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Maximum power point tracking (MPPT) system of small wind power generator using RBFNN approach Chun-Yao Lee a,, Po-Hung Chen b , Yi-Xing Shen a a Department of Electrical Engineering, Chung Yuan Christian University, Chung Li City, Taiwan b Department of Electrical Engineering, St. John’s University, Taipei County, Taiwan article info Keywords: Maximum power point tracking Radial basis function neural network Particle swarm optimization abstract A novel approach of combination of radial basis function neural network (RBFNN) and particle swarm optimization (PSO) is proposed to achieve the maximum power point tracking (MPPT) in this study. The measured data of the small wind generator (250 W), including wind speed, generator speed and out- put power of wind power generator, are applied to estimate the wind speed and output power by the pro- posed wind speed ANN wind and power estimation ANN Pe -PSO modules, respectively. Using the predicted results by the two modules of Matlab/Simulink, the MPPT point can be obtained by manipulating the gen- erator speeds. The experimental results show that the proposed RBFNN-based approach can increase the maximum output power of the wind power generator even if the wind speed and load varies. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Small wind power generators are widely used in metropolitan areas nowadays, and from the official reports of Taiwan Power Company, the installation capacities of wind generators in Taiwan have grown total 278MVA in past years (Bureau of Taiwan Energy, 2010). Thus, how to offer more power to electrical utilities by pro- moting the efficiency of wind power is the major concern to all researchers. The metropolitan wind energy always varies instanta- neously and the maximum power output cannot be easily ob- tained. Many literatures relating to the maximum power point tracking (MPPT) have been proposed (Li, Shi, & McLaren, 2005; Veerachary, Senjyu, & Uezato, 2003). These studies revealed that wind energy systems are nonlinear and difficult to be controlled. Neural networks (NNs) have been used for modeling of the com- plex systems because the models structured by NNs can descript the relationship between input and output of a complex nonlinear system without any detailed analytical model of the system (Hsu, 2010; Yilmaz & Oezer, 2009). In these literatures, a number of approaches based on the NN structure have emerged as a tool for the difficult control problem of the unknown nonlinear sys- tems. However, most of NN based approaches have to use all the training data as the neurons of hidden layer, and the higher com- plexity consequently consumes much computation time. And it is inappropriate to small wind generators in metropolitan areas whose wind energy sources always varied. To solve the problem, an appropriate NN for MPPT should have the characteristics of lower complexity and computation time, and the instantaneous wind energy might be easily and efficiently captured. We therefore propose a novel approach which combines the advantage of the radial basis function neural network (RBFNN) and particle swarm optimization (PSO) to estimate the appropriate speed of a wind turbine (Acharjee & Goswami, 2009; Balasubramanian, Palanivel, & Ramalingam, 2009; Chang, Wang, & Li, 2009; Chen & Yan, 2008; Cheng, Lin, & Huang, 2009; Dhanalakshmi, Palanivel, & Ramalingam, 2009; El-Zonkoly, Khalil, & Ahmied, 2009; Kuo et al., 2009; Lei, He, & Zi, 2009; Quah, 2008; Subashini, Ramalin- gam, & Palanivel, 2009; Sun, 2009; Tang, Zhuang, & Jiang, 2009; Tseng, Hsieh, & Jeng, 2009; Wu, 2010; Wu, Wang, Chiang, & Bai, 2009; Zahara & Kao, 2009). In this study, we used an experimental test based on a wind turbine testing platform to verify the superi- ority of the proposed approach in MPPT when the wind speed and load impedance vary simultaneously. 2. The experimental structure of a wind generator system The experimental structure of the wind power system is shown in Fig. 1, in which the system includes an artificial wind, anemom- eter, 250 W permanent-magnet synchronous generator (PMSG), three-phase dull bridge rectifier, boost converter and MPPT control subsystem. We controlled the artificial wind generated by a 3 Hp motor in our experimental testing platform to mimic actual wind, as shown in Fig. 2. We controlled the wind speed by manipulating the motor frequency and the power generated by the PMSG was connected to the load impedance R. The measured output power P and generator speed N can be illustrated as a P–N curve in various wind speeds, which are illustrated in Fig. 3, in which we can find 0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2011.02.054 Corresponding author. Tel.: +886 3 2654827; fax: +886 3 2654899. E-mail address: [email protected] (C.-Y. Lee). Expert Systems with Applications 38 (2011) 12058–12065 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa

