Research ArticleCoordinated Control Using Backstepping of DFIG-Based WindTurbine for Frequency Regulation in High Wind EnergyPenetrated System

Mohamed Nadour 1 Ahmed Essadki1 and Tamou Nasser2

1Research Center of Engineering and Health Sciences and Technologies High Normal School of Technical EducationMohammed V University Rabat Morocco2Research Center of Engineering and Health Sciences and TechnologiesHigher National School of Computer Science and Systems Analysis Mohammed V University Rabat Morocco

Correspondence should be addressed to Mohamed Nadour mohamednadourum5snetma

Received 9 September 2019 Revised 21 February 2020 Accepted 9 March 2020 Published 29 April 2020

Academic Editor Francesco Ripamonti

Copyright copy 2020 Mohamed Nadour et al ampis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

ampe expansion of renewable generation has raised some red flags in terms of power system stability control andmanagement Forinstance unlike traditional synchronous energy sources the doubly-fed induction generator- (DFIG-) based wind turbines (WTs)do not instinctively act against frequency deviations In fact the power electronics interfacing the generator merely controlled towarrant maximum wind power conversion make its output power and mechanical speed immune to the characteristics of theelectric network frequency Moreover significant wind power penetration (WPP) promotes the retirement of many traditionalgeneration groups consequently curtailing the power system corresponding inertia and displacing the primary reserves that areessential to retain the frequency within an acceptable range of variation ampis paper explores different control approaches usingbackstepping allowing DFIG-basedWTs to engage actively in frequency regulation using a coordinated control of the rotor speedand pitch angle to regulate the system during both partial- and full-load operation modes ampe first method momentarilydischarges part of the kinetic energy stored in the WT spinning masses and the second method follows a deloaded operationcharacteristic so as to keep a specific power reserve that can be automatically activated at the events of frequency excursions Astudy case considering an isolated power system that consists of synchronous generators DFIG-based wind farm static load and asudden frequency disturbance was performedampe simulation result in a MatlabSimulink environment highlights the robustnessand capability of the coordinated control scheme to furnish under variant operation conditions active power aid consequentlylifting the frequency nadir up to a superior level than that obtained with 0 wind power penetration in the system

1 Introduction

ampe progression from conventional generation groups tononconventional cleaner energy sources has pressured thepower system to encounter significant changes in terms of itsstructure operation control and management [1ndash3]ampat isto say as these renewables continue prospering worldwidethe power network will unavoidably confront multiplestability concerns For instance at the occurrence of fre-quency disruption which reflects a power imbalance be-tween demand and supply in contrary to synchronous

generation sources (reheat steam turbines nonreheat steamturbines hydraulics etc) where a natural short-term in-ertial response represented by an instantaneous absorptionor release of the kinetic energy stored in the turbinesspinning masses and primary reserve activation both servethe power system in restoring and maintaining the electricnetwork frequency within a tolerable spectrum of variationthe doubly-fed induction generator- (DFIG-) based windturbine (WT) which is the most prominent structure amongthe wind energy generation technologies [4] does not ac-quire this inherited characteristic [5 6] As a matter of fact

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 8287949 16 pageshttpsdoiorg10115520208287949

the power electronics interfacing the DFIG to the electricalnetwork are merely controlled to ensure maximum powerpoint tracking (MPPT) and therefore almost entirely dis-sociate its output power and mechanical speed from theelectric network frequency characteristics

Furthermore considerable wind power penetration(WPP) promotes the retirement and displacement of manyconventional generation groups Leading to the reduction ofthe power systemrsquos corresponding inertia hence lower in-ertial responses supporting the system (the situation is worseespecially in isolated systems since their equivalent inertia isalready limited) plus the curtailment of primary reservestypically needed to compensate for power imbalances be-tween the consumption and the production in order tosecure the permanent stability of the power systemamperefore some transmission system operators (TSOs) andgrid planners have early revised their grid code specificationsin order to securely fit in the wind power generation in theirpower system [2 7] Among which for instance the Eu-ropean Network of Transmission System Operator forElectricity (ENTSO-E) [8] expects that each of the trans-mission system operators (TSOs) shall obligate their grid-connected WTs to provide extra active power supportcomparable to that of conventional generation units to assistin the recovery process using the so-called ldquofrequency-sensitiverdquo control methods [9]

ampe industrial and academic proposed solutions thatallow variable speed WTs to engage in frequency regulationcan be categorized into two main classes ampe first classmakes use of the naturally inaccessible WT kinetic energythrough some appropriate rotor speed control designs ampisclass mainly contains two methods including first anldquoartificialrdquo inertial reaction using the kinetic energy storedin WTs spinning masses retrieved based on the frequencydeviation to counteract frequency disruptions for short-termduration [1 8 10] A study by authors in [6 11] shows thatvariable speed WT grants more access to the kinetic energycompared to a traditional synchronous generator withequivalent inertia constant being that the wider the range ofspeed variation generators can tolerate the more the kineticenergy can be extracted However this method cannot beused alone since it provides assistance only during thetransient and has no reaction for quasi-steady state [1]ampenthere is the long-term frequency support where the proposedcontrol strategy expects the WT to shift from MPPT tosuboptimal operationmode and a droop controller is used toadapt the WT active power output as a proportion of thefrequency deviation [12] ampe second class uses the bladepitching to create the power reserve but only when the activepower output is higher than the nominal value (full-loadoperation mode) [13ndash15]

ampis subject is recognized and fairly discussed over thepast years However some concerns still require furtheranalysis For instance plenty of published papers such as[11 13 16 17] have only considered the full-load operationof WT whereas this mode represents only a small scale ofWT operation time As an example the production ofPortuguese grid-connected WTs is beyond the half of itsnominal power only during 10 of the global operation time

[9] Moreover few have been the works that have suggested amix between rotor speed control through power electronicsand pitch control for frequency regulation purposes ampeauthors in [16] have examined a coordinated controlscheme which only incorporates only the short-term inertialresponse and pitch control comparing the results withexisting rotor speed controllers

ampis paper explores different control approaches used toenhance WT capability to engage in frequency regulationFirst rotor speed control methods namely the artificialinertial and the primary frequency regulation responses aredeveloped ampe control is done through the DFIG sideconverter (DSC) using nonlinear backstepping methodol-ogyampen an innovative pitch angle control method utilizedto protect the WTagainst overspeeding and to maintain thepower reserve even during a full-load operation mode ispresented

A study case considering an isolated power system thatcontains synchronous generators DFIG-based wind farmand static loads was examined to compare the capability ofeach control scheme individually in terms of furnishingextra active power assistance at the event of a sudden fre-quency disruption ampen the simulation results show that acombination of the three control approaches enhances theperformance of the DFIG-based wind farm by bringing thefrequency nadir up to a higher level than that where theWPPis of 0 in the power system

2 Modelling and Control of DFIG-Based WT

ampis section presents some preliminary knowledge in-cluding a brief description of WT and DFIG modelling andcontrol using backstepping As we shall see in the Resultssection compared to the classical control schemes thiscontrol strategy enhances the system stability and robustnessespecially when parametric variations are registered whichis often the case due to some physical phenomena ormodelling uncertainties related to the accuracy of themeasuring devices and identification methodologies [4 18]

21 Wind Turbine Model ampe aerodynamic power PT cap-tured from the wind power Pw is expressed as follows

PT Pw middot Cp(λ β) ρπR2v3w

2Cp(λ β) (1)

where R is the blade radius ρ is the air density vw is the windspeed λ is the tip speed ratio β is the blade angles and Cp isthe aerodynamic efficiency or the power coefficientapproached by the expression given in Appendix [18] WithΩT being the WT rotor speed we have

λ R middotΩT

vw

(2)

ampe gearbox that adapts the mechanical speed Ωm of theDFIG to the rotor speed ΩT of the WT is modelledneglecting the mechanical energy losses by a simple gainGTsuch that

2 Mathematical Problems in Engineering

Ωm GT middotΩT

TT GT middot Tg(3)

where TT and Tg are the torques at the gearbox input andoutput respectively ampen with Tem being the electromag-netic torque of the generator Jwt the system (WTand DFIG)total inertia and f the friction according to the fundamentalequation of dynamic we can write

Jwt

dΩm

dt Tg minus Tem minus f middotΩm (4)

22 DFIG Modelling and Control In this work we haveadopted the field-oriented control joining the stator flux tothe d-axis of the Park reference frame (ψsq 0 and ψsdψs)in order to dissociate the control of active power Ps andreactive power Qs Neglecting the stator resistance Rs whichis a realistic approximation for high-power generators [4]the state model of the DFIG can be determined by thefollowing equation [19]

_Ps μ Vrq + RrIrq + χIr d minus η1113872 1113873

_Irq minus σ Vrq + RrIrq + χIr d minus η1113872 1113873

z1 Ps

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

_Qs μ Vr d + RrIr d minus χIrq1113872 1113873

_Ir d minus σ Vrq + RrIr d minus χIq1113872 1113873

z2 Qs

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(5)

with α (1 minus (M2LrLs)) μ (VsMαLrLs) χ gωsαLr

η g(MVsLs) σ (1αLr)ampe subscripts d and q denote the two axes of the Park

rotating reference frame and vr vs ir and is are beingrespectively the rotor and the stator voltages (V) andcurrents (A) ωs and ωr are the angular speeds of the rotatingstator and the rotor electromagnetic fields (rads)M Lr andLs are themutual rotor and stator inductances (H) and Rr isthe rotor resistance

Moreover with p being the pair of poles the electro-magnetic torque can be determined by the followingequation

Tem pM

Ls

Ψs dirq (6)

ampe benefit of the backstepping control approach relieson its ability to dissociate complex nonlinear systems intomultiple simplified design problems (called steps or sub-systems) using the so-called virtual control variables(VCVs) In each step we virtually deal with a simple single-input and single-output subsystem and each step providesvirtual reference for the following one using Lyapunovrsquosfunctions to guarantee the stability of the subsystem In thelast step the actual control variable (ACV) that insures thestability of the overall system can be finally determined [19]

ampe DFIG side converter (DSC) in Figure 1 is controlledto regulate the stator active power Ps and the stator reactivepower Qs to their references Psr and Qsr respectively From

equation (4) we have two second-order systems thereforethe backstepping control design for each is divided into twosubsystems as shown in Figure 2

23 Subsystem A (Current Reference VCV) First we selectLyapunovrsquos quadratic functions V1 and V2 and then wedefine the error variables such that

V1 12

e21

V2 12

e22

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

e1 Plowasts minus Ps⟶ _e1 _Plowasts minus _Ps

e2 Qlowasts minus Qs⟶ _e2 _Qlowasts minus _Qs

⎧⎪⎨

⎪⎩(7)

According to backstepping theory in order to ensure astable tracking behavior the derivative of prechosen Lya-punovrsquos functions must be strictly negative such that

_V1 e1 middot _e1 minus h1e21

_V2 e2 middot _e1 minus h2e22

⎧⎨

⎩ (8)

with h1 and h2 being the positive backstepping tuning co-efficients ampe current reference VCVs can then be mathe-matically obtained using equations (5) (7) and (8) such that

_Ilowastrq

1μRr

_Plowasts + h1e11113872 1113873 minus

1Rr

Vrq + χIr d minus η1113872 1113873

_Ilowastr d

1μRr

_Qlowasts + h2e21113872 1113873 minus

1Rr

Vr d minus χIr d( 1113857

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(9)

24 Subsystem B (Voltage Reference ACV) Note that theVCVs (Ilowastr d and Ilowastrq) from the previous step (equation (9)) arethe desired variables for this step amperefore we selectLyapunovrsquos functions V3 and V4 and define the errorvariables

V3 12

e21 + e

231113872 1113873

V4 12

e22 + e

241113872 1113873

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

e3 Ilowastr d minus Irq⟶ _e3 _Ilowastrq minus _Irq

e4 Ilowastr d minus Ir d⟶ _e4 _Ilowastr d minus _Ir d

⎧⎪⎪⎨

⎪⎪⎩

(10)

Similarly in order to secure a stable tracking behavioraccording to the backstepping theory the derivative ofLyapunovrsquos functions must be strictly negative such that

_V3 e1 middot _e1( 1113857 e3 middot _e3( 1113857 minus h1e21 minus h3e

23

_V4 e2 middot _e2( 1113857 e4 middot _e4( 1113857 minus h2e22 minus h4e

24

⎧⎨

⎩ (11)

Using the same steps the voltage reference ACV can bemathematically determined using equations (5) (10) and(11)

Vlowastrq minus h3e3 minus _Ilowastrq minus μe11113966 1113967

1σ

minus RrIrq + χIr d + η1113966 1113967

Vlowastr d minus h4e4 minus _Ilowastr d minus μe21113966 1113967

1σ

minus RrIr d minus ϕIr d1113864 1113865

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(12)

Mathematical Problems in Engineering 3

with h1 h2 h3 and h4 being some strictly positive constantscalled the backstepping setting coefficients used on the onehand to guarantee the stability of the system and on the otherhand to ensure a quick dynamic response of the groupcontroller system

3 ldquoElectric Network Frequency-Sensitiverdquo Control

Figure 1 illustrates the complete DFIG-based WT structureincluding the network side converter (NSC) used to regulatethe DC link voltage Vdc and the reactive power exchangedthrough the filter Qtr ampe DFIG side converter (DSC) usedto regulate the stator reactive powerQs to zero in order to geta unity power factor at the point of common coupling(PCC) until the electric network operator demands oth-erwise and to adjust almost instantaneously the stator

active power Ps according to the electric network frequency-sensitive control loops Finally the pitch angle controlleradapts the mechanical power to maintain the frequencyregulation capability even under the full-load operationcondition Each controller will be analysed thoroughly in thenext subsections

31Artificial InertialResponse ampe inertial response permitsthe DFIG to reproduce synchronous generators behaviourproviding an active power support for the power systemduring the transient It consists in customizing the elec-tromagnetic torque reference Temr hence the active powerreference Psr as a proportion of the rate of change of thefrequency (ROCOF) At the event of frequency disruptionthe electromagnetic torque set point rises by ΔTem-IN causinga deceleration of the WT rotor speed Ωm and as a

vw

Turbine Gearbox

DFIG DSC NSC

Grid

Rtr Ltr

DSC control NSC control

PT

(Ps Qs)

(Ptr Qtr)Pr

QsrPsr

Qtr

DC bus voltage control

PCC

Pitch control

Speed control Power control

Ptr

ΩT

Ωmβ

Inertial and droop basedfrequency responses

Figure 1 ampe complete structure of frequency-sensitive DFIG-based WT control

dq

abc

DFIG

PWM

Pslowast

Ps

Qslowast Ilowastrd

Ird

Vlowastrd

Ilowastrq Vlowastrq

Irq

Qs

VCVcomputation

ACVcomputation

VCVcomputation

ACVcomputation

DSC

Electric network

DSC control

PLLddt

ndash+

A

B

B

ωs

ƪ

θs

θr

θrθ

ω

A

Figure 2 DSC backstepping control

4 Mathematical Problems in Engineering

consequence discharging a portion of the kinetic energystored in the WTspinning masses ampe mechanism is chosento be proportionate to that of synchronous generators andthus the additional power injected to the network can beexpressed as follows

ΔPIN(pu) 2HT middot fpudfpu

dt (13)

where fpu is the per-unit system frequency and HT the totalinertia constant (DFIG and WT) given by [5]

HT HDFIG + HWT HDFIG +12

JTΩ2ratedSrated

(14)

S rated and Ωrated are respectively the rated power andrated mechanical speed ampe equation that relates theelectromagnetic torque to the frequency can be determinedfrom equation (13) by the following expression

ΔTemminus IN(pu) 2HT middot fpudfpu

dt

1Ωm(pu)

(15)

Furthermore since the frequency is estimated by meansof a phase-locked loop (PLL) a low-pass filter needs to beintroduced into the control scheme in order to reduce theimpact of the small noises as shown in Figure 3 where TINrepresents the time constant of the filter and KIN its gain thatdetermines the amount of additional injected wind power incase of a frequency excursion

32 Speed Droop Control ampe artificial inertial response canonly be utilized to assist the system during the transitoryphase known as ldquodynamic frequency variationrdquo [20]However in order to enable the WT to provide active powersupport for an extended period of time another electricnetwork frequency-sensitive control loop that takes underconsideration the quasi-steady-state frequency deviationshould be added as shown in Figure 3ampe latter obligates theWT to operate following a ldquodeloaded operation character-istic (DL)rdquo as illustrated in Figure 4 creating a specificpower reserve that can be automatically activated to supportthe power systemwhen active power is needed at the event of

frequency disruption ampe creation of the power reserve isdone through the acceleration of mechanical speed Ωm byacting on the electromagnetic torque reference Tlowastemrminus DLhence the active power reference Plowasts moving the operationpoint from A (which corresponds to the maximum powerpoint tracking (MPPT) operation) to B (which corresponds

KINs1 + TINsX ΔTemndashIN

ΔPIN

++

Inertial response

fpu ΔPIN(pu)Xdivide

XΩm ΩmΩmRGT

Ωm

vwndashest(ρπR2GTv3

wndashest2Ωm) Cpe

λlowast

Clowastp

β

ΔPrsc_ +

Δf

f

fr

Eq (16)

Rotor speed control

TlowastemndashDL

Tlowastem

Eq (14)λ(Cp β)

XPlowasts

2HWT Pn

divide

Figure 3 Coordinated frequency-sensitive control scheme

0 05 1 15 WT rotor speed (pu)

0

01

02

03

04

05

06

07

08

09

1

Act

ive p

ower

(pu)

12

11ms

10ms

9ms

8ms

7ms

6ms

Speed limit

E

B

A

C

Power reserve

MPPT

DL

Figure 4 Deloaded operation

Define λi (i = 01hellipn) ampβj(i = 01hellipm)

Start

Compute Cp (λi βj) table(expression in the appendix)

Read βlowast

Cp (λi) = interp2(λi βj Cpprime λi βlowast)

2D interpolation of the tableCp (λi) for βk = βlowast Read Cp

lowast

λlowast = interp1(Cp (λi) λi Cplowast ldquolinearrdquo)

1D interpolation of λlowast

for Cp (λlowast) = Cplowast

Write λlowast

End

Figure 5 Organigram for the tip speed ratio referencecomputation

Mathematical Problems in Engineering 5

to the deloaded power point tracking (DL) operation) asshown in Figure 3 such that

PB 1 minus Rf1113872 1113873PA

ΩB≻ΩA Ωmppt

⎧⎨

⎩ (16)

where Rf is the reserve factor and PA and ΩA are beingrespectively the active power and the mechanical speed ofMPPT operation given by

PA ρπR2GT

2Ωm

v3wminus estCpmax1113890 1113891Ωm⟶ MPPT

vwminus est RΩm

GTλmppt

λmppt optimal tip speed ratio

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(17)

ampeoretically speaking the creation of the reserve canalso be achieved by decelerating the mechanical speedHowever it is preferred to use the acceleration method topreserve and even increase the amount of kinetic energystored in the WT At the event of frequency drop thecontroller changes the electromagnetic torque referencedecelerating the WT (moving from the point B through thepoint E to the maximum point A) as shown in Figure 4consequently rising the wind power production by a specificquantity ΔPrsc chosen to be proportionate to the frequencydeviation such thatΔPrsc K middot f minus fr( 1113857 K middot Δf

ΔPrscminus max Rf lowastPA⟶ total power reserve⎧⎨

⎩ (18)

with f and fr being respectively the measured and nominalfrequency 50Hz and K is an energy factor determined as afunction of the droop parameter δ

K Prated

δfr

1113888 1113889 (19)

with Prated being the generatorrsquos rated powerampe creation and activation (as function of ΔPrsc ) of the

power reserve are achieved through modifying the powercoefficient reference Cp

lowast and the tip speed ratio reference λlowastin equation (17) amperefore the power coefficient new ref-erence Cp

lowast can be determined from equation (1) by thefollowing expression

Clowastp λlowast β( 1113857 1 minus Rf1113872 1113873Cpmax lowastΔPrsc

05ρπR2v3w

Clowastp λlowast β( 1113857 1 minus Rf1113872 1113873Cpmax if ΔPrsc 0

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(20)

lowast plowast p While the reference of the tip speed ratio λlowast

which depends on the power coefficient reference Cplowast andfhe angle of orientation of the blades β can be determinedusing linear interpolation adopting the algorithm presentedin Figure 5

ampe block diagram of rotor speed control is illustrated inFigure 3

Finally the rotor speed controller along with the inertialresponseΔPIN sets the active power reference Psr for the DSCcontrol according to the following expressions

Plowasts Tlowastem middotΩm

Tlowastem Tlowastemminus DL + ΔTemminus IN1113896 (21)

33 Pitch Control ampe contribution of a WT to the globalpower reserve can be achieved either by accelerating therotor speed or by the orientation of the pitch angle Duringpartial-load operation mode (wind speed below rated) thefirst method could be used alone in case of a tolerable powerreserve However it becomes incapable if a larger reserve isrequested since the rotor speed should not exceed itsmaximum value (point B in Figure 4) In that case thesecond method is then called to take over ampe pitch con-troller calculates the appropriate pitch angle βref that pre-vents the generator speed from surpassing the maximumvalue 12 pu and βref is then transferred to the pitch systemwhich will either direct the fluid to the cylinders or the powerto the motors depending on the actuator to increase theangle of the blades consequently adjusting their lift forfurther mechanical power curtailment

For high wind speeds the WT is at full-load operationmode and the pitch system is already activated to keep therotor speed at its maximum value (point C in Figure 4) Notethat contrary to the classical WT control the regulationusing pitch angle control could be activated for all windconditions ampe dynamic of the pitch actuator can bemodelled using the following transfer function with Tpbeing the time constant of the pitch system [21]

β 1

1 + Tpsβref (22)

As previously mentioned the pitch angle β is used toregulate the rotor speedΩm ampe process is highly nonlinearand there is no direct relationship between these two var-iables Traditionally a gain scheduling control method isimplemented to make up for the existent nonlinear aero-dynamic behaviour [21] However the deloaded operationof the WT used for frequency regulation purposes com-plicates the control since the adjustment of the process gainnow depends on not only the wind speed but also the powerset point [21] Accordingly a simpler and more efficientapproach is presented in this paper It is based on Cp (λ β)table inversion since the nonlinear characteristic is essen-tially brought by its curve ampe architecture of the controlapproach is depicted in Figure 6

ampe reference of the pitch angle βref is determined usingthe reference of the power coefficient Clowastp an estimation oftip speed ratio λlowast and an inversion of the Cp (λ β) tableMoreover λlowast is determined using the rotor speed mea-surement and Clowastp is obtained from the aerodynamic torquereference TlowastT after inverting each element of the WTmodel(equation (1) to equation (4)) (note that in the steady stateTem Tg) As a consequence the process view by the con-troller becomes linear and electromagnetic torque reference

6 Mathematical Problems in Engineering

Tlowastem could be provided using a simple constant gain PIcontroller A dynamic saturation is used to limit Clowastp ref-erence to Clowastpminus up(λ β 30deg) and Clowastpminus down(λ β 0 1

deg)

ampe inversion of the Cp (λ β) table could be applied toany mathematical approximation It is based on 1- and 2-dimensional linear interpolations and it can be depicted inthe organigram (Figure 7)

4 Results and Discussions

41 General Discussion ampe power system is exposed tomany forms of disturbances A load change results in var-iation of the electrical torque Te output of all generators anda change in the production results in variation of the me-chanical torque Tm of all generators ampe frequency devia-tions reflect the mismatches between the electrical Te andmechanical Tm torques as represented by the followingequation of motion [22]

Tm minus Te 2Hdωdt

2Hdf

dt (23)

whereH is the power systemrsquos corresponding inertia constantand ω and f are the (per unit) rotational speed and the ENFrespectively [23] Equation (20) can be expressed in terms ofthe electrical Pe and mechanical Pm powers such that

Pm1 minus Pe1( 1113857 + ΔPm minus ΔPe( 1113857 ω1 minus Δω( 1113857 Tm1 minus Te1( 11138571113858

+ ΔTm minus ΔTe( 11138571113859

(24)

where we denote the deviations by the prefix (Δ) and thesteady-state values by the subscript (1) with ω1(pu) 1 andby ignoring the higher order terms and adopting the realistic

assumption of Pm1Pe1 and Tm1Te1 in the steady stateEquation (24) can further be adjusted into [22]

ΔPm minus ΔPe( 1113857 ΔTm minus ΔTe( 1113857 (25)

Replacing into equation (23) we can write

ΔPm minus ΔPe 2HdΔωdt

2HdΔfdt

(26)

In this work we have considered the load sensitivity tofrequency deviations Being that practically an abruptchange in frequency will cause a variation of the powerdemand [22] ampe overall network frequency-dependentcharacteristic of loads can be represented by the followingequation

ΔPe ΔPl + DΔf (27)

with ΔPl being the non-frequency-sensitive load variationand DΔω is frequency-sensitive load variation ampe coeffi-cient D represents the self-regulation of loads and it is

1GT

1GT

GT

1GT

ΩTRvw

1Jwts + fΩm

Ωlowastm

ΩT

Temr

GearboxTurbine Transmission

β

vw

λ

_+

2ΩlowastmTlowastaρπR2v3

w

_+

Cp(λ β)

Cp(λ β)(ρπR2v32ΩT)

Ωmndashr

ΩlowastTΩTRvw

PI

λlowast

Tlowasta Tlowast

em

Tg

Clowastp_down

Clowastp_up

Clowastp

Pitch system

βref

β(Cp λ)

TT

Figure 6 Block diagram of the rotor speed control

Define λi (i = 0 1hellipn)ampβj (i = 0 1hellipm)

Start

Compute Cp (λi βi) table(expression in the appendix)

Read λlowast

Cp (βi) = interp2 (β λ Cp β λlowast ldquolinearrdquo)

2D interpolation of the tableCp (βi) for λk = λlowast Read Clowast

p

βref = interp1(Cp (βi) β Clowastp ldquolinearrdquo)

1D interpolation of βreffor Cp = Clowast

p

Write βref

End

Figure 7 Organigram of the Cp table inversion

Mathematical Problems in Engineering 7

expressed as a percent change in load for 1 deviation infrequency [22] Substituting into equation (26) we can write

ΔPm minus ΔPl 2HdΔfdt

+ DΔf (28)

42 Power System Modelling To investigate the perfor-mances of the proposed control strategies a model of a smallpower system based on the scheme illustrated in Figure 8was designed inMatlabSimulink environment It consists offour identical conventional generating units (n 4 mediumpower hydroelectric generators) [2 22] each has a powerrating of Si 100MVA an inertia constant of Hi 50 s on100 MVA base and a droop for the speed governor δi 02feeding a total load of 220MW For the analysis of frequencyregulation capability we are concerned with the collectivebehaviour of all generators in the power system ampereforein this study all conventional synchronous generators arerepresented by a single equivalent machine driven by themechanical outputs of each turbine [22]ampe power rating ofthe equivalent generator is of Seq nSi and the equivalentdroop δeq and the corresponding inertia constant of thepower system Heq can be determined using the followingequations

Heq nHiSi

Seq

δeq δi

n

(29)

Note that the synchronous generators are operatingwithout automatic generation control (AGC) and onlyprimary frequency regulation is considered in this studywhich is practically sufficient for the research objectives

43 Artificial Inertial Response Evaluation In order to ex-amine the implemented artificial inertial control behaviourwe have compared three simulation scenarios as summa-rized in Table 1

ampe first scenario S1 represents the reference case wherethe first second and third synchronous generation unitsprovide both inertial response and primary frequencycontrol (PFC) while the fourth synchronous generation unitis providing only its inherited inertial reaction withoutprimary frequency response (no PFC) ampus according toequation (29) the system equivalent inertia remains con-stant Heq 50 s but the equivalent droop coefficient is nowδeq 0066 ampe remaining scenarios represent the casewhere the fourth synchronous generation unit is replacedwith a wind farm (WF) with an equivalent power ratingwhere S2 and S3 are respectively the wind farm caseswithout and with inertial control implemented In this casethe wind power penetration rises up to LP 25 thereforethe equivalent inertia constant is decreased to Hrsquoeq Heq(1minus Lp) 375 while the equivalent droop remains constantδrsquoeq 0066 A sudden rise in load by 20MW (005 pu systembase) is introduced to the system at t 300 s

