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Design, modeling and implementation of a novel pitch angle control system for wind turbine
Renewable Energy 81 (2015) 599e608
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Technical note
Design, modeling and implementation of a novel pitch angle control system for wind turbine Xiu-xing Yin, Yong-gang Lin*, Wei Li, Ya-jing Gu, Xiao-jun Wang, Peng-fei Lei The State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Zheda Rd.38, 310027 Hangzhou, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 April 2014 Accepted 16 March 2015 Available online
A novel pitch angle control system is proposed to smooth output power and drive-train torque fluctuations for wind turbine. This system is characterized by an outer open control loop for enhancing the direct pitching motion and an intrinsic hydro-mechanical position control loop offering the benefit of sensor-less pitch control. A pragmatic design procedure is provided and several key design parameters are determined or optimized. Modeling, stability analysis and dynamic characteristics of this pitch control system are also presented. Comparative experimental results have validated the effectiveness and efficiency of this system in power and torque regulations. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Wind turbine Pitch angle control system Hydro-mechanical position control loop System modeling Stability analysis Dynamic characteristics
1. Introduction Pitch angle control systems are commonly employed in medium to large wind turbines to keep the captured wind power close to the rated value above the rated wind speed, bringing about the benefits of better control flexibility and power quality. Such systems can also alleviate the structural wind loads and protect the wind turbine from fatigue damage during strong wind gusts. Thus, these systems have an immediate influence on the wind power regulation and are of significant importance for variable pitch wind turbines. Moreover, high performance and reliability oriented advanced pitch control systems can meet the ever increasing stringent performance requirements specified by modern turbines and hence are essential to enhance the competitiveness of wind energy technology [1]. There are fundamentally two types of such systems: electromechanical and hydraulic types. For the electromechanical type, the pitch actions can be achieved by using an electric motor. This system has been extensively investigated in the literature including system design [2], analysis of dynamic characteristics [3], double closed-loop control [4], direct torque pitch control [5], adaptive pitch control [6], and fuzzy logic pitch control [7]. Although
* Corresponding author. Tel.: þ86 182 6712 0581. E-mail address: [email protected] (Y.-g. Lin). http://dx.doi.org/10.1016/j.renene.2015.03.042 0960-1481/© 2015 Elsevier Ltd. All rights reserved.
relatively compact and accurate, the robustness and power-mass ratio of this system could be relatively low. For the hydraulic pitch system, a value controlled hydraulic cylinder is commonly employed to generate the final pitch actions through a slider-crank mechanism [8]. Recent studies on this system mainly include pitch control strategies [9,10], reliability evaluation [11], system modeling [12], and independent pitch control [13]. Chiang et al. [14] developed a variable-speed pumpcontrolled hydraulic pitch control system and an adaptive fuzzy pitch controller. However, despite of such various control methods in the literature, sufficiently detailed dynamic analysis of this system was not provided. Although the hydraulic pitch control system may be advantageous in high power/mass ratio and relatively high reliability, the control accuracy of this system is relatively poor due to the use of the slider-crank mechanism [8]. The major contributions of this paper are a novel pitch angle control system and the detailed analysis methods such as design procedure, system modeling, stability and dynamic analysis. By integrating the fundamentally different working mechanisms of the aforementioned two types, this novel system holds the advantages of both the two types while overcoming their well-known practical performance limitations. The power/mass ratio of the conventional electromechanical pitch system can be enhanced by using a hydraulic motor in the proposed system where the electric motor is used for control, not for actuation in the electromechanical system. The pitch control accuracy of the conventional hydraulic type can be significantly improved in the novel system by
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incorporating a rotary hydraulic servo instead of a slider-crank mechanism. This is because the resulting pitch angle is directly proportional to the angular displacement of the hydraulic servo and can be precisely controlled by an intrinsic hydro-mechanical position closed-loop in the servo. Therefore, this novel system not only holds the advantages such as compactness, high power/mass ratio, higher reliability, and good control precision in particular but also can be utilized in medium or large scale wind turbines with better precision as compared with the conventional pitch systems. Hence, such significant performance improvements make the proposed pitch control system a promising choice for industrial applications.
pitch angle signals and hence allow sensor-less pitch control, whereas a large variety of sensors or transducers are always used in other pitch systems. (c) Compact structure and integration design make this pitch system appropriate for individual pitch control. (d) This system can be controlled directly by a host computer without using additional controllers or sensors, which provides significantly cost-effective potentials. (e) The novel pitch control system works in the outer open-loop with an internal hydro-mechanical position control loop and hence has a wider range of pitch rate and lower maintenance cost as compared with other conventional pitch systems.
2. System description As shown in Fig. 1, this novel pitch control system, consisting of a digital electric motor, a hydraulic servo and a pitch gear set mounted in the nacelle, is an integrated electro-hydraulic position servo system with an intrinsic feedback closed-loop. The digital electric motor acts as a converter transmitting the digital pitch control command to the hydraulic servo. The pitch gear set is used to adapt the high shaft speed of the hydraulic servo to the relatively low pitch rate. The hydraulic servo consists of a spool type rotational valve, a screw and nut combination and a rotary actuator. The rotational motion from the digital electric motor opens the valve and ports the oil flow from a constant hydraulic power supply to this actuator whose motion is fed back through the screw and nut combination and subtracted from the input motion so as to stroke the valve and close this loop. Hence, such motions automatically create an intrinsic hydro-mechanical position control loop in the hydraulic servo. The rotary actuator can be sized to handle expected pitch loads and has the hydraulic natural frequency large enough to meet overall response requirements. Generally, a hydraulic axial piston motor can be employed as the rotary actuator. Significant features of this pitch control system are as follows. (a) The pitch angle control can be eventually achieved by a rotary hydraulic actuator with high payload capability and high power to weight ratio rather than an electric motor or a hydraulic cylinder in other pitch systems. Thus, relatively high pitch control accuracy and power/mass ratio make this system suitable for large-scale wind turbines. (b) The intrinsic hydro-mechanical closed control loop enables this system to avoid the necessity to measure or feedback the
3. System design 3.1. Pitch loads The calculation of pitch loads is first presented as it is an important prerequisite for the system design. Such loads mainly stem from aerodynamics, gravity and dynamic interactions [15]. In particular, the inertia moment arising from the blade centrifugal force is the predominant source of loads associated with the pitch actions and is discussed in detail as follows. As illustrated in Fig. 2, the plane of rotation is aligned with the axis o-x and perpendicular to the surface of this paper. The pitch axis passes through the center of gravity of each blade cross section and lies in the plane of rotation. The first principal axis of the blade cross sections lies along the chord line for this symmetric aero-foil [16]. Two coordinate systems are established at the same origin O. The reference frame (x, y) is rotated about the frame (x1, y1) with the pitch angle b between them. Consider an incremental part of the blade at a radius r from the rotational axis and the point B with an incremental mass dm. The incremental centrifugal force acting on this point is
dFc ¼ rB u2 dm
(1)
and the radius rB can be represented as
rB ¼
LOB $sin g sin 4
(2)
Substituting equation (2) into (1) yields
dFc ¼
LOB $sin g 2 u dm sin 4
(3)
where
u e the angular velocity of the wind rotor; LOB e the length of the line segment OeB; g e the angle between the line OeB and the plane of rotation; 4 e the angle between the pitch axis and the incremental centrifugal force dFc. The force dFc can be decomposed into a component dFn perpendicular to the blade cross section and a component dFt parallel to this cross section. The force dFt can be described as
dFt ¼ dFc $sin 4 ¼
Fig. 1. Schematic of the proposed pitch control system.
