Renewable Energy 129 (2018) 75e91
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Optimization of sizing parameters and multi-objective control of trailing edge flaps on a smart rotor Wenguang Zhang a, Xuejian Bai b, *, Yifeng Wang b, Yue Han b, Yong Hu b a
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, PR China b Beijing Key Laboratory of New Technology and System on Measuring and Control for Industrial Process, North China Electric Power University, Beijing 102206, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 October 2017 Accepted 27 May 2018 Available online 28 May 2018
In this study, a wind turbine model with a smart rotor is presented to optimize the sizing parameters of the trailing edge flap (TEF) and design the multi-objective TEF controller. The proposed model consists of TEF actuators, and the aerodynamic, applied load, structural, drive chain, and generator models. Additionally, under standard wind turbine control, the present model shows good agreements with FAST at different wind conditions. At the rated steady wind condition, the TEFs yield exactly the same effects as those elicited by FAST. An approach is proposed using two orthogonal experiments to optimize the TEF sizing parameters for maximizing the TEF effects on blade load alleviation and wind turbine output power smoothness. As a result, a group of optimal TEF sizing parameters is obtained. A multi-objective TEF controller adopting multivariable dynamic matrix control (MeDMC) and nonlinear dynamic matrix control (NeDMC) is used to control the flapwise blade root moment and output power. The simulations indicate that the average reduction rates of the flapwise root moment power spectral density (PSD) of blade 1 are within the range of 87e97% at 1 P frequency, and that the average reduction rate of the generator power standard deviation is within the range of 8e42%. © 2018 Elsevier Ltd. All rights reserved.
Keywords: Smart rotor model Trailing edge flaps Sizing parameter optimization Load alleviation Power smoothness Multi-objective control
1. Introduction With the rapid development of the global wind energy industry in recent years, the demand for improving the rated power of the wind turbine has increased in conjunction with the need for larger rotor diameters and longer blades. For instance, the Siemens SWTe8.0e154 wind turbine has a rated power of 8 MW and blades with a length of 75 m [1]. The aforementioned trend is prompted by the desire for increased generation capacity installations without excessive numbers of turbines [2]. However, large blades aggravate the issues of fatigue and extreme loads on wind turbines within their 20-year lifespan [3], thereby leading to increases in the weight and cost of components, and control difficulties. At present, traditional pitch control can adjust the aerodynamic properties of the blades by changing their pitch angles, but the performance of this approach is limited by the relatively slow pitch actuators and its capacity to preserve the actuators and blade bearings [4,5]. The TEF
* Corresponding author. E-mail address:
[email protected] (X. Bai). https://doi.org/10.1016/j.renene.2018.05.091 0960-1481/© 2018 Elsevier Ltd. All rights reserved.
device can effectively change the aerodynamic pressure distribution around the blade [6], in a similar manner to the ability of a structure to modify the aerodynamic properties of an airfoil by changing its camber. It is possible for TEF to compensate for the load variations due to the fluctuating local wind speed that the rotating blades are subjected to [5]. Adding a TEF to a blade is one of the ways used to achieve load alleviation in spite of the TEF's negative effect on the wind turbine output power. Extensive experimental work focusing on the development of TEF has been performed. At Sandia National Laboratories, a rotor has been designed, built, and tested with integrated sensors and rigid TEFs, and was installed on the 9 m long blades, ultimately showing that TEF can reduce microstrains effectively while the output power is reduced to a certain extent [7,8]. Castaignet et al. [3,9] performed a full-scale test on a Vestas V27 wind turbine equipped with one active 70 cm long TEF on one of the 13 m long blades. Results showed that an average flapwise blade root load reduction of 14% was achieved during a 38 min test by using a frequency-weighted model predictive control approach. Abdelrahman et al. [10] designed a modular blade based on an S833 airfoil with two individual activated TEFs, and they concluded from
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the field test that a) the relationship between the load reduction and the deflection angle is linear, and b) the highest reduction is caused by the TEF that is farthest from the rotor center. Apart from the experimental studies, other numerical investigations have been implemented on different types of aeroservoelastic platforms. Lackner et al. [11] investigated the load reduction capabilities of TEFs in the operation of a 5 MW wind turbine and compared a TEF feedback control approach with the individual pitch control in the aeroelastic design code GH-bladed. Chen et al. [12] utilized the aeroservoelastic multi-body code HAWC2 to investigate the blade optimization with individual pitch control and trailing edge flap control. Zhang et al. [13] investigated the influence of TEF's sizing and placement on the blade fatigue load reduction based on FAST/ Aerodyn codes. Recently, the optimization of the TEF sizing parameters has also been investigated. The optimization of the TEF sizing parameters is mainly focused on load alleviation or power capture. For load alleviation, Andersen et al. [6] investigated the optimum position for a flap on a 5 MW reference turbine, and concluded that for a stiff blade, the flap should be placed 59 m away from the blade root, whereas for a fully elastic blade this distance dropped to 45 m. Zhang et al. [13] investigated the effects of TEF's sizing and placement on blade fatigue load reduction and obtained an inexact group of TEF parameters. For power capture, Smit et al. [14] investigated the effects of the sizing and location of flap configuration on a possible increase in energy production and concluded that flap elements near the blade tip were the most effective. However, the optimization of the TEF sizing parameters that considered both the load alleviation and power smoothness, including power capture, and power fluctuation, have not been extensively studied or reported. Moreover, researchers have investigated the TEF control performance on load alleviation [5,6,9,10,12,15e23] or power capture [14]. In China, wind energy is mainly utilized in the form of largescale wind farms for grid-connected power generation. In 2016, the wind power curtailment reached 49.7 TW h due to the negative influence of the output power fluctuation generated by traditional wind turbines in wind farms on wind power integration [24]. As a result, a study of multi-objective TEF control on both load alleviation and power smoothness is urgently needed. To address this research problem, we develop herein a wind turbine model with a smart rotor and validate it by comparing it with FAST at Region 2, 3 step wind and the normal turbulent model (NTM) wind conditions in Section 2. And the TEF effects are also validated at the rated steady wind condition. In Section 3, an approach is proposed to optimize TEF sizing parameters for maximizing the effects of TEF on the blade load alleviation and wind turbine output power smoothness by utilizing two orthogonal experiments. In this way, the optimal group of TEF sizing parameters is validated via estimation approaches. In Section 4, a multiobjective TEF controller is presented adopting MeDMC and NeDMC to control flapwise blade root moment and output power, respectively. Finally, Section 5 outlines the conclusions of this study.
inputs to the rotor. Therefore, a modified version of FAST is developed to validate the present model. The present model is based on the NREL 5 MW reference wind turbine [26], as shown in Fig. 1.
2.1. Correction of lift and drag coefficient In this study, XFOIL [27] is used to design the airfoils with TEFs as well as rapidly calculate the lift and drag coefficient. However, XFOIL tends to weaken the stall effect and underestimate drag. Therefore, Fluent [28] is used to correct the lift and drag coefficients obtained by XFOIL. The comparison of the lift coefficient and drag coefficient of the NACA64_A17 airfoil is shown in Fig. 2. Compared to the original data from XFOIL, the correction data from Fluent has an obvious improvement, and is closer to the wind tunnel data.
