Energy Conversion and Management 157 (2018) 587–599
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Energy Conversion and Management
journal homepage: www.elsevier.com/locate/enconman
Maximum power extraction for wind turbines through a novel yaw control
solution using predicted wind directions
T
⁎
Dongran Songa, Jian Yanga, Xinyu Fanb, , Yao Liuc, Anfeng Liua, Guo Chend, Young Hoon Jooe
a
School of Information Science and Engineering, Central South University, Changsha, China
School of Automation, Beijing Institute of Technology, Beijing, China
c
Guangdong Power Grid Corp, Zhuhai Power Supply Bur, Zhuhai, China
d
School of Electrical Engineering and Computing, University of Newcastle, Callaghan, Australia
e
Department of Control and Robotics Engineering, Kunsan National University, Kunsan, Republic of Korea
b
A R T I C L E I N F O
A B S T R A C T
Keywords:
Maximum power extraction
Yaw control
Wind direction prediction
ARIMA-KF
Model predictive control
For modern horizontal axis wind turbines (WTs), a yaw drive mechanism is utilized to adjust the nacelle position
to face the wind direction. Depending on historical signals from wind direction sensors, conventional yaw
control methods could not provide sufficient performance in tracking winds, and thus result in a reduction of
wind power extraction. This issue needs to be tackled using advanced control solutions. Taking advantage of
predicted wind directions, a novel control solution is proposed in this study. Specifically, the proposed solution
refers to a novel control structure that consists of a wind direction predictive model and a novel yaw control
method. Under the proposed control structure, a hybrid autoregressive integrated moving average method-based
Kalman filter (ARIMA-KF) model is used to predict the wind direction, and two novel yaw control methods are
proposed: one created by using the predicted wind direction as the tracking reference, and the other based on a
model predictive control (MPC) using a finite control set. To demonstrate the feasibility and the superiority of
the proposed solution, two novel yaw controllers are developed and tested through some simulation tests using
industrial data. Their performance is compared to the one of two industrial yaw controllers. Comparison results
show that the two novel yaw controllers are capable of reducing yaw error, and thus increase wind power
extraction for the WTs. Meanwhile, it is noticeable that the MPC-based controller has an advantage in the aspect
of reducing yaw actuator usage.
1. Introduction
As the increasing demands of wind energy, the focus of research
today in wind turbines (WTs) lies in maximizing the power production
per unit investment. To make wind energy more competitive with other
sources of renewable energy, optimal solutions have been developed
constantly for WTs [1], where the control technology plays an indispensable role that directly affects performance of the WTs in the both
aspects of power production [2] and component loads [3]. Modern WTs
with horizontal axis have three control actuators: pitch actuator, torque
actuator, and yaw actuator. The former two actuators are considered as
the two dominating ones, since they can provide a fast response that
answers to the rapid variation of wind force. Accordingly, there are
large quantities of literature that focus on control methods for the pitch
and torque actuators. By comparison, the literature about the yaw
system control is limited. Nevertheless, the function of the yaw system
should not be neglected.
⁎
The operation of the yaw system may affect performance of the WT.
On the one hand, a yaw misalignment leads to a decreased wind power
capture. Theoretically, the wind power captured by a horizontal axis
WT is decreased by the cube of the yaw error [4]. Although empirical
data have shown that the relationship could be cosine-squared instead
of cosine-cubed [5], it is obvious that the yaw error results in the power
reduction of the WT. On the other hand, a yaw misalignment may bring
about an increment of component loads. The impact of yaw misalignment on loads of the WTs has been investigated and validated by researchers using calculation and measurement methods. For instance,
Schepers conducted a comparison investigation between calculations
and measurements on a small WT with 10 m rotor diameter in yaw,
which revealed that the yaw misalignment had effects on blade root and
shaft loads on a sectional level [6]. Boorsma presented a report of
power and loads for a 2.5 MW WT in yawed flow conditions, in which
the edgewise fatigue equivalent loads were found to be increased along
with the increasing yaw error [7]. Kragh et al. [8] showed the potential
Corresponding author.
E-mail address: fanzyzl@163.com (X. Fan).
https://doi.org/10.1016/j.enconman.2017.12.019
Received 18 September 2017; Received in revised form 15 November 2017; Accepted 6 December 2017
0196-8904/ © 2017 Elsevier Ltd. All rights reserved.