LOB $sin g 2 $u $dm$sin 4 ¼ u2 $LOB $sin g$dm sin 4 (4)
The resulting inertia moment about the pitch axis due to the centrifugal force is
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Fig. 2. The centrifugal forces.
dTc ¼ dFt $LOA ¼ u2 $LOB $sin g$dm$LOA
(5)
The coordinates of point B in the reference frame (x, y) are
xB ¼ LOA yB ¼ LOB $sin g
(6)
8 y1B sin b > > > < xB ¼ x1B cos b cos b cos b ¼ x1B cos b y1B sin b > y y sin b > > sin b ¼ x1B sin b þ y1B cos b : yB ¼ 1B þ x1B 1B cos b cos b (10)
Substituting equation (6) into (5) yields
dTc ¼ u2 $xB $yB $dm ¼ u2 $xB $yB $rb $ds$dr
Substituting equation (10) into (9) yields
(7)
Z Jxy ¼
xB yB ds sb
where
Z h i x21B y21B sin b cos b þ x1B y1B cos2 b sin2 b ds
¼
LOA e the length of the line segment O-A;
sb
rb e the density of the blade material;
(11)
ds e the cross sectional area at the point B; dr e the incremental radius at the radius r.
The product of inertia of the area ds about the principal axes o-x1 and o-y1 is zero [17].
Integrating equation (7) over the blade radius yields
ZR Z Tc ¼ rb u2
xB yB dsdr ¼ rb u2 0
x1B y1B ds ¼ 0
ZR
sb
Jxy dr
Substituting equation (12) into (11) yields
(8)
0
Z Jxy ¼
where
xB yB ds ¼ sb
Tc e the total inertia moment acting on the blade; R e the total radius of the rotor; sb e the area of this airfoil section at the local radius r; Jxy e the product of inertia of the area sb about the axes o-x and o-y.
"
Z
x21B dsz0:0446$
Jy1 ¼ sb
y21B dsz0:0464$
Jx1 ¼ sb
1 2
Z x21B y21B sinð2bÞds sb
1 ¼ sin 2 b Jy1 Jx1 2 where
Jy1 e the moment of inertia of the area sb about the axis o-y1; Jx1 e the moment of inertia of the area sb about the axis o-x1;
# 0:008 4 0:008 3 c 4 h 3 4 1 1 1 $ $D $ c h D c
Z Jxy ¼
xB yB ds
(13)
# 4 0:008 4 0:008 c h $ 1 1 1 $ $D4 c h D c
"
Z
(12)
(9)
sb
Transforming the coordinates of point B (x1B, y1B) in the reference frame (x1, y1) to the frame (x, y) yields
c e the airfoil chord length; h e the airfoil thickness; D e the wind rotor diameter. Substituting equation (13) into (8) yields
(14)
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r u2 Tc ¼ b 2
ZR h
i sin 2 b Jy1 Jx1 dr
(15)
dup upmax ¼ dt tp
(23)
0
Substituting equation (23) into (22) yields
Dividing the blade into a set of span-wise blade sections gives an alternative expression of equation (15).
Tc ¼
R h i r b u2 X Jy1 Jx1 $sin 2 b$Dr 2 r¼0
iopt (16)
ummin ummax iopt upmin upmax
Dr e the incremental radius of the blade. The actual pitch load Tp for design can be closely approximated by considering the pitch bearing efficiency h [18].
Tc h
(24)
The optimal ratio iopt must satisfy the practical constraint of limiting the maximum pitch rate.
where
Tp ¼
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u upmax uJb $ tp þ Tp ¼t u Jm $ pmax tp
(17)
3.2. Pitch gear ratio The shaft of the hydraulic servo is coupled to the blade root through the pitch gear set with the gear ratio i. The pitch gear ratio can be reasonably calculated based on the actual pitch load Tp presented in section 3.1. Thus, the torque balance equation on the servo side is
(25)
where iopt e the optimal pitch gear ratio; ummax, ummin e maximum and minimum values of the shaft speed of the hydraulic servo; upmax, upmin e maximum and minimum values of the pitch rate; tp e the time required by the pitch rate to reach its maximum value. Therefore, the optimal pitch gear ratio can be obtained from equations (24) and (25).
3.3. Hydraulic servo
Tm ¼ Jm
dup Tp dum þ Jb þ dt i$dt i
(18)
where Tm e the torque generated by the hydraulic servo; Jm e the mass moment of inertia of the hydraulic servo; Jb e the mass moment of the blade about its longitudinal axis; um e the shaft speed of the hydraulic servo; up e pitch rate. The speed um is related to the pitch rate up by
um ¼ i$up
(19)
Jm þ
dup Tp Jb þ $i$ dt i i2
iopt ¼
du
Jm $ dtp
(26)
qm ¼ Cw xv
rffiffiffiffiffi ps r
(27)
The power extracted from the servo is
(21)
Solving equation (21) yields
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u dup uJb $ þ Tp dt t
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðps pL Þ r
(20)
It is desirable for this servo to operate at the optimal pitch gear ratio where the output torque Tm is minimized. This optimal ratio iopt can be determined by differentiating equation (20) with respect to i and setting the result equal to zero.
dup Jb dup Tp dTm ¼ Jm $ 2$ 2 ¼0 di dt i dt i
qL ¼ Cw xv
The maximum flow rate of this valve is
Substituting equation (19) into (18) yields
Tm ¼
The volumetric displacement Dm and the maximum flow rate qm rank as the two important parameters for the design of this hydraulic servo. The two parameters can also be determined based on the calculated parameters in section 3.2, such as the torque and the shaft speed of the hydraulic servo. The flow rate of the rotational valve is
(22)
The time derivative of the pitch rate up can be represented as
Phs ¼ Cw xv
rffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffi ps p p $ps $ L $ 1 L r ps ps
(28)
where qL e the flow rate of the rotational valve; qm e the maximum flow rate of the rotational valve; Phs e the power extracted from the hydraulic servo; Cw e constant coefficient associated with the rotational valve; xv e the linear spool displacement of the rotational valve; ps e constant supply pressure; r e mass density of the hydraulic oil; pL e load pressure. Differentiating equation (28) with respect to pL and setting the result equal to zero yields
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pLp ¼
2 ps 3
(29)
qm ¼ xv
Kq Dm s
Combining equations (26), (27) and (29) yields
qm qLp ¼ pffiffiffi 3
(30)
s2 u2h
þ
2 uxhh
!
(36)
sþ1
where t e the helical pitch of the screw and nut combination;
The maximum power extracted from the servo occurs at the point where the load pressure pL and flow rate qL obtain the particular values in equations (29) and (30) [19]. The hydraulic servo should be able to handle the largest pitch load at this maximum power point. Thus,
pLp Dm ¼ Tmmax 2p
603
(31)
qm e the rotary displacement of the hydraulic motor; qv e the spool displacement of the rotational valve; Kq e flow gain of the rotational valve;
uh e hydraulic natural frequency; xh e hydraulic damping ratio.
Equations (35) and (36) are the basic representations of this position control loop and can be illustrated by using the block diagram in Fig. 3. Thus, the open loop transfer function is
and
qLp ¼ ummax Dm
(32)
where
pffiffiffi 3 3$p$Tmmax $ummax ps
!
(37)
sþ1
Tcp ðsÞ ¼
1 s3 Kv $u2h
h þ 2 Kvx$u s2 þ Ksv þ 1 h
(38)
where
(33) Kv ¼
Substituting equations (30) and (33) into (32) yields
qm ¼
þ
2 uxhh
Kv e velocity gain of this control loop; s e Laplace operator.
Substituting equation (29) into (31) yields the
3p$Tmmax ps
s
s2 u2h
and the closed-loop transfer function is
Dm e the volumetric displacement; qLp e the flow rate of the hydraulic servo at the maximum power point; pLp e the load pressure of the hydraulic servo at the maximum power point;
Dm ¼
Kv
Top ðsÞ ¼
(34)
Thus, the volumetric displacement and the maximum flow rate of the hydraulic servo can be calculated by using equations (33) and (34). In practice, the values of the two parameters should be slightly increased to compensate for the power losses due to the friction and leakage in the servo.
t$Kq 2pDm
(39)
The free s in the denominator of equation (37) indicates a first order integral part so that this control loop is type one and has zero position error. As shown in Fig. 3, this intrinsic position control loop is generated automatically with a unit negative feedback. Thus, sensor-less position control of this pitch system can be achieved due to this direct feedback closed-loop.
