Energy Conversion and Management 101 (2015) 489–502

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Energy Conversion and Management

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

A proposed strategy for power optimization of a wind energy conversionsystem connected to the grid

http://dx.doi.org/10.1016/j.enconman.2015.05.0470196-8904/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: dja_rekioua@yahoo.fr (D. Rekioua).

S. Taraft a, D. Rekioua a,⇑, D. Aouzellag b, S. Bacha c

a Laboratoire de Technologie Industrielle et de l’Information (LTII), Université de Bejaia, Algeriab Departement de Génie Electrique, Université de Bejaia, Algeriac G2elab Laboratory, INPG Grenoble, France

a r t i c l e i n f o

Article history:Received 10 January 2015Accepted 21 May 2015Available online 16 June 2015

Keywords:Wind turbineDoubly fed induction generatorOptimizationMatrix converterPower controlSliding mode control

a b s t r a c t

Many strategies have been developed in last decade to optimize power extracted from wind energy con-version system where many of them can produce only 30% more than the rated power. With the consid-ered strategy, the generated wind power can reach twice its nominal value using a fast and reliable fullyrugged electrical control. Indeed, by employing a suitable control technique where the produced power insuper-synchronous mode is derived from both the stator and the rotor. Also, the rotor provided power inthis case grows up 100% comparing to stator rated power. However, this solution permits to maintain thewind energy conversion system operation in its stable area.

The considered system consists of a double fed induction generator whose stator is connected directlyto the grid and its rotor is supplied by matrix converter. In this paper, the sliding mode approach toachieve active and reactive power control is used. This latter is combined with de Perturbation andObservation Maximum Power Point Tracking used in the second operation zone. The obtained simula-tions results are assessed and carried out using Matlab/Simulink package and show the performanceand the effectiveness of the proposed control.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction control method for a doubly fed induction generator used in wind

Due to its advantages, wind energy attracts many researchers inthe last decade. Some authors focused their research on problemsrelating to the storage of this energy like John and David who leda study on probabilistic energy storage and its use with intermittentrenewable energy [1]. Xiaosong et al. made comparative study ofthree electrochemical energy buffers applied to a hybrid busPowertrain with optimal sizing and energy management [2].Others are more interested in improving the quality of energy pro-duced and injected into the grid and working on models and variouscontrol techniques. In [3], the authors propose a model to control awind turbine associated with a flywheel energy storage system toimprove the quality of power injected into the grid. In [4], a gridpower flux control of a variable speed wind generator which con-sists of a doubly fed induction generator is investigated. A new con-trol strategy for small wind farm is proposed in [5] to improvesupplying reactive power and transient stability. To avoid strongtransients in the turbine components, a cascaded nonlinear con-troller is designed in [6] for a variable speed wind turbine equippedwith a doubly fed induction generator. In [7], authors proposed a

energy conversion systems. Three different controllers are pre-sented: proportional-integral, polynomial RST and linear quadraticGaussian. As an alternative to conventional methods, a nonlinearpredictive control approach is developed for a doubly fed inductiongenerator in [8]. In [9], authors presented the design and the imple-mentation of a model reference adaptive control. The active andreactive power regulation which is achieved below synchronousspeed of a grid connected wind turbine based on a doubly fedinduction generator is investigated. To reduce the total harmonicdistortion and enhance power quality during disturbances, anunconventional power electronic interface for a wind energy con-version system is presented in [10]. Other researchers haveexploited the advantages of matrix converters which are betteradapted to the AC/AC conversion over the classic converter topolo-gies as back to back converters. Indeed, in [11] a grid connectedwind power generation scheme using a doubly fed induction gener-ator with a direct AC/AC matrix converter is presented. To reducelarge active and reactive power ripples which is one of the maindrawbacks on conventional method, a new strategy is developedin [12] for a matrix converter-fed doubly fed induction generator.In [13], authors investigated a three-level sparse matrix converterassociated to a grid connected variable speed wind generationscheme using a doubly fed induction generators.

Nomenclature

vwind wind velocityq air densityR turbine radiusCp power coefficientk tip speed ratiokopt optimal tip speed ratiob blade pitch angleTt turbine torquef coefficient of viscous frictionXmec mechanical speedXmec opt optimal mechanical speedG gear ratioPwind wind powerPmec mechanical powerPmec opt optimal mechanical powerPs stator active powerPr rotor active powerPg ; Pg ref grid active power and it’s referenceva; vb;vc input voltage of the MCQs;Qs ref stator reactive power and it’s referenceQr rotor reactive powerQrg reactive power from the converter grid side

