Combined Pitch and Trailing Edge Flap Control for Load ... - MDPI

energies Article

Combined Pitch and Trailing Edge Flap Control for Load Mitigation of Wind Turbines Keshan He 1,2 , Liangwen Qi 1 , Liming Zheng 1 and Yan Chen 1, * 1 2

*

Engineering College, Shantou University, Shantou 515063, China; [email protected] (K.H.); [email protected] (L.Q.); [email protected] (L.Z.) Department of Mechatronics Engineering, Shantou Polytechnic, Shantou 515078, China Correspondence: [email protected]; Tel.: +86-754-865-045-87

Received: 24 August 2018; Accepted: 18 September 2018; Published: 21 September 2018







Abstract: Using active control methods for load mitigation in wind turbines could greatly reduce the cost of per kilowatt hour of wind power. In this work, the combined pitch and trailing edge flap control (CPFC) for load mitigation of wind turbines is investigated. The CPFC includes an individual pitch control (IPC) loop and a trailing edge flap control (TEFC) loop, which are combined by a load frequency division control algorithm. The IPC loop is mainly used to mitigate the low frequency loads, and the TEFC loop is mainly used to mitigate the high frequency loads. The CPFC adopts both an azimuth angle feed-forward and a loads feedback control strategy. The azimuth angle feed-forward control strategy should mitigate the asymmetrical loads caused by observable disturbances. and the loads feedback control strategy should decrease asymmetrical loads by closed loop control. A simulation is carried out on the joint platform of FAST and MATLAB. The simulation results show that the damage equivalent load (DEL) of blade root out-of-plane bending moment is reduced by 53.7% while using CPFC, compared to collective pitch control (CPC); and the standard deviation of blade tip out-of-plane deflection is reduced by 50.2% while using CPFC, compared to CPC. The results demonstrate that the CPFC can mitigate the fatigue loads of wind turbines as anticipated. Keywords: wind energy; wind turbine; loads mitigation; combined pitch and trailing edge flap control; load frequency division control algorithm; individual pitch control; trailing edge flap control

1. Introduction Wind turbines are always suffering aerodynamic loads, gravitational and inertial loads, actuation loads and so on. during their lifetime [1]. The aerodynamic loads are the main source of fatigue loads in wind turbines. The asymmetrical loads caused by wind shear, tower shadow effects, turbulence and other factors will lead to fatigue damage of blades, towers, drive trains, etc. Veers pointed out that if innovative blade design and control methods could result in decreased aerodynamic loads, the fatigue loads of wind turbines would be significantly mitigated [2]. That would be helpful to effectively reduce the cost per kilo-Watt hour (kWh) of wind power. The aerodynamic loads active control technology could dynamically regulate the aerodynamic properties (such as change angle of attack or lift coefficients) of blades based on appropriate sensor inputs [3], so active control methods, such as individual pitch control (IPC) and trailing edge flap control (TEFC), are more suitable for handling the complex and unsteady aerodynamics loads of wind turbines. Therefore, the IPC and TEFC are widely studied for their engineering prospects. The IPC regulates the pitch angle of each blade, respectively, to improve the aerodynamic performance. Bossanyi designed an IPC controller for wind turbines, and found that the fatigue loads was reduced significantly when IPC was applied both in simulation and field tests on Controls Advanced Research Turbines (CART) [4,5]. Engelen found that the fatigue loads on the blades was Energies 2018, 11, 2519; doi:10.3390/en11102519

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reduced by up to 17% and the extreme loads in certain cases dropped 50% by using a multi-rotational mode IPC (higher harmonics control) [6]. Houtzager found that IPC can significantly reduce the vibrations in the wind turbine structure with considerably less high-frequent control action [7]. The TEFC can quickly adjust the aerodynamic properties of the blade by regulating the trailing edge flaps’ (TEFs) deflection angle. Gaunaa found that TEFC could reduce 10–14.5% of the fatigue equivalent damage loads (DELs) on the blade root moments in simulations, decrease 50–60% of standard deviation of the lift coefficient in wind tunnel tests, and reduce about 14% of the fatigue loads and 20% of the 1P frequency loads in field tests on the Vestas V27 wind turbine [8–10]. Barlas found that the fatigue DELs of flap-wise moments were reduced 54% in simulation by TEFC, and a reduction of 50% is measured in wind tunnel experiments [11]. Zhang and Yu found that the reduction of flap-wise root moments and tip deflections by using TEFC were up to 20.4% and 15.7% for the normal turbulence model (NTM); and up to 15.0% and 11.9% for the extreme turbulence model (ETM) [12,13]. Since IPC has the advantage of a wide regulation range and the disadvantage of slow response, IPC is considered more suitable to mitigate low frequency loads. TEFC has the characteristics of fast response and local control capability, which makes it more suitable to mitigate the high frequency loads. It therefore should be beneficial to use IPC and TEFC to complement each other. However, relevant studies combining IPC and TEFC are rarely reported. In this work, the proposed combined pitch and trailing edge flap control (CPFC) combining the IPC loop and TEFC loop and based on a loadfrequency division control algorithm is investigated. The effect of CPFC for loads mitigation is analyzed. The outline of this paper is as follows: in Section 2, the sources of fatigue loads of wind turbines are briefly analyzed, and the aerodynamics model and structural model of wind turbines are briefly described. In Section 3, the control strategy of CPFC is described in details. In Section 4, the simulation case of CPFC is demonstrated, and the simulation results are discussed. The conclusions are presented in the final section. 2. The Fatigue Loads of Wind Turbines 2.1. The Sources of Fatigue Loads of Wind Turbines Wind is highly variable, both geographically and temporally. With the large-scale development of wind turbines, the fatigue loads caused by wind variation will greatly increase with the increment of rotor swept area. The main factors that cause the fatigue loads of wind turbines are wind shear, tower shadow effect and turbulence. Wind shear is known as the increase of mean wind speed with height [14]. The wind shear can be described by a logarithmic power law profile as follows: V (h) = V (h0 )(

h α ) h0

(1)

where V (h0 ) is the wind speed at the reference height of h0 , generally referred to the hub height; V (h) is the wind speed at the height h; α is the empirical wind shear exponent, which relates to the ground roughness and the atmospheric stability. A conservative value specified by the IEC standard is generally given as α = 0.20 for normal onshore wind conditions. The tower shadow effect refers to the wind speed reduction caused by towers blocking the air
flow [14]. The tower shadow effect is only valid for the region of ψ ∈ π2 , 3π 2 , where ψ is the azimuth angle. From potential flow theory, the stream function of wind around the tower can be derived by superposing a doublet on uniform flow as follows:   V ( x, y) = V0 1 −



