Maximum power point tracking-based control algorithm for PMSG wind generation system without mechanical sensors

Energy Conversion and Management 69 (2013) 58–67

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Energy Conversion and Management

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Maximum power point tracking-based control algorithm for PMSG windgeneration system without mechanical sensors

Chih-Ming Hong a, Chiung-Hsing Chen a,⇑, Chia-Sheng Tu b

a Department of Electronic Communication Engineering, National Kaohsiung Marine University, Kaohsiung 811, Taiwan, ROCb Institute of Nuclear Energy Research, Atomic Energy Council, Taoyuan 325, Taiwan, ROC

a r t i c l e i n f o a b s t r a c t

Article history:Received 18 September 2012Received in revised form 5 December 2012Accepted 5 December 2012Available online 1 March 2013

Keywords:Radial basis function network (RBFN)Modified particle swarm optimization(MPSO)Wind turbine generator (WTG)Permanent magnet synchronous generator(PMSG)Maximum power point tracking (MPPT)

0196-8904/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.enconman.2012.12.012

⇑ Corresponding author. Tel.: +886 7 3617141x331E-mail address: [email protected] (C.

This paper presents maximum-power-point-tracking (MPPT) based control algorithms for optimal windenergy capture using radial basis function network (RBFN) and a proposed torque observer MPPT algo-rithm. The design of a high-performance on-line training RBFN using back-propagation learning algo-rithm with modified particle swarm optimization (MPSO) regulating controller for the sensorlesscontrol of a permanent magnet synchronous generator (PMSG). The MPSO is adopted in this study toadapt the learning rates in the back-propagation process of the RBFN to improve the learning capability.The PMSG is controlled by the loss-minimization control with MPPT below the base speed, which corre-sponds to low and high wind speed, and the maximum energy can be captured from the wind. Then theobserved disturbance torque is feed-forward to increase the robustness of the PMSG system.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Wind generation systems are attracting great attention as cleanand safe renewable power sources, and can be operated with con-stant speed or variable speed operations using power electronicconverters. Among them, the variable-speed generation system ismore attractive than the fixed-speed system because of theimprovement in wind energy production and the reduction ofthe flicker problem. Variable-speed power generation enablesoperation of the turbine at its maximum power coefficient over awide range of wind speeds, obtaining a large energy capture char-acter. And, the wind turbine can be operated at the maximumpower operating point for various wind speeds by adjusting theshaft speed optimally to achieve maximum efficiency at all windvelocities [1,2]. All these characteristics are advantage of the vari-able-speed wind energy conversion systems (WECSs). In order toachieve the maximum power control, some control schemes havebeen studied [3,4].

One of the problems associated with variable-speed wind sys-tems today is the presence of the gearbox coupling the wind tur-bine to the generator. Many of the generators of research interestand for practical use in wind generation are induction machineswith wound-rotor or cage-type rotor [5]. Recently, the interest in

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8; fax: +886 7 3650833.-H. Chen).

PM synchronous generators is increasing. The desirable featuresof the PMSG are its compact structure, high air–gap flux density,high power density, high torque-to-inertia ratio, and high torquecapability. Moreover, compared with an induction generator, aPMSG has such advantages as higher efficiency, due to the absenceof rotor losses and lower no-load current below the rated speed;and its decoupling control performance is much less sensitive tothe parameter variations of the generator [6–8]. Therefore, high-performance variable-speed generation including high efficiencyand high controllability is expected by using a PMSG for a windgeneration system [9].

In this paper, an alternative approach for WTG MPPT control isdescribed. The mathematical model of the PMSG using the ex-tended electromotive force (EMF) in the rotating reference frameis utilized in order to estimate both position and speed. The opti-mum torque of PMSG is calculated from the generator speed basedon the model of the wind turbine in order that the maximum avail-able generator input power from a wind turbine corresponding tothe wind speed can be obtained [10,11]. The torque of PMSG is con-trolled by the current regulated pulse width modulator (PWM)converter. Since high performance control of PMSG needs informa-tion of the rotor speed and position, the speed and position sensorsare usually attached to the shaft. Such sensors are eliminated in theproposed system, and the speed and position are estimated byinformation of the voltage and current [12,13].