4.2. Stability analysis 4. System modeling and analysis The dynamic performances of this system are mainly dominated by the hydro-mechanical position control loop. Thus, this control loop, including the screw and nut combination and the hydraulic portion, is modeled and analyzed in detail as follows.
Stability is probably the most important characteristic of this pitch system. The analysis of this loop dynamics is usually centered on the requirements for stability. The Routh-Hurwitz stability criterion [24] is used to ascertain the stability of this system. The characteristic equation of the closed-loop transfer function is
s3 þ 2uh $xh $s2 þ u2h $s þ Kv $u2h ¼ 0 4.1. System modeling The linear spool displacement of the rotational valve is
xv ¼
t ðqv qm Þ 2p
(35)
The hydraulic portion of this loop can be viewed as a valve controlled hydraulic motor and can be described by the following transfer function.
Fig. 3. Block diagram of the position control loop.
(40)
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ub e the break frequency of the linear factor; unc e the natural frequency of the quadratic factor or the resonant frequency;
xnc e the hydraulic damping ratio of the quadratic factor or closed-loop damping ratio. The following approximations can be made by comparing equation (38) with (42).
ub zKv ; unc zuh
Fig. 4. Closed-loop frequency response of the position control loop.
Applying Routh-Hurwitz stability criterion to equation (40) yields
Kv < 2xh uh
(41)
Equation (41) indicates that the stability of this system is directly related to the velocity gain, hydraulic natural frequency and damping ratio. Since damping ratios of 0.1 and 0.2 are characteristics of this system, the velocity gain is always limited to 20e40% of the hydraulic natural frequency. This fundamental result provides a rule of thumb useful for design purposes. 4.3. Dynamic characteristics The denominator of the closed-loop transfer function in equation (38) can be represented by a linear and a quadratic factor. Thus,
Tcp ðsÞ ¼
1
s ub
þ1
s2
u2nc
þ 2 uxncnc s þ 1
(42)
where
As plotted in Fig. 4, the closed-loop frequency response function is a measure of response capability of this system. The closed-loop bandwidth of the system is roughly equal to the break frequency ub at which the frequency response has declined 3 dB from its low frequency value. This -3-dB bandwidth and the resonant frequency unc are directly related to the speed of the transient response of this system. Thus, dynamic response of this system can be fundamentally dominated by the velocity gain Kv and the hydraulic natural frequency uh when considering equation (43). High values of these two parameters are desirable for achieving fast response. However, the constraint, indicated by equation (41), requires a tradeoff between the stability margin and the transient response of this system when selecting such parameters. Hence, an optimal approach to improving the dynamic and steady-state performances of this system is to increase the value of hydraulic damping ratio xh. 5. Results and discussion As shown in Fig. 5, the novel pitch control system has been implemented and tested in an experimental setup that mainly includes a wind turbine simulator, a host computer, and the proposed pitch control system. The wind turbine simulator is employed to accurately reproduce the dynamic and static characteristics of a 1.5 MW variable-speed variable-pitch wind turbine for given wind speed profiles. This simulator mainly consists of a speed controlled wind rotor and a target computer. The wind rotor, including nacelle, small-scaled turbine blades, and pitch mechanism, is built to replicate the actual effects of various pitching motions. The target computer, equipped with the commercial software package GH Bladed [21], is employed to control the wind rotor and model other turbine subsystems such as aerodynamics, electrical generator and structural dynamics. System parameters such as pitch angle, wind speed, output power and torque are fed back to the host computer. The host computer, equipped with a digital motor driver and the
The proposed pitch y control system
Control signals for the wind rotor
Pitching actions
Rotational speed of the wind rotor Pitch angle
Pitch control command u
Digital motor driver
Host computer
Wind rotor Wind turbine simulator
PI Output power Pg
Pgr Pitch angle controller
(43)
Pitch angle, drive-train torque, wind speed
Fig. 5. Experimental setup.
GH Bladed software package Aerodynamics, structural dynamics, gearbox and generator
Target computer
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LabView software from the National Instruments Corporation, is employed to receive such data and display them on the computer screen. A proportional integral (PI) pitch angle controller was designed in the host computer by using the LabView software to generate the pitch control command based on the error between the rated output power and its actual value. This PI pitch angle controller can be represented as
u ¼ kp1 Pgr Pg þ ki1
Zt
Pgr Pg dt
(44)
0
u e pitch control command; Pg, Pgr e output power and its rated value; kp1, ki1 e proportional and integral gains. The gains kp1 and ki1 were tuned by ZieglereNichols tuning method [20] to ensure satisfactory pitch control performances. The generated pitch control command can then be sent to the pitch control system and wind turbine simulator through the digital motor driver and hence pitching motions take place. In practice, the following methods can be taken into consideration to further facilitate the low-cost industrial implementation of the pitch angle controller and the novel pitch control system. (a) The designed pitch angle controller can be directly implemented by using a low-cost programmable logic controller (PLC) that has gained extensive applications in industry due to its high relatively. For instance, the controller can be reasonably programmed by using the Siemens S7-200 series PLC and Step 7-Micro/WIN ladder logic programming (LLP) package [22]. (b) The designed PI pitch angle controller can be easily programmed in the PLC since there always exist pre-defined and auto-tuned PI controller modules in the PLC. Thus, the programming time and cost can be significantly reduced. (c) The pitch angle controller and pitch control system can be designed and implemented in industrial wind turbines without using additional PLC expansion modules, pitch angle transducers and analog to digital converters since the pitch
system can be digitally actuated by the digital electric motor and controlled by the intrinsic hydro-mechanical closed control loop. Therefore, the novel pitch control system is an obviously cost-effective alternative to other conventional pitch systems. (d) The pitch angle controller can be integrated into the novel pitch control system to avoid using long cables and hence to alleviate external disturbances. Thus, the overall pitch control system can be configured into a single compact package to reduce overall system size, complexity and cost. Experimental results of this novel pitch control system have been compared to a conventional hydraulic pitch system that mainly consists of a hydraulic cylinder and a directional electrohydraulic proportional valve [8]. The hydraulic cylinder is attached to a crank swing block and is controlled by the proportional valve to achieve the pitch control motions. Comparative experiment of this conventional pitch system was performed by using the aforementioned PI pitch angle controller under the same operating conditions as the experiment of the proposed pitch control system. Major experimental parameters are summarized in Table 1.
5.1. Pitch angle tracking performance As shown in Fig. 6, the settling time of the square response is about 0.26 s for the proposed novel pitch control system, whereas the settling time is about 0.43 s for the conventional pitch system. The proposed pitch control system can track the square pitch control command with zero steady-state error, whereas the conventional system exhibits significant oscillations at the steadystate. Therefore, the proposed novel pitch control system has faster dynamic response and better steady-state pitch angle tracking performance as compared with the conventional pitch system. As illustrated in Fig. 7, the proposed novel pitch control system can track the sinusoidal reference pitch angle with higher accuracy, whereas there are considerably large pitch angle tracking error and phase lag when the conventional pitch system is used. Therefore, the novel pitch system can track the bidirectional pitch angle trajectory with better accuracy as compared with the conventional system.
Table 1 Major experimental parameters. Components
Specifications
Wind turbine simulator
Rated power:1.5 MW Pitch angle range:5 ~ 25-degree Digital servo motor: SGMGH-30PCA21 Hydraulic motor: LY-A6V80HD1DFZ20182 Hydraulic motor displacement: 4.3 106 m3/rad Pitch gear ratio:78:1 Servo-valve: Parker BD760AAAN10 Pressure sensor: EPXH-X01-2.5 KP Cylinder: DB2HXTS23A with built-in LVDT sensor Proportional valve: 4WRE10E1-50-2X with amplifier card Hydraulic pump: Rexroth A4VSO125DR/10RPPA11 Maximum flow rate: 68 L/min Constant supply pressure: 128 bar Advantech Industrial Personal Computer IPC-610 (1.8 GHz 120 GB) Sampling interval:1 ms Proportional gain: 18.2 Integral gain: 2.8
The proposed pitch control system
Conventional pitch system
Hydraulic power supply
Computers PI pitch angle controller
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Desired pitch angle RVP SVP
25
Pitch angle(degree)
20 15 10 5 0 -5
0
1
2
3 Time(second)
4
5
6
Fig. 6. Square response.
5.2. Output power smoothing As shown in Fig. 8 (a), a 10 min data set of effective wind speed along the span of the turbine blade is used for the comparative experiments. This speed profile has the mean value of 18 m/s at the hub height. As illustrated in Fig. 8 (b) and (c), the pitch angle varies between 10 and 20-degree and the pitch rate varies significantly between 0.4 /s and 0.7 /s when the novel pitch control system is used, whereas the pitch angle varies between 12 and 18-degree and the pitch rate varies between 0.4 /s and 0.2 /s when the conventional pitch system is applied. Hence, the novel pitch control system has a wider range of pitch rate and exerts more pitch actions than the conventional pitch system. Such additional pitch control efforts of the novel pitch control system are necessary for better smoothing output power fluctuations. As illustrated in Fig. 8 (d) and (e), the output power varies significantly between 1.34 MW and 1.7 MW and the variation rate of output power fluctuates significantly between 0.15 MW/s and 0.15 MW/s when the conventional pitch system is applied, whereas the output power can be well maintained around the rated value 1.5 MW and the variation rate of output power can be significantly reduced by using the novel pitch control system. These comparative results clearly demonstrate that the novel pitch control system can be capable of fully smoothing the output power fluctuations with higher efficiency as compared with the conventional pitch system.
25
Desired pitch angle
Pitch angle(degree)
20
RVP SVP
15 10 5
Fig. 8. Comparative results of output power smoothing.
0 -5
0
1
2 3 Time(second) Fig. 7. Sinusoidal response.
4
5
As shown in Fig. 8 (f), the amplitude of the power spectral density for the output power can be significantly reduced from about 15 dB to 30 dB by using the novel pitch control system. Therefore, the output power fluctuations around the rated
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5.3. Mitigation of drive-train torque fluctuations A wind speed profile shown in Fig. 9 (a) is applied to the wind turbine simulator to evaluate the two pitch control systems in smoothing drive-train torque fluctuations. This wind speed profile has the mean value of 20 m/s and 18% turbulence intensity. As indicated in Fig. 9 (b) and (c), the pitch angle generated from the conventional pitch system varies between 12 and 18-degree and the pitch rate varies between 0.8 /s and 0.8 /s, whereas the pitch angle produced by the proposed novel pitch control system varies significantly between 10 and 20-degree and the pitch rate varies between 1.8 /s and 1.8 /s. Therefore, the pitch angle generated by the proposed novel pitch control system responds to wind speed variations faster than that in the conventional pitch control system. Additional pitch actions and increased pitch rate activity can be produced by using the proposed novel pitch control system. Such additional pitch control efforts arising from the novel pitch control system can be employed to achieve the improvements in the pitch control accuracy and tighter regulations of drive-train torque fluctuations as compared with the conventional pitch system. As indicated in Fig. 9 (d) and (e), the drive-train torque fluctuates considerably between 1.34 per unit and 0.8 per unit and the torque variation rate also varies between 0.4 MN m/s and 0.3 MN m/s when the conventional pitch system is used, whereas the drive-train torque can be well maintained around the rated value and its variation rate can be significantly reduced by using the proposed novel pitch control system. Therefore, the novel pitch control system exhibits significantly more effectiveness and better dynamic stability than the conventional pitch system in mitigating drive-train torque fluctuations. The proposed novel pitch control system can be further employed in large scale wind turbines for the fast power and torque control to enhance the overall power system stability and increase the lifetime of wind turbines. As shown in Fig. 9 (f), the amplitude of the power spectral density for the drive-train torque can be significantly reduced from about 20 dB to 40 dB by using the novel pitch control system. This result agrees well with that in Fig. 9 (d) and (e), and implies that the drive-train torque fluctuations can be significantly mitigated by using the novel pitch control system. Therefore, the proposed novel pitch control system can more effectively and accurately reduce the drive-train torque fluctuations around the rated rotational speed of the wind rotor (0.68 Hz) as compared with the conventional pitch system. 6. Conclusion
Fig. 9. Comparative results for mitigating drive-train torque fluctuations.
rotational speed of the wind rotor (0.68 Hz) can be better suppressed by using the novel pitch control system. The rated output power can be better maintained by using novel pitch control system as compared with the conventional pitch system.
A novel pitch angle control system has been proposed to smooth the output power and drive-train torque fluctuations for wind turbine. The proposed pitch control system works in an outer open control loop and has an intrinsic hydro-mechanical position control loop that can enhance the pitch angle tracking control accuracy. The detailed design procedure, system modeling, dynamic characteristics and stability analysis of the proposed novel pitch control system have been presented. This novel pitch control system has been tested in an experimental set-up. Experimental results have demonstrated that the proposed pitch control system has faster response and better pitch angle trajectory tracking performance as compared with the conventional pitch system. The proposed pitch control system also has significant improvements in smoothing output power and drive-train torque fluctuations as compared with the conventional pitch system. Further, the proposed novel pitch control system can potentially work with relatively high efficiency and large payload capability for large-scale wind turbines.
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Our future research will include field test and developments in the theoretical and pragmatic pitch angle control strategies to further improve the control performances of the proposed system in output power and torque regulations for large scale turbines. Acknowledgments This work was supported in part by the Science Fund for Creative Research Groups of National Natural Science Foundation of China under Grant No. 51221004, the National Natural Science Fund of China under Grant No. 51275448 and the Fundamental Research Funds for the Central Universities. References [1] Boukhezzar B, Lupu L, Siguerdidjane. Multivariable control strategy for variable speed, variable pitch wind turbines. Renew Energy 2007;43(4):1273e87. [2] Yongwei L, Shuxia L, Jiazhong W. Design of control system for wind turbine electric pitch. In: ICMTMA'09. International Conference, vol. 2. IEEE; 2009. p. 50e3. [3] Dai JC, Hu YP, Liu DS. Modelling and characteristics analysis of the pitch system of large scale wind turbines. Proc Ins Mech Eng Part C J Mech Eng Sci 2011;225:558e67. [4] Hui Z, Jiang H. The study and simulation of pitch control servo system in mega-watt class wind turbine. Adv Mater Res 2012;181:7216e20. [5] Qin Bin, Jiang Xuexiang, Wang Xin, Song Ceng. Electric pitch PMSM servo system based on direct torque control. Chinese Automation Congress (CAC), 2013 IEEE 2013:442e7. [6] Dong HY, Sun CH, Wei ZH. The adaptive control of electric pitch servo system. Adv Mater Res 2011;317:1398e402.
