A Robust Wind Turbine Control using a Neural Network BasedWind Speed Estimator

Oscar Barambones, Member, IEEE

Abstract— Modern wind turbines are capable to work invariable speed operations. These wind turbines are providedwith adjustable speed generators, like the double feed inductiongenerator. One of the main advantage of adjustable speedgenerators is that they improve the system efficiency comparedto fixed speed generators because turbine speed is adjusted asa function of wind speed to maximize output power. In thissense, to implement maximum wind power extraction, mostcontroller designs of the variable-speed wind turbine generatorsemploy anemometers to measure wind speed in order to obtainthe desired optimal generator speed. In this paper a NeuralNetwork based wind speed estimator for a wind turbine controlis proposed. The design uses a feedforward Artificial NeuralNetwork (ANN) to implement a wind speed estimator.

In this work, a sliding mode control for variable speedwind turbines is also proposed. The stability analysis of theproposed controller is provided under disturbances and pa-rameter uncertainties by using the Lyapunov stability theory.Finally simulated results show, on the one hand that theproposed control scheme using an ANN estimator provideshigh-performance dynamic characteristics, and on the otherhand that this scheme is robust under uncertainties that usuallyappear in the real systems and under wind speed variations.

I. INTRODUCTION

Remarkable advances in the wind power design havebeen achieved due to modern technological developments.Since 1980, advances in aerodynamics, structural dynamics,and micrometeorology have contributed to a 5% annualincrease in the energy yield of the turbines. Current researchtechniques are producing stronger, lighter and more efficientblades for the turbines. The annual energy output for turbinehas increased enormously and the weights of the turbine andthe noise they emit have been halved over the last few years.We can generate more power from wind energy by establish-ment of more number of wind monitoring stations, selectionof wind farm site with suitable wind electric generator,improved maintenance procedure of wind turbine to increasethe machine availability, use of high capacity machine, lowwind regime turbine, higher tower height, wider swept areaof the rotor blade, better aerodynamic and structural de-sign, faster computer-based machining technique, increasingpower factor and better policies from Government.

The worldwide wind power installed capacity reaches121188 MW in 2008, and it is expected an annual growthrate of 31000 MW in 2009 and 38000 MW in 2010 [14].

Wind energy is expected to play an increasingly importantrole in the future national energy scene. Wind turbines

Oscar Barambones is with the Department of Automatic Control andSystem Engineering, University of the Basque Country, EUI de Vitoria.Nieves cano 12, 01006 Vitoria, Spain. (phone: +34 945013235; email:oscar.barambones@ehu.es ).

convert the kinetic energy of the wind to electrical energyby rotating the blades. Greenpeace states that about 10%electricity can be supplied by the wind by the year 2020.At good windy sites, it is already competitive with thatof traditional fossil fuel generation technologies. With thisimproved technology and superior economics, experts predictwind power would capture 5% of the world energy market bythe year 2020. Advanced wind turbine must be more efficient,more robust and less costly than current turbines.

This paper investigates a robust speed control method forvariable speed wind turbines with Double Fed InductionGenerator (DFIG) using a Neural Network based wind speedestimator. The control objective is to make the rotor speedtrack the desired speed in spite of system uncertainties. Thisis achieved by regulating the rotor current of the DFIGusing the sliding mode control theory. In the design a vectororiented control theory is used in order to decouple the torqueand the flux of the induction machine. The proposed controlscheme leads to obtain the maximum wind power extractionfrom the different wind speeds that appear along time.

To implement maximum wind power extraction, most con-troller designs of the variable-speed Wind Turbines employanemometers to measure wind speed in order to derivethe desired optimal shaft speed for adjusting the generatorspeed. In most cases, a number of anemometers are placedsurrounding the wind turbine at some distance to provideadequate wind speed information. These mechanical sensorsincrease the cost (e.g., equipment and maintenance costs) andreduce the reliability of the overall WTG system [7].

