Research ArticlePower Extraction Control of Variable Speed Wind TurbineSystems Based on Direct Drive Synchronous Generator in AllOperating Regimes

Youssef Errami ,1 Abdellatif Obbadi,1 Smail Sahnoun,1

Mohammed Ouassaid,2 andMohamedMaaroufi2

1Laboratory of Electronics, Instrumentation and Energy, Team of Exploitation and Processing of Renewable Energy,Department of Physics, Faculty of Science, Chouaib Doukkali University, El Jadida, Morocco2Department of Electrical Engineering, Mohammadia School of Engineers, University Mohammed V, Rabat, Morocco

Correspondence should be addressed to Youssef Errami; errami.emi@gmail.com

Received 10 January 2018; Accepted 18 March 2018; Published 20 May 2018

Academic Editor: Andrea Bonfiglio

Copyright © 2018 Youssef Errami et al.This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Due to the increased penetration of wind energy into the electrical power systems in recent years, the turbine controls are activelyoccupied in the research. This paper presents a nonlinear backstepping strategy to control the generators and the grid sides ofa Wind Farm System (WFS) based Direct Drive Synchronous Generator (DDSG). The control objectives such as Tracking theMaximum Power (TMP) from the WFS, pitch control, regulation of dc-link voltage, and reactive and active power generation atvaryingwind velocity are included. To validate the proposed control strategy, simulation results for 6-MW-DDSGbasedWind FarmSystem are carried out by MATLAB-Simulink. Performance comparison and evaluation with Vector Oriented Control (VOC) areprovided under a wide range of functioning conditions, three-phase voltage dips, and the probable occurrence of uncertainties.Theproposed control strategy offers remarkable characteristics such as excellent dynamic and steady state performance under varyingwind speed and robustness to parametric variations in the WFS and under severe faults of grid voltage.

1. Introduction

In the past decades, various renewable energy sources havereceived increasing attention as alternatives of fossil fuels [1,2]. Among various modern renewable resources, wind poweris considered the backbone of renewable power generation. Itis regarded as a clean energy resource and it is easily acces-sible and cost effective. So, wind power penetration greatlyincreases in the electric power systems and it is anticipatedto keep steady growth in the upcoming years [3, 4]. On theother hand, in modern wind power systems, three of themost promising types of wind turbine generators are theDoubly Fed Induction Generator (DFIG), the Direct DriveSynchronous Generator (DDSG) with permanent magnet,and the Squirrel Cage Induction Generator (SCIG) [5–12].But, the main advantage of DDSG is the absence of gearboxcoupling the wind turbine to the DDSG and the dc externalexcitation current. So, during the past few years direct driven

DDSGs become very attractive in wind energy applicationbecause of their high power density, flexible magnet topolo-gies, reducedmaintenance, high effectiveness, high operatingefficiency, excellent operation performance, and increasedreliability [13–19]. In the area of wind power generationtechnology, Variable Speed Wind Power Generation System(VS-WPGS) has many advantages over fixed speed onessuch as better power quality, higher overall efficiency, lowermechanical stress, and increased energy capture. So, it can becontrolled to enable the turbine to operate at its maximumcoefficient of power and to ensure the Maximum PowerTracking (MPT) ability [20–22]. To control the VS-WPGSbased DDSG, full scale power electronic converter systemsare generally used as the interface between the VS-WPGSand the electrical network for satisfying the new standardsand grid connection requirements [23, 24]. Thus, they allowcontrolling the wind turbine system, decoupling the DDSGfrom the power grid, and the VS-WPGS does not need to

HindawiJournal of Electrical and Computer EngineeringVolume 2018, Article ID 3837959, 17 pageshttps://doi.org/10.1155/2018/3837959

2 Journal of Electrical and Computer Engineering

Turbine

DDSGAC

DC

DC

AC

FilterGrid

PWMPWM

Pitch angleGrid

operatorcontrol system

Power/SpeedController

Wind turbine control level

Grid Side Controller

Rotor Side Controller

IＡ？Ｈ

s

PＬ？＠ QＬ？＠

QＬ？＠

U＞＝

U＞＝

IＡＬＣ＞

UＡＬＣ＞

U＞＝-Ｌ？＠

PＬ？＠-ＡＬＣ＞

PＧ？；Ｍ

Figure 1: Configuration of a VS-WPGS based DDSG.

synchronize its rotational speed with the electrical networkfrequency [25].Thus, VS-WPGS is able to attain high efficacyand performance when connected to the electrical network,not only under normal working conditions but also underirregular and faulty network conditions. Figure 1 illustratesthe general control structure for VS-WPGS. This consistsof a DDSG side and a grid side inverter interconnectedthrough a dc-link system. So, at the DDSG sides, the speedis controlled to ensure the MPT. The grid side converter isemployed to regulate the dc-link voltage for a proper transferof power [13, 19, 26, 27]. Also, the inverter system oughtto have the ability to regulate reactive and active powerthat the VS-WPGS exchange with the electrical network andattain unity power factor (UPF) of total system [28]. Variouspower electronic device configurations were presented in theliterature for VS-WPGS based DDSG [29–31]. On the otherhand, to increase the annual energy yield of VS-WPGS, MPTcontrol is essential under the rated wind velocity. Then, bychanging the rotor velocity of DDSG according to the varyingwind velocity, maximum power is extracted from availablewind [21, 22, 32, 33].

Also, variable speed wind turbines frequently employpitch control system, either active stall or pitch to feather, toreduce the aerodynamic power captured [34, 35].

According to Fault Ride-Through (FRT) requirements,during faults of grid voltage, theWFSmust remain connectedto the electric network. As an example, Figure 2 presents adiagramof the FRT requirements in some countries. So, theserequirements present a considerable challenge to the well-establishedWFS technologies and their control [36]. Besides,developing effective control approaches WFS will improvethe system availability to extract as much power from thewind as possible whereas it is available. On the basic aspect,Vector Oriented Control (VOC) is widely used because of itssimple control configuration, ease of design, and economical

cost. In [37, 38], control strategy has been developed forintegrated control of wind turbine based PMSG. The works[39, 40] have presented LowVoltage Ride-Through (LVRT) ofWECS. But, this technique cannot offer satisfactory controlperformance if the controlled system is highly nonlinearand uncertain. Moreover, it generally works at particularoperating range and it is obligatory to retune the controller ifthe operating range is modified, whereas the WFS is usuallyaffected by varying the operating condition and outsidedisturbance.

