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Power Generation from
Renewable Energy Sources
Fall 2013
Instructor: Xiaodong Chu
Email：[email protected]
Office Tel.: 81696127
Flashbacks of Last Lecture
• How much energy might be expected from a wind
turbine in various wind regimes?
1
1
Pavg  ( Av3 ) avg  A(v 3 ) avg
2
2
• With the probability of wind speeds
– For discrete distribution
(v 3 ) avg  [vi3  probabilit y(v  vi )]
i
– For continuous probability density function

(v )avg   v3  f (v)dv
3
0
Flashbacks of Last Lecture
• The Weibull probability density function is often used to
characterize the statistics of wind speeds
k v
f (v )   
c c
k 1
  v k 
exp    
  c  
where k is called the shape parameter and c the scale
parameter
• When little detail is known about the wind regime at a site, it
usually assumes k = 2, and the p.d.f. is the Rayleigh p.d.f.
  v 2 
2v
f (v)  2 exp    
c
  c  
Flashbacks of Last Lecture
• With average wind speed estimated by an anemometer and
the assumption that the wind speed distribution follows
Rayleigh, the average value of the cube of wind speed can be
derived as
2


0
0
(v 3 ) avg   v 3  f (v)dv   v 3 
and
 v
2v
exp
  
2
c
  c 

3 3
 dv  c 
4

3
(v 3 ) avg 
3
6
 2v 

  v 3  1.91v 3
4
  
• With Rayleigh statistics, the average power in the wind
P
6 1
 Av 3
 2
Flashbacks of Last Lecture
• A large number of wind turbines will be installed when a good
wind site is found, which is called a wind farm or a wind park
• How many turbines can be installed at a given site?
– Wind turbines located too close together will result in upwind turbines
interfering with the wind received by those located downwind
– Studies of square arrays with uniform, equal spacing illustrate the
degradation of performance when wind turbines are too close
together
Flashbacks of Last Lecture
• Example 6.10 on page 346 of the
textbook
• Example 6.11 on page 350 of the
textbook
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• From simple estimates of overall system efficiency associated
with wind probability statistics to techniques applied to
individual wind turbines based on their own specific
performance characteristics
• To understand how rotor blades extract energy from the wind,
we start from some parameters associated with aerodynamics
of wind turbines
– Lift and drag forces
– Angle of attack
– Pitch angle
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• Lift and drag forces
– Air flow over a stationary airfoil produces two forces, a lift force
perpendicular to the air flow and a drag force in the direction of air
flow
– The air flows smoothly over both sides of the airfoil and the air flowing
over the top of the airfoil has to speed up because of a greater
distance to travel, which causes a slight decrease in pressure
– The air pressure on top is lower than that under the airfoil, which
creates the lift force perpendicular to the direction of air flow
– The air moving over the airfoil also produces a drag force in the
direction of the air flow, which is a loss term
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• An airfoil is the shape of a wing or blade (of a propeller, rotor
or turbine) or sail as seen in cross-section
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• Lift and drag forces
– A rotating turbine blade sees air moving toward it not only from the
wind itself, but also from the relative motion of the blade as it rotates
– The combination of the two is moving across the blade at the correct
angle to obtain a lift force while a drag force is accompanying
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• Lift and drag forces
– The lift and drag forces can be split into components parallel and
perpendicular to the direction of the wind itself, and these
components combined to form the net force F1 the net force F2
– The force F1 is available to do useful work whereas the force F2 must
be considered in the design of the turbine blades to assure structural
integrity
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• Angle of attack
– It is the angle between the chord line of the turbine blade and the
resulting wind direction
• The chord line is the straight line connecting the leading and trailing edges of the
blade
– It is a dynamic angle, depending on both the speed of the blade and
the speed of the wind
• The blade speed at a distance r from the hub and an angular velocity ωm is rωm
• A blade with twist will have a variation in angle of attack from hub to tip because of
the variation of blade speed with distance from the hub
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• Blade with twist
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• Angle of attack
– Up to a point, increasing the angle of attack improves lift at the
expense of increased drag
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• Angle of attack
– Up to a point, increasing the angle of attack improves lift at the
expense of increased drag
– However, increasing the angle of attack too much can result in a
phenomenon known as stall, where the air flow over the top no longer
sticks to the surface and the resulting turbulence destroys lift
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• Angle of attack
– The angle of attack of the wind changes much more dramatically at
the root of the blade (yellow line) than at the tip of the blade (red line)
as the wind changes
– If the wind becomes powerful enough to make the blade stall, it will
start stalling at the root of the blade
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• Pitch angle
– It is the angle between the chord line of the blade and the plane of
rotation
• The plane of rotation is the plane in which the blade tips lie as they rotate
• The blade tips actually trace out a circle which lies on the plane of rotation
• Full power output would normally be obtained when the wind direction is
perpendicular to the plane of rotation
– When the blade is twisted, the pitch angle will change from hub to tip
•
In this situation, the pitch angle measured 3/4 of the distance out from the hub is
selected as the reference
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• Plane of rotation
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• Pitch angle
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• The most important technical information for a specific wind
turbine is the power curve, showing the relationship between
wind speed and generator electrical output
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• The cut-in wind speed VC is the minimum needed to generate
net power
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• When winds reach the rated wind speed VR, the generator is
delivering as much power as it is designed for and above VR,
there must be some way to shed some of the wind’s power or
else the generator may be damaged
• Three power control approaches are commonly used: stall
control, pitch control and active stall control
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• Stall control
– The blades are carefully designed to automatically reduce efficiency
when winds are excessive
– There are no moving parts, so this is referred to as passive control
– The aerodynamic design of the blades, especially their twist as a
function of distance from the hub, must be very carefully done so that
a gradual reduction in lift occurs as the blades rotate faster
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• Pitch control
– An electronic system monitors the generator output power; if it
exceeds specifications, the pitch of the turbine blades is adjusted to
shed some of the wind
– A hydraulic system slowly rotates the blades about their axes, turning
them a few degrees at a time to reduce or increase their efficiency as
conditions dictate
– The strategy is to reduce the blade’s angle of attack when winds are
high
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• Pitch control vs. stall control
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• Active stall control
– The blades rotate just as they do in the active, pitch-control approach
– However, when winds exceed the rated wind speed, instead of
reducing the angle of attack of the blades, it is increased to induce
stall
Wind Power Systems – Specific Wind
Turbine Performance Calculations
• At a wind speed VF , called the cut out or the furling wind
speed, the machine must be shut down to prevent the wind
turbine from danger and above VF , output power obviously is
zero
Wind Power Systems – Optimizing Rotor
Diameter and Generator Rated Power
• There are trade-offs between rotor diameter and generator
size as ways to increase the energy delivered by a wind
turbine
– Increasing the rotor diameter, while keeping the same generator, shifts
the power curve upward so that rated power is reached at a lower
wind speed
– Keeping the same rotor but increasing the generator size allows the
power curve to continue upward to the new rated power
Wind Power Systems – Optimizing Rotor
Diameter and Generator Rated Power
• There are trade-offs between rotor diameter and generator
size as ways to increase the energy delivered by a wind
turbine
– Increasing the rotor diameter, while keeping the same generator, shifts
the power curve upward so that rated power is reached at a lower
wind speed
– Keeping the same rotor but increasing the generator size allows the
power curve to continue upward to the new rated power