for Air Density (cont’d)
Temperature and altitude corrections for
air density can be made using correction
factors as follows:
ρ = 1.225KTKA
where the correction factors for
temperature KT and
altitude KA are given
in the table:
Impact of Tower Height
One way to get more power output from
a wind system is to increase the height
to which the blades are exposed. This is
because friction close to the ground
reduces wind speed. One expression
used to characterize the impact of the
roughness of the Earth’s surface to wind
speed is:

v  H 
   

 v0   H 0 
where v is the windspeed at height H, v0
is the windspeed at height H0 and α is
the friction coefficient.
Impact of Tower Height (cont’d)
The friction coefficient, α, depends on the
terrain over which the wind is blowing.
For open terrain, a value of 1/7 is used.
Friction coefficients for various terrains
are given in the table below:
Impact of Tower Height (cont’d)
The below figures shows the impact
of tower height on windspeed and
power for different values of α.
Impact of Tower Height (cont’d)
Example 6.6
This example illustrates an important
point – a blade at the top of its rotation
can experience much higher wind
speeds than at the bottom of its
rotation. This results in significant
stressing of the blades and can result
in blade fatigue and failure.
Maximum Rotor Efficiency
The analysis we will consider to
determine the maximum efficiency of a
wind turbine was first developed by Betz
in Germany in 1919.
Wind approaching a turbine is slowed
down as a portion of its kinetic energy is
extracted (see figure below):
Maximum Rotor Efficiency (cont’d)
The wind leaving the turbine is slower
and of lower pressure than the incident
wind and therefore its volume expands.
The envelope of the air mass passing
through the turbine is called a “stream
tube”.
The wind velocity cannot drop to zero as
it passes through the turbine otherwise
there would be no further wind to come
through the rotor. Also, the wind velocity
after the turbine must be less than
before otherwise no kinetic energy
would be extracted.
Maximum Rotor Efficiency (cont’d)
Therefore there must be a maximum
power that can be extracted from the
wind (just like the maximum power point
for a solar module).
Let the upwind velocity be v, the velocity
at the blades, vb, and the downwind
velocity be vd. The mass flow rate
through the stream tube, m, is constant.
The power extracted by the blades Pb is
given by:
1
2
2
Pb  m (v  vd )
2
Maximum Rotor Efficiency (cont’d)
The mass flow rate, m, is given by:
m  Avb
Assuming vb = (v+vd)/2, we get:
1  v  vd  2 2
Pb  A
 ( v  vd )
2  2 
Defining λ as v/vd , we get:
1  v  v  2
2 2
Pb  A
(
v


v )

2  2 
1
3 1
2 
 Av . (1   )(1   )
2
2

Power in the wind
Fraction extracted
Maximum Rotor Efficiency (cont’d)
Thus the rotor efficiency, Cp , is given by:
1
C p  (1   )(1  2 )
2
In order to find the max. efficiency, we
need to determine dCp/dλ and set it to
zero.
The result is λ=⅓, i.e. the max. efficiency
of the rotor occurs when the downstream
velocity is slowed to ⅓ of its upwind
velocity. This gives a max. rotor
efficiency Cp of 59.3%. This is known as
the Betz efficiency or Betz’s law.
Maximum Rotor Efficiency (cont’d)
For a given wind speed, the rotor
efficiency depends on the speed of
rotation of the blades. Too slow
means low efficiency – to much air
passing by without being converted to
electrical energy. Too fast also means
low efficiency because turbulence
created by one blade affects the next
blade. Rotor efficiency is therefore a
function of tip-speed ratio which is
defined as the ratio of rotor tip speed
to wind speed.
Maximum Rotor Efficiency (cont’d)
A plot of typical efficiency vs. tip-speed
ratio is shown in the below graph:
Maximum Rotor Efficiency (cont’d)
Example 6.7
Wind Turbine Generators
The blades convert the kinetic energy
from the wind into rotating shaft
power. This rotational energy is
converted to electrical energy using a
generator. In a generator, conductors
move through a magnetic field to
generate voltage and current.
Synchronous generators are
sometimes used for wind turbines but
more commonly, induction generators
are employed because of their lower
maintenance requirements.
Synchronous Generators
The magnetic field in very small
synchronous generators may be created
by a permanent magnet. However, more
commonly, the magnetic field in a
synchronous generator is created by dc
current applied to the rotor using slip
rings and brushes. An exciter is used to
rectify the ac input voltage.
Induction Generators
Most wind turbines use induction
generators rather than synchronous
machines. Since they do not rotate at a
fixed speed, these are referred to as
asynchronous generators. The magnetic
field in an induction machine is created
in the stator winding by rotating the
magnetic flux through windings in the
stator. This induces a current and net
motion in the conductors of the rotor.
No slip rings or brushes are needed and
so induction generators are cheaper to
run and maintain compared to
synchronous generators.
Induction Generators (cont’d)
The rotating magnetic flux in the
stator of an induction generator is
shown in the diagram below:
Induction Generators (cont’d)
A squirrel cage rotor consists of
conductor bars shorted together to
create a “treadmill”. The conductors
are embedded in an iron core of
steel laminations to minimize eddy
current losses. As the magnetic field
moves around, the current induced
in the conductors causes the rotor to
turn.
Induction Generators (cont’d)
When excitation current is provided to
the stator and the shaft is connected
to the wind turbine and gearbox, the
induction machine will start motoring
up to its synchronous speed. Once
the wind speed is high enough that
the generator exceeds synchronous
speed, the induction machine
becomes a generator delivering
power to its stator windings.
However, what happens if no power
grid is available to excite the current
in the stator?
Induction Generators (cont’d)
A self-excited generator can be
created by exciting a resonance
between the inductance of the stator
field windings and external
capacitors. A remnant magnetic field
in the rotor provides the initial
stimulus to excite the resonance.
Speed Control for Maximum Power
To ensure high efficiency, the tip-speed
ratio should be ~ 4-6, i.e. blade speed
should be 4-6 x wind speed. Thus turbine
blades should change their speed as
wind speed changes. The power delivered
at different wind speeds and blade
speeds is shown below:
Speed Control for Maximum Power (cont’d)
For grid-connected wind turbines, a
fixed output frequency is required.
Therefore, we would like to have a
variable rotor speed but a fixed
generator speed.
There are several ways to effectively
change speeds, including:
• Change number of poles on the
generator;
• Multiple gearboxes;
• Varying the slip of induction
generators using external resistors.
Speed Control for Maximum Power (cont’d)
Another approach is to indirectly
connect to the grid by using power
electronics to transform variable speed
generated power to clean, fixed
frequency ac output as shown below: