wind energy i. lesson 9. control strategies
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Wind Energy I
Michael Hölling, WS 2010/2011 slide 1
Control strategies
Wind Energy I
slideMichael Hölling, WS 2010/2011 2
Class content
4 Wind power
5 Wind turbines in general 6/7 Wind - blades
interaction
9 Control strategies
8 Power losses at the rotor blade
10 Generator
11 Electrics / grid
3 Wind field characterization
2 Wind measurements
Wind Energy I
slideMichael Hölling, WS 2010/2011 3
Control objectives and strategies
Development of a wind turbine control system can be divided into four major steps:
define clearly control objectives
selection of suitable control strategies which determines the operation point of the wind turbine for each wind speed
decide how the control strategy will be realized --> selection of the control schemes, the controlled variables, the reference signals, the switching procedure between different controllers, etc.
design of the input-output map, meaning the characteristics of the controller according to the specifications
Wind Energy I
slideMichael Hölling, WS 2010/2011 4
Control objectives for wind turbines
Control objectives
Energy capture: Maximization of energy capture taking into account safe operation restrictions such as rated power, rated speed and cut-out wind speed, etc.
Mechanical loads: Preventing WECS from excessive dynamic mechanical loads. This general goal includes reduction of transient loads, reduction of high frequency loads and resonance avoidance.
Power quality: Conditioning the generated power to comply with interconnection standards.
Wind Energy I
slideMichael Hölling, WS 2010/2011 5
Operation point
Where / what is the steady-state of operation ?
the steady-state of operation is reached when the aerodynamic torque developed by the rotor equals the reaction torque of the generator
net torque applied to the system is zero
At the steady-state operation point the aerodynamical power equals the converted power (minus losses at the generator):
Pae = Pgen
Tae · ! = Tgen · !
! · (Tae ! Tgen) = 0" Tae ! Tgen = 0
Wind Energy I
slideMichael Hölling, WS 2010/2011 6
Torque and power coefficient
Aerodynamic torque Tae:
Tae =12
· ! · " · R2 · u21 · R · cT
Tae = Fae · R · cT
The power converted by the WEC is given by:
PWEC = Tae · ! = Pair · cp
! cT = cp · 1!
How does the aerodynamic torque change with u1 ?
Wind Energy I
slideMichael Hölling, WS 2010/2011 7
Aerodynamic torque
The torque coefficient can be determined from the power coefficient. Until now we determined the maximum power coefficient by taking into consideration:
Betz limit with the expansion by Schmitz
losses at the rotor blades (drag losses and tip losses)
0 5 10 15 200.0
0.2
0.4
0.6
!
cp
r(!
)
cpSchmitz
cpSchmitz, z=3,"(#)=60
These curve represents the maximum power coefficient for each tip speed ratio BUT design is only possible for one tip speed ratio λ0!
λ0
Wind Energy I
slideMichael Hölling, WS 2010/2011 8
Aerodynamic torque
0 5 10 15 200.0
0.2
0.4
0.6
!
cpr(!)
λ0
Without control system the WEC is designed and optimized for one u1 and one ω.
β
α
u2= 2/3.u1
ures
urot
α*
β*
u2= 2/3.u*1
u*res
urotby changing u1 to u*1 and with
it λ το λ*
the angle of attack changes
and cl(α) to cl(α*) and cd(α) to cd(α*)
as well
Wind Energy I
slideMichael Hölling, WS 2010/2011 9
Aerodynamic torque
0 5 10 15 200.0
0.2
0.4
0.6
!
cpr(!)
λ0
0.0 0.5 1.00.0
0.2
0.4
0.6
u3/u1
cp
cp
λ0
0 5 10 15 200.0
0.2
0.4
0.6
!
cp
r(!
)cpSchmitz
cpSchmitz,
z=3,"(#)=60
cp!0(!,#)
λ0
From Betz we know that there is one optimum ratio between u3 and u1. The WEC meets this at the design for λ0.