Maximum power point tracking (MPPT) system of small wind power generator using RBFNN approach

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Page 1: Maximum power point tracking (MPPT) system of small wind power generator using RBFNN approach

Expert Systems with Applications 38 (2011) 12058–12065

Contents lists available at ScienceDirect

Expert Systems with Applications

journal homepage: www.elsevier .com/locate /eswa

Maximum power point tracking (MPPT) system of small wind powergenerator using RBFNN approach

Chun-Yao Lee a,⇑, Po-Hung Chen b, Yi-Xing Shen a

a Department of Electrical Engineering, Chung Yuan Christian University, Chung Li City, Taiwanb Department of Electrical Engineering, St. John’s University, Taipei County, Taiwan

a r t i c l e i n f o

Keywords:Maximum power point trackingRadial basis function neural networkParticle swarm optimization

0957-4174/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.eswa.2011.02.054

⇑ Corresponding author. Tel.: +886 3 2654827; fax:E-mail address: [email protected] (C.-Y. Lee).

a b s t r a c t

A novel approach of combination of radial basis function neural network (RBFNN) and particle swarmoptimization (PSO) is proposed to achieve the maximum power point tracking (MPPT) in this study.The measured data of the small wind generator (250 W), including wind speed, generator speed and out-put power of wind power generator, are applied to estimate the wind speed and output power by the pro-posed wind speed ANNwind and power estimation ANNPe-PSO modules, respectively. Using the predictedresults by the two modules of Matlab/Simulink, the MPPT point can be obtained by manipulating the gen-erator speeds. The experimental results show that the proposed RBFNN-based approach can increase themaximum output power of the wind power generator even if the wind speed and load varies.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Small wind power generators are widely used in metropolitanareas nowadays, and from the official reports of Taiwan PowerCompany, the installation capacities of wind generators in Taiwanhave grown total 278MVA in past years (Bureau of Taiwan Energy,2010). Thus, how to offer more power to electrical utilities by pro-moting the efficiency of wind power is the major concern to allresearchers. The metropolitan wind energy always varies instanta-neously and the maximum power output cannot be easily ob-tained. Many literatures relating to the maximum power pointtracking (MPPT) have been proposed (Li, Shi, & McLaren, 2005;Veerachary, Senjyu, & Uezato, 2003). These studies revealed thatwind energy systems are nonlinear and difficult to be controlled.Neural networks (NNs) have been used for modeling of the com-plex systems because the models structured by NNs can descriptthe relationship between input and output of a complex nonlinearsystem without any detailed analytical model of the system(Hsu, 2010; Yilmaz & Oezer, 2009). In these literatures, a numberof approaches based on the NN structure have emerged as a toolfor the difficult control problem of the unknown nonlinear sys-tems. However, most of NN based approaches have to use all thetraining data as the neurons of hidden layer, and the higher com-plexity consequently consumes much computation time. And it isinappropriate to small wind generators in metropolitan areaswhose wind energy sources always varied. To solve the problem,an appropriate NN for MPPT should have the characteristics of

ll rights reserved.

+886 3 2654899.

lower complexity and computation time, and the instantaneouswind energy might be easily and efficiently captured. We thereforepropose a novel approach which combines the advantage of theradial basis function neural network (RBFNN) and particle swarmoptimization (PSO) to estimate the appropriate speed of a windturbine (Acharjee & Goswami, 2009; Balasubramanian, Palanivel,& Ramalingam, 2009; Chang, Wang, & Li, 2009; Chen & Yan,2008; Cheng, Lin, & Huang, 2009; Dhanalakshmi, Palanivel, &Ramalingam, 2009; El-Zonkoly, Khalil, & Ahmied, 2009; Kuoet al., 2009; Lei, He, & Zi, 2009; Quah, 2008; Subashini, Ramalin-gam, & Palanivel, 2009; Sun, 2009; Tang, Zhuang, & Jiang, 2009;Tseng, Hsieh, & Jeng, 2009; Wu, 2010; Wu, Wang, Chiang, & Bai,2009; Zahara & Kao, 2009). In this study, we used an experimentaltest based on a wind turbine testing platform to verify the superi-ority of the proposed approach in MPPT when the wind speed andload impedance vary simultaneously.