2.2. Import of TEFs angles The lift coefficient Cl and drag coefficient Cd of the airfoil with TEF vary with the angle of attack a and the TEF angle g. In this study, XFOIL, Fluent, and AirfoilPrep [29] are utilized to obtain the airfoil aerodynamic data at different TEF angles. First, based on the original airfoil, XFOIL is applied to design the airfoils with TEFs. XFOIL is then utilized to calculate Cl and Cd at different a values. Third, Fluent is leveraged to correct Cl and Cd . AirfoilPrep is then used to generate the airfoil data files needed by Aerodyn [30] using a values that varying within the range of 180 to 180 . Finally, the 2D lift coefficient Cl ða; gÞ and drag coefficient Cd ða; gÞ data files are obtained by combining the airfoil data files, and the Cl ða; gÞ and Cd ða; gÞ coefficients can be determined at different a and g values by using an interpolation method from the 2D airfoil files.
2.3. Model description The present model consists of the TEF actuator, and the aerodynamic, applied load, structural, drive chain, and generator models (see Fig. 3). Considering the delay between the reference TEF angle signal and the actual TEF angle, a first-order low-pass filter model is used to describe the TEF actuator [31]. The TEF actuator model is
TEF1 TEF1
Blade 1
2. Modeling of wind turbine with smart rotor To research the optimal sizing parameters and the control performance of TEF, a wind turbine model with a smart rotor is developed in this section, which has TEF actuators installed on the blades. FAST, an open source code developed by the National Renewable Energy Laboratory (NREL) is a comprehensive aeroelastic simulator capable of predicting the extreme and fatigue loads of two- and three-bladed, horizontal-axis wind turbines [25]. However, the baseline version of FAST does not include TEFs as
Blade 3
TEF3
Fig. 1. Diagram for the smart rotor.
Blade 2
TEF2
W. Zhang et al. / Renewable Energy 129 (2018) 75e91
2.5
0.08 Wind tunnel data Original data from XFOIL Correction data from Fluent
1.5
Wind tunnel data Original data from XFOIL Correction data from Fluent
0.07
Drag coeffcient
2.0
Lift coefficient
77
1.0 0.5 0.0
0.06 0.05 0.04 0.03 0.02
-0.5
0.01
(a)
-1.0 -10
-5
0
5
10
15
0.00
20
(b) -10
Angle of attack [deg]
-5
0
5
10
15
20
Angle of attack [deg]
Fig. 2. Lift coefficient and drag coefficient of NACA64_A17 airfoil: (a) Lift coefficient and (b) drag coefficient.
TEF angles
TEF actuator model
Gravity loads Applied load model
Centrifugal loads Wind speed Aerodynamic model Pitch angles
Rotor torque
Aerodynamic loads
Structural model
Drive chain model
Generator model
Flapwise blade tip deflection Flapwise blade root moment
Generator angular speed Generator output power
Fig. 3. Diagram for the present model.
g_ ¼
1 ðg gÞ Tg r
b1
(1)
b3
where g denotes the actual TEF angles, gr denotes the reference TEF angles and Tg denotes the time constant. The aerodynamic model is based on BEM [32] for its rapid calculation and increased precision. Considering Prandtl's tip loss, Glauert correction, and that the TEF angles are imported as inputs, the aerodynamic load vector is calculated based on the aerodynamic model
paero ¼ ½ 0
pN
pT T
0 cos qtwist sin qtwist
0 cos qcone sin qtwist 54 sin qcone cos qtwist 0
sin qcone cos qcone 0
tilt
cone
The transformation matrix C bG , which transforms vectors from the global frame G into the undeformed blade frame b, is calculated by
1 C bG ¼ 4 0 0
B2 G2
(2)
32
B
G
G3
B1
b2 B3
G1
where pN denotes the load normal to the rotor plane, and pT denotes the load tangential to the rotor plane. Three main coordinate systems are chosen to describe the wind turbine, namely the global frame G, the undeformed blade frame b, and the deformed blade frame B, respectively [33], as shown in Fig. 4.
2
b
Fig. 4. Diagram for the coordinate systems of the wind turbine.
3
0 05 1
C BG ¼ C bG C
(3)
where
where qcone denotes the rotor cone angle (see Fig. 4), and qtwist denotes the twist angle of each blade element.
The transformation matrix C BG , which transforms vectors from the global frame G into the undeformed blade frame B is calculated by
C¼
(4)
T T ~ 1 14qG qG D þ 12qG qG q G T
1 þ 14qG qG
(5)
T denotes the transpose operator, D denotes the 3 3 identity
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Jr
matrix, and qG ¼ 2 tanðbr =2ÞðC bG ÞT e, where br denotes the rotation magnitude, e ¼ ½ e1 e2 e3 T , and eT e ¼ 1. The gravity load is a sinusoidal load owing to the earth's gravitational field [32]. Considering that the tilt angle is qtilt (see Fig. 4) and the azimuthal angle is qwing , the gravity load of a blade element with respect to the global frame G is
2
cos qwing 0 sin qwing 2 3 gm 4 0 5 0
4 pG g ¼
0 1 0
32
sin qwing cos qtilt 54 sin qtilt 0 cos qwing 0
sin qtilt cos qtilt 0
3
Tr
K
0 05 1
TL
TH
JG
N
C L
H
G
TG
(6) where g denotes the gravity constant, and m is the mass per unit length of each blade element. The gravity load of a blade element with respect to the deformed frame B is
pBg ¼ C BG pG g
(7)
The centrifugal load is caused by the rotation of the wind turbine, and the centrifugal load of a blade element with respect to the global frame G is
2 pG c ¼ ru m
0
0
T
(8)
r Fig. 5. Equivalent diagram of the drive chain model.
The generator model is acquired by modifying doubly fed induction generator (DFIG) demo in MATLAB/Simulink under Reference [35]. The parameters of the 5 MW generator are based on reference [36], as shown in Fig. 6. 2.4. Model validation
where r denotes the local radius, and u denotes the angular velocity of the rotor. The centrifugal load of the blade element with respect to the deformed frame B is
At Region 2, 3 step wind and NTM wind conditions, the present model is validated by FAST using standard wind turbine control [37].
pBc ¼ C BG pG c
2.4.1. Validation of wind turbine performance based on a step wind in Region 2 The time series is obtained using an 800 s simulation of the present model for a step wind speed increase of 1 m/s every 100 s, i.e., the wind condition is considered to be a step wind function with velocity ranging from 4 to 11 m/s in Region 2 below the rated operation. Compared to FAST, the maximum deviation of the flapwise root moment of blade 1, flapwise tip deflection of blade 1, angular speed of generator and output power of generator are 3.16%, 1.96%, 0.21%, and 0.51% respectively, as shown in Fig. 7.