Tem electromagnetic torque of the DFIGr the leakage coefficientRs;Rr per phase stator and rotor resistancesLs; Lr total cyclic stator and rotor inductancesLm magnetizing inductanceusd;usq;urd;urq two-phase stator and rotor fluxesvsd; vsq;vrd;v rq two-phase stator and rotor voltagesisd; isq; ird; irq two-phase stator and rotor currentsP number of pole pairsg generator efficiencys generator slipxs stator angular speedxr rotor angular speedx angular speedSijðtÞ switch functionvA; vB;vC output voltage of the MCiA; iB; iC output current of the MCXN nominal speed of DFIGWECS wind energy conversion systemMC matrix converterDFIG doubly fed induction generatorSMC sliding mode control

490 S. Taraft et al. / Energy Conversion and Management 101 (2015) 489–502

Other researchers are interested on the study of wind genera-tors themselves to improve their performances. Indeed, severalstudies have used different control strategies in order to optimizethe extracted power from variable speed wind turbine. In [14],an autonomous induction generator driven with a wide speedrange turbines controlled by the strategy of saturation effect com-pensation is presented but the maximum speed using this strategydoes not exceed 13% of the rated speed.

Unconventional converter is proposed in [15]. To improve theused conversion energy system, the proposed converter has beenconnected to the rotor of the doubly fed generator with a fractionequal to 30% of the total power. This explains that, the generatorspeed does not exceed 30% in excess of the synchronism speed. Ahigh dynamic control of a generator with the speed range up to20% is developed in [16]. A nonlinear robust control system tech-nique for converting wind energy is performed in [17]. However,once again, the speed does not exceed 30% of its nominal value.In all above cited research works, the rated power and speed havebeen dealt with improving the generated power quality, with outexceeding 30% of rotor rated power. Yong et al. conducted a veryinteresting work where they have operated a double stator induc-tion machine to reach the speed up to twice the nominal value[18]. But the maximum power extracted using their system donot have been doubled since one of the generator stators is con-trolled by static excitation. A solution to double a rated power ata double speed, is proposed in [19]. However, the system is entirelygrid interfaced, ie requiring two power converters. In this context,the present deals and focuses on improving the performances of aWECS based on DFIG, using one power converter, expanding thespeed variation range and arriving to extract a power that canreach the twice the rated power. Obviously, this cannot be donewithout taking into account the electrical and mechanical con-straints related to the wind turbine operation in the range of highspeeds. For this, we proceed as follows: When the turbine torque isless than its nominal value the MPPT algorithm is applied.Otherwise, the MPPT strategy is stopped and limits the turbine tor-que at its nominal value. Several MPPT algorithms are proposed inthe literature. The most used is that named Perturbation andObservation (P&O). It is to note that it was always used in the

Zone-I. In our case, an extension to the Zone-II is performed to tak-ing into account the above-cited electrical constraints.Consequently, the stator power is also fixed, leaving the turbinespeed increase above its synchronous value and the rotor becomesa generator of electric power that increases and reaches its nomi-nal value when the turbine speed is doubled. Thus, the power gen-erated by the rotor is added to that of the stator that are injected tothe grid. In terms of control techniques, the sliding mode control,which is a robust and reliable approach is suitable and gives anadded value to WECS based on DFIG. In [20] one found the impacton the active and reactive powers values is important for PI con-troller where as it is almost non-existent for SMC controller. In[21] sliding mode control strategy is used for tracking power pho-tovoltaic system. In [22], robustness is tested with the respect theuncertainties parameters. Thus, the SMC is chosen as a controltechnique for the studied system. The global system, representedin Fig. 1, is modeled and simulated under Matlab/Simulink andthe obtained simulations results are presented to prove the validityof the proposed strategy.

2. Proposed system

The proposed system consists of (WECS) based on a DFIG of1.5 MW supplied by a matrix converter and connected to the grid(Fig. 1). An optimization program, based on the Perturbation andObservation (P&O) method is used to determinate the optimal val-ues of power and speed which will be used in the control of activeand reactive power. This control is achieved using sliding modecontroller (SMC). The matrix converter is dimensioned at 100% ofrated power generator. The wind turbine is designed to operatein over rated speed.

3. Modeling of the global system

3.1. Wind generator modeling

3.1.1. Modeling of the wind turbineThe power available and recoverable from the turbine is

expressed by the following relationship [23]:

DFIG

mecΩ

θ

Tg

Qrg

Sliding Mode Control

Pg

Pg_ref _+ +

_

Qs

Ps

Filter

A

ab c

C B

Grid

Pmec_opt

mec _ opΩOptimization

Programp.∫

η

Qs_ref

1Pr

0

-0,4

-0,2

0

0,2

0,4

0,6

Qr

0

Pg-

0

mecΩ

4

6

8

10

12

14

16

0

vwind

Fig. 1. Proposed system.