 D ( x,y) 2 2


 x 2 − y2   2 ( x 2 + y2 )

(2)

  D ( x, y )  2 2 2    x −y 2   V ( x= , y ) V0  1 − 2  x2 + y 2  

(

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(

)



)    

(2) 3 of 16

where V ( x, y ) is the flow velocity in the x direction at the position of ( x, y ) ; V0 is the uniform where V ( x, y) is the flow velocity in the x direction at the position of ( x, y); V0 is the uniform flow; x flow; x and y are the longitudinal and lateral coordinates with respect to the tower centre; and y are the longitudinal and lateral coordinates with respect to the tower centre; D ( x, y) is the tower D( x, y ) isatthe diameter diameter thetower position of ( x, yat).the position of ( x, y ) . The of wind wind turbines turbines are are illustrated illustrated in in Figure Figure 1. 1. The wind wind shear shear and and tower tower shadow shadow effect effect of

Figure 1. 1. The The wind wind shear shear and and tower tower shadow shadow effect effect of of wind wind turbines. turbines. Figure

Turbulence refers to wind speed fluctuations on a fast time scale [15,16]. The variation of turbulent Turbulence refers to wind speed fluctuations on a fast time scale [15,16]. The variation of wind speed generally obeys a Gaussian distribution. The turbulence intensity can be defined as: turbulent wind speed generally obeys a Gaussian distribution. The turbulence intensity can be defined as: σµ (3) I= σ µV (3) I= V wind speed. where σµ is turbulence standard deviation, V is the mean

where σ µ is turbulence standard deviation, V is the mean wind speed. 2.2. The Aerodynamic Model and Structural Model of Wind Turbine TheAerodynamic aerodynamic loads wind turbines computed by blade element momentum 2.2. The Model and of Structural Model of can WindbeTurbine theory [17]. Assuming that the wind turbine rotor consists of B identical blades, a blade element The aerodynamic loads of wind turbines can be computed by blade element momentum theory span length is dr, and the chord length is c. The differential rotor thrust and differential rotor torque of [17]. Assuming that the wind turbine rotor consists of B identical blades, a blade element span length annular radius of r can be represented as follows: is dr, and the chord length is c. The differential rotor thrust and differential rotor torque of annular radius of r can be represented as follows: 1 2 dT = ρVrel (4) (Cl cos φ + Cd sin φ) Bcdr 2 dM =

1 2 ρV (C sin φ − Cd cos φ) Bcrdr 2 rel l

(5)

where ρ is the density of the air; Vrel is the relative wind speed; Cl and Cd are the lift coefficient and drag coefficient of the airfoil, respectively. Then the rotor thrust and rotor torque can be obtained by integrating the annular radius along the span direction.

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The structural model of wind turbine considers the blades as flexible cantilevered beams [17]. Appling the normal mode summation method, the deflection of the flexible beam can be presented as follows: N

u(z, t) =

∑ φa ( z ) q a ( t )

(6)

a =1

where u(z,t) is the lateral deflection of the distance z along the beam; φa (z) is the normal mode shape for mode a; qa (t) is their associated generalized coordinate. The flexible beam motion at a specific natural mode can be written in matrix form as follows:

(−ω 2 [ M] + [K ]){C } = {0}

(7)

where {C } is the coefficient vector; ω 2 is the eigenvalues, which being the square of the natural frequency ω. The generalized mass matrix [ M] and generalized stiffness matrix [K ] can be derived from the kinetic energy and potential energy of the beam [18]. 3. Combined Pitch and Trailing Edge Flap Control The CPFC includes the IPC loop and TEFC loop, which are combined by the load frequency division control algorithm. The IPC loop is mainly used to mitigate low frequency loads, and the TEFC loop is mainly used to mitigate high frequency loads. The CPFC adopts both an azimuth angle feed-forward and a loads feedback control strategy for improving the control performance. The feed-forward control strategy should mitigate the asymmetrical loads caused by observable system input disturbances, such as variable azimuth angles and wind speed. The feedback control strategy should decrease the system output errors (asymmetrical loads) and the expected closed loop control value. The feed-forward control loop should provide beneficial compensation for the feedback control loop. 3.1. IPC Based on Azimuth Angle Feed-forward Control Strategy 3.1.1. The Collective Pitch Control Generally, the collective pitch control (CPC) is used for regulating the rotor speed to limit the excess of wind power above rated wind conditions [19]. By classical proportional-integral-derivative (PID) control law, the equation of pitch angle perturbation which is related to rotor speed perturbation can be represented as follows: θ (t) = K pcpc NGear ∆Ω(t) + Kicpc

Zt

.

NGear ∆Ω(t)dt + Kdcpc NGear ∆Ω(t)

(8)

0

where ∆θ (t) is the small perturbation of the blade pitch angle about operating point; ∆Ω(t) is the . small perturbation of low-speed shaft rotational speed about reference speed; ∆Ω(t) is the low-speed shaft rotational acceleration; NGear is the high-speed to low-speed gearbox ratio; K pcpc , Kicpc and Kdcpc are the proportional, integral, and derivative gains of blade collective pitch controller, respectively. where θcpc0 is the blade initial pitch angle. 3.1.2. IPC Based on Azimuth Angle Feed-Forward Control Strategy Due to wind shear and tower shadow effect, the blade loads are strongly related to the azimuth angle of the blades. The IPC based on azimuth angle feed-forward control strategy should be used to mitigate loads caused by wind shear and tower shadow effects. This method uses the weight

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coefficients to regulate the pitch angle of each blade, respectively [20–22]. For a three blades wind turbine, the weight coefficients can be represented as follows: l

