Reduction of Wind Turbine Torque Fluctuation Using Individual Pitch Control Based on Edgewise Moment

In order to eliminate the nonuniform force on the wind rotor caused by wind shear, tower shadow and turbulence and smooth the torque fluctuation of the wind turbine and the unbalanced loads on the wind turbine, a new individual pitch control strategy based on edgewise moment using single neuron PID controller is proposed. That is, the presented control strategy directly controls the blade edgewise moment generated by aerodynamic force. At the same time, to simulate the wind turbine loads, a dynamic model of three-bladed upwind horizontal axis wind turbine is built. Thus, the influence rules of the wind turbine torque fluctuation are deduced at length. Finally, to verify the effectiveness of the proposed individual pitch control system with the single neuron PID controller, the 2MW wind turbine generator system is modeled and simulated. The performance of the controller is illustrated its capability of not only reducing the wind turbine fluctuation, but also smoothing the fluctuation of the flapwise moment, the yaw moment and the tilt moment.


INTRODUCTION
Wind power generation is one of the most mature and well-developed power generation technologies in renewable energy area.In order to enable great role of wind energy in power production, it is necessary to increase the size and the power of wind turbine unit (Hau, 2006;Manwell et al., 2002.).With the increasing size of the wind turbine, the turbine is subjected to extreme unbalanced loads because of the uneven distribution caused by wind shear, tower shadow, turbulence and so on Hansen (2008).The unbalanced loads lead to serious damage to the wind turbine, such as blade edgewise vibration, blade flapwise vibration, drive train torsion and tower bending and cause great fatigue loads to the key components of the wind turbine.Moreover, the unbalanced loads will bring many problems to the wind turbine mechanical strength and the power grid quality (Fadaeinedjad et al., 2009;Haiyun et al., 2010).For large-scale wind turbine with one hundred meter of diameter, these problems are particularly prominent, thus it is necessary to reduce the unbalanced loads on the wind turbine.
The pitch actuator mechanism, regardless of electrical servo or hydraulic servo, usually adopts the Collective Pitch Control strategy (CPC) which the pitch angles of all blades are same.Assuming the wind distribution in the wind rotor plane is uniform without the effects of wind shear, tower shadow and turbulence, the blade pitch angle usually is decided by the effective wind speed or the average wind speed.If every blade of the wind rotor is adjusted by Individual Pitch Control (IPC) according to some certain rules, the forces on blade tend to uniformly in the rotation plane and the amplitudes of the blade root moments in two directions reduce in different degrees according to the theoretical aerodynamic analysis.Moreover, the fluctuation of the wind turbine torque and the unbalance loads reduce.
Recently, the studies of IPC mainly focuses on cyclic pitch control, D-Q axis transformation IPC, Coleman transformation IPC, weight coefficient distribution IPC, the smart rotor control and so on.The first cyclic pitch control is a compensation control using aerodynamic force generated by cycle pitch change based on the measured tilt moment and yaw moment (Lescher et al., 2005;Markou et al., 2011).The second D-Q axis transformation IPC is to control the load components, which come from the measured blade root loads by the D-Q axis transformation (Bossanyi, 2003(Bossanyi, , 2005;;Liu et al., 2006;Jelavic et al., 2008;Wilson et al., 2009).Assuming there is no interaction between the orthogonal coordinate axes, the classical control method for single input single output can used to control the load components.The third Coleman transformation IPC is the wind turbine multivariable control, which the pitch control loop is decoupled into three independent linear time-invariant feedback control loops by the Coleman transformation.The three independent control loops are the control loop of wind rotor speed, the yaw control loop and the tilt control loop respectively (Geyler and Caselitz, 2007;Kanev and Van, 2010;Selvam et al., 2009;Van, 2006).The