Recently, mechanical sensorless maximum power pointtracking controls have been reported in which the wind speedis estimated, or the maximum power point is determined,without the need of the wind speed information [1], [7],[12]. However, these methods may result in a complexand time-consuming calculation, therefore, reducing systemperformance.

Artificial neural networks (ANNs) are well known as a toolto implement nonlinear time-varying input-output mapping.In this sense, it is possible to design the estimators ofthe wind speed using Artificial Neural Networks, whichdo not require a mathematical model of the system andtherefore the performance of this approach do not exhibitany dependence with the modeling errors. In ANN basedestimators, if the ANN uses a supervised training technique,then the estimator is based on information available for thetraining and this information is obtained from system inputand output measurements previously calculated for training

978-1-4244-8126-2/10/$26.00 ©2010 IEEE

purposes.On the other hand, it has been proved that Artificial

Neural Network can approximate a wide range of nonlinearfunctions to any desired degree of accuracy under certainconditions [8].

Due to the above mentioned characteristics, in the past fewyears, active research has been carried out in Artificial NeuralNetwork applied to identification and control of complexdynamical systems [10].

Although diverse neural architecture and learning algo-rithms can be used, we have chosen a particular one, themultilayer feedforward network and the so-called backpropa-gation with momentum algorithm which is a gradient descentalgorithm of the performance function. Properly trainedbackpropagation networks tend to give reasonable answerswhen they are presented with inputs that they have nevercomputed [3].

This paper is organized as follows. The wind turbinemodelling is presented in section II. Then, the artificial neuralnetwork model for the wind speed estimation is introducedin Section III. The wind turbine robust control scheme iscarried out in Section IV. Then, some simulation results arepresented in section V. Finally, some concluding remarks arestated in Section VI.

II. WIND TURBINE SYSTEM MODELLING

Figure 1 shows the functional scheme of the wind turbinegenerator. The main parts of this scheme are the wind turbine,the gearbox and generator. In a typical turbine design, rotorblades are attached to a shaft that runs into a gearbox. Thegearbox, or transmission, increases the speed of the bladesrotation, from 18 revolutions per minute (RPM) up to 1,800RPM. The fast spinning shaft turns inside the generator,producing AC (alternating current) electricity. Electricitymust be produced at just the right frequency and voltageto be compatible with the utility grid.

Fig. 1. Functional scheme of the wind turbine generator

The speed of the wind hitting the rotors affects howmuch energy a turbine captures. Modern wind turbines aredesigned to work most efficiently at wind speeds between15 and 35 MPH. Because the wind blows stronger than thissome of the time, a wind turbine must adapt itself to theprevailing wind speed to operate most efficiently. There aretwo basic approaches used to control and protect a windturbine: pitch-control and stall-control. In pitch-controlledturbines, an anemometer mounted atop the nacelle, or a windspeed estimator constantly checks the wind speed and sendssignals to a pitch actuator, adjusting the angle of the bladesto capture the energy from the wind most efficiently. On astall-regulated wind turbine, the blades are locked in placeand do not adjust during operation. Instead the blades aredesigned and shaped to increasingly stall the blades angleof attack with the wind to both maximize power outputand protect the turbine from excessive wind speeds. Thereare relative advantages to both design approaches. A pitch-regulated turbine, for example, is generally considered tobe slightly more efficient than a stall-regulated turbine. Onthe other hand, stall-regulated turbines are often consideredmore reliable because they do not have the same level ofmechanical and operational complexity as pitch-regulatedturbines.

In this paper the first approach is considered, and thereforean anemometer or a wind speed estimator is needed. Inthis section an ANN based wind speed estimator for apitch-controlled wind turbines is designed. The wind speedestimator will provide the wind speed that is necessary forcontrol the wind turbine system in order to optimize theenergy production.

The aerodynamic model of a wind turbine can be char-acterized by the well-known Cp − λ − β curves. Cp is thepower coefficient, which is a function of both tip-speed-ratioλ and the blade pitch angle β . The tip-speed-ratio is definedby:

λ =Rw

v(1)

where R is the blade length in m, w is the wind turbinerotor speed in rad/s, and v is the wind speed in m/s. TheCp −λ−β curves depend on the blade design and are givenby the wind turbine manufacturer.

