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Electr Eng (2008) 90:479491

DOI 10.1007/s00202-008-0097-3

ORIGINAL PAPER

Self tuning control of wind turbine using neural network identifier

M. Sedighizadeh

A. Rezazadeh

Received: 26 September 2007 / Accepted: 15 December 2007 / Published online: 13 February 2008

Springer-Verlag 2008

Abstract Thenonlinearcharacteristicsof thewind turbines

and electric generators necessitate that grid connected windenergy conversion systems (WECS) use nonlinear controls.

The present paper proposes an adaptive self tuning control

strategy with neural network Morlet wavelet for WECS con-

trol. The proposed strategy is based on single layer feedfor-

ward neural networks with hidden nodes of adaptive Morlet

wavelet functionscontroller and an infinite impulse response

recurrent structure. The neuro controller is based on a cer-

tain model structure to approximately identify the system

dynamics of WECS, and control its response. The proposed

controller is studied in three situations: without noise, with

measurement input noise and with disturbance output noise.

Finally, the results of the performance of the new controller

werecomparedwitha multilayerperceptron networkproving

a more precise modeling and control of WECS.

Keywords Adaptive control Morlet wavelets Wind energy conversion system

1 Introduction

The increasing interest in environmental concerns has forced

the industrial and academic communities to look for cleansources of energy. The wind energy is one of the viable can-

didates to replace the conventional energies. The new energy

sources require new power devices technologies, new circuit

topologies and novel control strategies for their efficiency.

M. Sedighizadeh (B) A. RezazadehFaculty of Electrical and Computer Engineering,

Shahid Beheshti University, Tehran, Iran

e-mail: [email protected]

Therefore, the environmental and safety energy demands

have led to worldwide research efforts in achieving controlstrategies compatible with the renewable energy sources.

Currently, the wind energy conversion systems (WECS)

are constructed with standalone topology or hybrid topol-

ogy or grid topology. The turbines are traditionally linked

with induction generators (squirrel cage or wound rotor) to

achieve a robust, low maintenance and cost-effective system.

However, there is a drawback in this structure. Being a highly

nonlinear system, it requires a nonlinear control strategy to

set the system in its optimal operation point. So in the previ-

ous works, different methods based on classic methods and

intelligent methods for controlling of WECS are introduced.

But regarding to nonlinear structure of WECS, stochastic

parameters of wind and other uncertainties in system, the

intelligent methods are more attractive than classic meth-

ods. Many authors [14] survey fuzzy logic control, neural

network control, expert system control and synthesis intelli-

gent control methods that used in the stability, speed control

system and maximum-power transfer of WECS and showed

that the intelligent control approaches are robust and exhibit

a superior performance to classic control methods.

Traditional self tuning adaptive control approaches are

interesting alternatives for identifying and control of WECS

nonlinear dynamics systems. But they cannot deal with com-

plex nonlinear systems. The problem is exacerbated when

the complex functions describing the systems are unknown

and change with time. Developments in the self tuning adap-

tive neuro controller design have proved to be useful for a

wide class of practical situations [5]. Mayosky and Cancelo

[6] used this idea for controlling the WECS. They proposed

a neural-network-based structure that consists of two com-

bined control actions, a supervisory control and an RBF

(radial basis function) network-based self tuning adaptive

controller.

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Lekutai and VanLandingham [7] presented an innovative

combination of the wavelet transform theory with the basic

concept of neural networks, proposing a new mapping net-

work. The resulting network called neural network adaptive

wavelets or wavenets is presented as an alternative to feed-

forward neural network to approximate arbitrary nonlinear

functions. It is found that this new controller is very useful

for identification and control of systems with unknown andhighly nonlinear dynamics [7].

Sedighizadeh et al. [8,9] used idea of self-tuning control

of nonlinear systems using neural network adaptive frame

wavelets and WECS model presented by Mayosky and

Cancelo, for identification and control of WECS. They sug-

gested an adaptive PI and PID controller using rational func-

tion with second-order poles (RASP1) wavenets for Wind

turbine control. Sedighizadeh et al. [10] also suggested an

adaptive controller using Morlet wavelets frames neural net-

work for identification and control of WECS. Their wavenet

consists of a single layer feed forward neural network with

hidden nodes of adaptive wavelet functions followed withan infinite impulse response (IIR) recurrent structure. The

IIR cascaded to the neural network to provide local structure

network, to improve the speed of learning. A neural network

estimator approximates the unknown dynamics of the plant,

and then the parameters of the proposed controller are set

within a feedback loop based on algebraic computations fol-

lowing the sampled input-output data.