Figure 9 portrays the dynamic reaction of the electricnetwork frequency for the three simulation scenarios Withscenario S1 being the reference case it can be observed that thedeepest frequency nadir the worst case is obtained withscenario S2 where the artificial inertial response of WTs isdisabled ampat is mainly due to the reduction of the systemequivalent inertia caused by the increase of the wind powerpenetration Lp to 25 in the system Meanwhile the narrowfrequency nadir the finest case is obtained with scenario S3where the inertial response is enabled and with an appropriategain KIN choice the inertial support from the WTs could beeven greater than that obtained from the synchronous gen-eration unit Since the wider the range of speed variation thebigger the amount of kinetic energy can be extracted

Figures 10ndash12 show the dynamic behaviour of a singleWT for different operation conditions Initially (before thedisturbance) the rotor speed and the active power output aremaintained to their optimal values corresponding to MPPTAt the event of frequency drop t 120 s and when the windspeed is below rated vw 65ms (partial-load operationmode) the sequence of events that occur can be summarizedas follows

(i) ampe controller adjusts the electromagnetic torquereference causing a deceleration of the rotor speed(Figure 10(a))

(ii) ampe rotor speed is below its maximum value(gt12 pu) therefore the pitch angle is kept at zero(Figure 11(a))

(iii) ampe reduction of the rotor speed causes the ex-traction of a portion of the kinetic energy stored inthe spinning masses (Figure 12(a)) ampis extra activepower will be used to support the power system inrecovering the frequency to 50Hz

(iv) ampe countering spike of the output power(Figure 12(a)) at roughly t 310 s can be explained

++ +++ ndash

WF

n-synchronous generation units

Primary frequency control (δeq)AGC

LpΔPWF

ΔPsyn

ΔPL

ΔfΔPm 12Heqs + D

Figure 8 Electric network frequency regulation control scheme ofa power system

Table 1 Simulation scenarios

Scenarios S1 S2 S3Generation units 1 2 and 3 C C C

Generation unit 4 Cno PFC NC NC

Wind farm NC Cno IC

Conly IC

C connected NC nonconnected PFC primary frequency control ICinertial control

8 Mathematical Problems in Engineering

as follows let us consider that theWTwas operatingat pointA (Figure 4) with the rotor speed reductionthe WTwill move to a suboptimal power extractionoperation point at the end of the inertial reactionamperefore less power will be delivered until fullrecovery of the WT

For a high wind speed vw 15ms (full-load operationmode) the sequence of events that occur can be summarizedas follows

(i) ampe pitch controller (Figure 11(b)) maintains therotor speed at its maximum value (asymp12 pu)(Figure 10(b))

(ii) ampe controller tries to adjust rotor speed but sincethe pitch controller is activated in this mode itcounteracts the action by reducing the pitch anglethus indirectly exploiting the mechanical power thatwas already curtailed by the positive pitch angle tocreate the power surge (Figure 12(b)) Not that thepower response at this mode requires no recoveryprocess since the pitching system is the one re-sponsible for the contribution

In order to highlight the merits of using a backsteppingcontrol algorithm instead of classical controllers it is par-ticularly important to analyse the system performance undersome kind of disturbances amperefore since the machineparameters are usually exposed to many forms of inaccur-acies especially due to the measuring devices identificationmethodology or several natural phenomena a robustnesstest was carried out to compare the performance of theproposed control strategy versus classical PI controllerswhen parametric variations are registered ampe test consistsin purposefully modifying the rotor resistance Rr of theDFIG by 50 and the stator inductance Ls by 10 from theirnormal values

Figures 12 and 13 show respectively the evolution of theDFIG stator active and reactive powers and Figures 14 and15 respectively show the evolution of d and q componentsof the rotor currents ampe test highlights the high sensitivityof classical PI controllers towards parametric variationwhich is notably observed due to the appearance of a sig-nificant static error in all simulation results whereas the

proposed backstepping control algorithm demonstrates anexquisite disturbance rejection being that all the outputsconverge correctly to their designated references Moreoverthe three-phased stator current sinusoidal waveform isshown in Figure 16

44 SpeedDroopControlEvaluation ampe performance of theproposed speed droop control will be evaluated for thefollowing simulation cases

Case 1 partial-load operation mode (wind speedvw 65ms)Case 1 Full-load operation mode (wind speedvw 15ms)

ampe set of results shown in the following figures dem-onstrates the capability of the proposed control strategy torespond to a sudden active power call at t 150 s Before thearrival of the frequency drop the WT is running at a ro-tational speed higher than the optimum (ΩgtΩmppt) inorder to lower the aerodynamic conversion efficiency rep-resented by Cp and therefore to operate following adeloaded operation characteristic with the power reservebeing created For the research objectives this work pre-sumes that the WT is operating with a reserve factorRf 10 while on the practical level the power margins aregenerally specified by the grid codes

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under partial-load operationmode can be summarized as follows

(i) ampe step in the output power reference (by ΔPrscFigure 3) modifies the electromagnetic torque ref-erence Tlowastem causing the rotor speed reduction asshown in Figure 17(a)

(ii) ampe rotor speed is below its maximum value thepitch control is not required in this case andtherefore the pitch angle is maintained at zero(Figure 18(a))

(iii) ampe rotor speed deceleration rises the power coef-ficient Cp to its maximum value (Figure 4) as shownin Figure 19(a) allowing consequently the WT toactivate its full power reserve

(iv) ampe power reserve activation rises the output powerof the WT by ΔPrsc (Figure 20(a)) thereforeallowing it to participate in the frequency recoveryprocess

(v) ampe power peaks induced as shown in Figure 20(a)demonstrate the benefit from creating the powerreserve by acceleration of the rotor speed the leftside of the power curve Figure 4 since now morekinetic energy is at our disposal and it can be usedwhenever the WT is decelerating

(vi) When the frequency recovers at t 400 s the controlstrategy reaccelerates the WT (Figure 17(a)) low-ering the power coefficient (Figure 19(a)) in order

S1S2S3

300 350 400250 Time (sec)

492

494

496

498

50

Fre

quen

cy (H

z)

Figure 9 Electric network frequency deviation for differentscenarios

Mathematical Problems in Engineering 9

to recreate the power reserve (Figure 20(a)) for thenext use

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under full-load operationmode can be summarized as follows

(i) ampe pitch control is now activated as shown inFigure 18(b) to keep the rotor speed at its maxi-mum value (Figure 17(b)) and to create the powerreserve (Figure 19(b)) since the rotor speed can nolonger be accelerated

(ii) ampe active power call (ΔPrsc Figure 4) reduced thepitch angle to make use of the mechanical powercurtailed by the positive β

(iii) β reduction increases the power coefficient CP asshown in Figure 19(b)consequently rising the

output according to the amount of power specifiedby ΔPrsc (Figure 20(b))

(iv) When the frequency recovers at t 400 s the pitchcontrol strategy rises the pitch angle (Figure 18(b))lowering the power coefficient (Figure 19(b)) inorder to recreate the power reserve (Figure 20(b))for the next use

45 Coordinated Control ampe artificial inertial reaction thespeed droop control and the pitch control could be usedaltogether to further enhance the frequency regulationcapability of WTs In this subsection we compared thesimulation scenarios summarized in Table 2 with S1 beingthe reference case where the wind power penetration isLp 0 For the other simulation scenarios the fourthgeneration synchronous is replaced with a WF with an

084

085

086

087

088

089

09

091

092Ro

tor s

peed

(pu)

110 120 130 140 150 160100Time (s)

(a)

116

12

124

Roto

r spe

ed (p

u)

110 120 130 140 150 160100Time (s)

(b)

Figure 10 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

10

Pitc

h an

gle (

deg)

110 120 130 140 150 160100Time (s)

ndash5

0

5

(a)

175

205Pi

tch

angl

e (deg)

110 120 130 140 150 160100Time (s)

18

185

19

195

20

(b)

Figure 11 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

10 Mathematical Problems in Engineering

equivalent power rating and the wind power penetrationrises to Lp 25 with S2 S3 S3 and S4 being respectivelythe cases without any frequency control the inertial reactiononly speed droop control only and all controllers

Figure 21 portrays the dynamic reaction of the frequencyfor each scenario All simulations were performed for amedium wind speed of vw 9ms and a sudden rise in loadby 005 pu system base is introduced to the system att 200 s

ampe results show that the severest case is obtained withthe simulation scenario S2 the case where the WF is

connected with no frequency regulation ability Comparedto the reference case S1 where the wind power penetrationLp 0 the frequency curve for the second simulationscenario S2 falls to a deeper nadir due to the reduction of thesystemrsquos equivalent inertia caused by increasing the windpower penetration Lp 25 On the other hand in the casewhere the inertial control is implemented S3 the WT de-celerates to release a portion of its kinetic energy transientlyimproving the frequency deviation Consequently the fre-quency nadir is lifted up to the level of the reference case S1However the quasi-steady-state frequency does not get any

Pslowast

Ps (PI)Ps (Bs)

ndash034

ndash032

ndash03

ndash028

ndash026

ndash024

ndash022W

T ou

tput

pow

er (p

u)

110 120 130 140 150 160100Time (seconds)

(a)

Pslowast

Ps (PI)Ps (Bs)

ndash105

ndash1

ndash095

ndash09

ndash085

WT

outp

ut p

ower

(pu)

110 120 130 140 150 160100Time (s)

(b)

Figure 12 Active power evolution for partial-load (a) and full-load (b) operation modes

QslowastQs (PI)Qs (Bs)

ndash5000

0

5000

Reac

tive p

ower

Qs (

Var)

110 120 130 140 150 160100Time (s)

(a)

QslowastQs (PI)Qs (Bs)

times104

ndash1

ndash05

0

05

1

Reac

tive p

ower

(Var

)

110 120 130 140 150 160100Time (s)

(b)

Figure 13 Reactive power evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 11

better with only the inertial control being enabled since itprovides only short-term frequency support With the speeddroop controller being enabled simulation scenario S4 itcan be observed that the WTcontribution is higher since themaximum transient and the quasi-steady-state frequencydeviations are both optimised Finally with both controllersbeing simultaneously enabled simulation scenario S5 thefrequency curve will further be improved for both short- andlong-term durations

As mentioned previously with only the inertial controlbeing activated at the event of frequency excursion the

rotor speed deceleration will impose a suboptimal powerextraction and then less power will be delivered until the fullrecovery of theWTto its optimum speed (Figure 10(c))ampisrecovery phase that generally lasts tens of seconds could beavoided when both controllers are simultaneously activatedgiven that the droop speed controller forces the WT tooperate at a higher rotational speed (ΩgtΩmppt) left side ofthe curve (Figure 4)amperefore when theWTdecelerates theoperating point will climb toward the optimum point and asa result there will be no need for the WT to recover at theend of the inertial response

Irqlowast

Irq (PI)Irq (Bs)

500

600

700

800

900

1000

1100Irq

110 120 130 140 150 160100Time (s)

(a)

Irqlowast

Irq (PI)Irq (Bs)

2600

2700

2800

2900

3000

3100

Irq

110 120 130 140 150 160100Time (s)

(b)

Figure 14 Active current Irq evolution for partial-load (a) and full-load (b) operation modes

Irdlowast

Ird (PI)Ird (Bs)

130

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(a)

Irdlowast

Ird (PI)Ird (Bs)

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(b)

Figure 15 Reactive current Ird evolution for partial-load (a) and full-load (b) operation modes

12 Mathematical Problems in Engineering

110 11005 1101 11015 1102

ndash1000

ndash500

0

500

1000

Is (A

)

110 120 130 140 150 160100Time (s)

(a)

ndash2000

ndash1000

0

1000

2000

Is (A

)

110 120 130 140 150 160100Time (s)

110 11005 1101 11015 1102

(b)

Figure 16 Stator current evolution for partial-load (a) and full-load (b) operation modes

08

09

1

11

12

Roto

r spe

ed (p

u)

200 300 400 500100Time (s)

(a)

11

115

12

125

13Ro

tor s

peed

(pu)

200 300 400 500100Time (s)

(b)

Figure 17 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

ndash5

0

5

10

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(a)

18

19

20

21

22

23

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(b)

Figure 18 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 13

Powerreserve

Cplowast

CpCpopt

200 300 400 500100Time (s)

042

044

046

048

05

Cp

(a)

Powerreserve

Cplowast

CpoptCp

011

012

013

014

015

016

Cp

150 200 250 300 350 400 450 500100 Time (s)

(b)

Figure 19 Power coefficient evolution for partial-load (a) and full-load (b) operation modes

Powerreserve

Power peaks

PrefPoptP

ndash03

ndash028

ndash026

ndash024

ndash022

ndash02

WT

outp

ut p

ower

(pu)

150 200 250 300 350 400 450 500100 Time (s)

(a)

Powerreserve

PrefPoptP

ndash105

ndash1

ndash095

ndash09

ndash085

ndash08

ndash075

ndash07

WT

outp

ut p

ower

(pu)

200 300 400 500100 Time (s)

(b)

Figure 20 WR output power evolution for partial-load (a) and full-load (b) operation modes

Table 2 Simulation scenarios

Scenarios S1 S2 S3 S3 S4Generation units 1 2 and 3 C C C C CGeneration unit 4 C NC NC NC NCWind farm NC C no control C only IC C only PFC C IC and PFCC connected NC nonconnected PFC primary frequency control IC inertial control

14 Mathematical Problems in Engineering

5 Conclusion

ampis paper explores different control approaches thatallow DFIG-based WTs to engage actively in frequencyregulation via coordinating the rotor speed and the pitchangle controllers In a short-term duration the inertialcontrol permits the WT to emulate the synchronousgenerator natural behaviour Accordingly at the event offrequency excursion the controller decelerates the WTin order to extract a portion of its kinetic energy shortlyproviding extra active power support for the powersystem However the inertial reaction alone is heavilydependent on the initial point of operation and a goodtuning of the controller gain is required since for in-stance at low wind speeds the rotor speed should notexceed its minimum value 06 pu for the stable operationof the WT ampe speed droop controller enables the WT toprovide active power assistance over an extended periodimproving the robustness of the system It forces the WTto operate following a deloaded characteristic creating acertain power reserve that can be automatically triggeredat the event of frequency deviations Moreover an in-novative pitch angle control is utilized to protect the WTagainst over speeding and to maintain the frequencyregulation capability under various operationconditions

Finally a study case considering an isolated powersystem that consists of synchronous generators DFIG-basedwind farm and static loads was examined to compare theperformance of each controller ampese simulation resultsshow that the coordination of the controllers improves boththe dynamic and the quasi-steady-state frequency deviationand brings the frequency nadir up to a far superior level thanthat obtained with the wind farm being disconnected (0wind power penetration)

Appendix

Wind turbine parameters

Rated power P 2MW blade radius R 45m gearboxG 90 WT inertia HWT 435 s damping coefficientf 0017Nmiddotmmiddotsrd and air density ρ 12 kgm3

DFIG parameters

Rated power P 2MW rated torque 127 kNm gridrated voltage and frequency Vs 690V and fs 50Hz polepair p 2 generator inertia HG 05 s stator and rotorresistances Rs 26mΩ and Rr 29mΩ stator and rotorinductance Ls 20mH and Lr 20mH and mutual in-ductance M 3253mH

Power coefficient expression

Cp X1X2

λ + 0008βminus00035 middot X2

β3 + 11113888 1113889 minus X3β minus X41113888 1113889

middot expX5

λ + 0008βminus00035 middot X5

β3 + 11113888 1113889 + X6λ

X1 05109

X2 116

X3 04

A4 5

X5 21

X6 00068

(A1)

Data Availability

No data were used to support this study

Disclosure

ampis paper is an expanded version of a paper entitled ldquoIn-ertial Response using Backstepping Control from DFIGbased Wind Power Plant for Short-Term Frequency Regu-lationrdquo presented at 2019 International Conference onControl Decision and Information Technologies held inParis France from 23 to 26 April 2019

Conflicts of Interest

ampe authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] Y Li Z Xu J Zhang and K P Wong ldquoVariable gain controlscheme of DFIG-based wind farm for over-frequency sup-portrdquo Renewable Energy vol 120 pp 379ndash391 2018

[2] N R Ullah T ampiringer and D Karlsson ldquoTemporaryprimary frequency control support by variable speed windturbines- potential and applicationsrdquo IEEE Transactions onPower Systems vol 23 no 2 pp 601ndash612 2008

[3] A Molina-Garcia I Munoz-Benavente A D Hansen andE Gomez-Lazaro ldquoDemand-side contribution to primaryfrequency control with wind farm auxiliary controlrdquo IEEE

S4S5

S1

S3S2

492

494

496

498

50

Freq

uenc

y (H

z)

150 200Time (s)

250 300

Figure 21 Deviation of the frequency for each simulation scenario

Mathematical Problems in Engineering 15

Transactions on Power Systems vol 29 no 5 pp 2391ndash23992014

[4] F Poitiers T Bouaouiche and M Machmoum ldquoAdvancedcontrol of a doubly-fed induction generator for wind energyconversionrdquo Electric Power Systems Research vol 79 no 7pp 1085ndash1096 2009

[5] Z-S Zhang Y-Z Sun J Lin and G-J Li ldquoCoordinatedfrequency regulation by doubly fed induction generator-basedwind power plantsrdquo IET Renewable Power Generation vol 6no 1 pp 38ndash47 2012

[6] R Chakib M Cherkaoui and A Essadki ldquoInertial responseused for a short term frequency control for DFIG windturbine controlled by ADRCrdquo ARPN Journal of Engineeringand Applied Sciences vol 11 no 5 2016

[7] Y-K Wu S-M Chang and P Mandal ldquoGrid-connectedwind power plants a survey on the integration requirementsin modern grid codesrdquo in Proceedings of the 2019 IEEEIAS55th Industrial and Commercial Power Systems TechnicalConference (IampCPS) pp 1ndash9 Canada Canada May 2019

[8] L Ruttledge and D Flynn ldquoEmulated inertial response fromwind turbines gain scheduling and resource coordinationrdquoIEEE Transactions on Power Systems vol 31 no 5pp 3747ndash3755 2015

[9] A I Estanqueiro J M F De Jesus J Ricardo A dos Santosand J A P Lopes ldquoBarriers (and solutions) to Very HighWind Penetration in Power Systemsrdquo in Proceedings of the2007 IEEE Power Engineering Society General Meetingpp 1ndash7 Tampa FL USA June 2007

[10] Y Wang G Delille H Bayem X Guillaud and B FrancoisldquoHigh wind power penetration in isolated power systems-assessment of wind inertial and primary frequency re-sponsesrdquo IEEE Transactions on Power Systems vol 28 no 3pp 2412ndash2420 2013

[11] P-K Keung P Li H Banakar and B T Ooi ldquoKinetic energyof wind-turbine generators for system frequency supportrdquoIEEE Transactions on Power Systems vol 24 no 1 pp 279ndash287 2008

[12] H Ye W Pei and Z Qi ldquoAnalytical modeling of inertial anddroop responses from a wind farm for short-term frequencyregulation in power systemsrdquo IEEE Transactions on PowerSystems vol 31 no 5 pp 3414ndash3423 2015

[13] H Liu and Z Chen ldquoContribution of VSC-HVDC to fre-quency regulation of power systems with offshore windgenerationrdquo IEEE Transactions on Energy Conversion vol 30no 3 pp 918ndash926 2015

[14] R M Kamel A Chaouachi and K Nagasaka ldquoampree controlstrategies to improve the microgrid transient dynamic re-sponse during isolated mode a comparative studyrdquo IEEETransactions on Industrial Electronics vol 60 no 4pp 1314ndash1322 2012

[15] S Wang J Hu X Yuan and L Sun ldquoOn inertial dynamics ofvirtual-synchronous-controlled DFIG-based wind turbinesrdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1691ndash1702 2015

[16] H T Ma and B H Chowdhury ldquoWorking towards frequencyregulation with wind plants combined control approachesrdquoIET Renewable Power Generation vol 4 no 4 pp 308ndash3162010

[17] I A Gowaid A El-Zawawi and M El-Gammal ldquoImprovedinertia and frequency support from grid-connected DFIGwind farmsrdquo in Proceedings of the Power Systems Conferenceand Exposition (PSCE) pp 1ndash9 Phoenix AZ USA March2011

[18] M Nadour A Essadki and T Nasser ldquoComparative analysisbetween PI amp backstepping control strategies of DFIG drivenby wind turbinerdquo International Journal of Renewable EnergyResearch vol 7 no 3 pp 1307ndash1316 2017

[19] M Nadour A Essadki M Fdaili and T Nasser ldquoAdvancedbackstepping control of a wind energy conversion systemusing a doubly-fed induction generatorrdquo in Proceedings of the2017 International Renewable and Sustainable Energy Con-ference (IRSEC) pp 1ndash6 Tangier Morocco December 2017

[20] Y Rebours A Comprehensive Assessment of Markets forFrequency and Voltage Control Ancillary Services PhD thesisUniversity of Manchester Manchester England 2008

[21] P Venne X Guillaud R Teodorescu and J MahseredjianldquoGeneralized gain scheduling for deloaded wind turbineoperationrdquo Wind Engineering vol 34 no 2 pp 219ndash2392010

[22] P Kundur N J Balu andM G Lauby Power System Stabilityand Control Vol 7 McGraw-Hill New York NY USA 1994

[23] J Van de Vyver J D M De Kooning B MeersmanL Vandevelde and T L Vandoorn ldquoDroop control as analternative inertial response strategy for the synthetic inertiaon wind turbinesrdquo IEEE Transactions on Power Systemsvol 31 no 2 pp 1129ndash1138 2016

16 Mathematical Problems in Engineering

Ωm GT middotΩT

TT GT middot Tg(3)

where TT and Tg are the torques at the gearbox input andoutput respectively ampen with Tem being the electromag-netic torque of the generator Jwt the system (WTand DFIG)total inertia and f the friction according to the fundamentalequation of dynamic we can write

Jwt

dΩm

dt Tg minus Tem minus f middotΩm (4)

22 DFIG Modelling and Control In this work we haveadopted the field-oriented control joining the stator flux tothe d-axis of the Park reference frame (ψsq 0 and ψsdψs)in order to dissociate the control of active power Ps andreactive power Qs Neglecting the stator resistance Rs whichis a realistic approximation for high-power generators [4]the state model of the DFIG can be determined by thefollowing equation [19]

_Ps μ Vrq + RrIrq + χIr d minus η1113872 1113873

_Irq minus σ Vrq + RrIrq + χIr d minus η1113872 1113873

z1 Ps

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

_Qs μ Vr d + RrIr d minus χIrq1113872 1113873

_Ir d minus σ Vrq + RrIr d minus χIq1113872 1113873

z2 Qs

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(5)

with α (1 minus (M2LrLs)) μ (VsMαLrLs) χ gωsαLr

η g(MVsLs) σ (1αLr)ampe subscripts d and q denote the two axes of the Park

rotating reference frame and vr vs ir and is are beingrespectively the rotor and the stator voltages (V) andcurrents (A) ωs and ωr are the angular speeds of the rotatingstator and the rotor electromagnetic fields (rads)M Lr andLs are themutual rotor and stator inductances (H) and Rr isthe rotor resistance

Moreover with p being the pair of poles the electro-magnetic torque can be determined by the followingequation

Tem pM

Ls

Ψs dirq (6)

ampe benefit of the backstepping control approach relieson its ability to dissociate complex nonlinear systems intomultiple simplified design problems (called steps or sub-systems) using the so-called virtual control variables(VCVs) In each step we virtually deal with a simple single-input and single-output subsystem and each step providesvirtual reference for the following one using Lyapunovrsquosfunctions to guarantee the stability of the subsystem In thelast step the actual control variable (ACV) that insures thestability of the overall system can be finally determined [19]

ampe DFIG side converter (DSC) in Figure 1 is controlledto regulate the stator active power Ps and the stator reactivepower Qs to their references Psr and Qsr respectively From

equation (4) we have two second-order systems thereforethe backstepping control design for each is divided into twosubsystems as shown in Figure 2

23 Subsystem A (Current Reference VCV) First we selectLyapunovrsquos quadratic functions V1 and V2 and then wedefine the error variables such that

V1 12

e21

V2 12

e22

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

e1 Plowasts minus Ps⟶ _e1 _Plowasts minus _Ps

e2 Qlowasts minus Qs⟶ _e2 _Qlowasts minus _Qs

⎧⎪⎨

⎪⎩(7)

According to backstepping theory in order to ensure astable tracking behavior the derivative of prechosen Lya-punovrsquos functions must be strictly negative such that

_V1 e1 middot _e1 minus h1e21

_V2 e2 middot _e1 minus h2e22

⎧⎨

⎩ (8)

with h1 and h2 being the positive backstepping tuning co-efficients ampe current reference VCVs can then be mathe-matically obtained using equations (5) (7) and (8) such that

_Ilowastrq

1μRr

_Plowasts + h1e11113872 1113873 minus

1Rr

Vrq + χIr d minus η1113872 1113873

_Ilowastr d

1μRr

_Qlowasts + h2e21113872 1113873 minus

1Rr

Vr d minus χIr d( 1113857

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(9)

24 Subsystem B (Voltage Reference ACV) Note that theVCVs (Ilowastr d and Ilowastrq) from the previous step (equation (9)) arethe desired variables for this step amperefore we selectLyapunovrsquos functions V3 and V4 and define the errorvariables

V3 12

e21 + e

231113872 1113873

V4 12

e22 + e

241113872 1113873

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

e3 Ilowastr d minus Irq⟶ _e3 _Ilowastrq minus _Irq

e4 Ilowastr d minus Ir d⟶ _e4 _Ilowastr d minus _Ir d

⎧⎪⎪⎨

⎪⎪⎩

(10)

Similarly in order to secure a stable tracking behavioraccording to the backstepping theory the derivative ofLyapunovrsquos functions must be strictly negative such that

_V3 e1 middot _e1( 1113857 e3 middot _e3( 1113857 minus h1e21 minus h3e

23

_V4 e2 middot _e2( 1113857 e4 middot _e4( 1113857 minus h2e22 minus h4e

24

⎧⎨

⎩ (11)

Using the same steps the voltage reference ACV can bemathematically determined using equations (5) (10) and(11)

Vlowastrq minus h3e3 minus _Ilowastrq minus μe11113966 1113967

1σ

minus RrIrq + χIr d + η1113966 1113967

Vlowastr d minus h4e4 minus _Ilowastr d minus μe21113966 1113967

1σ

minus RrIr d minus ϕIr d1113864 1113865

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(12)

Mathematical Problems in Engineering 3

with h1 h2 h3 and h4 being some strictly positive constantscalled the backstepping setting coefficients used on the onehand to guarantee the stability of the system and on the otherhand to ensure a quick dynamic response of the groupcontroller system

3 ldquoElectric Network Frequency-Sensitiverdquo Control

Figure 1 illustrates the complete DFIG-based WT structureincluding the network side converter (NSC) used to regulatethe DC link voltage Vdc and the reactive power exchangedthrough the filter Qtr ampe DFIG side converter (DSC) usedto regulate the stator reactive powerQs to zero in order to geta unity power factor at the point of common coupling(PCC) until the electric network operator demands oth-erwise and to adjust almost instantaneously the stator

active power Ps according to the electric network frequency-sensitive control loops Finally the pitch angle controlleradapts the mechanical power to maintain the frequencyregulation capability even under the full-load operationcondition Each controller will be analysed thoroughly in thenext subsections