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C.-M. Hong et al. / Energy Conversion and Management 69 (2013) 58–67 59

Previous research has focused on three types of maximum windpower extraction methods, namely tip speed ratio (TSR) control,power signal feedback (PSF) control and hill-climb searching(HCS) control. Andrea and Lorenzo presents estimator based adap-tive fuzzy logic (EAFL) technique controls the output voltage andthe electrical generator rotational speed [5]. The EAFL controllerapplied to such a wind system has been tested with two differentdisturbance action patterns. Li et al. proposed a small wind gener-ation system with neural network principles applied for windspeed estimation and PI control of maximum wind power extrac-tion [6]. Wang and Chang proposed an advanced HCS method tak-ing into account the wind-turbine inertia [8]. However, it requiredan additional intelligent memory method with an on-line trainingprocess, and applying the intelligent memory data to control theinverter for maximum wind power extraction, without the needfor either knowledge of wind turbine characteristic or the mea-surements of mechanical quantities such as wind speed and tur-bine rotor speed. Morimoto developed a sensorless variable-speed wind generation system using an interior permanent-mag-net synchronous generator (IPMSG) [9,15]. Wai et al. proposed no-vel maximum-power-extraction algorithm (MPEA) schemewithout mechanical sensors certainty reduces the cost of buildinga small-scale wind generation system [11]. Tan and Islam pre-sented three sensorless control methods: wind prediction, fixedvoltage scheme for inverter and current-controlled inverter [12].Simoes et al. developed a fuzzy controller for tracking the genera-tor rotor velocity corresponding to the wind speed to extract themaximum power [14].

2. Analysis of wind generation system

2.1. Composition of wind generation system

The wind power generation system studied in this paper isshown in Fig. 1. The wind turbine is coupled to the shaft of anPMSG through a gear box, where the converter loss of the speedupgear is ignored in this study. The PMSG is connected with thepower converter and inverter circuit, and the terminal voltage orthe phase current can be controlled. The wind power (Pw) is con-verted into mechanical (Pm) and thereafter into electrical power(Pe) and is directly supplied to the power system.

2.2. Wind turbine characteristics

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 genera-tor rotor [10–12]. For a variable speed wind turbine, the outputmechanical power available from a wind turbine could be ex-pressed as

Fig. 1. Wind generation s

Pm ¼12qACpðk; bÞV3

x ð1Þ

where q and A are air density and the area swept by blades, respec-tively. Vx is the wind velocity (m/s), and Cp is called the power coef-ficient, and is given as a nonlinear function of the TSR k by

k ¼ xrrVx

ð2Þ

where r is wind turbine blade radius, xr is the turbine speed.According to the manufacturer’s data of the wind turbine and thecurve-fitting technique, the power coefficient (Cp) can be repre-sented with adjustable pitch angle (b) of the blade as

Cp ¼ 0:73151ki� 0:58b� 0:002b2:14 � 13:2

� �e�18:4

ki

ki ¼1

1k�0:02b� 0:003

b3þ1

ð3Þ

By using (3), the typical CP versus k curve is shown in Fig. 2. In awind turbine, there is an optimum value of tip speed ratio kopt thatleads to maximum power coefficient Cpmax. When the TSR in (2) isadjusted to its optimum value kopt ¼ 6:9, and the power coefficientreaches Cpmax = 0.4412 with b = 0�, and the maximum power extrac-tion is arrived. From (1) and (2), we get

Pmax ¼1

2k3opt

pqCp maxr5x3opt ð4Þ

This equation shows the relationship between turbine powerand turbine speed at the maximum power point. For maximumpower, it must be taken into account that turbine power mustnever be higher than generator rated power. Once generator ratedpower is reached at rated wind velocity, output power must belimited. For variable-speed wind turbine, a mechanical actuatoris usually employed to change the pitch angle of the blades in orderto reduce power coefficient and maintain the power at its rated va-lue [14,15].