S. Taraft et al. / Energy Conversion and Management 101 (2015) 489–502 491

Pwind ¼12q � p � R2 � v3

wind ð1Þ

where q is the air density, R is the blade length and vwind the windvelocity.

The turbine converts some of the recoverable power to an aero-dynamic power on the rotating shaft which is given by [24,25]:

Pmec ¼12q � p � R2Cp k; bð Þ � v3

wind ð2Þ

where Cp is the power coefficient of the turbine, k is tip speed ratio(TSR) and b is the blade pitch angle.

In this case, the blade pitch angle b is set zero, so the variation ofthe power coefficient Cp is considered as function of the tip speedratio k (Fig. 2).

The aerodynamic torque of the turbine is defined by the ratio ofmechanical power to the rotational speed of the blades [25].

Tt ¼Pmec

Xtð3Þ

Therefore, the mechanical torque from the gearbox applied tothe generator shaft is connected to the aerodynamic torque withthe following expression [25]:

Tg ¼Tt

Gð4Þ

3 3,5 4 4,5 5 5,5 6 6,5 7 7,50,38

0,40,42

0,440,46

0,480,5

0.52

Tip speed ration λ

Pow

er c

oeffi

cien

t (C p

)

Fig. 2. Power coefficient for the wind turbine model.

where G is gearbox.

3.1.2. DFIG modelingThe Park transformation applied for the electrical equations of

the DFIG [26,36] where the reference is related to the rotating fieldallows us to achieve the following electrical system equations:

v sd ¼ Rsisd þ dusddt �xsusq

v sq ¼ Rsisq þdusq

dt þxsusd

v rq ¼ Rrird þ durddt � ðxs �xÞurq

v rq ¼ Rrirq þdusq

dt þ ðxs �xÞurd

8>>>>>>><>>>>>>>:

ð5Þ

The flux equations written in d–q reference frame are:

usd ¼ Lsisd þ Lmird

usq ¼ Lsisq þ Lmirq

urd ¼ Lrird þ Lmisd

urq ¼ Lrirq þ Lmisq

8>>><>>>:

ð6Þ

The mechanical equation is given by:

Tem ¼ Tr þ JdXmec

dtþ fXmec ð7Þ

The electromagnetic torque Tem can be written as follow:

Tem ¼ PLm

Lsusqird �usdirq

� �ð8Þ

The active and reactive power stator and rotor are expressed by:

Ps ¼ vsdisd þ v sqisq

Q s ¼ v sqisd � vsdisq

Pr ¼ v rdird þ v rqirq

Q r ¼ v rqird � v rdirq

8>>><>>>:

ð9Þ

The stator and rotor angular velocities are linked by the follow-ing relation:

xs ¼ xþxr

492 S. Taraft et al. / Energy Conversion and Management 101 (2015) 489–502

where

xs: Stator angular speed (rad/s).xr: Rotor angular velocity (rad/s).x: Angular speed (rad/s).

The active and reactive powers of the DFIG are expressed by:

Pg ¼ Pr þ Ps

Q g ¼ Q rg þ Q s

�ð10Þ

where

Qrg: Reactive power from the converter grid side.Qg: Reactive power injected into the grid.Qs: Reactive power of the stator.

The matrix converter (MC) offers the possibility of controllingthe input power factor [26–30]. In this work, the grid is assumedstable. Therefore, to improve the efficiency of the wind power gen-erator, the stator reactive power is maintained at zero value.

3.2. Matrix converters modeling

The MC is an AC/AC converter which converts input line voltageinto variable voltage with unrestricted frequency without using anintermediate storage unit [27]. This is achieved by a matrix of ninepower switches connecting each input phase (a; b; cÞ to each outputphase (A;B;CÞ. It is recommended to close only one switch in eachgroup to avoid short-circuiting the source. Similarly, the converteroften feeding an inductive load, the opening of all the switches inthe same group causes high voltages that can damage the circuit[31]. The simplified three phases- three phases MC topology incor-porated in system of wind generator is shown in Fig. 3. The matrixconverter is modeled by its output voltages and input currents interms of switching functions which are expressed by the followingmatrices:

Matrix con

bn

va

vb

vc

a

c

ia

ib

ic

Side-1Input system frequency

fi

Fig. 3. Matrix

vAðtÞvBðtÞvCðtÞ

264

375 ¼

SaAðtÞ SbAðtÞ ScAðtÞSaBðtÞ SbBðtÞ ScBðtÞSaCðtÞ SbCðtÞ ScCðtÞ

264

375

vaðtÞvbðtÞvcðtÞ

264

375 ð11Þ

iaðtÞibðtÞicðtÞ

264

375 ¼

SaAðtÞ SaBðtÞ SaCðtÞSbAðtÞ SbBðtÞ SbCðtÞScAðtÞ ScBðtÞ ScCðtÞ

264

375

iAðtÞiBðtÞiCðtÞ

264

375 ð12Þ

General form of the switching pattern is shown in Fig. 4.The connection function that describes the logic state of each

switch [32] is:

SijðtÞ ¼ 1 if the switch Tij is closed:SijðtÞ ¼ 0 if the switch Tij is open:

where i 2 fa; b; cg; j 2 fA;B;Cg.In order to avoid short-circuited input terminals and

open-circuited output phases, these switching functions shouldsatisfy the following constraint equation:

Saj þ Sbj þ Scj ¼ 1 ð13Þ

Several techniques are published for switching the MC. In ourcase, we have adopted for the indirect vector modulation whichoffers better performances [33,34].

Vector modulation for matrix converter describes a fictionalequivalent circuit combining two stages, inverter and rectifierstage, which are linked by a fictional DC voltage VDC (Fig. 5(a)).

The space vector rectifier current is seen Fig. 5(b). Fig. 5(c)shows the vectors that the output inverter can form by applyingthe DC-link voltage to the output terminals.

I�I ¼ 23 ðIa þ aIb þ a2IcÞ

V�o ¼ 23 ðVa þ aVb þ a2VcÞ

(ð14Þ

The position of the reference vectors, voltages and currentsV�o; I�I respectively, in the space phasor, allows the switchingsequences generation [35].

N

verter

VB

VA

VC

ScB

SaC

SbC

ScC

SaA

SbA

ScA

SaB

SbB B

iA

iB

iC

C

A

Side-2Output system frequency

fo

converter.

SaA=1 SbA=1 ScA=1

ScB=1SbB=1SaB=1

SaC=1 SbC=1 ScC=1

taA tbA tcA

tcBtbBtaB

taC tbC tcC

Output phase A

Output phase B

Output phase C

RepeatsTseq (Sequence time)

Fig. 4. General form of the switching pattern.

VB

VC

VA va

vc

vb iA

iB

iC

ia

ib

ic

Nn

S1 S3 S5 S7 S9 S11

S2 S4 S6 S8 S10 S12

Side-2Output system frequency

fo

Side-1Input system frequency

fi

0

VDC

VDC+ IDC

+

VDC--

IDC--

(a)

(b)

I2 (ac)

I3 (bc)

I4 (ba)

I5 (ca)

I6 (cb)

I1 (ab)

II*

1d Iγ

2d Iδ

cθ

(c)

V2 (110)V3 (010)

V4 (011)

V5 (001)

V1 (100)

V6 (101)

V0*

Vθ2d VΒ

1d Vα

Fig. 5. Indirect matrix converter. (a) Indirect matrix converter circuit. (b) Rectifier current hexagon. (c) Inverter voltage hexagon

S. Taraft et al. / Energy Conversion and Management 101 (2015) 489–502 493

3.3. Control power of WECS

3.3.1. Determination of the turbine reference valuesAs already mentioned, in the region of stable operation, the

optimal reference values of the power ðPmec optÞ have to be injectedinto the grid and the rotational speed of the turbine (Xmec optÞ on

the input shaft will be determined by the optimization algorithmbased on the Perturbation and Observation (P&O) method (Fig. 6).

Optimal power reference to inject in the grid is determined asfollows:

pg ref ¼ �g � pmec opt ð15Þ

494 S. Taraft et al. / Energy Conversion and Management 101 (2015) 489–502

Mechanical speed reference is maintained equal to the optimalmechanical speed

Xmec ref ¼ Xmec opt ð16Þ

The rate power of the considered machine is 1.5 MW, the ironlosses and mechanical losses are neglected, the DFIG efficiency isestimated to 95% and the converter losses are supposed neglected.The developed operating principle can be illustrated by Fig. 7.

3.3.2. Stator flux oriented controlBy choosing a diphase reference frame d–q related to the stator

spinning field pattern and aligning the stator vector flux with theaxis d, we can write [31]

Zone I

No

No

yes

yes

No

∆Tt(k)= Tt(k)-Tt(k-1)

em t(k)T (k) T (k) J

t(k)ΔΩ= −Δ

∆Tem(k)= Tem(k)-Tem(k-1)

emT 0Δ >

Tem(k+1) = Tem(k)+∆TTem(k+1) = Tem(k)-∆T

yes

N(k)Ω ≤ Ω

P(k)=Tt(k).

