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Energy 35 (2010) 2440e2447

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Energy

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Intelligent approach to maximum power point tracking control strategy forvariable-speed wind turbine generation system

Whei-Min Lin, Chih-Ming Hong*

Department of Electrical Engineering, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan, ROC

a r t i c l e i n f o

Article history:Received 6 July 2009Received in revised form12 February 2010Accepted 22 February 2010Available online 2 April 2010

Keywords:Wilcoxon radial basis function networkModified particle swarm optimizationPermanent magnet synchronous generatorMaximum power point trackingHill-climb searching

* Corresponding author. Tel.: þ886 7 5252000x411E-mail address: d943010014@student.nsysu.edu.tw

0360-5442/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.energy.2010.02.033

a b s t r a c t

To achieve maximum power point tracking (MPPT) for wind power generation systems, the rotationalspeed of wind turbines should be adjusted in real time according to wind speed. In this paper, a Wilcoxonradial basis function network (WRBFN) with hill-climb searching (HCS) MPPT strategy is proposed fora permanent magnet synchronous generator (PMSG) with a variable-speed wind turbine. A high-performance online training WRBFN using a back-propagation learning algorithm with modified particleswarm optimization (MPSO) regulating controller is designed for a PMSG. The MPSO is adopted in thisstudy to adapt to the learning rates in the back-propagation process of the WRBFN to improve thelearning capability. The MPPT strategy locates the system operation points along the maximum powercurves based on the dc-link voltage of the inverter, thus avoiding the generator speed detection.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Recently, wind generation systems are attracting great attentionsas clean and safe renewable power sources. Wind generation can beoperated by constant speed and variable-speed operations usingpower electronic converters. Variable-speed generation is attractivebecause of its characteristic to achieve maximum efficiency at allwind velocities [1e5], the improvement in energy production, andthe reduction of the flicker problem. In the variable-speed genera-tion system, the wind turbine can be operated at the maximumpower operating point for variouswind speeds by adjusting the shaftspeed. These characteristics are advantages of variable-speed windenergy conversion systems (WECS). In order to achieve themaximum power control, some control schemes have been studied.

A variable-speed wind power generation system (WPGS) needsa power electronic converter and inverter, to convert variable-frequency, variable-voltage power into constant-frequencyconstant-voltage, to regulate the output power of the WPGS.Traditionally a gearbox is used to couple a low speed wind turbinerotor with a high speed generator in a WPGS. Great efforts havebeen placed on the use of a low speed direct-drive generator toeliminate the gearbox. Many of the generators of research interest

5; fax: þ886 7 5254199.(C.-M. Hong).

All rights reserved.

and for practical use in wind generation are induction machineswith wound-rotor or cage-type rotor [6e9]. Recently, the interest inPM synchronous generators is increasing. High-performance vari-able-speed generation including high efficiency and high control-lability is expected by using a permanent magnet synchronousgenerator (PMSG) for a wind generation system.

Previous research has focused on three types of maximumwindpower extraction methods, namely, tip-speed ratio (TSR) control,power signal feedback (PSF) control and hill-climb searching (HCS)control. TSR control regulates the wind turbine rotor speed tomaintain an optimal TSR. PSF control requires the knowledge of thewind turbine’s maximum power curve, and tracks this curvethrough its control mechanisms. Among previously developedwind turbine maximum power point tracking (MPPT) strategies,the TSR direction control method is limited by the difficulty inwindspeed and turbine speed measurements [10e14]. Many MPPTstrategies were then proposed to eliminate the measurements bymaking use of the wind turbine maximum power curve, but theknowledge of the turbine’s characteristics is required. HCS controlhas been proposed to continuously search for the peak outputpower of the wind turbine. In comparison, the HCSMPPT is populardue to its simplicity and independence of system characteristics. Inthis paper, a Wilcoxon radial basis function network (WRBFN)-based with HCS MPPT strategy is proposed for PMSG wind turbinegenerator (WTG). The proposed control structure, WRBFN withmodified particle swarm optimization (MPSO) algorithm forces the

Fig. 1. Typical CP versus l curve.