31Artificial InertialResponse ampe inertial response permitsthe DFIG to reproduce synchronous generators behaviourproviding an active power support for the power systemduring the transient It consists in customizing the elec-tromagnetic torque reference Temr hence the active powerreference Psr as a proportion of the rate of change of thefrequency (ROCOF) At the event of frequency disruptionthe electromagnetic torque set point rises by ΔTem-IN causinga deceleration of the WT rotor speed Ωm and as a

vw

Turbine Gearbox

DFIG DSC NSC

Grid

Rtr Ltr

DSC control NSC control

PT

(Ps Qs)

(Ptr Qtr)Pr

QsrPsr

Qtr

DC bus voltage control

PCC

Pitch control

Speed control Power control

Ptr

ΩT

Ωmβ

Inertial and droop basedfrequency responses

Figure 1 ampe complete structure of frequency-sensitive DFIG-based WT control

dq

abc

DFIG

PWM

Pslowast

Ps

Qslowast Ilowastrd

Ird

Vlowastrd

Ilowastrq Vlowastrq

Irq

Qs

VCVcomputation

ACVcomputation

VCVcomputation

ACVcomputation

DSC

Electric network

DSC control

PLLddt

ndash+

A

B

B

ωs

ƪ

θs

θr

θrθ

ω

A

Figure 2 DSC backstepping control

4 Mathematical Problems in Engineering

consequence discharging a portion of the kinetic energystored in the WTspinning masses ampe mechanism is chosento be proportionate to that of synchronous generators andthus the additional power injected to the network can beexpressed as follows

ΔPIN(pu) 2HT middot fpudfpu

dt (13)

where fpu is the per-unit system frequency and HT the totalinertia constant (DFIG and WT) given by [5]

HT HDFIG + HWT HDFIG +12

JTΩ2ratedSrated

(14)

S rated and Ωrated are respectively the rated power andrated mechanical speed ampe equation that relates theelectromagnetic torque to the frequency can be determinedfrom equation (13) by the following expression

ΔTemminus IN(pu) 2HT middot fpudfpu

dt

1Ωm(pu)

(15)

Furthermore since the frequency is estimated by meansof a phase-locked loop (PLL) a low-pass filter needs to beintroduced into the control scheme in order to reduce theimpact of the small noises as shown in Figure 3 where TINrepresents the time constant of the filter and KIN its gain thatdetermines the amount of additional injected wind power incase of a frequency excursion

32 Speed Droop Control ampe artificial inertial response canonly be utilized to assist the system during the transitoryphase known as ldquodynamic frequency variationrdquo [20]However in order to enable the WT to provide active powersupport for an extended period of time another electricnetwork frequency-sensitive control loop that takes underconsideration the quasi-steady-state frequency deviationshould be added as shown in Figure 3ampe latter obligates theWT to operate following a ldquodeloaded operation character-istic (DL)rdquo as illustrated in Figure 4 creating a specificpower reserve that can be automatically activated to supportthe power systemwhen active power is needed at the event of

frequency disruption ampe creation of the power reserve isdone through the acceleration of mechanical speed Ωm byacting on the electromagnetic torque reference Tlowastemrminus DLhence the active power reference Plowasts moving the operationpoint from A (which corresponds to the maximum powerpoint tracking (MPPT) operation) to B (which corresponds

KINs1 + TINsX ΔTemndashIN

ΔPIN

++

Inertial response

fpu ΔPIN(pu)Xdivide

XΩm ΩmΩmRGT

Ωm

vwndashest(ρπR2GTv3

wndashest2Ωm) Cpe

λlowast

Clowastp

β

ΔPrsc_ +

Δf

f

fr

Eq (16)

Rotor speed control

TlowastemndashDL

Tlowastem

Eq (14)λ(Cp β)

XPlowasts

2HWT Pn

divide

Figure 3 Coordinated frequency-sensitive control scheme

0 05 1 15 WT rotor speed (pu)

0

01

02

03

04

05

06

07

08

09

1

Act

ive p

ower

(pu)

12

11ms

10ms

9ms

8ms

7ms

6ms

Speed limit

E

B

A

C

Power reserve

MPPT

DL

Figure 4 Deloaded operation

Define λi (i = 01hellipn) ampβj(i = 01hellipm)

Start

Compute Cp (λi βj) table(expression in the appendix)

Read βlowast

Cp (λi) = interp2(λi βj Cpprime λi βlowast)

2D interpolation of the tableCp (λi) for βk = βlowast Read Cp

lowast

λlowast = interp1(Cp (λi) λi Cplowast ldquolinearrdquo)

1D interpolation of λlowast

for Cp (λlowast) = Cplowast

Write λlowast

End

Figure 5 Organigram for the tip speed ratio referencecomputation

Mathematical Problems in Engineering 5

to the deloaded power point tracking (DL) operation) asshown in Figure 3 such that

PB 1 minus Rf1113872 1113873PA

ΩB≻ΩA Ωmppt

⎧⎨

⎩ (16)

where Rf is the reserve factor and PA and ΩA are beingrespectively the active power and the mechanical speed ofMPPT operation given by

PA ρπR2GT

2Ωm

v3wminus estCpmax1113890 1113891Ωm⟶ MPPT

vwminus est RΩm

GTλmppt

λmppt optimal tip speed ratio

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(17)

ampeoretically speaking the creation of the reserve canalso be achieved by decelerating the mechanical speedHowever it is preferred to use the acceleration method topreserve and even increase the amount of kinetic energystored in the WT At the event of frequency drop thecontroller changes the electromagnetic torque referencedecelerating the WT (moving from the point B through thepoint E to the maximum point A) as shown in Figure 4consequently rising the wind power production by a specificquantity ΔPrsc chosen to be proportionate to the frequencydeviation such thatΔPrsc K middot f minus fr( 1113857 K middot Δf

ΔPrscminus max Rf lowastPA⟶ total power reserve⎧⎨

⎩ (18)

with f and fr being respectively the measured and nominalfrequency 50Hz and K is an energy factor determined as afunction of the droop parameter δ

K Prated

δfr

1113888 1113889 (19)

with Prated being the generatorrsquos rated powerampe creation and activation (as function of ΔPrsc ) of the

power reserve are achieved through modifying the powercoefficient reference Cp

lowast and the tip speed ratio reference λlowastin equation (17) amperefore the power coefficient new ref-erence Cp

lowast can be determined from equation (1) by thefollowing expression

Clowastp λlowast β( 1113857 1 minus Rf1113872 1113873Cpmax lowastΔPrsc

05ρπR2v3w

Clowastp λlowast β( 1113857 1 minus Rf1113872 1113873Cpmax if ΔPrsc 0

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(20)

lowast plowast p While the reference of the tip speed ratio λlowast

which depends on the power coefficient reference Cplowast andfhe angle of orientation of the blades β can be determinedusing linear interpolation adopting the algorithm presentedin Figure 5

ampe block diagram of rotor speed control is illustrated inFigure 3

Finally the rotor speed controller along with the inertialresponseΔPIN sets the active power reference Psr for the DSCcontrol according to the following expressions

Plowasts Tlowastem middotΩm

Tlowastem Tlowastemminus DL + ΔTemminus IN1113896 (21)

33 Pitch Control ampe contribution of a WT to the globalpower reserve can be achieved either by accelerating therotor speed or by the orientation of the pitch angle Duringpartial-load operation mode (wind speed below rated) thefirst method could be used alone in case of a tolerable powerreserve However it becomes incapable if a larger reserve isrequested since the rotor speed should not exceed itsmaximum value (point B in Figure 4) In that case thesecond method is then called to take over ampe pitch con-troller calculates the appropriate pitch angle βref that pre-vents the generator speed from surpassing the maximumvalue 12 pu and βref is then transferred to the pitch systemwhich will either direct the fluid to the cylinders or the powerto the motors depending on the actuator to increase theangle of the blades consequently adjusting their lift forfurther mechanical power curtailment

For high wind speeds the WT is at full-load operationmode and the pitch system is already activated to keep therotor speed at its maximum value (point C in Figure 4) Notethat contrary to the classical WT control the regulationusing pitch angle control could be activated for all windconditions ampe dynamic of the pitch actuator can bemodelled using the following transfer function with Tpbeing the time constant of the pitch system [21]

β 1

1 + Tpsβref (22)

As previously mentioned the pitch angle β is used toregulate the rotor speedΩm ampe process is highly nonlinearand there is no direct relationship between these two var-iables Traditionally a gain scheduling control method isimplemented to make up for the existent nonlinear aero-dynamic behaviour [21] However the deloaded operationof the WT used for frequency regulation purposes com-plicates the control since the adjustment of the process gainnow depends on not only the wind speed but also the powerset point [21] Accordingly a simpler and more efficientapproach is presented in this paper It is based on Cp (λ β)table inversion since the nonlinear characteristic is essen-tially brought by its curve ampe architecture of the controlapproach is depicted in Figure 6

ampe reference of the pitch angle βref is determined usingthe reference of the power coefficient Clowastp an estimation oftip speed ratio λlowast and an inversion of the Cp (λ β) tableMoreover λlowast is determined using the rotor speed mea-surement and Clowastp is obtained from the aerodynamic torquereference TlowastT after inverting each element of the WTmodel(equation (1) to equation (4)) (note that in the steady stateTem Tg) As a consequence the process view by the con-troller becomes linear and electromagnetic torque reference

6 Mathematical Problems in Engineering

Tlowastem could be provided using a simple constant gain PIcontroller A dynamic saturation is used to limit Clowastp ref-erence to Clowastpminus up(λ β 30deg) and Clowastpminus down(λ β 0 1

deg)

ampe inversion of the Cp (λ β) table could be applied toany mathematical approximation It is based on 1- and 2-dimensional linear interpolations and it can be depicted inthe organigram (Figure 7)

4 Results and Discussions

41 General Discussion ampe power system is exposed tomany forms of disturbances A load change results in var-iation of the electrical torque Te output of all generators anda change in the production results in variation of the me-chanical torque Tm of all generators ampe frequency devia-tions reflect the mismatches between the electrical Te andmechanical Tm torques as represented by the followingequation of motion [22]

Tm minus Te 2Hdωdt

2Hdf

dt (23)

whereH is the power systemrsquos corresponding inertia constantand ω and f are the (per unit) rotational speed and the ENFrespectively [23] Equation (20) can be expressed in terms ofthe electrical Pe and mechanical Pm powers such that

Pm1 minus Pe1( 1113857 + ΔPm minus ΔPe( 1113857 ω1 minus Δω( 1113857 Tm1 minus Te1( 11138571113858

+ ΔTm minus ΔTe( 11138571113859

(24)

where we denote the deviations by the prefix (Δ) and thesteady-state values by the subscript (1) with ω1(pu) 1 andby ignoring the higher order terms and adopting the realistic

assumption of Pm1Pe1 and Tm1Te1 in the steady stateEquation (24) can further be adjusted into [22]

ΔPm minus ΔPe( 1113857 ΔTm minus ΔTe( 1113857 (25)

Replacing into equation (23) we can write

ΔPm minus ΔPe 2HdΔωdt

2HdΔfdt

(26)

In this work we have considered the load sensitivity tofrequency deviations Being that practically an abruptchange in frequency will cause a variation of the powerdemand [22] ampe overall network frequency-dependentcharacteristic of loads can be represented by the followingequation

ΔPe ΔPl + DΔf (27)

with ΔPl being the non-frequency-sensitive load variationand DΔω is frequency-sensitive load variation ampe coeffi-cient D represents the self-regulation of loads and it is

1GT

1GT

GT

1GT

ΩTRvw

1Jwts + fΩm

Ωlowastm

ΩT

Temr

GearboxTurbine Transmission

β

vw

λ

_+

2ΩlowastmTlowastaρπR2v3

w

_+

Cp(λ β)

Cp(λ β)(ρπR2v32ΩT)

Ωmndashr

ΩlowastTΩTRvw

PI

λlowast

Tlowasta Tlowast

em

Tg

Clowastp_down

Clowastp_up

Clowastp

Pitch system

βref

β(Cp λ)

TT

Figure 6 Block diagram of the rotor speed control

Define λi (i = 0 1hellipn)ampβj (i = 0 1hellipm)

Start

Compute Cp (λi βi) table(expression in the appendix)

Read λlowast

Cp (βi) = interp2 (β λ Cp β λlowast ldquolinearrdquo)

2D interpolation of the tableCp (βi) for λk = λlowast Read Clowast

p

βref = interp1(Cp (βi) β Clowastp ldquolinearrdquo)

1D interpolation of βreffor Cp = Clowast

p

Write βref

End

Figure 7 Organigram of the Cp table inversion

Mathematical Problems in Engineering 7

expressed as a percent change in load for 1 deviation infrequency [22] Substituting into equation (26) we can write

ΔPm minus ΔPl 2HdΔfdt

+ DΔf (28)

42 Power System Modelling To investigate the perfor-mances of the proposed control strategies a model of a smallpower system based on the scheme illustrated in Figure 8was designed inMatlabSimulink environment It consists offour identical conventional generating units (n 4 mediumpower hydroelectric generators) [2 22] each has a powerrating of Si 100MVA an inertia constant of Hi 50 s on100 MVA base and a droop for the speed governor δi 02feeding a total load of 220MW For the analysis of frequencyregulation capability we are concerned with the collectivebehaviour of all generators in the power system ampereforein this study all conventional synchronous generators arerepresented by a single equivalent machine driven by themechanical outputs of each turbine [22]ampe power rating ofthe equivalent generator is of Seq nSi and the equivalentdroop δeq and the corresponding inertia constant of thepower system Heq can be determined using the followingequations

Heq nHiSi

Seq

δeq δi

n

(29)

Note that the synchronous generators are operatingwithout automatic generation control (AGC) and onlyprimary frequency regulation is considered in this studywhich is practically sufficient for the research objectives

43 Artificial Inertial Response Evaluation In order to ex-amine the implemented artificial inertial control behaviourwe have compared three simulation scenarios as summa-rized in Table 1

ampe first scenario S1 represents the reference case wherethe first second and third synchronous generation unitsprovide both inertial response and primary frequencycontrol (PFC) while the fourth synchronous generation unitis providing only its inherited inertial reaction withoutprimary frequency response (no PFC) ampus according toequation (29) the system equivalent inertia remains con-stant Heq 50 s but the equivalent droop coefficient is nowδeq 0066 ampe remaining scenarios represent the casewhere the fourth synchronous generation unit is replacedwith a wind farm (WF) with an equivalent power ratingwhere S2 and S3 are respectively the wind farm caseswithout and with inertial control implemented In this casethe wind power penetration rises up to LP 25 thereforethe equivalent inertia constant is decreased to Hrsquoeq Heq(1minus Lp) 375 while the equivalent droop remains constantδrsquoeq 0066 A sudden rise in load by 20MW (005 pu systembase) is introduced to the system at t 300 s

Figure 9 portrays the dynamic reaction of the electricnetwork frequency for the three simulation scenarios Withscenario S1 being the reference case it can be observed that thedeepest frequency nadir the worst case is obtained withscenario S2 where the artificial inertial response of WTs isdisabled ampat is mainly due to the reduction of the systemequivalent inertia caused by the increase of the wind powerpenetration Lp to 25 in the system Meanwhile the narrowfrequency nadir the finest case is obtained with scenario S3where the inertial response is enabled and with an appropriategain KIN choice the inertial support from the WTs could beeven greater than that obtained from the synchronous gen-eration unit Since the wider the range of speed variation thebigger the amount of kinetic energy can be extracted

Figures 10ndash12 show the dynamic behaviour of a singleWT for different operation conditions Initially (before thedisturbance) the rotor speed and the active power output aremaintained to their optimal values corresponding to MPPTAt the event of frequency drop t 120 s and when the windspeed is below rated vw 65ms (partial-load operationmode) the sequence of events that occur can be summarizedas follows

(i) ampe controller adjusts the electromagnetic torquereference causing a deceleration of the rotor speed(Figure 10(a))

(ii) ampe rotor speed is below its maximum value(gt12 pu) therefore the pitch angle is kept at zero(Figure 11(a))

(iii) ampe reduction of the rotor speed causes the ex-traction of a portion of the kinetic energy stored inthe spinning masses (Figure 12(a)) ampis extra activepower will be used to support the power system inrecovering the frequency to 50Hz

(iv) ampe countering spike of the output power(Figure 12(a)) at roughly t 310 s can be explained

++ +++ ndash

WF

n-synchronous generation units

Primary frequency control (δeq)AGC

LpΔPWF

ΔPsyn

ΔPL

ΔfΔPm 12Heqs + D

Figure 8 Electric network frequency regulation control scheme ofa power system

Table 1 Simulation scenarios

Scenarios S1 S2 S3Generation units 1 2 and 3 C C C

Generation unit 4 Cno PFC NC NC

Wind farm NC Cno IC

Conly IC

C connected NC nonconnected PFC primary frequency control ICinertial control

8 Mathematical Problems in Engineering

as follows let us consider that theWTwas operatingat pointA (Figure 4) with the rotor speed reductionthe WTwill move to a suboptimal power extractionoperation point at the end of the inertial reactionamperefore less power will be delivered until fullrecovery of the WT

For a high wind speed vw 15ms (full-load operationmode) the sequence of events that occur can be summarizedas follows

(i) ampe pitch controller (Figure 11(b)) maintains therotor speed at its maximum value (asymp12 pu)(Figure 10(b))

(ii) ampe controller tries to adjust rotor speed but sincethe pitch controller is activated in this mode itcounteracts the action by reducing the pitch anglethus indirectly exploiting the mechanical power thatwas already curtailed by the positive pitch angle tocreate the power surge (Figure 12(b)) Not that thepower response at this mode requires no recoveryprocess since the pitching system is the one re-sponsible for the contribution

In order to highlight the merits of using a backsteppingcontrol algorithm instead of classical controllers it is par-ticularly important to analyse the system performance undersome kind of disturbances amperefore since the machineparameters are usually exposed to many forms of inaccur-acies especially due to the measuring devices identificationmethodology or several natural phenomena a robustnesstest was carried out to compare the performance of theproposed control strategy versus classical PI controllerswhen parametric variations are registered ampe test consistsin purposefully modifying the rotor resistance Rr of theDFIG by 50 and the stator inductance Ls by 10 from theirnormal values

Figures 12 and 13 show respectively the evolution of theDFIG stator active and reactive powers and Figures 14 and15 respectively show the evolution of d and q componentsof the rotor currents ampe test highlights the high sensitivityof classical PI controllers towards parametric variationwhich is notably observed due to the appearance of a sig-nificant static error in all simulation results whereas the

proposed backstepping control algorithm demonstrates anexquisite disturbance rejection being that all the outputsconverge correctly to their designated references Moreoverthe three-phased stator current sinusoidal waveform isshown in Figure 16

44 SpeedDroopControlEvaluation ampe performance of theproposed speed droop control will be evaluated for thefollowing simulation cases

Case 1 partial-load operation mode (wind speedvw 65ms)Case 1 Full-load operation mode (wind speedvw 15ms)

ampe set of results shown in the following figures dem-onstrates the capability of the proposed control strategy torespond to a sudden active power call at t 150 s Before thearrival of the frequency drop the WT is running at a ro-tational speed higher than the optimum (ΩgtΩmppt) inorder to lower the aerodynamic conversion efficiency rep-resented by Cp and therefore to operate following adeloaded operation characteristic with the power reservebeing created For the research objectives this work pre-sumes that the WT is operating with a reserve factorRf 10 while on the practical level the power margins aregenerally specified by the grid codes

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under partial-load operationmode can be summarized as follows

(i) ampe step in the output power reference (by ΔPrscFigure 3) modifies the electromagnetic torque ref-erence Tlowastem causing the rotor speed reduction asshown in Figure 17(a)

(ii) ampe rotor speed is below its maximum value thepitch control is not required in this case andtherefore the pitch angle is maintained at zero(Figure 18(a))

(iii) ampe rotor speed deceleration rises the power coef-ficient Cp to its maximum value (Figure 4) as shownin Figure 19(a) allowing consequently the WT toactivate its full power reserve

(iv) ampe power reserve activation rises the output powerof the WT by ΔPrsc (Figure 20(a)) thereforeallowing it to participate in the frequency recoveryprocess

(v) ampe power peaks induced as shown in Figure 20(a)demonstrate the benefit from creating the powerreserve by acceleration of the rotor speed the leftside of the power curve Figure 4 since now morekinetic energy is at our disposal and it can be usedwhenever the WT is decelerating

(vi) When the frequency recovers at t 400 s the controlstrategy reaccelerates the WT (Figure 17(a)) low-ering the power coefficient (Figure 19(a)) in order

S1S2S3

300 350 400250 Time (sec)

492

494

496

498

50

Fre

quen

cy (H

z)

Figure 9 Electric network frequency deviation for differentscenarios

Mathematical Problems in Engineering 9

to recreate the power reserve (Figure 20(a)) for thenext use

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under full-load operationmode can be summarized as follows

(i) ampe pitch control is now activated as shown inFigure 18(b) to keep the rotor speed at its maxi-mum value (Figure 17(b)) and to create the powerreserve (Figure 19(b)) since the rotor speed can nolonger be accelerated

(ii) ampe active power call (ΔPrsc Figure 4) reduced thepitch angle to make use of the mechanical powercurtailed by the positive β

(iii) β reduction increases the power coefficient CP asshown in Figure 19(b)consequently rising the

output according to the amount of power specifiedby ΔPrsc (Figure 20(b))

(iv) When the frequency recovers at t 400 s the pitchcontrol strategy rises the pitch angle (Figure 18(b))lowering the power coefficient (Figure 19(b)) inorder to recreate the power reserve (Figure 20(b))for the next use

45 Coordinated Control ampe artificial inertial reaction thespeed droop control and the pitch control could be usedaltogether to further enhance the frequency regulationcapability of WTs In this subsection we compared thesimulation scenarios summarized in Table 2 with S1 beingthe reference case where the wind power penetration isLp 0 For the other simulation scenarios the fourthgeneration synchronous is replaced with a WF with an

084

085

086

087

088

089

09

091

092Ro

tor s

peed

(pu)

110 120 130 140 150 160100Time (s)

(a)

116

12

124

Roto

r spe

ed (p

u)

110 120 130 140 150 160100Time (s)

(b)

Figure 10 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

10

Pitc

h an

gle (

deg)

110 120 130 140 150 160100Time (s)

ndash5

0

5

(a)

175

205Pi

tch

angl

e (deg)

110 120 130 140 150 160100Time (s)

18

185

19

195

20

(b)

Figure 11 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

10 Mathematical Problems in Engineering

equivalent power rating and the wind power penetrationrises to Lp 25 with S2 S3 S3 and S4 being respectivelythe cases without any frequency control the inertial reactiononly speed droop control only and all controllers

Figure 21 portrays the dynamic reaction of the frequencyfor each scenario All simulations were performed for amedium wind speed of vw 9ms and a sudden rise in loadby 005 pu system base is introduced to the system att 200 s

ampe results show that the severest case is obtained withthe simulation scenario S2 the case where the WF is

connected with no frequency regulation ability Comparedto the reference case S1 where the wind power penetrationLp 0 the frequency curve for the second simulationscenario S2 falls to a deeper nadir due to the reduction of thesystemrsquos equivalent inertia caused by increasing the windpower penetration Lp 25 On the other hand in the casewhere the inertial control is implemented S3 the WT de-celerates to release a portion of its kinetic energy transientlyimproving the frequency deviation Consequently the fre-quency nadir is lifted up to the level of the reference case S1However the quasi-steady-state frequency does not get any

Pslowast

Ps (PI)Ps (Bs)

ndash034

ndash032

ndash03

ndash028

ndash026

ndash024

ndash022W

T ou

tput

pow

er (p

u)

110 120 130 140 150 160100Time (seconds)

(a)

Pslowast

Ps (PI)Ps (Bs)

ndash105

ndash1

ndash095

ndash09

ndash085

WT

outp

ut p

ower

(pu)

110 120 130 140 150 160100Time (s)

(b)

Figure 12 Active power evolution for partial-load (a) and full-load (b) operation modes

QslowastQs (PI)Qs (Bs)

ndash5000

0

5000

Reac

tive p

ower

Qs (

Var)

110 120 130 140 150 160100Time (s)

(a)

QslowastQs (PI)Qs (Bs)

times104

ndash1

ndash05

0

05

1

Reac

tive p

ower

(Var

)

110 120 130 140 150 160100Time (s)

(b)

Figure 13 Reactive power evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 11

better with only the inertial control being enabled since itprovides only short-term frequency support With the speeddroop controller being enabled simulation scenario S4 itcan be observed that the WTcontribution is higher since themaximum transient and the quasi-steady-state frequencydeviations are both optimised Finally with both controllersbeing simultaneously enabled simulation scenario S5 thefrequency curve will further be improved for both short- andlong-term durations

As mentioned previously with only the inertial controlbeing activated at the event of frequency excursion the

rotor speed deceleration will impose a suboptimal powerextraction and then less power will be delivered until the fullrecovery of theWTto its optimum speed (Figure 10(c))ampisrecovery phase that generally lasts tens of seconds could beavoided when both controllers are simultaneously activatedgiven that the droop speed controller forces the WT tooperate at a higher rotational speed (ΩgtΩmppt) left side ofthe curve (Figure 4)amperefore when theWTdecelerates theoperating point will climb toward the optimum point and asa result there will be no need for the WT to recover at theend of the inertial response

Irqlowast

Irq (PI)Irq (Bs)

500

600

700

800

900

1000

1100Irq

110 120 130 140 150 160100Time (s)

(a)

Irqlowast

Irq (PI)Irq (Bs)

2600

2700

2800

2900

3000

3100

Irq

110 120 130 140 150 160100Time (s)

(b)

Figure 14 Active current Irq evolution for partial-load (a) and full-load (b) operation modes

Irdlowast

Ird (PI)Ird (Bs)

130

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(a)

Irdlowast

Ird (PI)Ird (Bs)

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(b)

Figure 15 Reactive current Ird evolution for partial-load (a) and full-load (b) operation modes

12 Mathematical Problems in Engineering

110 11005 1101 11015 1102

ndash1000

ndash500

0

500

1000

Is (A

)

110 120 130 140 150 160100Time (s)

(a)

ndash2000

ndash1000

0

1000

2000

Is (A

)

110 120 130 140 150 160100Time (s)

110 11005 1101 11015 1102

(b)

Figure 16 Stator current evolution for partial-load (a) and full-load (b) operation modes

08

09

1

11

12

Roto

r spe

ed (p

u)

200 300 400 500100Time (s)

(a)

11

115

12

125

13Ro

tor s

peed

(pu)

200 300 400 500100Time (s)

(b)

Figure 17 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

ndash5

0

5

10

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(a)

18

19

20

21

22

23

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(b)

Figure 18 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 13

Powerreserve

Cplowast

CpCpopt

200 300 400 500100Time (s)

042

044

046

048

05

Cp

(a)

Powerreserve

Cplowast

CpoptCp

011

012

013

014

015

016

Cp

150 200 250 300 350 400 450 500100 Time (s)

(b)

Figure 19 Power coefficient evolution for partial-load (a) and full-load (b) operation modes

Powerreserve

Power peaks

PrefPoptP

ndash03

ndash028

ndash026

ndash024

ndash022

ndash02

WT

outp

ut p

ower

(pu)

150 200 250 300 350 400 450 500100 Time (s)

(a)

Powerreserve

PrefPoptP

ndash105

ndash1

ndash095

ndash09

ndash085

ndash08

ndash075

ndash07

WT

outp

ut p

ower

(pu)

200 300 400 500100 Time (s)

(b)

Figure 20 WR output power evolution for partial-load (a) and full-load (b) operation modes