2.3. PMSG

For a three-phase PMSG. The mechanical torque (Tm) and elec-trical torque (Te) can be expressed as

Tm ¼Pm

xrð5Þ

Te ¼Pe

xe¼ 2

PPe

xrð6Þ

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

Jdxr

dt¼ Tm � Bxr � Te ð7Þ

ystem configuration.

Fig. 2. Typical CP versus k curve.

Fig. 3. Flowchart of wind-power emulation.

60 C.-M. Hong et al. / Energy Conversion and Management 69 (2013) 58–67

where xe and P are electrical angular frequency, and the number ofpoles. J is the inertia moment of WTG, and B is the friction coeffi-cient of the generator.

3. Vector control of PM synchronous generator

The machine model of a PMSG can be described in the rotorrotating d–q reference frame as [16,17]

vq ¼ Riq þ pkq þxskd

vd ¼ Rid þ pkd �xskq ð8Þ

and

kq ¼ Lqiq

kd ¼ Ldid þ LmdIfd ð9Þxs ¼ Pxr ð10Þ

where vd, vq is the d, q axis stator voltages; id, iq is the d, q axis statorcurrents; Ld, Lq is the d, q axis stator inductances; kd; kq is the d, qaxis stator flux linkages; R is the stator resistance; xs is the inverterfrequency Ifd is the equivalent d-axis magnetizing current; Lmd isthe d-axis mutual inductance

The electric torque and generator dynamics are stated as [18]

Te ¼ 3P½LmdIfdiq þ ðLd � LqÞidiq�=2 ð11Þ

Those artificial and real wind-speed data and the generatorspeed are implemented via a PC-based wind-power emulating con-troller with a processing flowchart as shown in Fig. 3. The config-uration of a sensorless field-oriented PMSG system is shown inFig. 4a, which consists of a PMSG, a current-controlled PWM volt-age source converter, a field-orientation mechanism, including thevector rotator, current controller, and a speed controller. By usingfield-oriented mechanism, the PMSG system can be representedby the block diagram shown in Fig. 4b and c, in which

Te ¼ Kti�q ð12Þ

HpðsÞ ¼1

Jsþ Bð13Þ

where Kt = 3PLmdIfd/2, i�q is the torque current command generatedfrom the speed controller.

3.1. Position and speed sensorless control of PMSG

In order to achieve the optimal current vector control of PMSG,information of the position and speed of PMSG is required. A sens-orless control based on the estimation of an extended EMF is ap-plied to the proposed system. In the position and speed

sensorless drive system, the rotor position is not detected. So, ther–d frame, which lags he from the d–q Reference frame and rotatesat speed xr , is the electrical angle divided by the number of polepairs, as shown in Fig. 5. The mathematical model in the estimatedrotating r–d frame is derived using extended EMF (er, ed) as follows.

v r

vd

� �¼

Rþ ddt Ld �xrLq

xrLq Rþ ddt Ld

" #ir

id

� �þ

er

ed

� �ð14Þ

er

ed

� �¼ Eex

� sin he

cos he

� �þ ðxr �xrÞ

�idir

� �ð15Þ

Eex ¼ xrfðLd � LqÞid þ wag � ðLd � LqÞddt

iq

� �ð16Þ

where ir, id = r and d axis armature currents; vr, vd = r and d axis ter-minal voltages.

Assuming that the error of the estimated speed xr is sufficientlysmall, the estimated position error can be derived from the ex-tended EMF estimated by the observer as

he ¼ tan�1 � er

ed

� �ð17Þ

The estimated position hr and the estimated speed xr are compen-sated by the PI compensator so that he becomes zero [14,15].