Pmec_opt

Start algorithm

Initialization Tt0 , Ω0 , t0, ΩN

T(k)Δ ≤ ε

Tem(k+

∆Ω(k)= Ω(k)-Ω(k-1)

∆t(k)= t(k)-t(k-1)

Measure Tt(k), Ω(k),t(k)

Fig. 6. Flowchart of the op

usd ¼ /s

usq ¼ 0

(ð17Þ

For high and medium wind power, the voltage drop across thestator resistance can be neglected, so we can obtain the stator volt-ages and fluxes as follows:

vsd ¼ 0; v sq ¼ Vs ¼ xs/s

usd ¼ /s ¼ Lsisd þ Lmird; urd ¼ Lrird þ Lmisd

usq ¼ 0 ¼ Lsisq þ Lmirq; urq ¼ Lrirq þ Lmisq

8><>: ð18Þ

The torque expression Eq. (8) can be rewritten by the Eq. (19)which depends only on the component irq

Zone II

No

yes

NoN(k) 2Ω ≤ Ω

mec _ optΩ

Nem tT (k 1) T+ − ≤ ε

Pitch control

Ω(k)

,TtN

em t(k)T (k) T (k) J

t(k)ΔΩ= −Δ

∆Tem(k)= Tem(k)-Tem(k-1)

emT 0Δ >

Tem(k+1) =Tem(k)+∆T1) = Tem(k)-∆T

yes

yes

No

mec _ optΩ

timization algorithm.

0 50 100 150 200 250 300 350-4

-3

-2

-1

0

1

Ωmec (rad/s)

3 MW

1.5MW

Zone I Zone II

C Cp pmax

opt

T Tt tN

=

λ=λ

<

C Cp pmax<

; T =Topt t tNλ > λ

PrPs Pg

NΩN2Ω

Sub-synchronous Super-synchronous Po

wer

(MW

)

Fig. 7. Power flow of the studied system.

S. Taraft et al. / Energy Conversion and Management 101 (2015) 489–502 495

Tem ¼ �PLm

Ls/sirq ð19Þ

By using Eqs. (9), (10) and (18), the active, reactive stator power andthe rotor voltages can be written as follow:

Ps ¼ �VsLmLs

irq

Pr ¼ �sPs

Q s ¼ V2s

xsLs� Lm

Lsird

Pg ¼ �VsLmLsð1� sÞirq

8>>>><>>>>:

ð20Þ

Vrd ¼ Rrird þ Lr � L2m

Ls

� �dirddt � sxs Lr � L2

mLs

� �irq

Vrd ¼ Rrirq þ Lr � L2m

Ls

� �dirq

dt þ sxs Lr � L2m

Ls

� �ird þ s LmVs

Ls

8><>: ð21Þ

where s is the slip of DFIG.The rotor current can be expressed by:

dirddt ¼ 1

Lrr Vrd � Rrird þ sxsLrrirq� �

dirq

dt ¼ 1Lrr Vrq � Rrirq � sxsLrrird � s LmVs

Ls

� �8<: ð22Þ

r ¼ 1� L2m

LrLs

where r is the leakage coefficient.

3.3.3. Sliding mode controlSliding mode is a variable structure control technique devel-

oped to solve the drawbacks of the nonlinear other designs controlsystem. It is based on adjusting feedback by previously defining asurface. The controlled system will be forced to that area and thenthe system operating point will slide to the desired equilibriumpoint. To this end, we only need to drive the error to be in theswitching surface. The system driven by sliding mode, its behavioris not affected by any modeling uncertainties and/or disturbances.In the following, the design of the control system will be presentedfor a nonlinear system presented in the state form:

_x ¼ f ðx; tÞ � Uðx; tÞ; x 2 Rn; U 2 Rm; ranðBðx; tÞÞ ¼ m ð23Þ

The aim of the control with sliding mode is to keep the systemmotion on the area S, which is defined as:

S ¼ x : eðx; tÞ ¼ 0f ge ¼ xref � x

�ð24Þ

where e is the tracking error vector, xref is the desired state and x isthe state vector. The control input value (UÞ is defined to guaranteethat the motion of the system described in (20) is restricted tobelong to the area S in the state space. The Lyapunov function forthe sliding mode control should be chosen to satisfy the Lyapunovstability criteria:

V ¼ 12

SðxÞ2 ð25Þ

_V ¼ SðxÞ � _SðxÞ ð26Þ

This can be assured for:

_V ¼ �djSðxÞj ð27Þ

It is to note that is strictly positive. Principally, Eq. (25) states

that the squared ‘‘distance’’ to the surface, measured by eðxÞ2,decreases along all system trajectories. Therefore, Eqs. (26) and(27) satisfy the Lyapunov condition. The selected Lyapunov func-tion guaranteeing the stability of the whole control system andhas the following form:

U ¼ Ueq þ Un ð28Þ

With U is the control vector, Ueq is the equivalent control vector andUn is the correction factor calculated so that the stability conditionsfor the selected control are satisfied.