(9)
As mentioned before, the applied load of the blade element is constituted by the aerodynamic load, gravity load, and centrifugal load, with respect to the deformed frame B, and is expressed as
pAL ¼ paero þ pBg þ pBc
(10)
The structural model is based on a multi-modal flexible model [34], which is formulated to describe the flapwise deformation of the blades. The drive chain model of a wind turbine can be regarded as a system consisting of a finite number of inertial, elastic, and damping units. In this study, the drive chain model adopts a twomass model that neglects the moment of inertia of the gearbox wheels and treats the high-speed shaft as a rigid shaft, and the lowspeed shaft as a flexible shaft (see Fig. 5). The dynamic equations of drive chain system are as follows
8 > qr Tr TL ¼ Jr ,€ > > > > T ¼ K,ð q qL Þ þ C q_ r q_ L > r > < L TL ¼ N,TH > qL ¼ qH =N > > > > > q ¼ qG > : H TH TG ¼ JG ,€ qG
2.4.2. Validation of wind turbine performance based on a step wind in Region 3 The time series is obtained using a 1400 s simulation of the present model for a step wind increase of 1 m/s every 100 s, i.e., the wind condition is a step wind condition with velocities ranging from 11 to 24 m/s in Region 3 above the rated operation. Compared to FAST, the maximum deviation of the flapwise root moment of blade 1, flapwise tip deflection of blade 1, pitch angle of blade 1, and output power of the generator are 9.97%, 5.71%, 0.58%, and 0.89%, respectively, as shown in Fig. 8.
(11)
where Jr and JG denote the moment of inertias of the rotor and generator, respectively, qr , qL , qH , and qG , denote the rotation angles of the rotor, low-speed shaft, high-speed shaft and generator respectively, Tr , TL , TH , and TG , denote the torques of the rotor, lowspeed shaft, high-speed shaft, and generator respectively, K and C denote the stiffness and the damping constants of the low-speed shaft, and N denotes the gearbox ratio.
Fig. 6. Generator model of the 5 MW wind turbine.
0
(a) 0
200
400
600
800
Time [s] 150
Present model FAST
100
50
0
(c) 0
200
400
600
800
Flapwise tip deflection of blade 1[m]
5000
Output power of generator [kW]
Present model FAST
10000
Angular speed of generator [rad/s]
Flapwise root moment of blade 1 [kNm]
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2
0
(b) 0
200
400
600
800
Time [s]
6000
Present model FAST 4000
2000
0
(d) 0
200
Time [s]
400
600
800
Time [s]
10000
5000
0
(a) 0
200
400
600
800
1200
1400
Time [s] 30
Pitch angle of blade 1 [deg]
1000
Present model FAST
25 20 15 10 5 0
(c) 0
200
400
600
800
Time [s]
1000
1200
1400
Flapwise tip deflection of blade 1 [m]
Present model FAST
Output power of generator [kW]
Flapwise root moment of blade 1 [kNm]
Fig. 7. Wind turbine performance based on step wind with wind speeds in the range of 4e11 m/s: (a) flapwise root moment of blade 1, (b) flapwise tip deflection of blade 1, (c) angular speed of generator, and (d) output power of generator.
Present model FAST
6
4
2
0
(b) 0
200
400
600
800
1000
1200
1400
Time [s]
8000
Present model FAST
7000 6000 5000 4000 3000 2000
(d)
1000 0
0
200
400
600
800
1000
1200
1400
Time [s]
Fig. 8. Wind turbine performance based on step wind for velocities ranging from 11 to 24 m/s: (a) flapwise root moment of blade 1, (b) flapwise tip deflection of blade 1, (c) pitch angle of blade 1, and (d) output power of generator.
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2.4.3. Validation of wind turbine performance at the NTM wind condition The time series is obtained using a 300 s simulation of the present model for an NTM wind condition with 5% turbulence intensity and a mean wind speed of 11.4 m/s, as generated by Turbsim [38]. Compared to FAST, the maximum deviation of the flapwise root moment of blade 1, flapwise tip deflection of blade 1, pitch angle of blade 1, and output power of the generator are 12.06%, 9.35%, 10.48%, and 1.65%, respectively, as shown in Fig. 9. 2.4.4. Validation of TEF effects at the rated steady wind condition To compare the influence of TEF in the present model and in the modified version of FAST, a 300 s simulation is used on the 11.4 m/s steady wind condition. The TEF sizing parameters in this section are determined according to the conclusion in Ref. [13]. Fig. 10 shows the flapwise root moment and the flapwise tip deflection in different TEF angle variation conditions. Compared to FAST, the maximum deviation of flapwise root moment of blade 1 and flapwise tip deflection of blade 1 are 3.54% and 3.02%, respectively, as respectively shown in Fig. 10(a) and (b). Additionally, compared to the modified version of FAST, the maximum deviation of flapwise root moment of blade 1 and flapwise tip deflection of blade 1 are 2.54% and 4.66%, respectively, as respectively shown in Fig. 10(c) and (d). In conclusion, at Region 2, 3 step wind and NTM wind conditions, the wind turbine performance and the TEF effects predicted by the present model and established in this section are in good agreement with FAST. The time domain results show the same overall trend, and only a slight difference is reported.
eight airfoils [26]. For an orthogonal experimental design, the blade comprises 29 blade elements. Definition of these elements is achieved by dividing the blades into a series of elements with a length of 2.05 m starting from the DU35_A17 airfoil to the NACA64_A17 airfoil. The structural diagram of the NREL 5 MW blade is shown in Fig. 11. 3.1. Orthogonal experimental design TEF can potentially reduce the flapwise blade root fatigue load, but it also reduces the output power of the wind turbine. Thus, the orthogonal experimental design optimizes the TEF sizing parameters, including the TEF length, angle range, chord length ratio, and central position, to meet the following two optimization objectives: A. Maximize the effect of TEF on blade load alleviation B. Maximize the effect of TEF on wind turbine output power smoothness Considering the optimization objectives listed above, the optimization experiment indicators are obtained as follows: 1) For objective A: the variation ratio of the flapwise blade root moment y1 , the variation ratio of the flapwise blade root moment standard deviation y2 , the variation ratio of the flapwise blade tip deflection y3 , and the variation ratio of flapwise blade tip deflection standard deviation y4 2) For objective B: the variation ratio of the output power of generator y5 and the variation ratio of the output power of the generator standard deviation y6
3. Optimization of TEF sizing parameters
Present model FAST
12000
8000
4000
0
(a) 0
50
100
150
200
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300
Time [s]
Pitch angle of blade 1 [deg]
8
Present model FAST
6
4
2
0
(c) 0
50
100
150
Time [s]
200
250
300
Flapwise tip deflection of blade 1 [m]
16000
The wind condition of the orthogonal experiment design is for a steady wind of 11.4 m/s. In the present model, a time-domain
Output power of generator [kW]
Flapwise root moment of blade 1 [kNm]
The length of the NREL 5 MW blade is 61.5 m and consists of
Present model FAST
8
6
4
2
0
(b) 0
50
100
150
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250
200
250
300
Time [s] Present model FAST
8000
6000
4000
2000
0
(d) 0
50
100
150
300
Time [s]
Fig. 9. Wind turbine performance on a wind speed of 11.4 m/s at the NTM wind condition: (a) flapwise root moment of blade 1, (b) flapwise tip deflection of blade 1, (c) pitch angle of blade 1, and (d) output power of the generator.