4. Maximum power point tracking algorithm

4.1. Design of RBFN control system based on MPSO

4.1.1. Radial basis function network (RBFN)A three-layer neural network as shown in Fig. 6 is adopted to

implement the proposed RBFN controller [19]. The RBFN withMPSO learner is proposed, and the control law i�q is generated fromthe RBFN with MPSO. The input is xð1Þ1 and xð1Þ2 of the first layer,where xð1Þ1 ¼ x�r � xr ¼ e and xð1Þ2 ¼ Tm=Kt in this study. Tm is theestimated torque to be discussed later. The number of units inthe input, hidden, and output layers are two, nine and one, respec-tively. The signal propagation and the basic function of each layeris introduced in the following.

(a)

(b)

(c)Fig. 4. Block diagram of sensorless field-oriented PMSG system. (a) Configuration of control system. (b) Simplified control system using PI controller. (c) Simplified controlsystem using RBFN with MPSO algorithm.


4.1.1.1. Layer 1: input layer. The nodes at this layer are used to di-rectly transmit the numerical inputs to the next layer. That is, forthe ith node of layer 1, the net input and output are represented as

netð1Þi ¼ xð1Þi ðNÞ

yð1Þi ðNÞ ¼ f ð1Þi netð1Þi ðNÞ� �

¼ netð1Þi ðNÞ; i ¼ 1;2 ð18Þ

Fig. 5. Space–vector diagram of PMSG.

Fig. 6. Architecture of the RBFN network.


4.1.1.2. Layer 2: hidden layer. Every node performs a Gaussian func-tion. The Gaussian function, a particular example of radial basicsfunctions, is used here as a membership function. We have

netð2Þj ðNÞ ¼ �ðX �MjÞTX

jðX �MjÞ

yð2Þj ðNÞ ¼ f ð2Þj netð2Þj ðNÞ� �

¼ expðnetð2Þj ðNÞÞ j ¼ 1; . . . ;9 ð19Þ

where Mj ¼ ½m1j m2j � � � mij �T andP

j ¼ diag½1=r21j 1=r2

2j � � �1=r2

ij�T denote respectively, the mean (or center) and the standard

deviation, STD, (or width) of the Gaussian function.

4.1.1.3. Layer 3: output layer. The single node k in this layer is de-noted by R, which computes the overall output as the summationof all incoming signals by

netð3Þk ¼ Rj

wjyð2Þj ðNÞ

yð3Þk ðNÞ ¼ f ð3Þk ðnetð3Þk ðNÞÞ ¼ netð3Þk ðNÞ ¼ i�q ð20Þ

where the connection weight wj are the connective weight betweenthe hidden and the output layers.

Once the RBFN has been initialized, a supervised learning law isused 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 of the RBFN byusing the training patterns. By recursive application of the chainrule, the error term for each layer is first calculated. The adaptationof weights to the corresponding layer is then given. The purpose ofsupervised learning is to minimize the error function E expressedas

E ¼ 12

x�r � xr� 2 ð21Þ

where x�r and xr represent the rotor speed reference and estimatedrotor speed of the generator.

4.1.1.4. Layer 3: update weight wj. At this layer, the adjust weightsare wj. The error term to be propagated is given by

dk ¼ �@E

@netð3Þk

¼ � @E

@yð3Þk

@yð3Þk

@netð4Þk

" #ð22Þ

Then the weight wj is adjusted by the amount

Dwj ¼ �@E@wj¼ � @E

@yð3Þk

@yð3Þk

@netð3Þk

" #@netð3Þk

@wj

!¼ dkyð2Þj ð23Þ

Hence, the consequence weight is updated by

wjðN þ 1Þ ¼ wjðNÞ þ gwDwjðNÞ ð24Þ

where gw is the learning rate for adjusting the parameter wj.