The cp coming from Betz in combination with the changing angle of attack for different u1, we get a power coefficient that depends on λ and α - cp(λ,α)
Wind Energy I
slideMichael Hölling, WS 2010/2011 10
Aerodynamic torque
Note: In reality λmax and λ0 must NOT necessarily coincide !!
cp(λ) and cT(λ) can be plotted:! cT = cp · 1!
With
0 4 8 120.0
0.2
0.4
0.6
0.00
0.05
0.10
0.15
!
cp(!)
cp(!)
cT(!)
cT(!)
Wind Energy I
slideMichael Hölling, WS 2010/2011 11
Aerodynamic torque
How does the torque change with changing ω for different but fixed u1?
0 4 8 120.0
0.2
0.4
0.6
!
cp(!)
cp(!)
Tae =12
· ! · " · R2 · u31 · cp
!# · R
u1
"
# $% &!
· 1#
!
cp(!)
Wind Energy I
slideMichael Hölling, WS 2010/2011 12
Aerodynamic torque
How does the torque change with changing ω for different but fixed u1?
Tae =12
· ! · " · R2 · u31 · cp
!# · R
u1
"
# $% &!
· 1#
!
cp(!)
!
torq
ue
[N
m]
u1 = 25m/s
Wind Energy I
slideMichael Hölling, WS 2010/2011
!
torq
ue
[N
m]
u1 = 25m/s
u1 = 22m/s
!
cp(!)
13
Aerodynamic torque
How does the torque change with changing ω for different but fixed u1?
Tae =12
· ! · " · R2 · u31 · cp
!# · R
u1
"
# $% &!
· 1#
Wind Energy I
slideMichael Hölling, WS 2010/2011
!
cp(!)
!
torq
ue
[N
m]
u1 = 25m/s
u1 = 22m/s
u1 = 20m/s
14
Aerodynamic torque
How does the torque change with changing ω for different but fixed u1?
Tae =12
· ! · " · R2 · u31 · cp
!# · R
u1
"
# $% &!
· 1#
Wind Energy I
slideMichael Hölling, WS 2010/2011
!
torq
ue
[N
m]
u1 = 25m/s
u1 = 22m/s
u1 = 20m/s
u1 = 17m/s
!
cp(!)
15
Aerodynamic torque
How does the torque change with changing ω for different but fixed u1?
Tae =12
· ! · " · R2 · u31 · cp
!# · R
u1
"
# $% &!
· 1#
Wind Energy I
slideMichael Hölling, WS 2010/2011
!
cp(!)
!
torq
ue
[N
m]
u1 = 25m/s
u1 = 22m/s
u1 = 20m/s
u1 = 17m/s
u1 = 14m/s
16
Aerodynamic torque
How does the torque change with changing ω for different but fixed u1?
Tae =12
· ! · " · R2 · u31 · cp
!# · R
u1
"
# $% &!
· 1#
Wind Energy I
slideMichael Hölling, WS 2010/2011
!
torq
ue
[N
m]
u1 = 25m/s
u1 = 22m/s
u1 = 20m/s
u1 = 17m/s
u1 = 14m/s
u1 = 12m/s
!
cp(!)
17
Aerodynamic torque
How does the torque change with changing ω for different but fixed u1?
Tae =12
· ! · " · R2 · u31 · cp
!# · R
u1
"
# $% &!
· 1#
Wind Energy I
slideMichael Hölling, WS 2010/2011
!
cp(!)
!
torq
ue
[N
m]
u1 = 25m/s
u1 = 22m/s
u1 = 20m/s
u1 = 17m/s
u1 = 14m/s
u1 = 12m/s
u1 = 10m/s
18
Aerodynamic torque
How does the torque change with changing ω for different but fixed u1?