[7] Hai Ying Dong, Zhan Hong Wei, Xiang Gui Zhao, Xiao Qing Li. Electric pitch control system based on Fuzzy Control with variable region. Appl Mech Mater 2012;229:2352e6. [8] Zhang Dahai. Improved control of individual blade pitch for wind turbines. Sensor Actuat A Phys 2013;198:8e14. [9] Chen L, Shi F, Patton R. Active FTC for hydraulic pitch system for an off-shore wind turbine. In: Control and Fault-Tolerant Systems (SysTol), 2013 Conference. IEEE; 2013. p. 510e5. [10] Xiu-xing Yin, Yong-gang Lin, Wei Li, Ya-jing Gu, Shan Lou, Hong-wei Liu. Study on variable pitch-controlled technology based on electro-hydraulic planetary bevel gear motor. J Zhejiang Univ (Engineering Science); 48(2): 206e213. [11] Yang X, Li J, Liu W. Petri net model and reliability evaluation for wind turbine hydraulic variable pitch systems. Energies 2011;4:978e97. [12] Kong Y, Wang Z. Modelling and analysing the hydraulic variable-pitch mechanism for a variable-speed wind turbine. Wind Eng 2007;31:341e52. [13] Fenny CA. Independent blade control system with hydraulic pitch link: U.S. Patent Application 13/565,554. 2012-8e2. [14] Chiang MH. A novel pitch control system for a wind turbine driven by a variable-speed pump-controlled hydraulic servo system. Mechatronics 2011;21(4):753e61. [15] Qiang Li, Xing Jia Yao, Lei Chen. Analysis on pitch-regulated structure of MW wind turbine group. J Shenyang Univ Technol Apr. 2004;26(2). [16] Martin OL Hansen. Aerodynamics of wind turbines. 2nd ed. p. 98e128. [17] Den Hartog Jacob Pieter. Advanced strength of materials. Courier Dover Publications; 2012. [18] McGowan Jon G, Rogers Anthony L. Wind energy explained: theory, design and application. John Wiley & Sons; 2010. [19] Anderson Wayne. Controlling electrohydraulic systems/Wayne Anderson. New York: M. Dekker; 1988. [20] Bishop Robert H, Dorf Richard C. Modern control systems. Prentice Hall College Division; 2004. [21] Bossanyi EA. Bladed for windows, user manual. 2002. [22] Siemens S7e200 programmable controller system manual. 08/2005.
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Technical note
Design, modeling and implementation of a novel pitch angle control system for wind turbine Xiu-xing Yin, Yong-gang Lin*, Wei Li, Ya-jing Gu, Xiao-jun Wang, Peng-fei Lei The State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Zheda Rd.38, 310027 Hangzhou, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 April 2014 Accepted 16 March 2015 Available online
A novel pitch angle control system is proposed to smooth output power and drive-train torque fluctuations for wind turbine. This system is characterized by an outer open control loop for enhancing the direct pitching motion and an intrinsic hydro-mechanical position control loop offering the benefit of sensor-less pitch control. A pragmatic design procedure is provided and several key design parameters are determined or optimized. Modeling, stability analysis and dynamic characteristics of this pitch control system are also presented. Comparative experimental results have validated the effectiveness and efficiency of this system in power and torque regulations. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Wind turbine Pitch angle control system Hydro-mechanical position control loop System modeling Stability analysis Dynamic characteristics
1. Introduction Pitch angle control systems are commonly employed in medium to large wind turbines to keep the captured wind power close to the rated value above the rated wind speed, bringing about the benefits of better control flexibility and power quality. Such systems can also alleviate the structural wind loads and protect the wind turbine from fatigue damage during strong wind gusts. Thus, these systems have an immediate influence on the wind power regulation and are of significant importance for variable pitch wind turbines. Moreover, high performance and reliability oriented advanced pitch control systems can meet the ever increasing stringent performance requirements specified by modern turbines and hence are essential to enhance the competitiveness of wind energy technology [1]. There are fundamentally two types of such systems: electromechanical and hydraulic types. For the electromechanical type, the pitch actions can be achieved by using an electric motor. This system has been extensively investigated in the literature including system design [2], analysis of dynamic characteristics [3], double closed-loop control [4], direct torque pitch control [5], adaptive pitch control [6], and fuzzy logic pitch control [7]. Although
* Corresponding author. Tel.: þ86 182 6712 0581. E-mail address: [email protected] (Y.-g. Lin). http://dx.doi.org/10.1016/j.renene.2015.03.042 0960-1481/© 2015 Elsevier Ltd. All rights reserved.
relatively compact and accurate, the robustness and power-mass ratio of this system could be relatively low. For the hydraulic pitch system, a value controlled hydraulic cylinder is commonly employed to generate the final pitch actions through a slider-crank mechanism [8]. Recent studies on this system mainly include pitch control strategies [9,10], reliability evaluation [11], system modeling [12], and independent pitch control [13]. Chiang et al. [14] developed a variable-speed pumpcontrolled hydraulic pitch control system and an adaptive fuzzy pitch controller. However, despite of such various control methods in the literature, sufficiently detailed dynamic analysis of this system was not provided. Although the hydraulic pitch control system may be advantageous in high power/mass ratio and relatively high reliability, the control accuracy of this system is relatively poor due to the use of the slider-crank mechanism [8]. The major contributions of this paper are a novel pitch angle control system and the detailed analysis methods such as design procedure, system modeling, stability and dynamic analysis. By integrating the fundamentally different working mechanisms of the aforementioned two types, this novel system holds the advantages of both the two types while overcoming their well-known practical performance limitations. The power/mass ratio of the conventional electromechanical pitch system can be enhanced by using a hydraulic motor in the proposed system where the electric motor is used for control, not for actuation in the electromechanical system. The pitch control accuracy of the conventional hydraulic type can be significantly improved in the novel system by
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incorporating a rotary hydraulic servo instead of a slider-crank mechanism. This is because the resulting pitch angle is directly proportional to the angular displacement of the hydraulic servo and can be precisely controlled by an intrinsic hydro-mechanical position closed-loop in the servo. Therefore, this novel system not only holds the advantages such as compactness, high power/mass ratio, higher reliability, and good control precision in particular but also can be utilized in medium or large scale wind turbines with better precision as compared with the conventional pitch systems. Hence, such significant performance improvements make the proposed pitch control system a promising choice for industrial applications.
pitch angle signals and hence allow sensor-less pitch control, whereas a large variety of sensors or transducers are always used in other pitch systems. (c) Compact structure and integration design make this pitch system appropriate for individual pitch control. (d) This system can be controlled directly by a host computer without using additional controllers or sensors, which provides significantly cost-effective potentials. (e) The novel pitch control system works in the outer open-loop with an internal hydro-mechanical position control loop and hence has a wider range of pitch rate and lower maintenance cost as compared with other conventional pitch systems.
2. System description As shown in Fig. 1, this novel pitch control system, consisting of a digital electric motor, a hydraulic servo and a pitch gear set mounted in the nacelle, is an integrated electro-hydraulic position servo system with an intrinsic feedback closed-loop. The digital electric motor acts as a converter transmitting the digital pitch control command to the hydraulic servo. The pitch gear set is used to adapt the high shaft speed of the hydraulic servo to the relatively low pitch rate. The hydraulic servo consists of a spool type rotational valve, a screw and nut combination and a rotary actuator. The rotational motion from the digital electric motor opens the valve and ports the oil flow from a constant hydraulic power supply to this actuator whose motion is fed back through the screw and nut combination and subtracted from the input motion so as to stroke the valve and close this loop. Hence, such motions automatically create an intrinsic hydro-mechanical position control loop in the hydraulic servo. The rotary actuator can be sized to handle expected pitch loads and has the hydraulic natural frequency large enough to meet overall response requirements. Generally, a hydraulic axial piston motor can be employed as the rotary actuator. Significant features of this pitch control system are as follows. (a) The pitch angle control can be eventually achieved by a rotary hydraulic actuator with high payload capability and high power to weight ratio rather than an electric motor or a hydraulic cylinder in other pitch systems. Thus, relatively high pitch control accuracy and power/mass ratio make this system suitable for large-scale wind turbines. (b) The intrinsic hydro-mechanical closed control loop enables this system to avoid the necessity to measure or feedback the
3. System design 3.1. Pitch loads The calculation of pitch loads is first presented as it is an important prerequisite for the system design. Such loads mainly stem from aerodynamics, gravity and dynamic interactions [15]. In particular, the inertia moment arising from the blade centrifugal force is the predominant source of loads associated with the pitch actions and is discussed in detail as follows. As illustrated in Fig. 2, the plane of rotation is aligned with the axis o-x and perpendicular to the surface of this paper. The pitch axis passes through the center of gravity of each blade cross section and lies in the plane of rotation. The first principal axis of the blade cross sections lies along the chord line for this symmetric aero-foil [16]. Two coordinate systems are established at the same origin O. The reference frame (x, y) is rotated about the frame (x1, y1) with the pitch angle b between them. Consider an incremental part of the blade at a radius r from the rotational axis and the point B with an incremental mass dm. The incremental centrifugal force acting on this point is
dFc ¼ rB u2 dm
(1)
and the radius rB can be represented as
rB ¼
LOB $sin g sin 4
(2)
Substituting equation (2) into (1) yields
dFc ¼
LOB $sin g 2 u dm sin 4
(3)
where
u e the angular velocity of the wind rotor; LOB e the length of the line segment OeB; g e the angle between the line OeB and the plane of rotation; 4 e the angle between the pitch axis and the incremental centrifugal force dFc. The force dFc can be decomposed into a component dFn perpendicular to the blade cross section and a component dFt parallel to this cross section. The force dFt can be described as
dFt ¼ dFc $sin 4 ¼
Fig. 1. Schematic of the proposed pitch control system.
