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Maximization of the Annual Energy Production of Wind Power Maximization of the Annual Energy Production of Wind Power
Plants by Optimization of Layout and Yaw-Based Wake Control Plants by Optimization of Layout and Yaw-Based Wake Control
Pieter Gebraad
National Renewable Energy Laboratory
Jared Thomas
Brigham Young University
, jaredthomas68@gmail.com
Andrew Ning
Brigham Young University
, aning@byu.edu
Paul Fleming
National Renewable Energy Laboratory
Katherine Dykes
National Renewable Energy Laboratory
Follow this and additional works at: https://scholarsarchive.byu.edu/facpub
Part of the Mechanical Engineering Commons
Original Publication Citation Original Publication Citation
Gebraad, P., Thomas, J. J., Ning, A., Fleming, P., and Dykes, K., “Maximization of the Annual
Energy Production of Wind Power Plants by Optimization of Layout and Yaw-Based Wake
Control,” Wind Energy, May 2016. doi:10.1002/we.1993
BYU ScholarsArchive Citation BYU ScholarsArchive Citation
Gebraad, Pieter; Thomas, Jared; Ning, Andrew; Fleming, Paul; and Dykes, Katherine, "Maximization of the
Annual Energy Production of Wind Power Plants by Optimization of Layout and Yaw-Based Wake Control"
(2016).
Faculty Publications
. 1739.
https://scholarsarchive.byu.edu/facpub/1739
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WIND ENERGY
Wind Energ. 0000; 00:1–11
DOI: 10.1002/we
Maximization of the annual energy production of wind power
plants by optimization of layout and yaw-based wake control
Pieter M.O. Gebraad
1
, Jared J. Thomas
2
, Andrew Ning
2
, Paul A. Fleming
1
, and Katherine Dykes
1
1
National Renewable Energy Laboratory
2
Brigham Young University
ABSTRACT
This paper presents a wind plant modeling and optimization tool that enables the maximization of wind plant annual energy
production (AEP) using yaw-based wake steering control and layout changes. In order to make predictions of wind plant
AEP, necessary extensions of the original wind plant wake interaction model include the coupling with a detailed rotor
model and a control policy for turbine blade pitch and rotor speed. This coupling allows the prediction of power production
with wake effects throughout a range of wind speeds. Results of an optimization study on a wind plant based on the Princess
Amalia Wind Park show increases of 5% in AEP by combined optimization of layout and wake steering control. Looking
at the wind speed dependence of the possible power gains shows that power gains from wake steering control are highest
in Region 1.5, and continue to be present to some extent for above-rated inflow speeds. The results show that layout
optimization and wake steering are complementary to each other, in the sense that significant AEP improvements can be
achieved with wake steering in a wind plant layout that is already optimized to reduce wake losses. Copyright © 0000 John
Wiley & Sons, Ltd.
KEYWORDS
wind plant optimization; wind turbine control; wind turbine wakes; wind plant systems engineering
Received . . .
1. INTRODUCTION
Wind turbines in wind power plants impact each others performance through their wakes. This interaction reduces the
total energy output of the plant. The negative effects of this aerodynamic interaction can be mitigated by placing the
turbines further away from each other in the most prevalent wind directions. Therefore, plant design typically involves
a plant layout optimization step where turbine placement is optimized to maximize the energy production by taking into
account the effects of wakes [1]. In recent years, research has focused on improving power production of the wind plant by
using coordinated control techniques between the turbines to mitigate the wake effects in the wind plant [2]. Recently, [3]
proposed a combined optimization of wind plant layout and controls during the design phase, in order to realize a further
increase of the power production of new wind plants. A limitation of many previous studies on wind plant wake control,
including the combined optimization study of [3], is that only a single wind speed operating condition is considered, rather
than taking into account the full range of wind plant operation conditions that a wind plant experiences throughout the
year in order to maximize the annual energy production (AEP). This paper addresses this issue, and presents a wind plant
optimization tool for the maximization of the AEP of the wind plant using the combination of wake control and layout
changes.