In the present paper, the suggested controller in [10] was

simulated in three situations: without noise, with measure-

ment input noise and disturbance output noise to control

WECS. The results have also been compared with the MLP

based performance.

This paper is organized as follows. Section 2 illustrates

the WECS system dynamics and model. Section 3 presents a

wavenet control strategy and discusses the adaptive network

algorithmic implementation, providing the neuro controller

design architecture. Section 4 identifies WECS dynamics

using the proposed neural network with various number of

Morlet wavelets in a hidden layer. After identification, the

section also discusses controlling the system in three differ-

ent situations regarding to the noise of the system. Finally,

Sect. 5 presents the conclusions.

2 Wind energy conversion systems

2.1 Wind turbine characteristics

The dynamic model of horizontal-axis type wind turbine

which is the most commonly used wind turbine is discussed

in this section. The output mechanical power gained from a

wind turbine is calculated as [6].

P = 0.5Cp(V)3A, (1)

Fig. 1 Power coefficient Cp versus turbine speed

where is the air density, A is the area swept by the blades,

and V is the wind speed. Cp, is power coefficient and is

approximated as follows,

Cp = + 2 + 3, (2)

where,

= R/V (3)

R is the radius of the turbine and is the rotational speed.

, and are constructive parameters for a given turbine.

Figure 1 illustrates typical Cp versus turbine speed curves,

with the wind speed or V as a parameter. It can be noticed

that maximum value for Cp which is represented as Cpmax ,

is a constant for any given turbine. Replacing this value in

(1), yields the maximum output power for the given wind

speed. This maximum output power is achieved in a certain

rotational speed, opt, according to a certain wind speed, V.

The resulting torque by the wind turbine is calculated as

[6]:

Tl = 0.5

Cp

(V)

2R2 (4)

The torque/speedcurves of a typical wind turbine, with V as

a parameter is shown in Fig. 2. It can be seen that maximum

generated power do not coincide with maximum developed

torque points.

Superimposed to those curves is the curve of Pmax. As it

can be seen (Fig. 2), the maximum generated power and the

maximum torqueare notachieved at thesame speed.Optimal

performance of the turbine is achieved when it operates at the

Pmax condition. Setting the turbine at the Pmax in specified

wind speed is the control objective of the present paper.

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Electr Eng (2008) 90:479491 481

Fig. 2 Torque/speed curves (solid) ofa typical wind turbine.The curve

ofCp max is also plotted (dotted)

Fig. 3 Slip recovery using a static Kramer drive

2.2 Induction generators and slip power recovery

WECSs mainly use induction generators to produce elec-

tricity and are available in two basic configurations namely,

variable speed and constant speed. Due to their higher per-

formance, variable speed configuration WECSs are more

popular. The induction generators used for variable speed

constant frequency (VSCF) applications are of two types:

cage rotor machines and wound rotor machines.

Figure 3 illustrates a typical wound machine configura-

tion. The power generation and generators torque can be

controlled by varying the firing angle , of inverter in Static

Kramer drive [6].

Static Kramer drive which is a combination of a rectifier

and an inverter is used to inject slip power to the AC line as in

Fig. 3. As the wind speed changes, the Cp will also change.

The firing angle of the inverter must be controlled to achieve

the maximum power with changing the Torque- speed curve

of the generator.

Thetorquedeveloped by thegenerator/Kramer drivecom-

bination is [6]:

Tg =3V2s Req

s

(s Rs + Req)2 + (ssLls + ssLlr)2 , (5)

where

Req =sn22s Rb + (n1|cos()|)2Rs1 n1|cos()|

((n2s) (n1|cos()|)2)Rb = Rr + 0.55Rf

= 2n2

2Rbs Rs + (n2s Rs )2

+ n2

2(ssLls + ssLlr)2

+ (n2Rb)2 n1|cos()|(sLls + sLlr)2

(6)

and

n1: transformation ratio between rotor and stator

wounds;

n2: turn ratio of the transformer between the Kra-

mer drive output and the AC line;

Rr, Rs , Rf : Rotor, stator, and dc link resistances;

Lls : stator dispersion inductance;

Llr : rotor dispersion inductance;

: firing angle;

s : synchronous pulsation;

s : synchronous machine rotational speed;

V: stator voltage

s: slip

: firing angle of inverter

(all values referred to the rotor side).