LOB $sin g 2 $u $dm$sin 4 ¼ u2 $LOB $sin g$dm sin 4 (4)
The resulting inertia moment about the pitch axis due to the centrifugal force is
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601
Fig. 2. The centrifugal forces.
dTc ¼ dFt $LOA ¼ u2 $LOB $sin g$dm$LOA
(5)
The coordinates of point B in the reference frame (x, y) are
xB ¼ LOA yB ¼ LOB $sin g
(6)
8 y1B sin b > > > < xB ¼ x1B cos b cos b cos b ¼ x1B cos b y1B sin b > y y sin b > > sin b ¼ x1B sin b þ y1B cos b : yB ¼ 1B þ x1B 1B cos b cos b (10)
Substituting equation (6) into (5) yields
dTc ¼ u2 $xB $yB $dm ¼ u2 $xB $yB $rb $ds$dr
Substituting equation (10) into (9) yields
(7)
Z Jxy ¼
xB yB ds sb
where
Z h i x21B y21B sin b cos b þ x1B y1B cos2 b sin2 b ds
¼
LOA e the length of the line segment O-A;
sb
rb e the density of the blade material;
(11)
ds e the cross sectional area at the point B; dr e the incremental radius at the radius r.
The product of inertia of the area ds about the principal axes o-x1 and o-y1 is zero [17].
Integrating equation (7) over the blade radius yields
ZR Z Tc ¼ rb u2
xB yB dsdr ¼ rb u2 0
x1B y1B ds ¼ 0
ZR
sb
Jxy dr
Substituting equation (12) into (11) yields
(8)
0
Z Jxy ¼
where
xB yB ds ¼ sb
Tc e the total inertia moment acting on the blade; R e the total radius of the rotor; sb e the area of this airfoil section at the local radius r; Jxy e the product of inertia of the area sb about the axes o-x and o-y.
"
Z
x21B dsz0:0446$
Jy1 ¼ sb
y21B dsz0:0464$
Jx1 ¼ sb
1 2
Z x21B y21B sinð2bÞds sb
1 ¼ sin 2 b Jy1 Jx1 2 where
Jy1 e the moment of inertia of the area sb about the axis o-y1; Jx1 e the moment of inertia of the area sb about the axis o-x1;
# 0:008 4 0:008 3 c 4 h 3 4 1 1 1 $ $D $ c h D c
Z Jxy ¼
xB yB ds
(13)
# 4 0:008 4 0:008 c h $ 1 1 1 $ $D4 c h D c
"
Z
(12)
(9)
sb
Transforming the coordinates of point B (x1B, y1B) in the reference frame (x1, y1) to the frame (x, y) yields
c e the airfoil chord length; h e the airfoil thickness; D e the wind rotor diameter. Substituting equation (13) into (8) yields
(14)
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r u2 Tc ¼ b 2
ZR h
i sin 2 b Jy1 Jx1 dr
(15)
dup upmax ¼ dt tp
(23)
0
Substituting equation (23) into (22) yields
Dividing the blade into a set of span-wise blade sections gives an alternative expression of equation (15).
Tc ¼
R h i r b u2 X Jy1 Jx1 $sin 2 b$Dr 2 r¼0
iopt (16)
ummin ummax iopt upmin upmax
Dr e the incremental radius of the blade. The actual pitch load Tp for design can be closely approximated by considering the pitch bearing efficiency h [18].
Tc h
(24)
The optimal ratio iopt must satisfy the practical constraint of limiting the maximum pitch rate.
where
Tp ¼
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u upmax uJb $ tp þ Tp ¼t u Jm $ pmax tp
(17)
3.2. Pitch gear ratio The shaft of the hydraulic servo is coupled to the blade root through the pitch gear set with the gear ratio i. The pitch gear ratio can be reasonably calculated based on the actual pitch load Tp presented in section 3.1. Thus, the torque balance equation on the servo side is
(25)
where iopt e the optimal pitch gear ratio; ummax, ummin e maximum and minimum values of the shaft speed of the hydraulic servo; upmax, upmin e maximum and minimum values of the pitch rate; tp e the time required by the pitch rate to reach its maximum value. Therefore, the optimal pitch gear ratio can be obtained from equations (24) and (25).
3.3. Hydraulic servo
Tm ¼ Jm
dup Tp dum þ Jb þ dt i$dt i
(18)
where Tm e the torque generated by the hydraulic servo; Jm e the mass moment of inertia of the hydraulic servo; Jb e the mass moment of the blade about its longitudinal axis; um e the shaft speed of the hydraulic servo; up e pitch rate. The speed um is related to the pitch rate up by
um ¼ i$up
(19)
Jm þ
dup Tp Jb þ $i$ dt i i2
iopt ¼
du
Jm $ dtp
(26)
qm ¼ Cw xv
rffiffiffiffiffi ps r
(27)
The power extracted from the servo is
(21)
Solving equation (21) yields
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u dup uJb $ þ Tp dt t
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðps pL Þ r
(20)
It is desirable for this servo to operate at the optimal pitch gear ratio where the output torque Tm is minimized. This optimal ratio iopt can be determined by differentiating equation (20) with respect to i and setting the result equal to zero.
dup Jb dup Tp dTm ¼ Jm $ 2$ 2 ¼0 di dt i dt i
qL ¼ Cw xv
The maximum flow rate of this valve is
Substituting equation (19) into (18) yields
Tm ¼
The volumetric displacement Dm and the maximum flow rate qm rank as the two important parameters for the design of this hydraulic servo. The two parameters can also be determined based on the calculated parameters in section 3.2, such as the torque and the shaft speed of the hydraulic servo. The flow rate of the rotational valve is
(22)
The time derivative of the pitch rate up can be represented as
Phs ¼ Cw xv
rffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffi ps p p $ps $ L $ 1 L r ps ps
(28)
where qL e the flow rate of the rotational valve; qm e the maximum flow rate of the rotational valve; Phs e the power extracted from the hydraulic servo; Cw e constant coefficient associated with the rotational valve; xv e the linear spool displacement of the rotational valve; ps e constant supply pressure; r e mass density of the hydraulic oil; pL e load pressure. Differentiating equation (28) with respect to pL and setting the result equal to zero yields
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pLp ¼
2 ps 3
(29)
qm ¼ xv
Kq Dm s
Combining equations (26), (27) and (29) yields
qm qLp ¼ pffiffiffi 3
(30)
s2 u2h
þ
2 uxhh
!
(36)
sþ1
where t e the helical pitch of the screw and nut combination;
The maximum power extracted from the servo occurs at the point where the load pressure pL and flow rate qL obtain the particular values in equations (29) and (30) [19]. The hydraulic servo should be able to handle the largest pitch load at this maximum power point. Thus,
pLp Dm ¼ Tmmax 2p
603
(31)
qm e the rotary displacement of the hydraulic motor; qv e the spool displacement of the rotational valve; Kq e flow gain of the rotational valve;
uh e hydraulic natural frequency; xh e hydraulic damping ratio.
Equations (35) and (36) are the basic representations of this position control loop and can be illustrated by using the block diagram in Fig. 3. Thus, the open loop transfer function is
and
qLp ¼ ummax Dm
(32)
where
pffiffiffi 3 3$p$Tmmax $ummax ps
!