W.-M. Lin, C.-M. Hong / Energy 35 (2010) 2440e2447 2441

system to reach its equilibrium quickly where the turbine inertiaeffect is minimized. HCS can be fast and effective in spite of thevariations in wind speeds and the presence of turbine inertia.

Intelligent control approaches such as neural network and fuzzysystem do not require mathematical models and have the ability toapproximate nonlinear systems. Therefore, there were manyresearchers using intelligent control approaches to representcomplex plants and construct advanced controllers. Moreover, thelocally tuned and overlapped receptive field is a well-knownstructure that has been studied in regions of cerebral cortex, visualcortex, and so on [15]. Based on the biological receptive fields, theRBFN that employs local receptive fields to perform functionmappings was proposed in [16]. Furthermore, the RBFN hasa similar feature to the fuzzy system. First, the output value iscalculated using the weighted sum method. Second, the number ofnodes in the hidden layer of the RBFN is the same as the number ofifethen rules in the fuzzy system. Finally, the receptive field func-tions of the RBFN are similar to the membership functions of thepremise part in the fuzzy system. Therefore, the RBFN is very usefulto be applied to control the dynamic systems [17].

2. Analysis of wind generation system

2.1. Wind turbine characteristics and modeling

In order to capture the maximal wind energy, it is necessary toinstall the power electronic devices between the WTG and the gridwhere the frequency is constant. The input of a wind turbine is thewind and the output is the mechanical power turning the generatorrotor [7e9]. Foravariable-speedwind turbine, theoutputmechanicalpower available from awind turbine could be expressed as

Pm ¼ 12rACpðl;bÞV3

u (1)

where r and A are air density and the area swept by blades,respectively. Vu is the wind velocity (m/s), and Cp is called thepower coefficient, and is given as a nonlinear function of the TSRldefined by

l ¼ urrVu

(2)

where r is wind turbine blade tip radius, and ur is the turbinespeed. Cp is the function of the l and the blade pitch angle b, generaldefined as follows:

Cp ¼ 0:73�151li

� 0:58b� 0:002b2:14 � 13:2�e

�18:4li

li ¼1

1l� 0:02b

� 0:003

b3 þ 1

ð3Þ

By using (3), the typical Cp versus l curve is shown in Fig. 1. Ina wind turbine, there is an optimum value of TSR lopt that leads tomaximum power coefficient Cpmax. When TSR in (2) is adjusted toits optimum value lopt ¼ 6:9 with the power coefficient reachingCpmax ¼ 0:4412, the control objective of the maximum powerextraction is achieved.

2.2. PMSG

The wind generator is a three-phase PMSG, where the mechan-ical torque (Tm) and electrical torque (Te) can be expressed as

Tm ¼ Pmur

(4)

Te ¼ Peue

¼ 2PPeur

(5)

In general, the mechanical dynamic equation of a PMSG is givenby

Jdur

dt¼ Tm � ðP=2ÞTe (6)

where ue and P are electrical angular frequency, and the number ofpoles. J is the inertia moment of WTG.

2.3. Wind turbine emulation

The emulation of the wind turbine is implemented by a dcmotor drive with torque control. In the prototype, a 1.5 kW,1980 rpm dc motor was used. A computer program reads the windinput file obtained with various test conditions, and calculates thewind turbine torque by taking into account wind velocity, turbinerotational speed, and the wind turbine power coefficient curve. Thecontrol algorithms for turbine emulation are implemented ina control board dSPACE DS1102. This board is a commercial systemdesigned for rapid prototyping of real control algorithms; it is basedon the Texas Instruments TMS320C32 floating-point DSP. TheDS1102 board is hosted by a personal computer.