W. Zhang et al. / Renewable Energy 129 (2018) 75e91
30 20
8000
10
TEF angle with step change
0 -10
0
0
50
100
150
200
250
20
4
0
2
-10 0
50
100
60 50 40 30
8000
20
TEF angle with periodic change
10
4000
0
Flapwise tip deflection of blade 1 [m]
Flapwise root moment of blade 1 [kNm]
Present model Modified version of FAST
12000
0
-10 0
50
100
150
150
200
250
300
Time [s] 10
TEF angle [deg]
(c)
10
TEF angle with step change
Time [s] 16000
40 30
6
0
300
(b)
8
50
200
250
Present model Modified version of FAST
60 50 40
6
30
4
TEF angle with periodic change
2 0
300
(d)
8
20 10 0
TEF angle [deg]
4000
Present model Modified version of FAST
TEF angle [deg]
40
12000
Flapwise tip deflection of blade 1 [m]
(a)
10
50
Present model Modified version of FAST
TEF angle [deg]
Flapwise root moment of blade 1 [kNm]
16000
81
-10 0
50
Time [s]
100
150
200
250
300
Time [s]
Fig. 10. Time domain results of TEF effects on a wind speed of 11.4 m/s at a steady wind condition: (a) flapwise root moment of blade 1 (TEF angle with step change), (b) flapwise tip deflection of blade 1 (TEF angle with step change), (c) flapwise root moment of blade 1 (TEF angle with periodic change), and (d) flapwise tip deflection of blade 1 (TEF angle with periodic change).
Cylinder1 Cylinder2 DU40_A17 5.60m DU35_A17 DU30_A17 8.33m DU25_A17 11.75m 19.95m
DU21_A17
NACA64_A17
24.05m 32.25m 40.45m 61.50m Fig. 11. Structural diagram for NREL 5 MW blade.
simulation is performed within a period of 300 s without TEFs using standard wind turbine control. The simulation data from 100 to 300 s are chosen for analysis to avoid the start of a wind turbine. The parameter values of the wind turbine without the TEFs are listed in Table 1. The variation ratios of the six parameters above are
Table 1 Parameter values of wind turbine without TEFs.
yi ðkÞ ¼
~i ðkÞ b yi y ði ¼ 1; 2; 3; 4; 5; 6Þ b yi
~i denotes the where b y i denotes the parameter values without TEFs, y parameter values with TEFs, and k denotes the kth experiment. Additionally, the normalized change rates of these six parameters are
yinor ðkÞ ¼
Parameters
Unit
Values
Average of flapwise blade root moment b y1 standard deviation of flapwise blade root moment b y2 Average of flapwise blade tip deflection b y3 standard deviation of flapwise blade tip deflection b y4 Average of output power of generator b y5 standard deviation of output power of generator b y6
kN$m kN$m m m kW kW
10107.96 269.97 5.38 0.15 5339.94 0.19
(12)
yi ðkÞ ði ¼ 1; 2; 3; 4; 5; 6Þ maxfyi ð1Þ; yi ð2Þ; yi ð3Þ; /g (13)
For objective A, smaller values of b y1, b y2 , b y 3 , and b y 4 , refer to better load alleviation. For objective B, larger values of b y 5 represent better power capture, while smaller b y 6 values indicate less power fluctuation, and they both represent better power smoothness performance. Comprehensive score indices are designed to
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estimate the effects of TEFs. After normalization processing, larger values of y1nor ðkÞ, y2nor ðkÞ, y3nor ðkÞ, and y4nor ðkÞ, indicate better effects on blade load alleviation, while smaller values of y5nor ðkÞ and y6nor ðkÞ indicate better effects on wind turbine output power smoothness. To meet the optimization objectives listed above, two comprehensive score indices are proposed in accordance to
z1 ðkÞ ¼ y1nor ðkÞ þ y2nor ðkÞ þ y3nor ðkÞ þ y4nor ðkÞ y5nor ðkÞ y6nor ðkÞ (14)
z2 ðkÞ ¼
1 ½y ðkÞ þ y2nor ðkÞ þ y3nor ðkÞ þ y4nor ðkÞ 4 1nor 1 ½y5nor ðkÞ þ y6nor ðkÞ 2
(15)
The TEF sizing parameters, which are also the four factors in the orthogonal experiment, including TEF length A, angle range B, chord length ratio C and central position D. Factor A comprises 9 levels (1e9 times blade element length of 2.05 m), factor B comprises 4 levels (2.5e2.5 , 5 to 5 , 7.5e7.5 , and 10 to 10 ), factor C comprises 10 levels (5%, 10%, /, 45%, 50%), and factor D comprises 19 levels (10the28th blade element). This optimization experimental design is made up of two orthogonal experiments because of the high number of factors levels.
1 2 3 4 5
Factor A 1 3 5 7
Factor B
2.5e2.5 5 to 5 7.5e7.5 10 to 10
The factors and levels for the first orthogonal experiment are selected evenly, as listed in Table 2. As listed in Table 3, the first orthogonal table is in the form of L25 ð42 52 Þ, which is modified by orthogonal table of L25 ð56 Þ [39]. According to Table 3, under standard wind turbine control and individual flap proportion-integration-differentiation (PID) control, 25 simulations with different TEF parameters are performed. The results of first range analysis are listed in Table 4, and the importance of the factors is A > D > B > C, while the optimal group of the TEF sizing parameters obtained by range analysis is A4B4C2D5. Variance analysis is performed to obtain the optimal TEF sizing parameters. Table 5 lists the F ratios of the first variance analysis in which the symbol * denotes significant factors. Table 6 lists the results of the first variance analysis, and the optimal group of the TEF sizing parameters obtained by variance analysis is A3B4C2D4. According to the 25 group simulation results and the two group simulation results from the range analysis and variance analysis in accordance to Eqs. (12)e(15), the normalized change rates of the 27 group parameters and the comprehensive score indices are shown in Fig. 12. The largest comprehensive score indices z1 and z2 occur in the 19th experiment. Thus, the optimal group of the TEF sizing parameters in the first orthogonal experiment is A4B4C2D5, i.e., the TEF length A is 7 times of 2.05 m, angle range B is 10 to 10 , the chord length ratio C is 20%, and the central position D is 26th. 3.3. Second orthogonal experiment
Table 2 Factors and levels of the first orthogonal experiment. Level
3.2. First orthogonal experiment
Factor C
Factor D
10% 20% 30% 40% 50%
10 14 18 22 26
Based on the results of the first orthogonal experiment, the factors and levels of the second orthogonal experiment are listed in Table 7. The second orthogonal table is in the form of L25 ð42 52 Þ, which is modified in Table 3 by replacing factor A with factor D in the table header. Under standard wind turbine control and individual flap
Table 3 Orthogonal table of L25 ð42 52 Þ. Factors
Factor A
Factor C
Factor D
Experiment No.\Column No.