Table 2 Simulation scenarios

Scenarios S1 S2 S3 S3 S4Generation units 1 2 and 3 C C C C CGeneration unit 4 C NC NC NC NCWind farm NC C no control C only IC C only PFC C IC and PFCC connected NC nonconnected PFC primary frequency control IC inertial control

14 Mathematical Problems in Engineering

5 Conclusion

ampis paper explores different control approaches thatallow DFIG-based WTs to engage actively in frequencyregulation via coordinating the rotor speed and the pitchangle controllers In a short-term duration the inertialcontrol permits the WT to emulate the synchronousgenerator natural behaviour Accordingly at the event offrequency excursion the controller decelerates the WTin order to extract a portion of its kinetic energy shortlyproviding extra active power support for the powersystem However the inertial reaction alone is heavilydependent on the initial point of operation and a goodtuning of the controller gain is required since for in-stance at low wind speeds the rotor speed should notexceed its minimum value 06 pu for the stable operationof the WT ampe speed droop controller enables the WT toprovide active power assistance over an extended periodimproving the robustness of the system It forces the WTto operate following a deloaded characteristic creating acertain power reserve that can be automatically triggeredat the event of frequency deviations Moreover an in-novative pitch angle control is utilized to protect the WTagainst over speeding and to maintain the frequencyregulation capability under various operationconditions

Finally a study case considering an isolated powersystem that consists of synchronous generators DFIG-basedwind farm and static loads was examined to compare theperformance of each controller ampese simulation resultsshow that the coordination of the controllers improves boththe dynamic and the quasi-steady-state frequency deviationand brings the frequency nadir up to a far superior level thanthat obtained with the wind farm being disconnected (0wind power penetration)

Appendix

Wind turbine parameters

Rated power P 2MW blade radius R 45m gearboxG 90 WT inertia HWT 435 s damping coefficientf 0017Nmiddotmmiddotsrd and air density ρ 12 kgm3

DFIG parameters

Rated power P 2MW rated torque 127 kNm gridrated voltage and frequency Vs 690V and fs 50Hz polepair p 2 generator inertia HG 05 s stator and rotorresistances Rs 26mΩ and Rr 29mΩ stator and rotorinductance Ls 20mH and Lr 20mH and mutual in-ductance M 3253mH

Power coefficient expression

Cp X1X2

λ + 0008βminus00035 middot X2

β3 + 11113888 1113889 minus X3β minus X41113888 1113889

middot expX5

λ + 0008βminus00035 middot X5

β3 + 11113888 1113889 + X6λ

X1 05109

X2 116

X3 04

A4 5

X5 21

X6 00068

(A1)

Data Availability

No data were used to support this study

Disclosure

ampis paper is an expanded version of a paper entitled ldquoIn-ertial Response using Backstepping Control from DFIGbased Wind Power Plant for Short-Term Frequency Regu-lationrdquo presented at 2019 International Conference onControl Decision and Information Technologies held inParis France from 23 to 26 April 2019

Conflicts of Interest

ampe authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] Y Li Z Xu J Zhang and K P Wong ldquoVariable gain controlscheme of DFIG-based wind farm for over-frequency sup-portrdquo Renewable Energy vol 120 pp 379ndash391 2018

[2] N R Ullah T ampiringer and D Karlsson ldquoTemporaryprimary frequency control support by variable speed windturbines- potential and applicationsrdquo IEEE Transactions onPower Systems vol 23 no 2 pp 601ndash612 2008

[3] A Molina-Garcia I Munoz-Benavente A D Hansen andE Gomez-Lazaro ldquoDemand-side contribution to primaryfrequency control with wind farm auxiliary controlrdquo IEEE

S4S5

S1

S3S2

492

494

496

498

50

Freq

uenc

y (H

z)

150 200Time (s)

250 300

Figure 21 Deviation of the frequency for each simulation scenario

Mathematical Problems in Engineering 15

Transactions on Power Systems vol 29 no 5 pp 2391ndash23992014

[4] F Poitiers T Bouaouiche and M Machmoum ldquoAdvancedcontrol of a doubly-fed induction generator for wind energyconversionrdquo Electric Power Systems Research vol 79 no 7pp 1085ndash1096 2009

[5] Z-S Zhang Y-Z Sun J Lin and G-J Li ldquoCoordinatedfrequency regulation by doubly fed induction generator-basedwind power plantsrdquo IET Renewable Power Generation vol 6no 1 pp 38ndash47 2012

[6] R Chakib M Cherkaoui and A Essadki ldquoInertial responseused for a short term frequency control for DFIG windturbine controlled by ADRCrdquo ARPN Journal of Engineeringand Applied Sciences vol 11 no 5 2016

[7] Y-K Wu S-M Chang and P Mandal ldquoGrid-connectedwind power plants a survey on the integration requirementsin modern grid codesrdquo in Proceedings of the 2019 IEEEIAS55th Industrial and Commercial Power Systems TechnicalConference (IampCPS) pp 1ndash9 Canada Canada May 2019

[8] L Ruttledge and D Flynn ldquoEmulated inertial response fromwind turbines gain scheduling and resource coordinationrdquoIEEE Transactions on Power Systems vol 31 no 5pp 3747ndash3755 2015

[9] A I Estanqueiro J M F De Jesus J Ricardo A dos Santosand J A P Lopes ldquoBarriers (and solutions) to Very HighWind Penetration in Power Systemsrdquo in Proceedings of the2007 IEEE Power Engineering Society General Meetingpp 1ndash7 Tampa FL USA June 2007

[10] Y Wang G Delille H Bayem X Guillaud and B FrancoisldquoHigh wind power penetration in isolated power systems-assessment of wind inertial and primary frequency re-sponsesrdquo IEEE Transactions on Power Systems vol 28 no 3pp 2412ndash2420 2013

[11] P-K Keung P Li H Banakar and B T Ooi ldquoKinetic energyof wind-turbine generators for system frequency supportrdquoIEEE Transactions on Power Systems vol 24 no 1 pp 279ndash287 2008

[12] H Ye W Pei and Z Qi ldquoAnalytical modeling of inertial anddroop responses from a wind farm for short-term frequencyregulation in power systemsrdquo IEEE Transactions on PowerSystems vol 31 no 5 pp 3414ndash3423 2015

[13] H Liu and Z Chen ldquoContribution of VSC-HVDC to fre-quency regulation of power systems with offshore windgenerationrdquo IEEE Transactions on Energy Conversion vol 30no 3 pp 918ndash926 2015

[14] R M Kamel A Chaouachi and K Nagasaka ldquoampree controlstrategies to improve the microgrid transient dynamic re-sponse during isolated mode a comparative studyrdquo IEEETransactions on Industrial Electronics vol 60 no 4pp 1314ndash1322 2012

[15] S Wang J Hu X Yuan and L Sun ldquoOn inertial dynamics ofvirtual-synchronous-controlled DFIG-based wind turbinesrdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1691ndash1702 2015

[16] H T Ma and B H Chowdhury ldquoWorking towards frequencyregulation with wind plants combined control approachesrdquoIET Renewable Power Generation vol 4 no 4 pp 308ndash3162010

[17] I A Gowaid A El-Zawawi and M El-Gammal ldquoImprovedinertia and frequency support from grid-connected DFIGwind farmsrdquo in Proceedings of the Power Systems Conferenceand Exposition (PSCE) pp 1ndash9 Phoenix AZ USA March2011

[18] M Nadour A Essadki and T Nasser ldquoComparative analysisbetween PI amp backstepping control strategies of DFIG drivenby wind turbinerdquo International Journal of Renewable EnergyResearch vol 7 no 3 pp 1307ndash1316 2017

[19] M Nadour A Essadki M Fdaili and T Nasser ldquoAdvancedbackstepping control of a wind energy conversion systemusing a doubly-fed induction generatorrdquo in Proceedings of the2017 International Renewable and Sustainable Energy Con-ference (IRSEC) pp 1ndash6 Tangier Morocco December 2017

[20] Y Rebours A Comprehensive Assessment of Markets forFrequency and Voltage Control Ancillary Services PhD thesisUniversity of Manchester Manchester England 2008

[21] P Venne X Guillaud R Teodorescu and J MahseredjianldquoGeneralized gain scheduling for deloaded wind turbineoperationrdquo Wind Engineering vol 34 no 2 pp 219ndash2392010

[22] P Kundur N J Balu andM G Lauby Power System Stabilityand Control Vol 7 McGraw-Hill New York NY USA 1994

[23] J Van de Vyver J D M De Kooning B MeersmanL Vandevelde and T L Vandoorn ldquoDroop control as analternative inertial response strategy for the synthetic inertiaon wind turbinesrdquo IEEE Transactions on Power Systemsvol 31 no 2 pp 1129ndash1138 2016

16 Mathematical Problems in Engineering

with h1 h2 h3 and h4 being some strictly positive constantscalled the backstepping setting coefficients used on the onehand to guarantee the stability of the system and on the otherhand to ensure a quick dynamic response of the groupcontroller system

3 ldquoElectric Network Frequency-Sensitiverdquo Control

Figure 1 illustrates the complete DFIG-based WT structureincluding the network side converter (NSC) used to regulatethe DC link voltage Vdc and the reactive power exchangedthrough the filter Qtr ampe DFIG side converter (DSC) usedto regulate the stator reactive powerQs to zero in order to geta unity power factor at the point of common coupling(PCC) until the electric network operator demands oth-erwise and to adjust almost instantaneously the stator

active power Ps according to the electric network frequency-sensitive control loops Finally the pitch angle controlleradapts the mechanical power to maintain the frequencyregulation capability even under the full-load operationcondition Each controller will be analysed thoroughly in thenext subsections

31Artificial InertialResponse ampe inertial response permitsthe DFIG to reproduce synchronous generators behaviourproviding an active power support for the power systemduring the transient It consists in customizing the elec-tromagnetic torque reference Temr hence the active powerreference Psr as a proportion of the rate of change of thefrequency (ROCOF) At the event of frequency disruptionthe electromagnetic torque set point rises by ΔTem-IN causinga deceleration of the WT rotor speed Ωm and as a

vw

Turbine Gearbox

DFIG DSC NSC

Grid

Rtr Ltr

DSC control NSC control

PT

(Ps Qs)

(Ptr Qtr)Pr

QsrPsr

Qtr

DC bus voltage control

PCC

Pitch control

Speed control Power control

Ptr

ΩT

Ωmβ

Inertial and droop basedfrequency responses

Figure 1 ampe complete structure of frequency-sensitive DFIG-based WT control

dq

abc

DFIG

PWM

Pslowast

Ps

Qslowast Ilowastrd

Ird

Vlowastrd

Ilowastrq Vlowastrq

Irq

Qs

VCVcomputation

ACVcomputation

VCVcomputation

ACVcomputation

DSC

Electric network

DSC control

PLLddt

ndash+

A

B

B

ωs

ƪ

θs

θr

θrθ

ω

A

Figure 2 DSC backstepping control

4 Mathematical Problems in Engineering

consequence discharging a portion of the kinetic energystored in the WTspinning masses ampe mechanism is chosento be proportionate to that of synchronous generators andthus the additional power injected to the network can beexpressed as follows

ΔPIN(pu) 2HT middot fpudfpu

dt (13)

where fpu is the per-unit system frequency and HT the totalinertia constant (DFIG and WT) given by [5]

HT HDFIG + HWT HDFIG +12

JTΩ2ratedSrated

(14)

S rated and Ωrated are respectively the rated power andrated mechanical speed ampe equation that relates theelectromagnetic torque to the frequency can be determinedfrom equation (13) by the following expression

ΔTemminus IN(pu) 2HT middot fpudfpu

dt

1Ωm(pu)

(15)

Furthermore since the frequency is estimated by meansof a phase-locked loop (PLL) a low-pass filter needs to beintroduced into the control scheme in order to reduce theimpact of the small noises as shown in Figure 3 where TINrepresents the time constant of the filter and KIN its gain thatdetermines the amount of additional injected wind power incase of a frequency excursion

32 Speed Droop Control ampe artificial inertial response canonly be utilized to assist the system during the transitoryphase known as ldquodynamic frequency variationrdquo [20]However in order to enable the WT to provide active powersupport for an extended period of time another electricnetwork frequency-sensitive control loop that takes underconsideration the quasi-steady-state frequency deviationshould be added as shown in Figure 3ampe latter obligates theWT to operate following a ldquodeloaded operation character-istic (DL)rdquo as illustrated in Figure 4 creating a specificpower reserve that can be automatically activated to supportthe power systemwhen active power is needed at the event of

frequency disruption ampe creation of the power reserve isdone through the acceleration of mechanical speed Ωm byacting on the electromagnetic torque reference Tlowastemrminus DLhence the active power reference Plowasts moving the operationpoint from A (which corresponds to the maximum powerpoint tracking (MPPT) operation) to B (which corresponds

KINs1 + TINsX ΔTemndashIN

ΔPIN

++

Inertial response

fpu ΔPIN(pu)Xdivide

XΩm ΩmΩmRGT

Ωm

vwndashest(ρπR2GTv3

wndashest2Ωm) Cpe

λlowast

Clowastp

β

ΔPrsc_ +

Δf

f

fr

Eq (16)

Rotor speed control

TlowastemndashDL

Tlowastem

Eq (14)λ(Cp β)

XPlowasts

2HWT Pn

divide

Figure 3 Coordinated frequency-sensitive control scheme

0 05 1 15 WT rotor speed (pu)

0

01

02

03

04

05

06

07

08

09

1

Act

ive p

ower

(pu)

12

11ms

10ms

9ms

8ms

7ms

6ms

Speed limit

E

B

A

C

Power reserve

MPPT

DL

Figure 4 Deloaded operation

Define λi (i = 01hellipn) ampβj(i = 01hellipm)

Start

Compute Cp (λi βj) table(expression in the appendix)

Read βlowast

Cp (λi) = interp2(λi βj Cpprime λi βlowast)

2D interpolation of the tableCp (λi) for βk = βlowast Read Cp

lowast

λlowast = interp1(Cp (λi) λi Cplowast ldquolinearrdquo)

1D interpolation of λlowast

for Cp (λlowast) = Cplowast

Write λlowast

End

Figure 5 Organigram for the tip speed ratio referencecomputation

Mathematical Problems in Engineering 5

to the deloaded power point tracking (DL) operation) asshown in Figure 3 such that

PB 1 minus Rf1113872 1113873PA

ΩB≻ΩA Ωmppt

⎧⎨

⎩ (16)

where Rf is the reserve factor and PA and ΩA are beingrespectively the active power and the mechanical speed ofMPPT operation given by

PA ρπR2GT

2Ωm

v3wminus estCpmax1113890 1113891Ωm⟶ MPPT

vwminus est RΩm

GTλmppt

λmppt optimal tip speed ratio

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(17)

ampeoretically speaking the creation of the reserve canalso be achieved by decelerating the mechanical speedHowever it is preferred to use the acceleration method topreserve and even increase the amount of kinetic energystored in the WT At the event of frequency drop thecontroller changes the electromagnetic torque referencedecelerating the WT (moving from the point B through thepoint E to the maximum point A) as shown in Figure 4consequently rising the wind power production by a specificquantity ΔPrsc chosen to be proportionate to the frequencydeviation such thatΔPrsc K middot f minus fr( 1113857 K middot Δf

ΔPrscminus max Rf lowastPA⟶ total power reserve⎧⎨

⎩ (18)

with f and fr being respectively the measured and nominalfrequency 50Hz and K is an energy factor determined as afunction of the droop parameter δ

K Prated

δfr

1113888 1113889 (19)

with Prated being the generatorrsquos rated powerampe creation and activation (as function of ΔPrsc ) of the

power reserve are achieved through modifying the powercoefficient reference Cp

lowast and the tip speed ratio reference λlowastin equation (17) amperefore the power coefficient new ref-erence Cp

lowast can be determined from equation (1) by thefollowing expression

Clowastp λlowast β( 1113857 1 minus Rf1113872 1113873Cpmax lowastΔPrsc

05ρπR2v3w

Clowastp λlowast β( 1113857 1 minus Rf1113872 1113873Cpmax if ΔPrsc 0

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(20)

lowast plowast p While the reference of the tip speed ratio λlowast

which depends on the power coefficient reference Cplowast andfhe angle of orientation of the blades β can be determinedusing linear interpolation adopting the algorithm presentedin Figure 5

ampe block diagram of rotor speed control is illustrated inFigure 3

Finally the rotor speed controller along with the inertialresponseΔPIN sets the active power reference Psr for the DSCcontrol according to the following expressions

Plowasts Tlowastem middotΩm

Tlowastem Tlowastemminus DL + ΔTemminus IN1113896 (21)

33 Pitch Control ampe contribution of a WT to the globalpower reserve can be achieved either by accelerating therotor speed or by the orientation of the pitch angle Duringpartial-load operation mode (wind speed below rated) thefirst method could be used alone in case of a tolerable powerreserve However it becomes incapable if a larger reserve isrequested since the rotor speed should not exceed itsmaximum value (point B in Figure 4) In that case thesecond method is then called to take over ampe pitch con-troller calculates the appropriate pitch angle βref that pre-vents the generator speed from surpassing the maximumvalue 12 pu and βref is then transferred to the pitch systemwhich will either direct the fluid to the cylinders or the powerto the motors depending on the actuator to increase theangle of the blades consequently adjusting their lift forfurther mechanical power curtailment

For high wind speeds the WT is at full-load operationmode and the pitch system is already activated to keep therotor speed at its maximum value (point C in Figure 4) Notethat contrary to the classical WT control the regulationusing pitch angle control could be activated for all windconditions ampe dynamic of the pitch actuator can bemodelled using the following transfer function with Tpbeing the time constant of the pitch system [21]

β 1

1 + Tpsβref (22)

As previously mentioned the pitch angle β is used toregulate the rotor speedΩm ampe process is highly nonlinearand there is no direct relationship between these two var-iables Traditionally a gain scheduling control method isimplemented to make up for the existent nonlinear aero-dynamic behaviour [21] However the deloaded operationof the WT used for frequency regulation purposes com-plicates the control since the adjustment of the process gainnow depends on not only the wind speed but also the powerset point [21] Accordingly a simpler and more efficientapproach is presented in this paper It is based on Cp (λ β)table inversion since the nonlinear characteristic is essen-tially brought by its curve ampe architecture of the controlapproach is depicted in Figure 6

ampe reference of the pitch angle βref is determined usingthe reference of the power coefficient Clowastp an estimation oftip speed ratio λlowast and an inversion of the Cp (λ β) tableMoreover λlowast is determined using the rotor speed mea-surement and Clowastp is obtained from the aerodynamic torquereference TlowastT after inverting each element of the WTmodel(equation (1) to equation (4)) (note that in the steady stateTem Tg) As a consequence the process view by the con-troller becomes linear and electromagnetic torque reference

6 Mathematical Problems in Engineering

Tlowastem could be provided using a simple constant gain PIcontroller A dynamic saturation is used to limit Clowastp ref-erence to Clowastpminus up(λ β 30deg) and Clowastpminus down(λ β 0 1

deg)

ampe inversion of the Cp (λ β) table could be applied toany mathematical approximation It is based on 1- and 2-dimensional linear interpolations and it can be depicted inthe organigram (Figure 7)

4 Results and Discussions

41 General Discussion ampe power system is exposed tomany forms of disturbances A load change results in var-iation of the electrical torque Te output of all generators anda change in the production results in variation of the me-chanical torque Tm of all generators ampe frequency devia-tions reflect the mismatches between the electrical Te andmechanical Tm torques as represented by the followingequation of motion [22]

Tm minus Te 2Hdωdt

2Hdf

dt (23)

whereH is the power systemrsquos corresponding inertia constantand ω and f are the (per unit) rotational speed and the ENFrespectively [23] Equation (20) can be expressed in terms ofthe electrical Pe and mechanical Pm powers such that

Pm1 minus Pe1( 1113857 + ΔPm minus ΔPe( 1113857 ω1 minus Δω( 1113857 Tm1 minus Te1( 11138571113858

+ ΔTm minus ΔTe( 11138571113859

(24)

where we denote the deviations by the prefix (Δ) and thesteady-state values by the subscript (1) with ω1(pu) 1 andby ignoring the higher order terms and adopting the realistic

assumption of Pm1Pe1 and Tm1Te1 in the steady stateEquation (24) can further be adjusted into [22]

ΔPm minus ΔPe( 1113857 ΔTm minus ΔTe( 1113857 (25)

Replacing into equation (23) we can write

ΔPm minus ΔPe 2HdΔωdt

2HdΔfdt

(26)

In this work we have considered the load sensitivity tofrequency deviations Being that practically an abruptchange in frequency will cause a variation of the powerdemand [22] ampe overall network frequency-dependentcharacteristic of loads can be represented by the followingequation

ΔPe ΔPl + DΔf (27)

with ΔPl being the non-frequency-sensitive load variationand DΔω is frequency-sensitive load variation ampe coeffi-cient D represents the self-regulation of loads and it is

1GT

1GT

GT

1GT

ΩTRvw

1Jwts + fΩm

Ωlowastm

ΩT

Temr

GearboxTurbine Transmission

β

vw

λ

_+

2ΩlowastmTlowastaρπR2v3

w

_+

Cp(λ β)

Cp(λ β)(ρπR2v32ΩT)

Ωmndashr

ΩlowastTΩTRvw

PI

λlowast

Tlowasta Tlowast

em

Tg

Clowastp_down

Clowastp_up

Clowastp

Pitch system

βref

β(Cp λ)

TT

Figure 6 Block diagram of the rotor speed control

Define λi (i = 0 1hellipn)ampβj (i = 0 1hellipm)

Start

Compute Cp (λi βi) table(expression in the appendix)

Read λlowast

Cp (βi) = interp2 (β λ Cp β λlowast ldquolinearrdquo)

2D interpolation of the tableCp (βi) for λk = λlowast Read Clowast

p

βref = interp1(Cp (βi) β Clowastp ldquolinearrdquo)

1D interpolation of βreffor Cp = Clowast

p

Write βref

End

Figure 7 Organigram of the Cp table inversion

Mathematical Problems in Engineering 7

expressed as a percent change in load for 1 deviation infrequency [22] Substituting into equation (26) we can write

ΔPm minus ΔPl 2HdΔfdt

+ DΔf (28)

42 Power System Modelling To investigate the perfor-mances of the proposed control strategies a model of a smallpower system based on the scheme illustrated in Figure 8was designed inMatlabSimulink environment It consists offour identical conventional generating units (n 4 mediumpower hydroelectric generators) [2 22] each has a powerrating of Si 100MVA an inertia constant of Hi 50 s on100 MVA base and a droop for the speed governor δi 02feeding a total load of 220MW For the analysis of frequencyregulation capability we are concerned with the collectivebehaviour of all generators in the power system ampereforein this study all conventional synchronous generators arerepresented by a single equivalent machine driven by themechanical outputs of each turbine [22]ampe power rating ofthe equivalent generator is of Seq nSi and the equivalentdroop δeq and the corresponding inertia constant of thepower system Heq can be determined using the followingequations

Heq nHiSi

Seq

δeq δi

n

(29)

Note that the synchronous generators are operatingwithout automatic generation control (AGC) and onlyprimary frequency regulation is considered in this studywhich is practically sufficient for the research objectives

43 Artificial Inertial Response Evaluation In order to ex-amine the implemented artificial inertial control behaviourwe have compared three simulation scenarios as summa-rized in Table 1

ampe first scenario S1 represents the reference case wherethe first second and third synchronous generation unitsprovide both inertial response and primary frequencycontrol (PFC) while the fourth synchronous generation unitis providing only its inherited inertial reaction withoutprimary frequency response (no PFC) ampus according toequation (29) the system equivalent inertia remains con-stant Heq 50 s but the equivalent droop coefficient is nowδeq 0066 ampe remaining scenarios represent the casewhere the fourth synchronous generation unit is replacedwith a wind farm (WF) with an equivalent power ratingwhere S2 and S3 are respectively the wind farm caseswithout and with inertial control implemented In this casethe wind power penetration rises up to LP 25 thereforethe equivalent inertia constant is decreased to Hrsquoeq Heq(1minus Lp) 375 while the equivalent droop remains constantδrsquoeq 0066 A sudden rise in load by 20MW (005 pu systembase) is introduced to the system at t 300 s

Figure 9 portrays the dynamic reaction of the electricnetwork frequency for the three simulation scenarios Withscenario S1 being the reference case it can be observed that thedeepest frequency nadir the worst case is obtained withscenario S2 where the artificial inertial response of WTs isdisabled ampat is mainly due to the reduction of the systemequivalent inertia caused by the increase of the wind powerpenetration Lp to 25 in the system Meanwhile the narrowfrequency nadir the finest case is obtained with scenario S3where the inertial response is enabled and with an appropriategain KIN choice the inertial support from the WTs could beeven greater than that obtained from the synchronous gen-eration unit Since the wider the range of speed variation thebigger the amount of kinetic energy can be extracted

Figures 10ndash12 show the dynamic behaviour of a singleWT for different operation conditions Initially (before thedisturbance) the rotor speed and the active power output aremaintained to their optimal values corresponding to MPPTAt the event of frequency drop t 120 s and when the windspeed is below rated vw 65ms (partial-load operationmode) the sequence of events that occur can be summarizedas follows

(i) ampe controller adjusts the electromagnetic torquereference causing a deceleration of the rotor speed(Figure 10(a))

(ii) ampe rotor speed is below its maximum value(gt12 pu) therefore the pitch angle is kept at zero(Figure 11(a))

(iii) ampe reduction of the rotor speed causes the ex-traction of a portion of the kinetic energy stored inthe spinning masses (Figure 12(a)) ampis extra activepower will be used to support the power system inrecovering the frequency to 50Hz

(iv) ampe countering spike of the output power(Figure 12(a)) at roughly t 310 s can be explained

++ +++ ndash

WF

n-synchronous generation units

Primary frequency control (δeq)AGC

LpΔPWF

ΔPsyn

ΔPL

ΔfΔPm 12Heqs + D

Figure 8 Electric network frequency regulation control scheme ofa power system

Table 1 Simulation scenarios

Scenarios S1 S2 S3Generation units 1 2 and 3 C C C

Generation unit 4 Cno PFC NC NC

Wind farm NC Cno IC

Conly IC

C connected NC nonconnected PFC primary frequency control ICinertial control

8 Mathematical Problems in Engineering

as follows let us consider that theWTwas operatingat pointA (Figure 4) with the rotor speed reductionthe WTwill move to a suboptimal power extractionoperation point at the end of the inertial reactionamperefore less power will be delivered until fullrecovery of the WT

For a high wind speed vw 15ms (full-load operationmode) the sequence of events that occur can be summarizedas follows

(i) ampe pitch controller (Figure 11(b)) maintains therotor speed at its maximum value (asymp12 pu)(Figure 10(b))

(ii) ampe controller tries to adjust rotor speed but sincethe pitch controller is activated in this mode itcounteracts the action by reducing the pitch anglethus indirectly exploiting the mechanical power thatwas already curtailed by the positive pitch angle tocreate the power surge (Figure 12(b)) Not that thepower response at this mode requires no recoveryprocess since the pitching system is the one re-sponsible for the contribution

In order to highlight the merits of using a backsteppingcontrol algorithm instead of classical controllers it is par-ticularly important to analyse the system performance undersome kind of disturbances amperefore since the machineparameters are usually exposed to many forms of inaccur-acies especially due to the measuring devices identificationmethodology or several natural phenomena a robustnesstest was carried out to compare the performance of theproposed control strategy versus classical PI controllerswhen parametric variations are registered ampe test consistsin purposefully modifying the rotor resistance Rr of theDFIG by 50 and the stator inductance Ls by 10 from theirnormal values