Kb ( ψ ) =

3V b (ψ) 3

l

b = 1, 2, 3

(9)

∑ Vb

b =1

where V b is the weighted wind speed of bth blade [15,23]; the wind speed at radius 3R4 b of each blade is using as weighting in this work, Rb is the radius of the rotor; the weighted wind speed can be derived from the hub height wind speed by the wind shear and tower shadow effect model; l is the exponent coefficient, considering the aerodynamic torque is proportionate to the square of the equivalent wind speed, the value of l = 2 is used in this work. In order to keep the power output consistent with CPC, the sum of weight coefficients have to equal to 3 for three blades wind turbines, which can be represented as follows: 3

∑ Kb ( ψ ) = 3

(10)

b =1

Therefore, the pitch angle of bth blade by IPC based on azimuth angle feed-forward control strategy can be represented as follows: ff

θb (t) = Kb (ψ) θcpc (t)

b = 1, 2, 3

(11)

where θcpc (t) is the blade pitch angle by CPC. 3.2. The IPC Based on Loads Feedback Control Strategy 3.2.1. Multi-Blade Coordinate Transformation The blade root bending moments of a wind turbine can be measured by optical strain gauge sensors, so they are usually used as signals for the loads feedback control strategy, but the blade root bending moments are generally expressed in blade rotating frames. This is a periodic linear time-varying system (LTV) and much more challenging to design controllers. The multi-blade coordinate transformation (MBC) or d-q axis transformation can convert the measured loads into a fixed hub frame [24]. Then the single-input and single-output linear time-invariant (LTI) controller can be used to mitigate the nP (per revolution) harmonic frequency loads. Assuming that the azimuth angle ψ1 = 0 implies the first (reference) blade is vertically up. Then the azimuth angles of the three blades can be represented as follows: ψb = ψ1 +

2π ( b − 1) 3

b = 1, 2, 3

(12)

The transformations from three rotating blades to hub fixed frame for nP frequency components can be represented as follows: 2 P(nψ) = 3

sin(nψ1 ) sin(nψ2 ) sin(nψ3 ) cos(nψ1 ) cos(nψ2 ) cos(nψ3 )

! (13)

where n is fixed frame referenced degrees of freedom, which is used to represent the nP harmonics frequency components of rotor angular velocity.

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The transformations from hub fixed frame back to three rotating blades for nP frequency components can be represented as follows: 

 sin(nψ1 ) cos(nψ1 )   P−1 (nψ) =  sin(nψ2 ) cos(nψ2 )  sin(nψ3 ) cos(nψ3 )

(14)

3.2.2. The IPC Based on Loads Feedback Control Strategy The IPC based on loads feedback control strategy is mainly used to mitigate 1P frequency loads in this work. The 1P frequency component of blade root out-of-plane bending moments are scaled and filtered by a band-pass filter from strain gauge sensors. The transfer function of band-pass filter for 1P frequency component is defined as follows: 2ζ 1p ω1p s

1p

Gbp (s) =

s2

(15)

2 + 2ζ 1p ω1p s + ω1p

where ω1p and ζ 1p are frequency and damping for 1P frequency component of blade root bending moments. The 1P frequency components of blade root bending moments from three rotating blades to hub fixed frame can be represented as follows:  1p    Mys (t) =

2 3

 1p   Myc (t) =

2 3

3

1p

b =1 3

1p

∑ Myb (t) sin ψb (t)

(16)

∑ Myb (t) cos ψb (t)

b =1

1p

1p

where Myb (t) is the blade root bending moment 1P frequency component of bth blade; Mys (t) 1p

and Myc (t) are the yaw component and tilt component of 1P frequency loads in hub fixed frame respectively. The yaw component and tilt component of 1P frequency loads can be seen as almost independent. Then PID controllers can be used to regulate the yaw component and tilt component respectively. Since the control objective is to minimize the asymmetrical loads, the reference values are set to zero. By PID control law, the governing equations for the yaw component and tilt component of 1P frequency loads can be represented as follows:  1p Rt d(0− Mys (t)) 1p 1p  θ (t) = K s psipc (0 − Mys ( t )) + Kisipc 0 (0 − Mys ( t )) dt + Kdsipc dt 1p Rt d(0− Myc (t))  1p 1p θc (t) = K pcipc (0 − Myc (t)) + Kicipc 0 (0 − Myc (t))dt + Kdcipc dt

(17)

where θs (t) and θc (t) are the blade pitch angles of yaw component and tilt component in the hub fixed frame respectively; K psipc , Kisipc , Kdsipc , K pcipc , Kicipc and Kdcipc are the proportional, integral, and derivative gains of yaw component controller and tilt component controller by IPC respectively. The phase lag caused by the filter should be compensated by add a small phase offset to blade azimuth angle. Then the pitch angles from hub fixed frame back to three rotating blades by IPC based on loads feed-back control strategy can be represented as follow: fb

θb (t) = θs (t) sin(ψb (t) + δ1p ) + θc (t) cos(ψb (t) + δ1p ) fb

b = 1, 2, 3

(18)

where θb (t) is the pitch angle of bth blade by IPC based on loads feed-back control strategy; δ1p is the phase offset for 1P frequency component of blade root bending moment.

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The pitch actuator is described by a second-order model in this work. The transfer function of actuators for IPC is defined as follows: 2 ω1p

1p

Gac (s) =

(19)

2 s2 + 2ζ 1p ω1p s + ω1p

In order to describe how the anti-windup scheme should finally be implemented into the wind turbine, the pitch actuator model includes minimum and maximum pitch angle, maximum pitch rate. 3.3. The TEFC Based on Loads Feedback Control Strategy The TEFC based on loads feedback control strategy is similar to the IPC. The TEFC is mainly used to mitigate 2P frequency loads in this work. The transfer function of band-pass filter for 2P frequency component is defined as follows: 2ζ 2p ω2p s

2p

Gbp (s) =

(20)

2 s2 + 2ζ 2p ω2p s + ω2p

where ω2p and ζ 2p are frequency and damping for 2P frequency component of blade root bending moments. The 2P frequency component of blade root bending moments from three rotating blades to hub fixed frame can be represented as follows:  2p    Mys (t) =