10
1
Factor B 20
2
3
4
5
6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 1 1 1 1 1
1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5
1 2 3 4 1 1 2 3 4 1 1 2 3 4 1 1 2 3 4 1 1 2 3 4 1
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
1 2 3 4 5 2 3 4 5 1 3 4 5 1 2 4 5 1 2 3 5 1 2 3 4
1 2 3 4 5 3 4 5 1 2 5 1 2 3 4 2 3 4 5 1 4 5 1 2 3
1 2 3 4 5 4 5 1 2 3 2 3 4 5 1 5 1 2 3 4 3 4 5 1 2
1 2 3 4 5 5 1 2 3 4 4 5 1 2 3 3 4 5 1 2 2 3 4 5 1
W. Zhang et al. / Renewable Energy 129 (2018) 75e91
83
Table 4 Results of first range analysis. Parameters
Factors importance order
The best level\the second best level A
A>B>D>C A>D>B>C D>B>A>C D>A>B>C B>C>A>D A>B>D>C A>D>B>C
y1 y2 y3 y4 y5 y6 Results
B
10 to 10 \e7.5e7.5 7.5e7.5 \e10 to 10 10 to 10 \e7.5e7.5 5 to 5 \e7.5e7.5 2.5e2.5 \e5 to 5 5 to 5 \e10 to 10 10 to 10
5\7 7\5 5\7 7\5 1\3 7\1 7
Table 5 F ratios of the first variance analysis. Factors
y1
y2
y3
y4
y5
y6
A B C D
6.44* 6.36* 2.50 3.72*
10.86* 3.92* 0.56 4.24*
5.32* 5.76* 1.08 5.96*
5.97* 3.07 0.37 5.93*
5.68* 7.43* 3.88* 2.39
1.40 3.79* 0.99 0.84
C
D
50%\40% 20%\50% 50%\40% 10%\20% 20%\10% 20%\30% 20%
26th\18th 26th\22nd 22nd\18th 22nd\18th 26th\10th 26th\10th 26th
simulation results based on range and variance analyses in accordance to Eqs. (12)e(15), the normalized change rates of the 27 group parameters and the comprehensive score indices are shown in Fig. 13. The largest comprehensive score indices z1 and z2 occur in the 26th experiment. Thus, the optimal group of the TEF sizing parameters is A3B4C4D3. 3.4. Optimal parameter validation
Table 6 Results of the first variance analysis. Parameters
Significance factors
The best level of groups\the second best level of groups
y1 y2 y3 y4 y5 y6
A>B>D A>D>B D>B>A A>D B>A>C B
A3B4D4\ A4B3D3 A4D5B3\ A3D4B4 D4B4A3\D3B3A2 A4D4\A3D3 A1B1C2\A3B4C1 B2\B4
To validate the accuracy of the optimal group obtained in the orthogonal experiment, it is necessary to estimate the intervals of the optimal group parameters [39], which are verified by the actual simulation results. 3.4.1. Point estimation According to the statistical models of the analysis methods, the
Table 7 Factors and levels of the second orthogonal experiment.
PID control, 25 simulations with different TEF parameters are performed. Table 8 lists the results of the second range analysis. The importance of the factors is A > C > B > D, and the optimal group of the TEF sizing parameters obtained by range analysis is A3B4C4D3. According to the 25 group simulation results and the two group
Level
Factor A
Factor B
Factor C
Factor D
1 2 3 4 5
5 6 7 8 9
2.5e2.5 5 to 5 7.5e7.5 10 to 10
10% 15% 20% 25% 30%
23 24 25 26
7 6
0.8 0.6
5
0.4 4
0.2 0.0 -0.2
y1 y2
-0.4
y3
-0.6
y5
-0.8
3
2.71
2
y4 z1
y6
0.55
z2
1 0
-1.0 5
10
15
20
25
Experiment No. Fig. 12. Normalized change rates and comprehensive score indices of the first orthogonal experiment.
Values of score index
Normalized change rates of parameters
1.0
84
W. Zhang et al. / Renewable Energy 129 (2018) 75e91
Table 8 Results of the second range analysis. The F ratios of variance analysis are listed in Table 9, whereby the symbol * denotes significant factors. Parameters
Factors importance order
The best level\the second best level A
A>C>B>D C>D>B>A A>C>B>D A>D>C>B C>A>B>D A>B>C>D A>C>B>D
y1 y2 y3 y4 y5 y6 Results
B
7.5e7.5 \e10 to 10 5 to 5 \e7.5e7.5 10 to 10 \e7.5e7.5 10 to 10 \e7.5e7.5 2.5e2.5 \e5 to 5 10 to 10 \e7.5e7.5 10 to 10
7\5 9\8 7\5 9\8 7\6 7\5 7
Table 9 F ratios of the second variance analysis. The results of the second variance analysis are summarized in Table 10, and the optimal group of the TEF sizing parameters obtained by variance analysis is A2B4C2D5. Factors
y1
y2 *
A B C D
6.61 1.58 3.55* 0.32
1.37 3.72* 5.86* 5.17*
y3
y4 *
4.54 1.65 4.12* 0.36
y5 *
6.06 1.80 1.21 4.46*
y6 *
3.81 1.70 3.78* 0.29
2.15 3.80* 1.63 1.53
estimations of the general mean and effect of every factor level can be obtained with the least-squares method. Based on Table 10, the significance factors of y1 are A and C, and the estimations of A3C4 are
8 > >
> c 4 ¼ T C4 y1 ¼ 0:046% :b
(16)
D
15%\20% 30%\25% 25%\20% 25%\30% 10%\30% 25%\30% 25%
23rd\24th 25th\26th 24th\25th 25th\24th 26th\25th 25th\23rd 25th
Parameters
Significance factors
The best level of groups\the second best level of groups
y1 y2 y3 y4 y5 y6
A>C C>D>B A>C A>D A>C B
A2C2\ A3C3 C5D5B2\ C4D4B4 A1C2\A2C3 A2D5\A1D4 A4C1\A2C2 B4\B3
where Se denotes the quadratic error sum, and fe denotes the DOF of the error. To improve the accuracy of the variance estimation, the following equation is required
Se ¼ Se þ S0 fe ¼ fe þ f0
(21)
The confidence interval of y1 in 1 a is
(17)
3.4.2. Interval estimation b 3:4: is the linear combination of the independent Assume that m normal variables y1;1 ; y1;2 ; /; y1;i ; /; y1;n (where y1;i denotes the value of y1 in the ith experiment of the second orthogonal experiment), and it is expressed as
bþb b 3:4: ¼ m m a3 þ b c4 ¼ T A3 þ T C4 y1 25 X ¼ ki y1;i
C
Table 10 Results of the second variance analysis.