forth weight coefficient distribution IPC is the pitch angle adjusted by the dynamic weight coefficient along with the aerodynamic force change (Trudnowski and LeMieux, 2002).The last smart rotor control is to adopt a new-type rotor whose blade are equipped with a number of control devices that locally change the lift profile on the blade and combined with appropriate sensors and controllers (Barlas et al., 2006;Lackner and Van Kuik, 2010).Because MW-scale Wind Turbine Generator System (WTGS) are grid-connected, the torque fluctuation of wind turbine easily results in many problems, such as the fluctuant power output of WTGS and the poor power grid quality.However, the above IPC strategies mainly focus on the reduction of the blade flapwise moment or improving the blade structure without considering the torque fluctuation of wind turbine or the blade edgewise moment.
In this study, to reduce the wind turbine torque fluctuation, a novel control strategy using IPC based on edgewise moment is proposed.Moreover, the single neuron PID controller is used to IPC.This controller adjust the pitch angle individually according to the measured blade edgewise moment and the ideal reference edgewise moment calculated by the effective wind speed without taking into account of any influenced factors.Furthermore, the fluctuation rules of the wind turbine torque are deduced in details based on the dynamic wind turbine model.Finally, to verify the effectiveness of the proposed IPC with single neuron PID controller, the model of a 2MW WTGS is set up.The simulation results show that this proposed IPC system with single neuron PID controller can not only directly smooth the fluctuation of wind turbine torque and the blade edgewise moment, but also indirectly reduce the fluctuations of the blade flapwise moment, the yaw moment and the tilt moment.These provide certain guiding significance to the IPC implementation in wind field.
The analysis of loads on the blade and the torque fluctuation of the wind turbine: Because the mechanical energy is converted from the kinetic energy of wind by the wind rotor, the loads on the turbine, the tower and the hub come from the external loads on the blade (Li et al., 2004).The blade loads are aerodynamic, gravity, inertia and so on.
The total edgewise moment of a single blade is mainly composed of the edgewise moment generated by aerodynamic force on the blade and the edgewise moment generated by the blade gravity according to the aerodynamic theory, the other blade loads are so small that they are neglected.That is: , , , where, M Edgewise, i = The blade i-th total edgewise moment M Gravity, i = The blade i-th gravity moment M Edge, i = The blade i-th edgewise moment generated by the aerodynamic force For the three-bladed upwind horizontal axis wind turbine, the wind turbine torque is the sum of the edgewise moment from three blades: where, M Trubine is the wind turbine torque.
The other aerodynamic load on the blade is the flapwise moment and the vector sum of M flapwise, i are yaw moment and tilt moment respectively: 3 , 1 sin( ) where, M flapwise, i = The blade i-th root flap wise moment   = The blade i-th azimuth M yaw = The yaw moment on the tower M tilt = The tilt moment on the tower Take the blade of 2 MW wind turbine as an example, the loads on the blade 1 are calculated based on the element theory according to the blade geometry parameters, the blade aerofoil parameters, the blade mass and the blade stiffness parameters.The relationship among M Edgewise, 1 , M Edge, 1 and M gravity, 1 is shown in Fig. 1.Although the edgewise moment component caused by the aerodynamic force is significantly less than the edgewise moment component caused by the gravity, the former moment is the main influencing factor and cannot be neglected.By analyzing the aerodynamic loads on the wind turbine, the blade edgewise moment generated by aerodynamic force on the blade is the main fluctuation factor of the wind turbine torque and the wind turbine power output.In addition, the fluctuations of the yaw moment and the tilt moment derive from are the blade flapwise moment.If the edgewise moment on the blade is controlled by the IPC strategy, the wind turbine torque fluctuation is directly reduced and the wind turbine power output remains stable.