2.3 Turbine/generator model

The dominant dynamics of the whole system (turbine plus

generator) are those related to the total moment of inertia.

Therefore, ignoring torsion in the shaft, generators electric

dynamics, and other higher order effects, the approximate

systems dynamic model is

J = Tl (, V) Tg(,), (7)

where Jis the total moment of inertia. Regarding (4)and(5),

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482 Electr Eng (2008) 90:479491

Fig. 4 Control strategy proposed. The firing angle is adjusted so that

the turbines operation point settles to theCp max condition

systems model becomes

= 1J

0.5

Cp

(V)

2R2

3V2s Req

s

(s Rs + Req)2 + (ssLls + ssLlr)2

, (8)

where Req depends nonlinearly on the control action cos()

according to (6). Cp, and are nonlinear functions ofV(2). Variation of generator parameters due to aging and tem-

perature, leads to using a nonlinear adaptive control strategy.

This control strategy system aims at placing the turbine inits maximum power generation point, despite the variations

in the wind speed and generators parameters. The turbine

torque,Tl , for a given V, and the generated torque,Tg , fora given cos(), are sketched in Fig. 4. It should be mentioned

that for a given wind speed, the turbines operational curve

and optimum generation point are fixed. According to (7),

the intersection ofTl and Tg curves represents the equi-librium point ( = 0) of the turbine-generator pair. Thecontrol strategy converges the rotational speed, , and tur-

bine torque,Tl , to their optimal values by changing the firing

angle of the inverter, as the wind speed changes [6].

The general form of, is a nonlinear function of and depending on the turbine and generator characteristics as

in (8). The designing of system is so that the maximum tur-

bine torque occurs 0.5 to 0.7 of the generator torque peak.

Regarding to the generator torque curves in this region Tg is

considered as a linear expression [6]. The generated torque

curve in optimal point is shown in Fig. 4. The expression for

Tg in (5), can be rewritten as:

Tg = K1 + K2 cos(). (9)

Thus the whole system will have the following expression.

= 1J

0.5

Cp

(V)

2R2 + K1 + K2 cos()

.

(10)

The standard normal form for (10) is

= f() + bu, (11)

where f is a nonlinear function of rotational speed, , b is a

constant and u is the system input which is the cosine of the

firing angle, .

3 Control strategy

3.1 Structure and algorithms

In order to deal with the tracking operationusing a neuralnet-work based controller, theunknown nonlinear WECS should

be identified according to a particular model. In this particu-

lar identification process, the model consists of a neural net-

work topology with the wavelet transform used in the hidden

units. This network is named wavenet. The concept of wave-

net introduces a super-wavelet, which is a linear combina-

tion of daughter wavelets that is also a wavelet. The daughter

wavelets are simply a dilated and shifted version of the ori-

ginal wavelet or mother wavelet. The super-wavelet allows

the shape of the wavelet to adapt to a particular problem,

a concept which goes beyond adapting the parameters of a

fixed shape wavelet. This network has shown good results innonlinear system and signal identification and control [11].

A local infinite impulse response (IIR) block structure is

cascaded with the network (Fig. 5). The IIR synopsis net-

work is used to createdouble local network architecture. This

architecture provides a computationally efficient method for

training the system, resulting in quick learning and fast

convergence [7]. The algorithm of proposed neural network

adaptive wavelets is similar to those in [7] where any desi-

red signal y(t) can be modeled by a linear combination of

Morlet daughter wavelets ha,b(t). Here ha,b(t) are gener-

ated by dilation, a, and translation, b, from a Morlet mother

wavelet:

ha,b(t) = h

t ba

= cos

o

t b

a

exp

0.5

t b

a

2(12)

With the dilation factor a > 0. The o is the wavelet fre-

quency which is chosen o = 4 which meets approximatelythe admissibility condition [7].

