Preview control
Cooperation issues
Distributed feedforward control of wind farms:
prospects and open problems
Maxim Kristalny
Joint work with Daria Madjidian and Anders Rantzer
Department of Automatic Control, LTH
Brussels, Belgium
Preview control
Cooperation issues
The main idea
Load reduction in turbines located in farm
• Nowadays each turbine controlled separately
• Accounting for the whole farm might be beneficial
- sharing wind speed measurements with neighbors
- cooperation in terms of power production
wind speed
...
Preview control
Cooperation issues
The main idea
Load reduction in turbines located in farm
• Nowadays each turbine controlled separately
• Accounting for the whole farm might be beneficial
- sharing wind speed measurements with neighbors
- cooperation in terms of power production
wind speed
Distributed feedforward control
- assess potential of this scheme
- outline open theoretical problems
...
Preview control
Cooperation issues
Outline
1 Preview control of individual turbine
individual turbine model
problem formulation and solution
simulation results
2 Cooperation between turbines in the farm
wind farm model
open theoretical challenges
preliminary simulation results
Preview control
Outline
1 Preview control of individual turbine
2 Cooperation between turbines in the farm
Cooperation issues
Preview control
Cooperation issues
Individual turbine model
NREL 5 MW turbine with standard internal controller
(IV’th operating region)
Inputs:
V
F
T
z
w
P
u = pref
β
Neglecting electrical circuit dynamics
Linearized around operating point
V - wind speed; pref - power reference;
Outputs:
F - thrust force; T - shaft torque
w - rotor speed; β - pitch angle;
(power production = power reference)
(all signals represent deviaitons)
Preview control
Cooperation issues
Problem formulation
Measured disturbance attenuation
V
z
P
u
K
n
u
Deviations of wind speed V are disturbances measured with noise n
The aim is to keep deviations of turbine outputs small
Preview control
Cooperation issues
Problem formulation
Measured disturbance attenuation
V
e−sh
z
P
u
K
n
u
Deviations of wind speed V are disturbances measured with noise n
The aim is to keep deviations of turbine outputs small
Availability of preview is captured by delay operator e−sh
Preview control
Cooperation issues
Problem formulation
Measured disturbance attenuation
WV
V
e−sh
Wz
Wp
z
P
u
K
n
Wn
u
Deviations of wind speed V are disturbances measured with noise n
The aim is to keep deviations of turbine outputs small
Availability of preview is captured by delay operator e−sh
Preview control
Cooperation issues
Model matching
Problem can be cast as model matching optimization
e
e−sh
w
G1
−
min ||e−sh G1 − G3 KG2 ||2
G3
K
G2
K∈H ∞
• Unified setting for estimation and feedforward control
• Preview is captured by delay operator e−sh
- may improve performance ⌣
¨
- renders problem infinite dimensional ⌢
¨
Preview control
Cooperation issues
Model matching
Problem can be cast as model matching optimization
e
e−sh
w
G1
−
min ||e−sh G1 − G3 KG2 ||2
G3
K
G2
K∈H ∞
• Unified setting for estimation and feedforward control
• Preview is captured by delay operator e−sh
- may improve performance ⌣
¨
- renders problem infinite dimensional ⌢
¨
Is there convenient numerically feasible solution
• one-side problem is well studied (without measurement noise)
• recently solution was extended to two-side problem
(Kristalny & Mirkin, MTNS 2010)
Preview control
Cooperation issues
Solution properties
• explicit state-space formulae are available
• based on:
- two Sylvester equations
- two Riccati equations
(asymptotic performance)
(transient performance)
of the same dimension as in preview-free case
• solution structure is convenient for implementation
(Contains finite dimensional blocks and FIR)
• influence of preview length on performance can be analyzed
Preview control
Cooperation issues
Performance vs. preview length
2
min(||H|| )
4.7e5
3.6e5
0
1.7
h [sec]
• The relevant scale of preview is a number of seconds
• 98 % of improvement achieved with 1.7 sec preview
Preview control
Cooperation issues
Simulation results
4
x 10
0.4
β [rad]
F [N]
4
0
0.2
0
−0.2
−4
0
4
8
12
0
4
8
12
8
12
−3
0.02
w [rad/sec]
tower def. [m]
x 10
0
−0.02
0
4
8
t [sec]
12
4
0
−4
0
4
t [sec]
Preview control
Cooperation issues
Simulation results
4
x 10
0.4
β [rad]
F [N]
4
0
0.2
0
−0.2
−4
0
4
8
12
0
4
8
12
8
12
8
12
−3
0.02
w [rad/sec]
tower def. [m]
x 10
0
−0.02
0
4
8
4
0
−4
12
0
4
t [sec]
t [sec]
5
x 10
Shaft def. [rad]
P [W]
10
5
0
−5
0
4
8
t [sec]
12
0.04
0
−0.04
0
4
t [sec]
Preview control
Outline
1 Preview control of individual turbine
2 Cooperation between turbines in the farm
Cooperation issues
Preview control
Cooperation issues
Wind farm model
Wake effects: mean speed deficit, increase of turbulence
• important in quasi-static analysis of farm
(distribution of nominal powers among turbines in farm)
• less important for dynamics around specified operating point
Neglect influence of pitch on wind flow
zn
zn−1
Pn
...