The concept of wind plant wake control, which was first proposed in [4], is that the performance of the wind plant as
a whole can be improved by coordinating the control operations across the wind turbines in such a way that wake losses
are mitigated. Typically the wind plant controller coordinates the upstream turbines to reduce their power production in
order to reduce the wake effects on downstream turbines, and increase the total power production of the wind plant. A
review of the literature on different wake control strategies is found in [2]. Wake control techniques have different ways
of using the turbine control degrees of freedom to affect the wakes. Most wind plant control studies in the literature use
axial-induction-based control, in which generator torque or blade pitch is altered to optimize wake velocities. Alternatively,
yaw offsets are used to redirect the wakes and steer them away from downstream turbines. In [5], we found that yaw-based
Copyright © 0000 John Wiley & Sons, Ltd. 1
Prepared using weauth.cls [Version: 2010/06/17 v1.00]
Maximization of the annual energy production of wind power plants by optimization of layout and wake control P.M.O. Gebraad et al.
wake steering control was the most effective of both approaches, based on high-fidelity simulations of the wind flow and
wind turbine dynamics in a small turbine array using NREL’s Simulator fOr Wind Farm Applications (SOWFA) [6].
For yaw-based wake steering control, Delft University of Technology and NREL developed an optimization strategy
based on the FLOw Redirection and Induction in Steady-state (FLORIS) control-oriented model. FLORIS is a
computationally efficient model that predicts the steady-state wake characteristics, and the resulting power production
of each turbine in the wind plant, as a function of the yaw angles and the positions of the turbines. The model can be used
to maximize the power production of wind plants by predicting the optimal yaw angles. In [7], the FLORIS-based yaw
control approach has been successfully tested in an online implementation in SOWFA. In [3], the FLORIS model was used
in a wind plant system engineering approach with combined optimization of yaw control and wind plant layout. It was
found that a further increase of the power density (generated electrical power per land area) of new wind plants can be
achieved through this combined optimization. This can lead to reduced costs for the rest of the plant, including the costs
of roads, electric cables, and land leasing costs.
The previous work [7] and [3] on optimization of wake steering only considered a single wind speed of the inflow of
the wind farm. This is because the FLORIS wake model was only suited to predict the operation in the Region 2 control
operating point of the wind turbine, with a fixed blade pitch angle and tip-speed ratio. In order to predict and optimize the
Annual Energy Production (AEP) of the wind plant with specific wind resource characteristics consisting of both a wind
speed and a wind direction distribution, the wind plant model needs to be suited to predict the power output of the wind
plant for the full range of wind speeds in which the wind plant operates.
To arrive at such a model describing the full wind plant operational range, in this paper we couple the FLORIS wake
model with a more comprehensive rotor model, and we include the power and speed control policy of the turbine. The
rotor model consist of the WISDEM CCBlade blade element momentum (BEM) code [8], and the coupling of the models
is performed through the WISDEM framework for wind plant modeling. WISDEM (Wind-Plant Integrated System Design
and Engineering Model) [9] is a set of models for assessing overall wind plant cost and production, that is built using
the Open-source platform for Multidisciplinary Design, Analysis, and Optimization (OpenMDAO) [10]. We use efficient
gradient-based optimization techniques available in the WISDEM toolset, to perform an optimization of AEP in a case
study on a full size wind plant using yaw control and layout changes. We discuss in detail how the rotor characteristics
combined with the power and speed control policy affect the power production increases that can be achieved through
yaw-based wake steering control.
In section 2 we introduce the objective and optimization variables of the wind plant AEP optimization problem
considered in this paper. In section 3 we present the new WISDEM FLORIS wind plant AEP model. More details on
the optimization strategies and tools used to solve the AEP optimization problem are provided in section 4. In section 5
we present the optimization case study on a full size wind plant (based on the Princess Amalia Wind Park). Finally, we
discuss our conclusions in section 6.
2. OPTIMIZATION OBJECTIVE AND VARIABLES
In this study, we focus on the problem of optimizing the AEP of a wind plant for a given site with layout constraints
(a bounded area in which turbines can be placed, and a minimum spacing between the turbines) and with an expected
wind distribution for the site, using the set-points for the yaw angles and the positions of the turbines as the optimization
variables. While the positions of the turbines are fixed, the yaw set-point will be adjusted to wind speed and direction.
The wind distribution will be described by the wind rose, which consists of a two-dimensional histogram of the wind
speed and wind direction with a fine resolution (i.e. a large number of bins). The center wind speed and direction of each
bin b in the wind rose are respectively denoted as V
b
and
b
. The frequency of occurence of each bin is written as p
b
, and
expresses the portion of annual hours, i.e. 0 p
b
1. We denote the number of bins in the wind rose as N
B
.
The optimization variables considered are the location (x
t
, y
t
) of each turbine t, and the yaw angles of each turbine for
each wind speed and direction bin,
b,t
. The number of turbines in the wind plant is denoted as N
T
.