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Electr Eng (2008) 90:479491 483

Fig. 5 IIR adaptive wavelet

network structure: a neural

network architecture, b IIR

model

+

+

+

The approximated signal of the network y(t) can be mod-eled by [7]:

y(t) =Mi=0

ciz(t i)u(t) +N

j=1dj y(t j)v(t), (13)

where

z(t) =K

k=1Wkhak,bk(t) (14)

K is the number of wavelets, wk is the kth weight coeffi-

cient. M is the number of feedforward delays and cj is the

feedforward coefficient of the IIR filter. N is the number of

feedbackdelays and dj is therecursive filter coefficients.The

signals u(t) and v(t) are the input (cosine of firing angle) and

co-input to the system at time t, respectively. Input v(t) is

usually kept small for feedback stability purposes [7].

The neural network parameters ak, bk, ci , wk and dj can

be fined by optimizing the following objective function bymeans of least mean square (LMS) minimization

E= 12

Tt=1

e2(t), (15)

where e(t) is time varying error function and y(t) is the desi-

red response (rotational speed of wind turbine).

e(t) = y(t) y(t). (16)

To minimize the cost function, we may use the method of

steepest descent which requires the gradients Ewk

, Ebk

, Eak

,Eci

and Edj

for updating the incremental changes of each

particular parameter wk, bk, ak, ci and dj respectively. For

Morlet mother wavelet, gradients ofEare

E

wk = T

t=1 u(t)e(t)

Mi=0 ci h( i), (17)

E

bk=

Tt=1

u(t)e(t)

Mi=0

ci wkh( i)

bk, (18)

E

ak=

Tt=1

u(t)e(t)

Mi=0

ci wkh( i)

bk= E

bk, (19)

E

ci=

Tt=1

u(t)e(t)z(t i), (20)

E

dj=

Tt=1

v(t)e(t) y(t i), (21)

where = (t bk)/ak and we have

ha,b(t)

b= 1

a

o sin

o

t b

a

exp

0.5

t b

a

2

+

t ba

ha,b

t b

a

.

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484 Electr Eng (2008) 90:479491

The incremental changes of each parameter are simply the

negative of their gradients,

w = Ew

, b = Eb

, a = Ea

,

c = Ec

, and d= Ed

, (22)

Thus each coefficient vector w, b, a, c and dof the networkis updated in accordance with the following rules

w(n + 1) = w(n) + ww, (23)b(n + 1) = b(n) + bb, (24)a(n + 1) = a(n) + aa, (25)c(n + 1) = c(n) + cc, (26)d(n + 1) = d(n) + dd, (27)where the coefficient values are fixed learning rate param-

eters.

3.2 System model and controller design

Consider a general single input singleoutput (SISO)dynami-

cal system, similar to (11) represented by thestate equations:

x = f(x(t), u(t), t) (28)y(t) = g(x(t), t) (29)The Eqs. (28) and (29) can be written in discrete time space

as:

x(k+ 1) = f(x(k), u(k), k),(30)

y(k) = g(x(k), k),where x(k) Rn and u(k), y(k) R. The only accessi-ble data are the input u and output y. if the linear system

around the equilibrium state is observable, an input-output

representation exists which has the form:

y(k+ 1) = (y(k), y(k 1) , . . . , y(k n + 1),u(k), u(k 1) , . . . , u(k n + 1)) (31)

i.e. a function (.) exists that maps y(k) and u(k), and their

n 1 past values, onto y(k+ 1). In this light, a neural net-work model

canbe trained to approximate over the inter-

est domain. Practically if an exact model of the plant wereavailable, approximate models would be adapted to update

the control parameters. Thealternative model of an unknown

plant that can simplify the computation of the control input

is described by the following equation

y(k+ 1) = (y(k), y(k 1) , . . . , y(k n + 1),u(k)u(k 1) , . . . , u(k n + 1))+ (y(k), y(k 1) , . . . , y(k n + 1),u(k), u(k 1) , . . . , u(k n + 1))u(k). (32)

Fig. 6 Closed loop block diagram

Because the system in (11) is first order, we can express the

above equation as follows:

y(k+ 1) = (y(k)) + (y(k)).u(k), (33)where y(k) and u(k) denote the input and the output at the

kth instance of time.