Energy Conversion and Management 157 (2018) 587–599
D. Song et al.
Nomenclature
N
number of distribution zones of yaw error
θyej
averaged yaw error at the j th zone
f j ∈ [0,1] distribution probability of θyej in the j th zone
(cos(θye ))eq equivalent cosine of yaw error
Pa
wind power extracted by a horizontal axis WT
Pred,Pideal reduced power extraction and ideal power extraction
the kth sampling period
k
sampling period
Ts
Tc
control period
Ah1,Ah2,Ah3 amplitude thresholds predefined in yaw control algorithm
Th1,Th2,Th3 time thresholds predefined in yaw control algorithm
nacelle position measured at kth sampling period
θnp (k )
̇ (j )
θnp
permissible yaw speed
̇ (k )
yaw speed during the kth control period
θnp
w1,w2,w3 weighting factors in the quality function
θwd (k )
measured wind direction sampled at the kth sampling
period
θwd (k + 1|k ) predicted wind direction at the kth sampling period
θye (k + 1|k )
θye (k + 1|k ) predicted yaw error at the kth sampling period
10s 30s 60s
θye
,θye ,θye mean wind directions averaged at the sampling periods
of 10 s,30 s,60 s
θwd (k + 1|k )Ts = 10s,θwd (k + 1|k )Ts = 30s,θwd (k + 1|k )Ts = 60s predicted
mean values of wind direction at the kth sampling period,
Ts = 10 s,30 s,60 s
θye (k + 1|k )Ts = 10s,θye (k + 1|k )Ts = 30s,θye (k + 1|k )Ts = 60s predicted mean
values of yaw error at the kth sampling period,
Ts = 10 s,30 s,60 s
Abbreviations
WT
MPP
HCM
ARIMA
KF
MPC
MY
NREL
MAE
RMSE
MAPE
QF
SCADA
wind turbine
maximum power point
hill climbing method
autoregressive integrated moving average
Kalman filter
model predictive control
Ming Yang
National Renewable Energy Laboratory
mean absolute error
root mean squared error
mean absolute percentage error
quality function
Supervisory Control and Data Acquisition System
Symbols
ρ
Ar
Cp
V0
θye
θwd
θnp
tyaw
Cyaw
ξ
air density
rotor area
aerodynamic power coefficient
free stream wind speed
yaw misalignment error
wind direction
nacelle position
yaw action time
yaw action count
reduction factor of wind power extraction caused by yaw
error
Table 1. The employed techniques are broadly categorized into four
types: free of measurement, normal measurement, advanced measurement and indirect measurement. Accordingly, relevant control methods
can be also categorized into four types and they have the following
features:
of alleviating blade load variations induced by the wind shear through
yaw misalignment for wind speeds above rated wind speed. From their
studies, it is observed that the operation of the yaw system significantly
affects the performance of the WTs. A study of operating WTs revealed a
fact that there was a static yaw error of 10 degree for wind speeds
below 20 m/s and 5 degree for wind speeds above 20 m/s, which unavoidably reduced wind power extraction of the WTs [9]. Besides, an
early survey of failures in wind power systems showed that the portion
of downtime caused by yaw failure comprised 13.3% of the total
downtime, and the yaw system failure rate comprised 6.7% [10]; and a
recent analysis for wind turbine reliability concluded that the failure
rate of wind turbines was increased up to 12.5% [11]. Thus, the controls for the yaw system deserve more attention than they received.
In the literature, the control methods for yaw systems are directly
relevant to the measurement techniques which can be seen from
• Controls
without wind direction measurement, which originates
from early WTs limited by the wind measurement technology.
Because the main objective of yaw control system is to maximize
wind power extraction, the mechanism for controls without wind
direction measurement is to directly search the maximum power
point (MPP). Hill climbing method (HCM) was proposed to find the
desired yaw angle corresponding to the MPP [12], and bisectingplane algorithm was presented to enhance the efficiency and accurateness of conventional HCM [13]. Besides, a combined maximum
Table 1
Summary of the yaw control methods recorded in the literature.
Measurement
Control objective
Method
WT capacity
Refs.
Free
Searching optimal power
Searching optimal power
Tracking optimal rotor speed
HCM
Modified HCM
PI
< 50 kW
1.5 MW
1.1 kW/2.5 MW
[12]
[13]
[14]
Normal
Tracking
Tracking
Tracking
Tracking
Fuzzy-PID
Logic control
Logic control
Logic control
Unclear
2 kW
600 kW
1.5 MW
[15]
[16]
[17]
[18]
Advanced
Tracking wind direction
Tracking wind direction
Logic control
Conventional MPC
600 kW
5 MW
[19–21]
[22]
Indirect
Maximizing power production/minimizing structural loads
Searching optimal power
Conventional MPC
Logic control
1 MW
1.1 kW
[23]
[24]
wind
wind
wind
wind
direction
direction
direction
direction
588
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D. Song et al.
•
•
•
direction, which aims at extracting maximum wind power for the WTs
with a moderate yaw actuator usage. With regards to the literature, the
major contributions of this paper are threefold.
power point tracking and yaw control technique aiming at tracking
the optimal rotor speed was presented in [14]. In theory, this type of
controls may provide better performance than normal measurement-based one which may suffer from the inaccurate measurements disturbed by operation of the WTs. However, the MPP of WTs
is changing following the variation of wind speed, besides the wind
direction. As a result, the real difficulty for controls without measurements consists in locating the MPP, which remains an open issue
in wind energy research community.
Controls with normal measurements, which are currently widely
employed by modern WTs. This type of controls employs active yaw
control strategies to face the turbine into the wind by acquiring
signals from wind vanes installed at the rear of the nacelle. Although
a fuzzy-PID strategy is introduced to track the wind direction, the
motivation is unclear [15]. By comparison, most of control strategies employ some predefined logic controls [16–18], where the yaw
actuators are activated when the yaw error measured by wind vanes
exceeds some thresholds. Although the strategies are simple, the
difficulty consists in obtaining a proper reference to adjust the nacelle position. The measurements from the wind vanes are always
mixed with disturbing noises and outliers. Meanwhile, the wind
direction constantly changing is different from the future wind direction. Consequently, the controls with normal measurements
could not provide sufficient performance [9–11].
Controls with advanced measurements, which have been recently
proposed in some advanced wind energy projects. To obtain accurate wind direction measurement, remote sensing instruments based
on Lidar and hypersonic (Sodar) technologies have been employed.