To overcome the above problems, Direct Control Tech-niques (DCT) were proposed to substitute the VOC strategyfor both rectifier systems and electrical network connectioncontrol. Direct power control (DPC) and Direct TorqueControl (DTC) of a three-phase converter for fault tolerantDDSG drive were proposed in [29]. The works [19, 41]have proposed TMP algorithm using DTC for DDSG windturbines. The most important advantages of DCT strategiesinclude low sensitivity to the accuracy ofWFS parameter esti-mation, rapid dynamic response, and easy implementationand they do not necessitate space vector modulation (SVM).But, they can suffer from high torque ripple and variableswitching frequency of the power electronic converters andtheir performances deteriorate at low speed.

On the other hand, modern WFS necessitate efficientand supple technologies that adapt to modifications in loadand generation. Also, in order to increase the availabilityand reliability of WFS, effective strategies are consideredcrucial means to achieve these goals and to improve theelectrical network connected operation capability. Recently,backstepping control approach has received worldwide atten-tion due to its systematic and recursive design methodologyfor nonlinear control [42]. The stabilization of a virtualcontrol state is the fundamental idea of the backsteppingalgorithm. This nonlinear control method is principally

Journal of Electrical and Computer Engineering 3

Volta

ge (%

)

must remainconnected

DenmarkDS & TS

Italy

(msec)

–DS<30 kV

100

90858075

50

252015

750625150

30002000150012001000700500100

GermanyTS

HydroQuebec

IrelandIreland

- DS

SpainTS

GBTS

US- FERC&

AESO AlbertaTS

Figure 2: National grid codes [36].

interesting due to its capacity to design adaptive controllersfor nonlinear systems and to analyze the problem of stability.The advantages of backstepping control are related to theemployment of the Lyapunov functions to ensure the robust-ness and stability of the system, consequently enhancing theperformance of system [43]. Also, because of the flexibilityto avoid cancellations of suitable nonlinearities and attainthe objectives of tracking and stabilization, the backsteppingapproach has been generally applied in control systems. In thework of [44] backstepping control is developed to deal withthe Tracking the Maximum Power (TMP) from the WFS.The work of [45] presents a backstepping control strategy todesign a permanent magnet liner synchronous motor servodrive system with uncertainty. Wai et al. [46] proposed thebackstepping design for a grid-connected inverter. Ruan etal. [47] proposed an adaptive control strategy using backstep-ping technique for the Voltage Source Converter (VSC) basedHigh Voltage dc (HVDC) system to develop its dynamicperformance.The idea of backstepping approach is to chooserecursively some suitable functions of state variables likepseudo-control inputs for lower dimension subsystems of theentire system. The most attractive point of this technique isto employ the virtual control variable to create the originalhigh order system simple. It decomposes a difficult controlproblem into simpler ones and it chooses recursively suitablefunctions of state variables which are the virtual controlvariables. Each backstepping step results in a novel virtualcontrol to deal with a decomposed subsystem problem. So,this virtual control becomes a reference to the next algorithmstep for another subsystem. Also, it produces a related errorvariable that can be stabilized by carefully choosing propercontrol inputs which can be determined using Lyapunovstability analysis [43]. When the procedure is finished, atrue control input for the original control objectives can begenerated by summing up the Lyapunov functions associatedwith each individual design step [48].

This study presents a backstepping control design for theWFS using PMSG, connected to the electrical network. So, abackstepping scheme is developed in the sense of Lyapunovstability theorem to ensure the control objectives of Trackingthe Maximum Power (TMP) from the WFS, pitch control,regulation of dc-link voltage, and reactive and active powergeneration at varying wind velocity. In the first place, mathe-matical model ofWFS is described. In the meanwhile, designof the backstepping technique is provided. Then, simulationstudies usingMATLAB/Simulink are carried out in Section 3.Finally, some conclusions are summarized in Section 4.

2. Description of the Proposed WFS

This section describes the proposed wind energy conversionsystem using DDSG and presents its modelling and controlstrategies.

2.1. System Description. The schematic diagram of the grid-connected DDSG-WTS is shown in Figure 3. It is composedof three wind turbines directly linked to DDSGs connectedto the grid throughout a converter, which consists of a gridside inverter (GSI) and a generator-side rectifier (MSR). TheMSR control theDDSGs to extract themaximumpower fromthe wind [49]. The GSI sustains a constant dc-link voltageand controls the active and reactive power that the WTSexchanges with the electrical power.

So, the converters allow adapting frequencies and voltagesbetween the DDSG terminals and the grid.

2.2. Wind Turbine Characteristics. According to aerodynam-ics, the maximum power extracted by the rotor blades isexpressed as [50]:

𝑃𝑤-max = 12𝜌𝑤𝜋𝐴2𝑟𝑤𝐶𝑤-max (𝜆𝑤-𝑚, 𝛽𝑤) V3𝑤, (1)

4 Journal of Electrical and Computer Engineering

Elec

tric

Grid

Bus 5 Bus 6

Bus 3

Bus 2

Transmission

Load 2

Load 3

Fault

Bus 4DDSG1

Bus 1

Load 1

DDSG2AC

AC

AC

DC

DC

DC

Nonlinear Backstepping Control

DDSG3AC

DC

20kV/60 kV

1 km

1 km1 km

1 km

P2 = 1 MW

P3 = 100 KWP1 = 100 KW

380 V/22 kVYn YN

Figure 3: Configuration of the VS-WFS.