If the nonlinearity terms (.) and (.) are known exactly,

the requiredcontrol u(k) fortrackinga desired outputr(k+1)can be computed at every time instance using the formula

u(k) = r(k+ 1) (y(k))(y(k))

. (34)

However, if(.) and (.) are unknown, the idea is to use

the neural network adaptive wavelets model to approximate

the system dynamics i.e.,

y(k+ 1) = (y(k), ) + (y(k), )u(k). (35)Comparing the model of (35) with the (13) we can conclude

that

(y(k), ) =N

j=1

dj y(k j)v(k), (36)

(y(k), ) =Mi=0

ciz(k i). (37)

After approximation of(.) and (.) nonlinearities as (.)

and (.), by two distinct neural network functions with

adjustable parameters (including weights wk, dilations ak,

translations bk, IIR feedforward coefficients ck, IIRfeedback

coefficients dk), represented by and respectively, the

control u(k) for tracking a desired output r(k+ 1) can beobtained from

u(k) = r(k+ 1) (y(k),)(y(k), )

. (38)

The neuro controller for self-tuning control WECS is pro-

vided in Fig. 6.

The optimum shaft rotational speed opt is obtained for

each wind speed Vw, and used as a reference for the close

loop control of WECS. Note that wind speed also acts as a

perturbation on the turbines model. Actually, the turbine is

coupled with the generators shaft using a gearbox, which

imposes an additional unknown dynamic to the model.

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Electr Eng (2008) 90:479491 485

The characteristics of the turbine/generator pair used for

the simulations in this paper are summarized in [6], but they

are considered unknown for the controller. For this reason,

the number of wavelets was obtained on a trial-and-error

basis.

4 Simulation results

4.1 Identification of WECS

Using the wind turbine data extracted from [12], the wave-

netnetwork with different size of Morlet mother wavelets is

employed to identify thewind turbine model.IIR block struc-

ture with 3 feedforward delay blocks and 3 feedback blocks

is also implemented. Wavelets are local basis functions pro-

viding less interference than globalones. This leads to a non-

complex dependency in the neural network parameters [7].

We will now confirm the aforementioned idea by presenting

several observations derived from the results of the MAT-LAB simulations. Assuming the training data are stationary

and sufficiently rich, optimal performance can usually be

achieved with a small learning rate. Therefore, all learning

rate parameters for weights, dilations, translations, IIR feed-

forward coefficients, and feedback coefficients are fixed at

0.005, 0.025, 0.025, 0.01, and 0.01, respectively. All initial

weights wk and dilations ak are set to 0 and 10, respectively.

The learning epoch will terminate when the desired normal-

ized error of 0.032 is reached. The following simulations

will describe the results of the wavenetnetwork performance

employing Morlet super-mother wavelet. Figures 7, 8, 9, 10

capture the learning performance of the wavenetnetwork

using 13 and 24 Morlet wavelets, respectively. We can con-

clude that the wavenetnetwork composed of more wavelets

can reach initial convergence with reference to the number

of iterations very rapidly. However, to reach the desired error

goal 0.032, networks with a large number of wavelets cannot

converge easily and the error performance starts to oscillate.

Large choosing of the step size of learning rate, will cause

the iteration process to bounce between two opposite sides

of a valley rather than following the natural gradient contour

(as shown in Fig. 10). As we can see, when the number of

wavelets K is small, for example, K

=4, it takes 36 itera-

tions to reach error of0.85while it takes 28 iterations to reach

error of 0.35 for K = 40, but when the error of 0.032 is thetarget, K = 13 takes 75 iterations while K = 40 takes 212iterations. Large Kis also undesirable because of more coef-

ficients to be updated. Small Kcan also take a large amount

of time to compute; as for K = 4, it takes more than 1,109iterations to reach error of 0.05. Table 1 provides numerical

values of the simulation for different number of wavelets. In

conclusion, the number of Morlet wavelets between K = 13

to K = 21 is sufficient to identify the unknown WECS model.