4.1.1.5. Layer 2: update mij and rij. The multiplication operation isdone in this layer. The adaptive rules for mij and rij are as follows.Then, the adaptive rule for mij is

Dmij ¼ �@E@mij

¼ � @E

@netð3Þk

@netð3Þk

@yð2Þj

@yð2Þj

@mij

" #

¼ dkwjyð2Þj

2ðxð1Þi �mijÞðrijÞ2

ð25Þ

and the adaptive rule for rij is

Drij ¼ �@E@rij¼ � @E

@netð3Þk

@netð3Þk

@yð2Þj

@yð2Þj

@rij

" #¼ dkwj

2ðxð1Þi �mijÞ2

ðrijÞ3ð26Þ

Thus the updated rules for mij and rij are

mijðkþ 1Þ ¼ mijðkÞ þ gmDmij

rijðkþ 1Þ ¼ rijðkÞ þ grDrij ð27Þ

where gm and gr are the learning rates for adjusting the parametersmij and rij, respectively. This completes the derivation of the super-vised gradient descent learning algorithm.

Since the shape of the membership function is defined by thecenter value mij and the width rij, the objective E consists of thetuning parameters mij, rij, and wj. The learning of neural networksinvolves minimizing the error function in (21). We wish to derive alearning algorithm that will derive E to zero.

4.1.2. Modified particle swarm optimization algorithmPSO is a population-based optimization method first proposed

by 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 through simu-lation of bird flocking in two-dimensional space [20,21].


4.1.2.1. Step 1: define basic conditions. In the first step of MPSO, oneshould determine the parameters needed to be optimized withminimum and maximum ranges. The number of groups, popula-tion size, and initial radius of each gbest are also assumed in thisstep.

4.1.2.2. Step 2: initialize random swarm location and velocity. Initiallocation Rd

i ðNÞ and velocities vdi ðNÞ of all particles are generated

randomly in the search space. Moreover, the population size isset to P = 15 and the dimension of the particle is set to d = 3 in thisstudy. The generated particles Rd

i ¼ R1i ;R

2i ;R

3i

h iare the RBFN learn-

ing rates (gw, gm, gr), respectively. The initial pbest of a particle isset by its current position, and the gbest of a group is selectedamong the pbests in the group.

The range of random generation Rdi ðNÞ is

Rdi � U gd

min;gdmax

�where gmin, gmax are the lower and upper bounds of the learningrates.

4.1.2.3. Step 3: update velocity. In the classical PSO algorithm, everyparticle in the swarm is updated using (28) and (29). Two pseudo-random sequences r1 � U(0, 1) and r2 � U(0, 1) are used to affectthe stochastic nature of the algorithm. For all dimensions d, letRd

i , Pbestdi ; and vd

i be the current position, current personal best po-sition. The velocity update step is

vdi ðN þ 1Þ ¼ wvd

i ðNÞ þ c1 � r1 � Pbestdi � Rd

i ðNÞ� �

þ c2 � r2

� Gbestd � Rdi ðNÞ

� �ð28Þ

4.1.2.4. Step 4: update position. The new velocity is then added tothe current position of the particle to obtain its next position

Rdi ðN þ 1Þ ¼ Rd

i ðNÞ þ vdi ðN þ 1Þ; i ¼ 1; . . . ; P ð29Þ

4.1.2.5. Step 5: update pbests. If the current position of a particle islocated within the analysis space and does not intrude territory ofother gbests, the objective function of the particle is evaluated. Ifthe current fitness is better than the old pbest value, pbest is re-placed by the current position. The calculated fitness value of eachparticle is select as

FIT ¼ 10:1þ absðPm � PwÞ

ð30Þ

4.1.2.6. Step 6: update gbests. In the conventional PSO, gbest is re-placed by the best pbest among the particles. Each particle Rd

i mem-orises its own fitness value and chooses the maximum one that isthe best so far as pbestd

i and the maximum vector in the populationpbestd

i ¼ ½pbestd1; pbestd

2; . . . pbestdp� is obtained. Moreover, each par-

ticle Rdi is set directly to pbestd

i in the first iteration, and the particlewith the best fitness value among pbest is set to be the global bestgbest.

4.1.2.7. Step 7: check convergence. Steps 3–6 are repeated until allparticles are gathered around the gbest of each group, or a maxi-mum iteration is encountered. The final Gbestd

i is the optimal learn-ing rate (gw, gm, gr) of RBFN.