Figures 12 and 13 show respectively the evolution of theDFIG stator active and reactive powers and Figures 14 and15 respectively show the evolution of d and q componentsof the rotor currents ampe test highlights the high sensitivityof classical PI controllers towards parametric variationwhich is notably observed due to the appearance of a sig-nificant static error in all simulation results whereas the

proposed backstepping control algorithm demonstrates anexquisite disturbance rejection being that all the outputsconverge correctly to their designated references Moreoverthe three-phased stator current sinusoidal waveform isshown in Figure 16

44 SpeedDroopControlEvaluation ampe performance of theproposed speed droop control will be evaluated for thefollowing simulation cases

Case 1 partial-load operation mode (wind speedvw 65ms)Case 1 Full-load operation mode (wind speedvw 15ms)

ampe set of results shown in the following figures dem-onstrates the capability of the proposed control strategy torespond to a sudden active power call at t 150 s Before thearrival of the frequency drop the WT is running at a ro-tational speed higher than the optimum (ΩgtΩmppt) inorder to lower the aerodynamic conversion efficiency rep-resented by Cp and therefore to operate following adeloaded operation characteristic with the power reservebeing created For the research objectives this work pre-sumes that the WT is operating with a reserve factorRf 10 while on the practical level the power margins aregenerally specified by the grid codes

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under partial-load operationmode can be summarized as follows

(i) ampe step in the output power reference (by ΔPrscFigure 3) modifies the electromagnetic torque ref-erence Tlowastem causing the rotor speed reduction asshown in Figure 17(a)

(ii) ampe rotor speed is below its maximum value thepitch control is not required in this case andtherefore the pitch angle is maintained at zero(Figure 18(a))

(iii) ampe rotor speed deceleration rises the power coef-ficient Cp to its maximum value (Figure 4) as shownin Figure 19(a) allowing consequently the WT toactivate its full power reserve

(iv) ampe power reserve activation rises the output powerof the WT by ΔPrsc (Figure 20(a)) thereforeallowing it to participate in the frequency recoveryprocess

(v) ampe power peaks induced as shown in Figure 20(a)demonstrate the benefit from creating the powerreserve by acceleration of the rotor speed the leftside of the power curve Figure 4 since now morekinetic energy is at our disposal and it can be usedwhenever the WT is decelerating

(vi) When the frequency recovers at t 400 s the controlstrategy reaccelerates the WT (Figure 17(a)) low-ering the power coefficient (Figure 19(a)) in order

S1S2S3

300 350 400250 Time (sec)

492

494

496

498

50

Fre

quen

cy (H

z)

Figure 9 Electric network frequency deviation for differentscenarios

Mathematical Problems in Engineering 9

to recreate the power reserve (Figure 20(a)) for thenext use

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under full-load operationmode can be summarized as follows

(i) ampe pitch control is now activated as shown inFigure 18(b) to keep the rotor speed at its maxi-mum value (Figure 17(b)) and to create the powerreserve (Figure 19(b)) since the rotor speed can nolonger be accelerated

(ii) ampe active power call (ΔPrsc Figure 4) reduced thepitch angle to make use of the mechanical powercurtailed by the positive β

(iii) β reduction increases the power coefficient CP asshown in Figure 19(b)consequently rising the

output according to the amount of power specifiedby ΔPrsc (Figure 20(b))

(iv) When the frequency recovers at t 400 s the pitchcontrol strategy rises the pitch angle (Figure 18(b))lowering the power coefficient (Figure 19(b)) inorder to recreate the power reserve (Figure 20(b))for the next use

45 Coordinated Control ampe artificial inertial reaction thespeed droop control and the pitch control could be usedaltogether to further enhance the frequency regulationcapability of WTs In this subsection we compared thesimulation scenarios summarized in Table 2 with S1 beingthe reference case where the wind power penetration isLp 0 For the other simulation scenarios the fourthgeneration synchronous is replaced with a WF with an

084

085

086

087

088

089

09

091

092Ro

tor s

peed

(pu)

110 120 130 140 150 160100Time (s)

(a)

116

12

124

Roto

r spe

ed (p

u)

110 120 130 140 150 160100Time (s)

(b)

Figure 10 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

10

Pitc

h an

gle (

deg)

110 120 130 140 150 160100Time (s)

ndash5

0

5

(a)

175

205Pi

tch

angl

e (deg)

110 120 130 140 150 160100Time (s)

18

185

19

195

20

(b)

Figure 11 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

10 Mathematical Problems in Engineering

equivalent power rating and the wind power penetrationrises to Lp 25 with S2 S3 S3 and S4 being respectivelythe cases without any frequency control the inertial reactiononly speed droop control only and all controllers

Figure 21 portrays the dynamic reaction of the frequencyfor each scenario All simulations were performed for amedium wind speed of vw 9ms and a sudden rise in loadby 005 pu system base is introduced to the system att 200 s

ampe results show that the severest case is obtained withthe simulation scenario S2 the case where the WF is

connected with no frequency regulation ability Comparedto the reference case S1 where the wind power penetrationLp 0 the frequency curve for the second simulationscenario S2 falls to a deeper nadir due to the reduction of thesystemrsquos equivalent inertia caused by increasing the windpower penetration Lp 25 On the other hand in the casewhere the inertial control is implemented S3 the WT de-celerates to release a portion of its kinetic energy transientlyimproving the frequency deviation Consequently the fre-quency nadir is lifted up to the level of the reference case S1However the quasi-steady-state frequency does not get any

Pslowast

Ps (PI)Ps (Bs)

ndash034

ndash032

ndash03

ndash028

ndash026

ndash024

ndash022W

T ou

tput

pow

er (p

u)

110 120 130 140 150 160100Time (seconds)

(a)

Pslowast

Ps (PI)Ps (Bs)

ndash105

ndash1

ndash095

ndash09

ndash085

WT

outp

ut p

ower

(pu)

110 120 130 140 150 160100Time (s)

(b)

Figure 12 Active power evolution for partial-load (a) and full-load (b) operation modes

QslowastQs (PI)Qs (Bs)

ndash5000

0

5000

Reac

tive p

ower

Qs (

Var)

110 120 130 140 150 160100Time (s)

(a)

QslowastQs (PI)Qs (Bs)

times104

ndash1

ndash05

0

05

1

Reac

tive p

ower

(Var

)

110 120 130 140 150 160100Time (s)

(b)

Figure 13 Reactive power evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 11

better with only the inertial control being enabled since itprovides only short-term frequency support With the speeddroop controller being enabled simulation scenario S4 itcan be observed that the WTcontribution is higher since themaximum transient and the quasi-steady-state frequencydeviations are both optimised Finally with both controllersbeing simultaneously enabled simulation scenario S5 thefrequency curve will further be improved for both short- andlong-term durations

As mentioned previously with only the inertial controlbeing activated at the event of frequency excursion the

rotor speed deceleration will impose a suboptimal powerextraction and then less power will be delivered until the fullrecovery of theWTto its optimum speed (Figure 10(c))ampisrecovery phase that generally lasts tens of seconds could beavoided when both controllers are simultaneously activatedgiven that the droop speed controller forces the WT tooperate at a higher rotational speed (ΩgtΩmppt) left side ofthe curve (Figure 4)amperefore when theWTdecelerates theoperating point will climb toward the optimum point and asa result there will be no need for the WT to recover at theend of the inertial response

Irqlowast

Irq (PI)Irq (Bs)

500

600

700

800

900

1000

1100Irq

110 120 130 140 150 160100Time (s)

(a)

Irqlowast

Irq (PI)Irq (Bs)

2600

2700

2800

2900

3000

3100

Irq

110 120 130 140 150 160100Time (s)

(b)

Figure 14 Active current Irq evolution for partial-load (a) and full-load (b) operation modes

Irdlowast

Ird (PI)Ird (Bs)

130

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(a)

Irdlowast

Ird (PI)Ird (Bs)

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(b)

Figure 15 Reactive current Ird evolution for partial-load (a) and full-load (b) operation modes

12 Mathematical Problems in Engineering

110 11005 1101 11015 1102

ndash1000

ndash500

0

500

1000

Is (A

)

110 120 130 140 150 160100Time (s)

(a)

ndash2000

ndash1000

0

1000

2000

Is (A

)

110 120 130 140 150 160100Time (s)

110 11005 1101 11015 1102

(b)

Figure 16 Stator current evolution for partial-load (a) and full-load (b) operation modes

08

09

1

11

12

Roto

r spe

ed (p

u)

200 300 400 500100Time (s)

(a)

11

115

12

125

13Ro

tor s

peed

(pu)

200 300 400 500100Time (s)

(b)

Figure 17 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

ndash5

0

5

10

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(a)

18

19

20

21

22

23

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(b)

Figure 18 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 13

Powerreserve

Cplowast

CpCpopt

200 300 400 500100Time (s)

042

044

046

048

05

Cp

(a)

Powerreserve

Cplowast

CpoptCp

011

012

013

014

015

016

Cp

150 200 250 300 350 400 450 500100 Time (s)

(b)

Figure 19 Power coefficient evolution for partial-load (a) and full-load (b) operation modes

Powerreserve

Power peaks

PrefPoptP

ndash03

ndash028

ndash026

ndash024

ndash022

ndash02

WT

outp

ut p

ower

(pu)

150 200 250 300 350 400 450 500100 Time (s)

(a)

Powerreserve

PrefPoptP

ndash105

ndash1

ndash095

ndash09

ndash085

ndash08

ndash075

ndash07

WT

outp

ut p

ower

(pu)

200 300 400 500100 Time (s)

(b)

Figure 20 WR output power evolution for partial-load (a) and full-load (b) operation modes

Table 2 Simulation scenarios

Scenarios S1 S2 S3 S3 S4Generation units 1 2 and 3 C C C C CGeneration unit 4 C NC NC NC NCWind farm NC C no control C only IC C only PFC C IC and PFCC connected NC nonconnected PFC primary frequency control IC inertial control

14 Mathematical Problems in Engineering

5 Conclusion

ampis paper explores different control approaches thatallow DFIG-based WTs to engage actively in frequencyregulation via coordinating the rotor speed and the pitchangle controllers In a short-term duration the inertialcontrol permits the WT to emulate the synchronousgenerator natural behaviour Accordingly at the event offrequency excursion the controller decelerates the WTin order to extract a portion of its kinetic energy shortlyproviding extra active power support for the powersystem However the inertial reaction alone is heavilydependent on the initial point of operation and a goodtuning of the controller gain is required since for in-stance at low wind speeds the rotor speed should notexceed its minimum value 06 pu for the stable operationof the WT ampe speed droop controller enables the WT toprovide active power assistance over an extended periodimproving the robustness of the system It forces the WTto operate following a deloaded characteristic creating acertain power reserve that can be automatically triggeredat the event of frequency deviations Moreover an in-novative pitch angle control is utilized to protect the WTagainst over speeding and to maintain the frequencyregulation capability under various operationconditions

Finally a study case considering an isolated powersystem that consists of synchronous generators DFIG-basedwind farm and static loads was examined to compare theperformance of each controller ampese simulation resultsshow that the coordination of the controllers improves boththe dynamic and the quasi-steady-state frequency deviationand brings the frequency nadir up to a far superior level thanthat obtained with the wind farm being disconnected (0wind power penetration)

Appendix

Wind turbine parameters

Rated power P 2MW blade radius R 45m gearboxG 90 WT inertia HWT 435 s damping coefficientf 0017Nmiddotmmiddotsrd and air density ρ 12 kgm3

DFIG parameters

Rated power P 2MW rated torque 127 kNm gridrated voltage and frequency Vs 690V and fs 50Hz polepair p 2 generator inertia HG 05 s stator and rotorresistances Rs 26mΩ and Rr 29mΩ stator and rotorinductance Ls 20mH and Lr 20mH and mutual in-ductance M 3253mH

Power coefficient expression

Cp X1X2

λ + 0008βminus00035 middot X2

β3 + 11113888 1113889 minus X3β minus X41113888 1113889

middot expX5

λ + 0008βminus00035 middot X5

β3 + 11113888 1113889 + X6λ

X1 05109

X2 116

X3 04

A4 5

X5 21

X6 00068

(A1)

Data Availability

No data were used to support this study

Disclosure

ampis paper is an expanded version of a paper entitled ldquoIn-ertial Response using Backstepping Control from DFIGbased Wind Power Plant for Short-Term Frequency Regu-lationrdquo presented at 2019 International Conference onControl Decision and Information Technologies held inParis France from 23 to 26 April 2019

Conflicts of Interest

ampe authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] Y Li Z Xu J Zhang and K P Wong ldquoVariable gain controlscheme of DFIG-based wind farm for over-frequency sup-portrdquo Renewable Energy vol 120 pp 379ndash391 2018

[2] N R Ullah T ampiringer and D Karlsson ldquoTemporaryprimary frequency control support by variable speed windturbines- potential and applicationsrdquo IEEE Transactions onPower Systems vol 23 no 2 pp 601ndash612 2008

[3] A Molina-Garcia I Munoz-Benavente A D Hansen andE Gomez-Lazaro ldquoDemand-side contribution to primaryfrequency control with wind farm auxiliary controlrdquo IEEE

S4S5

S1

S3S2

492

494

496

498

50

Freq

uenc

y (H

z)

150 200Time (s)

250 300

Figure 21 Deviation of the frequency for each simulation scenario

Mathematical Problems in Engineering 15

Transactions on Power Systems vol 29 no 5 pp 2391ndash23992014

[4] F Poitiers T Bouaouiche and M Machmoum ldquoAdvancedcontrol of a doubly-fed induction generator for wind energyconversionrdquo Electric Power Systems Research vol 79 no 7pp 1085ndash1096 2009

[5] Z-S Zhang Y-Z Sun J Lin and G-J Li ldquoCoordinatedfrequency regulation by doubly fed induction generator-basedwind power plantsrdquo IET Renewable Power Generation vol 6no 1 pp 38ndash47 2012

[6] R Chakib M Cherkaoui and A Essadki ldquoInertial responseused for a short term frequency control for DFIG windturbine controlled by ADRCrdquo ARPN Journal of Engineeringand Applied Sciences vol 11 no 5 2016

[7] Y-K Wu S-M Chang and P Mandal ldquoGrid-connectedwind power plants a survey on the integration requirementsin modern grid codesrdquo in Proceedings of the 2019 IEEEIAS55th Industrial and Commercial Power Systems TechnicalConference (IampCPS) pp 1ndash9 Canada Canada May 2019

[8] L Ruttledge and D Flynn ldquoEmulated inertial response fromwind turbines gain scheduling and resource coordinationrdquoIEEE Transactions on Power Systems vol 31 no 5pp 3747ndash3755 2015

[9] A I Estanqueiro J M F De Jesus J Ricardo A dos Santosand J A P Lopes ldquoBarriers (and solutions) to Very HighWind Penetration in Power Systemsrdquo in Proceedings of the2007 IEEE Power Engineering Society General Meetingpp 1ndash7 Tampa FL USA June 2007

[10] Y Wang G Delille H Bayem X Guillaud and B FrancoisldquoHigh wind power penetration in isolated power systems-assessment of wind inertial and primary frequency re-sponsesrdquo IEEE Transactions on Power Systems vol 28 no 3pp 2412ndash2420 2013

[11] P-K Keung P Li H Banakar and B T Ooi ldquoKinetic energyof wind-turbine generators for system frequency supportrdquoIEEE Transactions on Power Systems vol 24 no 1 pp 279ndash287 2008

[12] H Ye W Pei and Z Qi ldquoAnalytical modeling of inertial anddroop responses from a wind farm for short-term frequencyregulation in power systemsrdquo IEEE Transactions on PowerSystems vol 31 no 5 pp 3414ndash3423 2015

[13] H Liu and Z Chen ldquoContribution of VSC-HVDC to fre-quency regulation of power systems with offshore windgenerationrdquo IEEE Transactions on Energy Conversion vol 30no 3 pp 918ndash926 2015

[14] R M Kamel A Chaouachi and K Nagasaka ldquoampree controlstrategies to improve the microgrid transient dynamic re-sponse during isolated mode a comparative studyrdquo IEEETransactions on Industrial Electronics vol 60 no 4pp 1314ndash1322 2012

[15] S Wang J Hu X Yuan and L Sun ldquoOn inertial dynamics ofvirtual-synchronous-controlled DFIG-based wind turbinesrdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1691ndash1702 2015

[16] H T Ma and B H Chowdhury ldquoWorking towards frequencyregulation with wind plants combined control approachesrdquoIET Renewable Power Generation vol 4 no 4 pp 308ndash3162010

[17] I A Gowaid A El-Zawawi and M El-Gammal ldquoImprovedinertia and frequency support from grid-connected DFIGwind farmsrdquo in Proceedings of the Power Systems Conferenceand Exposition (PSCE) pp 1ndash9 Phoenix AZ USA March2011

[18] M Nadour A Essadki and T Nasser ldquoComparative analysisbetween PI amp backstepping control strategies of DFIG drivenby wind turbinerdquo International Journal of Renewable EnergyResearch vol 7 no 3 pp 1307ndash1316 2017

[19] M Nadour A Essadki M Fdaili and T Nasser ldquoAdvancedbackstepping control of a wind energy conversion systemusing a doubly-fed induction generatorrdquo in Proceedings of the2017 International Renewable and Sustainable Energy Con-ference (IRSEC) pp 1ndash6 Tangier Morocco December 2017

[20] Y Rebours A Comprehensive Assessment of Markets forFrequency and Voltage Control Ancillary Services PhD thesisUniversity of Manchester Manchester England 2008

[21] P Venne X Guillaud R Teodorescu and J MahseredjianldquoGeneralized gain scheduling for deloaded wind turbineoperationrdquo Wind Engineering vol 34 no 2 pp 219ndash2392010

[22] P Kundur N J Balu andM G Lauby Power System Stabilityand Control Vol 7 McGraw-Hill New York NY USA 1994

[23] J Van de Vyver J D M De Kooning B MeersmanL Vandevelde and T L Vandoorn ldquoDroop control as analternative inertial response strategy for the synthetic inertiaon wind turbinesrdquo IEEE Transactions on Power Systemsvol 31 no 2 pp 1129ndash1138 2016

16 Mathematical Problems in Engineering

consequence discharging a portion of the kinetic energystored in the WTspinning masses ampe mechanism is chosento be proportionate to that of synchronous generators andthus the additional power injected to the network can beexpressed as follows

ΔPIN(pu) 2HT middot fpudfpu

dt (13)

where fpu is the per-unit system frequency and HT the totalinertia constant (DFIG and WT) given by [5]

HT HDFIG + HWT HDFIG +12

JTΩ2ratedSrated

(14)

S rated and Ωrated are respectively the rated power andrated mechanical speed ampe equation that relates theelectromagnetic torque to the frequency can be determinedfrom equation (13) by the following expression

ΔTemminus IN(pu) 2HT middot fpudfpu

dt

1Ωm(pu)

(15)

Furthermore since the frequency is estimated by meansof a phase-locked loop (PLL) a low-pass filter needs to beintroduced into the control scheme in order to reduce theimpact of the small noises as shown in Figure 3 where TINrepresents the time constant of the filter and KIN its gain thatdetermines the amount of additional injected wind power incase of a frequency excursion

32 Speed Droop Control ampe artificial inertial response canonly be utilized to assist the system during the transitoryphase known as ldquodynamic frequency variationrdquo [20]However in order to enable the WT to provide active powersupport for an extended period of time another electricnetwork frequency-sensitive control loop that takes underconsideration the quasi-steady-state frequency deviationshould be added as shown in Figure 3ampe latter obligates theWT to operate following a ldquodeloaded operation character-istic (DL)rdquo as illustrated in Figure 4 creating a specificpower reserve that can be automatically activated to supportthe power systemwhen active power is needed at the event of

frequency disruption ampe creation of the power reserve isdone through the acceleration of mechanical speed Ωm byacting on the electromagnetic torque reference Tlowastemrminus DLhence the active power reference Plowasts moving the operationpoint from A (which corresponds to the maximum powerpoint tracking (MPPT) operation) to B (which corresponds

KINs1 + TINsX ΔTemndashIN

ΔPIN

++

Inertial response

fpu ΔPIN(pu)Xdivide

XΩm ΩmΩmRGT

Ωm

vwndashest(ρπR2GTv3

wndashest2Ωm) Cpe

λlowast

Clowastp

β

ΔPrsc_ +

Δf

f

fr

Eq (16)

Rotor speed control

TlowastemndashDL

Tlowastem

Eq (14)λ(Cp β)

XPlowasts

2HWT Pn

divide

Figure 3 Coordinated frequency-sensitive control scheme

0 05 1 15 WT rotor speed (pu)

0

01

02

03

04

05

06

07

08

09

1

Act

ive p

ower

(pu)

12

11ms

10ms

9ms

8ms

7ms

6ms

Speed limit

E

B

A

C

Power reserve

MPPT

DL

Figure 4 Deloaded operation

Define λi (i = 01hellipn) ampβj(i = 01hellipm)

Start

Compute Cp (λi βj) table(expression in the appendix)

Read βlowast

Cp (λi) = interp2(λi βj Cpprime λi βlowast)

2D interpolation of the tableCp (λi) for βk = βlowast Read Cp

lowast

λlowast = interp1(Cp (λi) λi Cplowast ldquolinearrdquo)

1D interpolation of λlowast

for Cp (λlowast) = Cplowast

Write λlowast

End

Figure 5 Organigram for the tip speed ratio referencecomputation

Mathematical Problems in Engineering 5

to the deloaded power point tracking (DL) operation) asshown in Figure 3 such that

PB 1 minus Rf1113872 1113873PA

ΩB≻ΩA Ωmppt

⎧⎨

⎩ (16)

where Rf is the reserve factor and PA and ΩA are beingrespectively the active power and the mechanical speed ofMPPT operation given by

PA ρπR2GT

2Ωm

v3wminus estCpmax1113890 1113891Ωm⟶ MPPT

vwminus est RΩm

GTλmppt

λmppt optimal tip speed ratio

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(17)

ampeoretically speaking the creation of the reserve canalso be achieved by decelerating the mechanical speedHowever it is preferred to use the acceleration method topreserve and even increase the amount of kinetic energystored in the WT At the event of frequency drop thecontroller changes the electromagnetic torque referencedecelerating the WT (moving from the point B through thepoint E to the maximum point A) as shown in Figure 4consequently rising the wind power production by a specificquantity ΔPrsc chosen to be proportionate to the frequencydeviation such thatΔPrsc K middot f minus fr( 1113857 K middot Δf

ΔPrscminus max Rf lowastPA⟶ total power reserve⎧⎨

⎩ (18)

with f and fr being respectively the measured and nominalfrequency 50Hz and K is an energy factor determined as afunction of the droop parameter δ

K Prated

δfr

1113888 1113889 (19)

with Prated being the generatorrsquos rated powerampe creation and activation (as function of ΔPrsc ) of the

power reserve are achieved through modifying the powercoefficient reference Cp

lowast and the tip speed ratio reference λlowastin equation (17) amperefore the power coefficient new ref-erence Cp

lowast can be determined from equation (1) by thefollowing expression

Clowastp λlowast β( 1113857 1 minus Rf1113872 1113873Cpmax lowastΔPrsc

05ρπR2v3w

Clowastp λlowast β( 1113857 1 minus Rf1113872 1113873Cpmax if ΔPrsc 0

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(20)

lowast plowast p While the reference of the tip speed ratio λlowast

which depends on the power coefficient reference Cplowast andfhe angle of orientation of the blades β can be determinedusing linear interpolation adopting the algorithm presentedin Figure 5

ampe block diagram of rotor speed control is illustrated inFigure 3

Finally the rotor speed controller along with the inertialresponseΔPIN sets the active power reference Psr for the DSCcontrol according to the following expressions

Plowasts Tlowastem middotΩm

Tlowastem Tlowastemminus DL + ΔTemminus IN1113896 (21)

33 Pitch Control ampe contribution of a WT to the globalpower reserve can be achieved either by accelerating therotor speed or by the orientation of the pitch angle Duringpartial-load operation mode (wind speed below rated) thefirst method could be used alone in case of a tolerable powerreserve However it becomes incapable if a larger reserve isrequested since the rotor speed should not exceed itsmaximum value (point B in Figure 4) In that case thesecond method is then called to take over ampe pitch con-troller calculates the appropriate pitch angle βref that pre-vents the generator speed from surpassing the maximumvalue 12 pu and βref is then transferred to the pitch systemwhich will either direct the fluid to the cylinders or the powerto the motors depending on the actuator to increase theangle of the blades consequently adjusting their lift forfurther mechanical power curtailment

For high wind speeds the WT is at full-load operationmode and the pitch system is already activated to keep therotor speed at its maximum value (point C in Figure 4) Notethat contrary to the classical WT control the regulationusing pitch angle control could be activated for all windconditions ampe dynamic of the pitch actuator can bemodelled using the following transfer function with Tpbeing the time constant of the pitch system [21]

β 1

1 + Tpsβref (22)

As previously mentioned the pitch angle β is used toregulate the rotor speedΩm ampe process is highly nonlinearand there is no direct relationship between these two var-iables Traditionally a gain scheduling control method isimplemented to make up for the existent nonlinear aero-dynamic behaviour [21] However the deloaded operationof the WT used for frequency regulation purposes com-plicates the control since the adjustment of the process gainnow depends on not only the wind speed but also the powerset point [21] Accordingly a simpler and more efficientapproach is presented in this paper It is based on Cp (λ β)table inversion since the nonlinear characteristic is essen-tially brought by its curve ampe architecture of the controlapproach is depicted in Figure 6

ampe reference of the pitch angle βref is determined usingthe reference of the power coefficient Clowastp an estimation oftip speed ratio λlowast and an inversion of the Cp (λ β) tableMoreover λlowast is determined using the rotor speed mea-surement and Clowastp is obtained from the aerodynamic torquereference TlowastT after inverting each element of the WTmodel(equation (1) to equation (4)) (note that in the steady stateTem Tg) As a consequence the process view by the con-troller becomes linear and electromagnetic torque reference

6 Mathematical Problems in Engineering

Tlowastem could be provided using a simple constant gain PIcontroller A dynamic saturation is used to limit Clowastp ref-erence to Clowastpminus up(λ β 30deg) and Clowastpminus down(λ β 0 1

deg)

ampe inversion of the Cp (λ β) table could be applied toany mathematical approximation It is based on 1- and 2-dimensional linear interpolations and it can be depicted inthe organigram (Figure 7)

4 Results and Discussions

41 General Discussion ampe power system is exposed tomany forms of disturbances A load change results in var-iation of the electrical torque Te output of all generators anda change in the production results in variation of the me-chanical torque Tm of all generators ampe frequency devia-tions reflect the mismatches between the electrical Te andmechanical Tm torques as represented by the followingequation of motion [22]

Tm minus Te 2Hdωdt

2Hdf

dt (23)

whereH is the power systemrsquos corresponding inertia constantand ω and f are the (per unit) rotational speed and the ENFrespectively [23] Equation (20) can be expressed in terms ofthe electrical Pe and mechanical Pm powers such that

Pm1 minus Pe1( 1113857 + ΔPm minus ΔPe( 1113857 ω1 minus Δω( 1113857 Tm1 minus Te1( 11138571113858

+ ΔTm minus ΔTe( 11138571113859

(24)

where we denote the deviations by the prefix (Δ) and thesteady-state values by the subscript (1) with ω1(pu) 1 andby ignoring the higher order terms and adopting the realistic

assumption of Pm1Pe1 and Tm1Te1 in the steady stateEquation (24) can further be adjusted into [22]

ΔPm minus ΔPe( 1113857 ΔTm minus ΔTe( 1113857 (25)

Replacing into equation (23) we can write

ΔPm minus ΔPe 2HdΔωdt

2HdΔfdt

(26)

In this work we have considered the load sensitivity tofrequency deviations Being that practically an abruptchange in frequency will cause a variation of the powerdemand [22] ampe overall network frequency-dependentcharacteristic of loads can be represented by the followingequation