2. The experimental structure of a wind generator system

The experimental structure of the wind power system is shownin Fig. 1, in which the system includes an artificial wind, anemom-eter, 250 W permanent-magnet synchronous generator (PMSG),three-phase dull bridge rectifier, boost converter and MPPT controlsubsystem. We controlled the artificial wind generated by a 3 Hpmotor in our experimental testing platform to mimic actual wind,as shown in Fig. 2. We controlled the wind speed by manipulatingthe motor frequency and the power generated by the PMSG wasconnected to the load impedance R. The measured output powerP and generator speed N can be illustrated as a P–N curve in variouswind speeds, which are illustrated in Fig. 3, in which we can find

Page 2: Maximum power point tracking (MPPT) system of small wind power generator using RBFNN approach

Artificial wind Bridge rectifier Impendence

R2C1C

Voltagecontrol

Boost converter

conV

ω DCVDCIAnemometerPWM

MPPT

PMSG

Fig. 1. The structure of wind power measurement system.

Fig. 2. The experiment platform of wind power system.

Fig. 3. The generator power curves.

inV

Diode

oVC

L

inI

oIinZ

RT

Fig. 4. The boost converter circuit.

C.-Y. Lee et al. / Expert Systems with Applications 38 (2011) 12058–12065 12059

the relationship between the power output and generator speed insix wind speeds from 5.9 to 15.9 m/s. In study, all of the maximumpower point curves were measured and recorded as a database sothat we can find out the maximum power output in any specificwind and generator speed. Consequently, the maximum poweroutput can be controlled by manipulating the thyristor in the boost

converter. In this experimental structure, we used the MPPT con-trol subsystem to manipulate the switching frequency of the thy-ristor in the boost converter to search the optimal operationspeed of the generator.

The structure of the boost converter is shown in Fig. 4, in whichthe equivalent impedance Zin is calculated by (1) where R is anadjustable electric impedance. In the MPPT control method, thethyristor T in Fig. 4 is used to control the duty cycle D and theequivalent impedance Zin. Thus, we can control the duty cycle Dto manipulate the equivalent impedance Zin so that the generatorspeed can optimally operate which can deliver the maximum out-put power for varied loads.

Zin ¼Vin

Iin¼ Voð1� DÞ2

Io¼ R � ð1� DÞ2 ð1Þ

Page 3: Maximum power point tracking (MPPT) system of small wind power generator using RBFNN approach

1X

2X

nX

1( )F x

( )mF x

1θmθ1

1w1mw

2mw

21w

kmw

1kw

layerInput layerHidden layerOutput

Fig. 5. The structure of radial basis function neural network.

1 2, , , swg g gP P P*

wVANNwind

gP

ωANNPg PSO

R

*conV

1 2, , , swcon con conV V V

MPPT

Fig. 6. The MPPT structure.

conV

R *gP∑

*wV

ANNwindgP

ω

Fig. 8. The ANNpe structure based on RFBNN.

12060 C.-Y. Lee et al. / Expert Systems with Applications 38 (2011) 12058–12065

3. Radial basis function neural network

The RBFNN is one kind of feed forward structures consisting of asingle hidden layer and an output layer, as shown in Fig. 5. All hid-den units are constructed by a number of radial basis functions(Venkatesan & Anitha, 2006). In application of the n-dimensiontraining database, x, the ith data are selected as the central of hid-den-layer where kx� zik is Euclidean distance, wi is the weightingand /iðk � zikÞ is the functions of Euclidean distance of zi and x. Fi-nally, we can obtain the m outputs Fm(x) by the m output layers, asshown in (1). The study uses the optimal RBFNN to construct twoestimation modules, namely wind speed estimation ANNwind andpower estimation ANNPe-PSO. The combination of the two modulesand the PSO method was structured to obtain the optimal genera-tor speed and output power. The construct of the study is shown asFig. 6, in which the predicted wind speed V�w can be obtained by the2-input 1-output network ANNwind module where the inputs arethe generator speed x and power output Pg, shown as Fig. 7. Andwe use the estimated wind speed V�w, resister R, and the Vn

con tobe input of the ANNPe-PSO and optimal V�con, relates to the poweroutput P�g , can be obtained.

For details, the structure of ANNPe based on RFBNN is shown asFig. 8. We used the estimated wind speed V�w, resister R, and theVn

con to be input of the ANNPe and the estimated power output P�gcan be obtained where V�w was the controlling value of the thyris-tor to adjust the equivalent impedance Zin in aforementioned Eq.