3. HCS control method

3.1. System configuration

Fig. 2 presents the block diagram of theWTgeneration system inour research, where a PMSG is driven by aWT to feed the extractedpower from wind resources to the grid through a single-phaseinverter. A variable-speed WPGS needs a power electronicconverter and inverter, to convert variable-frequency, variable-voltage AC power from a generator to DC and then into constant-frequency constant-voltage power. In the dc-link of the inverter,a blocking diode DB is used to improve the power deliveringcapability as well as to guarantee that the dc-link voltage transfersto the output voltage. An inverter controller is designed to dealwith two aspects, the MPPT control for power maximization andthe current control for output PWM to inverter. The dc-link voltageand current, Vdc and Idc are sampled to provide the power(Pdc ¼ Vdc,Idc) input to the controller, and Vdc reference signal V*

dcis updated in real time using an HCS method so as to lead thesystem to its optimal operation point. On the other hand, a WRBFNcontroller is designed to force Vdc to follow V*

dc by adjusting the loadcurrent reference for the inverter current controller.

Fig. 2. PMSG WT generation system.

W.-M. Lin, C.-M. Hong / Energy 35 (2010) 2440e24472442

3.2. Optimal DC-link voltage (Vdc) search

From the Cpel characteristics, the turbine mechanical powerPm can be shown as a function of Vdc, and an optimal Vdc existsfor the maximum Pm output, provided that a PMSG is employedin the generation system. Fig. 3 shows a group of PmeVdc curvesand the corresponding maximum power curve formed withvarious optimal operating points, where wind speedsu1 < u2 < u3 < u4. In order to extract maximum power fromwind, the optimal Vdc is searched in real time using the HCSmethod. With HCS, if the previous increment of V*

dc is followed byan increase of Pm, then the search of V*

dc continues in the samedirection; otherwise, the search reverses its direction. Anexample can be seen in Fig. 3, where the wind change fromu3/u4/u2 with the search of Vdc from A/B/C/D/E. Theincrement of Pm is approximated by that of Pdc, and the search isexecuted at dynamic equilibrium operation points where Pdc isapproximately equal to Pm and the effect of turbine inertia J canbe minimized. In dynamic states, V*

dc will be held and the WRBFNwill adjust the load current in real time to drive the system to itsequilibrium point as soon as possible. Fig. 3 illustrates thesearching process ðABCDEÞ for the maximum power points whenthe wind speed varies.

Fig. 3. Principle of HCS control method.

4. The proposed intelligent MPPT control algorithm

4.1. Wilcoxon radial basis function network

The linearWilcoxon regressor is quite robust against outliers [18],which motivates the design of Wilcoxon neural networks. A three-layer neural network shown in Fig. 4 is adopted to implement theproposedWRBFN. TheWRBFNwithMPSO controller is used, and thecontrol law Id is generated from theWRBFN TheWRBFN input is xð1Þ1and xð1Þ2 of the first layer, where xð1Þ1 ¼ Vdc � V*

dc ¼ e and xð1Þ2 ¼ _e inthis study. In the proposedWRBFN, the units in the input, hidden, andoutput layers are two, nine and one, respectively. The signal propa-gation and the basic function in each layer can be found [19].

Layer 1: input layer. The nodes at this layer are used to directlytransmit the numerical inputs to the next layer. That is, for the ithnode of layer 1, the net input and output are defined by

Fig. 4. Architecture of the WRBFN.

W.-M. Lin, C.-M. Hong / Energy 35 (2010) 2440e2447 2443

netð1Þi ¼ xð1Þi ðNÞ

yð1Þi ðNÞ ¼ f ð1Þi

�netð1Þi ðNÞ

�¼ netð1Þi ðNÞ i ¼ 1;2 (7)

Layer 2: hidden layer. At this layer, every node performsa Gaussian basis function. The Gaussian basis function, a particularexample of radial basic functions, is used here as a membershipfunction. Then

netð2Þj ðNÞ ¼ �Xni¼1

�xð1Þi � cij

�2=vij

yð2Þj ðNÞ ¼ f ð2Þj

�netð2Þj ðNÞ

�¼ exp

�netð2Þj ðNÞ

�j ¼ 1;.;9 (8)

where cj ¼ ½ c1j c2j / cij �T and vij denote respectively, themean and the standard deviation (STD) of the Gaussian basisfunction.

Layer 3: output layer. The single node k in this layer is denoted byS, which computes the overall output as the summation of allincoming signals by

netð3Þk ¼Xmj�1

wjkyð2Þj ðNÞ

yð3Þk ðNÞ ¼ f ð3Þk

�netð3Þk ðNÞ

�¼ netð3Þk ðNÞ ¼ Id (9)

where the connectionweightwjk is the connective weight betweenthe hidden node, and the output layer k.