2 3

 2p   Myc (t) =

2 3

3

2p

∑ Myb (t) sin(2ψb (t))

b =1 3

∑

b =1

(21)

2p Myb (t) cos(2ψb (t))

2p

2p

where Myb (t) is the blade root bending moment 2P frequency component of bth blade; Mys (t) 2p

and Myc (t) are the yaw component and tilt component of 2P frequency loads in hub fixed frame respectively. Similar to the IPC, the governing equations for the yaw component and tilt component of 2P frequency loads can be represented as follows:  2p Rt d(0− Mys (t)) 2p 2p  β (t) = K s ps f lap (0 − Mys ( t )) + Kis f lap 0 (0 − Mys ( t )) dt + Kds f lap dt 2p Rt d(0− Myc (t))  2p 2p β c (t) = K pc f lap (0 − Myc (t)) + Kic f lap 0 (0 − Myc (t))dt + Kdc f lap dt

(22)

where β s (t) and β c (t) are the TEFs deflection angles of yaw component and tilt component in the hub fixed frame respectively; K ps f lap , Kis f lap , Kds f lap , K pc f lap , Kic f lap and Kdc f lap are the proportional, integral, and derivative gains of yaw component controller and tilt component controller by TEFC respectively. The TEFs deflection angles from hub fixed frame back to three rotating blades by TEFC can be represented as follows: β b (t) = β s (t) sin(2ψb (t) + δ2p ) + β c (t) cos(2ψb (t) + δ2p )

b = 1, 2, 3

(23)

where β b (t) is the current TEF deflection angle of bth blade; δ2p is the phase offset for 2P frequency component of blade root bending moment.

where βb (t ) is the current TEF deflection angle of

bth blade; δ 2 p is the phase offset for 2P

frequency component of blade root bending moment. The TEFs actuator is also described by a second-order model in this work. The transfer function Energies 2018, 11, 2519 8 of 16 of actuators for TEFC is defined as follows:

ω2

2p The TEFs actuator is also described model in this work. The transfer function Ga2cp ( sby ) =a second-order (24) 2 2 of actuators for TEFC is defined as follows: s + 2ζ 2 pω2 p s + ω2 p

2 Similar to the pitch actuator model, the TEFs deflection actuator model includes minimum and ω2p 2p G ( s ) = (24) ac maximum deflection angle, maximum deflection rate.ω s + ω 2 s2 + 2ζ 2p

2p

2p

3.4. The CPFC on Load Frequency Division Control Strategy Similar toBased the pitch actuator model, the TEFs deflection actuator model includes minimum and maximum deflection angle, The CPFC adopts loadmaximum frequencydeflection division rate. control algorithm to combine IPC loop and TEFC loop. The complete transfer function of IPC loop for 1P frequency can be represented as follows: 3.4. The CPFC Based on Load Frequency Division Control Strategy K isipc K dsipc s   The CPFC adopts load frequency division Kcontrol to combine IPC loop and TEFC loop. 0  ＋ psipc＋ algorithm 1 + sτ s 1p 1p   I 3×3IPC P −1 (ψloop ) Gac ( s )of ) ( ) ) I 3follows: Gip1 pc ( sfunction P G = + δ1 for ψ The complete transfer 1P frequency can be represented (25) ×3 p bp ( sas K icipc K dcipc s   ＋  0 K pcipc＋K  ! Kdsipc s 1 + sτ  K isipc 0 1p 1p 1p psipc + s + 1+sτ −1 Gipc (s) = Gac (s) I3×3 P (ψ + δ1p ) P(ψ) Gbp (s) I3×3 (25) Kdcipc s Kicipc can be represented as follows: The complete transfer function of TEFC loop 0 Kfor + frequency + pcipc2P s

1+sτ

K isflap K dsflap s   The complete transfer function of TEFC loop can 0 be represented as follows: K psflapfor ＋ 2P frequency ＋ 1 s s τ + −1 2p 2p  P! (2ψ )Gbp2 p ( s ) I 3×3 G flap ( s ) Gac ( s ) I 3×3 P (2ψ + δ 2 p )  = (26) K s K K K s is f lapicflap ds f lap  dcflap + 0 Kps0f lapK+ 2p 2p 2p ＋ ＋ −1 1+sτ  pcflap s (26) G f lap (s) = Gac (s) I3×3 P (2ψ + δ2p ) Ks 1K+ sfτlap s P(2ψ) Gbp (s) I3×3  0 K pc f lap + icsf lap + dc 1+sτ In this work, the IPC loop adopts both azimuth angle feed-forward control strategy and loads In this work,strategy. the IPC loop both pitch azimuth angle feed-forward strategy andcan loads feedback control Thenadopts the current angle is the sum of two control components, which be feedback control strategy. Then the current pitch angle is the sum of two components, which can be represented as follows: represented as follows: f f ff f bfb )= 1, 2, 2,3 (27) θbθ(bt()t= θθb b (t()t )++θθbb ((tt)) bb== 1, 3 (27)

The CPFC CPFC scheme scheme is is illustrated illustrated in in Figure Figure2. 2. The Reference Generator Speed

-

CPC Controller

Wind IPC_FF Controller

Filter (1P) Filter (2P)

P(ψ)

IPC_FB Controller

P(2ψ)

TEFC Controller

P-1(ψ+δ1P)

+

-1

P (2Ψ+δ2P)

Pitch Actuator

Blade Pitch Angles

TEFs Actuator

TEFs Defletion Angles

Blade Azimuth Angles

Actuator

CPFC Controller

Generator Speed

Blade Root Moments Wind Turbine

Figure Figure 2. 2. The The CPFC CPFC scheme. scheme.

4. Simulation and Discussion 4.1. The Reference Wind Turbine 4.1.1. Specifications of Reference Wind Turbine The 5 MW reference wind turbine is described by Jonkman [17]. The wind turbine under consideration is onshore, upwind, with three blades, variable speed and collective pitch controlled. Its design specifications are given in Table 1.

The 5 MW reference wind turbine is described by Jonkman [17]. The wind turbine under consideration is onshore, upwind, with three blades, variable speed and collective pitch controlled. Its design specifications are given in Table 1. Table 1. The 5 MW reference wind turbine specifications.