Fig. 7 Wavenet simulations with 13 Morlet waveletsSolid: plant out-

put and dotted: NN output

4.2 Control

Afterthe identificationmodelis completed, the trackingoper-

ation takes command of the neuro process control to track

the desired setpoint opt. The co-input v(t) is set to 0.95. In

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486 Electr Eng (2008) 90:479491

Fig. 8 Wavenet parameter updates with 13 Morlet wavelets

the following figures, the results of the wind turbine control

using theproposed self-tuning neuro wavenetcontroller with

16 Morlet is compared with the results of the wind turbine

control using the MLP networks. In these figures, a sequence

of step-shaped wind gusts is applied to the system.

4.3 Controller with prior NN training

Figure 11(up) illustrates the results of the setpoint control

using theproposed self-tuning neuro wavenetcontrollerwith

16 Morlet wavelets. The same control u(k) is fed to both

the actual plant and the neural network identifier. The mean

squared error between the setpoint reference, opt and actual

plant output, (k) is obtained as 0.022 and the one bet-

ween the setpoint reference, opt and the NN output res-

ponse, (k) is obtained as 0.007. Figure 11 (down) shows

the control input u(k). In input, the fluctuations period is the

Fig. 9 Wavenet simulations with 24 Morlet wavelets (Solid: plant

output and Dotted: NN output)

result of the training effort in controller which would take

longer without Prior training [12]. Figure 12a provides the

network parameter updates. This demonstrates that after the

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Electr Eng (2008) 90:479491 487

Fig. 10 Wavenet parameter updates with 24 Morlet wavelets

identification process of the wavenetnetwork, the network

parameters become very stable around the equilibrium state.

Figure 12b shows the update of the nonlinearity terms (.)

and (.).

A base line comparison is demonstrated in this paper by

providing a traditional feed forward MLP neural network

structure based on the back propagation (BPP) algorithms.

50 100 150 200 250 300 350 400 450 500350

400

450

500

550

Speed(rpm)

50 100 150 200 250 300 350 400 450 5000

0.2

0.4

0.6

0.8

Time(sec)

cos(alpha)

1

2

3

Fig. 11 Up: Self-tuning neuro wavenet controller responses to a

sequence of wind gusts: 1 setpoint reference 2 NN output response,

3 plant output response,Down: wavenet control input

Two layer perceptron networks (1 hidden layer, 1 output

layer) are simulated with 16 hidden nodes.

The bias for each node is set at 0.5. Initial weights of

both layers are set at random. Adaptive learning rate and

its momentum coefficient are initially set at 0.005 and 0.95,

respectively. Hyperbolic tangents are employed in the hid-

den nodes as an activation function. Figure 13 illustrates the

results of the set point control using the BPP algorithms. The

tracking response of theplant needs a longertime to reach the

desired target. Theneural networkemulator inFigure13 indi-

cates that its response could not capture thedynamic changes

on real time and thus, could never provide the good one steppredictive control performance to the tracking operation.

4.4 Controller with the input noise problem

The block diagram of an input noise model can be equiv-

alently interpreted the same as the block diagram of Fig. 6

with the measurement noise input is added to the input port

or output port of the NN. In Fig. 14 the noise is added to

the output port of the NN. The wavenetoutput response with

noisy input w(k) added to the input port of the network is

represented by

Table 1 Number of iterations

vs. number of Morlet wavelets

employed

Number of iterations Number of wavelets

4 10 13 21 24 33 40 53

Error of 0.85 36 8 7 5 5 4 3 2

Error of 0.35 303 22 25 18 16 25 28 33

Error of 0.05 1109 55 50 39 62 77 90 234

Error of 0.032 5003 80 75 74 150 170 212 892

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488 Electr Eng (2008) 90:479491

Fig. 12 Self-tuning wavenet parameters tracking to set-point refer-

ence

Fig. 13 MLP controller responses to a sequence of wind gusts.1 Set-

point reference, 2 plant output response,3 NN output response

optV

opt

)(ke

)( k

)(ku )(kWavenet Controller WECS

NN Aproximator+

noise

Fig. 14 Equivalent identification to input noise immunity system

y(k+ 1) = (.) + (.)(u(k) + w(k))

= (.) + (.)u(k) + (.)w(k)

= (.) + (.)u(k) + w(k). (39)

The wavenetresponse to the noise added to the network out-

put is represented by

y(k+ 1) = (.) + (.)u(k) + w(k). (40)It is seen that (39) and (40) provide the same results to the

identification performance.