4.2. The network training and learning process

Once the WRBFN has been initialized, a supervised learning lawis used to train this system. The basis of this algorithm is gradientdescent. The derivation is the same as that of the back-propagationalgorithm. It is employed to adjust the parameters wjk, cij, vij of theWRBFN by using the training patterns. By recursive application ofthe chain rule, the error term for each layer is first calculated. Theadaptation of weights to the corresponding layer is then given. Thepurpose of supervised learning is to minimize the error function Eexpressed as

E ¼ 12

�Vdc � V*

dc

�2 ¼ 12e2L (10)

where V*dc and Vdc represent the dc-link voltage reference and

actual dc-link voltage feedback of the generator.Layer 3: update weight wjkAt this layer, the error term to be propagated is given by

dk ¼ � vE

vnetð3Þk

¼24� vE

vyð3Þk

vyð3Þk

vnetð4Þk

35 (11)

Then the weight wjk is adjusted by the amount

Dwjk ¼ � vEvwjk

¼24� vE

vyð3Þk

vyð3Þk

vnetð3Þk

35 vnetð3Þk

vwjk

!¼ dky

ð2Þj (12)

We have

wjkðN þ 1Þ ¼ wjkðNÞ þ hwDwjkðNÞ (13)

where hw is the learning rate for adjusting the parameter wjk.Layer 2: update cij and vij. The multiplication operation is done in

this layer. The adaptive rule for cij is

Dcij ¼ � vEvcij

¼24� vE

vnetð3Þk

vnetð3Þk

vyð2Þj

vyð2Þj

vcij

35

¼ dkwjkyð2Þj

2�xð1Þi � cij

�vij

(14)

and the adaptive rule for vij is

Dvij¼� vEvvij

¼24� vE

vnetð3Þk

vnetð3Þk

vyð2Þj

vyð2Þj

vvij

35¼ dkwjk

2�xð1Þi �cij

�2�vij�2 (15)

We have

cijðkþ 1Þ ¼ cijðkÞ þ hmDcij

vijðkþ 1Þ ¼ vijðkÞ þ hsDvij (16)

where hm and hs are the learning rates for adjusting the parameterscij andvij, respectively. The exact calculation of the jacobian of thesystem, which is contained in vE=vyð3Þk , cannot be determined dueto the uncertainty of the PMSG dynamic. To overcome this problemand to increase the on-line learning ability of the connectiveweights, the delta adaptation law [19] is implemented as follows tosolve the difficulty

dkheL þ _eL

The learning rates hw, hm, hs are adjusted by MPSO as stated below.

5. WRBFN learning rates adjustment using MPSO

PSO is a population-based optimization method first proposedby Kennedy and Eberhart. PSO technique finds the optimal solutionusing a population of particles. Each particle represents a candidatesolution to the problem. PSO is basically developed throughsimulation of bird flocking in two-dimensional space [20].

Step 1: Define basic conditions. In the first step of MPSO, oneshould determine the parameters that need to be optimized andgive them minimum and maximum ranges. The number of groups,population size of each group, and initial radius of each gbest arealso assumed in this step.

Step 2: Initialize random swarm location and velocity. To begin,initial location Rdi ðNÞand velocitiesvdi ðNÞof all particles are gener-ated randomly in whole search space. Moreover, the populationsize is set to P ¼ 15 and the dimension of the particle is set tod ¼ 3 in this study. The generation particles are Rdi ¼ ½R1i ;R2i ;R3i �,where R1i ;R

2i ;R

3i are the RBFN learning rates, respectively. The

initial pbest of a particle is set by its current position. Then, gbest ofa group is selected among the pbests in the group.

The random generation of Rdi ðNÞ initial value ranged as

Rdi wUhhdmin; h

dmax

iwhere hmin; hmax are the lower and upper bound of the learningrates.

Step 3: Update velocity: In the classical PSO algorithm, thevelocity of a particle was determined according to the relativelocation from pbest and gbest.