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Property

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Value

Table 1. The 5 MW reference wind turbine Rated power 5 MWspecifications.

Rotor diameter Property Hub Ratedheight power

Rotor diameter Blade number Hub height Cut-in wind speed Blade number Rated wind speed Cut-in wind speed Cut-out windspeed speed Rated wind Rated Cut-outrotor windspeed speed Rated speed Basicrotor control Basic control

126Value m

905 m MW

126 3 m 90 m 3 m/s 3 11.4 m/s 3 m/s 2511.4 m/s m/s 12.125rpm m/s 12.1 rpm Variable speed, collective pitch

Variable speed, collective pitch

4.1.2. The TEFs Aerodynamic Characteristics 4.1.2. The TEFs Aerodynamic Characteristics Suppose that each blade is equipped with one TEF, mounted in the blade section with airfoil of Suppose eachThe blade is equipped with mounted the blade section on with airfoil of of NACA 64-618 that profile. TEFs extends for 30%one of TEF, the blade spanin length, distributed 66–96% NACA 64-618 profile. The TEFs extends for 30% of the blade span length, distributed on 66–96% of span-wise; and extends for 10% of the airfoil chord ratio [25]. The TEFs configuration is illustrated in span-wise; Figure 3. and extends for 10% of the airfoil chord ratio [25]. The TEFs configuration is illustrated in Figure 3. 0.12 0

0.1

o

-10 +10

0.08

o o

0.06

y/c

0.04

0.02

0

-0.02

-0.04

-0.06

-0.08 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x/c

(a)

(b)

Figure 3. The TEFs configuration. (a) The layout of TEFs; (b) The airfoil profile of TEFs deflection Figure configuration. (a) The layout of TEFs; (b) The airfoil profile of TEFs deflection angles 3. at The ±10◦TEFs . angles at ±10°.

The aerodynamic characteristics of the NACA 64-618 airfoil with TEFs are calculated by XFOIL aerodynamic characteristics of the NACA 64-618 with TEFs areon calculated by XFOIL and The extended by Airfoil Prep spreadsheets. The TEFs haveairfoil a significant effect the lift coefficients and extended by Airfoil Prep spreadsheets. The TEFs have significant of effect on the lift coefficients Cl , drag coefficients Cd and moment coefficients Cm . The liftacoefficients NACA 64-618 airfoil with Energies 2018, 11, x FOR PEER REVIEW 10 of 17 , drag coefficients and moment coefficients of NACA 64-618 airfoil TEFs as function of both of attackcoefficients and TEFs deflection angles are shown in Figure 4. Cm . The lift C Cd angles l

with TEFs as function of both angles of attack and TEFs deflection angles are shown in Figure 4.

Figure 4. The lift coefficients as function of both angles of attack (±180◦ ). and TEFs deflection angles (±15◦ ).

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4.1.3. The Anti-Windup Scheme of Blades and TEFs Considering the dynamic characteristics of blades and TEFs, the blade-pitch rate is limited to 8◦ /s in absolute value; and the minimum and maximum blade pitch angles are limited to [0◦ –90◦ ]. The TEFs deflection rate is limited to 40◦ /s in absolute value; and the minimum and maximum TEFs deflection angles are limited to [−15◦ –+15◦ ]. 4.2. Simulation Environment 4.2.1. Simulation Platform The simulation is carried out on the joint simulation platform of FAST code and MATLAB software. The FAST code is used to perform time marching simulation of aero-elastic response of wind turbines. The MATLAB software is used to implement the control strategy. The FAST code needs to modify and recompile for integrating TEFs interface. Then FAST code is used as S-function which is called by MATLAB software. 4.2.2. Design Loads Case The design loads cases (DLC) focus on the wind turbines fatigue loads of normal power production, according to DLC 1.2 of IEC 61400-1 [26]. The turbulent wind is assumed to belong to Class IIB, normal turbulence model (NTM) with Von Karman spectrum. The turbulence intensity Ire f is 0.14 while the reference wind speed Vre f is 42.5 m/s. The hub height mean wind speed is assumed to 20 m/s, and wind shear model with power law exponent is 0.2. The turbulent wind data are generated by turbulent-wind simulator Turbsim code. The hub height wind speed is shown in Energies 2018, 11, x FOR PEER REVIEW 11 of 17 Figure 5. 24 Wind Speed

23

22

Wind Speed [m/s]

21

20

19

18

17 100

110

120

130

140

150

160

Time [s]

Figure 5. The hub height wind speed. Figure 5. The hub height wind speed.

4.3. Results and Discussion 4.3. Results and Discussion The simulation results by CPC, IPC and CPFC are demonstrated. The discussion is based on the The simulation results by of CPC, IPC and results during simulation time 100–160 s. CPFC are demonstrated. The discussion is based on the results during simulation time of 100–160 s. 4.3.1. The Blade Root Bending Moments 4.3.1. The Blade Root Bending Moments The blade 1 root bending moments of wind turbine by CPC, IPC, CPFC are shown in Figure 6, Thedetails blade of 1 root bending moments of wind turbine by CPC, IPC, CPFCinare shown Figure and the standard deviation (Std) are given in Table 2. As shown Figure 6a,inthe blade6, and out-of-plane the details ofbending standardmoment deviation (Std) are given in Table 2. Asby shown Figure 6a, the decreases blade root root (RootMyc1) fluctuates wildly CPC. in The fluctuation out-of-planeby bending moment (RootMyc1) fluctuates wildlyIPC. by The CPC. The fluctuation decreases significantly IPC. The Std is reduced by 47.9% while using fluctuation further decreases significantly by IPC. The Std is reduced by 47.9% while using IPC. The fluctuation further decreases considerably by CPFC. The Std of moment is reduced by 55.3% while using CPFC. Since the fatigue considerably by CPFC. The Std of moment is reduced by 55.3% while using CPFC. Since the fatigue loads are mainly caused by the fluctuation of aerodynamic loads, the reduction of fluctuation would helpful to mitigate the fatigue loads of wind turbines. As shown in Figure 6b, the fluctuation of blade root in-plane bending moments (RootMxc1) just decrease slightly by IPC and CPFC, since it is not treated as a main control target in this work.