The measurement noise w(k) of random distribution with

a variance of 0.01 is inserted at the input port of the wavenet

network. Simulations of wavenet and MLP control methodsare shown in Figs. 15 and 17. All initial values of parameters

are assumed the same as previous section. The simulation of

the plant and NN output responses with application of neuro

wavenetcontroller, is shown in Fig. 15(up). Figure15(down)

shows thecorresponding control effort to theactualplant and

the noisy control to the wavenetnetwork simulator. Figure16

provides the necessary parameter updates of the network and

the control. It can be seen that when noises are mixed in the

control process, the tracking operation of the actual plant to

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Electr Eng (2008) 90:479491 489

50 100 150 200 250 300 350 400 450 50035

400

450

500

550

Speed(rpm)

50 100 150 200 250 300 350 400 450 5000.1

0.2

0.3

0.4

0.5

0.6

Time(sec)

cos(alpha)

1

2

3

1

2


sequence of wind gusts (1 setpoint reference, 2 NN output response, 3

plant output response),down: wavenet control input (1 control Action

to NN Emulator, 2 control action to actual plant)

the desired reference is inferior with the noise level. Note

that the measurement noise is only added to the input to the

NN emulator, but not to the actual plant. However, the plant

responses to the control action are noisy. As in Fig. 15 is

shown, the wavenetnetwork setpoint tracking response is

better than the plant response. It can be concluded that with

this type of control scheme, noises are the main distraction

for the actual plant system of the tracking operation.

With the same initialization, the simulation result of the

input noise problem study for the two-layer feed forward

NN with back propagation algorithms is shown in Fig. 17.

The neural network output hardly responds to the trackingoperation, and the plant output is noisy. Unlikewavenets, the

back propagation algorithms do not signify the interpolation

characteristic, thus noise interferes the NN responses.

4.5 Controller with the output noise problem

The block diagram of an output noise model can be equiv-

alently interpreted the same as the block diagram of Fig. 6

with the disturbance noise output is added to the input port

or output port of the of the plant. In Fig. 18 the plant with

the input noise is shown. In (41) and (42) it is shown that we

can use the input noise to the plant rather than modeling the

noise in the plant output. When the model that noise added

to output of the plant is used, the error becomes

e(k) = (y(k) + w(k)) y(k),(41)

e(k) = [(.)(.)]+[(.)u(k)(.)u(k)]+w(k).

And the error of the model with input added noise to the

plant is

Fig. 16 Self-tuning wavenet parameters tracking to set-point refer-

ence

e(k)=[(.)(.)]+[(.)u(k)(.)u(k)]+(.)w(k),e(k)=[(.)(.)]+[(.)u(k)(.)u(k)]+ w(k).

(42)

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490 Electr Eng (2008) 90:479491


point reference, 2 plant output response,3 NN output response

Wavenet Controlleropt WECS

NN Aproximator

V opt

)(ke

(k)

)(ku (k)

noise

-

+

Fig. 18 Equivalent identification to output noise immunity system

50 100 150 200 250 300 350 400 450 500-500

0

500

1000

1500

2000

Speed

(rpm)

50 100 150 200 250 300 350 400 450 500-0.5

0

0.5

1

1.5

2

Time(sec)

cos(alpha)

1

2

3


sequence of wind gusts: 1 setpoint reference, 2 NN output response,

3 plant output response,Down: wavenet control input

Thus, the two identification models provide similar algorith-

mic approximation.

After the identification process for the unknown WECS

system has been completed, the control action is activated to

track the same desired set-point reference. The disturbanceFig. 20 Self-tuning wavenet parameters tracking to set-point refer-

ence

123


13/13

Electr Eng (2008) 90:479491 491

50 100 150 200 250 300 350 400 450 500200

300

400

500

600

Speed(rpm)

50 100 150 200 250 300 350 400 450 5000.1

0.2

0.3

0.4

0.5

0.6

Time(sec)

cos(alpha)

1 2

3


point reference, 2 plant output response,3 NN output response,Down:

wavenet control input

noise w(k), witha varianceof 0.01 isinserted atthe input portof the nonlinear plant. Simulations of two control methods

(wavenet and MLP) are shown in Figs. 19 and 21. The simu-

lation result of the plant and NN output responses with neuro

wavenetcontroller is shown in Fig. 19(up). Figure 19(down)

demonstrates the corresponding control action to both the

actual plant and the wavenetnetwork identifier. Figure 20

provides thenecessaryparameterupdatesof thenetwork.The

results show that there is an offset between theplant response

and the set-point due to the disturbance at the output port of

the plant.

