Extreme learning machine based wind speed estimation and sensorless control for wind turbine power generation system

Neurocomputing 102 (2013) 163–175

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Neurocomputing journal homepage: www.elsevier.com/locate/neucom

Extreme learning machine based wind speed estimation and sensorless control for wind turbine power generation system$ Si Wu a,n, Youyi Wang a, Shijie Cheng b a b

School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan, PR China

a r t i c l e i n f o

abstract

Available online 19 June 2012

This paper proposes a precise real-time wind speed estimation method and sensorless control for variable-speed variable-pitch wind turbine power generation system (WTPGS). The wind speed estimation is realized by a nonlinear input–output mapping extreme learning machine (ELM). A specific design characteristic of the wind turbine is used for improving the mapping accuracy with considering the variable pitch angle. Moreover, since the design is independent of the environmental air density, the proposed ELM wind speed estimation method is robust to the air density variations. The estimated wind speed is then used to determine the optimal rotational speed command for maximum power point tracking. A fast and effective ELM mapping based pitch controller is proposed too when the WTPGS operates in its high wind speed region. The ELM pitch controller can act much faster and more precise than conventional pitch controllers. Furthermore, the complicated design precess for the parameters of conventional pitch controllers will be avoided in the proposed method. The effectiveness of the proposed methods are verified both by simulations and experiments on a WTPGS installed with Permanent Magnet Synchronous Generator (PMSG). & 2012 Elsevier B.V. All rights reserved.

Keywords: Wind speed estimation Sensorless control Wind turbine power generation system Extreme learning machine

1. Introduction Due to the environmental problem and shortage of power, wind power, as a renewable energy, has received much interest and considerable attention all over the world. In all kinds of wind power generation system, variable-speed wind turbine power generation system (WTPGS) is more superior than others because of its high power extraction efficiency and high power quality [1,2]. In the operating wind speed range, in order to achieve the Maximum Power Point Tracking (MPPT) of wind turbine, the turbine shaft rotational speed should be adjusted optimally with respect to the variable wind speed. Such turbine rotor speed control should base on the real-time information of wind speed. Normally, wind speed anemometers are employed for the wind speed estimation. However, high cost of precise anemometer limits the extensive use of this equipment. For example, the surrounded installed anemometers cannot provide adequate and accurate wind speed information for every wind turbine in wind farms [3] and precise anemometer does not deserve to be used for a distributed small WTPGS.

$ The financial support from the National Natural Science Foundation of China (50937002) is greatly appreciated. n Corresponding author. E-mail address: [email protected] (S. Wu).

0925-2312/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.neucom.2011.12.051

Recently, the mechanical sensorless MPPT controls have been reported in literatures. Some of the literatures propose turbine maximum power extraction controls independent of wind speed information. It can avoid the difficulties of wind speed measurements or estimations. For instance, a fuzzy-logic-based control is given in [4]. The fuzzy control adaptively performs an online incremental/decremental searcher to drive the WTPGS rotational speed until the extracted power maintains at its maximum condition. However, this method associates with the system’s dynamics to some extent. If the wind speed is in sharply changing, the relative slow search speed of this method may not make the maximum power extraction realized opportunely. Some other literatures show their sensorless MPPT control methods based on wind speed on-line estimations [5,6]. The lookup table can be used as one estimation method [6]; however, it requires too much memory space to ensure the estimation accuracy and may result in a time-consuming search for the solution. The real-time calculation method of the nonlinear function roots [5] was used to solve the inverse function problem for estimating the real-time wind speed. However, it may result in complex calculations and high computational burden for the computer, therefore, reducing system performance. Alternatively, a novel algorithm based on the theory of support-vector regression (SVR) for wind-speed estimation in wind power generation systems is proposed in [7]. After the off-line training, a specified model is obtained to determine the wind speed online from the