ω

gP

*wV∑

Fig. 7. The ANNwind structure based on RFBNN.

(1). Herein the actual Pe is not only the input signal of the ANNwind

module but also the target in the training procedure of ANNPe.Therefore, the module of ANNwind is trained before the module ofANNPe is training until the accurate rate of Vw� is achieved theexpectation; the training procedure of ANNPe is then implemented.

FmðxÞ ¼Xk

i¼1

wim � /iðk � zikÞ þ hm ¼

Xk

i¼0

wim � /iðk � zikÞ ð2Þ

where x ¼ ðx1; x2; . . . ; xnÞT is the input vectors and hm ¼ w0m is the

adjustable bias.

4. Particle swarm optimization

Particle swarm optimization (PSO) is a computational methodwhich can optimize a problem by iteratively to improve a candidatesolution. PSO is a population-based searching algorithm. PSO ran-domly produces npopu particles in the D-dimensional searchingspace, and each particle includes position Xi and velocity Vi, whereXi is the position of the ith particle, Xi = (Xi1, . . . , Xij, . . . , XiD), and Vi

is the velocity of ith particle, Vi = (Vi1, . . . , Vij, . . . , ViD). The positionof the ith particle represents a potential solution to the problem,and the velocity of ith particle represents its displacement in thesearching space. Pbestt

i is the best previous position of ith particle,and Gbestt is the best previous position of the population. Fit(�) isthe fitness function of optimization problem, the best previous po-sition of each particle is as shown in (3). The best previous positionof the population is as shown in (4). Moreover, every particle isguide to its previous velocity and distances of its current positionfrom its pervious best position and population’s pervious best posi-tion. The inertia weight method is applied to update the velocityand position of the particles, as shown in (4) and (5), and the inertiaweight is decrease linearly from 0.9 to 0.4 (Lee, Shen, Cheng, Chang,& Li, 2009). Given the PSO method described above, the process ofthe PSO is shown as the following steps:

Step 1: Initialize positions and velocity of all particles randomlyin D-dimension space, and record Pbestt

i and Gbestt.Step 2: Evaluate the fitness value of all particles.Step 3: Update the Pbesti by applying (3).Step 4: Update the Gbest by applying (4).Step 5: If stopping criterion is satisfied (e.g., maximum iterationnumber), the procedure goes to the end; otherwise, proceed toStep 4.Step 6: Update the particle position and velocity by applying (5)and (6), and then go back to Step 2.

Pbestti ¼

Pbestt�1i if Fit ðXt

i Þ 6 Fit�

Pbestt�1i

Xti if Fit ðXt

i Þ > Fit�

Pbestt�1i

8><>:

ð3Þ

Gbestt ¼ arg maxPbestt

i

nFit�

Pbestti

�oð4Þ

Page 4: Maximum power point tracking (MPPT) system of small wind power generator using RBFNN approach

Fig. 9. The MPPT control system.

C.-Y. Lee et al. / Expert Systems with Applications 38 (2011) 12058–12065 12061

Vtþ1ij ¼w �Vt

ijþ c1 � randð�Þ � ðPbesttij�Xt

ijÞþ c2 � randð�Þ � ðGbesttj �Xt

ijÞð5Þ

Xtþ1ij ¼ Xt

ij þ Vtþ1ij ð6Þ

where: c1 is acceleration coefficient, c1 = 2; c2 is acceleration coeffi-cient, c2 = 2; w is inertia weight factor; wmax is initial inertia weightfactor; wmin is final inertia weight factor; t is current iterationnumber; tmax is maximum iteration number; rand(�) is uniformlydistributed random number between 0 and 1.

Pbestti ¼ ðPbestt

i1; . . . Pbesttij . . . Pbestt

iDÞGbestt ¼ ðGbestt

1; . . . Gbesttj . . . Gbestt

w ¼ wmax � t � ðwmax �wminÞtmax

5. The structure of MPPT control

The MPPT control system is shown in Fig. 9, in which we usedMatlab/Simulink to construct the modules ANNwind and ANNPe-PSO. The PWM control module receives the comments from AD/DA cards, which relates to the optimal Dopt.