Dynamic wind turbine aerodynamic model for IPC:
In order to analyze the operation principle of the IPC, the loads on the wind rotor and the blade influenced by wind shear, tower shadow and turbulence should be simulated.The traditional model of the wind turbine is built based on the known wind turbine torque coefficient.Because the pitch angle and its impact on the wind turbine aerodynamic torque are coupled, the pitch angle influences on the lift force and the drag force on the blade cannot be analyzed separately (Abdin and Xu, 2000).In order to implement the IPC strategy, the built wind turbine model can calculate the aerodynamic force and the corresponding loads on the blade element.
The aerodynamic force dF on the blade element dr generate from the action of the airflow with the speed of w.The dF can be decomposed into the dL and dD along with the direction of vertical and parallel to the relative speed and it also can be decomposed into the dF a and dF u along the direction of vertical and parallel to the rotating plane, which are shown in Fig. 2. The edgewise moment and the flapwise moment on the blade element derive from the dF u and the dF a , respectively.Because the diameter of the MW-level wind turbine is usually up to hundred of meters, there is a great difference between the torque at the blade tip element and the torque at the blade root element, as in (Dou et al., 2011).Considering that the number of blade elements cannot increase without limitation, the number of the blade element is re-optimized by the weight coefficient assignment.Assuming the total number of blade element is p, the blade elements is divided into n feature regions according to the parameters variation of the airfoil and the number of the blade element distributed in each region is determined by the weight coefficient k t , that is: where, ∑    =1 = 1 The aerodynamic loads on the blade are calculated by integrating the whole blade.In order to simple realize and accurate calculation, the blade dr is equivalent to the Δr variation and the length of blade element chord is the average length of both ends of this segment.
The aerodynamic model simulates the wind speed of the blade tip, the wind turbine torque, the loads on the blade 1 and the loads on the tower underling the wind, as shown in Fig. 3.The turbulence intensity of wind is 0.15, the wind shear coefficient is 0.2 and the average wind speed is 12 m/s.Considering the effects of the wind shear, the tower shadow and the turbulence, the wind speed of the blade tip is relative maximum when the blade rotates to the top of the wind rotor plane, but the wind speed is relative minimum when the blade 1 rotates to the bottom of the wind rotor plane, as shown in Fig. 3a.Considering none of the influence factors, the wind speed distribution is uniform, the wind turbine torque and the loads on the blade 1 are constant and the yaw moment and the tilt moment on the tower are zero (Normal curve), as shown in Fig. 3b-3f.Considering only the wind shear effect, the edgewise moment and the flapwise on the blade 1 are minimum when the blade 1 rotates to the bottom of the wind rotor plane.The edgewise moment and the flapwise on the blade 1 are maximum when the blade 1 rotates to the top of the wind rotor plane, as shown in Fig. 3c and 3d.Considering the effect of the tower shadow, the wind speed decrease rapidly when the blade 1 rotates into the tower shadow region and the edgewise moment and the flapwise on the blade 1 decrease with the wind speed.Considering the wind shear effect and the tower shadow effect, the loads fluctuation on the blade 1 are maximum compared with the wind shear effect or the tower shadow effect.Considering the effect of the wind shear, the tower shadow and the turbulence, the general change of the loads on blade 1 is consistent with the loads fluctuation affected by wind shear and tower shadow.In addition, the fluctuations of the wind turbine torque, the yaw moment and the tilt moment are proportional to the wind speed variation, as shown in Fig. 3b-f.The amplitude of torque fluctuation caused by the tower shadow is 5.85% compared with the rated wind turbine torque (Normal curve).The amplitude of