Tae =12
· ! · " · R2 · u31 · cp
!# · R
u1
"
# $% &!
· 1#
Wind Energy I
slideMichael Hölling, WS 2010/2011
!
torq
ue
[N
m]
u1 = 25m/s
u1 = 22m/s
u1 = 20m/s
u1 = 17m/s
u1 = 14m/s
u1 = 12m/s
u1 = 10m/s
u1 = 8m/s
!
cp(!)
19
Aerodynamic torque
How does the torque change with changing ω for different but fixed u1?
Tae =12
· ! · " · R2 · u31 · cp
!# · R
u1
"
# $% &!
· 1#
Wind Energy I
slideMichael Hölling, WS 2010/2011
!
cp(!)
!
torq
ue
[N
m]
u1 = 25m/s
u1 = 22m/s
u1 = 20m/s
u1 = 17m/s
u1 = 14m/s
u1 = 12m/s
u1 = 10m/s
u1 = 8m/s
u1 = 6m/s
20
Aerodynamic torque
How does the torque change with changing ω for different but fixed u1?
Tae =12
· ! · " · R2 · u31 · cp
!# · R
u1
"
# $% &!
· 1#
Wind Energy I
slideMichael Hölling, WS 2010/2011
!
torq
ue
[N
m]
u1 = 25m/s
u1 = 22m/s
u1 = 20m/s
u1 = 17m/s
u1 = 14m/s
u1 = 12m/s
u1 = 10m/s
u1 = 8m/s
u1 = 6m/s
u1 = 4m/s!
cp(!)
21
Aerodynamic torque
How does the torque change with changing ω for different but fixed u1?
Tae =12
· ! · " · R2 · u31 · cp
!# · R
u1
"
# $% &!
· 1#
Wind Energy I
slideMichael Hölling, WS 2010/2011
!
torq
ue [N
m]
u1 = 25m/s
u1 = 22m/s
u1 = 20m/s
u1 = 17m/s
u1 = 14m/s
u1 = 12m/s
u1 = 10m/s
u1 = 8m/s
u1 = 6m/s
u1 = 4m/s
Tcpmax
22
Aerodynamic torque
How does the torque change with changing ω for different but fixed u1?
Tae =12
· ! · " · R2 · u31 · cp
!# · R
u1
"
# $% &!
· 1#
!
cp(!)
Wind Energy I
slideMichael Hölling, WS 2010/2011
!
torq
ue
[N
m]
u1 = 25m/s
u1 = 22m/s
u1 = 20m/s
u1 = 17m/s
u1 = 14m/s
u1 = 12m/s
u1 = 10m/s
u1 = 8m/s
u1 = 6m/s
u1 = 4m/s
Tcpmax
Trated power
23
Aerodynamic torque
How does the torque change with changing ω for different but fixed u1?
Tae =12
· ! · " · R2 · u31 · cp
!# · R
u1
"
# $% &!
· 1#
!
cp(!)
Wind Energy I
slideMichael Hölling, WS 2010/2011 24
Control strategies
fixed-speed, fixed-pitch (FS-FP)
variable-speed, fixed-pitch (VS-FP)
fixed-speed, variable-pitch (FS-VP)
variable speed, variable-pitch (VS-VP)
Points in this torque-rotational speed plane (Tae-ω plane) that intersect with the generator torque define the steady-state operating conditions of the WEC. Different WEC control strategies results in different power curves P(u1), power coefficients cp(u1) and dynamical behavior.
Different strategies are:
Wind Energy I
slideMichael Hölling, WS 2010/2011 25
Control strategies
The interesting region for the control system is marked in the red box.
!
torq
ue [N
m]
u1 = 25m/s
u1 = 22m/s
u1 = 20m/s
u1 = 17m/s
u1 = 14m/s
u1 = 12m/s
u1 = 10m/s
u1 = 8m/s
u1 = 6m/s
u1 = 4m/s
Tcpmax
Trated power
Wind Energy I
slideMichael Hölling, WS 2010/2011 26
Fixed-speed, fixed-pitch
Fixed rotational-speed ω0 is realized by coupling an asynchronous generator directly to the grid.