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instantaneous turbine information. The SVR model is too slow due to the large number of support vectors generated. Especially, it is much slower than feed-forward neural networks. The high performance of using SVR to make real-time estimation cannot be guaranteed [8]. Artificial neural networks (ANNs) are used to implement nonlinear time-varying input-output mapping instead of the lookup table and SVR based mapping in some literatures [3,16]. It has been proved that ANN methods can overcome the drawbacks of the previous mapping methods. Ref. [3] proposes a ANN based wind speed estimation method for a direct-drive small WTPGS. This method achieves fast and smooth wind speed estimation based on an ideal WTPGS. However, the power loss of the wind turbine is neglected which sometimes cannot be ignored. Moreover, and the method cannot be applied on variable-pitch WTPGS. In [16], Gaussian radial basis function network (GRBFN) wind speed estimation based sensorless output maximization control is proposed with considering the pitch activation and the power loss. Although the estimation and control performances are both good, the performance of this method can still be improved to some extent. For example, intensive sampling data of the three training inputs always include too much data. In order to finish the training, the number of the data should be decreased which will reduce the regression accuracy of the ANN theoretically. Furthermore, this method is not robust against the air density variations and no test is given when the pitch angle system is activated. The accuracy of ANN based wind speed estimation can be improved mainly by two general ways. One is using advanced training algorithm to improve the estimation accuracy. The other is simplifying the structure of ANN as much as possible which can accelerate the estimation speed and improve the estimation accuracy as well [8]. In this paper, extreme learning machine (ELM) ANN based input–output mapping of a specific design characteristic of the wind turbine is proposed for the WTPGS sensorless control with wind speed on-line estimation. ELM is a perfect algorithm [8–15]. It takes lots of advantages such as fast training speed, high training accuracy, easy design process and no manual tuning. By observing the information of the wind turbine, the two real-time inputs of ELM ANN can be calculated. This process not only reduces the number of training inputs to reduce the ANN structure and increase the estimation accuracy, but makes the ELM mapping independent of the air density. Thus the wind speed estimation in the entire operating region can be achieved effectively and robustly and the maximum turbine power extraction control is dominated from this estimated wind speed. Additionally, when the generated power exceeds its rated value, an ELM based pitch angle controller puts into operation to limit the captured power. The commonly used pitch angle control strategy is the classical proportional-integral-derivative (PID) control [17,18]. It is always designed based on a linearized wind turbine model around a specific operating point [19]. So its global robust fast response and stability may not be ensured. The well trained ELM ANN controller could replace the conventional controller with the advantage of increasing execution speed precisely [8]. The validity of the proposed method is verified by simulations on WTPGS installed with a Permanent Magnet Synchronous Generator (PMSG) in the Matlab/Simulink environment. The experimental investigations on a small emulated PMSG WTPGS are also given. This paper is organized as follows. In Section 2, the modeling of wind turbine power generation system is discussed. In Section 3, a brief introduction of ELM technique is given first, then the processes of the proposed sensorless control and the applications of ELM on wind speed estimation and pitch control system are investigated. Section 4 gives some analysis of

simulation and experimental results. Some concluding remarks are made in Section 5.

2. Wind turbine power generation system modeling This paper mainly focuses on the wind turbine activation and control, thus the class and structure of the generator will not affect the performance of the proposed method. It is reasonable to establish a WTPGS installed with PMSG for the investigation of the proposed method. 2.1. Aerodynamic modeling of wind turbine According to Betz theory, the wind turbine extracted power Pw from the wind is a cubic function with respect to the wind speed [21] 1 Pw ¼ pR2 rC p ðl, bÞV 3 ¼ T w om , 2

ð1Þ

where r is the air density (kg=m3 ), R is the radius of the blade swept area (m), V is the wind speed (m/s), om is the mechanical rotational speed of the turbine shaft, Tw is wind mechanical torque on the turbine shaft, C p ðl, bÞ expresses the power coefficient with respect to the tip speed ratio (TSR) l ¼ om R=V and the pitch angle b which is described as   151 2:14 C p ðl, bÞ ¼ 0:73 0:58b0:002b 13:2 e18:4=li ,

li

1

1 0:003 ¼  : li l0:02b 1þ b3

ð2Þ

Rewrite (1) as C p ðl, bÞ

l3

¼

2P w

rpR5 o3m

¼

2T w

rpR5 o2m

:

ð3Þ

3

Obviously, C p ðl, bÞ=l is a function of l and b. With the increase of wind speed, the turbine rotational speed is adjusted until reaching its rated value such that l remains at the maximum power point, while the turbine pitch control is deactivated. If the optimal rotational speed command is given higher than the rated value, the speed control activates to maintain the rotational speed at its rated value. And the turbine pitch control is still deactivated until that the extracted power goes beyond its rated value. When the extracted power increases above the rated value, the pitch control is activated to maintain the mechanical extracted power at the rated value [1]. 2.2. Shaft system modeling of wind turbine Assume that the drive train to a sufficient level of accuracy can be described by two inertias interconnected by a spring and damper with viscous friction on each inertia. The external forces to this two-mass system are the aerodynamic torque Tw on the low speed shaft and generator reaction torque Tg on the high speed shaft. The motion equations are given by [22] _ m ¼ T w Bm om mðom og ÞK yD , Jm o _ g ¼ T g Bg og þ mðom og Þ þ K yD , Jg o

y_ D ¼ om og ,

ð4Þ

where om and og are the turbine and generator rotational speed, respectively; yD is the position deviation between the two shafts. Jm and Jg are the moment of inertias of the turbine and the generator, respectively; Bm and Bg are the mechanical damping coefficients of the turbine and the generator, respectively; m is the damping coefficient of the flexible coupling between the two masses and K is the shaft stiffness.

