Wind turbine arrays can be viewed as large coupled networks, wherein wake effects limit the available power extraction of turbines downstream. In this paper, we incorporate wake steering and time dependent wind estimation models into a multiobjective wind farm control problem for improving power extraction. We further aim to mitigate the effects of turbulence and power spikes caused by wind passing through upstream turbines. We expand upon a previous heuristic method for the far-field wake problem and apply the algorithm on a model predictive control framework. Simulation results are given, demonstrating improved power output as compared to algorithms that do not incorporate wake steering or wind estimation models.

1.
A.
Bonanni
,
T.
Banyai
,
B.
Conan
,
J.
VanBeeck
,
H.
Deconinck
, and
C.
Lacor
, “
Wind farm optimization based on CFD model of single wind turbine wake
,”
Wind Energy
2
,
726
735
(
2012
).
2.
M. A.
Ahmad
,
S. I.
Azuma
, and
T.
Sugie
, “
A model-free approach for maximizing power production of wind farm using multi-resolution simultaneous perturbation stochastic approximation
,”
Wind Turbines
7
,
5624
5646
(
2014
).
3.
S.
Minna
,
M.
De Prada Gil
,
F. D.
Bianchi
,
C.
Ocampo-Martinez
, and
B. D.
Schutter
, “
A multi-objective predictive control strategy for enhancing primary frequency support with wind farms
,”
IOP Conf. Ser.: J. Phys.: Conf. Ser.
1037
,
032034
(
2018
).
4.
L.
Buccafusca
,
C.
Beck
, and
G.
Dullerud
, “
Modeling and maximizing power in wind turbine arrays
,”
IEEE Conference on Control Technology and Applications
(
2017
).
5.
K. E.
Johnson
,
L. J.
Fingersh
,
M. J.
Balas
, and
L. Y.
Pao
, “
Methods for increasing region 2 power capture on a variable speed HAWT
,”
J. Sol. Energy Eng.
126
,
1092
1100
(
2004
).
6.
S.
Frandsen
,
R.
Barthelmie
,
S.
Pryor
,
O.
Rathmann
,
S.
Larsen
,
J.
Højstrup
, and
M.
Thøgersen
, “
Analytical modelling of wind speed deficit in large offshore wind farms
,”
Wind Energy
9
(
1–2
),
39
53
(
2006
).
7.
A.
Rez Mamouri
,
A.
Bak Khoshnevis
, and
E.
Lakzian
, “
Experimental study of the effective parameters on the offshore wind turbine's airfoil in pitching case
,”
Ocean Eng.
198
,
106955
(
2020
).
8.
See http://environment.govmu.org/English/eia/Documents/Reports/suzlonwindfarm/annex8.pdf for “
Wind turbine generator technical specifications S95-2.1 MW
,” SUZLON Energy (2018).
9.
J.
Jonkman
, https://wind.nrel.gov/forum/wind/viewtopic.php?f=2&t=582 for “
NREL 5-MW reference turbine—CP, CQ, CT coefficients
” (
2012
).
10.
L.
Buccafusca
,
J.
Jansch-Porto
,
G. E.
Dullerud
, and
C. L.
Beck
, “
An application of nested control synthesis for wind farms
,”
8th IFAC Workshop on Distributed Estimation and Control in Networked Systems
(
2019
).
11.
S.
Heier
,
Grid Integration of Wind Energy Conversion Systems
(
John Wiley and Sons
,
New York
,
1998
).
12.
A.
Betz
,
Introduction to the Theory of Flow Machines
, edited by
D. G.
Randall
(
Pergamon Press
,
Oxford
,
1966
).
13.
P.
Fleming
,
J.
Annoni
,
A.
Scholbrock
,
E.
Quon
,
S.
Dana
,
S.
Schreck
,
S.
Raach
,
F.
Haizmann
, and
D.
Schlipf
, “
Full-scale field test of wake steering
,”
J. Phys.: Conf. Ser.
854
,
012013
(
2017
).
14.
P.
Fleming
,
J.
Annoni
,
J. J.
Shah
,
L.
Wang
,
S.
Anathan
,
Z.
Zhang
,
K.
Hutchings
,
P.
Wang
,
W.
Chen
, and
L.
Chen
, “
Field test of wake steering at an offshore wind farm
,”
Wind Energy Sci.
2
(
1
),
229
239
(
2017
).
15.
J.
Annoni
,
P.
Gebraad
,
A.
Scholbrock
,
P.
Fleming
, and
J.
van Wingerden
, “
Analysis of axial-induction-based wind plant control using an engineering and a high-order wind plant model
,”
Wind Energy
19
(
6
),
1135
1150
(
2016
).
16.
E.
Thøgersen
,
B.
Tranberg
,
J.
Herp
, and
M.
Greiner
, “
Statistical meandering wake model and itsapplication to yaw-angle optimisation of wind farms
,”
J. Phys.: Conf. Ser.
854
,
012017
(
2017
).
17.
G. C.
Larsen
,
H. A.
Madsen
,
K.
Thomsen
, and
T. J.
Larsen
, “
Wake meandering: A pragmatic approach
,”
Wind Energy
11
,
377
395
(
2008
).