Using the shorthand notation {a
i
}
N
i=1
for the set of variables a
1
,...,a
N
, the optimization problem can be written as
follows:
maximize
x,y,
AEP
✓
{x
t
,y
t
}
N
T
t=1
,
n
{
b,t
}
N
T
t=1
; V
b
,
b
,p
b
o
N
B
b=1
◆
subject to layout c o n st ra ints (1)
The AEP is calculated as the weighted sum of the total wind plant power production P
b
for each wind rose bin b. The
weighting is given by the frequency of each bin, p
b
, times the number of hours in the year, N
h
=8760:
AEP =
N
B
X
b=1
N
h
P
b
⇣
{x
t
,y
t
}
N
T
t=1
, {
b,t
}
N
T
t=1
; V
b
,
b
⌘
p
b
(2)
2 Wind Energ. 0000; 00:1–11 © 0000 John Wiley & Sons, Ltd.
DOI: 10.1002/we
Prepared using weauth.cls
P.M.O. Gebraad et al. Maximization of the annual energy production of wind power plants by optimization of layout and wake control
The control variables of the wind turbine other than the yaw angle, typically blade pitch and generator torque, are not
considered optimization variables here. They are set using a fixed turbine power and rotor speed control policy. In this
optimization scheme, we assume that the yaw control is set by a plant-level control that uses wake steering to minimize
the wake losses and maximize energy production, while the power and speed controller operates on the individual turbine
level, and adjusts the pitch and generator torque such that the turbine is operating within certain limits. For example, it
assures that the turbine’s rotor speed and power are at or below their rated levels for each wind speed and yaw setting. The
coupling of each of the submodels in the wind plant model will be discussed in the next Section 3.
3. WIND PLANT MODELING
In this section we discuss the wind plant model that is used to predict and optimize the wind plant AEP. It consists of the
FLORIS wake model coupled with other WISDEM submodels.
The FLORIS wake model was presented in [7]. It is a combination of an extended Jensen wake model [11] and a model
for wake deflection caused by yaw offsets proposed by Jim
´
enez et al. [12]. The Jensen model, which uses a uniform velocity
deficit with a top-hat profile that decays and widens with downstream distance, was augmented by including several wake
zones, each with their own expansion and recovery properties, to better model situations with partial wake overlap, which
is relevant for yaw-based wake control. The FLORIS model is a parametric model for which the parameters are tuned
based on measured data or data from high-fidelity simulations. The full description of the original FLORIS model in [7]
includes a detailed example of tuning FLORIS based on high-fidelity comput simulation data generated by the SOWFA
tool.
The original FLORIS presented in [7] included a highly simplified characterization of the rotor that assumed a constant
axial-induction factor a =1/3, and idealized relationships between the axial-induction factor and the thrust and power
coefficients. Influences of the tip-speed ratio and pitch were not included, and therefore the rotor model was only applicable
in region 2 when the turbine operates at peak efficiency with a constant pitch and tip-speed ratio.
In order to model the AEP of a wind plant with wake steering control, we use the WISDEM modeling framework to
couple the FLORIS wake model to a BEM code that provides the thrust and power characteristics of the wind turbine
rotors for all operating points, and to a model of the power and speed controller of the turbine. This enables the model to
make predictions of power production for the full range of wind speeds in which the wind plant operates.
3.1. Overview of the simulation and optimization scheme
An overview of the coupled model scheme for wind plant AEP simulation and optimization is given in Figure 1. The
chart was created using the XDSM (eXtended Design Structure Matrix) standards [13]. The main diagonal contains all
the components. Inputs and outputs are connected to the relevant submodels by thick gray lines. Inputs to components
are shown in the same column. Outputs from components are shown in the same row. System inputs are listed in the
first row, system outputs are to the left of the first column. Ovals represent optimization algorithms or solvers, rectangles
represent system components. The flow of execution is shown by the thin black lines. The “stacked” labels indicate parallel
execution.
x
o
t
,y
o
t
,
o
t,b
Airfoil Data, Power/Speed Control Policy
b
D
t
, V
b
, ⇢
p
b
x
⇤
t
,y
⇤
t
,
⇤
t,b
,AEP
⇤
Optimization
x
t
,y
t
t,b
x
t
,y
t
FPI
ˆv
t,b
Rotor Model
C
P,t,b
,C
T,t,b
,a
t,b
Reference Frame
ˆx
t,b
, ˆy
t,b
v
t,b
FLORIS Wake Model
P
b
AEP
AEP Calc.