S. Wu et al. / Neurocomputing 102 (2013) 163–175

165

Alternatively, for some small wind turbine or direct drive WTPGS, the torque dynamic equation on the shaft can be described as one-mass lumped systems [23] Jt

dog ¼ Dt og þT w T g , dt

ð5Þ

where Dt expresses the damping constant of turbine and Jt is the moment of inertia of the lumped system. Fig. 1. Block diagram of ORC uncertainties observer structure.

2.3. PMSG modeling The PMSG is a a,b,c phase alternating current (AC) electric system. Transferring it to direct current (DC) system by the park transformation, the electrical dynamic model of a PMSG in its rotating synchronous reference frame is [21] disd þ Ls oisq , dt disq Ls oisd þ oc, U sq ¼ Rs isq Ls dt

U sd ¼ Rs isd Ls

ð6Þ

where Rs is the generator resistance, c is the magnet flux and o is the generator electric speed. The inductances of d,q axes are equal, Lq ¼ Ld ¼ Ls . If the pole pair number is p, then o ¼ pog . The electromagnetic torque is given as Tg ¼

3 3 pðcisq ðLd Lq Þisd Þ ¼ pcisq : 2 2

ð7Þ

According to (7), the electromagnetic torque is only relevant to the quadrature current component. The stator generated power is P g ¼ T g o.

3. Wind speed estimation and sensorless control In this section, a two-loop linear observer is first proposed for estimation of the turbine mechanical information, the wind mechanical torque on the shaft and the rotational speed. Then the ELM principle is introduced and applied on the design of the wind speed estimator and the pitch angle controller. 3.1. Two-loop linear observer The system (4) can be written as the general state space form with x ¼ ½om og yD T as the state vector x_ ¼ Ax þ Dm T w þ Dg T g , om ¼ C m x, og ¼ C g x, where 2 Bm þ m 6  Jm 6 6 m A¼6 6 4 Jg 2

1 0

3

6 7 Dg ¼ 4 1 5, 0

m Jm Bg þ m  Jg 1  Cm ¼ 1

ð8Þ

3.2. Extreme learning machine Single-hidden layer feed-forward neural networks (SLFN) are widely used to approximate complex nonlinear mappings directly from the input samples. The input weights and hidden layer biases of SLFN can be randomly assigned if the activation functions in the hidden layer are infinitely differentiable. After the input weights and the hidden layer biases are randomly chosen, SLFNs can be simply considered as a linear system and the output weights of SLFNs can be analytically determined through simple generalized inverse operation of the hidden layer output matrices. Extreme learning machine (ELM) which can obtain better generalization performance is emerged based on this concept [8–12]. Different from traditional learning algorithms the ELM not only tends to reach the smallest training error but also the smallest norm of weights which makes the regression performance better [8]. For N arbitrary distinct samples ðxi ,ti Þ, where xi ¼ ½xi1 ,xi2 ,    ,xin T A Rn and ti ¼ ½t i1 ,t i2 ,    ,t in T A Rm , standard SLFNs with N~ hidden nodes and activation function g(x) are mathematically modeled as N~ X

3 K  7 Jm 7 K 7 7, 7 Jg 5

2 3 1 6 7 Dm ¼ 4 0 5, 0

i¼1

 Cg ¼ 0

bi g i ðxj Þ ¼

N~ X

bi g i ðwi xj þ bi Þ ¼ oj , j ¼ 1,    ,N,

ð10Þ

i¼1

where wi ¼ ½wi1 ,wi2 ,    ,win T is the weight vector connecting the ith hidden node and the input nodes, bi ¼ ½bi1 , bi2 ,    , bim T is the weight vector connecting the ith hidden node and the output nodes, and the bi is the threshold of the ith hidden node. wi xj denotes the inner product of wi and xj . That standard SLFNs with N~ hidden nodes with activation function g(x) can approximate P~ these N samples with zero error means that N j ¼ 1 Joi tj J ¼ 0, i.e., there exist bi , wi and bi such that

0  0 ,

where the observer gain L is designed by the Kalman Filtering (KF) approach [22]. An ORC two pieces cascaded coupled linear observer is proposed to estimate Tw and om . The basic structure is given in Fig. 1 [25]. The inner-loop is a Kalman filter designed with respect to (9). The outer-loop ORC operates as a dynamic tracking configuration with the real-time og as the tracking objective. Normally, conventional PI or PID controller is used for the outer-loop dynamic tracking. However, the performance of ORC loop was proved perfect far beyond the capability of PI or PID loop. Theoretically, ORC supports the outer-loop tracking with perfect performance. The asymptotic tracking of the observer can be ensured as long as that the ORC observer is well designed [22,25]. The turbine mechanical torque Tw can be estimated as the ORC output. The previous works [24,25] give the design process of ORC.