Fig. 10. The MPPT control structu

5.1. Wind speed estimated module ANNwind

The Vg and Ig are the analog signals of voltage and current of theboost converter respectively captured by the sensors, and the sig-nals are delivered to the AD/DA card, as shown in aforementionedFig. 9. The generator senor captures the generator speed x and del-iveres to the AD/DA card. The inputs of ANNwind module are x andPg, which is the multiplication of Vg and Ig. Using the AD/DA card,the analog signals are transformed into digital signals which canbe considered the input signals of ANNwind for estimating windspeed and further delivering to ANNPe.

5.2. Optimal duty cycle estimated module ANNPe-PSO

The voltage and current sensors captured the analog signals, Vo,Io and delivered to the AD/DA card where Vo and Io are the voltageand current of the load respectively, as shown in aforementionedFig. 9. The inputs of ANNPe are designated as the predicted windspeed V�w, equivalent impedance R and duty cycle Dn

(D1, D2, . . . , Dsw) which is produced by the PSO module where AN-NPe is the fitness function of PSO, Fit(�), for searching the optimalduty cycle Dopt. In the searching process, the control system initial-izes Di. The signals, Pe, x and R, are considered constants until thestopping criterion is satisfied, and the control voltage Vcon is deliv-ered to the PWM circuit, where Vcon is the DC voltage level,0 � 10 V, for adjusting the duty cycle D. Subsequently, the MPPTcontrol system adjusts duty cycle D in order to reach Dopt byPWM circuit and makes the generator operate at the maximumpower point. The MPPT control system is accomplished by Mat-lab/Simulink, and the real-time control interface is shown inFig. 10. The Di and sw are the positions of the ith particle and thepopulation size of PSO respectively. The output signals of ANNPe,P�e1; P

�e2; . . . ; P�e;sw, are the fitness solution of particle positions, D1,

D2,. . ., Dsw, respectively.

6. Experiment results

6.1. Wind estimated module ANNwind

The data of the generator speed, output power, and mimic windspeed are gathered for training ANNwind, and the trained results of

re based on Matlab/Simulink.

Page 5: Maximum power point tracking (MPPT) system of small wind power generator using RBFNN approach

Fig. 11. The three-dimensional curve of ANNwind.

Fig. 12. The three-dimensional curve of ANNPe. (a) Load impedance 50 X. (b) Load impedance 30 X.

Fig. 13. The power output curves of the generator.

12062 C.-Y. Lee et al. / Expert Systems with Applications 38 (2011) 12058–12065

Page 6: Maximum power point tracking (MPPT) system of small wind power generator using RBFNN approach

Fig. 14. The MPPT under various wind speeds and load impedances. (a) Wind speed. (b) Load impedance. (c) Vcon. (d) Output power.

Table 1The experimental MPPT results when generator speed rises and descends (49.07 X).

From Fig. 14(d)

Wind speed(m/s)

Output power (W) Absoluteerror (%)

Expectation Actual

Rising speed Descending speed

7.6 40.5 29.8 46.0 6.9810.6 92.9 84.8 116.7 7.7613.0 175.9 161.6 186.3 1.09

Table 2The experimental MPPT results when generator speed rises and descends (22.07 X).

From Fig. 14(d)

Wind speed(m/s)

Output power (W) Absoluteerror (%)

Expectation Actual

Rising speed Descending speed

7.6 40.5 27.6 53.3 0.1710.6 92.9 73.4 126.2 6.9313.0 175.9 145.1 202.0 1.32

C.-Y. Lee et al. / Expert Systems with Applications 38 (2011) 12058–12065 12063

ANNwind are illustrated in Fig. 11. Based on the results, the instan-taneous wind speed can be estimated by the ANNwind module, and

the problems of aging or displacement of the anemometer could beinconsiderable.

Page 7: Maximum power point tracking (MPPT) system of small wind power generator using RBFNN approach

Fig. 15. The actual wind speed and tip speed ratio. (a) Fixed wind speed and Load impedance and (b) varied wind speed and load impedance.

12064 C.-Y. Lee et al. / Expert Systems with Applications 38 (2011) 12058–12065

6.2. Module of power estimated ANNPe

The duty cycle, estimated wind speed, load impedance, and out-put power are gathered for training ANNPe, and the trained resultsof ANNPe in the conditions of load impedance 50 and 30 X areshown in Fig. 12 (a) and (b) respectively. The three-dimensionaldiagram shows that the estimated wind speed, duty cycle, and out-put power are closely related. That is, each wind speed correspondsto one optimal duty cycle which generates the maximum poweroutput with specific load impedances.