Layout Constraints
Layout Constraints Calc.
Figure 1. XDSM chart of the WISDEM FLORIS wind plant AEP modeling and optimization tool.
Wind Energ. 0000; 00:1–11 © 0000 John Wiley & Sons, Ltd. 3
DOI: 10.1002/we
Prepared using weauth.cls
Maximization of the annual energy production of wind power plants by optimization of layout and wake control P.M.O. Gebraad et al.
Like in previous equations (1) and (2), in the model scheme we use the indexing (·)
t
for a variable that applies to a
turbine t for all wind rose bins, and (·)
t,b
for a turbine variable that depends on the bin b that the wind plant is operating
in. The starting value of each optimization variable is indicated as (·)
o
, and the final solution as (·)
⇤
.
As explained in the previous section, the optimization algorithm maximizes the total AEP of the wind plant by
optimizing the yaw angles
t,b
and the positions of the turbines x
t
, y
t
, with some predefined constraints on the layout. In
each iteration of the optimization, the model calculates the power of each turbine in the wind plant for each bin b in the
wind rose, with a center wind direction
b
and center free-stream wind speed V
b
, and sums up the turbine powers to get
total wind plant power production P
b
for each wind rose bin b. The calculation of the total power P
b
for each bin b can be
performed in parallel. After that, the AEP is calculated through equation (2).
In order to estimate the powers of the turbines, the FLORIS wake model needs the air density ⇢, the turbine yaw angles
t,b
, rotor diameters D
t
, and positions in the downwind-crosswind reference frame ˆx
t,b
, ˆy
t,b
(see section 3.2 of [7]). Also,
the wake model needs the power and thrust coefficients C
P,t,b
, C
T,t,b
and the axial-induction factor a
t,b
of each turbine,
which are supplied by the rotor model. The power coefficient C
P,t,b
determines the efficiency with which the wind kinetic
power is converted to electrical power by the rotor, and the thrust coefficient C
T,t,b
then determines the reduction of
velocity over the rotor plane (represented by the axial-induction factor, a
t,b
) to the initial velocity of the wake just behind
the rotor. The rotor model is in a feedback loop with the wake, which is solved using OpenMDAO’s fixed-point iterator
(FPI) that iterates on the effective wind speed at each turbine, v
t,b
, as will be explained in more detail in the next section.
3.2. The rotor model
The rotor model is based on the WISDEM CCBlade BEM code [8] calculating the power coefficient C
P
and the thrust
coefficient C
T
of the rotor based on the wind speed. The rotor model also includes the possible influences of the pitch
and rotor speed operating point set by the power and speed control policy, and the yaw angle of each rotor. In our model
scheme in Figure 1, the yaw angle is an external input to the rotor model, that is set by the optimizer. The different parts of
the rotor model are coupled in series, as follows:
• First, V
o
, the component of the rotor-effective wind speed V that is orthogonal to the possibly yawed rotor plane, is
calculated, through V
o
= V cos(), where is the yaw angle of the rotor.
• A wind turbine power and speed control policy is applied, that sets the collective blade pitch and rotor speed as a
function of the orthogonal wind speed component V
o
(see Figure 2, for example). Note that this is an abstraction of
the steady-state behavior of a real controller (which generally uses no knowledge of the wind speed directly).
• The WISDEM CCBlade BEM code generates the C
P
- and C
T
- coefficients of the rotor based on the wind speed,
yaw angle, rotor speed, and blade pitch angle.
• Finally, the axial-induction factor is calculated from the C
T
-factor based on rotor theory with the Glauert correction:
[14]:
a =
⇢
0.143 +
p
0.0203 0.6427 (0.889 C
T
)ifC
T
> 0.96,
1
2
1
p
1 C
T
else.
(3)
The combination of these parts yields the turbine’s power and thrust coefficient surfaces as a function of wind speed
and yaw, shown in Figure 3.
Figure 2. Blade pitch and rotor speed control policy of the NREL 5-MW reference wind turbine as applied in the rotor model, based
on the controller description in [15].
4 Wind Energ. 0000; 00:1–11 © 0000 John Wiley & Sons, Ltd.
DOI: 10.1002/we
Prepared using weauth.cls
![Table I. Wake model parameters for the new FLORIS model. Parameter values that are different from the values reported in [7], are in bold.](/figures/table-i-wake-model-parameters-for-the-new-floris-model-3s2l9cqu.webp)