 1 :

The generator electrical torque Tg and the generator speed og can be measured. The state estimator is designed by propagating the input signals, Tw and Tg, through (8). The states are furthermore updated by a scaling, L, of the error in estimated output as described as

i¼1

^ g Þ, x^_ ¼ Ax^ þBm T w þ Bg T g þ Lðog o

Hðw1 ,    ,wN~ ,b1 ,    ,bN~ ,x1 ,    ,xN Þ

ð9Þ

N~ X

bi g i ðwi xj þbi Þ ¼ tj , j ¼ 1,    ,N:

ð11Þ

The above N equations can be written compactly as Hb ¼ T, where

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2

gðw1 x1 þb1 Þ



gðwN~ x1 þ bN~ Þ

^



^

6 ¼4

gðw1 xN þ b1 Þ 2 T3 6

b1

7

7 b¼6 4 ^ 5 bTN~ ~

,

N m

   gðwN~ xN þ bN~ Þ 2 T3 t1 6 7 T¼4 ^ 5 : tTN

3 7 5

Training an ELM is simply equivalent to find a least-squares solution b^ of above the linear system, b^ ¼ Hy T, where Hy is the Moore–Penrose generalized inverse of matrix H, wi and bi are randomly chosen and g(x) is the sigmoid function in this paper [8].

, NN~

ð12Þ

Nm

3.3. ELM based wind speed estimation Commonly, no matter what the wind speed estimation methods are, the ideas are based on the power characteristic function. Given the turbine power Pw, the rotational speed om and the blade pitch angle b, the wind speed can be calculated from the nonlinear inverse function of (1). The ANN technique has been successfully used to solve input– output mapping problem of nonlinear inverse function [3,16]. The ½P w , om , b three input vector is always set as the input of the ANN and the V^ is the output of the ANN which represents the estimated wind speed. The traditional ANNs such as BP-SLFN and conventional RBF are trained off-line using a training data set that covers the entire operating range of the wind turbine. The samples of the rotor speed om , wind speed V and the pitch angle b are generated evenly in the operating range with the increments of Do, DV and Db, respectively. At each data sample of them oðiÞ, V(i) and bðiÞ, the turbine power sample Pw(i) is calculated from (1). However, these methods have some disadvantages as the following:

8000 7000 6000 5000 4000 3000 2000 1000 0

Power=900w Rotor Speed=19rad/s Line

15

V2 10 Wind Spe

5 V1 ed(m/s)

0

0

25 30 15 20 5 10 /s) d a peed(r Rotor S

Fig. 2. Characteristic of turbine captured power.

Fig. 3. ELM based wind speed estimation.

Cp/lam3 (Cp expresses Power Coefficient, lam expresses Tip Speed Ratio)

Power(w)

Power Characteristic versus Wind Speed & Rotor Speed (pitch angle 0 degree)

3

x 10−3 Beta = 0 degree Beta = 1 degree Beta = 2 degree Beta = 10 degree

2.5

Maximum values of Cp/lam3 exist at tip speed ratio 3.98−4.02

2 1.5 1 0.5 0 0

2

4

6

8

10

lam (Tip Speed Ratio) 3

Fig. 4. Characteristic curves of C p ðl, bÞ=l vs. l of different b.

12

14

S. Wu et al. / Neurocomputing 102 (2013) 163–175

1. Although the training data set do not need to be stored in the WTPGS hardware, the large amount of data for training are hard to be obtained by nominal computer. They may make the training speed very slow even reduce the approximation performance. For example, the training data set of the three training inputs may include the number of elements of 1000ðVÞ  900ðbÞ  200ðom Þ in a 4-byte float format. The total four input-and-outputs requires 2880 Megabytes memory for storing the training data set. The larger the operating range of the wind turbine or the smaller the sampling interval is, the larger amount of training data and longer the training time will be. It always makes the normal computer out of memory which means that the training process cannot easily be done by normal computers. That is inconvenient for the estimator design. In order to avoid the problem, the sampling intervals always should be increased to decrease the number of elements of the training data set which inevitably will decrease the estimation performance and accuracy of the wind speed. 2. With a same number of hidden neurons, the estimation accuracy of a three inputs ANN is worse than that of a two inputs ANN when operating as function approximation tools trained by the same algorithm. In order to achieve a similar approximation accuracy, there must be more hidden neurons for the three inputs ANN theoretically which will make the wind speed estimation slow and need more memory space of WTPGS hardware.