0 4 8 120.0
0.2
0.4
0.6
!
cp(!)
cp(!)
!
torq
ue
[N
m]
u1 = 17m/s
u1 = 8m/s
u1 = 4m/s
Trated power
Tcpmax
u1min
u1max
!0AA
B
B
CC
D
D
Wind Energy I
slideMichael Hölling, WS 2010/2011 27
Fixed-speed, fixed-pitch
For the characterization of the WEC power curve P(u1) and cp(u1) are of interest. For FS-FP the P(u1) curve looks in principle like:
!
torq
ue
[N
m]
u1 = 17m/s
u1 = 8m/s
u1 = 4m/s
Trated power
Tcpmax
u1min
u1max
!00 5 10 15 20 25 30
u1 [m/s]
P(u
1)/
Pra
ted
ideal power curve
power curve
C
C
BB
A A
D
D
Wind Energy I
slideMichael Hölling, WS 2010/2011 28
Fixed-speed, fixed-pitch
For the characterization of the WEC power curve P(u1) and cp(u1) are of interest. For FS-FP the cp(u1) curve looks in principle like:
!
torq
ue
[N
m]
u1 = 17m/s
u1 = 8m/s
u1 = 4m/s
Trated power
Tcpmax
u1min
u1max
!00 5 10 15 20 25 30
u1 [m/s]
cp(u
1)
ideal cp
real cp
AA
B
B
CC D
D
Wind Energy I
slideMichael Hölling, WS 2010/2011 29
Fixed-speed, fixed-pitch
Power regulation by passive stall
Wind Energy I
slideMichael Hölling, WS 2010/2011 30
Variable-speed, fixed-pitch
For a variable-speed, fixed.pitch machine the rotational speed ωrot can be adapted to meet the optimum tip speed ratio λ0.
!rot ="0 · u1
R
The rotational speed ωrot changes linearly with the ambient wind speed u1.This is applied in the region below rated wind speed.
Wind Energy I
slideMichael Hölling, WS 2010/2011 31
Variable-speed, fixed-pitch
Variable rotational-speed ωrot is realized by adding AC/DC-DC/AC converter before feeding into the grid.
0 4 8 120.0
0.2
0.4
0.6
!
cp(!)
cp(!)A-E
D
G
Wind Energy I
slideMichael Hölling, WS 2010/2011 32
For the characterization of the WEC power curve P(u1) and cp(u1) are of interest. For VS-FP the P(u1) curve looks in principle like:
Variable-speed, fixed-pitch
Wind Energy I
slideMichael Hölling, WS 2010/2011 33
For the characterization of the WEC power curve P(u1) and cp(u1) are of interest. For VS-FP the cp(u1) curve looks in principle like:
Variable-speed, fixed-pitch
Wind Energy I
slideMichael Hölling, WS 2010/2011 34
Fixed-speed, variable-pitch
There are two different ways to adjust the pitch to keep the power above rated wind speed constant:
pitch to feather pitch to stall
Wind Energy I
slideMichael Hölling, WS 2010/2011 35
Fixed-speed, variable-pitch
By adjusting the angle of attack the cp(λ) curves are different for each pitch angle:
tip speed ratio
Wind Energy I
slideMichael Hölling, WS 2010/2011 36
Fixed-speed, variable-pitch
These modified cp(λ) curves result in modified torque above rated wind speed to meet the rated power:
Wind Energy I
slideMichael Hölling, WS 2010/2011 37
For the characterization of the WEC power curve P(u1) and cp(u1) are of interest. For FS-VP the P(u1) curve looks in principle like:
Fixed-speed, variable-pitch
Wind Energy I
slideMichael Hölling, WS 2010/2011 38
For the characterization of the WEC power curve P(u1) and cp(u1) are of interest. For FS-VP the cp(u1) curve looks in principle like:
Fixed-speed, variable-pitch
Wind Energy I
slideMichael Hölling, WS 2010/2011 39
Variable-speed, variable-pitch
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