ΔPe ΔPl + DΔf (27)

with ΔPl being the non-frequency-sensitive load variationand DΔω is frequency-sensitive load variation ampe coeffi-cient D represents the self-regulation of loads and it is

1GT

1GT

GT

1GT

ΩTRvw

1Jwts + fΩm

Ωlowastm

ΩT

Temr

GearboxTurbine Transmission

β

vw

λ

_+

2ΩlowastmTlowastaρπR2v3

w

_+

Cp(λ β)

Cp(λ β)(ρπR2v32ΩT)

Ωmndashr

ΩlowastTΩTRvw

PI

λlowast

Tlowasta Tlowast

em

Tg

Clowastp_down

Clowastp_up

Clowastp

Pitch system

βref

β(Cp λ)

TT

Figure 6 Block diagram of the rotor speed control

Define λi (i = 0 1hellipn)ampβj (i = 0 1hellipm)

Start

Compute Cp (λi βi) table(expression in the appendix)

Read λlowast

Cp (βi) = interp2 (β λ Cp β λlowast ldquolinearrdquo)

2D interpolation of the tableCp (βi) for λk = λlowast Read Clowast

p

βref = interp1(Cp (βi) β Clowastp ldquolinearrdquo)

1D interpolation of βreffor Cp = Clowast

p

Write βref

End

Figure 7 Organigram of the Cp table inversion

Mathematical Problems in Engineering 7

expressed as a percent change in load for 1 deviation infrequency [22] Substituting into equation (26) we can write

ΔPm minus ΔPl 2HdΔfdt

+ DΔf (28)

42 Power System Modelling To investigate the perfor-mances of the proposed control strategies a model of a smallpower system based on the scheme illustrated in Figure 8was designed inMatlabSimulink environment It consists offour identical conventional generating units (n 4 mediumpower hydroelectric generators) [2 22] each has a powerrating of Si 100MVA an inertia constant of Hi 50 s on100 MVA base and a droop for the speed governor δi 02feeding a total load of 220MW For the analysis of frequencyregulation capability we are concerned with the collectivebehaviour of all generators in the power system ampereforein this study all conventional synchronous generators arerepresented by a single equivalent machine driven by themechanical outputs of each turbine [22]ampe power rating ofthe equivalent generator is of Seq nSi and the equivalentdroop δeq and the corresponding inertia constant of thepower system Heq can be determined using the followingequations

Heq nHiSi

Seq

δeq δi

n

(29)

Note that the synchronous generators are operatingwithout automatic generation control (AGC) and onlyprimary frequency regulation is considered in this studywhich is practically sufficient for the research objectives

43 Artificial Inertial Response Evaluation In order to ex-amine the implemented artificial inertial control behaviourwe have compared three simulation scenarios as summa-rized in Table 1

ampe first scenario S1 represents the reference case wherethe first second and third synchronous generation unitsprovide both inertial response and primary frequencycontrol (PFC) while the fourth synchronous generation unitis providing only its inherited inertial reaction withoutprimary frequency response (no PFC) ampus according toequation (29) the system equivalent inertia remains con-stant Heq 50 s but the equivalent droop coefficient is nowδeq 0066 ampe remaining scenarios represent the casewhere the fourth synchronous generation unit is replacedwith a wind farm (WF) with an equivalent power ratingwhere S2 and S3 are respectively the wind farm caseswithout and with inertial control implemented In this casethe wind power penetration rises up to LP 25 thereforethe equivalent inertia constant is decreased to Hrsquoeq Heq(1minus Lp) 375 while the equivalent droop remains constantδrsquoeq 0066 A sudden rise in load by 20MW (005 pu systembase) is introduced to the system at t 300 s

Figure 9 portrays the dynamic reaction of the electricnetwork frequency for the three simulation scenarios Withscenario S1 being the reference case it can be observed that thedeepest frequency nadir the worst case is obtained withscenario S2 where the artificial inertial response of WTs isdisabled ampat is mainly due to the reduction of the systemequivalent inertia caused by the increase of the wind powerpenetration Lp to 25 in the system Meanwhile the narrowfrequency nadir the finest case is obtained with scenario S3where the inertial response is enabled and with an appropriategain KIN choice the inertial support from the WTs could beeven greater than that obtained from the synchronous gen-eration unit Since the wider the range of speed variation thebigger the amount of kinetic energy can be extracted

Figures 10ndash12 show the dynamic behaviour of a singleWT for different operation conditions Initially (before thedisturbance) the rotor speed and the active power output aremaintained to their optimal values corresponding to MPPTAt the event of frequency drop t 120 s and when the windspeed is below rated vw 65ms (partial-load operationmode) the sequence of events that occur can be summarizedas follows

(i) ampe controller adjusts the electromagnetic torquereference causing a deceleration of the rotor speed(Figure 10(a))

(ii) ampe rotor speed is below its maximum value(gt12 pu) therefore the pitch angle is kept at zero(Figure 11(a))

(iii) ampe reduction of the rotor speed causes the ex-traction of a portion of the kinetic energy stored inthe spinning masses (Figure 12(a)) ampis extra activepower will be used to support the power system inrecovering the frequency to 50Hz

(iv) ampe countering spike of the output power(Figure 12(a)) at roughly t 310 s can be explained

++ +++ ndash

WF

n-synchronous generation units

Primary frequency control (δeq)AGC

LpΔPWF

ΔPsyn

ΔPL

ΔfΔPm 12Heqs + D

Figure 8 Electric network frequency regulation control scheme ofa power system

Table 1 Simulation scenarios

Scenarios S1 S2 S3Generation units 1 2 and 3 C C C

Generation unit 4 Cno PFC NC NC

Wind farm NC Cno IC

Conly IC

C connected NC nonconnected PFC primary frequency control ICinertial control

8 Mathematical Problems in Engineering

as follows let us consider that theWTwas operatingat pointA (Figure 4) with the rotor speed reductionthe WTwill move to a suboptimal power extractionoperation point at the end of the inertial reactionamperefore less power will be delivered until fullrecovery of the WT

For a high wind speed vw 15ms (full-load operationmode) the sequence of events that occur can be summarizedas follows

(i) ampe pitch controller (Figure 11(b)) maintains therotor speed at its maximum value (asymp12 pu)(Figure 10(b))

(ii) ampe controller tries to adjust rotor speed but sincethe pitch controller is activated in this mode itcounteracts the action by reducing the pitch anglethus indirectly exploiting the mechanical power thatwas already curtailed by the positive pitch angle tocreate the power surge (Figure 12(b)) Not that thepower response at this mode requires no recoveryprocess since the pitching system is the one re-sponsible for the contribution

In order to highlight the merits of using a backsteppingcontrol algorithm instead of classical controllers it is par-ticularly important to analyse the system performance undersome kind of disturbances amperefore since the machineparameters are usually exposed to many forms of inaccur-acies especially due to the measuring devices identificationmethodology or several natural phenomena a robustnesstest was carried out to compare the performance of theproposed control strategy versus classical PI controllerswhen parametric variations are registered ampe test consistsin purposefully modifying the rotor resistance Rr of theDFIG by 50 and the stator inductance Ls by 10 from theirnormal values

Figures 12 and 13 show respectively the evolution of theDFIG stator active and reactive powers and Figures 14 and15 respectively show the evolution of d and q componentsof the rotor currents ampe test highlights the high sensitivityof classical PI controllers towards parametric variationwhich is notably observed due to the appearance of a sig-nificant static error in all simulation results whereas the

proposed backstepping control algorithm demonstrates anexquisite disturbance rejection being that all the outputsconverge correctly to their designated references Moreoverthe three-phased stator current sinusoidal waveform isshown in Figure 16

44 SpeedDroopControlEvaluation ampe performance of theproposed speed droop control will be evaluated for thefollowing simulation cases

Case 1 partial-load operation mode (wind speedvw 65ms)Case 1 Full-load operation mode (wind speedvw 15ms)

ampe set of results shown in the following figures dem-onstrates the capability of the proposed control strategy torespond to a sudden active power call at t 150 s Before thearrival of the frequency drop the WT is running at a ro-tational speed higher than the optimum (ΩgtΩmppt) inorder to lower the aerodynamic conversion efficiency rep-resented by Cp and therefore to operate following adeloaded operation characteristic with the power reservebeing created For the research objectives this work pre-sumes that the WT is operating with a reserve factorRf 10 while on the practical level the power margins aregenerally specified by the grid codes

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under partial-load operationmode can be summarized as follows

(i) ampe step in the output power reference (by ΔPrscFigure 3) modifies the electromagnetic torque ref-erence Tlowastem causing the rotor speed reduction asshown in Figure 17(a)

(ii) ampe rotor speed is below its maximum value thepitch control is not required in this case andtherefore the pitch angle is maintained at zero(Figure 18(a))

(iii) ampe rotor speed deceleration rises the power coef-ficient Cp to its maximum value (Figure 4) as shownin Figure 19(a) allowing consequently the WT toactivate its full power reserve

(iv) ampe power reserve activation rises the output powerof the WT by ΔPrsc (Figure 20(a)) thereforeallowing it to participate in the frequency recoveryprocess

(v) ampe power peaks induced as shown in Figure 20(a)demonstrate the benefit from creating the powerreserve by acceleration of the rotor speed the leftside of the power curve Figure 4 since now morekinetic energy is at our disposal and it can be usedwhenever the WT is decelerating

(vi) When the frequency recovers at t 400 s the controlstrategy reaccelerates the WT (Figure 17(a)) low-ering the power coefficient (Figure 19(a)) in order

S1S2S3

300 350 400250 Time (sec)

492

494

496

498

50

Fre

quen

cy (H

z)

Figure 9 Electric network frequency deviation for differentscenarios

Mathematical Problems in Engineering 9

to recreate the power reserve (Figure 20(a)) for thenext use

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under full-load operationmode can be summarized as follows

(i) ampe pitch control is now activated as shown inFigure 18(b) to keep the rotor speed at its maxi-mum value (Figure 17(b)) and to create the powerreserve (Figure 19(b)) since the rotor speed can nolonger be accelerated

(ii) ampe active power call (ΔPrsc Figure 4) reduced thepitch angle to make use of the mechanical powercurtailed by the positive β

(iii) β reduction increases the power coefficient CP asshown in Figure 19(b)consequently rising the

output according to the amount of power specifiedby ΔPrsc (Figure 20(b))

(iv) When the frequency recovers at t 400 s the pitchcontrol strategy rises the pitch angle (Figure 18(b))lowering the power coefficient (Figure 19(b)) inorder to recreate the power reserve (Figure 20(b))for the next use

45 Coordinated Control ampe artificial inertial reaction thespeed droop control and the pitch control could be usedaltogether to further enhance the frequency regulationcapability of WTs In this subsection we compared thesimulation scenarios summarized in Table 2 with S1 beingthe reference case where the wind power penetration isLp 0 For the other simulation scenarios the fourthgeneration synchronous is replaced with a WF with an

084

085

086

087

088

089

09

091

092Ro

tor s

peed

(pu)

110 120 130 140 150 160100Time (s)

(a)

116

12

124

Roto

r spe

ed (p

u)

110 120 130 140 150 160100Time (s)

(b)

Figure 10 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

10

Pitc

h an

gle (

deg)

110 120 130 140 150 160100Time (s)

ndash5

0

5

(a)

175

205Pi

tch

angl

e (deg)

110 120 130 140 150 160100Time (s)

18

185

19

195

20

(b)

Figure 11 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

10 Mathematical Problems in Engineering

equivalent power rating and the wind power penetrationrises to Lp 25 with S2 S3 S3 and S4 being respectivelythe cases without any frequency control the inertial reactiononly speed droop control only and all controllers

Figure 21 portrays the dynamic reaction of the frequencyfor each scenario All simulations were performed for amedium wind speed of vw 9ms and a sudden rise in loadby 005 pu system base is introduced to the system att 200 s

ampe results show that the severest case is obtained withthe simulation scenario S2 the case where the WF is

connected with no frequency regulation ability Comparedto the reference case S1 where the wind power penetrationLp 0 the frequency curve for the second simulationscenario S2 falls to a deeper nadir due to the reduction of thesystemrsquos equivalent inertia caused by increasing the windpower penetration Lp 25 On the other hand in the casewhere the inertial control is implemented S3 the WT de-celerates to release a portion of its kinetic energy transientlyimproving the frequency deviation Consequently the fre-quency nadir is lifted up to the level of the reference case S1However the quasi-steady-state frequency does not get any

Pslowast

Ps (PI)Ps (Bs)

ndash034

ndash032

ndash03

ndash028

ndash026

ndash024

ndash022W

T ou

tput

pow

er (p

u)

110 120 130 140 150 160100Time (seconds)

(a)

Pslowast

Ps (PI)Ps (Bs)

ndash105

ndash1

ndash095

ndash09

ndash085

WT

outp

ut p

ower

(pu)

110 120 130 140 150 160100Time (s)

(b)

Figure 12 Active power evolution for partial-load (a) and full-load (b) operation modes

QslowastQs (PI)Qs (Bs)

ndash5000

0

5000

Reac

tive p

ower

Qs (

Var)

110 120 130 140 150 160100Time (s)

(a)

QslowastQs (PI)Qs (Bs)

times104

ndash1

ndash05

0

05

1

Reac

tive p

ower

(Var

)

110 120 130 140 150 160100Time (s)

(b)

Figure 13 Reactive power evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 11

better with only the inertial control being enabled since itprovides only short-term frequency support With the speeddroop controller being enabled simulation scenario S4 itcan be observed that the WTcontribution is higher since themaximum transient and the quasi-steady-state frequencydeviations are both optimised Finally with both controllersbeing simultaneously enabled simulation scenario S5 thefrequency curve will further be improved for both short- andlong-term durations

As mentioned previously with only the inertial controlbeing activated at the event of frequency excursion the

rotor speed deceleration will impose a suboptimal powerextraction and then less power will be delivered until the fullrecovery of theWTto its optimum speed (Figure 10(c))ampisrecovery phase that generally lasts tens of seconds could beavoided when both controllers are simultaneously activatedgiven that the droop speed controller forces the WT tooperate at a higher rotational speed (ΩgtΩmppt) left side ofthe curve (Figure 4)amperefore when theWTdecelerates theoperating point will climb toward the optimum point and asa result there will be no need for the WT to recover at theend of the inertial response

Irqlowast

Irq (PI)Irq (Bs)

500

600

700

800

900

1000

1100Irq

110 120 130 140 150 160100Time (s)

(a)

Irqlowast

Irq (PI)Irq (Bs)

2600

2700

2800

2900

3000

3100

Irq

110 120 130 140 150 160100Time (s)

(b)

Figure 14 Active current Irq evolution for partial-load (a) and full-load (b) operation modes

Irdlowast

Ird (PI)Ird (Bs)

130

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(a)

Irdlowast

Ird (PI)Ird (Bs)

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(b)

Figure 15 Reactive current Ird evolution for partial-load (a) and full-load (b) operation modes

12 Mathematical Problems in Engineering

110 11005 1101 11015 1102

ndash1000

ndash500

0

500

1000

Is (A

)

110 120 130 140 150 160100Time (s)

(a)

ndash2000

ndash1000

0

1000

2000

Is (A

)

110 120 130 140 150 160100Time (s)

110 11005 1101 11015 1102

(b)

Figure 16 Stator current evolution for partial-load (a) and full-load (b) operation modes

08

09

1

11

12

Roto

r spe

ed (p

u)

200 300 400 500100Time (s)

(a)

11

115

12

125

13Ro

tor s

peed

(pu)

200 300 400 500100Time (s)

(b)

Figure 17 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

ndash5

0

5

10

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(a)

18

19

20

21

22

23

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(b)

Figure 18 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 13

Powerreserve

Cplowast

CpCpopt

200 300 400 500100Time (s)

042

044

046

048

05

Cp

(a)

Powerreserve

Cplowast

CpoptCp

011

012

013

014

015

016

Cp

150 200 250 300 350 400 450 500100 Time (s)

(b)

Figure 19 Power coefficient evolution for partial-load (a) and full-load (b) operation modes

Powerreserve

Power peaks

PrefPoptP

ndash03

ndash028

ndash026

ndash024

ndash022

ndash02

WT

outp

ut p

ower

(pu)

150 200 250 300 350 400 450 500100 Time (s)

(a)

Powerreserve

PrefPoptP

ndash105

ndash1

ndash095

ndash09

ndash085

ndash08

ndash075

ndash07

WT

outp

ut p

ower

(pu)

200 300 400 500100 Time (s)

(b)

Figure 20 WR output power evolution for partial-load (a) and full-load (b) operation modes

Table 2 Simulation scenarios

Scenarios S1 S2 S3 S3 S4Generation units 1 2 and 3 C C C C CGeneration unit 4 C NC NC NC NCWind farm NC C no control C only IC C only PFC C IC and PFCC connected NC nonconnected PFC primary frequency control IC inertial control

14 Mathematical Problems in Engineering

5 Conclusion

ampis paper explores different control approaches thatallow DFIG-based WTs to engage actively in frequencyregulation via coordinating the rotor speed and the pitchangle controllers In a short-term duration the inertialcontrol permits the WT to emulate the synchronousgenerator natural behaviour Accordingly at the event offrequency excursion the controller decelerates the WTin order to extract a portion of its kinetic energy shortlyproviding extra active power support for the powersystem However the inertial reaction alone is heavilydependent on the initial point of operation and a goodtuning of the controller gain is required since for in-stance at low wind speeds the rotor speed should notexceed its minimum value 06 pu for the stable operationof the WT ampe speed droop controller enables the WT toprovide active power assistance over an extended periodimproving the robustness of the system It forces the WTto operate following a deloaded characteristic creating acertain power reserve that can be automatically triggeredat the event of frequency deviations Moreover an in-novative pitch angle control is utilized to protect the WTagainst over speeding and to maintain the frequencyregulation capability under various operationconditions

Finally a study case considering an isolated powersystem that consists of synchronous generators DFIG-basedwind farm and static loads was examined to compare theperformance of each controller ampese simulation resultsshow that the coordination of the controllers improves boththe dynamic and the quasi-steady-state frequency deviationand brings the frequency nadir up to a far superior level thanthat obtained with the wind farm being disconnected (0wind power penetration)

Appendix

Wind turbine parameters

Rated power P 2MW blade radius R 45m gearboxG 90 WT inertia HWT 435 s damping coefficientf 0017Nmiddotmmiddotsrd and air density ρ 12 kgm3

DFIG parameters

Rated power P 2MW rated torque 127 kNm gridrated voltage and frequency Vs 690V and fs 50Hz polepair p 2 generator inertia HG 05 s stator and rotorresistances Rs 26mΩ and Rr 29mΩ stator and rotorinductance Ls 20mH and Lr 20mH and mutual in-ductance M 3253mH

Power coefficient expression

Cp X1X2

λ + 0008βminus00035 middot X2

β3 + 11113888 1113889 minus X3β minus X41113888 1113889

middot expX5

λ + 0008βminus00035 middot X5

β3 + 11113888 1113889 + X6λ

X1 05109

X2 116

X3 04

A4 5

X5 21

X6 00068

(A1)

Data Availability

No data were used to support this study

Disclosure

ampis paper is an expanded version of a paper entitled ldquoIn-ertial Response using Backstepping Control from DFIGbased Wind Power Plant for Short-Term Frequency Regu-lationrdquo presented at 2019 International Conference onControl Decision and Information Technologies held inParis France from 23 to 26 April 2019

Conflicts of Interest

ampe authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] Y Li Z Xu J Zhang and K P Wong ldquoVariable gain controlscheme of DFIG-based wind farm for over-frequency sup-portrdquo Renewable Energy vol 120 pp 379ndash391 2018

[2] N R Ullah T ampiringer and D Karlsson ldquoTemporaryprimary frequency control support by variable speed windturbines- potential and applicationsrdquo IEEE Transactions onPower Systems vol 23 no 2 pp 601ndash612 2008

[3] A Molina-Garcia I Munoz-Benavente A D Hansen andE Gomez-Lazaro ldquoDemand-side contribution to primaryfrequency control with wind farm auxiliary controlrdquo IEEE

S4S5

S1

S3S2

492

494

496

498

50

Freq

uenc

y (H

z)

150 200Time (s)

250 300

Figure 21 Deviation of the frequency for each simulation scenario

Mathematical Problems in Engineering 15

Transactions on Power Systems vol 29 no 5 pp 2391ndash23992014

[4] F Poitiers T Bouaouiche and M Machmoum ldquoAdvancedcontrol of a doubly-fed induction generator for wind energyconversionrdquo Electric Power Systems Research vol 79 no 7pp 1085ndash1096 2009

[5] Z-S Zhang Y-Z Sun J Lin and G-J Li ldquoCoordinatedfrequency regulation by doubly fed induction generator-basedwind power plantsrdquo IET Renewable Power Generation vol 6no 1 pp 38ndash47 2012

[6] R Chakib M Cherkaoui and A Essadki ldquoInertial responseused for a short term frequency control for DFIG windturbine controlled by ADRCrdquo ARPN Journal of Engineeringand Applied Sciences vol 11 no 5 2016

[7] Y-K Wu S-M Chang and P Mandal ldquoGrid-connectedwind power plants a survey on the integration requirementsin modern grid codesrdquo in Proceedings of the 2019 IEEEIAS55th Industrial and Commercial Power Systems TechnicalConference (IampCPS) pp 1ndash9 Canada Canada May 2019

[8] L Ruttledge and D Flynn ldquoEmulated inertial response fromwind turbines gain scheduling and resource coordinationrdquoIEEE Transactions on Power Systems vol 31 no 5pp 3747ndash3755 2015

[9] A I Estanqueiro J M F De Jesus J Ricardo A dos Santosand J A P Lopes ldquoBarriers (and solutions) to Very HighWind Penetration in Power Systemsrdquo in Proceedings of the2007 IEEE Power Engineering Society General Meetingpp 1ndash7 Tampa FL USA June 2007

[10] Y Wang G Delille H Bayem X Guillaud and B FrancoisldquoHigh wind power penetration in isolated power systems-assessment of wind inertial and primary frequency re-sponsesrdquo IEEE Transactions on Power Systems vol 28 no 3pp 2412ndash2420 2013

[11] P-K Keung P Li H Banakar and B T Ooi ldquoKinetic energyof wind-turbine generators for system frequency supportrdquoIEEE Transactions on Power Systems vol 24 no 1 pp 279ndash287 2008

[12] H Ye W Pei and Z Qi ldquoAnalytical modeling of inertial anddroop responses from a wind farm for short-term frequencyregulation in power systemsrdquo IEEE Transactions on PowerSystems vol 31 no 5 pp 3414ndash3423 2015

[13] H Liu and Z Chen ldquoContribution of VSC-HVDC to fre-quency regulation of power systems with offshore windgenerationrdquo IEEE Transactions on Energy Conversion vol 30no 3 pp 918ndash926 2015

[14] R M Kamel A Chaouachi and K Nagasaka ldquoampree controlstrategies to improve the microgrid transient dynamic re-sponse during isolated mode a comparative studyrdquo IEEETransactions on Industrial Electronics vol 60 no 4pp 1314ndash1322 2012

[15] S Wang J Hu X Yuan and L Sun ldquoOn inertial dynamics ofvirtual-synchronous-controlled DFIG-based wind turbinesrdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1691ndash1702 2015

[16] H T Ma and B H Chowdhury ldquoWorking towards frequencyregulation with wind plants combined control approachesrdquoIET Renewable Power Generation vol 4 no 4 pp 308ndash3162010

[17] I A Gowaid A El-Zawawi and M El-Gammal ldquoImprovedinertia and frequency support from grid-connected DFIGwind farmsrdquo in Proceedings of the Power Systems Conferenceand Exposition (PSCE) pp 1ndash9 Phoenix AZ USA March2011

[18] M Nadour A Essadki and T Nasser ldquoComparative analysisbetween PI amp backstepping control strategies of DFIG drivenby wind turbinerdquo International Journal of Renewable EnergyResearch vol 7 no 3 pp 1307ndash1316 2017

[19] M Nadour A Essadki M Fdaili and T Nasser ldquoAdvancedbackstepping control of a wind energy conversion systemusing a doubly-fed induction generatorrdquo in Proceedings of the2017 International Renewable and Sustainable Energy Con-ference (IRSEC) pp 1ndash6 Tangier Morocco December 2017

[20] Y Rebours A Comprehensive Assessment of Markets forFrequency and Voltage Control Ancillary Services PhD thesisUniversity of Manchester Manchester England 2008

[21] P Venne X Guillaud R Teodorescu and J MahseredjianldquoGeneralized gain scheduling for deloaded wind turbineoperationrdquo Wind Engineering vol 34 no 2 pp 219ndash2392010

[22] P Kundur N J Balu andM G Lauby Power System Stabilityand Control Vol 7 McGraw-Hill New York NY USA 1994

[23] J Van de Vyver J D M De Kooning B MeersmanL Vandevelde and T L Vandoorn ldquoDroop control as analternative inertial response strategy for the synthetic inertiaon wind turbinesrdquo IEEE Transactions on Power Systemsvol 31 no 2 pp 1129ndash1138 2016

16 Mathematical Problems in Engineering

to the deloaded power point tracking (DL) operation) asshown in Figure 3 such that

PB 1 minus Rf1113872 1113873PA

ΩB≻ΩA Ωmppt

⎧⎨

⎩ (16)

where Rf is the reserve factor and PA and ΩA are beingrespectively the active power and the mechanical speed ofMPPT operation given by

PA ρπR2GT

2Ωm

v3wminus estCpmax1113890 1113891Ωm⟶ MPPT

vwminus est RΩm

GTλmppt

λmppt optimal tip speed ratio

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(17)

ampeoretically speaking the creation of the reserve canalso be achieved by decelerating the mechanical speedHowever it is preferred to use the acceleration method topreserve and even increase the amount of kinetic energystored in the WT At the event of frequency drop thecontroller changes the electromagnetic torque referencedecelerating the WT (moving from the point B through thepoint E to the maximum point A) as shown in Figure 4consequently rising the wind power production by a specificquantity ΔPrsc chosen to be proportionate to the frequencydeviation such thatΔPrsc K middot f minus fr( 1113857 K middot Δf

ΔPrscminus max Rf lowastPA⟶ total power reserve⎧⎨

⎩ (18)

with f and fr being respectively the measured and nominalfrequency 50Hz and K is an energy factor determined as afunction of the droop parameter δ

K Prated

δfr

1113888 1113889 (19)

with Prated being the generatorrsquos rated powerampe creation and activation (as function of ΔPrsc ) of the

power reserve are achieved through modifying the powercoefficient reference Cp

lowast and the tip speed ratio reference λlowastin equation (17) amperefore the power coefficient new ref-erence Cp

lowast can be determined from equation (1) by thefollowing expression

Clowastp λlowast β( 1113857 1 minus Rf1113872 1113873Cpmax lowastΔPrsc

05ρπR2v3w

Clowastp λlowast β( 1113857 1 minus Rf1113872 1113873Cpmax if ΔPrsc 0

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(20)

lowast plowast p While the reference of the tip speed ratio λlowast

which depends on the power coefficient reference Cplowast andfhe angle of orientation of the blades β can be determinedusing linear interpolation adopting the algorithm presentedin Figure 5

ampe block diagram of rotor speed control is illustrated inFigure 3

Finally the rotor speed controller along with the inertialresponseΔPIN sets the active power reference Psr for the DSCcontrol according to the following expressions

Plowasts Tlowastem middotΩm

Tlowastem Tlowastemminus DL + ΔTemminus IN1113896 (21)