18.
M. D. Müller, “
Climate Lamma Island, Meteoblue Data Report
” (Meteoblue Point+,
2019
).
19.
J.
Tang
,
A.
Brouste
, and
K. L.
Tsui
, “
Some improvements of wind speed Markov chain modeling
,”
Renewable Energy
81
,
52
56
(
2015
).
20.
Z.
Song
,
X.
Geng
,
A.
Kusiak
, and
C.
Xu
, “
Mining Markov chain transition matrix from wind speed time series data
,”
Expert Syst. Appl.
38
(
8
),
10229
10239
(
2011
).
21.
S. A.
Pourmousavi Kani
and
M. M.
Ardehali
, “
Very short-term wind speed prediction: A new artificial neural network–Markov chain model
,”
Energy Convers. Manage.
52
(
1
),
738
745
(
2011
).
22.
A.
Sahin
and
Z.
Sen
, “
First-order Markov chain approach to wind speed modelling
,”
J. Wind Eng. Ind. Aerodyn.
89
(
3–4
),
263
269
(
2001
).
23.
F. H.
Mahmood
,
A. K.
Resen
, and
A. B.
Khamees
, “
Wind characteristic analysis based on Weibull distribution of Al-Salman site, Iraq
,”
Energy Rep.
6
(
3
),
79
87
(
2020
).
24.
Swiss Federal Office of Energy
, https://wind-data.ch/tools/weibull.php for “
Weibull wind speed distribution
,” The Swiss Wind Power Data Website (
2020
).
25.
F.
Bianchi
,
H.
de Battista
, and
R.
Mantz
, “
Wind turbine control systems principles
,”
Modelling and Gain Scheduling Design
(
Springer-Verlag
,
London
,
2007
).
26.
S.
Minna
,
F. D.
Bianchi
,
M.
De Prada Gil
, and
C.
Ocampo-Martinez
, “
A wind farm control strategy for power reserve maximization
,”
Renewable Energy
131
,
37
44
(
2019
).
27.
G. C.
Larsen
,
H.
Madsen Aagaard
,
F.
Bingöl
,
J.
Mann
,
S.
Ott
,
J. N.
Sørensen
,
V.
Okulov
,
N.
Troldborg
,
N. M.
Nielsen
,
K.
Thomsen
 et al., “
Dynamic Wake Meandering Modeling Technical report
,” Report No. Riso-R-16O7(EN) (Riso National Laboratory,
2007
).
28.
C. J.
Bay
,
J.
Annoni
,
T.
Taylor
,
L.
Pao
, and
K.
Johnson
, “
Active power control for wind farms using distributed model predictive control and nearest neighbor communication
,”
Annual American Control Conference
(
2018
), pp.
682
687
.
29.
J. R.
Marden
,
S. D.
Ruben
, and
L. Y.
Pao
, “
A model-free approach to wind farm control using game theoretic methods
,”
IEEE Trans. Control Syst. Technol.
21
(
4
),
1207
1214
(
2013
).
30.
L.
Pao
and
K.
Johnson
, “
Control of wind turbines: Approaches, challenges, and recent developments
,”
IEEE Control Syst. Mag.
31
(
2
),
44
62
(
2011
).
31.
P.
Fleming
,
P.
Gebraad
,
J.
van Wingerden
 et al., “
The SOWFA super-controller: A high-fidelity tool for evaluating wind plant control approaches
,”
European Wind Energy Association Conference
(
2013
).
32.
L.
Buccafusca
and
C. L.
Beck
, “
Maximizing power in wind turbine arrays with variable wind dynamics
,”
57th IEEE Conference on Decision and Control
(
2018
).
33.
E.
Bitar
and
P.
Seiler
, “
Coordinated control of a wind turbine array for power maximization
,”
American Controls Conference
(
2013
).
34.
M.
Rotea
, “
Dynamic programming framework for wind power maximization
,”
Int. Fed. Autom. Controlled
47
,
3639–3644
(
2014
).
35.
J.
de Oliveira
,
A.
Trofino
, and
C. E.
de Souza
, “
Robust H2 performance of LPV systems via parameter dependent Lyapunov function
,”
3rd IFAC Symposium on Robust Control Design, Prague, Czech Republic
,
2000
.
36.
S.
Boyd
,
L. E.
Ghaoui
,
E.
Feron
, and
V.
Balakrishnan
, “
Linear matrix inequalities in system and control theory
,”
SIAM Studies in Applied Mathematics
(
SIAM
,
Philadelphia, USA
,
1994
).
37.
M. A.
Soliman
,
H. M.
Hasanien
,
A.
Al-Durra
, and
M.
Debouza
, “
High performance frequency converter controlled variable-speed wind generator using linear-quadratic regulator controller
,”
IEEE Trans. Ind. Appl.
56
(
5
),
5489
5498
(
2020
).
38.
C. R.
Shapiro
,
G. M.
Starke
,
C.
Meneveau
, and
D. F.
Gayme
, “
A wake modeling paradigm for wind farm design and control
,”
Energies
12
(
15
),
2956
(
2019
).
39.
X.