b denotes the estimations of the general mean, y1 denotes where m the mean of the 25 y1 values elicited in the second orthogonal experiment, b a 3 denotes the estimation of factor A in level 3, b c4 denotes the estimation of factor C in level 4, T A3 denotes the factor A mean of y1 in level 3, and T C4 denotes the estimation of factor C as the mean of the y1 values in level 4. The unbiased estimation of y1 in the group A3C4 is
bþb b 3:4: ¼ m m a3 þ b c 4 ¼ 0:295%
(18)
b 3:4: ±t1a ðfe Þ b m s 2 b ¼ where s
pffiffiffiffiffi ne
(22)
pffiffiffiffiffiffiffiffiffiffiffi Se =fe . Then we obtain
8 Se ¼ Se þ SB þ SD ¼ 0:0004% > > < fe ¼ fe þ fA þ fD ¼ 17 qffiffiffiffiffiffiffiffiffiffiffi > s ¼ Se =fe ¼ 0:0005 >b : t0:995 ð17Þ ¼ 2:898
(23)
and the confidence interval of y1 in 0.99 is
0:0005 0:295%±2:898 pffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:381%; 0:208%Þ 2:778
(24)
Similarly, the confidence intervals of y2 , y3 , y4 , y5 , and y6 in 0.99 can be obtained. As listed in Table 11, the actual simulation values using the optimal group of TEF sizing parameters falls within the confidence interval of 0.99. These results indicate that the orthogonal experiment is accurate and the optimal group A3B4C4D3 meets
i¼1
b 2:2: is The variance of m
X 25 9 s2 b 3:4: ¼ Var m ki s2 ¼ s2 ¼ 25 ne i¼1
(19)
then ne ¼ 2:778. The unbiased estimation of s2 is
sb 2 ¼ Se =fe
(20)
Table 11 Comparison of the confidence intervals of each indicator and actual simulation values under the optimal group of TEF sizing parameters. Parameters Unbiased estimation y1 y2 y3 y4 y5 y6
b 3:4: m b :443 m b 3:4: m b 3::3 m b 3:4: m b :44: m
Confidence interval in 0.99
Actual simulation values
(e0.381%, 0.208%) (e138.494%, 82.709%) (e0.375%, 0.195%) (e55.870%, 19.926%) (e0.831%, 0.462%) (e14.043%, 60.151%)
0.344% 95.827% 0.247% 42.541% 0.601% 10.133%
W. Zhang et al. / Renewable Energy 129 (2018) 75e91
85
8
0.8
7
0.6 6
0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8
5
y1 y2
z1
y3
z2
y4
4 3
y5 2.44
y6
2
Values of score index
Normalized change rates of parameters
1.0
-1.0 1
-1.2
0.42
-1.4
0 5
10
15
20
25
Experiment No. Fig. 13. Results of the second orthogonal experiment.
TEF11 TEF12 22nd ~24th
25th ~28th
Fig. 14. Diagram of the optimal TEFs on blade 1.
the optimization objectives. Orthogonal experiments on steady wind speeds of 8 m/s and 16 m/s yield the same optimal group of TEF sizing parameters with those elicited at a steady wind speed of 11.4 m/s, which indicates that the optimal group is suitable for regions 2 and 3 and for rated wind conditions. In conclusion, the optimal group of TEF sizing parameters is A3B4C4D3, i.e., the TEF length A is 14.35 m, the angle range B is 10 to 10 , the chord length ratio C is 25%, the central position D is in the 25th blade element of 53.775 m, and the TEF is located on the blade elements from 22nd to 28th in the NACA64_A17 airfoil. 4. TEFs controller design TEFs can reduce fatigue load and adjust the output power of a generator. In this section, a multi-objective TEF controller is designed to decrease the variation of the flapwise blade root moment and smooth the output power. According to the optimal group of the TEF sizing parameters, two TEFs are installed on each blade, as shown in Fig. 14. 4.1. Multi-objective TEF controller According to Table 6, the larger central position of TEF shows a better effect on load alleviation. Therefore, TEF12, TEF22, and TEF32, are utilized for flapwise blade root moment control, while TEF11, TEF21, and TEF31, are utilized for power control. The dynamic matrix control (DMC) approach is applied in this study. For flapwise blade root moment control, MeDMC is aimed at decreasing the sinusoidal variation of flapwise blade root moment caused by the rotor rotation. This is achieved by controlling the
angles of TEF12, TEF22, and TEF32 which vary in a sinusoidal motion. For power control, the aim of the use of NeDMC is to smooth the output power. This is achieved by controlling the angles of TEF11, TEF21, and TEF31. Therefore, the coupling between the MeDMC and NeDMC is weak, and the two approaches can be controlled independently by neglecting their respective influences. The MeDMC adopts the individual flap control strategy, which uses the Coleman transform to convert a rotating coordinate system into a fixed coordinate system. The NeDMC adopts the generator angular speed as a feedback signal and the mean value of the generator angular speed in the previous 20 s as set value. The diagram of the multi-objective TEFs controller is shown in Fig. 15. The Coleman transform of the flapwise blade root moment is
0 3 cm ðtÞ Mave 1 1 cm 4 Myaw ðtÞ 5 ¼ @ 2 sin 41 ðtÞ 3 cm 2 cos 41 ðtÞ Mtilt ðtÞ 2 3 My1 ðtÞ 4 My2 ðtÞ 5 My3 ðtÞ 2
1 2 sin 42 ðtÞ 2 cos 42 ðtÞ
1 1 2 sin 43 ðtÞ A 2 cos 43 ðtÞ
(25) where My1 ðtÞ, My2 ðtÞ, and My3 ðtÞ denote the flapwise root moments of blade 1, 2, and 3 respectively, 41 ðtÞ, 42 ðtÞ, and 43 ðtÞ denote the cm ðtÞ, M cm ðtÞ, azimuth angles of blade 1, 2, and 3 respectively, Mave yaw cm ðtÞ denote the average, yaw wise, and tilt wise moments and Mtilt respectively. After obtaining the output control variable of MeDMC, the inverse Coleman transform of TEF angles is
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W. Zhang et al. / Renewable Energy 129 (2018) 75e91
3 0 gr12 ðtÞ 1 4 gr22 ðtÞ 5 ¼ @ 1 gr32 ðtÞ 1 2
sin 41 ðtÞ sin 42 ðtÞ sin 43 ðtÞ
3 12 cm gave ðtÞ cos 41 ðtÞ cm A 4 gyaw ðtÞ 5 cos 42 ðtÞ cos 43 ðtÞ gcm ailt ðtÞ
~1 ðk þ 1Þ eðk þ 1Þ ¼ yðk þ 1Þ y (26)
cm cm where gcm ave ðtÞ, gyaw ðtÞ, and gtilt ðtÞ denote the average, yaw wise, and tilt wise of TEF angles respectively, and gr12 ðtÞ, gr22 ðtÞ, and gr32 ðtÞ denote the reference angles of TEF12, TEF22, and TEF32 respeccm ðtÞ and gcm ðtÞ are ignored. tively. For this control strategy, Mave ave
~1 ðk þ 1jkÞ denote the actual and predicted where yðk þ 1Þ and y values at time k þ 1, respectively. The prediction of the output value ~cor ðk þ 1Þ is y y cor ðk
þ 1Þ ¼ y N1 ðkÞ þ heðk þ 1Þ 2
where 4.2. Dynamic matrix control
∞ X
ai Duðk iÞ
(27)
i¼1
where Duðk iÞ denotes the input gain value at time k i, and ai denotes the model parameter. The predicted values of output [41] ~M ðk þ ijkÞ along the horizon is y
~0 ðk þ ijkÞ þ ~M ðk þ ijkÞ ¼ y y
minðM;iÞ X
þ ADuM ðkÞ
(29)
2 3 3 ~M ðk þ 1jkÞ ~0 ðk þ 1jkÞ y y 6 6 7 7 ¼ 4 « « 5, y P0 ðkÞ ¼ 4 5 and A ¼ ~M ðk þ PjkÞ ~0 ðk þ PjkÞ y y 3 0 7 « 7 a1 7 7. 5 «
y PM ðkÞ
2
a1 / 6 « 1 6 6 am / 6 4 « 1 aP / aPMþ1 For rolling optimization, a cost function JðkÞ is calculated to minimize the controlled variable deviation and smoothen the rapid change of the control variable at each step time
minJðkÞ ¼
P X
M h i2 X ~M ðk þ ijkÞ þ qi wðk þ iÞ y rj Du2 ðk þ j 1Þ
i¼1
where wðk þ iÞ denotes the set value of the controlled variable, qi denotes the weight of the output deviation, and rj denotes the weight of the controlled variable deviation.