167

3. The traditional ANNs are designed on a rated constant air density without considering the variations. However, the air density decreases with increasing altitude, as does air pressure. It also changes with variances in temperature or humidity. For example, generally, the air temperature changing of 7 10 1C results the air density variation of 7 4%. The diurnal temperature varies around 715 1C or even more (seasonal/ annual more) in some places with WTPGS installed. It will make the real-time data Pw varying so as the output estimated wind speed. From (1), its inverse function of wind speed V is not proportional to Pw which will vary with air density r. So a new set of training data should be regenerated and the ANN should be retrained on-line with respected to the new air density manually. That’s unrealistic. 4. From Fig. 2, the inverse function of wind speed V from (1) is not always a function in the operating range. It means that given a set of Pw, o and b, the corresponding wind speed V sometimes is not unique (V1 and V2). In other words, not all the data in the operating range are suitable for training the ANN. However, no wind speed selection or exclusion law is given in the conventional ANN methods for picking the training data.

In addition, no wind speed estimation is tested under the condition when pitch control system is activating in the previous works.

Fig. 5. ELM based pitch control.

Fig. 6. Block diagrams of pitch control systems.

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S. Wu et al. / Neurocomputing 102 (2013) 163–175

In this paper, a wind speed estimation method based on ELM is proposed. The basic structure is shown in Fig. 3. ELM has been proved as a high performance function approximation tool due to its perfect regression capability beyond other kinds of ANNs [8]. To overcome the disadvantages of previous ANN methods, 3 C p ðl, bÞ=l which is a function with respect to only two states l and b is used as the objective function for ANN training instead of Pw. Since C p ðl, bÞ

l3

¼

2T^ w

rpR5 o^ 2m

,

C p ðl, bÞ

l3

^ m. can be online calculated by the real-time estimated T^ w and o 3 Due to that r is only used for calculation of C p ðl, bÞ=l , it is independent to the proposed ELM wind speed estimator. 3 The characteristic of C p ðl, bÞ=l vs. l of different b is given in Fig. 4. For a determined b, there exists an unique l denoted as lm 3 which corresponds the maximum value of C p ðl, bÞ=l . In the condition of any determined b, the corresponding lm and the 3 maximum value of C p ðl, bÞ=l will be given. The lm separates the 3 whole function of C p ðl, bÞ=l into two parts. According to this two parts, there are two solutions of inverse function of l with respect 3 to C p ðl, bÞ=l and b which denote as a low value l1 and a high value l2 , respectively. Since that the system sampling period is very short (i.e. 104 s) compared to the wind speed variation, the l of each two adjacent sampling time instants can be regarded as equivalent. Denote the V^ p as estimated wind speed at the previous time instant, the TSR of the previous time instant lp can be calculated as lp ¼ om R=V^ p . So the real-time TSR can be estimated as ( l2 , lp Z lm , l¼ ð13Þ l1 , lp o lm : Then the online wind speed can be estimated as V^ ¼ om R=l. In this two inputs ELM based estimation strategy, the training data may include the number of elements of 1000ðlÞ  900ðbÞ in a 4-byte float format for the three input-and-outputs. It requires only 10.8 Megabytes memory for the training data set. That can easily be taken by normal computers and the training precess can be very fast and precise. 3.4. ELM based pitch control strategy For the commonly used variable-speed variable-pitch (VSVP) WTPGS, the pitch control system for b is activated when the wind speed exceeds the rated value [1]. In other words, the pitch angle

should be controlled to make the power captured by the turbine maintaining at its rated value when the wind speed exceeds its rated value. According to (1), the pitch control can be regarded as a controller for limiting the power coefficient. Several pitch angle control methods have been reported so far, such as the classical PID controller [17,18]. However, most of the designs are based on a linearized turbine model at a specific operating point. It is obviously that the controllers may not provide identical performances when the turbine parameters or operating point deviates greatly. Some other pitch control strategies employ in nonlinear control schemes [19,20]. However, the design principles are always complicated which make the redesigns and extension applications hard for different kinds of WTPGS. Assume that the rated turbine extraction power is Pwr, the corresponding objective power coefficient C p ðl, bÞn is given as 3 C p ðl, bÞn ¼ 2P wr =rpR2 V^ , while l ¼ om R=V^ is obtained from Section 3.3. The pitch angle reference is given as bn ¼ f 0 ðC np ðl, bÞ, lÞ from its inverse b function of C p ðl, bÞ. Using the same ELM mapping technique as shown in Section 3.3, a twoinputs ELM pitch controller can be established. The structure is given in Figs. 5 and 6. Similarly, a simple selection law should be set to provide the pitch control command which corresponds to the turbine captured power at the previous sampling time instant Pwp. ( 0 n f ðC p ðl, bÞ, lÞ, Pwp 4 Pwr , n b ¼ ð14Þ 0, Pwp r Pwr : For the sensorless wind turbine, the proposed ELM pitch angle controller operates with considering the best cooperation of the turbine modeling, the real-time estimated rotational speed and the real-time estimated wind speed. The main advantages of the proposed controller are that it is more robust for different operating points with fast response capability than traditional linear controller. Moreover, it is much easier to be designed and applied in different kinds of WTPGS than some of the nonlinear controllers. 3.5. Entire sensorless control The proposed wind speed estimation and pitch control methods are obviously suitable for all classes of WTPGS. For simplification, a direct-drive variable-pitch PMSG WTPGS is employed to test the proposed methods. Due to that the observer given in Section 3.1 is also effective for one-order direct-drive wind turbine, it is reasonable to verify the effectiveness of the proposed