With the powerful remote measurement, performance of the yaw
control system can be potentially enhanced with simple logic controls [19–21]. Under the assumption that the wind direction preview
provided full information about wind direction over the future 60 s,
a conventional model predictive control (MPC) can provide an increment of 8% wind power extraction and some fatigue load reductions during an extreme direction change [22]. Nevertheless, the
solutions are expensive and thus, affordable only for high power
WTs [14].
Controls with indirect measurements, which have gradually gained
attentions by researchers. The short-term prediction of wind direction is incorporated into a conventional MPC for the yaw control
system, which aims at achieving structural loads minimization and
power production maximization simultaneously [23]. Besides, wind
direction is estimated by an inverted function of wind power and
wind speed, and then is employed into the yaw control system with
logic controls [24]. The controls with indirect measurements may be
potential for improving performance yaw system, but the presented
control solution ignoring prediction algorithms is incomplete and
needs to be further investigated.
• This paper proposes a novel control structure that consists of a wind
•
•
predictive model and a novel control method. To do this, a hybrid
autoregressive integrated moving average method-based Kalman
filter (ARIMA-KF) model is used to predict the wind direction. Then,
two novel yaw control strategies are proposed: one created by using
the predicted wind direction as the tracking reference, and the other
based on a model predictive control (MPC).
This paper introduces the novel MPC with a finite control set for
controlling the yaw system. The predicted wind directions are discrete data obtained at every sampling period, and thus the predictive model for yaw control system including predicted wind directions are internally discrete model. Thus, compared with the
conventional MPC with a continuous control set, the proposed MPC
strategy is more suitable for controlling yaw systems using predicted
wind directions. On one hand, the yaw command sets during each
sampling period can be categorized into a finite control set rather
than a continuous control set. On the other hand, the algorithm
solution is directly selected from available control sets, and thus
reduces the computational burden.
This paper discusses how wind power extraction of the WTs can
benefit from the predicted wind direction-based control structure
and introduces four performance indexes to evaluate the yaw control system performance, namely yaw error, yaw action time, yaw
action count, and power reduction factor.
The remainder of this work is organized as follows: the wind direction measurement, two industrial yaw control methods, and performance indexes of yaw system are discussed in Section 2; and Section
3 describes the novel yaw control solution. It is followed by simulation
tests and result discussions in Section 4. Finally, conclusions are drawn
in Section 5.
2. Yaw control system of industrial WTS
2.1. Wind direction measurement
2.1.1. Wind direction sensor
For current industrial WTs, the wind direction measurement is
normally provided by one or two wind direction sensors which are
installed on the rear of the nacelle. A typical wind direction sensor is
shown in Fig. 1, which is a product of Kriwan with number INT30 [33].
Its basic specification is given in Table 2.
2.1.2. Wind direction measurement
Fig. 2 shows the principle of wind direction measurements. Since
the wind direction sensor rotates along with the WT’s nacelle, it measures a yaw error rather than the wind direction. Besides the wind
From the above, it is concluded that controls with advanced measurements and with indirect measurements may improve performance
for the yaw system, because the wind direction information in the future can be utilized. By comparison to the advanced measurements, the
indirect measurements are normally cost-effective. Until now, some
developed forecasting approaches have been proposed, such as the
wind-power prediction by Azimi et al. [25], Yesilbudak et al. [26], and
Mohammadi et al. [27]; wind-speed prediction by Zameer et al. [28],
Zhang et al. [29], and Noorollahi et al. [30]; and wind direction prediction by Ouyang et al. [31] and Song et al. [32]. These studies addressed the prediction issues relevant to the wind source, but none of
them tried to employ the predicted wind data into the control application of the WTs.
Motivated by the aforementioned observations, this study proposes
a novel control solution by taking advantage of the predicted wind
Fig. 1. The outlook of a typical wind direction sensor [33].
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D. Song et al.
to reduce θye to zero. Since θye is normally disturbed by operation of the
WT operation, it is usually filtered before being employed as the controller reference.
Table 2
Specifications of a typical wind direction sensor [33].
Parameter
Value
Measuring range
Resolution
Accuracy
Start-up wind speed
Permitted ambient temperature
Permissible relative humility
0–360°
<1°
± 2.5°
<0.4 m/s
−40 to + 70°
0–100% . r . h.
2.2. Yaw control methods with normal measurements
For megawatt WTs, the yaw speed is normally designed in a range of
[0.2deg/s,0.8deg/s], because a fast movement of the yaw system may
induce high loads to the WT. Meanwhile, to avoid over-usage of yaw
actuator, the yaw system is always activated at discrete intervals. The
yaw control methods with normal measurements for modern WTs
normally employ the logic controls, where the yaw actuators are activated when the yaw error measured by wind vanes exceeds some
thresholds. In this study, two yaw control algorithms with normal
measurements are given and used as the baseline control algorithms.
North
Wi
nd
dir
ect
2.2.1. Yaw control algorithm I
The yaw control algorithm I is taken from the MY (Ming Yang)
1.5 MW WTs manufactured by China Ming Yang Wind Power, which is
illustrated in Fig. 3 and includes following four steps [18]:
ion
Blade rotor
(1) Yaw error filtering. In this step, the yaw error is averaged by three
averaged units with different averaged periods: 10 s, 30 s and 60 s;
10s 30s 60s
and thus, three averaged yaw errors (denoted as θye
,θye ,θye ) are
obtained.