The blade 1 root bending moments of wind turbine by CPC, IPC, CPFC are shown in Figure 6, and the details of standard deviation (Std) are given in Table 2. As shown in Figure 6a, the blade root out-of-plane bending moment (RootMyc1) fluctuates wildly by CPC. The fluctuation decreases significantly by IPC. The Std is reduced by 47.9% while using IPC. The fluctuation further decreases Energies 2018, 11, 2519 11 of 16 considerably by CPFC. The Std of moment is reduced by 55.3% while using CPFC. Since the fatigue loads are mainly caused by the fluctuation of aerodynamic loads, the reduction of fluctuation would helpful mitigate the fatigue of windofturbines. As shown Figure 6b, theoffluctuation blade loads aretomainly caused by theloads fluctuation aerodynamic loads,inthe reduction fluctuationofwould root in-plane bending moments (RootMxc1) just decrease slightly by IPC6b, and since of it blade is not helpful to mitigate the fatigue loads of wind turbines. As shown in Figure theCPFC, fluctuation treated as a main control target in this work. root in-plane bending moments (RootMxc1) just decrease slightly by IPC and CPFC, since it is not treated as a main control target in this work. 7000 CPC

6000

CPC

IPC

6000

IPC

5000

CPFC

CPFC

4000

5000

Blade root in-plane moment [kN.m]

Blade root out-of-plane moment [kN.m]

3000

4000

3000

2000

1000

2000

1000

0

-1000

-2000

-3000

0 100

110

120

130

140

150

100

160

110

120

130

140

150

160

Time [s]

Time [s]

(a)

(b)

Energies 2018, 6. 11,The x FOR PEER REVIEW 12 of 17 Figure blade root bending moments. (a) The blade root out-of-plane bending moments; (b) The

Figureroot 6. The bladebending root bending moments. (a) The blade root out-of-plane bending moments; (b) blade in-plane moments. Table 2. Standard deviation of blade root bending moments. The blade root in-plane bending moments. Table 2. Standard deviation of blade root bending moments.

RootMyc1 (kN·m) RootMxc1 RootMyc1 (kN·(kN·m) m) RootMxc1 (kN·m)

CPC CPC Std Std 1310.2 2662.7 1310.2

IPC CPFC IPC CPFC Std Reduction Std Reduction Reduction Reduction 682.7Std 47.9% 585.1 Std 55.3% 2543.1 682.7 4.5%47.9% 2558.0585.1 3.9% 55.3%

2662.7

2543.1

4.5%

2558.0

3.9%

4.3.2. The Yaw Moments and Tilt Moments 4.3.2.The Theyaw Yawmoments Moments(Myaw) and Tiltand Moments tilt moments (Mtilt) in hub fixed frame of wind turbine by CPC, IPC, The CPFC aremoments shown in(Myaw) Figure and 7, and details(Mtilt) of mean value andframe Std are giventurbine in Tableby3.CPC, The yaw tilt the moments in hub fixed of wind mean values of yaw moment and tilt moment decrease significantly by IPC. The mean values are IPC, CPFC are shown in Figure 7, and the details of mean value and Std are given in Table 3. The respectively by 99.7%and andtilt 94.8% whiledecrease using IPC. The fluctuation of The yaw mean moment and are tilt mean valuesreduced of yaw moment moment significantly by IPC. values moment decreases considerably by CPFC. The Std are respectively reduced by 29.9% and 22.1% respectively reduced by 99.7% and 94.8% while using IPC. The fluctuation of yaw moment and tilt while using CPFC.considerably It indicates by that IPC is helpful reduce the reduced asymmetrical loads CPFC is moment decreases CPFC. The Std aretorespectively by 29.9% andand 22.1% while helpfulCPFC. to mitigate the fatigue loads in hub frame. using It indicates that IPC is helpful to reduce the asymmetrical loads and CPFC is helpful to mitigate the fatigue loads in hub frame. 1500 3000

CPC

CPC

IPC

IPC

2500

CPFC

CPFC

1000

2000

500

1000

Mtilt [kN.m]

Myaw [kN.m]

1500

500

0

0

-500

-500

-1000

-1000

100

110

120

130

140

150

160

100

110

120

130

Time [s]

140

150

Time [s]

(a)

(b)

Figure 7. The yaw moments and tilt moments in hub frame. (a) The yaw moments; (b) The tilt moments. Figure 7. The yaw moments and tilt moments in hub frame. (a) The yaw moments; (b) The tilt moments.

Table 3. the Standard deviation of blade root bending moment and tip deflection.

Item Myaw (kN·m) Mtilt (kN·m)

Mean Std mean Std

CPC Value 1596.4 451.8 184.2 443.4

Value 5.2 502.7 9.6 442.2

IPC Reduction 99.7% −11.3% 94.8% 0.3%

Value 3.8 316.6 9.0 345.3

CPFC Reduction 99.8% 29.9% 95.1% 22.1%

160

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Table 3. The Standard deviation of blade root bending moment and tip deflection. CPC

Item

IPC

Value

Value

CPFC

Reduction

Value

Reduction

Myaw (kN·m)

Mean Std

1596.4 451.8

5.2 502.7

99.7% −11.3%

3.8 316.6

99.8% 29.9%

Mtilt (kN·m)

mean Std

184.2 443.4

9.6 442.2

94.8% 0.3%

9.0 345.3

95.1% 22.1%

4.3.3. The Blade Tip Deflections The blade tip deflections of wind turbine by CPC, IPC and CPFC are shown in Figure 8, and the details of Std are given in Table 4. As shown in Figure 8a, being compared to the Std of blade tip out-of-plane deflection (OoPDefl1) by CPC, the Std is reduced by 44.6% when using IPC, and it Energies 2018, 11, x FORby PEER REVIEW 13 of 17 is further reduced 50.2% when using CPFC. As shown in Figure 8b, the Std of blade tip in-plane deflection (IPDefl1) is also decreased significantly when using IPC and CPFC. 3 CPC

CPC

IPC

IPC

2.5

0.5

IPC+FLAP

IPC+FLAP

2

0

Blade tip in-plane deflection [m]

Blade tip out-of-plane deflection [m]

1.5

1

0.5

0

-0.5

-1

-0.5

-1.5

-1 110

100

120

130

140

150

160

100

110

120

130

140

150

160

Time [s]

Time [s]

(a)

(b)

Figure 8. The blade tip deflections. (a) The blade tip out-of-plane deflections; (b) The blade tip Figure 8.deflections. The blade tip deflections. (a) The blade tip out-of-plane deflections; (b) The blade tip in-plane in-plane deflections. Table 4. Standard deviation of blade tip deflections.