Given the power coefficient Cp, the mechanical power thatthe wind turbine extracts from the wind is calculated by [10].

Pm(v) =12Cp(λ, β)ρπR2v3 = f(v, w, β) (2)

where ρ is the air density in kg/m3, Ar = πR2 is the areaswept by the rotor blades in m2.

As it is well known, given a specific wind speed, there is aunique wind turbine rotational speed to achieve the maximumpower coefficient Cpmax , and thereby extract the maximummechanical (wind) power. If the wind speed is below therated value, the wind turbine operates in the variable speedmode, and the rotational speed is adjusted such that remains

Cp at the Cpmax point. In this operating mode, the windturbine pitch control is deactivated. However, if the windspeed increases above the rated value, the pitch control isactivated to increase the wind turbine pitch angle to reducethe mechanical power extracted from wind.

For a typical wind power generation system, the followingsimplified elements are used to illustrate the fundamentalwork principle. The system primarily consists of an aero-turbine, which converts wind energy into mechanical energy,a gearbox, which serves to increase the speed and decreasethe torque and a generator to convert mechanical energy intoelectrical energy.

Driving by the input wind torque Tm, the rotor of the windturbine runs at the speed w. The transmission output torqueTt is then fed to the generator, which produces a shaft torqueof Te at generator angular velocity of we. Note that the rotorspeed and generator speed are not the same in general, dueto the use of the gearbox.

The mechanical equations of the system can be character-ized by [11]:

Jmw +Bmw = Tm + T (3)

Jewe +Bewe = Tt + Te (4)

Ttwe = Tw (5)

where Jm and Je are the moment of inertia of the turbineand the generator, Bm and Be are the viscous frictioncoefficient of the the turbine and the generator, Tm is thewind generated torque in the turbine, T is the torque in thetransmission shaft before gear box, Tf is the torque in thetransmission shaft after gear box, and Te is the the generatortorque, w is the angular velocity of the turbine shaft and we

is the angular velocity of the generator rotor.The relation between the angular velocity of the turbine

w and the angular velocity of the generator we is given bythe gear ratio γ:

γ =we

w(6)

Then, using equations 3, 4, 5 and 6 it is obtained:

Jw +Bw = Tm + γTe (7)

with

J = Jm + γ2Je (8)

B = Bm + γ2Be (9)

Now we are going to consider the system electrical equa-tions. In this work a double feed induction generator (DFIG)is used. This induction machine is feed from both stator androtor sides. The stator is directly connected to the grid whilethe rotor is fed through a variable frequency converter (VFC).In order to produce electrical active power at constant voltageand frequency to the utility grid, over a wide operation range(from subsynchronous to supersynchronous speed), the activepower flow between the rotor circuit and the grid must becontrolled both in magnitude and in direction. Therefore, theVFC consists of two four-quadrant IGBT PWM converters

(rotor-side converter (RSC) and grid-side converter (GSC))connected back-to-back by a dc-link capacitor [9], [10].

In the stator-flux oriented reference frame, the d-axis isaligned with the stator flux linkage vector ψs, and then,ψds=ψs and ψqs=0 . This yields the following relationships[6]:

iqs =Lmiqr

Ls(10)

ids =Lm(ims − idr)

Ls(11)

Te =−Lmimsiqr

Ls(12)

Qs =32wsL

2mims(ims − idr)

Ls(13)

vdr = rridr + σLrdiqr

dt− swsσLriqr (14)

vqr = rriqr + σLrdiqr

dt(15)

+sws

(σLridr + L2

mims

Ls

)(16)

ims =vqs − rsiqs

wsLm(17)

σ = 1 − L2m

LsLr(18)

where i is the current, L is the inductance, v is the voltage,Te is the electromagnetic torque, Qs is the stator reactivepower, ims is the stator magnetizing current and σ is theleakage coefficient.

The subscripts r and s denotes the rotor and stator valuesrespectively, and the subscripts d and q denote the dq-axiscomponents in the stator-flux oriented reference frame.