10s 30s 60s
(2) Yaw error judgment. In this step, θye
,θye ,θye are compared to three
predefined amplitude thresholds (denoted as Ah1,Ah2,Ah3) respectively. When any of the three comparisons is satisfied, and the
sustaining time is longer than the corresponding predefined time
thresholds (denoted as Th1,Th2,Th3), the control loop goes on;
otherwise, the control loop is ended for this cycle.
(3) Yaw time calculation. In this step, the yaw action time is calculated
using the corresponding averaged yaw error divided by the yaw
speed (Yawspeed ).
(4) Yaw movement. In this step, yaw movement is activated during the
activation time. As a consequence, the nacelle moves toward facing
the wind.
wd
np
ye
Nacelle
Wind wane
Fig. 2. Schematic diagram of wind direction measurement [32].
direction sensor, there is another transducer used in yaw control
system, namely, nacelle position transducer. The yaw error is the difference between the wind direction and nacelle position, which can be
calculated by
θye = θwd−θnp
In Fig. 3, the parameters utilized are summarized in Table 3.
2.2.2. Yaw control algorithm II
The yaw control algorithm II is taken from the NREL CART3
(Controls Advanced Research Turbine 3-Bladed) turbine, which is illustrated in Fig. 4. The control logic is comparably simple and detailed
in [16,19,20]. The yaw error is filtered by two low-pass filters, one with
a time constant of 1 s, and the other 60 s, producing a more quickly
(1)
Since the wind direction varies along with the time, the yaw control
system is needed to adjust the nacelle position to track the wind direction. From Eq. (1), it is obtained that tracking the wind direction is
Step 2
Step 1
10s
ye
T(
10 s
ye
Step 3
Ah1) Th1
10 s
ye
Yes
Yaw _ speed
No
ye
30s
ye
T(
30 s
ye
Ah2) Th2
Yes
30 s
ye
Yaw _ speed
No
60s
ye
T(
60 s
ye
Ah3) Th3
Fig. 3. Schematic of the yaw control algorithm
for the MY 1.5 MW WTs [18].
60 s
ye
Yes
Yaw _ speed
No
Do nothing this cycle
590
Step 4
Start yaw
movement
Energy Conversion and Management 157 (2018) 587–599
D. Song et al.
Table 3
Yaw control parameters used in Fig. 3.
wd
Parameter
Ah1
Ah2
Ah3
Th1
Th2
Th3
Values
13°
10°
8°
10 s
5s
5s
2
changing measurement of error and a more slowly changing measurement. The quickly changing measurement error is integrated and
monitored. When the integrated error (notated AccErr in Fig. 4) reaches
a value such that it has been off by 10 degrees for 10 min, the yaw angle
of the turbine is moved to the location given by the slowly changing
measurement of the error.
(cos(θye ))eq =
N
(2)
̇ (t )| > 0)
(|θnp
(3)
The yaw action count (denoted as Cyaw ) is the activation count of the
yaw actuators. When the current yaw speed is different from the last
one, Cyaw is increased by one and it can be expressed as
Cyaw (t ) =
̇ (t ) = θnp
̇ (t −1)
∃ θnp
⎧Cyaw (t −1),
̇ (t ) ≠ θnp
̇ (t −1)
⎨Cyaw (t −1) + 1, ∃ θnp
⎩
erfast
Lowpass
TC=1s
N
∑ j=1 (cos(θyej))2 f j , θyej ∈ [−180°,180°]
Wind direction prediction approaches have been recently addressed
by some researchers, such as the data mining algorithm-based predicting approach by Ouyang et al. [31], and the ARIMA-KF based hybrid approach by Song et al. [32]. The ARIMA model is suitable for
Fig. 4. Schematic of the CART3 yaw controller [16].
AccErr
sign(erfast )* erfast
Do nothing
this cycle
2
erslow
Lowpass
TC=60s
(7)
3.1. Wind direction prediction
(4)
Since θye has a direct influence on wind power extraction of the WT,
the wind power Pa extracted by a horizontal axis WT should be also
evaluated and it can be expressed by [5]
ye
(6)
From the above, it is clear that the available yaw control algorithms
depend entirely on the historical data of the measured yaw error. To
handle the issue of the measured yaw error disturbed by operation of
the WT, averaging or low-pass filters are normally utilized to provide
the reference for the yawing movement, but they may bring about a
time delay. Besides, the filtered measurements only reflect the past yaw
error and may be different from the future wind directions. Therefore, it
is reasonable to use prediction values, which may improve the performance of the yaw control system. Hence, this study proposes a novel
solution. Fig. 5 shows its structure.Compared to the methods shown in
Figs. 3 and 4, the proposed method comprises two parts: a wind direction prediction module (depicted as 1) and a novel yaw control
module (depicted as 2). The module 1 is designed to estimate the future
wind direction θwd (k + 1|k ) at the kth sampling period (Ts ), and the
module 2 uses θwd (k + 1|k ) to make a decision for the yaw system action in the next control period. These two modules are explained as
follows.
|θye (t )|
t=1
(5)
3. Novel yaw control solution
N
∑
Yaw Command
where (cos(θye ))eq is calculated by
The yaw action time (denoted as tyaw ) is the activation time of the
̇ (t ) ), tyaw is
yaw actuators. When there is a yaw speed (denoted as θnp
cumulated and it can be expressed as
tyaw =
Novel yaw control
ξ = Pred/ Pideal = 1−((cos(θye ))eq)2
t=1
∑t = 1 (θye (t ))2
Yaw system
To better check the influence of θye with different yaw control algorithm on Pa , we introduce the power reduction factor (denoted as ξ )
which is calculated based on the following formula
N
1
N
(k )
Pa = ρAr Cp V03 (cos(θye ))2 /2
To evaluate performance of the yaw control system, two aspects
should be taken into account, one to measure the accuracy of the wind
direction tracking, and the other to measure the usage of the yaw actuators. The accuracy of the wind direction tracking can be evaluated
by checking the statistical value of yaw error, and the usage of the yaw
actuators by calculating the yaw action time and action count.