×106

Maximum power point

V1

V2

V3

V4

Vn

0

0.5

1

1.5

2

2.5

Pow

er (W

)

1 2 3 4 50

Wind generator speed (rd/s)

Figure 4: Wind turbine power curves at different values of windspeed.

where 𝜌𝑤 is the air density, 𝐴𝑟𝑤 is the rotator radius, V𝑤 isthe speed of wind, 𝜆𝑤-𝑚 is the optimal tip speed ratio (TSR),𝐶𝑤-max(𝜆𝑚, 𝛽𝑤) is the maximum value of the performancecoefficient of the turbine, and 𝛽𝑤 is the blade pitch angle.Thetip speed ratio 𝜆𝑤 is determined by the rotor speed𝜔𝑟 and thewind speed as

𝜆𝑤 = 𝜔𝑟𝐴𝑟𝑤V𝑤

. (2)

So, an efficient TMP is fundamental for WFS to develop theenergy capture effectiveness from wind and the pitch angle𝛽𝑤 is set as zero during the TMP operation.The optimal TSRstrategy is realized by directly regulating the tip speed ratio,

which is calculated by real time using wind velocity andgenerator speed, to follow a preobtained 𝜆𝑤-𝑚.Therefore, oneway tomodify the capturedwind power is to adjust theDDSGspeed, which is depicted in Figure 4 [51]. As seen, differentturbine velocities are associated with different captured windpower. Consequently, the generator-side rectifiers in Figure 3regulate the speeds of DDSGs to attain TMP in combinationwith the pitch control system. Figure 4 depicts the typicalwind turbine power-rotor velocity characteristic curves fordifferent wind velocities, where the optimal power curveillustrates the TMP at different conditions of wind speed.The maximum power extracted 𝑃𝑤-max can be obtained as afunction of the shaft velocity:

𝑃𝑤-max = 𝜌𝑤𝜋𝐴5𝑟𝑤𝐶𝑤-max2𝜆3𝑤-𝑚 𝜔3𝑟 = 𝐾max𝜔3𝑟 , (3)

where 𝐾max is the coefficient of rotational velocity for themaximum extracted power through 𝐶𝑤-max at the windgenerator. It should be noted that when the wind velocityis high, the generator velocity and power would exceed themaximum value if the MPPT control is still employed. Thepitch control is provided to limit the captured power and thegenerator speed. So, the pitch angle is set to zero to obtainTMP if the speed is below the maximum speed. But, if thevelocity exceeds its rated value, the pitch angle is controlledto limit the captured power to the maximum rated value andtheWFS would lead to deviating the TMP searching strategyto prevent overspeeding. The pitch control diagram is shownin Figure 5.

2.3. DDSG Dynamic Modelling. If the rotating referenceframe is aligned with the magnetic axis of the rotor, the

Journal of Electrical and Computer Engineering 5

MAX +

+

+

+

−

−

k

r

r-Ｌ；Ｎ？＞

PＬ；Ｎ？＞

PＮＯＬ＜ＣＨe

PI

Figure 5: Pitch control diagram for generator speed limiting.

electric dynamics equations of a three-phase DDSG can bewritten in a synchronously rotating𝑑𝑞 reference frame as [52]

[VsdVsq] = [𝑅𝑠 + 𝑝 ⋅ 𝐿 sd −𝜔𝑒𝐿 sq

𝜔𝑒𝐿 sd 𝑅𝑠 + 𝑝 ⋅ 𝐿 sd][𝑖sd𝑖sq] + [

0𝜔𝑒𝜓𝑠] , (4)

where Vsq, Vsd are stator terminal voltages in the 𝑑𝑞 frame (V);𝑖sq, 𝑖sd are direct and quadrature currents components in thestator windings (A); 𝐿 sq, 𝐿 sd are inductances of the DDSG inthe 𝑑𝑞 frame (H); 𝑅𝑠 is resistance of the stator windings (Ω);𝜓𝑠 is flux linkage generated by the permanent magnets (Wb).

The electrical angular velocity of the rotor, 𝜔𝑒, is definedas

𝜔𝑒 = 𝑝𝑛𝜔𝑟, (5)

where 𝑝𝑛 is the number of pole pairs of the generator; 𝜔𝑟 isthe mechanical angular velocity (rad/sec).

If the DDSG is assumed to have equal 𝑞-axis, 𝑑-axis ininductances (𝐿 sq = 𝐿 sd = 𝐿gs), the torque developed by theDDSG is

𝑇sg = 32𝑝𝑛 [𝜓𝑠𝑖sq] . (6)

The generator velocity in the one-mass model of the windturbine systems is given as follows:

𝑑𝜔𝑟𝑑𝑡 = 1𝐽𝑠 (𝑇sg − 𝑇wt − 𝐹𝑠𝜔𝑟) , (7)

where 𝐽𝑠 is the moment of inertia (Kg⋅m2), 𝐹𝑠 is the viscousfriction coefficient (Nm/rad⋅sec−1), and𝑇wt is themechanicaltorque developed by the wind turbine (WT) (Nm).

2.4. Backstepping Control Design for the MSR. To attain opti-mumpower effectiveness regardless of wind speed variations,the MSR is used to control the DDSG speeds. Control ofthe MSR permits the generators to regulate the rotationalvelocities according to the wind variation. On the other hand,the TMP algorithm adopted in this work is the tip speed ratiocontrol. The backstepping control is employed to performthe TMP control of the wind turbine systems. So, accordingto (2), the reference of the mechanical DDSG speed can bederived as

𝜔𝑟-ref = 𝜆𝑤V𝑤𝐴𝑟𝑤 . (8)

For each MSR, the major control objective is to track thevelocity reference as

𝛼𝜔 = 𝜔𝑟-ref − 𝜔𝑟. (9)

The dynamic of the velocity tracking error is expressed as

𝑑𝛼𝜔𝑑𝑡 = 𝑑𝜔𝑟-ref𝑑𝑡 − 𝑑𝜔𝑟𝑑𝑡 . (10)

From (6)-(7) and (10), we have

𝑑𝛼𝜔𝑑𝑡 = 𝑑𝜔𝑟-ref𝑑𝑡 − 1𝐽𝑠 (32𝑝𝑛 [𝜓𝑠𝑖sq] − 𝑇wt − 𝐹𝑠𝜔𝑟) . (11)

So, a first Lyapunov function candidate is defined as [53]

Γ1 = 12𝛼2𝜔. (12)

Differentiating (12) gives us

𝑑Γ1𝑑𝑡 = 𝛼𝜔 𝑑𝛼𝜔𝑑𝑡= 𝛼𝜔 𝑑𝜔𝑟-ref𝑑𝑡 − 𝛼𝜔𝐽𝑠 (

32𝑝𝑛 [𝜓𝑠𝑖sq] − 𝑇wt − 𝐹𝑠𝜔𝑟) .(13)