Reduction of torque fluctuation by individual pitch control in WTGS:
Wind shear, tower shadow and turbulence cause the nonuniform forces such as tower bending, drive train torsion, blade edgewise bending and blade flap wise bending of wind turbine, as shown in Fig. 4.Under the premise of the maximum wind power captured, the IPC control target is to eliminate the unbalanced loads as much as possible.When the wind rotor speed is equal to the rated rotor speed, the variation of pitch angle according to some certain rules (IPC) can result in the attack angle change of the blade.Because the change of attack angle causes the changes of the normal force coefficient and the lateral force coefficient, the forces on blade tend to uniformly in the rotation plane.Moreover, the aerodynamic loads on the blade reduce greatly and the wind turbine torque keeps stable.Because of the nonlinearity and complexity of the loads and the pitch angle according to the analysis of wind rotor loads, it is difficult to control by a conventional controller.A Single Neuron self-adaptive PID (SNPID) controller has adaptive and self-learning ability, which not only calculate easily with the simple structure, but also can adapt the environment change with strong robustness (Wu et al., 2008;Zhao and Yang, 2008).Therefore, the SNPID-IPC can be used to adjust the blade pitch angle to reduce the edgewise moment fluctuation of blade.The structure of the controller is shown in Fig. 5, where, r (k), y (k) is state convert input, x 1 , x 2 , x 3 are the state convert outputs which have the following relationship.
where, K = The single neuron proportional coefficient w i (k) = The weight coefficient of corresponding to = The output of the SNPID controller The functions of self-adaptive and selforganization of SNPID controller is implemented by adjusting the weight coefficient.In addition, the adjustment of weight coefficient realizes according to a rule of supervised Hebb learning.In order to guarantee the convergence of learning algorithm and the robustness of the control strategy, the weight coefficients should normalized.Compared to the traditional PID controller, the w 1 (k), w 2 (k), w 3 (k) is equivalent to the integral, proportional and differential item of the traditional controller, respectively.
where, η I , η P and η D are the rate of integration, proportional and differentiation respectively.Then the output of SNPID is as the following.
( ) ( ) ( ) ( ) The on-line learning of the parameters of PID are mainly related to e(k) e(k-1) z(k).So the corrected algorithm of weight coefficients for single neural selfadaptive PID controller are modified, which x i (k) is changed as e(k) + Δe(k), Δe(k) = e(k) -e(k-1) and z(k) = e(k).
The input of the SNPID-IPC controller is the difference between the ideal blade edgewise moment and the actual blade edgewise moment generated by the aerodynamic force.And the output of the controller is the deviation of pitch angle, that is, the blade pitch angle is the collective pitch angle minus the deviation of pitch angle.The initial value of SNPID-IPC controller are w 1 = 0.0067, w 2 = 0.007 and w 3 = 0.0001, ,the rate of learning is η I 0.15×10 -4 , η P = 0.3×10 -2 , η D = 0.15×10 -5 and the proportional coefficient of the single neuron is K = 0.3.

SIMULATION RESULT AND ANALYSIS
In this study, in order to verify the effectiveness of IPC with SNPID controller, a typical 2 MW three-blade upwind horizontal axis wind turbine is modeled and simulated with various wind conditions: a ramp wind speed and a turbulence wind speed.The parameters of the wind turbine are as shown in Table 1.
Figure 6 illustrates the blade root moments using CPC.The wind speed at the hub is a ramp wind speed as shown in Fig. 6a.Considering the effects of wind  is unchanged.In addition, though the average flapwise moment decreases, the flapwise moment fluctuation is 10 times as much as the edgewise moment fluctuation.
• Wind regime 1: a ramp wind: Figure 7 illustrates the response of the system using IPC underling the ramp wind speed.The variable of the wind at the hub is as shown in Fig. 6a and 7a illustrates the wind turbine torque (CPC at Hub curve) keeps as the rated wind turbine torque when the wind speed distributes uniformly in the rotating plane.
Considering the effects of wind shear and tower shadow, the wind turbine fluctuation (CPC curve) decreases in a small level (about 6%) compared to the rated wind turbine torque.In addition, the upper and lower fluctuation of the wind turbine torque is about 10% compared to the rated torque.After using the IPC with SNPID controller, the wind torque fluctuation (IPC curve) decreases greatly to 2.5% compared to the rated torque and the wind torque tends to the rated wind turbine torque, which maintains the generator output power unchanged.
Figure 7b illustrates the fluctuation of the edgewise moment on the blade 1 reduces directly by the IPC compared to the CPC.Because the wind turbine torque is the sum of the edgewise moments on the three blades and the phase of the edgewise moments on the two adjacent blades is equal to 120 deg, the variable of the blade1 edgewise moment is the same as some parts of the wind turbine torque fluctuation.In addition, the moment fluctuation of the blade 2 and the blade 3 is similar with the blade 1.
Figure 7c demonstrates the collective pitch angle changes (CPC curve) with the wind speed.The blade pitch angle not only relates to the wind speed, but also relates to the blade position in the rotating plane.When the blade rotates from the top position to the bottom position in the rotating plane, the pitch angle decreases; and when the blade rotates from the bottom position to the top position, the pitch angle increases.Meanwhile, the pitch angle phase of the adjacent blades (Blade i curve) keeps at 120 deg as the azimuth difference of two adjacent blades is 120 deg.
Furthermore, the flapwise moment fluctuation, the yaw moment fluctuation and the tilt moment fluctuation reduce significantly by individual pitch indirect control with SNPID controller compared to the CPC, as shown in Fig. 7d-7f.
These results indicate this IPC with SNPID controller not only smoothes the fluctuation of wind turbine torque, but also weakens the other loads on the blade.Therefore, this IPC has obvious advantages compared with the traditional CPC.
• Wind regime 2: a turbulence wind: Figure 8 illustrates the response of the system using IPC underling a turbulence wind.Figure 8a shows the variation of the wind speed at the hub. Figure 8b-8f demonstrates the changes of the loads (CPC curve) are in accord with the variable of the turbulence wind.Figure 8b shows the wind turbine torque (IPC curve) is close to the rated wind turbine torque (CPC at Hub curve) and the fluctuation becomes small compared to the CPC.In addition, the Figure 8g shows the pitch angle changes of the blade that meet the above-deduced IPC rules.However, the change rate of the pitch angle is so high, the frequency of the pitch action intensity increases which will put forwarded higher demands to the pitch actuator.
The other IPC based on multi-stage dynamic weight coefficient distribution of the pitch angle adjusts the pitch angle according to the dynamic weight coefficient (Dou et al., 2012).The WTGS with this IPC cannot feedback controlled without load sensors.According to the above Fig.7 and 8, the WTGS with the SNPID-IPC controller can smooth the fluctuation of the loads by sampling the blade edgewise moment and tracking feedback control.Moreover, this IPC system tracks the quick change of wind speed by means of selflearning and the adjustments of the SNPID controller.Because the wind variable in large-scale wind rotor rotating plane is severe, the WTGS with SNPID-IPC controller is obviously superior to the former system.