33 Pitch Control ampe contribution of a WT to the globalpower reserve can be achieved either by accelerating therotor speed or by the orientation of the pitch angle Duringpartial-load operation mode (wind speed below rated) thefirst method could be used alone in case of a tolerable powerreserve However it becomes incapable if a larger reserve isrequested since the rotor speed should not exceed itsmaximum value (point B in Figure 4) In that case thesecond method is then called to take over ampe pitch con-troller calculates the appropriate pitch angle βref that pre-vents the generator speed from surpassing the maximumvalue 12 pu and βref is then transferred to the pitch systemwhich will either direct the fluid to the cylinders or the powerto the motors depending on the actuator to increase theangle of the blades consequently adjusting their lift forfurther mechanical power curtailment

For high wind speeds the WT is at full-load operationmode and the pitch system is already activated to keep therotor speed at its maximum value (point C in Figure 4) Notethat contrary to the classical WT control the regulationusing pitch angle control could be activated for all windconditions ampe dynamic of the pitch actuator can bemodelled using the following transfer function with Tpbeing the time constant of the pitch system [21]

β 1

1 + Tpsβref (22)

As previously mentioned the pitch angle β is used toregulate the rotor speedΩm ampe process is highly nonlinearand there is no direct relationship between these two var-iables Traditionally a gain scheduling control method isimplemented to make up for the existent nonlinear aero-dynamic behaviour [21] However the deloaded operationof the WT used for frequency regulation purposes com-plicates the control since the adjustment of the process gainnow depends on not only the wind speed but also the powerset point [21] Accordingly a simpler and more efficientapproach is presented in this paper It is based on Cp (λ β)table inversion since the nonlinear characteristic is essen-tially brought by its curve ampe architecture of the controlapproach is depicted in Figure 6

ampe reference of the pitch angle βref is determined usingthe reference of the power coefficient Clowastp an estimation oftip speed ratio λlowast and an inversion of the Cp (λ β) tableMoreover λlowast is determined using the rotor speed mea-surement and Clowastp is obtained from the aerodynamic torquereference TlowastT after inverting each element of the WTmodel(equation (1) to equation (4)) (note that in the steady stateTem Tg) As a consequence the process view by the con-troller becomes linear and electromagnetic torque reference

6 Mathematical Problems in Engineering

Tlowastem could be provided using a simple constant gain PIcontroller A dynamic saturation is used to limit Clowastp ref-erence to Clowastpminus up(λ β 30deg) and Clowastpminus down(λ β 0 1

deg)

ampe inversion of the Cp (λ β) table could be applied toany mathematical approximation It is based on 1- and 2-dimensional linear interpolations and it can be depicted inthe organigram (Figure 7)

4 Results and Discussions

41 General Discussion ampe power system is exposed tomany forms of disturbances A load change results in var-iation of the electrical torque Te output of all generators anda change in the production results in variation of the me-chanical torque Tm of all generators ampe frequency devia-tions reflect the mismatches between the electrical Te andmechanical Tm torques as represented by the followingequation of motion [22]

Tm minus Te 2Hdωdt

2Hdf

dt (23)

whereH is the power systemrsquos corresponding inertia constantand ω and f are the (per unit) rotational speed and the ENFrespectively [23] Equation (20) can be expressed in terms ofthe electrical Pe and mechanical Pm powers such that

Pm1 minus Pe1( 1113857 + ΔPm minus ΔPe( 1113857 ω1 minus Δω( 1113857 Tm1 minus Te1( 11138571113858

+ ΔTm minus ΔTe( 11138571113859

(24)

where we denote the deviations by the prefix (Δ) and thesteady-state values by the subscript (1) with ω1(pu) 1 andby ignoring the higher order terms and adopting the realistic

assumption of Pm1Pe1 and Tm1Te1 in the steady stateEquation (24) can further be adjusted into [22]

ΔPm minus ΔPe( 1113857 ΔTm minus ΔTe( 1113857 (25)

Replacing into equation (23) we can write

ΔPm minus ΔPe 2HdΔωdt

2HdΔfdt

(26)

In this work we have considered the load sensitivity tofrequency deviations Being that practically an abruptchange in frequency will cause a variation of the powerdemand [22] ampe overall network frequency-dependentcharacteristic of loads can be represented by the followingequation

ΔPe ΔPl + DΔf (27)

with ΔPl being the non-frequency-sensitive load variationand DΔω is frequency-sensitive load variation ampe coeffi-cient D represents the self-regulation of loads and it is

1GT

1GT

GT

1GT

ΩTRvw

1Jwts + fΩm

Ωlowastm

ΩT

Temr

GearboxTurbine Transmission

β

vw

λ

_+

2ΩlowastmTlowastaρπR2v3

w

_+

Cp(λ β)

Cp(λ β)(ρπR2v32ΩT)

Ωmndashr

ΩlowastTΩTRvw

PI

λlowast

Tlowasta Tlowast

em

Tg

Clowastp_down

Clowastp_up

Clowastp

Pitch system

βref

β(Cp λ)

TT

Figure 6 Block diagram of the rotor speed control

Define λi (i = 0 1hellipn)ampβj (i = 0 1hellipm)

Start

Compute Cp (λi βi) table(expression in the appendix)

Read λlowast

Cp (βi) = interp2 (β λ Cp β λlowast ldquolinearrdquo)

2D interpolation of the tableCp (βi) for λk = λlowast Read Clowast

p

βref = interp1(Cp (βi) β Clowastp ldquolinearrdquo)

1D interpolation of βreffor Cp = Clowast

p

Write βref

End

Figure 7 Organigram of the Cp table inversion

Mathematical Problems in Engineering 7

expressed as a percent change in load for 1 deviation infrequency [22] Substituting into equation (26) we can write

ΔPm minus ΔPl 2HdΔfdt

+ DΔf (28)

42 Power System Modelling To investigate the perfor-mances of the proposed control strategies a model of a smallpower system based on the scheme illustrated in Figure 8was designed inMatlabSimulink environment It consists offour identical conventional generating units (n 4 mediumpower hydroelectric generators) [2 22] each has a powerrating of Si 100MVA an inertia constant of Hi 50 s on100 MVA base and a droop for the speed governor δi 02feeding a total load of 220MW For the analysis of frequencyregulation capability we are concerned with the collectivebehaviour of all generators in the power system ampereforein this study all conventional synchronous generators arerepresented by a single equivalent machine driven by themechanical outputs of each turbine [22]ampe power rating ofthe equivalent generator is of Seq nSi and the equivalentdroop δeq and the corresponding inertia constant of thepower system Heq can be determined using the followingequations

Heq nHiSi

Seq

δeq δi

n

(29)

Note that the synchronous generators are operatingwithout automatic generation control (AGC) and onlyprimary frequency regulation is considered in this studywhich is practically sufficient for the research objectives

43 Artificial Inertial Response Evaluation In order to ex-amine the implemented artificial inertial control behaviourwe have compared three simulation scenarios as summa-rized in Table 1

ampe first scenario S1 represents the reference case wherethe first second and third synchronous generation unitsprovide both inertial response and primary frequencycontrol (PFC) while the fourth synchronous generation unitis providing only its inherited inertial reaction withoutprimary frequency response (no PFC) ampus according toequation (29) the system equivalent inertia remains con-stant Heq 50 s but the equivalent droop coefficient is nowδeq 0066 ampe remaining scenarios represent the casewhere the fourth synchronous generation unit is replacedwith a wind farm (WF) with an equivalent power ratingwhere S2 and S3 are respectively the wind farm caseswithout and with inertial control implemented In this casethe wind power penetration rises up to LP 25 thereforethe equivalent inertia constant is decreased to Hrsquoeq Heq(1minus Lp) 375 while the equivalent droop remains constantδrsquoeq 0066 A sudden rise in load by 20MW (005 pu systembase) is introduced to the system at t 300 s

Figure 9 portrays the dynamic reaction of the electricnetwork frequency for the three simulation scenarios Withscenario S1 being the reference case it can be observed that thedeepest frequency nadir the worst case is obtained withscenario S2 where the artificial inertial response of WTs isdisabled ampat is mainly due to the reduction of the systemequivalent inertia caused by the increase of the wind powerpenetration Lp to 25 in the system Meanwhile the narrowfrequency nadir the finest case is obtained with scenario S3where the inertial response is enabled and with an appropriategain KIN choice the inertial support from the WTs could beeven greater than that obtained from the synchronous gen-eration unit Since the wider the range of speed variation thebigger the amount of kinetic energy can be extracted

Figures 10ndash12 show the dynamic behaviour of a singleWT for different operation conditions Initially (before thedisturbance) the rotor speed and the active power output aremaintained to their optimal values corresponding to MPPTAt the event of frequency drop t 120 s and when the windspeed is below rated vw 65ms (partial-load operationmode) the sequence of events that occur can be summarizedas follows

(i) ampe controller adjusts the electromagnetic torquereference causing a deceleration of the rotor speed(Figure 10(a))

(ii) ampe rotor speed is below its maximum value(gt12 pu) therefore the pitch angle is kept at zero(Figure 11(a))

(iii) ampe reduction of the rotor speed causes the ex-traction of a portion of the kinetic energy stored inthe spinning masses (Figure 12(a)) ampis extra activepower will be used to support the power system inrecovering the frequency to 50Hz

(iv) ampe countering spike of the output power(Figure 12(a)) at roughly t 310 s can be explained

++ +++ ndash

WF

n-synchronous generation units

Primary frequency control (δeq)AGC

LpΔPWF

ΔPsyn

ΔPL

ΔfΔPm 12Heqs + D

Figure 8 Electric network frequency regulation control scheme ofa power system

Table 1 Simulation scenarios

Scenarios S1 S2 S3Generation units 1 2 and 3 C C C

Generation unit 4 Cno PFC NC NC

Wind farm NC Cno IC

Conly IC

C connected NC nonconnected PFC primary frequency control ICinertial control

8 Mathematical Problems in Engineering

as follows let us consider that theWTwas operatingat pointA (Figure 4) with the rotor speed reductionthe WTwill move to a suboptimal power extractionoperation point at the end of the inertial reactionamperefore less power will be delivered until fullrecovery of the WT

For a high wind speed vw 15ms (full-load operationmode) the sequence of events that occur can be summarizedas follows

(i) ampe pitch controller (Figure 11(b)) maintains therotor speed at its maximum value (asymp12 pu)(Figure 10(b))

(ii) ampe controller tries to adjust rotor speed but sincethe pitch controller is activated in this mode itcounteracts the action by reducing the pitch anglethus indirectly exploiting the mechanical power thatwas already curtailed by the positive pitch angle tocreate the power surge (Figure 12(b)) Not that thepower response at this mode requires no recoveryprocess since the pitching system is the one re-sponsible for the contribution

In order to highlight the merits of using a backsteppingcontrol algorithm instead of classical controllers it is par-ticularly important to analyse the system performance undersome kind of disturbances amperefore since the machineparameters are usually exposed to many forms of inaccur-acies especially due to the measuring devices identificationmethodology or several natural phenomena a robustnesstest was carried out to compare the performance of theproposed control strategy versus classical PI controllerswhen parametric variations are registered ampe test consistsin purposefully modifying the rotor resistance Rr of theDFIG by 50 and the stator inductance Ls by 10 from theirnormal values

Figures 12 and 13 show respectively the evolution of theDFIG stator active and reactive powers and Figures 14 and15 respectively show the evolution of d and q componentsof the rotor currents ampe test highlights the high sensitivityof classical PI controllers towards parametric variationwhich is notably observed due to the appearance of a sig-nificant static error in all simulation results whereas the

proposed backstepping control algorithm demonstrates anexquisite disturbance rejection being that all the outputsconverge correctly to their designated references Moreoverthe three-phased stator current sinusoidal waveform isshown in Figure 16

44 SpeedDroopControlEvaluation ampe performance of theproposed speed droop control will be evaluated for thefollowing simulation cases

Case 1 partial-load operation mode (wind speedvw 65ms)Case 1 Full-load operation mode (wind speedvw 15ms)

ampe set of results shown in the following figures dem-onstrates the capability of the proposed control strategy torespond to a sudden active power call at t 150 s Before thearrival of the frequency drop the WT is running at a ro-tational speed higher than the optimum (ΩgtΩmppt) inorder to lower the aerodynamic conversion efficiency rep-resented by Cp and therefore to operate following adeloaded operation characteristic with the power reservebeing created For the research objectives this work pre-sumes that the WT is operating with a reserve factorRf 10 while on the practical level the power margins aregenerally specified by the grid codes

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under partial-load operationmode can be summarized as follows

(i) ampe step in the output power reference (by ΔPrscFigure 3) modifies the electromagnetic torque ref-erence Tlowastem causing the rotor speed reduction asshown in Figure 17(a)

(ii) ampe rotor speed is below its maximum value thepitch control is not required in this case andtherefore the pitch angle is maintained at zero(Figure 18(a))

(iii) ampe rotor speed deceleration rises the power coef-ficient Cp to its maximum value (Figure 4) as shownin Figure 19(a) allowing consequently the WT toactivate its full power reserve

(iv) ampe power reserve activation rises the output powerof the WT by ΔPrsc (Figure 20(a)) thereforeallowing it to participate in the frequency recoveryprocess

(v) ampe power peaks induced as shown in Figure 20(a)demonstrate the benefit from creating the powerreserve by acceleration of the rotor speed the leftside of the power curve Figure 4 since now morekinetic energy is at our disposal and it can be usedwhenever the WT is decelerating

(vi) When the frequency recovers at t 400 s the controlstrategy reaccelerates the WT (Figure 17(a)) low-ering the power coefficient (Figure 19(a)) in order

S1S2S3

300 350 400250 Time (sec)

492

494

496

498

50

Fre

quen

cy (H

z)

Figure 9 Electric network frequency deviation for differentscenarios

Mathematical Problems in Engineering 9

to recreate the power reserve (Figure 20(a)) for thenext use

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under full-load operationmode can be summarized as follows

(i) ampe pitch control is now activated as shown inFigure 18(b) to keep the rotor speed at its maxi-mum value (Figure 17(b)) and to create the powerreserve (Figure 19(b)) since the rotor speed can nolonger be accelerated

(ii) ampe active power call (ΔPrsc Figure 4) reduced thepitch angle to make use of the mechanical powercurtailed by the positive β

(iii) β reduction increases the power coefficient CP asshown in Figure 19(b)consequently rising the

output according to the amount of power specifiedby ΔPrsc (Figure 20(b))

(iv) When the frequency recovers at t 400 s the pitchcontrol strategy rises the pitch angle (Figure 18(b))lowering the power coefficient (Figure 19(b)) inorder to recreate the power reserve (Figure 20(b))for the next use

45 Coordinated Control ampe artificial inertial reaction thespeed droop control and the pitch control could be usedaltogether to further enhance the frequency regulationcapability of WTs In this subsection we compared thesimulation scenarios summarized in Table 2 with S1 beingthe reference case where the wind power penetration isLp 0 For the other simulation scenarios the fourthgeneration synchronous is replaced with a WF with an

084

085

086

087

088

089

09

091

092Ro

tor s

peed

(pu)

110 120 130 140 150 160100Time (s)

(a)

116

12

124

Roto

r spe

ed (p

u)

110 120 130 140 150 160100Time (s)

(b)

Figure 10 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

10

Pitc

h an

gle (

deg)

110 120 130 140 150 160100Time (s)

ndash5

0

5

(a)

175

205Pi

tch

angl

e (deg)

110 120 130 140 150 160100Time (s)

18

185

19

195

20

(b)

Figure 11 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

10 Mathematical Problems in Engineering

equivalent power rating and the wind power penetrationrises to Lp 25 with S2 S3 S3 and S4 being respectivelythe cases without any frequency control the inertial reactiononly speed droop control only and all controllers

Figure 21 portrays the dynamic reaction of the frequencyfor each scenario All simulations were performed for amedium wind speed of vw 9ms and a sudden rise in loadby 005 pu system base is introduced to the system att 200 s

ampe results show that the severest case is obtained withthe simulation scenario S2 the case where the WF is

connected with no frequency regulation ability Comparedto the reference case S1 where the wind power penetrationLp 0 the frequency curve for the second simulationscenario S2 falls to a deeper nadir due to the reduction of thesystemrsquos equivalent inertia caused by increasing the windpower penetration Lp 25 On the other hand in the casewhere the inertial control is implemented S3 the WT de-celerates to release a portion of its kinetic energy transientlyimproving the frequency deviation Consequently the fre-quency nadir is lifted up to the level of the reference case S1However the quasi-steady-state frequency does not get any

Pslowast

Ps (PI)Ps (Bs)

ndash034

ndash032

ndash03

ndash028

ndash026

ndash024

ndash022W

T ou

tput

pow

er (p

u)

110 120 130 140 150 160100Time (seconds)

(a)

Pslowast

Ps (PI)Ps (Bs)

ndash105

ndash1

ndash095

ndash09

ndash085

WT

outp

ut p

ower

(pu)

110 120 130 140 150 160100Time (s)

(b)

Figure 12 Active power evolution for partial-load (a) and full-load (b) operation modes

QslowastQs (PI)Qs (Bs)

ndash5000

0

5000

Reac

tive p

ower

Qs (

Var)

110 120 130 140 150 160100Time (s)

(a)

QslowastQs (PI)Qs (Bs)

times104

ndash1

ndash05

0

05

1

Reac

tive p

ower

(Var

)

110 120 130 140 150 160100Time (s)

(b)

Figure 13 Reactive power evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 11

better with only the inertial control being enabled since itprovides only short-term frequency support With the speeddroop controller being enabled simulation scenario S4 itcan be observed that the WTcontribution is higher since themaximum transient and the quasi-steady-state frequencydeviations are both optimised Finally with both controllersbeing simultaneously enabled simulation scenario S5 thefrequency curve will further be improved for both short- andlong-term durations

As mentioned previously with only the inertial controlbeing activated at the event of frequency excursion the

rotor speed deceleration will impose a suboptimal powerextraction and then less power will be delivered until the fullrecovery of theWTto its optimum speed (Figure 10(c))ampisrecovery phase that generally lasts tens of seconds could beavoided when both controllers are simultaneously activatedgiven that the droop speed controller forces the WT tooperate at a higher rotational speed (ΩgtΩmppt) left side ofthe curve (Figure 4)amperefore when theWTdecelerates theoperating point will climb toward the optimum point and asa result there will be no need for the WT to recover at theend of the inertial response

Irqlowast

Irq (PI)Irq (Bs)

500

600

700

800

900

1000

1100Irq

110 120 130 140 150 160100Time (s)

(a)

Irqlowast

Irq (PI)Irq (Bs)

2600

2700

2800

2900

3000

3100

Irq

110 120 130 140 150 160100Time (s)

(b)

Figure 14 Active current Irq evolution for partial-load (a) and full-load (b) operation modes

Irdlowast

Ird (PI)Ird (Bs)

130

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(a)

Irdlowast

Ird (PI)Ird (Bs)

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(b)

Figure 15 Reactive current Ird evolution for partial-load (a) and full-load (b) operation modes

12 Mathematical Problems in Engineering

110 11005 1101 11015 1102

ndash1000

ndash500

0

500

1000

Is (A

)

110 120 130 140 150 160100Time (s)

(a)

ndash2000

ndash1000

0

1000

2000

Is (A

)

110 120 130 140 150 160100Time (s)

110 11005 1101 11015 1102

(b)

Figure 16 Stator current evolution for partial-load (a) and full-load (b) operation modes

08

09

1

11

12

Roto

r spe

ed (p

u)

200 300 400 500100Time (s)

(a)

11

115

12

125

13Ro

tor s

peed

(pu)

200 300 400 500100Time (s)

(b)

Figure 17 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

ndash5

0

5

10

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(a)

18

19

20

21

22

23

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(b)

Figure 18 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 13

Powerreserve

Cplowast

CpCpopt

200 300 400 500100Time (s)

042

044

046

048

05

Cp

(a)

Powerreserve

Cplowast

CpoptCp

011

012

013

014

015

016

Cp

150 200 250 300 350 400 450 500100 Time (s)

(b)

Figure 19 Power coefficient evolution for partial-load (a) and full-load (b) operation modes

Powerreserve

Power peaks

PrefPoptP

ndash03

ndash028

ndash026

ndash024

ndash022

ndash02

WT

outp

ut p

ower

(pu)

150 200 250 300 350 400 450 500100 Time (s)

(a)

Powerreserve

PrefPoptP

ndash105

ndash1

ndash095

ndash09

ndash085

ndash08

ndash075

ndash07

WT

outp

ut p

ower

(pu)

200 300 400 500100 Time (s)

(b)

Figure 20 WR output power evolution for partial-load (a) and full-load (b) operation modes

Table 2 Simulation scenarios

Scenarios S1 S2 S3 S3 S4Generation units 1 2 and 3 C C C C CGeneration unit 4 C NC NC NC NCWind farm NC C no control C only IC C only PFC C IC and PFCC connected NC nonconnected PFC primary frequency control IC inertial control

14 Mathematical Problems in Engineering

5 Conclusion

ampis paper explores different control approaches thatallow DFIG-based WTs to engage actively in frequencyregulation via coordinating the rotor speed and the pitchangle controllers In a short-term duration the inertialcontrol permits the WT to emulate the synchronousgenerator natural behaviour Accordingly at the event offrequency excursion the controller decelerates the WTin order to extract a portion of its kinetic energy shortlyproviding extra active power support for the powersystem However the inertial reaction alone is heavilydependent on the initial point of operation and a goodtuning of the controller gain is required since for in-stance at low wind speeds the rotor speed should notexceed its minimum value 06 pu for the stable operationof the WT ampe speed droop controller enables the WT toprovide active power assistance over an extended periodimproving the robustness of the system It forces the WTto operate following a deloaded characteristic creating acertain power reserve that can be automatically triggeredat the event of frequency deviations Moreover an in-novative pitch angle control is utilized to protect the WTagainst over speeding and to maintain the frequencyregulation capability under various operationconditions

Finally a study case considering an isolated powersystem that consists of synchronous generators DFIG-basedwind farm and static loads was examined to compare theperformance of each controller ampese simulation resultsshow that the coordination of the controllers improves boththe dynamic and the quasi-steady-state frequency deviationand brings the frequency nadir up to a far superior level thanthat obtained with the wind farm being disconnected (0wind power penetration)

Appendix

Wind turbine parameters

Rated power P 2MW blade radius R 45m gearboxG 90 WT inertia HWT 435 s damping coefficientf 0017Nmiddotmmiddotsrd and air density ρ 12 kgm3

DFIG parameters

Rated power P 2MW rated torque 127 kNm gridrated voltage and frequency Vs 690V and fs 50Hz polepair p 2 generator inertia HG 05 s stator and rotorresistances Rs 26mΩ and Rr 29mΩ stator and rotorinductance Ls 20mH and Lr 20mH and mutual in-ductance M 3253mH

Power coefficient expression

Cp X1X2

λ + 0008βminus00035 middot X2

β3 + 11113888 1113889 minus X3β minus X41113888 1113889

middot expX5

λ + 0008βminus00035 middot X5

β3 + 11113888 1113889 + X6λ

X1 05109

X2 116

X3 04

A4 5

X5 21

X6 00068

(A1)

Data Availability

No data were used to support this study

Disclosure

ampis paper is an expanded version of a paper entitled ldquoIn-ertial Response using Backstepping Control from DFIGbased Wind Power Plant for Short-Term Frequency Regu-lationrdquo presented at 2019 International Conference onControl Decision and Information Technologies held inParis France from 23 to 26 April 2019

Conflicts of Interest

ampe authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] Y Li Z Xu J Zhang and K P Wong ldquoVariable gain controlscheme of DFIG-based wind farm for over-frequency sup-portrdquo Renewable Energy vol 120 pp 379ndash391 2018

[2] N R Ullah T ampiringer and D Karlsson ldquoTemporaryprimary frequency control support by variable speed windturbines- potential and applicationsrdquo IEEE Transactions onPower Systems vol 23 no 2 pp 601ndash612 2008

[3] A Molina-Garcia I Munoz-Benavente A D Hansen andE Gomez-Lazaro ldquoDemand-side contribution to primaryfrequency control with wind farm auxiliary controlrdquo IEEE

S4S5

S1

S3S2

492

494

496

498

50

Freq

uenc

y (H

z)

150 200Time (s)

250 300

Figure 21 Deviation of the frequency for each simulation scenario

Mathematical Problems in Engineering 15

Transactions on Power Systems vol 29 no 5 pp 2391ndash23992014

[4] F Poitiers T Bouaouiche and M Machmoum ldquoAdvancedcontrol of a doubly-fed induction generator for wind energyconversionrdquo Electric Power Systems Research vol 79 no 7pp 1085ndash1096 2009

[5] Z-S Zhang Y-Z Sun J Lin and G-J Li ldquoCoordinatedfrequency regulation by doubly fed induction generator-basedwind power plantsrdquo IET Renewable Power Generation vol 6no 1 pp 38ndash47 2012

[6] R Chakib M Cherkaoui and A Essadki ldquoInertial responseused for a short term frequency control for DFIG windturbine controlled by ADRCrdquo ARPN Journal of Engineeringand Applied Sciences vol 11 no 5 2016

[7] Y-K Wu S-M Chang and P Mandal ldquoGrid-connectedwind power plants a survey on the integration requirementsin modern grid codesrdquo in Proceedings of the 2019 IEEEIAS55th Industrial and Commercial Power Systems TechnicalConference (IampCPS) pp 1ndash9 Canada Canada May 2019

[8] L Ruttledge and D Flynn ldquoEmulated inertial response fromwind turbines gain scheduling and resource coordinationrdquoIEEE Transactions on Power Systems vol 31 no 5pp 3747ndash3755 2015

[9] A I Estanqueiro J M F De Jesus J Ricardo A dos Santosand J A P Lopes ldquoBarriers (and solutions) to Very HighWind Penetration in Power Systemsrdquo in Proceedings of the2007 IEEE Power Engineering Society General Meetingpp 1ndash7 Tampa FL USA June 2007

[10] Y Wang G Delille H Bayem X Guillaud and B FrancoisldquoHigh wind power penetration in isolated power systems-assessment of wind inertial and primary frequency re-sponsesrdquo IEEE Transactions on Power Systems vol 28 no 3pp 2412ndash2420 2013

[11] P-K Keung P Li H Banakar and B T Ooi ldquoKinetic energyof wind-turbine generators for system frequency supportrdquoIEEE Transactions on Power Systems vol 24 no 1 pp 279ndash287 2008

[12] H Ye W Pei and Z Qi ldquoAnalytical modeling of inertial anddroop responses from a wind farm for short-term frequencyregulation in power systemsrdquo IEEE Transactions on PowerSystems vol 31 no 5 pp 3414ndash3423 2015

[13] H Liu and Z Chen ldquoContribution of VSC-HVDC to fre-quency regulation of power systems with offshore windgenerationrdquo IEEE Transactions on Energy Conversion vol 30no 3 pp 918ndash926 2015

[14] R M Kamel A Chaouachi and K Nagasaka ldquoampree controlstrategies to improve the microgrid transient dynamic re-sponse during isolated mode a comparative studyrdquo IEEETransactions on Industrial Electronics vol 60 no 4pp 1314ndash1322 2012

[15] S Wang J Hu X Yuan and L Sun ldquoOn inertial dynamics ofvirtual-synchronous-controlled DFIG-based wind turbinesrdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1691ndash1702 2015

[16] H T Ma and B H Chowdhury ldquoWorking towards frequencyregulation with wind plants combined control approachesrdquoIET Renewable Power Generation vol 4 no 4 pp 308ndash3162010

[17] I A Gowaid A El-Zawawi and M El-Gammal ldquoImprovedinertia and frequency support from grid-connected DFIGwind farmsrdquo in Proceedings of the Power Systems Conferenceand Exposition (PSCE) pp 1ndash9 Phoenix AZ USA March2011

[18] M Nadour A Essadki and T Nasser ldquoComparative analysisbetween PI amp backstepping control strategies of DFIG drivenby wind turbinerdquo International Journal of Renewable EnergyResearch vol 7 no 3 pp 1307ndash1316 2017