Yao
,
C.
Guo
, and
Y.
Li
, “
LPV H-infinity controller design for variable-pitch variable-speed wind turbine
,”
IEEE 6th International Power Electronics and Motion Control Conference
(
2009
).
40.
F.
Shirazi
,
K.
Grigoiadis
, and
D.
Viassolo
, “
Wind turbine linear parameter varying control using fast code
,”
5th Annual Dynamic Systems and Control Conference
(
2012
).
41.
G.
Gao
,
K.
Grigoriadis
, and
Y.
Nyanteh
, “
LPV control for the full region operation of a wind turbine integrated with synchronous generator
,”
Sci. World J.
2015
,
638120
.
42.
J.
Jonkman
,
S.
Butterfield
,
W.
Musial
, and
G.
Scott
, “
Definition of a 5MW reference wind turbine for offshore system development
,”
Report No. NREL/TP-500-38060
(
2009
).
43.
N.
Kundu
and
C. M.
Crane
, “
Applying H-infinity control methods to wind turbines using MATLAB
,”
Int. J. Ambient Energy
16
(
3
),
131
(
1995
).
44.
L. J.
Vermeer
,
J. N.
Sørensen
, and
A.
Crespo
, “
Wind turbine wake aerodynamics
,”
Prog. Aerosp. Sci.
39
,
467
–510 (
2003
).
45.
L. J.
Vermeer
,
J. N.
Srensen
, and
A.
Crespo
,
Prog. Aerosp. Sci.
39
(
6–7
),
467
(
2003
).
46.
P. M. O.
Gebraad
,
F. C.
van Dam
, and
J.
van Wingerden
, “
A model-free distributed approach for wind plant control
,” American Control Conference, Washington, DC,
2013
, pp.
628
633
.
47.
S.
Boyd
,
L. E.
Ghaoui
,
E.
Feron
, and
V.
Balakrishnan
, “
Linear matrix inequalities in system and control theory
,”
SIAM Studies in Applied Mathematics Philadelphia
(
John Wiley & Sons, Ltd.
,
1994
).
48.
V.
Spudic
,
C.
Conte
,
M.
Baotic
, and
M.
Morari
, “
Cooperative distributed model predictive control for wind farms
,”
Optim. Control Appl. Methods
36
(
3
),
333
(
2015
).
49.
N.
Aouani
,
S.
Salhi
,
M.
Ksouri
, and
G.
Garcia
, “
H2 analysis for LPV systems by parameter-dependent Lyapunov functions
,”
IMA J. Math. Control Inf.
29
(
1
),
63
78
(
2011
).
50.
P. B.
Cox
,
S.
Weiland
, and
R.
Tóth
, “
Affine parameter-dependent Lyapunov functions for LPV systems with affine dependence
,”
IEEE Trans. Autom. Control
63
,
3865
(
2018
).
51.
T.
Iwasaki
and
G.
Shibata
, “
LPV system analysis via quadratic separator for uncertain implicit systems
,”
38th Conference on Decision and Control
(
1999
).
52.
F.
Wu
and
A.
Packard
, “
LQG control design for LPV systems
,”
Proceedings of American Control Conference
(
1995
).
53.
W. M.
Haddad
and
D. S.
Bernstein
, “
Parameter dependent Lyapunov functions and the Popov criterion in robust analysis and synthesis
,”
IEEE Trans. Autom. Control
40
,
536
(
1995
).
54.
J.
Oliveira
,
C. E.
de Souza
, and
A.
Trofino
, “
H2 analysis and synthesis of parameter dependent systems via LMI and parameter dependent Lyapunov functions
,”
Report No. UFSC/CTC/DAS
(
1999
).
55.
J. C.
Doyle
,
K.
Glover
,
P. P.
Khargonekar
, and
B. A.
Francis
, “
State-space solutions to standard H2 and H control problems
,”
IEEE Trans. Autom. Control
34
,
831
847
(
1989
).
56.
H.
Kwakernaak
and
R.
Sivan
,
Linear Optimal Control Systems
(
John Wiley and Sons
,
New York
,
1972
).
57.
G.
Becker
,
Quadratic Stability and Performance of Linear Parameter Dependent Systems
(
ProQuest Dissertations Publishing
,
1993
).
58.
M.
Green
and
D. J. N.
Limebeer
,
Linear Robust Control
(
Prentice-Hall
,
1995
).
59.
G. E.
Dullerud
and
F.
Paganini
,
A Course in Robust Control Theory: A Convex Approach
(
Springer-Verlag
,
New York
,
1999
).
60.
F.
Wu
,
X. H.
Yang
,
A.
Packard
, and
G.
Becker
, “
Induced l2-norm control for LPV system with bounded parameter variation rates
,”
Proceedings of the American Control Conference
(
1995
).
61.
C.
Cai
and
A.
Teel
, “
Input-output-to-state stability for discrete-time systems
,”
Automatica
44
,
326
336
(
2008
).
62.
T.
Burton
,
N.
Jenkins
,
D.
Sharpe
, and
E.
Bossanyi
,
Wind Energy Handbook
, 2nd ed. (
John Wiley and Sons
,
2011
).
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