During each iteration, every particle in the swarm is updatedusing (17) and (18). Two pseudorandom sequences r1wUð0;1Þ andr2wUð0;1Þ are used to produce the stochastic nature of the algo-rithm. For dimensions d, let Rdi ,Pbest

di ,and vdi be the current position,

current personal best position. The velocity update step is

W.-M. Lin, C.-M. Hong / Energy 35 (2010) 2440e24472444

vdi ðN þ 1Þ ¼ wvdi ðNÞ þ c1,randð Þ,�Pbestdi � Rdi ðNÞ

�þ c2,randð Þ,

�Gbestd � Rdi ðNÞ

�(17)

Step 4: Update position. The new velocity is then added to thecurrent position of the particle to obtain its next position

Rdi ðN þ 1Þ ¼ Rdi ðNÞ þ vdi ðN þ 1Þ i ¼ 1;.; P (18)

Step 5: Update pbests. If the current position of a particle is locatedwithin the analysis space and does not intrude territory of othergbests, the objective functionof theparticle is evaluated. If the currentfitness is better than the old pbest value, pbest is replaced by thecurrent position. The fitness value of each particle is calculated by

FIT ¼ 1

0:1þ abs�Vdc � V*

dc

� (19)

Step 6: Update gbests: In the conventional PSO, gbest is replaced bythe best pbest among the particles. However, when such a strategy isapplied to multimodal function optimization, some gbests ofdifferent groups can be overlapped. To maintain fast convergencerate of PSO, gbest of the group could be selected among the Pbestdi ¼½Pbestd1 ; Pbestd2 ;.Pbestdp � having high fitness value.

Fig. 5. Experimental results of the wind speed profile: (a) The maximum power trackingTip-speed ratio l.

Step 7: Repeat and check convergence. Steps 3e6 are repeateduntil all particles are gathered around the gbest of each group, oramaximum iteration number is encountered. The final Gbestdi is theoptimal learning rate ðhw; hm; hsÞof RBFN.

The inertia weight w in (17) is used to control the convergencebehavior of the PSO. Smallw results in rapid convergence usually ona suboptimal position, while a large value may cause divergence. Inthis paper, the inertia weight w is set according to the equation that

w ¼ wmax �wmax �wminitermax

,iter (20)

where itermax is maximum number of iterations, and iter is thecurrent iteration number.

6. Experimental results

The WRBFN with MPSO performance is compared with twobaseline controllers: the fuzzy [21] and the proportional-integral(PI) controller. The WRBFN with MPSO, fuzzy and PI methods weretested through experimental. The obtained performance with thedifferent controllers are shown in Figs. 5e7, and summarized inTable 1. Various cases were conducted, the wind profile is simula-tion with a 5 ms sampling time the wind profile is assumed

control signal. (b) The dc-link voltage tracking response. (c) Power coefficient CP . (d)

Fig. 6. Experimental results of the wind speed profile: (a) The maximum power tracking control signal. (b) The dc-link voltage tracking response. (c) Power coefficient Cp. (d)Tip-speed ratio l.

W.-M. Lin, C.-M. Hong / Energy 35 (2010) 2440e2447 2445

a volatile sinusoidal wave. The conventional PI-type controller iswidely used in the industry due to its simple control structure, easeof design and inexpensive cost. The average power of PI iscompared with that of WRBFN with MPSO algorithm and Fuzzy-Based algorithm.

The WTG system used for the experimental has the followingparameters:

(1) Wind turbine parameters: Pm ¼750 W; 3.75 A; 3000r/min;r ¼ 1.25 kg/m3; r ¼ 0.5 m; and J ¼ 1.32 �10�3N m s2

(2) Generator parameters: R ¼ 1.47 U; Ld ¼ Lq ¼ 5.33 mH; Lmd ¼4.8 mH; Ifd ¼ 46.75 A; Kt ¼ 0.6732 Nm/A

6.1. PI algorithm for Vdc control

The WRBFN with MPSO algorithm replaced by PI algorithm isshown in Fig. 2. Fig. 5 illustrates the experimental result for PIcontrol. The average power is 205 W for the same period. It can befound that TSR is always round 6.9 and Cp is 0.44. The verification ofmaximum power tracking control is shown in Fig. 5a. The dc-linkvoltage tracking response is shown in Fig. 5b. Fig. 5c and d showspower coefficient Cp and TSR l.