Un ¼ k � satðS xð ÞÞ ð29Þ

where satðSðxÞÞ is the saturation function and k is the controllergain.

The method in [37] is adopted for the switching surface func-tion to ensure the convergence of the: state variable x to its refer-ence value xref .

vrq_ref

vrd_ref

Pg

Qs_ref

irq

+_

Rr

s r

s m

L LV L

σ

KrdSAT(S(P))

Rr

Krq

dd

ird

dd t

_Qs

SAT(S(Q))+

Pg_ref

_

s r

s m

L LV L

σ

1

s

_

s rLω σird

m

s

L VL

+

+

+

+

-

-

+

+

s rLω σirq

+

Fig. 8. Block diagram of SMC.

θ

vrq

Electrical Grid

DFI

G d

ynam

ic m

odel

in P

ark’

s ref

eren

ce

Qs_ref

v rq_r

ef

v rd_r

ef

vrd

θ

Pg_ref

vwind

T tP m

ec_o

pt

Ωm

ec

OptimizationProgram

Wind Turbine

P − η

∫

2/3

Mat

rix

Con

vert

er

var

vbr

vcr

3/2

var_ref

θ

Ωm

ec_o

pt

Sliding Mode

Controller

(SMC)

Eqs (36, 37)

(See Fig.8)

Pg

Qs

ird

irq

s

vbr ref

vcr ref

Pg

Qs

ird

irq

Fig. 9. Block diagram of the proposed system.

496 S. Taraft et al. / Energy Conversion and Management 101 (2015) 489–502

SðxÞ ¼ ddtþ f

� �n�1

e ð30Þ

where e is the tracking error vector, f is a positive coefficient and nis the relative degree.

3.3.4. The DFIG controlThe active and reactive power errors are respectively defined

as:

SðPÞ ¼ Pg ref � Pg

SðQÞ ¼ Q s ref þ Q s

�ð31Þ

The first order derivate of Eq. (31), gives:

_SðPÞ ¼ _Pg ref � _Pg

_SðQÞ ¼ _Qs ref þ _Q s

(ð32Þ

Replacing the powers in Eq. (32) by their expressions given inEq. (20), we obtained:

tT

mecΩ

NtT

MaxtT

mec opt_Ω

tT0

Δ>

ΔΩ

N2.Ω

Zone I

tT0

Δ<

ΔΩ

Zone II

Fig. 10. Torque curves according to the rotational.

0 10 20 30 40 50 60 70 80 90 1004

6

8

10

12

14

16Vwind

v win

d (m

/s)

time (s)

Fig. 11. Wind speed profile.

0 10 20 30 40 50 60 70 80 90 100100

200

300

400

500

600

700

time (s)

Ω me

c(r

ad/s

)

Fig. 12. Random of the DFIG rotor.

S. Taraft et al. / Energy Conversion and Management 101 (2015) 489–502 497

_SðPÞ ¼ _Pgrefþ Vs

LmLsð1� sÞ_irq

_SðQÞ ¼ _Q s ref þ VsLmLs

_irq

8<: ð33Þ

Replacing the currents in Eq. (33) by their expressions given inEq. (22), we obtain:

_SðPÞ¼ _PgrefþVs

LmLsLrrð1� sÞ Vrq�Rrirq� sxsLrrird� sLmVs

Ls

� �_SðQÞ¼ _Q sref

þVsLm

LsLrrðVrd�Rrirdþ sxsLrrirqÞ

8<: ð34Þ

And replacing the voltages Vrdq by Vrdqeq þ Vrdqn, the Eq. (34)became:

0 10 20 30 40 50 60 70 80 90 1000

0,5

1

1,5

2

2,5

3

3,5Pmec

P mec

(MW

)

�me (s)

Fig. 13. Turbine mechanical Power.

100 200 300 400 500 600 7000

0,5

1

1,5

2

2,5

3

3,5

P mec

(MW

)

Ωmec (rad/s)

Fig. 14. Turbine mechanical power-rotational speed.