Since the stator is connected to the grid, and the influenceof the stator resistance is small, the stator magnetizingcurrent (ims) can be considered constant [9]. Therefore, theelectromagnetic torque can be defined as follows:

Te = −KT iqr (19)

where KT is a torque constant, and is defined as follows:

KT =Lmims

Ls(20)

Using equations (7) and (19) the following equation isobtained :

Pm

w= Tm = Jw +Bw + γKT iqr (21)

From this equation the mechanical power is calculatedusing the turbine speed and the electromagnetic torque.

III. NEURAL NETWORK MODEL FOR WIND SPEED

ESTIMATION

Equation 2 indicates that given the information of theturbine power Pm, the wind turbine rotational speed wt, andthe blade pitch angle β, the wind speed can be calculated

from the nonlinear inverse function of eqn. 2. A commonlyused method to implement an inverse function is using alookup table, however, this method requires much memoryspace and may result in a time-consuming search for thesolution.

The Artificial Neural Networks (ANN), are well knownas a tool for nonlinear complex time-varying input-outputmapping and can be an ideal technique to solve this problem.Therefore, the proposed wind speed estimation algorithmin this paper is build on an ANN-based input-output map-ping that approximates the nonlinear inverse function off(v, w, β).

In the proposed design a multilayer feedforward artificialneural network (FANN) was adopted as the neural networkparadigm. The neural network has three input signals, themechanical power Pm, the wind turbine rotor speed w andthe blade pitch angle β, and one output, v, which is theestimated wind speed.

The number of hidden layers and the number of nodesper layer are not definitive. There are no general guidelinesfor determining a priori which combinations of neurons andhidden layers will perform the best for a given problem. Inthis problem, the number of hidden layers and the numberof neurons in each hidden layer were chosen heuristically ona trial and error basis. The FANN selected has three hiddenlayers. The first hidden layer has 9 neurons, the second has11 neurons and the third hidden layer has 15 neurons. Thesehidden layers have a tansigmoid activation function, and theoutput layer has a linear activation function.

Then the output of the FANN will be,

y(k) = Γ3(W3Γ2(W2Γ1(u(k) + b1) + b2) + b3) (22)

where W1, W2 and W3 are the weight matrices, b1, b2 andb3 are the bias vectors, Γ1, Γ2 and Γ3 are the tansigmoidactivation functions, u = [Pm, w, β] is the input and y = vis the output of the neural network.

The training algorithm selected to train the neural networkis the backpropagation with momentum. This algorithm is anextension of the conventional error backpropagation trainingalgorithm. It is based on the minimization principle of acost function of the error between the desired output andthe actual output of a FANN. The minimization is achievedby varying the adjustable parameters of the FANN in thedirection of the gradient descent of the cost function. Besides,the momentum term allows a network to respond not onlyto the local gradient, but also to recent trends in the errorsurface. Acting like a low-pass filter, momentum allows thenetwork to ignore small features in the error surface. Withoutmomentum the network may get stuck in a shallow localminimum, however with momentum the network can slidethrough such a minimum [2].

In the backpropagation algorithm it is useful to rearrangethe elements of the weight matrices Wi and the bias vectorsbi into a vector θ which contains all the adjustable parameters

of the network. Then, the cost function in the backpropaga-tion algorithm is chosen to be:

Jk(θ) =1T

k+T−1∑n=k

[y(n) − yd(n)]2 (23)

where k denotes the time instant, the parameter T is referredto as the update window size and equals the number of timeinstants over which the gradient of the cost function J iscomputed, and yd is the desired output of the neural network.

The backpropagation algorithm begins by initially assign-ing small randomly chosen values for the weights and biases,and then during the training process this values are iterativelyadjusted to minimize the neural network cost function.