Table CPC 4. Standard deviation of blade tip deflections.CPFC IPC Std CPC

Std OoPDefl1 (m) 0.7738 IPDefl1 (m) (m) 0.5367 OoPDefl1 0.7738

Std IPCReduction

Std 0.4289 Reduction 44.6% 0.4251 20.8% 0.4289 44.6% 0.4251 20.8%

Std CPFC Reduction

Std 0.3851Reduction 50.2% 0.4237 50.2% 21.1% 0.3851 0.4237 21.1%

IPDefl1 (m) 0.5367 4.3.4. Power Spectral Density Analysis 4.3.4. Power Spectral Density Analysis The power spectral density (PSD) analysis of the blade root out-of-plane bending moment by spectral density (PSD) of the out-of-plane moment by CPC,The IPC,power CPFC are shown in Figure 9. Itanalysis can be seen thatblade thereroot are obvious peaksbending of 1P (about 0.2 Hz) CPC, IPC, CPFC are shown in Figure 9. It can be seen that there are obvious peaks of (about 0.2 1P and 2P (about 0.4 Hz) frequency load while using CPC. The 1P frequency peak is removed completely Hz) and (about Hz) load while using The 1P frequency peakusing is removed 2PIPC. while using Both0.4 the 1Pfrequency and 2P frequency peaks areCPC. removed completely when CPFC. completely while IPC. used Both to themitigate frequency peaks completely 1P and1P2P Since the IPC loopusing is mainly frequency loads, andare theremoved TEFC loop is mainlywhen used using CPFC.Since the IPCloads. loop is mainly used to mitigateconclusively TEFCfatigue loop is 1P frequency to mitigate 2P frequency The results demonstrate thatloads, CPFCand can the mitigate mainly to mitigate 2P frequency loads. The results demonstrate conclusively that CPFC can loads asused anticipated. mitigate fatigue loads as anticipated. 10 5

5

1P

CPC

4.5

IPC CPFC

4

3.5

e moment [kN.m]

3

2.5

2

2P

CPC, IPC, CPFC are shown in Figure 9. It can be seen that there are obvious peaks of 1P (about 0.2 Hz) and 2P (about 0.4 Hz) frequency load while using CPC. The 1P frequency peak is removed completely while using IPC. Both the 1P and 2P frequency peaks are removed completely when using CPFC.Since the IPC loop is mainly used to mitigate 1P frequency loads, and the TEFC loop is mainly used to mitigate 2P frequency loads. The results demonstrate conclusively that CPFC can Energies 2018, 11, 2519 13 of 16 mitigate fatigue loads as anticipated. 10

5

5

1P

CPC

4.5

IPC CPFC

4

3.5

2P

Blade 1 out-of-plane moment [kN.m]

3

2.5

2

1.5

1

0.5

0

Energies 2018, 11, x FOR PEER REVIEW 0

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0.2

0.3

0.4

0.5

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0.6

Frequency [Hz]

4.3.5. The Power Generation Figure Figure 9. 9. The The PSD PSD analysis analysis of of blade blade root root out-of-plane out-of-plane bending bendingmoments. moments. 4.3.5.The Thepower Powergenerations Generation of wind turbine by CPC, IPC, CPFC are shown in Figure 10. There’s no noticeable difference between these control strategies. This indicates that IPC and CPFC have no The power generations wind turbine by the CPC, IPC,speed CPFCexceeds are shown Figure 10. speed. There’sThe no significant impact on powerofgeneration when wind thein rated wind noticeable these control strategies. indicates that IPC research and CPFC havethat no potential ofdifference enhancedbetween power generation by CPFC also beThis widely studied. Smit’s shows significant impact on power generation when the wind speed exceeds the rated wind speed. The smart rotors equipped with TEFs could increase the power generation below rated wind speed [27]. potential enhanced power generation by CPFC alsoinbethis widely studied. research that However,ofthe main objective is to mitigate loads work, so noSmit’s deeply study shows on power smart rotors equipped with TEFs could increase the power generation below rated wind speed [27]. generation. However, the main objective is to mitigate loads in this work, so no deeply study on power generation. 5100 CPC

5080

IPC CPFC

5060

5040

Power [kW]

5020

5000

4980

4960

4940

4920

4900 100

110

120

140

130

150

160

Time [s]

Figure 10. The power generation of a wind turbine. Figure 10. The power generation of a wind turbine.

4.3.6. The Blade 1 Pitch Angles and TEFs Deflection Angles 4.3.6. The Blade 1 Pitch Angles and TEFs Deflection Angles The blade 1 pitch angles and TEFs deflection angles by CPC, IPC, CPFC are shown in Figure 11. Theinblade 1 pitch angles and TEFsofdeflection anglessmoothly by CPC, when IPC, CPFC shown Figure 11. As seen Figure 11a, the pitch angle blade 1 varies usingare CPC. Thein pitch angle As seen inaround Figurethe 11a, thepitch pitchangle angleatofthe blade 1 varies smoothly when angle fluctuates CPC 3P harmonics frequency whenusing usingCPC. IPC. The Thispitch may cause fluctuates around the CPC pitch angle at the harmonics frequency when using IPC. This may 3P increased pitch actuator duty to be required. The TEFC loop has no significant impact on pitch angle cause increased pitch actuator duty to be required. The TEFC loop has no significant impact on pitch because it is not treated as a main control target in this work. As shown in Figure 11b, The TEFs angle because it isofnot as a main control this work. As shown Figure 11b, deflection angles thetreated three blades fluctuate at target the 6Pin harmonic frequency forin mitigating theThe 2P TEFs deflection angles of the three blades fluctuate at the 6P harmonic frequency for mitigating the 2P frequency loads. The loads mitigation control strategy of TEFs has not been optimized in this work. Therefore, the loads mitigation capability of TEFs could be further improved.

