Transcript 幻灯片 1

Power Generation from
Renewable Energy Sources
Fall 2013
Instructor: Xiaodong Chu
Email：[email protected]
Office Tel.: 81696127
Flashbacks of Last Lecture
• Classification of AC generators used in wind
turbines
– Synchronous generators
• Wound rotor synchronous generators (WRSG)
• Permanent magnet synchronous generators (PMSG)
– Induction generators
• Squirrel cage induction generators (SCIG)
• Wound rotor induction generators (WRIG)
Flashbacks of Last Lecture
• Wind turbine rotor speed should follow wind speed that is
random in nature
• Limit the power in very high winds in order to avoid damage
to the wind turbine
• For grid-connected turbines, the challenge is to
accommodate variable rotor speed and fixed generator speed
Control
Type
Pole-changing induction
generators
Discrete control
Multiple gearboxes
Discrete control
Variable-slip induction
generators
Limited continuous control
Indirect grid connection
systems
Continuous control
Flashbacks of Last Lecture
• Slip of an induction machine is the difference of
rotating speed between magnetic field and rotor
s
NS  NR
N
 1 R
NS
NS
• Example 6.8 on page 333 of the textbook
Wind Power Systems – Average Power
in the Wind
• How much energy might be expected from a wind
turbine in various wind regimes?
– We cannot determine the average power in the wind by
substituting average wind speed
– We need to find the average value of the cube of wind
speed
Pavg
1
1
3
 ( Av ) avg  A(v 3 ) avg
2
2
Wind Power Systems – Average Power
in the Wind
• The average wind speed can be thought of as the total
meters, kilometers, or miles of wind that have blown past the
site, divided by the total time that it took to do so
[v  (hours @ v )]

  [v  (fraction of hours @ v )]
 hours
i
vavg
i
i
i
i
• Describe the average values in probabilistic terms
vavg   [vi  probabilit y(v  vi )]
i
i
Wind Power Systems – Average Power
in the Wind
• The average value of the cube of wind speed
(v 3 ) avg 
3
[
v
 i  (hours @ vi )]
i
 hours
  [vi3  (fraction of hours @ vi )]
i
• Describe the average values in probabilistic terms
(v 3 ) avg   [vi3  probabilit y(v  vi )]
i
Wind Power Systems – Average Power
in the Wind
Wind Power Systems – Average Power
in the Wind
• Probability density function (p.d.f.) of wind
speed
Wind Power Systems – Average Power
in the Wind
• Probability that the wind is between two speeds
v2
probabilit y(v1  v  v2 )   f (v)dv
v1

probabilit y(0  v  )   f (v)dv
0
• The number of hours per year that the wind blows between
any two wind speeds
v2
hours/year (v1  v  v2 )  8760  f (v)dv
v1
Wind Power Systems – Average Power
in the Wind
• The average wind speed

vavg   v  f (v)dv
0
• The average value of the cube of wind speed

(v )avg   v3  f (v)dv
3
0
Wind Power Systems – Average Power
in the Wind
• 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
Wind Power Systems – Average Power
in the Wind
• The shape parameter k of the Weibull probability density
function changes the look of the p.d.f.
• 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.
2

2v
v 
f (v)  2 exp    
c
  c  
Wind Power Systems – Average Power
in the Wind
• The impact of changing the scale parameter c for a Rayleigh
p.d.f. is that larger values of c shift the curve toward higher
wind speeds
• There is a direct relationship between the scaling parameter c
and average wind speed
2


0
0
v   v  f (v)dv  
 v 
2v 2

exp

dv

c  0.886c




c2
c
2
   
Wind Power Systems – Average Power
in the Wind
• From


0
0
v   v  f (v)dv  
it can be derived
c
  v 2 
2v 2

exp

dv

c  0.886c




c2
c
2
   
2
and

v  1.128v
   v 2 
f (v)  2 exp    
2v
 4  v  
v
Wind Power Systems – Average Power
in the Wind
• With average wind speed estimated by an anemometer and
the assumption that the wind speed distribution follows
Rayleigh statistics, 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
Wind Power Systems – Average Power
in the Wind
• Example 6.10 on page 346 of the textbook
Wind Power Systems – Simple
Estimates of Wind Turbine Energy
• How much of the energy in the wind can be captured
and converted into electricity?
• A number of factors should be considered including
the characteristics of the machine (rotor, gearbox,
generator, controls), the terrain (topography, surface
roughness, obstructions), and the wind regime
(velocity, timing, predictability)
Wind Power Systems – Simple
Estimates of Wind Turbine Energy
• With the wind power density evaluated and the
overall conversion efficiency into electricity obtained,
we can estimate the annual energy delivered
• Simple estimates can be made based on wind
classifications and overall efficiencies (about 30%)
• Example 6.11 on page 350 of the textbook
Wind Power Systems – Simple
Estimates of Wind Turbine Energy
• 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
Wind Power Systems – Simple
Estimates of Wind Turbine Energy
• Offshore wind farms:
 Wind turbines sitting on flat ocean
surface
 Near neutral atmospheric boundary layer
winds
 High wind speed with relatively low
ambient turbulence level
 Suffers from ‘deep array effect’
• Onshore wind farms:
 Wind turbines sitting over complex
terrains.
 Atmospheric stability is rarely close to
near-neutral (unstable during the day
time and highly stable conditions with
high shear at night time)
 Much higher ambient turbulence level
Wind Power Systems – Simple
Estimates of Wind Turbine Energy
Onshore wind farm
Wind Power Systems – Simple
Estimates of Wind Turbine Energy
• An array area should not be square, but rectangular with only
a few long rows perpendicular to the prevailing winds, with
each row having many turbines
• Experience has yielded some rough rules for tower spacing of
such rectangular arrays
– Recommended spacing is 3–5 rotor diameters separating towers
within a row and 5–9 diameters between rows