The adjustable parameter can be updated following agradient descendent with momentum procedure,

θ(k + T ) = θ(k) + Δθ(k) (24)

where the increment term of the adjustable parameters is

Δθ(k) = −α∂Jk(θ)∂θ

+ μΔθ(k − T ) (25)

where α is the learning rate and μ is the momentum constant,and the partial derivatives of J with respect to an adjustableparameters θ is given by,

∂Jk(θ)∂θ

=2T

k+T−1∑n=k

[y(n) − yd(n)]∂y(n)∂θ

(26)

The period of time comprising T time instants is calledan epoch, so that each adjustable parameter is updated onceevery epoch. The update window size T , the learning rateα and the momentum constant μ, are three parameters thathas an important role in the performance of the algorithm.If the learning rate is made too large, the algorithm becomesunstable, and if the learning rate is set too small, thealgorithm takes a long time to converge.

A multi-layer feedforward artificial neural network isproposed to approximate the wind speed. This neural networkhas three hidden layers, the first hidden layer has 7 neurons,the second has 9 neurons and the third hidden layer has 15neurons. The activation functions used in the three hiddenlayers are tansigmoid functions. The output layer has oneneuron and the activation function is a purelin function.The inputs to the neural network are the turbine power Pm,the wind turbine rotational speed wt, and the blade pitchangle β, and the output is the estimated wind speed vw.The training data for the neural network Pm, wt, and β areselected covering the entire operate range of the wind turbinegenerator. The network weights are adjusted such that thenetwork output error is minimized. The technique used totrain the network is the backpropagation with momentumalgorithm [2].

The parameters of the neural network training algorithmwas selected as follows: a learning rate of α = 0.25, amomentum gain of μ = 0.35 and an epoch of T = 5 timeinstants.

Once the neural network was well trained, the wind speedcan be obtained from the network output, using the networkinputs Pm, w, and β.

IV. WTG ROBUST CONTROL SCHEME

In order to extract the maximum active power from thewind, the shaft speed of the WTG must be adjusted to achievean optimal tip-speed ratio λopt, which yields the maximumpower coefficient Cpmax , and therefore the maximum power[5]. In other words, given a particular wind speed, there isa unique wind turbine speed required to achieve the goalof maximum wind power extraction. The value of the λopt

can be calculated from the maximum of the power coefficientcurves versus tip-speed ratio, which depends of the modelingturbine characteristics.

The power coefficient Cp, can be approximated by equa-tion (27) based on the modeling turbine characteristics [4]:

Cp(λ, β) = c1

(c2λi

− c3β − c4

)e

−c5λi + c6λ (27)

where the coefficients c1 to c6 depends on the wind turbinedesign characteristics, and λi is defined as

1λi

=1

λ+ 0.08β− 0.035β3 + 1

(28)

The value of λopt can be calculated from the roots ofthe derivative of the equation (27). Then, based on the windspeed, the corresponding optimal generator speed commandfor maximum wind power tracking is determined by:

w∗ =λopt · vR

(29)

The DFIG wind turbine control system generally consistsof two parts: the electrical control on the DFIG and themechanical control on the wind turbine blade pitch angle.Control of the DFIG is achieved controlling the variablefrequency converter (VFC), which includes control of therotor-side converter (RSC) and control of the grid-side con-verter (GSC) [6]. The objective of the RSC is to governboth the stator-side active and reactive powers independently;while the objective of the GSC is to keep the dc-link voltageconstant regardless of the magnitude and direction of therotor power. The GSC control scheme can also be designedto regulate the reactive power or the stator terminal voltageof the DFIG. A typical scheme of a DFIG equipped windturbine is shown in Figure 2 [6].

The RSC control scheme should be designed in order toregulate the wind turbine speed for maximum wind powercapture. Therefore, a suitably designed speed controller isessential to track the optimal wind turbine speed referencew∗ for maximum wind power extraction. This objectiveare commonly achieved by electrical generator rotor currentregulation on the stator-flux oriented reference frame [9].

Taken into account the wind turbine system electricalequations in the stator-flux oriented reference frame, pre-sented in section II; from equations (7) and (19) it is deduced

Fig. 2. Scheme of a DFIG equipped wind turbine

that the wind turbine speed can be controlled by regulatingthe q-axis rotor current components (iqr) while equation(13) indicates that the stator reactive power (Qs) can becontrolled by regulating the d-axis rotor current components,(ids). Consequently, the reference values of iqr and idr canbe determined directly from wr and Qs references.