Equation (13) can be reorganized as

𝑑Γ1𝑑𝑡 = −𝛿𝜔𝛼2𝜔 + 𝛼𝜔𝐽𝑠 (𝐽𝑠𝛿𝜔𝛼𝜔 + 𝑇wt −32𝑝𝑛𝜓𝑠𝑖sq + 𝐹𝑠𝜔𝑟

+ 𝐽𝑠 𝑑𝜔𝑟 ref𝑑𝑡 ) ,(14)

where 𝛿𝜔 is the positive closed-loop feedback constant.According to (14), the backstepping law can be designed asfollows:

𝑖sd-ref = 0, (15)

𝑖sq-ref = 23𝑝𝑛𝜓𝑠 (𝐽𝑠𝛿𝜔𝛼𝜔 + 𝐽𝑠𝑑𝜔𝑟 ref𝑑𝑡 + 𝐹𝑠𝜔𝑟 + 𝑇wt) . (16)

If the speed error can be made to zero by selecting propercontrol input, (14) can be simplified to [54]

𝑑Γ1𝑑𝑡 = −𝛿𝜔𝛼2𝜔 ≺ 0. (17)

6 Journal of Electrical and Computer Engineering

Consequently, by Lyapunov stability analysis, the velocitycontroller is asymptotically stable. To stabilize the currentscomponents 𝑖sd and 𝑖sq, define the following current errors:

𝛼sd = 𝑖sd-ref − 𝑖sd𝛼sq = 𝑖sq-ref − 𝑖sq, (18)

where 𝑖sq-ref, 𝑖sd-ref are the current references. Taking thederivative of 𝛼sd and 𝛼sq with respect to time and using (4),one can obtain

𝛼sd 𝑑𝛼sd𝑑𝑡 = 𝛼sd [− 1𝐿gs(Vsd + 𝐿gs𝜔𝑒𝑖sq − 𝑅𝑠𝑖sd)]

= −𝜆sd𝛼2𝑑 + 𝛼sd𝐿gs[−Vsd − 𝐿gs𝜔𝑒𝑖sq + 𝑅𝑠𝑖sd

+ 𝐿gs𝜆sd𝛼sd]𝛼sq 𝑑𝛼sq𝑑𝑡 = 𝛼sq [𝑑𝑖sq-ref𝑑𝑡 − 𝑑𝑖sq𝑑𝑡 ] = −𝜆sq𝛼2sq

+ 𝛼sq𝐿gs[𝐿gs

𝑑𝑖sq-ref𝑑𝑡 − Vsd + 𝜔𝑒𝜓𝑠 + 𝑅𝑠𝑖sq + 𝐿gs𝜔𝑒𝑖sd+ 𝜆sq𝐿gs𝛼sq] ,

(19)

where 𝜆sd and 𝜆sq are the positive closed-loop feedback con-stants.The second Lyapunov function candidate is defined as

Γ2 = Γ1 + 12𝛼2sq + 12𝛼2sd = 12𝛼2𝜔 + 12𝛼2sq + 12𝛼2sd. (20)

Differentiating (20) gives us

𝑑Γ2𝑑𝑡 = 𝛼𝜔 𝑑𝛼𝜔𝑑𝑡 + 𝛼sd 𝑑𝛼sd𝑑𝑡 + 𝛼sq 𝑑𝛼sq𝑑𝑡 . (21)

From (14) and (18)–(19), (21) can be reorganized as

𝑑Γ2𝑑𝑡 = −𝛿𝜔𝛼2𝜔 + 𝛼𝜔𝐽𝑠 (𝐽𝑠𝛿𝜔𝛼𝜔 + 𝑇wt −32𝑝𝑛𝜓𝑠𝑖sq

+ 𝐹𝑠𝜔𝑟 + 𝐽𝑠 𝑑𝜔𝑟ref𝑑𝑡 ) − 𝜆sq𝛼2sq + 𝛼sq𝐿gs[𝐿gs

𝑑𝑖sq-ref𝑑𝑡− Vsd + 𝜔𝑒𝜓𝑠 + 𝑅𝑠𝑖sq + 𝐿gs𝜔𝑒𝑖sd + 𝜆sq𝐿gs𝛼sq]− 𝜆sd𝛼2sd + 𝛼sd𝐿gs

[−Vsd − 𝐿gs𝜔𝑒𝑖sq + 𝑅𝑠𝑖sd+ 𝐿gs𝜆sd𝛼sd] .

(22)

The commands Vsq-ref and Vsd-ref are carried out from (22) as

Vsq-ref = 𝜔𝑒𝜓𝑠 + 𝑅𝑠𝑖sq + 𝐿gs𝜔𝑒𝑖sd + 𝐿gs𝑑𝑖sq-ref𝑑𝑡

+ 𝐿gs𝜆sq𝛼sqVsd-ref = 𝐿gs𝜆sd𝛼sd − 𝐿gs𝜔𝑒𝑖sq + 𝑅𝑠𝑖sd.

(23)

Using (16) and (23), (22) can be simplified to

𝑑Γ2𝑑𝑡 = −𝛿𝜔𝛼2𝜔 − 𝜆sd𝛼2sd − 𝜆sq𝛼2sq ≤ 0. (24)

Therefore, by Lyapunov stability analysis, the backsteppingregulator is asymptotically stable and the control of theDDSGspeeds is attained.The control diagram for individual MSR isdepicted in Figure 6.