498 S. Taraft et al. / Energy Conversion and Management 101 (2015) 489–502

_SðPÞ¼ _Pg ref þVsLm

LsLrrð1� sÞ VrqeqþVrqn�Rrirq� sxsLrrird� sLmVsLs

� �_SðQÞ¼ _Qs ref þVs

LmLsLrrðVrqeqþVrqn�Rrirdþ sxsLrrirqÞ

8<:

ð35Þ

During the sliding mode and in permanent mode we have:

SðPÞ ¼ 0; SðQÞ ¼ 0; _SðPÞ ¼ 0; _SðQÞ ¼ 0; Vrdn ¼ 0; Vrqn ¼ 0

We obtain equivalent control Vdqeq by using Eq. (35):

Vrdeq ¼ � _Qs refrLr LsVsLmþ Rrird � sxsLrrirq

Vrqeq ¼ � _Pg refrLr LsVsLm

11�sþ Rrirq þ sxsLrrird þ s LmVs

Ls

(ð36Þ

To obtain good performances, dynamic and commutationsaround the surfaces, the control vector applied as follows:

0 10 20 30 400.38

0.4

0.42

0.44

0.46

0.48

0.5

0.52

�m

Cp

0 1 20.498

0.5

30 33 36 400.498

0.5

1 1

2 2

1-zone I

2-zone II

Fig. 15. Power

Vrd ¼ Vrdeq þ Vrdn ¼ Vrdeq þ krd � satðS Pð ÞÞVrq ¼ Vrqeq þ Vrqn ¼ Vrqeq þ krq � satðS Qð ÞÞ

�ð37Þ

The sliding mode will exist only if the following condition isverified:

S � _S < 0 ð38Þ

The block diagram of SMC applied in our system is illustrated inFig. 8.

3.3.5. Control of the proposed systemThe block diagram of the studied system is shown in Fig. 9.

3.3.6. Description of P&O method

Zone I: the maximum torque of the turbine is less than thenominal torque DTt

DX .The search for the maximum points depends on whether thequantity DTt

DX is positive or negative. We increase or decreaserespectively the electromagnetic torque by acting on the cur-rent (see Eq. (19)). It results respectively an increase or adecrease of the rotational speed. The change of the quantitysign DTt

DX, provide us information about the zero crossing whichcorresponds to the desired point (Fig. 10).Zone II: The maximum torque of the turbine is greater than thenominal torque.

The search for the optimal point is determined by operating theturbine at its nominal mechanical torque. For this, we compare the

50 60 70 80 90 100

e (s)

85 90 95 1000.498

0.5

1 1

2

coefficient.

2

0 10 20 30 40 50 60 70 80 90 1004,5

5

5,5

6

6,5

7

7,5

time (s)

λ

2-zoneII

1 1 1 1 2 2

1-zoneI

Fig. 16. Speed tip ratio.

5 5,5 6 6,5 7 7,50,38

0,4

0,42

0,44

0,46

0,48

0,5

0,52

Cp

λ

Fig. 17. Power coefficient versus tip speed ratio.

S. Taraft et al. / Energy Conversion and Management 101 (2015) 489–502 499

torque of the turbine to the rated nominal torque as follows(Fig. 10).

Depending on whether the difference between the turbine tor-que and the nominal torque. We increase or decrease respectivelythe electromagnetic torque by acting on the current (see Eq. (19)).The desired value is obtained when the absolute difference is lessthan or equal to the desired accuracy.

The advantage of this method is that, it does not require knowl-edge of the mechanical characteristic of the turbine and the speedof the desired point [24]. However, its disadvantage lies in theoscillation around the desired value.

4. Simulation results and discussion

The dynamic behavior of the wind generator connected to astable grid is shown in Figs. 11–25. The simulation is carried out

100 200 300 402

3

4

5

6

7

8

9

10

T t(k

N.m

)

Ωmec (

ZoneI

Fig. 18. Turbine torque

by using Matlab/Simulink package and the parameters of DFIGand the wind turbine are respectively given in Tables 1 and 2.

Powers exchanged between the grid and the generator areobtained by stator flux orientation. The simulation results areobtained by forcing to zero the reactive power of the stator andthe rotor side of the grid. The reference for the active powerinjected into the grid is determined by an optimization program.The speed wind profile chosen is represented in Fig. 11.

Fig. 12 depicts the variation range of the DFIG mechanical rota-tion speed.

The mechanical power evolution as a function of time and therotational speed is illustrated in Figs. 13 and 14 respectively.Note that powers recovered in the operating modesub-synchronous and super-synchronous are nonlinear and linearfunctions respectively.

Power coefficient ðCpÞ and tip speed ratio (k) evolutions areshown in Figs. 15 and 16 respectively. In sub synchronous mode,Cp fluctuates around its maximum value 0.5 while tip speed ratiofluctuates around its optimal value 5. In super synchronous mode,Cp decreases to its minimum value, and tip speed ratio increases toits maximum value.

Fig. 17 shows clearly the evolution of the power coefficient ver-sus the specific speed.

The torque on the DFIG shaft is variable in the sub-synchronousoperation and is limited to its nominal value in the operating areaof super-synchronous (Figs. 18 and 19).

Fig. 20 illustrates the reactive rotor power, and which dependson the sign of the slip (Fig. 21).