Now we are going to design a robust speed control schemein order to regulate the wind turbine speed for maximumwind power capture. This wind turbine speed controller isdesigned in order to track the optimal wind turbine speedreference w∗ for maximum wind power extraction.

From equations (7) and (19) the following dynamic equa-tion is obtained for the system speed:

w =1J

(Tm − γKT iqr −Bw) (30)

= −aw + f − biqr (31)

where the parameters are defined as:

a =B

J, b =

γKT

J, f =

Tm

J; (32)

Now, we are going to consider the previous dynamicequation (31) with uncertainties as follows:

w = −(a+ �a)w + (f + �f) − (b+ �b)ieqs (33)

where the terms �a, �b and �f represents the uncertaintiesof the terms a, b and f respectively.

Let us define define the speed tracking error as follows:

e(t) = w(t) − w∗(t) (34)

where w∗ is the rotor speed command.

Taking the derivative of the previous equation with respectto time yields:

e(t) = w − w∗ = −a e(t) + u(t) + d(t) (35)

where the following terms have been collected in the signalu(t),

u(t) = f(t) − b iqr(t) − aw∗(t) − w∗(t) (36)

and the uncertainty terms have been collected in the signald(t),

d(t) = −�aw(t) + �f(t) −�b iqr(t) (37)

To compensate for the above described uncertainties thatare present in the system, a sliding control scheme is pro-posed. In the sliding control theory, the switching gain mustbe constructed so as to attain the sliding condition. In orderto meet this condition a suitable choice of the sliding gainshould be made to compensate for the uncertainties.

Now, we are going to define the sliding variable S(t) withan integral component as:

S(t) = e(t) +∫ t

0

(k + a)e(τ) dτ (38)

where k is a constant gain.

Then the sliding surface is defined as:

S(t) = e(t) +∫ t

0

(a+ k)e(τ) dτ = 0 (39)

Now, we are going to design a variable structure speedcontroller in order to control the wind turbine speed.

u(t) = −k e(t) − β sgn(S) (40)

where the k is the constant gain defined previously, β is theswitching gain, S is the sliding variable defined in eqn. (38)and sgn(·) is the signum function.

In order to obtain the speed trajectory tracking, the fol-lowing assumptions should be formulated:

(A 1) The gain k must be chosen so that the term (k+a)is strictly positive, therefore the constant k shouldbe k > −a.

(A 2) The gain β must be chosen so that β ≥ d whered ≥ supt∈R0+ |d(t)|.Note that this condition only implies that the un-certainties of the system are bounded magnitudes.

Theorem 1: Consider the induction motor given by equa-tion (33). Then, if assumptions (A 1) and (A 2) are verified,the control law (40) leads the wind turbine speed w(t), sothat the speed tracking error e(t) = w(t) − w∗(t) tends tozero as the time tends to infinity.

The proof of this theorem will be carried out using theLyapunov stability theory.

Proof : Define the Lyapunov function candidate:

V (t) =12S(t)S(t) (41)

Its time derivative is calculated as:

V (t) = S(t)S(t)=S · [e+ (k + a)e]=S · [(−a e+ u+ d) + (k e+ a e)]=S · [u+ d+ k e]=S · [−k e− β sgn(S) + d+ k e]=S · [d− β sgn(S)]≤−(β − |d|)|S|≤0 (42)

It should be noted that the eqns. (38), (35) and (40) andthe assumption (A 2) have been used in the proof.

Using the Lyapunov’s direct method, since V (t) is clearlypositive-definite, V (t) is negative definite and V (t) tendsto infinity as |S(t)| tends to infinity (i.e. V (t) is radiallyunbounded). Then the equilibrium at the origin S(t) = 0 isglobally asymptotically stable, and therefore S(t) tends tozero as the time tends to infinity. Moreover, all trajectoriesstarting off the sliding surface S = 0 must reach it in finitetime and then will remain on this surface. This system’sbehavior once on the sliding surface is usually called slidingmode.