...
e−sh
zi
Pn−1
nn
z1
P2
P1
u1
y2
n3
Wind propagation modeled as delay and additive noise
V
e−sh
u2
y3
ni+1
v1
e−sh
ui
yi+1
yn
v2
e−sh
z2
Pi
un−1
un
v3
vi+1
vn
e−sh
y1
n2
n1
Preview control
Cooperation issues
Distributed feedforward control
Preview control from previous part can be applied to each turbine in farm
zn
zn−1
Pn
...
un−1
Kn−1
...
e−sh
zi
Pn−1
un
v3
vi+1
vn
e−sh
ui
Ki
yn
nn
z2
Pi
...
v1
e−sh
z1
P2
...
ni+1
V
e−sh
P1
u2
K3
yi+1
v2
e−sh
u1
K2
y3
n3
K1
y2
n2
y1
n1
Drawback:
adjustment of turbines power ⇒ fluctuations in overall power production
Cooperation between turbines can be beneficial
- requires formulation that takes the entire farm into account
Preview control
Cooperation issues
Decentralized model matching
Problem can be cast as decentralized model matching optimization
e
w
G1
Λ̄
−
G3
K
Λ
G2
min||e−sh G1 − G3 KG2 ||2
for K = diag{K1 . . . KN } ∈ H ∞
Diagonal constraint on parameter K
• relevant in various distributed control problems
Complicated structure of delays (Λ, Λ̄)
• discretization leads to numerical difficulties
These problems are open!
(quadratic invariance)
Preview control
Cooperation issues
Decentralized model matching
Problem can be cast as decentralized model matching optimization
e
w
G1
Λ̄
−
G3
K
Λ
G2
min||e−sh G1 − G3 KG2 ||2
for K = diag{K1 . . . KN } ∈ H ∞
Diagonal constraint on parameter K
• relevant in various distributed control problems
• preliminary frequency domain solution
Complicated structure of delays (Λ, Λ̄)
• discretization leads to numerical difficulties
Approximate solution available.
(quadratic invariance)
(in terms of Hadamard product)
Preview control
Cooperation issues
Optimal controllers
Impulse responses of optimal controllers
Controller #1
5
x 10
Controller #2
5
x 10
0.5
0
−0.5
0.5
0
−0.5
0
2
4
6
8
time [s]
10
12
14
x 10
2
4
6
8
time [s]
10
12
14
10
12
14
Controller #5
5
x 10
0.5
0
−0.5
0
0
Controller #4
5
0.5
0
−0.5
2
4
6
8
time [s]
10
12
14
0
2
Each controller takes care of downwind turbines
4
6
8
time [s]
(peaks in time multiples of h)
Preview control
Cooperation issues
Simulation results
Turbine #1
Turbine #5
0.02
Nacelle disp. [m]
Nacelle disp. [m]
0.02
0
−0.02
0
2
4
6
8
10
12
0
−0.02
14
5
10
12
14
8
10
12
14
time [s]
16
18
20
16
18
20
x 10
Power [W]
x 10
Power [W]
8
5
2
0
2
0
−2
−2
0
2
4
6
time [s]
8
10
12
- Slight decrease in tower oscillations
- Demands more deviations in individual turbine powers
Preview control
Cooperation issues
Simulation results - improvement in overall power production
5
x 10
Farm power [W]
2
0
−2
0
2
4
6
8
10
time [s]
12
14
16
18
- decrease in deviations of overall farm power production
- without deterioration in terms of load reduction
20
Preview control
Cooperation issues
Summary
• Preview advantageous for load reduction
• Convenient methods for controller synthesis exist
• Next: considering turbine without internal controller
• Cooperation between turbines might be advantageous
• Distributed feedforward control scheme
- open theoretical problems
- requires reliable model of wind propogation
Preview control
Cooperation issues
Thank you for attention!