The yaw error is the difference between the wind direction and
nacelle position. In this paper, mean absolute error (MAE) and root
mean squared error (RMSE) of θye are calculated to evaluate the accuracy of the wind direction tracking. Their calculations are expressed as
∑
wd
Fig. 5. Block diagram of the novel yaw control solution.
2.3. Performance indexes for evaluating yaw control system
⎧
1
⎪ MAE (θye ) = N
⎨
⎪ RMSE (θye ) =
⎩
1
(k 1| k ) Wind direction
prediction
Yes
Yaw position
AccErr
yaw setpoint
Yaw to yaw
setpoint
Yes
Yaw setpoint
in cone?
Threshold
No
Stop the
turbine
591
No
Energy Conversion and Management 157 (2018) 587–599
D. Song et al.
errors rather than the filtered measurements. These differences may
change the performance of the yaw control system, which will be discussed in Section 4.
capturing short-range correlations and has been widely in a variety of
forecasting applications [34], but it has a difficulty of adjusting the
model’s parameters when the time series contains new information.
Thus, the ARIMA model in combination with a Kalman filter is used to
solve this problem [35]. In this study, the ARIMA-KF approach is employed because of its capability of providing accurate short-term prediction results. Here, it is worthy noticing that the ARIMA-KF methods
is not the only one that can be utilized here, and other machine
learning-based prediction approaches may provide more accurate results [36,37].
To build an ARIMA-KF predictive model for predicting the wind
direction, the relevant procedures refer to three steps, which are demonstrated in Fig. 6. Its details are given as follows:
3.2.2. Method II
The MPC enables a novel solution of a control problem while honoring the constraints imposed upon by the designers of the WT [38].
Meanwhile, it has a potential advantage that it is able to predict the
behavior of a plant in future using its model. There are two types of
MPC [39]: the MPC with a continuous control set, which requires solving a quadratic programming problem on line and thus has a computation burden, and the MPC with a finite control set, which has recently been proposed to control pitch angle and generator torque for
the WTs [40]. The control command for the yaw system can be categorized into a finite control set; therefore, the MPC with a finite control
set is proposed and employed in this study. As suggested in [39,40], the
MPC with a finite control set can be developed by following four steps:
(1) Choosing the original wind direction series. Since the yaw controller uses the mean values of wind direction data, three types of
wind direction data with different averaged periods: 10 s, 30 s and
60 s, are used to form the original data series.
(2) Defining the ARIMA initial model. In this step, the three types of
original data series are used to train the ARIMA predictive models,
in which a three iterative step is included: model identification,
parameter estimation, and diagnostic checking.
(3) Designing the KF-based predictive model. The KF is generally described as an approach consisting of a state equation and a measurement equation. The system state equation is created by reformulating the ARIMA model, and the measurement equation is
defined according to the relation of the measurement variables and
system state variables. Finally, the newly predicted values are obtained by using the KF iteration algorithm. KF algorithm also includes three steps: system modeling, measurement update and time
update filter gain.
(4) Outputting one-step prediction values. The ARIMA-KF predictive
models may provide multiple-step predictions, but multiple-step
predictions are with the considerable prediction error. Thus, only
the one-step prediction values are used in this study.
(1)
(2)
(3)
(4)
Define a quality function (QF).
Build a model of the target system and its possible control set.
Build a model of the controlled variables for prediction.
Evaluate the predicted value for each control set and select the one
with minimal value of QF.
The block diagram of the proposed MPC-based yaw control method
is shown in Fig. 8, which mainly refers to the construction of the predictive model and the QF. In this study, the primary control objective is
to track the predicted wind direction, which in other words is to decrease the yaw error. Thus, the predictive model is needed to predict
the yaw error. And, the secondary control objective is to avoid the yaw
actuator over-usage. In the QF, these two control objectives can be
evaluated using a convex function. In this way, both objectives of wind
direction tracking and actuator usage can be taken care by adjusting the
corresponding weighting factors. The proposed method is detailed as
follows.
3.2. Two novel yaw control methods
a. Finite control set for yaw actuator
In this section, the two novel yaw control methods are proposed and
discussed: one is created by using wind direction predictions as the
tracking references (Method I), and the other is based on the MPC using
a finite control set (Method II).
For modern WTs, the yaw system is driven by yaw motors. When the
yaw system is activated, the nacelle will be moved by the yaw motors at
a certain speed; otherwise, the nacelle position remains unchanged. The
permissible actions for the yaw actuators comprise three elements and
they can be categorized into a finite set as follows:
3.2.1. Method I
The schematic diagram of Method I is illustrated in Fig. 7, where
three types of predicted wind directions with different sampling periods: 10 s, 30 s, and 60 s, are used to provide the tracking references. As
a consequence, the resulted controller has three control periods. In
other words, the controller updates its output when the inputs are updated at each 10 s, 30 s, and 60 s.