The acceleration coefficient c1 and c2 can be used to control themove distance for a particle in a single iteration, typically set to 2.0,for simplicity. The inertia weight w in (28) is used to control theconvergence behavior of the PSO. Small values of w result in a morerapid convergence usually on a suboptimal position, while large

values may cause divergence. In general, the inertia weight w isset according to the equation that

w ¼ wmax �wmax �wmin

itermax� iter ð31Þ

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

4.2. Feed-forward torque observer algorithm

The block diagram of the sensorless field-oriented PMSG systemcombined with torque observer is shown in Fig. 3. Although thetorque observer is one of the most effective methods for on-lineparameters identification, it is difficult to get unbiased results inthis application due to the dynamic modeling of the plant beingdisturbed by the external mechanical torque. As shown inFig. 3b, the proposed torque observer to resolve the above diffi-culty. The torque observer uses the inverse dynamic of the gener-ator drive to obtain the observed torque, which is denoted Tm=Kt .The torque current command minus this value results in the unbi-ased identified parameters, J and B, which denote the estimated ro-tor inertia constant and friction constant with the adaptiveobserver. Then J and B in the torque observer are replaced by Jand B. By this recursive process, the identified J and B parametersand the observed mechanical torque will quickly converge to theirreal values [22].

The plant dynamics in Z-domain, with the zero-order hold(ZOH) conversion, when Tm is zero, is shown in Fig. 3b. we have

Z1� e�Ts

sKt=B

1þ ðJ=BÞs

� ¼ Z

Kt=Jsðsþ B=JÞ

� � Z

Kt=Je�Ts

sðsþ B=JÞ

( )

¼ ð1 - Z�1ÞZ Kt=Jsðsþ B=JÞ

�

¼ ð1� Z�1Þ

� Kt

B1

1� Z�1 �1

1� e�B=JTs Z�1

� �

¼ Kt=Bð1� e�B=JTs ÞZ�1

1� e�B=JTs Z�1 ¼ bZ�1

1� aZ�1 ð32Þ

where

a ¼ expð�TsB=JÞ; b ¼ Ktð1� aÞ=B ð33Þ

and Ts is the sampling time. The system model can be written as

xrðkþ 1Þ ¼ axrðkÞ þ bi�qðkÞ ð34Þ

From the above equation, a discrete torque observer used inestimating system parameters can be written as

HðkÞ ¼ Hðk� 1Þ þ KðkÞ½xrðkÞ � CðkÞHðk� 1Þ� ð35Þ

KðkÞ ¼ Pðk� 1ÞCðk� 1ÞT

1þ Cðk� 1ÞPðk� 1ÞCðk� 1ÞTð36Þ

PðkÞ ¼ 1a

Pðk� 1Þ � Pðk� 1ÞCðk� 1ÞT Cðk� 1ÞPðk� 1Þ1þ Cðk� 1ÞPðk� 1ÞCðk� 1ÞT

" #ð37Þ

where

CðkÞ ¼ xrðkÞ; i�qðkÞ � Tm=Kt

h ið38Þ

HðkÞ ¼ ½aðkÞ; bðkÞ� ð39Þ

The value of the forgetting factor a should be restricted to0 < a 6 1. After H(k) is obtained, the estimated values of J and Bcan be easily determined from Eq. (33). The convergence of theRLS algorithm with the torque observer will be shown by experi-mental results.

(a)

(b)

wP

mP

Max. power reference

Turbine power

Rotor speed reference

Actual and estimated rotor speed


5. Experimental results

The conventional proportional-integral (PI) type controllers arewidely used in industry due to their simple control structure, easeof design and inexpensive cost. However, the PI-type controllermay not provide perfect control performance if the controlledplant is highly nonlinear or the desired trajectory is varied withhigher frequency. For variable-speed wind turbines, a mechanicalactuator is usually employed to change the pitch angle of theblades in order to control power coefficient (Cp) and maintain thepower at its maximum value. In some wind turbines, when work-ing with the maximum power coefficient, rated speed is obtainedat a wind velocity lower than that of generator rated power, be-cause the choice of the generator rating is an optimization processbetween energy capture for the wind system and system cost [23].