Fig. 7. Entire sensorless control scheme for variable-pitch PMSG WTPGS.

S. Wu et al. / Neurocomputing 102 (2013) 163–175

methods on a direct-drive variable-pitch PMSG WTPGS as a representative of all kinds of WTPGS. The overall PMSG WTPGS configuration and sensorless control structures are shown in Fig. 7. Define the TSR optimal value as lopt and the rotational speed rated value as omr . The rotational speed should be real-time adjusted to the optimal value for MPPT. So the turbine rotational speed command is given as 8 > < lopt V^ , onm 4 omr , ð15Þ onm ¼ R > : omr , onm r omr :

When the turbine extracted power goes beyond the rated power value, the pitch angle control is activated to decrease the extracted power back to the rated value. The speed PI controller and PMSG current controllers are all designed by pole-placement method [26].

4. Simulation and experimental remarks The proposed wind speed estimation and pitch control methods is tested on a small distributed direct-drive variable-pitch PMSG WTPGS. All the simulations are set up in MatLab/Simulink.

Real Wind Speed Estimated Wind Speed

8 6 4 2

12 Wind Speed (m/s)

Wind Speed (m/s)

12 10

0

10 8 6 4 2 0

10

20

30

40

50 60 Time (s)

0.2 0.15 0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 −0.25

70

80

90

100

Wind Speed Estimation Error

0

10

20

30

40

50 60 Time (s)

70

80

90

0

Wind Speed Estimation Error (m/s)

0

Wind Speed Estimation Error (m/s)

169

10

20

30

40

0.5 0.4 0.3 0.2 0.1 0 −0.1 −0.2

100

50 60 Time (s)

70

80

90

100

Wind Speed Estimation Error

0

10

20

30

40

50 60 Time (s)

70

80

90

100

Wind Speed (m/s)

12

Real Wind Speed Estimated Wind Speed

10 8 6 4 2

Wind Speed (m/s)

Fig. 8. Wind speed estimation performances and errors under normal air density condition: (a) wind speed estimation performance of ELM, (b) wind speed estimation performance of RBF, (c) wind speed estimation error of ELM, and (d) wind speed estimation error of RBF.

0

10 8 6 4 2 0

10

20

30

40

0.2 0.15 0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 −0.25

50 60 Time (s)

70

80

90

100

Wind Speed Estimation Error

0

10

20

30

40

50 60 Time (s)

70

80

90

100

0

Wind Speed Estimation Error (m/s)

0

Wind Speed Estimation Error (m/s)

Real Wind Speed Estimated Wind Speed

12

10

20

30

40

50 60 Time (s)

70

80

90

100

Wind Speed Estimation Error

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 −0.1 −0.2 0

10

20

30

40

50 60 Time (s)

70

80

90

100

Fig. 9. Wind speed estimation performances and errors under abnormal air density condition: (a) wind speed estimation performance of ELM, (b) wind speed estimation performance of RBF, (c) wind speed estimation error of ELM, and (d) wind speed estimation error of RBF.

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Some performance comparisons of conventional methods and the proposed methods will be given. Some experimental testings on an emulated WTPGS are also implemented to verify the proposed methods. The cut-in wind speed and cut-out wind speed for both the simulation and experimental systems are given as 3 m=s and 16 m=s, respectively. All other WTPGS parameters are shown in the appendix.