2.5. Nonlinear dc-link Voltage Regulation. The GSI controlsthe dc-link voltage and transfers the power from turbine-DDSG to the grid. Also, it contributes to the reactive andactive power control of the overall DDSG system [55]. If thereference frame is rotating synchronously with the electricalgrid voltage vector, the dynamic model voltage equations ofthe electrical network connection in grid voltage orientedreference frame (𝑑, 𝑞) are represented as follows:

𝑑𝑖𝑑-grid𝑑𝑡 = 1𝐿𝑔𝑓 (𝑒𝑔𝑑 − 𝑅𝑔𝑓𝑖𝑑-grid + 𝜔𝑔𝐿𝑔𝑓𝑖𝑞-grid − 𝑈𝑠)𝑑𝑖𝑞-grid𝑑𝑡 = 1𝐿𝑔𝑓 (𝑒𝑔𝑞 − 𝑅𝑔𝑓𝑖𝑞-grid − 𝜔𝑔𝐿𝑔𝑓𝑖𝑑-grid) ,

(25)

where 𝑒𝑔𝑑, 𝑒𝑔𝑞 are the grid side inverter voltage (𝑑-𝑞)components (V); 𝑈𝑠 is the amplitude of the grid voltage (V);𝑅𝑔𝑓 (Ω) and 𝐿𝑔𝑓 (H) are the resistance and inductance of thefilter; 𝜔𝑔 is the angular frequency of grid; and 𝑖𝑑-grid and 𝑖𝑞-gridare the 𝑑-axis current and 𝑞-axis current (A) of the electricalgrid, respectively.The active 𝑃𝑔 and reactive power𝑄𝑔 can becalculated as follows [56]:

𝑃𝑔 = 32𝑈𝑠𝑖𝑑-grid𝑄𝑔 = 32𝑈𝑠𝑖𝑞-grid.

(26)

Equations (26) illustrate that the active and reactive powersare regulated to achieve the required voltage by changingthe respective current of the d-q-axis. The dc-link voltageequation can be formulated as in the following equation:

𝐶𝑑𝑉dc𝑑𝑡 = 𝑖𝑔 − 𝑖grid, (27)

where 𝐶 is the capacitance of the dc-link capacitor (F); 𝑉dcis dc-link voltage (V); 𝑖grid is the current between the dc-linkand the grid; and 𝑖𝑔 is the current between the dc-link and theDDSG stators (A). So, the active power along the side of theGSI is

𝑉dc𝑖grid = 32𝑈𝑠𝑖𝑑-grid. (28)

From (27)-(28), the dc-link voltage dynamics can be calcu-lated as

𝑑Vdc𝑑𝑡 = 𝑖𝑔 − 1𝐶 32 𝑈𝑠𝑉dc 𝑖𝑑-grid. (29)

Journal of Electrical and Computer Engineering 7

DDSGAC

DC

PWM

3 23

Equations (15)-(16)and (23)

MPPT& PitchControl

2

Turbine

r

r-Ｇ；Ｒ

r_Ｌ？＠

PＬ；Ｎ？＞

PＮＡwisa , isb , isc

isq isd ＭＫ-Ｌ？＠ Ｍ＞-Ｌ？＠

Udc

Figure 6: Control block diagram of MSR using backstepping approach.

Consequently, to transfer all of the active power generated inturbine-DDSG, the dc-link voltage𝑉dc must bemaintained ata constant value using the current control of 𝑖𝑑-grid. Equation(29) can be reorganized as

𝑉dc𝐶𝑑𝑉dc𝑑𝑡 = 𝑃Total − 32𝑈𝑠𝑖𝑑-grid, (30)

where 𝑃Total is the generated power of the DDSGs. Equation(30) can be expressed as

𝐶2𝑑𝑉2dc𝑑𝑡 = 𝑃Total − 32𝑈𝑠𝑖𝑑-grid. (31)

The tracking error of the dc-bus voltage is defined as

𝜀dc-link = 𝑉2dc−𝑟 − 𝑉2dc. (32)

The dc-link voltage tracking error has the following dynamic:

𝑑𝜀dc-link𝑑𝑡 = 𝑑𝑉2dc−𝑟𝑑𝑡 − 2𝐶 (𝑃Total − 32𝑈𝑠𝑖𝑑-grid-𝑟) , (33)

where 𝑖𝑑-grid-𝑟 is the current reference. Consider a thirdLyapunov function candidate:

Φdc-link = 12𝜀2dc-link. (34)

From (33), differentiating (34) gives us

𝑑Φdc-link𝑑𝑡 = 𝜀dc-link 𝑑𝜀dc-link𝑑𝑡= 𝜀dc-link [𝑑𝑉

2dc-𝑟𝑑𝑡 − 2𝐶 (𝑃Total − 32𝑈𝑠𝑖𝑑-grid-𝑟)] .

(35)

So, (35) can be reorganized as

𝑑Φdc-link𝑑𝑡 = −𝜆bus𝜀2dc-link + 𝜀dc-link [𝑑𝑉2dc-𝑟𝑑𝑡

− 2𝐶 (𝑃Total − 32𝑈𝑠𝑖𝑑-grid-r) + 𝜆bus𝜀dc-link] ,(36)

where 𝜆bus is the positive closed-loop feedback constant.According to (36), the backstepping law can be designed asfollows:

𝑖𝑑-grid-𝑟 = 1𝑈𝑠 [23𝑃Total − 𝐶3 (

𝑑𝑉2dc-𝑟𝑑𝑡 + 𝜆bus𝜀dc-link)] . (37)

From (37), (38) can be simplified to

𝑑Φdc-link𝑑𝑡 = −𝜆bus𝜀2dc-link ≤ 0. (38)

Consequently, by Lyapunov stability analysis, dc-link voltagecontroller is asymptotically stable. To stabilize the currentscomponents 𝑖d-grid and 𝑖q-grid, define the following currenterrors:

𝜉𝑑-grid = 𝑖𝑑-grid-𝑟 − 𝑖𝑑-grid (39)

𝜉𝑞-grid = 𝑖𝑞-grid-𝑟 − 𝑖𝑞-grid. (40)

The reference 𝑖𝑞-grid-𝑟 is calculated from the desired powerfactor. Based on (37) and (39), (33) can be reorganized as

𝑑𝜀dc-link𝑑𝑡 = −𝜆dc-link𝜀dc-link + 3𝐶𝑈𝑠𝜉d-grid. (41)

8 Journal of Electrical and Computer Engineering

Besides, from (25) and (39)-(40), one can obtain

𝜉𝑑-grid 𝑑𝜉𝑑-grid𝑑𝑡 = 𝜉𝑑-grid [𝑑𝑖𝑑-grid-𝑟𝑑𝑡 − 𝑑𝑖𝑑-grid𝑑𝑡 ]

= −𝜆𝑑-grid𝜉2𝑑-grid + 𝜉𝑑-grid𝐿𝑔𝑓 [𝐿𝑔𝑓 𝑑𝑖𝑑-grid-𝑟𝑑𝑡 − 𝑒𝑔𝑑+ 𝑈𝑠 + 𝑅𝑔𝑓𝑖𝑑-grid − 𝐿𝑔𝑓𝜔𝑔𝑖𝑞-grid+ 𝜆𝑑-grid𝐿𝑔𝑓𝜉𝑑-grid]