The optimum rotational speedx�r is obtained for each wind speedVx, and used as a reference for the closed loop. Generally the turbineis linked with the generator’s shaft using a gearbox, which imposesan additional transform relation in the model. The wind profile istested with a 0.005 s sampling time for the wind velocity, with thewind profile a volatile sinusoidal wave. The average power for PIwith torque observer is compared with that for RBFN with MPSOalgorithm and torque observer, RBFN with torque observer and fuz-zy-based algorithm with torque observer.

The wind turbine generator system used for the experimentalhas the following parameters:

(1) wind turbine parameters:

Pm ¼750 W; 3:75 A; 3000 r=min; q¼1:25 kg=m3; r¼0:5 m; J

¼1:32�10�3 Nm s2; B¼5:78�10�3 Nm s=rad

(2) generator parameters:

ePGenerator Power

R ¼ 1:47 X; Ld ¼ Lq ¼ 5:33 mH; Lmd ¼ 4:8 mH; Ifd

¼ 46:75 A; Kt ¼ 0:6732 Nm=A

(c)
5.1. PI controller with torque observer
With PI controller used in Fig. 4b. Fig. 7 illustrates the experi-mental result for PI control with torque observer. The averagepower is 209 W for the same period. It can be found that TSR is al-ways round 6.9 and Cp is 0.4412. Fig. 7a shows the performance ofthe PI controller with torque observer control system. Fig. 7b and cshows the verification of maximum power tracking control andpower coefficient Cp.

Fig. 7. Experimental results of the wind speed profile. (a) The wind profile speedtracking. (b) The maximum power tracking control signal. (c) Power coefficient Cp.

5.2. Fuzzy-based algorithm with torque observer

Replacing the PI with fuzzy-based algorithm in Fig. 4b, the fuzzylogic control (FLC) algorithm can be implemented, and is character-ized by ‘‘IF-THEN’’ rules. The algorithm is suitable for wind turbinecontrol with complex nonlinear models and parameters variation.Like the second algorithm, the fuzzy-based MPPT uses the pertur-bation and observation to track the maximum output power in thebelow rated wind speed without knowledge of wind turbine char-acteristic. The input variables of fuzzy-based MPPT are a rotationspeed tracking error and a mechanical torque observer.

Fig. 8 shows that 218 W (an increase of 4.3% compared withthat of PI control with torque observer) is obtained by the fuzzy-based algorithm with torque observer during the 50 s. It can befound that k and Cp are close to the optimal values of 6.9 and0.4412, respectively. Fig. 8a shows that shaft speed; it can be ob-served that the system tracks the maximum power under rated

generator speed. Fig. 8b shows that the verification of maximumpower tracking control. Fig. 8c shows that power coefficient Cp.

5.3. RBFN controller with torque observer

The RBFN with MPSO algorithm replace by RBFN as shown inFig. 4c. Fig. 9a shows that shaft speed; it can be observed that


(a)

(b)

(c)

wP

mP

eP

Max. power reference

Generator Power

Turbine power





the system tracks the maximum power under rated generatorspeed. The verification of maximum power tracking control asshown in Fig. 9b. Fig. 9c shows that power coefficient Cp, it canbe found that the Cp almost coincides with the optimal value, butperformance response slowly for start time. The average power is216 W. Compared with that from the PI control with torque obser-ver method, it increases by 3.35%.

5.4. RBFN with MPSO algorithm and torque observer

The RBFN with MPSO algorithm is shown in Fig. 4c. First, RBFNwith MPSO algorithm control and torque observer is consideredand the experimental result is shown in Fig. 10. Fig. 10a shows thatshaft speed; it can be observed that the system tracks the maxi-mum power under rated generator speed and the performance of

(a)



(b)

(c)

(d)

mP

wPMax. power reference

ePGenerator Power

Turbine power

Rotation speed error

Error=actual rotor speed-estimated rotor speed

Fig. 10. Experimental results of the wind speed profile. (a) The wind profile speed tracking, (b) Speed estimation error. (c) The maximum power tracking control signal. (d)Power coefficient Cp.