4.1. Simulation results and remarks

Turbine Rotational Speed (rad/s)

The torque dynamic model for the simulated small distributed direct-drive variable-pitch PMSG WTPGS uses the one-mass lumped modeling from (5). A testing pitch control system as shown in Section 3.4 is added to this simulated WTPGS for testing the performance of the proposed ELM pitch controller. The simulation performances of the proposed method for both low wind speed and high wind speed conditions are given. This paper

35

Rotor Speed for ELM Method Optimal Rotor Speed Reference

30 25 20 15 10 0

Turbine Rotational Speed (rad/s)

also gives the comparisons and analysis of the performances between the proposed method and conventional RBF for wind speed estimation as well as the proposed method and conventional PID pitch controller for pitch control. The rated rotational speed is set to be omr ¼ 33:75 rad=s and the turbine rated extracted power is Pwr ¼ 4000w. Under normal air density condition, the wind speed estimation performances and errors of ELM method and conventional RBF ANN method are given in Fig. 8, respectively. Although both the two methods can achieve good estimation performances, the proposed ELM based method is relatively more superior with less estimation error. Define an abnormal air density condition which is that the real air density increases by 6% to the design nominal value in this test. Under the abnormal condition, the wind speed estimation performances and errors of ELM method and conventional RBF ANN method are given in Fig. 9, respectively. It is obvious that the wind speed estimation accuracy of the conventional RBF ANN will

10

20

30

40

50 Time (s)

60

35

70

80

90

100

Rotor Speed for ELM Method Rotor Speed for RBF Method Optimal Rotor Speed Reference

30 25 20 15 10 0

10

20

30

40

50 Time (s)

60

70

80

90

100

8

Tip Speed Ratio

7 6 5 4 3 2

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be influenced by the air density variations. Once the air density changes by the variation of air temperature, the wind speed estimation error will increase evidently. Certainly, under this condition, the

Testing PMSG

rotor speed command cannot be given properly which will make the MPPT control failed. However, the proposed ELM based method would not be affected by the factor of air density.

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Fig. 14. Experimental results for low wind speed test. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

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In Fig. 10, the comparison of real rotational speed between the ELM method and the conventional RBF ANN method under the abnormal air density condition is shown. The comparison of TSR between the two methods is given as well. The sensorless MPPT rotational speed control is perfect by the ELM method. Using the conventional RBF ANN method instead, the rotational speed is always under relatively big deviation to the optimal rotor speed reference. So does the tip speed ratio. The TSR cannot be controlled to the optimal value (around 6.9) by the conventional RBF ANN based sensorless control which will make the turbine maximum power extraction control failed. Fig. 11 shows the wind speed estimation performance by the ELM method when the wind speed is mostly above the rated value. Due to the dynamics of the activated pitch angle system, the estimation error increases slightly, but the overall performance is still acceptable. This result also proves that the more dynamic inputs the ANN estimator has, the larger estimation error will be caused. In other words, the proposed mapping characteristic used in ELM method for decreasing the number of estimator’s inputs is reasonable and effective for improving the wind speed estimation accuracy. In Fig. 12, the pitch control performances of ELM pitch controller and conventional PI controller are compared. The wind speed is in the same high wind speed condition of that shown in Fig. 11. The first sub-figure gives the comparison of pitch angle responses and the turbine extracted power with the two pitch control methods are shown in the second sub-figure. It shows that the response of the ELM pitch controller is much faster than the

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conventional PI controller. The proposed pitch control can eliminate the big power extraction oscillations when the wind speed changes fast. However, the extracted power of ELM pitch controlled system sometimes has small fluctuations around the rated power which means that the ELM pitch controller results in more static error than the conventional PI controller. It may cause by the inevitable small wind speed estimation error. A correction law including the information of the real-time extracted power may be used for improving the pitch control performance and eliminating the static error. That is an interesting topic to be explored in the future work. 4.2. Application on hardware setup The proposed sensorless control is verified via implementation in an emulated WTPGS setup which is shown in Fig. 13. The ELM wind speed estimation and ELM pitch control performances are investigated. The experimental set-up was composed of a 600 W BLDC motor controlled by a DSP controller box which emulates the variable-pitch wind turbine, a 400 W PMSG and a dSPACE controller. The entire experimental system operates in low power and low wind speed conditions. Total PMSG stator resistance and inductance with filter Rs ¼ 1:3 O, Ls ¼ 4:1 mH and the PMSG magnet flux c ¼ 0:08333 T. An emulated pitch control system is considered including in the emulated the wind turbine. Sixty hidden neurons are chosen to build the ELM wind speed estimator. Actually, the number of hidden neurons can be determined by

Fig. 15. Experimental results for high wind speed test.