When comparing with the yaw control method shown in Fig. 3, the
proposed method shown in Fig. 7 has a main distinction that the update
period of its output depends on Ts of the predictive model. Besides, it
differs in following details: in Step 1, its inputs uses three types of
predicted yaw errors instead of filtered measurements; in Step 2, it
employs only three amplitude thresholds ( Ah1,Ah2,Ah3), without time
thresholds; and in Step 3, its tracking references use the prediction yaw
1
Original wind
direction series
2
ARIMA initial
model
⎧− Yawspeed, j = 0
̇ (j ) = Yawspeed, j = 1
θnp
⎨
⎩ 0, j = 2
(8)
b. Predictive model
Since the control objective is to decrease the yaw error, the yaw
error is selected as the predictive variable, which can be expressed as
follows:
̇ (j ) Tc
θye (k + 1|k ) = θwd (k + 1|k )−θnp (k )−θnp
(9)
where the control period Tc is equal to the sampling period Ts .
4
3
One-step
prediction
KF model
592
Fig. 6. Development of the ARIMA-KF wind-direction prediction model.
Energy Conversion and Management 157 (2018) 587–599
D. Song et al.
Step 1
wd
(k 1| k )Ts
10 s
ye
(k 1| k )Ts
wd
Step 2
10 s
(k 1| k )
ye
ye
(k )
Step 3
(k 1| k )Ts
10 s
Yes
Ah1
ye
(k 1| k )Ts
10 s
Yaw _ speed
Step 4
No
wd
(k 1| k )Ts
30 s
ye
(k 1| k )Ts
wd
30 s
(k 1| k )
ye
(k 1| k )Ts
ye
(k )
30 s
Ah2
60 s
Ah3
Yes
ye
(k 1| k )Ts
Start yaw
movement
30 s
Yaw _ speed
No
wd
(k 1| k )Ts
60 s
ye
(k 1| k )Ts
60 s
wd ( k 1| k )
ye
ye ( k )
(k 1| k )Ts
Yes
ye
(k 1| k )Ts
60 s
Yaw _ speed
No
Do nothing this cycle
Fig. 7. Schematic diagram of method I.
The yaw system
w1 , w2 , w3
np (
Minization
ye ( k 1| k )
of QF
j)
Predictive
model
Fig. 8. Block diagram of method II.
wd ( k )
np ( k )
Wind
direciton
prediction
2
1
np ( k )
wd ( k
model. The first two elements are linear functions which are the penalties on the increment of yaw error and yaw actuator action distance,
whereas the third element is established to punish the action count,
which uses a logical function where the value is w3 when the current
yaw action is different from the last one.
c. Quality function
The quality function is a representation of the control objectives
which are usually related to make the variables follow the references.
Hence, the quadratic value of the error, or its absolute value, is commonly employed to find the minimum value of the quality function. In
this study, minimization of yaw error and yaw actuator usage should be
achieved simultaneously, so they will be combined in a form of sum.
Since the yaw error has a direct influence on the power production
of the WT in a cosine-squared fashion, the first part (QF (1) ) of the
quality function can be chosen as follows:
QF (1) = w1 (θye (k + 1|k ))2
Apply
Obtaining
(10)
np
np
(k ),
(op)
wd
(k 1| k )
QF (op)
where w1 is the weighting factor to be adjusted.
The yaw actuator usage can be evaluated by two indexes: actuator
action distance and action count. These two indexes are combined to
form the second part (QF (2) ) of the quality function, which is given as
follows:
̇ (j )|Tc + w3 (θnp
̇ (k + 1) ≠ θnp
̇ (k ))
QF (2) = w2 |θnp
1| k )
for
ye
end
for(j=0:2)
(k 1| k )
wd
(k 1| k )
np
(k )
np
( j)Tc
(11)
Combining Eq. (11) with Eq. (10), the final QF is obtained as follows:
̇ (j )|Tc + w3 (θnp
̇ (k + 1) ≠ θnp
̇ (k ))
QF = w1 (θye (k + 1|k ))2 + w2 |θnp
If(QF(j)<QF(op))
QF(op) = QF(j); op=j;
End
(12)
As shown in Eq. (12), it is clear that one of the aspects where the
MPC shows its flexibility is the inclusion of different elements in a
Fig. 9. Flowchart of the implemented control algorithm.
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Energy Conversion and Management 157 (2018) 587–599
D. Song et al.
Wind direction [degree]
250
Fig. 10. Original wind data in a specific day: (a)
wind direction; (b) wind speed.
Original wind direction
Averaged wind direction/10s
Averaged wind direction/30s
Averaged wind direction/60s
200
150
100
50
0
0
4
8
12
16
20
24
16
20
24
Time [h]
(a)
Wind speed [m/s]
20
15
10
5
0
0
4
8
12
Time [h]
(b)
The control algorithm is detailed in Fig. 9 as a flow diagram.
As shown in Fig. 9, the minimization of the quality function is implemented as a “for” cycle predicting for three permissible control action, evaluating the quality function, and storing the minimum value
and the index value of the corresponding control action. By the flowchart, the proposed control algorithm can be easily implemented in the
wind turbine systems.
data shown in Fig. 10(a), where the first 20 h are used to establish the
models, and the leaving 4 h to check the model validity. Since the results have been detailed in [32], only the wind direction prediction
results in the form of time series are chosen to show and illustrated in
Fig. 11. Besides, three types of performance indexes (including MAE,
RMSE, and MAPE) are computed and summarized in Table 4. These
results show that the three types of the prediction results are in good
agreements with the original data. Therefore, these results will be
employed in the proposed novel yaw methods.