25

5

The blade 1 pitch angles and TEFs deflection angles by CPC, IPC, CPFC are shown in Figure 11. As seen in Figure 11a, the pitch angle of blade 1 varies smoothly when using CPC. The pitch angle fluctuates around the CPC pitch angle at the 3P harmonics frequency when using IPC. This may cause increased pitch actuator duty to be required. The TEFC loop has no significant impact on pitch angle because it is not treated as a main control target in this work. As shown in Figure 11b, The TEFs Energies 2018, 11, 2519 14 of 16 deflection angles of the three blades fluctuate at the 6P harmonic frequency for mitigating the 2P frequency loads. The loads mitigation control strategy of TEFs has not been optimized in this work. Therefore, the loads capability of TEFs couldof beTEFs further frequency loads. Themitigation loads mitigation control strategy hasimproved. not been optimized in this work. Therefore, the loads mitigation capability of TEFs could be further improved.

(a)

(b)

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Figure 11. The blade 1 pitch angles and TEFs deflection angles. (a) The blade 1 pitch angles; (b) The Figure 11. The blade 1 pitch angles and TEFs deflection angles. (a) The blade 1 pitch angles; (b) The TEFs deflection angles. 4.3.7.TEFs Thedeflection Damage angles. Equivalent Loads

4.3.7.The Thedamage Damageequivalent Equivalentloads Loads(DEL) of wind turbines are computed by the rain flow counting (RFC) algorithm Accounting the fatigue properties blade material, of 10 are The damage[28]. equivalent loadsfor (DEL) of wind turbines of arethe computed by the S-N rainslopes flow counting used for composite Thefor equivalent frequency of the DEL is 1 material, Hz. (RFC) algorithm [28].materials. Accounting the fatigue properties of the blade S-N slopes of 10 are fatigue DEL of windThe turbine by CPC, IPC, CPFC are DEL shown Figure 12; and the details of used The for composite materials. equivalent frequency of the is 1inHz. DELThe are fatigue given DEL in Table 5. Compared theIPC, DELCPFC of blade root out-of-plane moment of wind turbine by to CPC, are shown in Figure 12; bending and the details of (RootMyc1) by CPC, the DEL are reduced by 42.2% when using IPC, and it is further reduced by DEL are given in Table 5. Compared to the DEL of blade root out-of-plane bending moment (RootMyc1) 53.7% using CPFC. The DEL when of blade root moments (RootMyc1), yaw by CPC,when the DEL are reduced by 42.2% using IPC,in-plane and it isbending further reduced by 53.7% when using moments and tilt moments also reduce(RootMyc1), in different yaw degrees when(Myaw) using IPC CPFC. The(Myaw) DEL of blade root in-plane (Mtilt) bending moments moments andand tilt CPFC. moments (Mtilt) also reduce in different degrees when using IPC and CPFC. S-N slope = 10 3500 CPC IPC

3000

CPFC

2500

Fatigue DEL [kN.m]

2000

1500

1000

500

0 RootMyc1

RootMxc1

Mtilt

Myaw

Figure 12. The DEL of wind turbine.

Figure 12. The DEL of wind turbine. Table 5. The details of DEL. CPCTable 5. The details IPC of DEL. StdCPC

Std

RootMyc1 (kN·m) 1870Std RootMxc1 (kN · m) RootMyc1(kN·m)33601870 Mtilt (kN·m) 750 RootMxc1(kN·m)8013360 Myaw (kN·m)

1080 Std 3210 1080 770 3210 949 770 949

Mtilt(kN·m) Myaw(kN·m)

750 801

CPFC

Std IPCReduction CPFC Reduction 42.2% Std 865 53.7% Reduction Reduction 4.5% 3250 42.2% 865 53.7 % 3.3% −2.7% 562 25.1% 4.5% 3250 559 3.3% 30.28% −18.5% −2.7 % 562 25.1 % −18.5 % 559 30.28 %

5. Conclusions In this work, the CPFC for loads mitigation of wind turbines is investigated. The main

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5. Conclusions In this work, the CPFC for loads mitigation of wind turbines is investigated. The main conclusions are as follows: (1) The IPC and CPFC could effectively mitigate the fatigue loads and decrease the structural deflections of wind turbines. Compared to CPC, the DEL of blade root out-of-plane bending moment is reduced by 42.2% while using IPC, and it is further reduced by 53.7% while using by CPFC. The standard deviation of blade tip out-of-plane deflection is reduced by 44.6% while usinig IPC, and it is further reduced by 50.2% while using CPFC. (2) The CPFC could adopt a load frequency division control algorithm to combine the IPC loop and TEFC loop. The IPC loop is mainly used to mitigate low frequency loads, and the TEFC loop is mainly used to mitigate high frequency loads. Due to the fast response of TEFs, higher frequency loads can be further mitigated; and the combined control algorithm can be further optimized to enhance power generation and reduce excessive actuator action. (3) The CPFC adopts both an azimuth angle feed-forward and a loads feedback control strategy for improving control performance. The feed-forward control loop should anticipate the observable disturbances and provide beneficial compensation for feedback control loop. The advanced predictive model control and wind speed measurement by LIDAR could further improve the controller performance. (4) The power generation wind speed has no significant impact with CPFC while exceeding the rated. The effect of CPFC on power generation below rated wind speed should be further studied. Author Contributions: Conceptualization and Methodology, K.H.; Software and Data curation, L.Q.; Investigation and Validation, L.Z.; Supervision and Funding acquisition, Y.C. Acknowledgments: This work was supported by the National High-tech R&D Program of China (863 Program, Grant No. 2012AA051301), National Natural Science Foundation of China (Grant No. 51076088), Guangdong Science and Technology Planning Project (Grant No. 2015B020240003); Shantou Science and Technology Planning Project (Grant No. 2015-58; 2016-65). Conflicts of Interest: The authors declare no conflict of interest.

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