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manual adjustment to make the wind speed estimation error in the given tolerance. In Fig. 14, the experiment runs when the wind speed is under its rated value 3 m=s. Then the pitch control system is deactivated. Part (a) gives the real wind speed in red and the estimated wind speed in blue. In (b), the red curve expresses the optimal rotational speed reference and the blue one expresses the real rotor speed. In (c), the red curve and blue curve describe the turbine extracted power Pw and the stator generated power Pg, respectively. The wind speed estimation error (blue) and realtime pitch angle (red) are shown in (d). According to Fig. 14, the proposed ELM wind speed estimation and sensorless control are proved to be effective. In most of the time, the wind speed estimation error is less than 0:05 m=s. In Fig. 15, the experiment runs for when the wind speed is above its rated value 3 m=s. So the pitch control system is activated. The results are shown in the same sequence as in Fig. 14. It is easy to get the conclusion that the proposed ELM wind speed estimation and sensorless control are also effective when the pitch control system is activated. And the ELM based pitch control can achieve its power control objective. Due to the fast response of ELM pitch controller, the extracted power can be well maintained at its rated value (around 23w).

Moment of inertia of the lumped system, J g ¼ 1:08  102 kg m2 .

Appendix B. Experimental WTPGS parameters Turbine blade radius, R ¼ 1 m. Damping constant of turbine, Dg ¼ 1  104 . Moment of inertia of the lumped system, J g ¼ 1:2  104 kg m2 .

Appendix C. General parameters Maximum power coefficient, C pmax ¼ 0:4412. Optimal tip speed ratio, lopt ¼ 6:9077. Normal air density for estimator design, r ¼ 1:25 kg=m3 . Pitch rate limit, 61=s. Pitch system time constant T servo ¼ 0:05 s.

References 5. Conclusion In this paper, an ELM based wind speed estimation and sensorless control scheme is proposed for WTPGS. Due to that the estimation accuracy of the real-time wind speed is the key point for sensorless controlling of the WTPGS, a highly precise wind speed estimator based on ELM is designed to achieve the real-time wind speed precise estimation. The real-time turbine information are estimated by a fast two-loop ORC observer from the measurable generator information. Overall, the proposed method is much faster, more accurate and less time-consuming over the conventional lookup table, root calculation and SVR methods. Compared to traditional ANN methods, the proposed method is more precise and suitable for all classes of WTPGS which holds the advantages such as high accuracy training algorithm and special designed mapping characteristic. In addition, ELM is used for design the pitch controller. The ELM pitch controller is designed based on the mapping characteristic between the power coefficient and the turbine real-time information. This pitch control scheme not only avoids bad performance of conventional linear controllers caused by the fixed linearized operating point, but also removes the complicated design process of some conventional nonlinear controllers. The effectiveness of the proposed wind speed estimation and pitch control methods are verified on a direct-drive variable-pitch PMSG WTPGS as a representative by both the simulation and experiments. Alternatively, a correction law for the pitch control action against the inevitable wind speed estimation error can be explored in the future work to eliminate the static error and improve the pitch control performance further.

Acknowledgments The authors would like to thank Dr. Guang-Bin Huang for the valuable discussions and advices on ELM for this paper. Appendix A. Simulation WTPGS parameters Turbine blade radius, R ¼ 2 m. Damping constant of turbine, Dg ¼ 2  102 .

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Si Wu received his BEng degree from Wuhan University, China, in 2007, the MSc degree from Nanyang Technological University, Singapore, in 2008, both in electrical engineering. Currently, he is pursuing his PhD degree in School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. His research interests include the applications of advanced controls on power systems and wind turbine power generation systems.

Youyi Wang received his BEng degree from Beijing University of Science and Technology in 1982, the MEng degree from Tsinghua University, China, in 1984, and the PhD degree from the University of Newcastle, Australia, in 1991, all in electrical engineering. Currently, he is a full professor in the School of Electrical and Electronic Engineering, Nanyang Technological University (NTU). Since he joined NTU in 1991, Wang has published over 240 top referred international journal and conference papers on system theory, stability analysis, information storage systems, power and energy systems and control theory applications. His main research interests are in the area of applications of nonlinear control, robust control to power and energy systems, electric drive systems, information storage systems, fuel cell systems, renewable energy systems and MEMS systems. He is a senior member of IEEE.

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Shijie Cheng received the BEng degree from Xi’an Jiaotong University, China, in 1967, the MEng degree from Huazhong University of Science and Technology, China, in 1981, and the PhD degree from University of Calgary in Canada in 1986, all in electrical engineering. He is currently a full professor in the College of Electrical Engineering, Huazhong University of Science and Technology, Wuhan, PR China. He is the deputy director of Huazhong University of Science Academic Committee, director of Hubei Key Laboratory of Power, Safety and Efficiency, executive director of China Society of Electrical Engineering, committee member of Chinese Society of Electrical Engineering, committee member of China Power Systems Automation Committee, the vice president of Hubei Institute of Electrical Engineering. His main research interests are in the area of power system stability control based on high temperature superconducting magnetic energy storage systems and rotating energy storage systems, power system adaptive control, power system intelligent control and power system subsynchronous oscillation. He is a fellow of Chinese Academy of Sciences and a fellow of the IEEE.