4. Method validations
4.2. Validation of novel yaw control methods
The proposed methods are tested using wind data obtained from a
wind farm located in Guangdong Province of China, which was saved in
a SCADAS (Supervisory Control and Data Acquisition System) per
second. In this study, the data used are referred to a specific day, including 86, 400 data points. Fig. 10(a) and (b) shows the original wind
direction and wind speed series, respectively. Besides, the averaged
wind direction series are also illustrated in Fig. 10(a), which refer to
mean values averaged in 10 s, 30 s and 60 s periods, respectively. As
shown in Fig. 10, both the original data of wind direction and wind
speed are mixed with high-frequency noises. After averaging, the wind
direction data become much smooth, and thus they can be utilized as
inputs for the conventional yaw controllers.
After obtaining the wind direction prediction data, two novel yaw
controllers were developed using the Matlab software: the first one
(denoted as C1) followed the schematic illustrated in Fig. 7 and took the
parameters given in Table 3, whereas the second one (denoted as C2)
employed the flow chart illustrated in Fig. 9. For the C2, the control
period and the weighting factors in the QF have to be determined in
advance. In this study, the control period is set to Tc = 10 s , which is
chosen based on the fact that the predicted wind direction can provide
data per 10 s. By following the trial and error procedures introduced in
[41], the three weighting factors are chosen as: w1 = 1.0 , w2 = 14.0 and
w3 = 50.0 , respectively. Besides, the yaw speed is set to 0.5 deg/s, which
is the designing parameter of the yaw system for the MY 1.5 MW WT.
4.1. Wind direction prediction results
4.2.1. Results of time series
By using the wind direction data shown in Fig. 10(a), the two
proposed yaw controllers are simultaneously simulated in parallel with
d. Control algorithm
The ARIMA-KF predictive model is trained by using wind direction
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Energy Conversion and Management 157 (2018) 587–599
D. Song et al.
Fig. 11. Wind direction prediction results of (a) 10 s;
(b) 30 s; (c) 60 s.
the performance of a yaw controller can be evaluated in terms of three
performance indexes: yaw error, yaw action time and yaw action count,
these data were calculated during the simulation. The simulation results
are shown in Fig. 12, which are obtained from the four controllers and
refer to nacelle position, yaw error, yaw action time and yaw action
count, respectively.
In Fig. 12, all curves of nacelle position, yaw error, yaw action time
and yaw action count under the four controllers presented similar
trends, which prove that all the four controllers were in a normal work
condition. However, there were obvious differences among yaw error,
yaw action time and yaw action count under different controllers.
Fig. 12(b) shows that the variations of yaw error from different
Table 4
Indexes of the three prediction results.
MAE
RMSE
MAPE
Time series of 10 s
Time series of 30 s
Time series of 60 s
0.9218
1.3038
15.74%
0.9573
1.2839
12.91%
1.1954
1.6431
12.03%
each other. Also, for the sake of comparison, the results of the two
normal yaw controllers were collected together, where the ones from
MY and NREL are denoted as C4_MY and C3_NREL, respectively. Since
595
Energy Conversion and Management 157 (2018) 587–599
D. Song et al.
Nacelle position [degree]
200
Fig. 12. Simulation results of the four controllers
for: (a) nacelle position; (b) yaw error; (c) yaw
time; (d) yaw action count.
C3_NREL
C4_MY
C1
C2
150
100
50
0
4
8
12
16
20
24
Time [h]
(a)
Yaw error [degree]
50
C3_NREL
C4_MY
C1
C2
25
0
-25
-50
0
4
8
12
16
20
24
Time [h]
(b)
600
C3_NREL
C4_MY
C1
C2
Yaw time [min]
500
400
300
200
100
0
0
4
8
12
16
20
16
20
24
Time [h]
(c)
1400
C3_NREL
C4_MY
C1
C2
Yaw count [-]
1200
1000
800
600
400
200
0
0
4
8
12
Time [h]
24
(d)
controllers. It can be found out that among the four controllers,
C3_NREL has the biggest variation of the yaw error, C4_MY comes
secondly, and C1 and C2 have similar and smaller variations of the yaw
error. Fig. 12(c) and (d) shows the yaw time and yaw count, respectively. It is very clear that the trends of yaw time for different controllers are similar as the ones of yaw count. Among the four
596
Energy Conversion and Management 157 (2018) 587–599
D. Song et al.
3.41%. By comparison to the ones of the former two controllers, C1 and
C2 have less power reductions, being 2.43% and 2.24%, respectively.
These numerical data well justify the developed novel controllers in the
aspect of maximizing wind power extraction.
The above observations prove that C2 noticeably outperforms the
other three controllers in term of performance of wind power extraction
with a moderate yaw actuator usage, whereas C1 outperforms the two
industrial controllers in term of wind power extraction at the expense of
yaw actuator usage.
Table 5
Statistical data comparisons among the four controllers.
C3_NREL
C4_MY
C1
C2
MAE (θ ye )
9.69
7.96
6.73
6.23
RMSE (θ ye )
12.88
10.57
8.87
8.18
tyaw [min]
85.4
359.4
523.3
328.9
Cyaw [−]
168
876
1377
622
ξ [%]
4.53
3.41
2.43
2.24
5. Conclusions and future work
controllers, C1 and C4_MY take the first and second places of spending
the most yaw time and yaw count, respectively, C2 comes next, and
C3_NREL is with the last place. These observations indicate a fact that
the four controllers have different performance: C3_NREL has the best
and the worst performance in the aspect of yaw actuator usage and yaw
error reduction, respectively; C1 and C2 outperform the other two
controllers in terms of yaw error reduction, but C1 has a big payback of
yaw actuator usage; overall, C2 has the most favorable performance.