𝜉𝑞-grid 𝑑𝜉𝑞-grid𝑑𝑡 = [−𝑑𝑖𝑞-grid𝑑𝑡 ] = −𝜆𝑞-grid𝜉2𝑞-grid+ 𝜉𝑞-grid𝐿𝑔𝑓 [−𝑒𝑔𝑞 + 𝑅𝑔𝑓𝑖𝑞-grid + 𝐿𝑔𝑓𝜔𝑔𝑖𝑑-grid+ 𝜆𝑞-grid𝐿𝑔𝑓𝜆𝑞-grid] ,

(42)

where 𝜆𝑑-grid and 𝜆𝑞-grid are the positive closed-loop feedbackconstants. Consider the fourth Lyapunov function candidate:

ΦGSI = 12𝜀2dc-link + 12𝜉2𝑞-grid + 12𝜉2𝑑-grid . (43)

Differentiating (43) gives us

𝑑ΦGSI𝑑𝑡 = 𝜀dc-link 𝑑𝜀dc-link𝑑𝑡 + 𝜉𝑑-grid 𝑑𝜉d-grid𝑑𝑡+ 𝜉𝑞-grid 𝑑𝜉𝑞-grid𝑑𝑡 .

(44)

From (41) and (42), (44) can be reorganized as

𝑑ΦGSI𝑑𝑡 = −𝜆dc-link𝜀2dc-link − 𝜆𝑑-grid𝜉2𝑑-grid − 𝜆𝑞-grid𝜉2𝑞-grid+ 𝜉𝑑-grid𝐿𝑔𝑓 [3𝐿𝑔𝑓𝐶 𝑈𝑠𝜀dc-link + 𝐿𝑔𝑓 𝑑𝑖𝑑-grid-𝑟𝑑𝑡 − 𝑒𝑔𝑑+ 𝑅𝑔𝑓𝑖𝑑-grid − 𝐿𝑔𝑓𝜔𝑔𝑖𝑞-grid + 𝑈𝑠+ 𝜆𝑑-grid𝐿𝑔𝑓𝜉𝑑-grid] + 𝜉𝑞-grid𝐿𝑔𝑓 [−𝑒𝑔𝑞 + 𝑅𝑔𝑓𝑖𝑞-grid+ 𝐿𝑔𝑓𝜔𝑔𝑖𝑑-grid + 𝜆𝑞-grid𝐿𝑔𝑓𝜉𝑞-grid] .

(45)

According to (45), the backstepping law can be designed asfollows:

V𝑑-GSI = 3𝐿𝑔𝑓𝐶 𝑈𝑠𝜀dc-link + 𝐿𝑔𝑓 𝑑𝑖𝑑-grid-𝑟𝑑𝑡 + 𝑅𝑔𝑓𝑖𝑑-grid− 𝐿𝑔𝑓𝜔𝑔𝑖𝑞-grid + 𝑈𝑠 + 𝐿𝑔𝑓𝜆𝑑-grid𝜉𝑑-grid

V𝑞-GSI = 𝑅𝑔𝑓𝑖𝑞-grid + 𝐿𝑔𝑓𝜔𝑔𝑖𝑑-grid + 𝐿𝑔𝑓𝜆𝑞-grid𝜉𝑞-grid.(46)

Table 1: Parameters of the DDSG.

Parameter Value𝑃𝑟: rated power of DDSG 2 (MW)𝜔𝑚: rated mechanical speed 2.57 (rd/s)𝑅: stator resistance 0.008 (Ω)𝐿 𝑠: stator 𝑑-axis inductance 0.0003 (H)𝜓𝑓: permanent magnet flux 3.86 (wb)𝑝𝑛: pole pairs 60

Table 2: Parameters of the turbine.

Parameter ValueBlade number 3𝜌: the air density 1.08 kg/m3𝐴: area swept by blades 4775.94m2

V𝑤-𝑛: rated wind speed 12.4m/s

Table 3: System parameters.

Parameter Valuedc-link voltage reference 2100VGrid frequency 50HzGrid phase voltage 660VRatio𝑋Grid/𝑅Grid 5dc-link capacitor 38000 𝜇F

Using (37) and (46), (45) can be simplified to

𝑑ΦGSI𝑑𝑡 = −𝜆dc-link𝜀2dc-link − 𝜆𝑑-grid𝜉2𝑑-grid − 𝜆𝑞-grid𝜉2𝑞-grid≤ 0.

(47)

Therefore, by Lyapunov stability analysis, the backsteppingregulator is asymptotically stable and the control of the GSI isattained. The control diagram is depicted in Figure 7.

3. Simulation Result Analysis

The performance of the proposed nonlinear control strategyis demonstrated in this section. The controller is tested onthe WFS control strategy found in Section 2. The schematicof the overall control scheme of the WFS is illustrated inFigure 7. Numerical simulations are carried out using MAT-LAB/Simulink software to verify WFS performance. Systemdata used are listed in Tables 1, 2, and 3. The performancecoefficients of the turbines are evaluated as the followingform:

𝐶𝑤 (𝜆𝑤, 𝛽𝑤) = 12 (116𝜆𝑤𝑐 − 0.4𝛽𝑤 − 5) 𝑒−(21/𝜆𝑤𝑐)

1𝜆𝑤𝑐 =1𝜆𝑤 + 0.08𝛽𝑤 −

0.035𝛽3𝑤 + 1 ,(48)

where𝐶𝑤 reaches the maximum value𝐶𝑤-max = 0.4104when𝜆𝑤 is 𝜆𝑤-𝑚 = 8.1.

Journal of Electrical and Computer Engineering 9

3 2 3 2 3 2

Electricnetwork

PLL

TransformerDDSG1

AC

DC

DC

AC

PWM

Filter

Equation(46)

DDSG2AC

DC

DDSG3AC

DC

w1

w2

w3

q-＇３） d-＇３）iq-ＡＬＣ＞ id-ＡＬＣ＞ Us

Lgf, Rgf

ia, ib, ic

Qg-Ｌ？＠Udc-Ｌ？＠

Udc

0,8 KV/20 KV

Figure 7: Control block diagram of GSI.