For feedback compensation, the predicted value y N1 ðkÞ at time k is
¼ y N0 ðkÞ þ aDuðkÞ
þ 1Þ ¼ Sy cor ðk þ 1Þ
(34)
3 0 1 0 7 6« 1 1 7. where S ¼ 6 4« 0 15 0 / 0 1 For MeDMC, the basic equations remain the same, except that the matrices and vectors become large and appropriately partitioned [41]. The vector of the predicted outputs is now defined as 2
iT h ~ ¼ y1 ðt þ 1jtÞ; /; y1 ðt þ p1 jtÞ; /; yny ðt þ 1jtÞ; /; yny t þ pny t y
u ¼ ½Du1 ðtÞ;/; Du1 ðt þ m1 1Þ;/; Dunu ðtÞ;/; Dunu ðt þ mnu 1ÞT (36) For NeDMC, an output correction is added after feedback compensation to correct the control variable error caused by the nonlinear character of the control object. The output correction is
~ ðkÞ uðk 1Þ þ Gðuðk 1ÞÞ uðkÞ ¼ F aðNÞ, u
(37)
~ ðkÞ denote the control variables after and before where uðkÞ and u the output correction respectively, aðNÞ denotes the model vector, FðxÞ denotes the function in which the generator angular speed is input and in which the TEF angle is output, GðxÞ denotes the inverse function of FðxÞ, FðxÞ and GðxÞ are obtained with the least squares fitting method. In this study, the maximum range and the rates range of the TEF angles are 10 to 10 and 100 to 100 /s respectively. 4.3. Results and discussion
j¼1
(30)
y N1 ðkÞ
þ 1Þ at time kþ1 is
y N0 ðk
(28)
2
where
y N0 ðk
(35)
~0 ðk þ ijkÞ denotes the initial predicted value. Eq. (28) yields where y
¼
3 ~cor ðk þ 1jk þ 1Þ y 7 T « 5, h ¼ ½h1 ; /; hN denotes ~cor ðk þ Njk þ 1Þ y
and the array of future control signals is
¼ 1; /; N
y P0 ðkÞ
6 1Þ ¼ 4
aijþ1 Duðk þ j 1Þ; i
j¼1
y PM ðkÞ
y cor ðk þ
(33)
the weight coefficient vector. Finally, the initial predicted value
DMC is a development of model predictive control based on the step response of a control object [40]. DMC involves three steps: the prediction model, rolling optimization, and feedback compensation. For the prediction model, the step response model is
yðtÞ ¼
(32)
(31)
where y N0 ðkÞ denotes the free response vector at time k, and a ¼ ½a1 ; a2 ; /; aN T denotes the model vector. The output error eðk þ 1Þ is
A 600 s simulation is performed for an NTM wind condition with 3% turbulence intensity and a mean wind speed of 11.4 m/s in instances where no TEF, PIDeTEF, and DMCeTEF controls are applied. Fig. 16 and Table 12 show the simulation results. Fig. 16(a) and (b) show the control effect on flapwise blade root moment control. In Fig. 16(a), PIDeTEF control and DMCeTEF control reduce the flapwise root moment of blade 1. Correspondingly, the standard deviation of the reduction rates of the flapwise root moment of blade 1 during the period of 200 and 500 s are 21.88% and 23.74%, respectively. In Fig. 16(b), PIDeTEF control and DMCeTEF control reduce the PSD of blade 1 and the flapwise root moment at the 1 P frequency. The reduction rates are 72.48% and 80.99%, respectively. Fig. 16(c) and (d) show the control effect on power control. In Fig. 16(c), PIDeTEF control and DMCeTEF control the reduction of
W. Zhang et al. / Renewable Energy 129 (2018) 75e91
87
Fig. 15. Diagram of multi-objective TEFs controller.
the fluctuation of the generator's angular speed. Correspondingly, the standard deviation reduction rates of the generator angular speed during the period of 200 and 500 s are 14.51% and 25.41%, respectively. In Fig. 16(d), the generator output power is increased below the rated power and decreased above the rated power. This indicates that the applications of PIDeTEF control and DMCeTEF control can smooth the generator output power. Thus, the standard deviation reduction rates of the generator output power during the period of 200 and 500 s are 14.64% and 25.25%, respectively. In general, PIDeTEF control and DMCeTEF control can both achieve the control objectives by decreasing the variation of flapwise blade root moment and generating a smoother output power. Compared with PIDeTEF control, DMCeTEF control yields better control effects. Fig. 17 and Table 13 show the pitch angles and TEF angle results. In Fig. 17(a), PIDeTEF control and DMCeTEF control both reduce the total pitch motion time and pitch angle of blade 1. The reduction rates of the PIDeTEF control are 2.86% and 33.17%, respectively, and the reduction rates of DMCeTEF control are 17.02% and 68.13%, respectively. Compared with PIDeTEF control, DMCeTEF control is more effective in reducing the motion times and amplitudes of the pitch actuators to prolong their lifespans. In Fig. 17(b), TEF11 shows a sinusoidal angle change, which is negligibly affected by TEF12. This result indicates that the coupling between MeDMC and NeDMC is weak, and that these approaches can be controlled independently by neglecting their respective influences, as mentioned in Subsection 4.1.
Considering the randomness of the wind field, 10 group simulations were performed for NTM wind conditions with different random seeds at 8 m/s, 11.4 m/s, and 16 m/s, respectively. As shown in Figs. 18e20, compared to PIDeTEF control, upon application of DMCeTEF control, the reduction rates of the PSD of the flapwise root moment of blade 1 at the 1 P frequency, generator power standard deviation, and mean pitch angle, all show larger reductions. Table 14 lists the average reduction rates of the PSD of blade 1 flapwise root moment at the 1 P frequency, the generator power standard deviation, and the mean pitch angle in the simulations of the 10 groups at the speeds of 8 m/s, 11.4 m/s, and 16 m/s at the NTM wind conditions. The results indicate that DMCeTEF control yields a better control effect.