To operate the yaw system of the WTs effectively, a novel yaw
control solution using predicted wind direction data has been proposed
in this study. Using discrete data obtained at every sampling time for
prediction, this feature of the predicted wind direction was fully taken
into consideration for constructing the two novel methods. Three kinds
of wind direction prediction data (10 s, 30 s and 60 s mean values which
are provided by a hybrid ARIMA-KF model) were used by the first novel
yaw control method as the tracking references. The second novel
method employed the MPC with a finite control set, which utilized the
predicted wind direction with 10 s mean value to estimate future yaw
error and achieved multiple control objectives through explicitly including them into the quality function. The two novel methods are
transformed to two novel controllers, whose performance is compared
to the one of two industrial yaw controllers. Finally, the proposed two
novel yaw controllers developed by the proposed methods demonstrated the superiority and the applicability through some simulation
tests using wind direction data obtained from a wind farm located in
Guangdong Province of China. That is, comparison results showed that
the two novel controllers extracted 1% more wind power through an
accurate wind direction tracking in comparison with the two industrial
controllers. Also, C1 increased wind power extraction at the high expense of yaw actuator usage, while C2 showed its capability of maximizing power extraction and reducing yaw actuator usage at the same
time, which owed to the quality function, constructed by adding penalties on the two interesting control objectives.
Although encouraging results have been obtained by the proposed
novel solution, there are some uncovered issues to be addressed in future studies, such as incorporating advanced machine-learning based
prediction algorithms into the control solution, investigating the impacts of the prediction uncertainty on the control method, studying
adaptive algorithms for parameter adjustment corresponding to different wind conditions.
4.2.2. Statistical data comparison and discussion
To further evaluate the performance of the four controllers, the
numerical results from Fig. 12(b–d) are collected to obtain statistical
data, which are convenient for comparison and analysis. Accordingly,
the four performance indexes discussed in Section 2.3 are calculated
and summarized in Table 5.Table 5 shows the results of MAE (θye ) and
RMSE (θye ) . Among the four controllers, C3_NREL has the biggest
MAE (θye ) and RMSE (θye ) , which are 9.69 and 12.88, respectively.
C4_MY has smaller results, where MAE (θye ) and RMSE (θye ) are decreased by 17.86% (being 7.96) and by 17.93% (being 10.57), respectively. C1 and C2 have closer results, whereas C2 has the smallest
values, where MAE (θye ) and RMSE (θye ) are decreased by 35.71%
(being 6.23) and by 36.49% (being 8.18), respectively. These numerical
results are in good agreement with time series of yaw error shown in
Fig. 12(b), and they reveal that the developed two novel controllers
noticeably outweigh the other two controllers in reducing yaw error.
Table 5 also shows the total yaw action time (tyaw ) and yaw action
count (Cyaw ) of the four controllers during the day. Among the four
controllers, C3_NREL has the least yaw action time and action count,
which are 85.4 min and 168 times, respectively. C4_MY has a considerable yaw action time and action count, which are 359.4 min and
876 times, respectively. It means that the yaw actuators keep working
for one fourth of the time on that day, and are activated per two
minutes. The lengthy working time and frequent start may bring high
loads, thus shorten the lifetime of the yaw actuators. However, C1 has a
longer yaw time and frequenter action, which are increased by 45.6%
(being 523.3 s) and 57.2% (being 1377 times), respectively. The payback of reducing yaw error for C1 is enormous but reasonable, because
there is no time threshold for the C1. By comparison, C2 shows a satisfactory behavior: the yaw time is reduced by 8.6%, being 328.9 s,
whereas the yaw action count is decreased by 54.8%, going down to
622 times.
Finally, Table 5 shows the result of the reduction factor (ξ ) of different controller, the calculation of which is given in Appendix A. It can
be seen that C3_NREL has the most power reduction caused by the yaw
error, which is 4.53%, and C4_MY comes the second with the value of
Acknowledgments
This work is supported by the National Natural Science Foundation
of China under Grant 51777217, the Project of Innovation-driven Plan
in Central South University, the Australian Research Council under
Grant DE160100675 and the Project funded by China Postdoctoral
Science Foundation (2017M622605). This work is also financially
supported by the Basic Science Research Program through the National
Research Foundation of Korea (NRF) funded by the Ministry of
Education, NRF-2016R1A6A1A03013567.
Appendix A
The reduction factor ξ is calculated using Eqs. (6) and (7). To do this, θyej and their distribution probability ( f j ) are collected and calculated based
on the results in Fig. 12(b). The results of θyej and f j are shown in the form of histogram in Fig. 13(a) and (b), respectively. Based on these distribution
data, ξ of the four controllers can be calculated and obtained.
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Energy Conversion and Management 157 (2018) 587–599
D. Song et al.
Distribution probability [%]
5
Fig. 13. Distribution probability of yaw error
under (a) C4_MY and C3_NREL; (b) C1 and C2.
C3_NREL
C4_MY
4
3
2
1
0
-30
-20
-10
0
Yaw error [degree]
10
20
30
(a)
Distribution probability [%]
6
C1
C2
5
4
3
2
1
0
-30
-20
-10
0
Yaw error [degree]
10
20
30
(b)
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