6.3. Maximum power point tracking (MPPT)

In order to realize the maximum output power of the generatorfor different wind speeds, the load side is connected to the 600 Wvariable resistors. The relation between the output power and theload impedance is shown in Fig. 13, and the maximum outputpower is extracted under the specific load impedance for differentwind speeds. Therefore, the maximum powers is regarded as theexpected values (10.3, 38.5, 88.9, 167.6, 263.2 W) for the specificwind speeds (5.2, 7.6, 10.6, 13.1, and 15.0 m/s), as shown inFig. 13. To the MPPT control subsystem, an experimental examplewas designed to verify the advantage of the proposed approach invaried wind speed and load impedance simultaneously.

To simulate the conditions of both wind speed and load imped-ance variations, the artificial wind is controlled based on arbitraryvariation, as shown in Fig. 14 (a) (solid line), and the load imped-ance varies instantly from 49.07 to 22.07 X at the 150th second,as shown in Fig. 14 (b). The control voltage of the MPPT controlsystem varies along with the estimated wind speed and loadimpedance, as shown in Fig. 14 (c). The result of output power withMPPT is shown in Fig. 14 (d) (see ‘‘w/ MPPT Line’’). The instanta-neous output powers of the generator corresponding to the differ-ent wind speeds (7.6, 10.6, 13.0 m/s) and load impedances (49.07and 22.07 X) are recorded in Tables 1 and 2, where the absolute er-ror indicates the error between the expected value and the averageoutput power of the rising and falling generator speed.

The results demonstrate that the output power has a temporarydelay, and the maximum absolute error in conditions of fixed windspeed 10.6 m/s and load impedance 50 X is only 7.76%, as shown inTable 1, and its tip speed ratio is presented in Fig. 15 (a) (dash line).The tip speed ratio is considered a basis of MPPT examination sincethe absolute error is only 0.076%. On the other hand, in Fig. 15 (b)(dash line), the tip speed ratio in conditions of varied wind speed

and load impedance is almost the same as the tip speed ratio inFig. 15 (a). Therefore, the MPPT control system makes the genera-tor operate at the maximum power point even in the conditions ofvaried wind speed and load impedance. In addition, when compar-ing the w/o MPPT Line and the w/ MPPT Line, the average outputpowers are 60.5 and 105.8 W, respectively. The result reveals thatthe MPPT control system applied in this study can improve the out-put power by approximately 74.9%.

7. Conclusions

This paper proposes a new approach to solve the problem ofMPPT even if the wind speed and load varies simultaneously. Thecontrol system with the approach can estimates the instantaneouswind speed and output power of wind power generator using theproposed ANNwind and ANNPe-PSO modules respectively based ona software Matlab/Simulink. For achieving the maximum poweroutput point of a generator, PSO plays an exploratory role for con-trolling the optimal generator speed, and the RBFNN is appropri-ately adopted to estimated accurately the wind speed andgenerator power output. The experimental results show that theproposed approach can obtain the optimal power output and deli-ver to utility without using or calibrating an anemometer. In sum-mary, the combination of the two modules ANNwind and ANNPe–PSO based on the methodology of RBFNN and PSO can efficientlyimprove power output of a small wind power generator in the con-ditions of wind speed and load impedance variations.

Acknowledgment

The research was supported by the Ministry of Economic Affairsof the Republic of China, under Grant No. 99-2632-E-033-001-MY3.

References

Acharjee, P., & Goswami, S. K. (2009). Expert algorithm based on adaptive particleswarm optimization for power flow analysis. Expert Systems with Applications,36(3), 5151–5156.

Balasubramanian, M., Palanivel, S., & Ramalingam, V. (2009). Real time face andmouth recognition using radial basis function neural networks. Expert Systemswith Applications, 36(3), 6879–6888.

Bureau of Taiwan Energy (2010). Energy and Industrial Technology White Paper[On-line available in Chinese]: <http://psel.ccg.tw/phpbb/download/file.php?id=96&sid=ccb0103d55f659c3e6cf6db20d2b5895>.

Page 8: Maximum power point tracking (MPPT) system of small wind power generator using RBFNN approach

C.-Y. Lee et al. / Expert Systems with Applications 38 (2011) 12058–12065 12065

Chang, C. Y., Wang, H. J., & Li, C. F. (2009). Semantic analysis of real-world imagesusing support vector machine. Expert Systems with Applications, 36(7),10560–10569.