When the sliding mode occurs on the sliding surface (39),then S(t) = S(t) = 0, and therefore the dynamic behaviorof the tracking problem (35) is equivalently governed by thefollowing equation:

S(t) = 0 ⇒ e(t) = −(k + a)e(t) (43)

Then, under assumption (A 1), the tracking error e(t)converges to zero exponentially.

It should be noted that, a typical motion under slidingmode control consists of a reaching phase during whichtrajectories starting off the sliding surface S = 0 movetoward it and reach it in finite time, followed by sliding phaseduring which the motion will be confined to this surface andthe system tracking error will be represented by the reduced-order model (eqn. 43), where the tracking error tends to zero.

Finally, the torque current command, i∗qr(t), can be ob-tained from equations (40) and (36):

i∗qr(t) =1b

[k e+ β sgn(S) − aw∗ − w∗ + f ] (44)

Therefore, the proposed variable structure speed controlresolves the wind turbine speed tracking problem for variablespeed wind turbines in the presence of uncertainties. Thiswind turbine speed tracking let us obtain the maximum windpower extraction for all values of wind speeds.

V. SIMULATION RESULTS

In this section we will study the variable speed windturbine regulation performance using the proposed sliding-mode field oriented control scheme, using the proposedneural network based wind speed estimator. The objective ofthis control scheme is to maximize the wind power extractionin order to obtain the maximum electrical power from thewind for all wind speeds. In this sense, the wind turbinespeed must be adjusted continuously against the wind speed.

The simulation are carried out using the Matlab/Simulinksoftware and the turbine model is the one provided in theSimPowerSystems library [13].

In the example A 9-MW wind farm consisting of six1.5 MW wind turbines connected to a 25-kV distributionsystem exports power to a 120-kV grid through a 30-km,25-kV feeder. A 2300V, 2-MVA plant consisting of a motor

load (1.68 MW induction motor at 0.93 PF) and of a 200-kW resistive load is connected on the same feeder at this25-kV bus. The wind turbines use a doubly-fed inductiongenerator (DFIG) consisting of a wound rotor inductiongenerator and an AC/DC/AC IGBT-based PWM converter.The stator winding is connected directly to the 60 Hz gridwhile the rotor is fed at variable frequency through theAC/DC/AC converter. The DFIG technology allows to extractthe maximum energy from the wind by optimizing the turbinespeed, while minimizing mechanical stresses on the turbineduring gusts of wind. The optimum wind turbine speed thatproduces the maximum mechanical energy for a given windspeed value is proportional to the wind speed. In this examplethe wind speed in estimated using the proposed ANN, and thewind turbine speed is controlled using the proposed variablestructure control law.

The system has the following mechanical parameters. Thecombined generator and turbine inertia constant is J = 5.04sexpressed in seconds, the combined viscous friction factorB = 0.01pu in pu based on the generator rating and thereare three pole pairs [13].

In this simulation examples it is assumed that there is anuncertainty around 20% in the system parameters, that willbe overcome by the proposed sliding control.

Finally, the following values have been chosen for thecontroller parameters, k = 100, β = 30.

In this case study, the rotor is running at subsynchronousspeed for wind speeds lower than 10 m/s and it is runningat a super-synchronous speed for higher wind speeds.

In figure 3, the turbine mechanical power as function ofturbine speed is displayed in for wind speeds ranging from5 m/s to 16.2 m/s. The thin lines are the different turbineoutput power for the different wind speeds. As it can beseen in the figure, in order to obtain the maximum windpower extraction, the turbine speed should track the thickline, because this line passes through the maximum turbinepower values for the different wind speeds.