Besides, the simulation will be performed in three stepswith different objectives. The first scenario consists in opera-tion under changing wind velocities, the second is robustnessof proposed control strategy against electrical andmechanicalparameter changes, and the third is an AC voltage sag.

3.1. Case 1: Performance Evaluation under Normal Operationof Proposed Control. Figure 8 shows the wind velocities forthe different wind turbine systems (a), the individual pitchangle for each wind turbine (b), the performance coefficientsof the turbines (c), the speeds of DDSG (d), and the totalpower extracted by the wind farm (f). It has been noted thatthe speeds of DDSG are adapted relative to the variationof wind speed and the 𝐶𝑤 can be preserved at a maximumvalue which could yield to TMP by working the turbines atthe speed references. The pitch angle controls are activatedfor velocities above the rated wind velocity to control therated power of the DDSGs. If the wind turbines receivewind velocities which are lower than the rated speed, thepitch angles are set as 0∘ to generate the maximum extractedpower.Thewind turbine systems operated at theirsmaximumperformance coefficients and the pitch angle were kept attheir optimal values. The controller performs the powermaximization according to the wind velocity variation. But,pitch controls are activated to restrict the rotational velocitiesto below the maximum speed and to limit the powers ofturbines when the wind velocities are above the rated speed.In this study, the DDSG rated speed is 2.57 rad/s. So, in highwind velocity regions, the DDSG velocities and extractedpower would not exceed themaximum.The generated powerof the WFS is shown in Figure 8(f). Figure 8(e) shows windDDSG1 speed follows the optimal speed provided by the TMPoperation as the wind velocity varies. The DDSG1 velocity isable to track its optimal values precisely. Figures 8(g)–8(h)

show the currents of DDSG1, where the generator currentsare able to track their optimal values precisely. Figure 9illustrates the dc-link voltage response. The dc-link voltagecontroller tried to maintain the constant value so that the dc-link voltage had an approximately constant value of 2100V.Figure 10 shows the simulation result of reactive power whichis controlled to be zero. Figure 11 illustrates a detailed view ofthe grid currents and phase voltage during the wind variationwhere the proposed WFS produces sinusoidal currents atelectrical network with unity power factor. The simulationresults show that the proposed backstepping controllershave good performance and can guarantee acceptable globalregulation and tracking performance to extract and convertpower under varying wind speeds.

3.2. Case 2: WFS Response Subject to Parameter Uncertainties.In order to verify the robustness of the proposed controlstrategy against the variation of parameters, it is supposedthat the stator inductance 𝐿gs, the stator resistor 𝑅𝑠, and thetotal moment of inertia 𝐽𝑠 of the system values are increasedby 50% under the condition of nominal values. In Figures12–15, robustness against WFS parameter variations is testedfor the proposed strategy. In the simulation, 𝐿gs, 𝑅𝑠, and 𝐽𝑠are increased to 150% of their nominal values, and the othersimulation parameters are the same as those in first scenario.The simulation results of the backstepping control and theVOC strategy with and without the mentioned parametervariation are shown in Figures 12–15. The results with andwithout the parameter variations are marked by “A” and “B,”respectively. It can be seen that the backstepping strategy hasa fast dynamic response, a reduced settling time, and a lowerovershoot. The simulation results confirm that the proposedcontrol approach is robust against uncertainties in the WFScompared with conventional VOC.

10 Journal of Electrical and Computer Engineering

2 4 6 8 100

Time (s)

9

10

11

12

13

14In

stan

tane

ous w

ind

spee

ds (m

/s)

Wind turbine 1Wind turbine 2Wind turbine 3

Rated wind speed

(a) Wind speeds (m/s)

−0.5

0

0.5

1

1.5

2

2.5

3

Pitc

h an

gles

(in

degr

ee)

2 4 6 8 100

Time (s)

Turbine 1Turbine 2Turbine 3

(b) Pitch angles 𝛽𝑤 (in degree)

Wind turbine 1Wind turbine 2Wind turbine 3

2 4 6 8 100

Time (s)

0

0.1

0.2

0.3

0.4

0.5

Coe

ffici

ents

of p

ower

conv

ersio

n,Cp

(c) Coefficient of power, 𝐶𝑤

PMSG 1PMSG 2PMSG 3

0

0.5

1

1.5

2

2.5

3Ro

tatio

nal v

eloc

ities

of P

MG

s (rd

/s)

2 4 6 8 100

Time (s)

(d) Speed of DDSGs (rd/s)

Optimum speedGenerator speed

2 4 6 8 100

Time (s)

0

0.5

1

1.5

2

2.5

3

Gen

erat

or sp

eed,

opt

imum

spee

d (r

d/s)

(e) Speed of DDS1 (rd/s)

×106

0

1

2

3

4

5

6

7

Pow

er g

ener

ated

(W)

2 4 6 8 100

Time (s)

(f) Total power extracted (W)

Figure 8: Continued.

Journal of Electrical and Computer Engineering 11

iq

iq-r

0

500

1000

1500

2000

2500

3000

qax

is cu

rren

t com

pone

nt o

f PM

SG1

(A)

2 4 6 8 100

Time (s)

(g) Quadrature current component 𝑖sq of DDSG1 (A)

id

id-r

2 4 6 8 100

Time (s)

−500

0

500

d-a

xis c

urre

nt co

mpo

nent

of P

MSG

1 (A

)

(h) Direct current component 𝑖sd of DDSG1 (A)

Figure 8: Simulation of the WFS in normal operation and using backstepping strategy.

Udc-refUdc

2000

2050

2100

2150

2200

DC

link

volta

ge (V

)

2 4 6 8 100

Time (s)

Figure 9: dc-link voltage (V).

×105

−3

−2

−1

0

1

2

3

Reac

tive p

ower

(VA

R)

2 4 6 8 100

Time (s)

Figure 10: Reactive power (VAR).

12 Journal of Electrical and Computer Engineering

CurrentVoltage

−8000

−6000

−4000

−2000

0

2000

4000

6000

8000

Volta

ge (V

), Cu

rren

t (A

)

2 4 6 8 100

Time (s)

Volta

ge (V

), Cu

rren

t (A

)

CurrentVoltage

8000

6000

4000

2000

0

−2000

−4000

−6000

−80003.02 3.04 3.06 3.08 3.13

Time (s)

Figure 11: Simulation of the three-phase current and voltage of electrical network.