(37)
sþ1
Tcp ðsÞ ¼
1 s3 Kv $u2h
h þ 2 Kvx$u s2 þ Ksv þ 1 h
(38)
where
(33) Kv ¼
Substituting equations (30) and (33) into (32) yields
qm ¼
þ
2 uxhh
Kv e velocity gain of this control loop; s e Laplace operator.
Substituting equation (29) into (31) yields the
3p$Tmmax ps
s
s2 u2h
and the closed-loop transfer function is
Dm e the volumetric displacement; qLp e the flow rate of the hydraulic servo at the maximum power point; pLp e the load pressure of the hydraulic servo at the maximum power point;
Dm ¼
Kv
Top ðsÞ ¼
(34)
Thus, the volumetric displacement and the maximum flow rate of the hydraulic servo can be calculated by using equations (33) and (34). In practice, the values of the two parameters should be slightly increased to compensate for the power losses due to the friction and leakage in the servo.
t$Kq 2pDm
(39)
The free s in the denominator of equation (37) indicates a first order integral part so that this control loop is type one and has zero position error. As shown in Fig. 3, this intrinsic position control loop is generated automatically with a unit negative feedback. Thus, sensor-less position control of this pitch system can be achieved due to this direct feedback closed-loop.
4.2. Stability analysis 4. System modeling and analysis The dynamic performances of this system are mainly dominated by the hydro-mechanical position control loop. Thus, this control loop, including the screw and nut combination and the hydraulic portion, is modeled and analyzed in detail as follows.
Stability is probably the most important characteristic of this pitch system. The analysis of this loop dynamics is usually centered on the requirements for stability. The Routh-Hurwitz stability criterion [24] is used to ascertain the stability of this system. The characteristic equation of the closed-loop transfer function is
s3 þ 2uh $xh $s2 þ u2h $s þ Kv $u2h ¼ 0 4.1. System modeling The linear spool displacement of the rotational valve is
xv ¼
t ðqv qm Þ 2p
(35)
The hydraulic portion of this loop can be viewed as a valve controlled hydraulic motor and can be described by the following transfer function.
Fig. 3. Block diagram of the position control loop.
(40)
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ub e the break frequency of the linear factor; unc e the natural frequency of the quadratic factor or the resonant frequency;
xnc e the hydraulic damping ratio of the quadratic factor or closed-loop damping ratio. The following approximations can be made by comparing equation (38) with (42).
ub zKv ; unc zuh
Fig. 4. Closed-loop frequency response of the position control loop.
Applying Routh-Hurwitz stability criterion to equation (40) yields
Kv < 2xh uh
(41)
Equation (41) indicates that the stability of this system is directly related to the velocity gain, hydraulic natural frequency and damping ratio. Since damping ratios of 0.1 and 0.2 are characteristics of this system, the velocity gain is always limited to 20e40% of the hydraulic natural frequency. This fundamental result provides a rule of thumb useful for design purposes. 4.3. Dynamic characteristics The denominator of the closed-loop transfer function in equation (38) can be represented by a linear and a quadratic factor. Thus,
Tcp ðsÞ ¼
1
s ub
þ1
s2
u2nc
þ 2 uxncnc s þ 1
(42)
where
As plotted in Fig. 4, the closed-loop frequency response function is a measure of response capability of this system. The closed-loop bandwidth of the system is roughly equal to the break frequency ub at which the frequency response has declined 3 dB from its low frequency value. This -3-dB bandwidth and the resonant frequency unc are directly related to the speed of the transient response of this system. Thus, dynamic response of this system can be fundamentally dominated by the velocity gain Kv and the hydraulic natural frequency uh when considering equation (43). High values of these two parameters are desirable for achieving fast response. However, the constraint, indicated by equation (41), requires a tradeoff between the stability margin and the transient response of this system when selecting such parameters. Hence, an optimal approach to improving the dynamic and steady-state performances of this system is to increase the value of hydraulic damping ratio xh. 5. Results and discussion As shown in Fig. 5, the novel pitch control system has been implemented and tested in an experimental setup that mainly includes a wind turbine simulator, a host computer, and the proposed pitch control system. The wind turbine simulator is employed to accurately reproduce the dynamic and static characteristics of a 1.5 MW variable-speed variable-pitch wind turbine for given wind speed profiles. This simulator mainly consists of a speed controlled wind rotor and a target computer. The wind rotor, including nacelle, small-scaled turbine blades, and pitch mechanism, is built to replicate the actual effects of various pitching motions. The target computer, equipped with the commercial software package GH Bladed [21], is employed to control the wind rotor and model other turbine subsystems such as aerodynamics, electrical generator and structural dynamics. System parameters such as pitch angle, wind speed, output power and torque are fed back to the host computer. The host computer, equipped with a digital motor driver and the
The proposed pitch y control system
Control signals for the wind rotor
Pitching actions
Rotational speed of the wind rotor Pitch angle
Pitch control command u
Digital motor driver
Host computer
Wind rotor Wind turbine simulator
PI Output power Pg
Pgr Pitch angle controller
(43)
Pitch angle, drive-train torque, wind speed
Fig. 5. Experimental setup.
GH Bladed software package Aerodynamics, structural dynamics, gearbox and generator
Target computer
X.-x. Yin et al. / Renewable Energy 81 (2015) 599e608
LabView software from the National Instruments Corporation, is employed to receive such data and display them on the computer screen. A proportional integral (PI) pitch angle controller was designed in the host computer by using the LabView software to generate the pitch control command based on the error between the rated output power and its actual value. This PI pitch angle controller can be represented as
u ¼ kp1 Pgr Pg þ ki1
Zt
Pgr Pg dt
(44)
0
u e pitch control command; Pg, Pgr e output power and its rated value; kp1, ki1 e proportional and integral gains. The gains kp1 and ki1 were tuned by ZieglereNichols tuning method [20] to ensure satisfactory pitch control performances. The generated pitch control command can then be sent to the pitch control system and wind turbine simulator through the digital motor driver and hence pitching motions take place. In practice, the following methods can be taken into consideration to further facilitate the low-cost industrial implementation of the pitch angle controller and the novel pitch control system. (a) The designed pitch angle controller can be directly implemented by using a low-cost programmable logic controller (PLC) that has gained extensive applications in industry due to its high relatively. For instance, the controller can be reasonably programmed by using the Siemens S7-200 series PLC and Step 7-Micro/WIN ladder logic programming (LLP) package [22]. (b) The designed PI pitch angle controller can be easily programmed in the PLC since there always exist pre-defined and auto-tuned PI controller modules in the PLC. Thus, the programming time and cost can be significantly reduced. (c) The pitch angle controller and pitch control system can be designed and implemented in industrial wind turbines without using additional PLC expansion modules, pitch angle transducers and analog to digital converters since the pitch
system can be digitally actuated by the digital electric motor and controlled by the intrinsic hydro-mechanical closed control loop. Therefore, the novel pitch control system is an obviously cost-effective alternative to other conventional pitch systems. (d) The pitch angle controller can be integrated into the novel pitch control system to avoid using long cables and hence to alleviate external disturbances. Thus, the overall pitch control system can be configured into a single compact package to reduce overall system size, complexity and cost. Experimental results of this novel pitch control system have been compared to a conventional hydraulic pitch system that mainly consists of a hydraulic cylinder and a directional electrohydraulic proportional valve [8]. The hydraulic cylinder is attached to a crank swing block and is controlled by the proportional valve to achieve the pitch control motions. Comparative experiment of this conventional pitch system was performed by using the aforementioned PI pitch angle controller under the same operating conditions as the experiment of the proposed pitch control system. Major experimental parameters are summarized in Table 1.
5.1. Pitch angle tracking performance As shown in Fig. 6, the settling time of the square response is about 0.26 s for the proposed novel pitch control system, whereas the settling time is about 0.43 s for the conventional pitch system. The proposed pitch control system can track the square pitch control command with zero steady-state error, whereas the conventional system exhibits significant oscillations at the steadystate. Therefore, the proposed novel pitch control system has faster dynamic response and better steady-state pitch angle tracking performance as compared with the conventional pitch system. As illustrated in Fig. 7, the proposed novel pitch control system can track the sinusoidal reference pitch angle with higher accuracy, whereas there are considerably large pitch angle tracking error and phase lag when the conventional pitch system is used. Therefore, the novel pitch system can track the bidirectional pitch angle trajectory with better accuracy as compared with the conventional system.