Fig. 11. Experimental results of step wind speed profile with disturbance.


the RBFN controller with MPSO algorithm and torque observercontrol system. In this case, the EMF theory can tracked the actualspeed during the whole wind profile with very small errors.Fig. 10b shows the speed tracking error with approximately0.2 rad/s. The verification of maximum power tracking control asshown in Fig. 10c. The wind speed profiles of maximum power

tracking control Pw and the dynamic difference between the tur-bine power Pm and generator power Pe due to the system inertiaand friction are also shown in Fig. 10c. Fig. 10d shows power coef-ficient Cp it close to its maximum value during the whole windspeed profile. The efficiency of the maximum power extractioncan be clearly observed as the power coefficient is fixed at to theoptimum value Cp = 0.4412 and k ¼ 6:9. The average power is223 W. Compared with that from the PI control with torque obser-ver method, it increases by 6.7%.

5.5. Step wind speed profile with disturbances

This case considers temperature and magnetic effects whichcauses rotor resistance and inductance to increase by 20%, alsowith the increases of the rotor inertia and friction to three timesafter 25 s. For comparison purposes, three types controller of testswere conducted. Experimental results for the three types of con-trollers are shown in Fig. 11. The Fig. 11 shows the reference andtracking rotor speed using RBFN with MPSO, fuzzy-based, and PImethod.

The above experimental results, the following comments can begiven

Table 1Performance for various control methods.

Average power(Pm) (W)

Increasing powerpercentage (%)

Max. error of powercoefficient (%)

Max. powertracking error (W)

Response time (s)

RBFN with MPSO algorithm method 223 6.7 1.8 65 1.15Fuzzy-based algorithm method 218 4.3 9.8 79 2.17RBFN method 216 3.35 10.1 82 2.09PI method 209 – 18.2 98 3.25

The above experimental results, the following comments can be given.


(1) It shows that the wind velocity is well estimated with smallerrors is both cases. Note that the actual speed is closelytracked by the estimation obtained from the extended EMFtheory.

(2) It can be found that MPPT is important for either high or lowwind speed, as shown in Table 1. Table 1 shows that theaverage power and percentage of power increase from eachcontrol method are compared with those from the PImethod.

(3) The control methods for the average power generation fromthe largest to the smallest under any wind conditions duringthe 50 s as follows: RBFN with MPSO method, fuzzy-basedmethod, RBFN method and PI method.

(4) The system could capture the maximal wind energy shownin the figures, provides a perfect MPPT and can attain theoptimal Cp all the time. It shows a robust control perfor-mance of the proposed RBFN controller with MPSO algo-rithm and torque observer, both in the wind speedtracking and power regulation.

6. Conclusion

This paper has presented the performance of a direct-drivenPMSG used in variable-speed wind energy systems. When excitingthe system with a real wind profile, the system is able to trackmaximum power using generated power as input. The speed con-troller sets the generator torque command, which is achievedthrough a current control loop. The proposed system has beenimplemented in a real-time application, with a commercial PMSGand a dc drive that emulates the wind turbine behavior. The real-time process is running in a dSPACE board that includes aTMS320C32 floating-point DSP. Experimental results show theappropriate behavior of the system.

The four MPPT control algorithm involving torque observerwithout a wind speed sensor are proposed in this paper, namelyRBFN with MPSO algorithm method, fuzzy-based algorithm meth-od, RBFN method and PI method. It can be found that the PI meth-od with torque observer can almost operate at the optimal Cp.Torque observer is very efficient, especially, for an optimizationproblem that the objective function cannot be explicitly expressed.The proposed output maximization control of a wind generationsystem with the PMSG, in which a mechanical sensorless controlis applied this study for the speed control of WECS. This techniquecan maintain the system stability and reach the desired perfor-mance even with parameter uncertainties.

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Maximum power point tracking-based control algorithm for PMSG wind generation system without mechanical sensors