With this control scheme, the NN performance is noisy,

with fast response to the set point, while the plant outputperformance is affected by the disturbance of the noise.

Figure 21(up) shows the setpoint tracking response of the

output noise using the same two-layer perceptron network

with BPP algorithms. The control effort to the plant is illus-

trated in Fig. 21(down). With this conventional algorithm,

the plant response is noisy with a small offset and the NN

response never adjusts to the changes. Finally, the output

noise immunity studies show the worst scenario in the adap-

tive self-tuning control.

5 Conclusion

This paper emphasizes on self-tuning control applications

of an efficient neural network architecture based on a wave-

let theory called wavenets. The wavenetbased controllers

improve the performance of the trained network for fast

convergence, robustness to noise interference, and highcom-

plex ability to learn and track of WECSs. Two control sche-

mes were shown. One is based on an assumed plant model

and a wavenet -identifier that is used to construct adaptive

controllers. The other is a traditional neuro-control scheme

basedon thefeedforwardneural network structurewith back-

propagation(BPP) algorithms. This schemeis used fora base

line comparison to wavenets. The first scheme tends to pro-vide faster tracking adjustment to control changes. Finally,

the conventional scheme with BPP shows that it requires a

longer time for adapting to changes and performs poorly to

added noises. From the results studies, the worst scenario to

all of the control schemes, in terms of MSE, occurs when

noise is contaminated to the output port of the plant systems.

References

1. Junhua Y, Jie W, Jinming Y, Ping Y (2004) Apply intelligent con-

trol strategy in wind energy conversion system. In: Fifth worldcongress on intelligent control and automation, WCICA2004. vol

6, pp 51205124

2. Chedid R, Mrad F, Basman M (1999) Inteligent control of a class

of wind energy conversion system. IEEE T-EC 14(4):15971604

3. Kanellos FD, Hatziargyriou ND (2002) A new control scheme for

variable speed wind turbine using neural networks. IEEE Power

Eng Soc Winter Meeting 1(1):360365

4. Kyoungsoo Ro,Han-ho Choi (2005)Applicationof neuralnetwork

controllerfor maximum power extraction of a grid-connected wind

turbine system. Electr Eng (Archiv Elektrotech) 88(1):4553

5. Narendra KS, Parthasarathy K (1990) Identification and control of

dynmical systems using neural networks. IEEETrans Neural Netw

1(1):427

6. Mayosky MA,CanceloGIE (1999) Direct adaptivecontrolof wind

energy conversion systems using gaussian networks. IEEE TransNeural Netw 10(4):898906

7. Lekutai G, VanLandingham HF (1997) Self-tuning control of non-

linear systems usingneural network adaptiveframe wavelets. IEEE

Int Conf Systems Man Cybern 2:10171022

8. Sedighizadeh M, Kalantar M (2004) Adaptive PID control of wind

energy conversion systems using RASP1 mother wavelet basis

function networks. IEEE TENCON 2004, Chiang Mai

9. Sedighizadeh M, et al. (2005) Nonlinear model identification and

control of wind turbine using wavenets. In:Proceedings ofthe 2005

IEEE conference on control applications, Toronto, pp 10571062

10. Kalantar M, Sedighizadeh M (2004) Adaptive self tuning control

of wind energy conversion systems using Morlet mother wavelet

basis functions networks. In: 12th Mediterranean IEEEconference

on control and automation MED04, Kusadasi

11. Szu HH, Telfer BA, Kadambe S (1992) Neural network adap-tive wavelets for signal representation and classification. Opt Eng

31(9):19071916

12. Sedighizadeh M (2005) Modeling and adaptive-neural control of

windenergyconversion systemsusingwavelet functions.PhD The-

sis, Iran University of Science and Technology

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