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

5 m/sA

B

C12 m/s

D

16.2 m/s

Turbine speed (pu of generator synchronous speed)

Tur

bine

out

put p

ower

(pu

of n

omin

al m

echa

nica

l pow

er)

Turbine Power Characteristics (Pitch angle beta = 0 deg)

Fig. 3. Turbine Power Characteristics

The simulation example shows that the proposed control

0 5 10 15 20 25 30 35−5

0

5

10

15

20

25

30

Time (s)

Est

imat

ed a

nd R

eal W

ind

Spe

ed (

m/s

vv^

Fig. 4. Estimated and real wind speed (m/s)

0 5 10 15 20 25 30 350.7

0.8

0.9

1

1.1

1.2

1.3

1.4

Time (s)

Ref

eren

ce a

nd R

eal G

ener

ator

Spe

ed (

p.u)

w

w*

Fig. 5. Reference and real generator speed (pu)

scheme for the wind turbine performs well using the windspeed estimated by the ANN.

Figure 4 shows the estimated (solid line) and the real(dashed line) wind speed, in this figure it can be observedthat the ANN estimates the wind speed accurately.

Figure 5 shows the wind turbine generator speed (solidline) and the reference wind turbine generator speed (dashedline), that is obtained using the wind speed estimated by theNN. As it may be observed, after a transitory time in whichthe sliding mode is reached, the rotor speed tracks the desiredspeed in spite of system uncertainties. In this figure, the speedis expressed in the per unit system (pu), that is based in thegenerator synchronous speed ws = 125.60rad/s.

Figure 6 shows the reactive power (dashed line) and theactive power (solid line) generated by the wind-turbines,whose value is maximized by our proposed control scheme.As it can be observed in this figure, at time 16.3s, and 33.4sthe mechanical power (and therefore the generated activepower) should be limited by the pitch angle so as not toexceed the wind turbines rated power.

Figure 7 shows the pitch angle of the blades that should

0 5 10 15 20 25 30 35−4

−2

0

2

4

6

8

10

Time (s)

Act

ive

and

Rea

ctiv

e P

ower

(M

W)

PQ

Fig. 6. Active and reactive power

0 5 10 15 20 25 30 350

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time (s)

Pitc

h A

ngle

(de

g)

Fig. 7. Pitch angle of the blades

be controlled in order to limit the mechanical power insidethe values that the wind turbine can convert into electricalpower.

VI. CONCLUSION

A Robust control with a Neural Network wind speedestimator for variable speed wind turbine has been presented.The proposed control scheme avoids to employ anemometersto measure wind speed in order to track the desired optimalshaft speed. It should be noted that these mechanical sensorsincrease the cost and reduce the reliability of the wind turbinegenerator system. The proposed neural network estimatorscheme employs the field oriented control theory in order tosimplify the dynamic equations of the doubly fed inductiongenerators. A multilayer feedforward network and the so-called backpropagation with momentum algorithm which isa gradient descent algorithm of the performance function.The optimal wind turbine speed command is then determinedfrom the estimated wind speed in order to achieve themaximum wind power extraction.

The implemented control method allows the wind turbineto operate with the optimum power efficiency over a widerange of wind speed under system uncertainties and windspeed variations.

The simulations show that the proposed scheme suc-cessfully controls the variable speed wind turbine in orderto obtain the maximum power, within a range of normaloperational conditions. At wind speeds less than the ratedwind speed, the speed controller seeks to maximize the poweraccording to the maximum coefficient curve. As result, thevariation of the generator speed follows the slow variation inthe wind speed. At large wind speeds, the power limitationcontroller sets the blade angle to maintain the rated power.

Simulation studies have been carried out on a 9-MW windfarm consisting of six 1.5 MW wind turbines to verify theproposed sensorless control scheme. Results have shown thatthe wind speed was accurately estimated under both normaland transient operating conditions, and that the wind turbinespeed tracking objective is achieved. Terefore, the resultingWTG system delivered the maximum electrical power tothe grid with high efficiency and high reliability withoutmechanical anemometers, and under system uncertainties andwind speed variations.

ACKNOWLEDGMENT

The authors are very grateful to the Basque Govern-ment by the support of this work through the project S-PE09UN12 and to the UPV/EHU by its support throughprojects GUI07/08.

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