A

Rated speedB

2.38

2.39

2.4

2.41

2.42

2.43

2.44

2.45

2.46

Spee

d of

PM

SG1

(rd/

s)

2 2.05 2.1 2.151.95

Time (s)

(a) Backstepping control

A

Rated speedB

2.36

2.38

2.4

2.42

2.44

2.46

2.48

2.5

Spee

d of

PM

SG1

(rd/

s)

2.1 2.2 2.3 2.4 2.52

Time (s)

(b) VOC strategy

Figure 12: DDSG1 speed (rd/s).

3.3. Case 3: Simulation under Grid Fault Condition. Thissimulation example deals with the WFS behaviour duringa Three-Phase Grid Fault (3PGF) produced at 𝑡 = 5.5 s andcharacterised by a voltage drop of 200ms at Bus 3 (Figure 3).Figures 16 and 17 illustrate the voltage of the WFS at Bus 4 innormal and close zoom views, respectively, for backsteppingand VOC strategies. It can be observed that, by applying thebackstepping controller, the transient stability of theWFS hasbeen enhanced and the oscillations of the three-phase voltagehave been damped quickly when the fault is cleared. Besides,Figure 17 shows that the transient duration with the proposedcontrol is faster than that with the VOC and the three-phase

voltage oscillation amplitude at VOC is evidently larger thanthat at backstepping control. The results illustrated that thebackstepping control strategy can not only reduce the peakvalue of three-phase voltage but also shorten the transientresponse time compared with the VOC strategy. Comparedto the results depicted in Figure 18, it can be seen that the peakvalue of frequency deviations can be eliminated during gridvoltage drop with the proposed control strategy. Comparedwith VOC strategy, the peak value of frequency deviations isreduced from 1.9Hz to less than 0.25Hz with backsteppingstrategy. Figure 19 illustrates the dc-link voltage responseunder proposed control and VOC strategy. The voltage drop

Journal of Electrical and Computer Engineering 13

0.4102

0.4104

0.4106

0.4108

0.411

0.4112

Coe

ffici

ent o

f pow

er,C

p

2 2.05 2.1 2.151.95

Time (s)

B

A

(a) Backstepping control

A

B

0.4085

0.409

0.4095

0.41

0.4105

0.411

Coe

ffici

ent o

f pow

er,C

p

2 2.1 2.2 2.3 2.4 2.51.9

Time (s)

(b) VOC strategy

Figure 13: Coefficient of power.

Udc-refUdc

2000

2050

2100

2150

2200

DC

link

volta

ge (V

)

2 4 6 8 100

Time (s)

(a) Backstepping control

Udc-refUdc

1800

1900

2000

2100

2200

2300

DC

link

volta

ge (V

)

2 2.05 2.1 2.151.95

Time (s)

(b) VOC strategy

Figure 14: dc-link voltage (V) (with nominal values).

will not be transmitted to the dc-link system voltage andthe converter dc-link voltage is controlled invariable at thereference value 2100V as in Figure 19.

4. Conclusion

This paper has presented a nonlinear backstepping approachof WFS driven DDSG operating under normal and voltagedrop situations. A proposed control has been investigatedto deal with problems of simultaneous control of the DDSGspeeds and the dc-link voltage to achieve Maximum Power

Tracking and pitch control. Simulation research on a 6-MW-DDSG Wind Farm System validates the proposed controlstrategy. Performance comparison and evaluation with Vec-tor Oriented Control (VOC) are provided under a wide rangeof functioning conditions, three-phase voltage dips, and theprobable occurrence of uncertainties. The main conclusionsare summarized as follows: (1) The proposed backsteppingstrategy can guarantee acceptable global regulation andtracking performance. (2) The proposed control strategyoffers remarkable characteristics such as excellent dynamicand steady state performance under varying wind speed and

14 Journal of Electrical and Computer Engineering

Udc-refUdc

2000

2050

2100

2150

2200

DC

link

volta

ge (V

)

2 4 6 8 100

Time (s)

(a) Backstepping control

Udc-refUdc

Time (s)2.62.52.42.32.22.12

1800

1900

2000

2100

2200

2300

2400

DC

link

volta

ge (V

)

(b) VOC strategy

Figure 15: dc-link voltage (V) (with parameter variations).

2 4 6 8 100

Time (s)

−800

−600

−400

−200

0

200

400

600

800

Thre

e pha

se v

olta

ge (V

)

(a) Backstepping control

2 4 6 8 100

Time (s)

−1000

−500

0

500

1000

Thre

e pha

se v

olta

ge (V

)

(b) VOC strategy

Figure 16: Waveforms of three-phase voltage at Bus 4.

5.5 5.6 5.7 5.8 5.95.4

Time (s)

−800

−600

−400

−200

0

200

400

600

800

Thre

e-ph

ase v

olta

ge (V

)

(a) Backstepping control

−1000

−500

0

500

1000

5.5 5.6 5.7 5.8 5.95.4

Time (s)

Thre

e-ph

ase v

olta

ge (V

)

(b) VOC strategy

Figure 17: Zoom-in view of three-phase voltage at Bus 4.

Journal of Electrical and Computer Engineering 15

49.6

49.7

49.8

49.9

50

50.1

50.2

50.3

50.4

Freq

uenc

y (H

z)

2 4 6 8 100

Time (s)

(a) Backstepping control

49

49.5

50

50.5

51

51.5

52

Freq

uenc

y (H

z)

2 4 6 8 100

Time (s)

(b) VOC strategy

Figure 18: Frequency response of the VS-WFS under grid faults.

Udc-refUdc

2000

2050

2100

2150

2200

DC

link

volta

ge (V

)

2 4 6 8 100

Time (s)

(a) Backstepping control

Udc-refUdc

2 4 6 8 100

Time (s)

2000

2050

2100

2150

2200D

C lin

k vo

ltage

(V)

(b) VOC strategy

Figure 19: dc-link voltage (V).

robustness to parametric variations in the WFS and undersevere faults of grid voltage.

Conflicts of Interest

The authors declare that they have no conflicts of interestregarding the publication of this paper.

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