Table 1 Major experimental parameters. Components
Specifications
Wind turbine simulator
Rated power:1.5 MW Pitch angle range:5 ~ 25-degree Digital servo motor: SGMGH-30PCA21 Hydraulic motor: LY-A6V80HD1DFZ20182 Hydraulic motor displacement: 4.3 106 m3/rad Pitch gear ratio:78:1 Servo-valve: Parker BD760AAAN10 Pressure sensor: EPXH-X01-2.5 KP Cylinder: DB2HXTS23A with built-in LVDT sensor Proportional valve: 4WRE10E1-50-2X with amplifier card Hydraulic pump: Rexroth A4VSO125DR/10RPPA11 Maximum flow rate: 68 L/min Constant supply pressure: 128 bar Advantech Industrial Personal Computer IPC-610 (1.8 GHz 120 GB) Sampling interval:1 ms Proportional gain: 18.2 Integral gain: 2.8
The proposed pitch control system
Conventional pitch system
Hydraulic power supply
Computers PI pitch angle controller
605
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Desired pitch angle RVP SVP
25
Pitch angle(degree)
20 15 10 5 0 -5
0
1
2
3 Time(second)
4
5
6
Fig. 6. Square response.
5.2. Output power smoothing As shown in Fig. 8 (a), a 10 min data set of effective wind speed along the span of the turbine blade is used for the comparative experiments. This speed profile has the mean value of 18 m/s at the hub height. As illustrated in Fig. 8 (b) and (c), the pitch angle varies between 10 and 20-degree and the pitch rate varies significantly between 0.4 /s and 0.7 /s when the novel pitch control system is used, whereas the pitch angle varies between 12 and 18-degree and the pitch rate varies between 0.4 /s and 0.2 /s when the conventional pitch system is applied. Hence, the novel pitch control system has a wider range of pitch rate and exerts more pitch actions than the conventional pitch system. Such additional pitch control efforts of the novel pitch control system are necessary for better smoothing output power fluctuations. As illustrated in Fig. 8 (d) and (e), the output power varies significantly between 1.34 MW and 1.7 MW and the variation rate of output power fluctuates significantly between 0.15 MW/s and 0.15 MW/s when the conventional pitch system is applied, whereas the output power can be well maintained around the rated value 1.5 MW and the variation rate of output power can be significantly reduced by using the novel pitch control system. These comparative results clearly demonstrate that the novel pitch control system can be capable of fully smoothing the output power fluctuations with higher efficiency as compared with the conventional pitch system.
25
Desired pitch angle
Pitch angle(degree)
20
RVP SVP
15 10 5
Fig. 8. Comparative results of output power smoothing.
0 -5
0
1
2 3 Time(second) Fig. 7. Sinusoidal response.
4
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As shown in Fig. 8 (f), the amplitude of the power spectral density for the output power can be significantly reduced from about 15 dB to 30 dB by using the novel pitch control system. Therefore, the output power fluctuations around the rated
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5.3. Mitigation of drive-train torque fluctuations A wind speed profile shown in Fig. 9 (a) is applied to the wind turbine simulator to evaluate the two pitch control systems in smoothing drive-train torque fluctuations. This wind speed profile has the mean value of 20 m/s and 18% turbulence intensity. As indicated in Fig. 9 (b) and (c), the pitch angle generated from the conventional pitch system varies between 12 and 18-degree and the pitch rate varies between 0.8 /s and 0.8 /s, whereas the pitch angle produced by the proposed novel pitch control system varies significantly between 10 and 20-degree and the pitch rate varies between 1.8 /s and 1.8 /s. Therefore, the pitch angle generated by the proposed novel pitch control system responds to wind speed variations faster than that in the conventional pitch control system. Additional pitch actions and increased pitch rate activity can be produced by using the proposed novel pitch control system. Such additional pitch control efforts arising from the novel pitch control system can be employed to achieve the improvements in the pitch control accuracy and tighter regulations of drive-train torque fluctuations as compared with the conventional pitch system. As indicated in Fig. 9 (d) and (e), the drive-train torque fluctuates considerably between 1.34 per unit and 0.8 per unit and the torque variation rate also varies between 0.4 MN m/s and 0.3 MN m/s when the conventional pitch system is used, whereas the drive-train torque can be well maintained around the rated value and its variation rate can be significantly reduced by using the proposed novel pitch control system. Therefore, the novel pitch control system exhibits significantly more effectiveness and better dynamic stability than the conventional pitch system in mitigating drive-train torque fluctuations. The proposed novel pitch control system can be further employed in large scale wind turbines for the fast power and torque control to enhance the overall power system stability and increase the lifetime of wind turbines. As shown in Fig. 9 (f), the amplitude of the power spectral density for the drive-train torque can be significantly reduced from about 20 dB to 40 dB by using the novel pitch control system. This result agrees well with that in Fig. 9 (d) and (e), and implies that the drive-train torque fluctuations can be significantly mitigated by using the novel pitch control system. Therefore, the proposed novel pitch control system can more effectively and accurately reduce the drive-train torque fluctuations around the rated rotational speed of the wind rotor (0.68 Hz) as compared with the conventional pitch system. 6. Conclusion
Fig. 9. Comparative results for mitigating drive-train torque fluctuations.
rotational speed of the wind rotor (0.68 Hz) can be better suppressed by using the novel pitch control system. The rated output power can be better maintained by using novel pitch control system as compared with the conventional pitch system.
A novel pitch angle control system has been proposed to smooth the output power and drive-train torque fluctuations for wind turbine. The proposed pitch control system works in an outer open control loop and has an intrinsic hydro-mechanical position control loop that can enhance the pitch angle tracking control accuracy. The detailed design procedure, system modeling, dynamic characteristics and stability analysis of the proposed novel pitch control system have been presented. This novel pitch control system has been tested in an experimental set-up. Experimental results have demonstrated that the proposed pitch control system has faster response and better pitch angle trajectory tracking performance as compared with the conventional pitch system. The proposed pitch control system also has significant improvements in smoothing output power and drive-train torque fluctuations as compared with the conventional pitch system. Further, the proposed novel pitch control system can potentially work with relatively high efficiency and large payload capability for large-scale wind turbines.
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Our future research will include field test and developments in the theoretical and pragmatic pitch angle control strategies to further improve the control performances of the proposed system in output power and torque regulations for large scale turbines. Acknowledgments This work was supported in part by the Science Fund for Creative Research Groups of National Natural Science Foundation of China under Grant No. 51221004, the National Natural Science Fund of China under Grant No. 51275448 and the Fundamental Research Funds for the Central Universities. References [1] Boukhezzar B, Lupu L, Siguerdidjane. Multivariable control strategy for variable speed, variable pitch wind turbines. Renew Energy 2007;43(4):1273e87. [2] Yongwei L, Shuxia L, Jiazhong W. Design of control system for wind turbine electric pitch. In: ICMTMA'09. International Conference, vol. 2. IEEE; 2009. p. 50e3. [3] Dai JC, Hu YP, Liu DS. Modelling and characteristics analysis of the pitch system of large scale wind turbines. Proc Ins Mech Eng Part C J Mech Eng Sci 2011;225:558e67. [4] Hui Z, Jiang H. The study and simulation of pitch control servo system in mega-watt class wind turbine. Adv Mater Res 2012;181:7216e20. [5] Qin Bin, Jiang Xuexiang, Wang Xin, Song Ceng. Electric pitch PMSM servo system based on direct torque control. Chinese Automation Congress (CAC), 2013 IEEE 2013:442e7. [6] Dong HY, Sun CH, Wei ZH. The adaptive control of electric pitch servo system. Adv Mater Res 2011;317:1398e402.
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