6.2. Fuzzy-based algorithm for Vdc control

The WRBFN with MPSO algorithm replace by Fuzzy-Basedalgorithm as shown in Fig. 2. A fuzzy logic control (FLC) algorithm ischaracterized by “IFeTHEN” rules. The algorithm is suitable forwind turbine control with complex nonlinear models and param-eters variation. The input variables of Fuzzy-BasedMPPTare dc-linkpower tracking error and the difference of dc-link power trackingerror.

Fig. 6 shows that 217W (an increase of 5.36% compared withthat of PI control) is obtained by the Fuzzy-Based algorithm duringthe 50 s. It can be found that l and Cp are close to the optimal valuesof 6.9 and 0.44, respectively. The wind speed profiles of turbinepower Pm and dc-link power Pdc are also shown in Fig. 6a. The dc-link voltage tracking response is shown in Fig. 6b. Fig. 6c andd shows power coefficient Cp and TSR l.

6.3. WRBFN with MPSO algorithm for Vdc control

WRBFN with MPSO algorithm control is considered and theexperimental result is shown in Fig. 7. The verification of maximumpower tracking control is shown in Fig. 7a, where the wind speed

Fig. 7. Experimental results of the wind speed profile: (a) The maximum power tracking control signal. (b) The dc-link voltage tracking response. (c) Power coefficient Cp.(d) Tip-speed ratio l.

W.-M. Lin, C.-M. Hong / Energy 35 (2010) 2440e24472446

profiles of turbine power Pm and dc-link power Pdc are also shown.The dc-link voltage tracking response is shown in Fig. 7b. Fig. 7cshows power coefficient Cp which is close to its maximum valueduring the whole wind speed profile, same for l of Fig. 7d. Theefficiency of the maximum power extraction can be clearlyobserved as the power coefficient is fixed at the optimum valueCp ¼ 0:44 and l ¼ 6:9. The average power is 224W. Comparedwith that from the PI control method, it increases by 9.27%.

From the performance comparison for various methods aboveexperimental results, we can see that MPPT is important for eitherhigh or low wind speeds, as shown in Table 1. Table 1 shows theaverage power, maximum error of power coefficient, maximumerror of dc-link power and percentage of power increase from each

Table 1Performance for various control methods

Controller type Control characteristic

Average power(Pdc) (W)

Increasing powerpercentage (%)

WRBFN with MPSO algorithm method 224 9.27Fuzzy-based algorithm method 216 5.36PI method 205 e

control method. On the other hand, the maximum error of thepower coefficient is around 23% in [9], and the maximum powerdeviation is about 7% in [14]. The proposed method in comparisonwith other methods [9,14] has better performance.

7. Conclusion

This paper focuses on the development of maximum windpower extraction algorithms for inverter-based variable-speedWPGS. The HCS method is proposed in this paper for maximumpower searching with various turbine inertia. Without a need formeasurements of wind speed and turbine rotor speed, HCS issimple to implement. When exciting the system with a real wind

Max. error of powercoefficient (Cp) (%)

Max. error of dc-linkpower (%)

Max. error ofdclink voltage (%)

1.79 0.32 0.0749.95 1.4 0.9

18.4 2.58 2.25

W.-M. Lin, C.-M. Hong / Energy 35 (2010) 2440e2447 2447

profile, the system is able to track maximum power using gener-ated power as input. The proposed system has been implemented,with a commercial PMSG and a dc drive to emulate the windturbine behavior. The process is running in a dSPACE board thatincludes a TMS320C32 floating-point DSP. Experimental resultsshow the appropriate behavior of the system.

Three MPPT control algorithms are proposed in this paper,without any wind speed sensor. It is found that the PI method canoperate near the optimal Cp. However, the PI-type controller maynot provide perfect control performance if the controlled plant ishighly nonlinear or the desired trajectory is varied with higherfrequency. The proposed output maximization control of WRBFNcan maintain the system stability and reach the desired perfor-mance even with parameter uncertainties.