5. Conclusion In this study, the modeling of the wind turbine with a smart rotor, optimization of the TEF sizing parameters, and the design of a multi-objective TEFs controller, were investigated. The following conclusions can be drawn: 1) A wind turbine model with TEFs was developed, and under standard wind turbine control, time domain simulation results at Region 2, 3 step wind and NTM wind conditions yielded good agreement with those from FAST (with a maximum deviation percentage of 12.06%). At a wind speed of 11.4 m/s at a steady
(a)
10000
8000
No TEF control PID TEF control DMC TEF control
6000
4000 200
250
300
350
400
450
(b)
300
No TEF control PID TEF control DMC TEF control
1P
200
100
0
500
0.2
0.4
Time [s] 130 125
(c)
120 115 110
No TEF control PID TEF control DMC TEF control
105 100 200
250
300
0.6
0.8
Frequency [Hz]
350
400
450
500
Output power of generator [kW]
Angular speed of generator [rad/s]
12000
PSD of blade 1 flapwise root moment [(kNm)2]
W. Zhang et al. / Renewable Energy 129 (2018) 75e91
Flapwise root moment of blade 1 [kNm]
88
6000 5500
(d)
5000 4500
No TEF control PID TEF control DMC TEF control
4000 3500 200
250
300
350
Time [s]
400
450
500
Time [s]
Fig. 16. Simulation results for an NTM wind condition at a 11.4 m/s wind speed: (a) flapwise root moment of blade 1, (b) PSD of blade 1 flapwise root moment, (c) angular speed of generator, and (d) output power of generator. Table 12 Simulation results elicited within the time period of 150e250 s upon application of different control strategies. Values on PIDeTEF Values on DMCeTEF Reduction rates on PID control control eTEF control
Reduction rates on DMC eTEF control
standard deviation of blade 1 flapwise root moment [kN$m] PSD of blade 1 flapwise root moment at 1 P frequency [(kN$m)2] standard deviation of generator angular speed [rad/s] standard deviation of generator power [kW]
781.16
610.24
595.70
21.88%
23.74%
220.97
60.81
42.01
72.48%
80.99%
2.46
2.10
1.83
14.51%
25.41%
300.41
256.44
224.56
14.64%
25.25%
No TEF control PID TEF control DMC TEF control
5 4 3 2 1 0
(a) 0
100
200
300
400
500
600
TEFs angles of blade 1 [deg]
Values on no TEF control
Pitch angles of blade 1 [deg]
Parameters
5 0 -5 -10
TEF11 TEF12
0
100
Time [s]
(b) 200
300
400
500
600
Time [s]
Fig. 17. Pitch and TEF angle results on the NTM wind condition at a wind speed of 11.4 m/s: (a) pitch angles of blade 1 and (b) TEFs angles of blade 1 using DMCeTEF control. Table 13 Pitch control results elicited within the time period of 150e250 s with the use of different control strategies. Parameters
Values on no TEF control
Total pitch motion time 290.30 [s] Mean pitch angle [deg] 2.17
Values on PIDeTEF control
Values on DMCeTEF control
Reduction rates on PIDeTEF control
Reduction rates on DMCeTEF control
282.00
240.90
2.86%
17.02%
1.45
0.69
33.17%
68.13%
W. Zhang et al. / Renewable Energy 129 (2018) 75e91
89
Reduction rates of parameters [%]
100 DMC: PSD of blade 1 flapwise root moment
80
PID: PSD of blade 1 flapwise root moment
60
DMC: mean pitch angle PID: mean pitch angle
40
DMC: generator power standard deviation
20
PID: generator power standard deviation
0 1
2
3
4
5
6
7
8
9
10
Experiment No. Fig. 18. Reduction rates of parameters based on simulations of 10 groups at NTM wind conditions with a wind speed of 8 m/s and with different random seeds.
Reduction rates of parameters [%]
100 DMC: PSD of blade 1 flapwise root moment
80
PID: PSD of blade 1 flapwise root moment
60
DMC: mean pitch angle PID: mean pitch angle
40
DMC: generator power standard deviation
20
PID: generator power standard deviation
0 1
2
3
4
5
6
7
8
9
10
Experiment No. Fig. 19. Reduction rates of parameters based on simulations of 10 groups at NTM wind conditions with a wind speed of 11.4 m/s and with different random seeds.
wind condition, the TEFs also yielded exactly the same effects as those elicited by FAST. Such results indicate that the proposed model is capable of simulating the operational process of wind turbines with TEFs. 2) An optimal group of TEF sizing parameters was obtained by orthogonal experiments and was validated via estimation approaches. The optimal TEF sizing parameters are as follows: the TEF length was 14.35 m, angle range was 10 to 10 , chord length ratio was 25%, central position was in the 25th blade element at 53.775 m, and the TEF was located within the 22nd
to 28th blade elements in the NACA64_A17 airfoil. The proposed approach used to optimize the TEF sizing parameters can improve the optimization efficiency by using 50 simulations in order to obtain the optimal group from 6840 groups of TEF sizing parameters. 3) The multi-objective TEFs controller adopted MeDMC and NeDMC to control flapwise blade root moment and output power, respectively. Specifically, it controlled six TEFs on three blades independently. Simulation results yielded good control effects on reducing the variation of flapwise blade root moment
90
W. Zhang et al. / Renewable Energy 129 (2018) 75e91
Reduction rates of parameters [%]
100 DMC: PSD of blade 1 flapwise root moment
80
PID: PSD of blade 1 flapwise root moment
60
DMC: mean pitch angle PID: mean pitch angle
40
DMC: generator power standard deviation
20
PID: generator power standard deviation
0 1
2
3
4
5
6
7
8
9
10
Experiment No. Fig. 20. Reduction rates of parameters based on simulations of 10 groups at NTM wind conditions with a wind speed of 16 m/s and with different random seeds.
Table 14 Wind turbine parameters average reduction rates of 10 group simulations at the speeds of 8 m/s, 11.4 m/s, and 16 m/s at NTM wind conditions at different random seeds. Parameters
Average reduction rates on PIDeTEF control
Average reduction rates on DMCeTEF control
NTM wind conditions [m/s] PSD of blade1 flapwise root moment at 1 P frequency Generator power standard deviation Mean pitch angle
8 82.23% 1.98% 0%
8 91.12% 8.51% 0%
and smoothening the output power (with an average reduction rate of the blade 1 flapwise root moment PSD at the 1 P frequency in the range of 87e97%, and an average reduction rate of the generator power standard deviation in the range of 8e42%). DMCeTEF control can reduce the motion time and amplitude of pitch actuators, thereby benefiting the operation of wind turbines. Moreover, DMCeTEF control shows better control performance than the PIDeTEF control. The conclusions indicate that the wind turbine model with a smart rotor, the approach used to optimize the TEF sizing parameters, and the multi-objective TEF controller, are all efficient and reliable. Acknowledgements This work was supported by National Key R&D Program of China (Grant No. 2017YFB0602105). References [1] Siemens Wind Power GmbH & Co.KG. Offshore Direct Drive Wind Turbine SWTe8.0e154. https://www.siemens.com/global/en/home/markets/wind/ turbines/swte8e0e154.html. Accessed October 16, 2017. [2] Z.J. Chen, K.A. Stol, B.R. Mace, System identification and controller design for individual pitch and trailing edge flap control on upscaled wind turbines, Wind Energy 19 (2016) 1073e1088, https://doi.org/10.1002/we.1885. [3] D. Castaignet, I. Couchman, N.K. Poulsen, T. Buhl, J.J.W. Heinen, Frequencyweighted model predictive control of trailing edge flaps on a wind turbine blade, IEEE Trans. Contr. Syst. Technol. 21 (4) (2013) 1105e1116, https:// doi.org/10.1109/TCST.2013.2260750.
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16 89.29% 27.12% 0.36%
11.4 87.66% 20.57% 55.23%
16 96.68% 41.86% 2.13%
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