In Fig. 22, we have presented the rotor and stator active powerinjected to the grid which follows their references. Fig. 23 repre-sents the stator reactive power injected to the grid.

0 500 600 700

rad/s)

Zone II

–rotational speed.

time (s)

T em

(KN

m)

0 10 20 30 40 50 60 70 80 90 100

-14

-12

-10

-8

-6

-4

-2

0

2

2 1 2

1 : zone I2 : zone II

1

1Tem

Fig. 19. DFIG electromagnetic torque.

0 10 20 30 40 50 60 70 80 90 100-0.4

-0.2

0

0.2

0.4

0.6Qr

time (s)

Qr(

MVA

R)

Fig. 20. DFIG rotor side reactive power.

0 10 20 30 40 50 60 70 80 90 100

-1

-0,8

-0,6

-0,4

-0,2

0

0,2

0,4

0,6S

s

�me (s)

Fig. 21. DFIG slip.

0 10 20 30 40 50 60 70 80 90 100-3,5

-3

-2,5

-2

-1,5

-1

-0,5

0

1Ps Pr Pg Pg ref

time (s)

P r (M

W);

Ps (

MW

); P

g (M

W)

Fig. 22. Stator, rotor and grid actives powers.

500 S. Taraft et al. / Energy Conversion and Management 101 (2015) 489–502

0 10 20 30 40 50 60 70 80 90 100-0.25

-0.2-0.15

-0.1-0.05

00.050.1

0.150.2

0.25

Qs(M

Var)

time (s)

Qs

Fig. 23. Stator reactive power.

0 10 20 30 40 50 60 70 80 90 100-10

-8

-6

-4

-2

0

2

4

70.47 70.5-2

0

2

30 30.2-2

0

2

6 6.50

1.2

IarVar

�me (s)

V ar(k

V); I

ar(k

A)

synchronous sub-synchronous super-synchronous

Fig. 24. Rotor voltage and current.

0 10 20 30 40 50 60 70 80 90 100-10

-8

-6

-4

-2

0

2

4Ig0.5*Vg

2 2,03-2

0

2

30 30,03-202

75 75,03-202

time (s)

0.5*

V g(k

V); I

g(k

A)

super-synchronous sub-synchronous synchronous

Fig. 25. Grid voltage and current.

Table 1Wind generator parameters.

Parameters Values

Nominal power 1.5 MWNominal voltage 690 VStator resistance (RsÞ 0.012 XRotor resistance (RrÞ 0.021 XStator (LsÞ and rotor (LrÞ inductance 0.0137 HMagnetizing inductance (LmÞ 0.0135 HNumber of pole pair (PÞ 2Friction coefficient (f Þ 0.0071 N m s/rad

Table 2Wind turbine parameters.

Parameters Values

Radius (R) 36.5 mOptimal tip speed ratio kopt 5Number of blades 3Total inertia (Turbine + DFIG), J 500 kg m2

S. Taraft et al. / Energy Conversion and Management 101 (2015) 489–502 501

Fig. 24 represents the voltage and current of a rotor phasewhich are plotted corresponding to the operating modesub-synchronous, super-synchronous and near synchronousrespectively. Fig. 25 shows the grid side voltage and current, thesetwo values are in the opposition phase.

5. Conclusion

In this paper, the optimization of extracted power from a windenergy conversion system is presented. The solution is based onthe exploitation of the power generated by the rotor in super syn-chronous mode. In this case, we have suggested to fix the turbinetorque at its nominal value, leaving the rotor speed and powerincrease simultaneously. So the rotor speed and the total powercan reach twice their nominal values. Using a fast and reliable fullyrugged electrical control, we were able to control all the powersinvolved in such a system while maintaining stator reactive powerat zero value and ensuring unity power factor at the input ofmatrix converter. After the application of the proposed strategy,

502 S. Taraft et al. / Energy Conversion and Management 101 (2015) 489–502

we have shown on one hand, through the different simulationresults, the proper functioning of the system in sub synchronousand super synchronous modes. Furthermore, it was shown thatthe stator active power fluctuates around its nominal value alongthe super synchronous period, while the rotor active power varieslinearly and actually reaches its nominal value when the rotationalspeed reaches twice its nominal value. On another hand, it was alsoshown that in sub synchronous mode, the power coefficient fluctu-ates around its maximum value while tip speed ratio fluctuatesaround its optimal value. In super synchronous mode, the powercoefficient decreases to its minimum value and tip speed ratioincreases to its maximum value. This allows stable operation ofthe system. The power injected into the grid follows perfectly thereference calculated by the optimization program. The overallresults concerning the operation previously known as well as thoserelated to the strategy of optimizing the power extracted from awind energy conversion system proposed are of assured qualityto justify the reliability of the study in this work.

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