CONCLUSION
In this study, the blade loads and wind turbine loads are analyzed firstly and the blade edgewise moment generated by the aerodynamic force is proved to the main factor to the wind turbine torque fluctuation.To calculate the wind turbine torque and loads on the blade, a detailed dynamic aerodynamic model of the wind turbine is built based on the element theory.In addition, the influence rules of the wind turbine fluctuation caused by wind shear, tower shadow and turbulence are deduced based on this model.Moreover the IPC with SNPID controller to directly reduce the fluctuation of the edgewise moment is proposed and the SNPID controller is designed in detail.A typical 2MW WTGS is modeled and simulated with various winds.The simulation results show, the WTGS with the SNPID-IPC controller not only smoothes the wind turbine torque fluctuation and maintain the wind turbine torque at rated torque compared with the CPC WTGS, but also weakens significantly the unbalanced loads on the blade and the tower.

Fig. 1 :
Fig. 1: Relationship diagram of the loads on the blade 1

Fig. 2 :
Fig. 2: Diagram of force analysis and speed vector of blade element The lift coefficient of the blade element C d = The drag coefficient of the blade element l = The chord length of the blade element I = The flow angle, which can be expressed as I = β+i of the hub R = The radius of the blade F a = The axial force on the blade F u = The lateral force on the blade M Edge = The edgewise moment on the blade M flapwise = The flap wise moment on the blade

Fig
Fig.3: Loads on the wind turbine

Fig. 4 :
Fig. 4: Non uniform forces on the wind turbine Fig. 6: Blade root moments using CPC shear and tower shadow, the edgewise moment and the flapwise moment on the three blades using CPC are shown in Fig. 6b and 6c.As the difference of the adjacent blade positions is 120 deg, the phase of the edgewise moment and the flapwise moment of the adjacent blades are also equal to 120 deg.With the increasing of wind speed, the edgewise moment fluctuation increases, but the average edgewise moment Fig. 8: Control effect diagram using IPC with the turbulence wind