References

[1] Pena RS, Cardenas RJ, Asher GM, Clare JC. Vector controlled indction machinesfor stand-alone wind energy applications. Proc IEEE Ind Appl Annu Meeting2000;3:1409e15.

[2] Senjyu T, Sakamoto R, Urasaki N, Funabashi T, Sekine H. Output power levelingof wind farm using pitch angle control with fuzzy neural network. IEEE PowerEngineering Society General Meeting; 2006. p. 8.

[3] Sakamoto R, Senjyu T, Sakamoto R, Kaneko T, Urasaki N, Takagi T, Sugimoto S,Sekine H. Output power leveling of wind turbine generator by pitch anglecontrol using HN control. The IEEE PSCE Conf; 2006:2044e9.

[4] Ramtharan G, Ekanayake JB, Jenkins N. Frequency support from doubly fedinduction generator wind turbines. IET Renew Power Gener 2007;1(1):3e9.

[5] Fernandez LM, Garcia CA, Jurado F. Comparative study on the performance ofcontrol systems for doubly fed induction generator (DFIG) wind turbinesoperating with power regulation. Energy 2008;33(9):1438e52.

[6] Simoes MG, Bose BK, Spiegel RJ. Fuzzy logic-based intelligent control ofa variable speed cage machine wind generation system. IEEE Trans PowerElectron 1997;12(1):87e95.

[7] Li H, Shi KL, McLaren PG. Neural-network-based sensorless maximum windenergy capture with compensated power coefficient. IEEE Trans Ind Appl2005;41(6):548e56.

[8] Karrari M, Rosehart W, Malik OP. Comprehensive control strategy for a vari-able speed cage machine wind generation unit. IEEE Trans Energy Convers2005;20(2):415e23.

[9] Wang Q, Chang L. An intelligent maximum power extraction algorithm forinverter-based variable speed wind turbine systems. IEEE Trans Power Elec-tron 2004;19(5):1242e9.

[10] Thiringer T, Linders J. Control by variable rotor speed of a fixed-pitch windturbine operating in a wide speed range. IEEE Trans Energy Convers 1993;EC-8:520e6.

[11] Chedid R, Mrad F, Basma M. Intelligent control of a class of wind energyconversion systems. IEEE Trans Energy Convers 1999;EC-14:1597e604.

[12] Tanaka T, Toumiya T. Output control by hill-climbing method for a small windpower generating system. Renew Energy 1997;12(4):387e400.

[13] Morimoto S, Nakamura T, Sanada M, Takeda Y. Sensorless output maximiza-tion control for variable-speed wind generation system using IPMSG. IEEETrans Ind Appl 2005;41(1):60e7.

[14] Koutroulis E, Kalaitzakis K. Design of a maximum power tracking system forwind-energy-conversion applications. IEEE Trans Ind Electron 2006;53(2):486e94.

[15] Jang JSR, Sun CT. Neuro-fuzzy and soft computing: a computational approachto learning and machine intelligence. Upper Saddle River, NJ: Prentice-Hall;1997.

[16] Jang JSR, Sun CT. Function equivalence between radial basis function networksand fuzzy inference systems. IEEE Trans Neural Networks 1993;4(1):156e9.

[17] Seshagiri S, Khail HK. Output feedback control of nonlinear systems using RBFfunction equivalence between radial basis function neural networks. IEEETrans Neural Networks 2000;11(1):69e79.

[18] Hogg RV, McKean JW, Craig AT. Introduction to Mathematical Statistics. Sixthed. New Jersey: Prentice-Hall; 2005.

[19] Lin CT, George Lee CS. Neural fuzzy systems. Upper Saddle River, NJ: Prentice-Hall Inc; 1996.

[20] Esmin AA, Torres GL, Souza CZ. A hybrid particle swarm optimization appliedto loss power minimization. IEEE Trans Power Syst 2005;20(2):859e66.

[21] Chen Z, Gomez SA, McCormick M. A fuzzy logic controlled power electronicsystem for variable speed wind energy conversion systems. Eighth Int ConfPower Electron Variable Speed Drives; 2000:114e9.