Chen, C. H., & Yan, W. (2008). An in-process customer utility prediction system forproduct conceptualisation. Expert Systems with Applications, 34(4), 2555–2567.

Cheng, S. C., Lin, Y. T., & Huang, Y. M. (2009). Dynamic question generation systemfor web-based testing using particle swarm optimization. Expert Systems withApplications, 36(1), 616–624.

Dhanalakshmi, P., Palanivel, S., & Ramalingam, V. (2009). Classification of audiosignals using SVM and RBFNN. Expert Systems with Applications, 36(3),6069–6075.

El-Zonkoly, A. M., Khalil, A. A., & Ahmied, N. M. (2009). Optimal tunning of lead-lagand fuzzy logic power system stabilizers using particle swarm optimization.Expert Systems with Applications, 36(2), 2097–2106.

Hsu, C. L. (2010). Constructing transmitting interface of running parameters ofsmall-scaled wind-power electricity generator with WSN modules. ExpertSystems with Applications, 37(5), 3893–3909.

Kuo, I. H., Horng, S. J., Kao, T. W., Lin, T. L., Lee, C. L., Terano, T., et al. (2009). Anefficient flow-shop scheduling algorithm based on a hybrid particle swarmoptimization model. Expert Systems with Applications, 36(3), 7027–7032.

Lee, C.-Y., Shen, Y.-X., Cheng, J.-C., Chang, C.-W., & Li, Y.-Y. (2009). Optimizationmethod based MPPT for wind power generators. Proceedings of World Academyof Science, Engineering and Technology, 60, 169–172.

Lei, Y. G., He, Z. J., & Zi, Y. Y. (2009). Application of an intelligent classificationmethod to mechanical fault diagnosis. Expert Systems with Applications, 36(6),9941–9948.

Li, H., Shi, K. L., & McLaren, P. G. (2005). Neural-network-based sensorless maximumwind energy capture with compensated power coefficient. IEEE Transactions onIndustry Applications, 41(6), 1548–1556.

Quah, T. S. (2008). DJIA stock selection assisted by neural network. Expert Systemswith Applications, 35(1-2), 50–58.

Subashini, T. S., Ramalingam, V., & Palanivel, S. (2009). Breast mass classificationbased on cytological patterns using RBFNN and SVM. Expert Systems withApplications, 36(3), 5284–5290.

Sun, T. H. (2009). Applying particle swarm optimization algorithm to roundnessmeasurement. Expert Systems with Applications, 36(2), 3428–3438.

Tang, X. L., Zhuang, L., & Jiang, C. J. (2009). Prediction of silicon content in hot metalusing support vector regression based on chaos particle swarm optimization.Expert Systems with Applications, 36(9), 11853–11857.

Tseng, C. C., Hsieh, J. G., & Jeng, J. H. (2009). Active contour model via multi-population particle swarm optimization. Expert Systems with Applications, 36(3),5348–5352.

Veerachary, M., Senjyu, T., & Uezato, K. (2003). Neural-network-based maximum-power-point tracking of coupled-inductor interleaved-boost-converter-supplied PV system using fuzzy controller. IEEE Transactions on IndustrialElectronics, 50(4), 749–758.

Venkatesan, P., & Anitha, S. (2006). Application of a radial basis function neuralnetwork for diagnosis of diabetes mellitus. Current Science, 91(9), 1195–1199.

Wu, Q. (2010). A hybrid-forecasting model based on Gaussian support vectormachine and chaotic particle swarm optimization. Expert Systems withApplications, 37(3), 2388–2394.

Wu, J. D., Wang, Y. H., Chiang, P. H., & Bai, M. R. (2009). A study of fault diagnosis in ascooter using adaptive order tracking technique and neural network. ExpertSystems with Applications, 36(1), 49–56.

Yilmaz, A. S., & Oezer, Z. (2009). Pitch angle control in wind turbines above the ratedwind speed by multi-layer perceptron and radial basis function neuralnetworks. Expert Systems with Applications, 36(6), 9767–9775.

Zahara, E., & Kao, Y. T. (2009). Hybrid Nelder–Mead simplex search and particleswarm optimization for constrained engineering design problems. ExpertSystems with Applications, 36(2), 3880–3886.