[19] M Nadour A Essadki M Fdaili and T Nasser ldquoAdvancedbackstepping control of a wind energy conversion systemusing a doubly-fed induction generatorrdquo in Proceedings of the2017 International Renewable and Sustainable Energy Con-ference (IRSEC) pp 1ndash6 Tangier Morocco December 2017

[20] Y Rebours A Comprehensive Assessment of Markets forFrequency and Voltage Control Ancillary Services PhD thesisUniversity of Manchester Manchester England 2008

[21] P Venne X Guillaud R Teodorescu and J MahseredjianldquoGeneralized gain scheduling for deloaded wind turbineoperationrdquo Wind Engineering vol 34 no 2 pp 219ndash2392010

[22] P Kundur N J Balu andM G Lauby Power System Stabilityand Control Vol 7 McGraw-Hill New York NY USA 1994

[23] J Van de Vyver J D M De Kooning B MeersmanL Vandevelde and T L Vandoorn ldquoDroop control as analternative inertial response strategy for the synthetic inertiaon wind turbinesrdquo IEEE Transactions on Power Systemsvol 31 no 2 pp 1129ndash1138 2016

16 Mathematical Problems in Engineering

Tlowastem could be provided using a simple constant gain PIcontroller A dynamic saturation is used to limit Clowastp ref-erence to Clowastpminus up(λ β 30deg) and Clowastpminus down(λ β 0 1

deg)

ampe inversion of the Cp (λ β) table could be applied toany mathematical approximation It is based on 1- and 2-dimensional linear interpolations and it can be depicted inthe organigram (Figure 7)

4 Results and Discussions

41 General Discussion ampe power system is exposed tomany forms of disturbances A load change results in var-iation of the electrical torque Te output of all generators anda change in the production results in variation of the me-chanical torque Tm of all generators ampe frequency devia-tions reflect the mismatches between the electrical Te andmechanical Tm torques as represented by the followingequation of motion [22]

Tm minus Te 2Hdωdt

2Hdf

dt (23)

whereH is the power systemrsquos corresponding inertia constantand ω and f are the (per unit) rotational speed and the ENFrespectively [23] Equation (20) can be expressed in terms ofthe electrical Pe and mechanical Pm powers such that

Pm1 minus Pe1( 1113857 + ΔPm minus ΔPe( 1113857 ω1 minus Δω( 1113857 Tm1 minus Te1( 11138571113858

+ ΔTm minus ΔTe( 11138571113859

(24)

where we denote the deviations by the prefix (Δ) and thesteady-state values by the subscript (1) with ω1(pu) 1 andby ignoring the higher order terms and adopting the realistic

assumption of Pm1Pe1 and Tm1Te1 in the steady stateEquation (24) can further be adjusted into [22]

ΔPm minus ΔPe( 1113857 ΔTm minus ΔTe( 1113857 (25)

Replacing into equation (23) we can write

ΔPm minus ΔPe 2HdΔωdt

2HdΔfdt

(26)

In this work we have considered the load sensitivity tofrequency deviations Being that practically an abruptchange in frequency will cause a variation of the powerdemand [22] ampe overall network frequency-dependentcharacteristic of loads can be represented by the followingequation

ΔPe ΔPl + DΔf (27)

with ΔPl being the non-frequency-sensitive load variationand DΔω is frequency-sensitive load variation ampe coeffi-cient D represents the self-regulation of loads and it is

1GT

1GT

GT

1GT

ΩTRvw

1Jwts + fΩm

Ωlowastm

ΩT

Temr

GearboxTurbine Transmission

β

vw

λ

_+

2ΩlowastmTlowastaρπR2v3

w

_+

Cp(λ β)

Cp(λ β)(ρπR2v32ΩT)

Ωmndashr

ΩlowastTΩTRvw

PI

λlowast

Tlowasta Tlowast

em

Tg

Clowastp_down

Clowastp_up

Clowastp

Pitch system

βref

β(Cp λ)

TT

Figure 6 Block diagram of the rotor speed control

Define λi (i = 0 1hellipn)ampβj (i = 0 1hellipm)

Start

Compute Cp (λi βi) table(expression in the appendix)

Read λlowast

Cp (βi) = interp2 (β λ Cp β λlowast ldquolinearrdquo)

2D interpolation of the tableCp (βi) for λk = λlowast Read Clowast

p

βref = interp1(Cp (βi) β Clowastp ldquolinearrdquo)

1D interpolation of βreffor Cp = Clowast

p

Write βref

End

Figure 7 Organigram of the Cp table inversion

Mathematical Problems in Engineering 7

expressed as a percent change in load for 1 deviation infrequency [22] Substituting into equation (26) we can write

ΔPm minus ΔPl 2HdΔfdt

+ DΔf (28)

42 Power System Modelling To investigate the perfor-mances of the proposed control strategies a model of a smallpower system based on the scheme illustrated in Figure 8was designed inMatlabSimulink environment It consists offour identical conventional generating units (n 4 mediumpower hydroelectric generators) [2 22] each has a powerrating of Si 100MVA an inertia constant of Hi 50 s on100 MVA base and a droop for the speed governor δi 02feeding a total load of 220MW For the analysis of frequencyregulation capability we are concerned with the collectivebehaviour of all generators in the power system ampereforein this study all conventional synchronous generators arerepresented by a single equivalent machine driven by themechanical outputs of each turbine [22]ampe power rating ofthe equivalent generator is of Seq nSi and the equivalentdroop δeq and the corresponding inertia constant of thepower system Heq can be determined using the followingequations

Heq nHiSi

Seq

δeq δi

n

(29)

Note that the synchronous generators are operatingwithout automatic generation control (AGC) and onlyprimary frequency regulation is considered in this studywhich is practically sufficient for the research objectives

43 Artificial Inertial Response Evaluation In order to ex-amine the implemented artificial inertial control behaviourwe have compared three simulation scenarios as summa-rized in Table 1

ampe first scenario S1 represents the reference case wherethe first second and third synchronous generation unitsprovide both inertial response and primary frequencycontrol (PFC) while the fourth synchronous generation unitis providing only its inherited inertial reaction withoutprimary frequency response (no PFC) ampus according toequation (29) the system equivalent inertia remains con-stant Heq 50 s but the equivalent droop coefficient is nowδeq 0066 ampe remaining scenarios represent the casewhere the fourth synchronous generation unit is replacedwith a wind farm (WF) with an equivalent power ratingwhere S2 and S3 are respectively the wind farm caseswithout and with inertial control implemented In this casethe wind power penetration rises up to LP 25 thereforethe equivalent inertia constant is decreased to Hrsquoeq Heq(1minus Lp) 375 while the equivalent droop remains constantδrsquoeq 0066 A sudden rise in load by 20MW (005 pu systembase) is introduced to the system at t 300 s

Figure 9 portrays the dynamic reaction of the electricnetwork frequency for the three simulation scenarios Withscenario S1 being the reference case it can be observed that thedeepest frequency nadir the worst case is obtained withscenario S2 where the artificial inertial response of WTs isdisabled ampat is mainly due to the reduction of the systemequivalent inertia caused by the increase of the wind powerpenetration Lp to 25 in the system Meanwhile the narrowfrequency nadir the finest case is obtained with scenario S3where the inertial response is enabled and with an appropriategain KIN choice the inertial support from the WTs could beeven greater than that obtained from the synchronous gen-eration unit Since the wider the range of speed variation thebigger the amount of kinetic energy can be extracted

Figures 10ndash12 show the dynamic behaviour of a singleWT for different operation conditions Initially (before thedisturbance) the rotor speed and the active power output aremaintained to their optimal values corresponding to MPPTAt the event of frequency drop t 120 s and when the windspeed is below rated vw 65ms (partial-load operationmode) the sequence of events that occur can be summarizedas follows

(i) ampe controller adjusts the electromagnetic torquereference causing a deceleration of the rotor speed(Figure 10(a))

(ii) ampe rotor speed is below its maximum value(gt12 pu) therefore the pitch angle is kept at zero(Figure 11(a))

(iii) ampe reduction of the rotor speed causes the ex-traction of a portion of the kinetic energy stored inthe spinning masses (Figure 12(a)) ampis extra activepower will be used to support the power system inrecovering the frequency to 50Hz

(iv) ampe countering spike of the output power(Figure 12(a)) at roughly t 310 s can be explained

++ +++ ndash

WF

n-synchronous generation units

Primary frequency control (δeq)AGC

LpΔPWF

ΔPsyn

ΔPL

ΔfΔPm 12Heqs + D

Figure 8 Electric network frequency regulation control scheme ofa power system

Table 1 Simulation scenarios

Scenarios S1 S2 S3Generation units 1 2 and 3 C C C

Generation unit 4 Cno PFC NC NC

Wind farm NC Cno IC

Conly IC

C connected NC nonconnected PFC primary frequency control ICinertial control

8 Mathematical Problems in Engineering

as follows let us consider that theWTwas operatingat pointA (Figure 4) with the rotor speed reductionthe WTwill move to a suboptimal power extractionoperation point at the end of the inertial reactionamperefore less power will be delivered until fullrecovery of the WT

For a high wind speed vw 15ms (full-load operationmode) the sequence of events that occur can be summarizedas follows

(i) ampe pitch controller (Figure 11(b)) maintains therotor speed at its maximum value (asymp12 pu)(Figure 10(b))

(ii) ampe controller tries to adjust rotor speed but sincethe pitch controller is activated in this mode itcounteracts the action by reducing the pitch anglethus indirectly exploiting the mechanical power thatwas already curtailed by the positive pitch angle tocreate the power surge (Figure 12(b)) Not that thepower response at this mode requires no recoveryprocess since the pitching system is the one re-sponsible for the contribution

In order to highlight the merits of using a backsteppingcontrol algorithm instead of classical controllers it is par-ticularly important to analyse the system performance undersome kind of disturbances amperefore since the machineparameters are usually exposed to many forms of inaccur-acies especially due to the measuring devices identificationmethodology or several natural phenomena a robustnesstest was carried out to compare the performance of theproposed control strategy versus classical PI controllerswhen parametric variations are registered ampe test consistsin purposefully modifying the rotor resistance Rr of theDFIG by 50 and the stator inductance Ls by 10 from theirnormal values

Figures 12 and 13 show respectively the evolution of theDFIG stator active and reactive powers and Figures 14 and15 respectively show the evolution of d and q componentsof the rotor currents ampe test highlights the high sensitivityof classical PI controllers towards parametric variationwhich is notably observed due to the appearance of a sig-nificant static error in all simulation results whereas the

proposed backstepping control algorithm demonstrates anexquisite disturbance rejection being that all the outputsconverge correctly to their designated references Moreoverthe three-phased stator current sinusoidal waveform isshown in Figure 16

44 SpeedDroopControlEvaluation ampe performance of theproposed speed droop control will be evaluated for thefollowing simulation cases

Case 1 partial-load operation mode (wind speedvw 65ms)Case 1 Full-load operation mode (wind speedvw 15ms)

ampe set of results shown in the following figures dem-onstrates the capability of the proposed control strategy torespond to a sudden active power call at t 150 s Before thearrival of the frequency drop the WT is running at a ro-tational speed higher than the optimum (ΩgtΩmppt) inorder to lower the aerodynamic conversion efficiency rep-resented by Cp and therefore to operate following adeloaded operation characteristic with the power reservebeing created For the research objectives this work pre-sumes that the WT is operating with a reserve factorRf 10 while on the practical level the power margins aregenerally specified by the grid codes

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under partial-load operationmode can be summarized as follows

(i) ampe step in the output power reference (by ΔPrscFigure 3) modifies the electromagnetic torque ref-erence Tlowastem causing the rotor speed reduction asshown in Figure 17(a)

(ii) ampe rotor speed is below its maximum value thepitch control is not required in this case andtherefore the pitch angle is maintained at zero(Figure 18(a))

(iii) ampe rotor speed deceleration rises the power coef-ficient Cp to its maximum value (Figure 4) as shownin Figure 19(a) allowing consequently the WT toactivate its full power reserve

(iv) ampe power reserve activation rises the output powerof the WT by ΔPrsc (Figure 20(a)) thereforeallowing it to participate in the frequency recoveryprocess

(v) ampe power peaks induced as shown in Figure 20(a)demonstrate the benefit from creating the powerreserve by acceleration of the rotor speed the leftside of the power curve Figure 4 since now morekinetic energy is at our disposal and it can be usedwhenever the WT is decelerating

(vi) When the frequency recovers at t 400 s the controlstrategy reaccelerates the WT (Figure 17(a)) low-ering the power coefficient (Figure 19(a)) in order

S1S2S3

300 350 400250 Time (sec)

492

494

496

498

50

Fre

quen

cy (H

z)

Figure 9 Electric network frequency deviation for differentscenarios

Mathematical Problems in Engineering 9

to recreate the power reserve (Figure 20(a)) for thenext use

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under full-load operationmode can be summarized as follows

(i) ampe pitch control is now activated as shown inFigure 18(b) to keep the rotor speed at its maxi-mum value (Figure 17(b)) and to create the powerreserve (Figure 19(b)) since the rotor speed can nolonger be accelerated

(ii) ampe active power call (ΔPrsc Figure 4) reduced thepitch angle to make use of the mechanical powercurtailed by the positive β

(iii) β reduction increases the power coefficient CP asshown in Figure 19(b)consequently rising the

output according to the amount of power specifiedby ΔPrsc (Figure 20(b))

(iv) When the frequency recovers at t 400 s the pitchcontrol strategy rises the pitch angle (Figure 18(b))lowering the power coefficient (Figure 19(b)) inorder to recreate the power reserve (Figure 20(b))for the next use

45 Coordinated Control ampe artificial inertial reaction thespeed droop control and the pitch control could be usedaltogether to further enhance the frequency regulationcapability of WTs In this subsection we compared thesimulation scenarios summarized in Table 2 with S1 beingthe reference case where the wind power penetration isLp 0 For the other simulation scenarios the fourthgeneration synchronous is replaced with a WF with an

084

085

086

087

088

089

09

091

092Ro

tor s

peed

(pu)

110 120 130 140 150 160100Time (s)

(a)

116

12

124

Roto

r spe

ed (p

u)

110 120 130 140 150 160100Time (s)

(b)

Figure 10 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

10

Pitc

h an

gle (

deg)

110 120 130 140 150 160100Time (s)

ndash5

0

5

(a)

175

205Pi

tch

angl

e (deg)

110 120 130 140 150 160100Time (s)

18

185

19

195

20

(b)

Figure 11 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

10 Mathematical Problems in Engineering

equivalent power rating and the wind power penetrationrises to Lp 25 with S2 S3 S3 and S4 being respectivelythe cases without any frequency control the inertial reactiononly speed droop control only and all controllers

Figure 21 portrays the dynamic reaction of the frequencyfor each scenario All simulations were performed for amedium wind speed of vw 9ms and a sudden rise in loadby 005 pu system base is introduced to the system att 200 s

ampe results show that the severest case is obtained withthe simulation scenario S2 the case where the WF is

connected with no frequency regulation ability Comparedto the reference case S1 where the wind power penetrationLp 0 the frequency curve for the second simulationscenario S2 falls to a deeper nadir due to the reduction of thesystemrsquos equivalent inertia caused by increasing the windpower penetration Lp 25 On the other hand in the casewhere the inertial control is implemented S3 the WT de-celerates to release a portion of its kinetic energy transientlyimproving the frequency deviation Consequently the fre-quency nadir is lifted up to the level of the reference case S1However the quasi-steady-state frequency does not get any

Pslowast

Ps (PI)Ps (Bs)

ndash034

ndash032

ndash03

ndash028

ndash026

ndash024

ndash022W

T ou

tput

pow

er (p

u)

110 120 130 140 150 160100Time (seconds)

(a)

Pslowast

Ps (PI)Ps (Bs)

ndash105

ndash1

ndash095

ndash09

ndash085

WT

outp

ut p

ower

(pu)

110 120 130 140 150 160100Time (s)

(b)

Figure 12 Active power evolution for partial-load (a) and full-load (b) operation modes

QslowastQs (PI)Qs (Bs)

ndash5000

0

5000

Reac

tive p

ower

Qs (

Var)

110 120 130 140 150 160100Time (s)

(a)

QslowastQs (PI)Qs (Bs)

times104

ndash1

ndash05

0

05

1

Reac

tive p

ower

(Var

)

110 120 130 140 150 160100Time (s)

(b)

Figure 13 Reactive power evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 11

better with only the inertial control being enabled since itprovides only short-term frequency support With the speeddroop controller being enabled simulation scenario S4 itcan be observed that the WTcontribution is higher since themaximum transient and the quasi-steady-state frequencydeviations are both optimised Finally with both controllersbeing simultaneously enabled simulation scenario S5 thefrequency curve will further be improved for both short- andlong-term durations

As mentioned previously with only the inertial controlbeing activated at the event of frequency excursion the

rotor speed deceleration will impose a suboptimal powerextraction and then less power will be delivered until the fullrecovery of theWTto its optimum speed (Figure 10(c))ampisrecovery phase that generally lasts tens of seconds could beavoided when both controllers are simultaneously activatedgiven that the droop speed controller forces the WT tooperate at a higher rotational speed (ΩgtΩmppt) left side ofthe curve (Figure 4)amperefore when theWTdecelerates theoperating point will climb toward the optimum point and asa result there will be no need for the WT to recover at theend of the inertial response

Irqlowast

Irq (PI)Irq (Bs)

500

600

700

800

900

1000

1100Irq

110 120 130 140 150 160100Time (s)

(a)

Irqlowast

Irq (PI)Irq (Bs)

2600

2700

2800

2900

3000

3100

Irq

110 120 130 140 150 160100Time (s)

(b)

Figure 14 Active current Irq evolution for partial-load (a) and full-load (b) operation modes

Irdlowast

Ird (PI)Ird (Bs)

130

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(a)

Irdlowast

Ird (PI)Ird (Bs)

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(b)

Figure 15 Reactive current Ird evolution for partial-load (a) and full-load (b) operation modes

12 Mathematical Problems in Engineering

110 11005 1101 11015 1102

ndash1000

ndash500

0

500

1000

Is (A

)

110 120 130 140 150 160100Time (s)

(a)

ndash2000

ndash1000

0

1000

2000

Is (A

)

110 120 130 140 150 160100Time (s)

110 11005 1101 11015 1102

(b)

Figure 16 Stator current evolution for partial-load (a) and full-load (b) operation modes

08

09

1

11

12

Roto

r spe

ed (p

u)

200 300 400 500100Time (s)

(a)

11

115

12

125

13Ro

tor s

peed

(pu)

200 300 400 500100Time (s)

(b)

Figure 17 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

ndash5

0

5

10

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(a)

18

19

20

21

22

23

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(b)

Figure 18 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 13

Powerreserve

Cplowast

CpCpopt

200 300 400 500100Time (s)

042

044

046

048

05

Cp

(a)

Powerreserve

Cplowast

CpoptCp

011

012

013

014

015

016

Cp

150 200 250 300 350 400 450 500100 Time (s)

(b)

Figure 19 Power coefficient evolution for partial-load (a) and full-load (b) operation modes

Powerreserve

Power peaks

PrefPoptP

ndash03

ndash028

ndash026

ndash024

ndash022

ndash02

WT

outp

ut p

ower

(pu)

150 200 250 300 350 400 450 500100 Time (s)

(a)

Powerreserve

PrefPoptP

ndash105

ndash1

ndash095

ndash09

ndash085

ndash08

ndash075

ndash07

WT

outp

ut p

ower

(pu)

200 300 400 500100 Time (s)

(b)

Figure 20 WR output power evolution for partial-load (a) and full-load (b) operation modes

Table 2 Simulation scenarios

Scenarios S1 S2 S3 S3 S4Generation units 1 2 and 3 C C C C CGeneration unit 4 C NC NC NC NCWind farm NC C no control C only IC C only PFC C IC and PFCC connected NC nonconnected PFC primary frequency control IC inertial control

14 Mathematical Problems in Engineering

5 Conclusion

ampis paper explores different control approaches thatallow DFIG-based WTs to engage actively in frequencyregulation via coordinating the rotor speed and the pitchangle controllers In a short-term duration the inertialcontrol permits the WT to emulate the synchronousgenerator natural behaviour Accordingly at the event offrequency excursion the controller decelerates the WTin order to extract a portion of its kinetic energy shortlyproviding extra active power support for the powersystem However the inertial reaction alone is heavilydependent on the initial point of operation and a goodtuning of the controller gain is required since for in-stance at low wind speeds the rotor speed should notexceed its minimum value 06 pu for the stable operationof the WT ampe speed droop controller enables the WT toprovide active power assistance over an extended periodimproving the robustness of the system It forces the WTto operate following a deloaded characteristic creating acertain power reserve that can be automatically triggeredat the event of frequency deviations Moreover an in-novative pitch angle control is utilized to protect the WTagainst over speeding and to maintain the frequencyregulation capability under various operationconditions

Finally a study case considering an isolated powersystem that consists of synchronous generators DFIG-basedwind farm and static loads was examined to compare theperformance of each controller ampese simulation resultsshow that the coordination of the controllers improves boththe dynamic and the quasi-steady-state frequency deviationand brings the frequency nadir up to a far superior level thanthat obtained with the wind farm being disconnected (0wind power penetration)

Appendix

Wind turbine parameters

Rated power P 2MW blade radius R 45m gearboxG 90 WT inertia HWT 435 s damping coefficientf 0017Nmiddotmmiddotsrd and air density ρ 12 kgm3

DFIG parameters

Rated power P 2MW rated torque 127 kNm gridrated voltage and frequency Vs 690V and fs 50Hz polepair p 2 generator inertia HG 05 s stator and rotorresistances Rs 26mΩ and Rr 29mΩ stator and rotorinductance Ls 20mH and Lr 20mH and mutual in-ductance M 3253mH

Power coefficient expression

Cp X1X2

λ + 0008βminus00035 middot X2

β3 + 11113888 1113889 minus X3β minus X41113888 1113889

middot expX5

λ + 0008βminus00035 middot X5

β3 + 11113888 1113889 + X6λ

X1 05109

X2 116

X3 04

A4 5

X5 21

X6 00068

(A1)

Data Availability

No data were used to support this study

Disclosure

ampis paper is an expanded version of a paper entitled ldquoIn-ertial Response using Backstepping Control from DFIGbased Wind Power Plant for Short-Term Frequency Regu-lationrdquo presented at 2019 International Conference onControl Decision and Information Technologies held inParis France from 23 to 26 April 2019

Conflicts of Interest

ampe authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] Y Li Z Xu J Zhang and K P Wong ldquoVariable gain controlscheme of DFIG-based wind farm for over-frequency sup-portrdquo Renewable Energy vol 120 pp 379ndash391 2018

[2] N R Ullah T ampiringer and D Karlsson ldquoTemporaryprimary frequency control support by variable speed windturbines- potential and applicationsrdquo IEEE Transactions onPower Systems vol 23 no 2 pp 601ndash612 2008

[3] A Molina-Garcia I Munoz-Benavente A D Hansen andE Gomez-Lazaro ldquoDemand-side contribution to primaryfrequency control with wind farm auxiliary controlrdquo IEEE

S4S5

S1

S3S2

492

494

496

498

50

Freq

uenc

y (H

z)

150 200Time (s)

250 300

Figure 21 Deviation of the frequency for each simulation scenario

Mathematical Problems in Engineering 15

Transactions on Power Systems vol 29 no 5 pp 2391ndash23992014

[4] F Poitiers T Bouaouiche and M Machmoum ldquoAdvancedcontrol of a doubly-fed induction generator for wind energyconversionrdquo Electric Power Systems Research vol 79 no 7pp 1085ndash1096 2009

[5] Z-S Zhang Y-Z Sun J Lin and G-J Li ldquoCoordinatedfrequency regulation by doubly fed induction generator-basedwind power plantsrdquo IET Renewable Power Generation vol 6no 1 pp 38ndash47 2012

[6] R Chakib M Cherkaoui and A Essadki ldquoInertial responseused for a short term frequency control for DFIG windturbine controlled by ADRCrdquo ARPN Journal of Engineeringand Applied Sciences vol 11 no 5 2016

[7] Y-K Wu S-M Chang and P Mandal ldquoGrid-connectedwind power plants a survey on the integration requirementsin modern grid codesrdquo in Proceedings of the 2019 IEEEIAS55th Industrial and Commercial Power Systems TechnicalConference (IampCPS) pp 1ndash9 Canada Canada May 2019

[8] L Ruttledge and D Flynn ldquoEmulated inertial response fromwind turbines gain scheduling and resource coordinationrdquoIEEE Transactions on Power Systems vol 31 no 5pp 3747ndash3755 2015

[9] A I Estanqueiro J M F De Jesus J Ricardo A dos Santosand J A P Lopes ldquoBarriers (and solutions) to Very HighWind Penetration in Power Systemsrdquo in Proceedings of the2007 IEEE Power Engineering Society General Meetingpp 1ndash7 Tampa FL USA June 2007

[10] Y Wang G Delille H Bayem X Guillaud and B FrancoisldquoHigh wind power penetration in isolated power systems-assessment of wind inertial and primary frequency re-sponsesrdquo IEEE Transactions on Power Systems vol 28 no 3pp 2412ndash2420 2013

[11] P-K Keung P Li H Banakar and B T Ooi ldquoKinetic energyof wind-turbine generators for system frequency supportrdquoIEEE Transactions on Power Systems vol 24 no 1 pp 279ndash287 2008

[12] H Ye W Pei and Z Qi ldquoAnalytical modeling of inertial anddroop responses from a wind farm for short-term frequencyregulation in power systemsrdquo IEEE Transactions on PowerSystems vol 31 no 5 pp 3414ndash3423 2015

[13] H Liu and Z Chen ldquoContribution of VSC-HVDC to fre-quency regulation of power systems with offshore windgenerationrdquo IEEE Transactions on Energy Conversion vol 30no 3 pp 918ndash926 2015

[14] R M Kamel A Chaouachi and K Nagasaka ldquoampree controlstrategies to improve the microgrid transient dynamic re-sponse during isolated mode a comparative studyrdquo IEEETransactions on Industrial Electronics vol 60 no 4pp 1314ndash1322 2012

[15] S Wang J Hu X Yuan and L Sun ldquoOn inertial dynamics ofvirtual-synchronous-controlled DFIG-based wind turbinesrdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1691ndash1702 2015

[16] H T Ma and B H Chowdhury ldquoWorking towards frequencyregulation with wind plants combined control approachesrdquoIET Renewable Power Generation vol 4 no 4 pp 308ndash3162010

[17] I A Gowaid A El-Zawawi and M El-Gammal ldquoImprovedinertia and frequency support from grid-connected DFIGwind farmsrdquo in Proceedings of the Power Systems Conferenceand Exposition (PSCE) pp 1ndash9 Phoenix AZ USA March2011

[18] M Nadour A Essadki and T Nasser ldquoComparative analysisbetween PI amp backstepping control strategies of DFIG drivenby wind turbinerdquo International Journal of Renewable EnergyResearch vol 7 no 3 pp 1307ndash1316 2017

[19] M Nadour A Essadki M Fdaili and T Nasser ldquoAdvancedbackstepping control of a wind energy conversion systemusing a doubly-fed induction generatorrdquo in Proceedings of the2017 International Renewable and Sustainable Energy Con-ference (IRSEC) pp 1ndash6 Tangier Morocco December 2017

[20] Y Rebours A Comprehensive Assessment of Markets forFrequency and Voltage Control Ancillary Services PhD thesisUniversity of Manchester Manchester England 2008

[21] P Venne X Guillaud R Teodorescu and J MahseredjianldquoGeneralized gain scheduling for deloaded wind turbineoperationrdquo Wind Engineering vol 34 no 2 pp 219ndash2392010

[22] P Kundur N J Balu andM G Lauby Power System Stabilityand Control Vol 7 McGraw-Hill New York NY USA 1994

[23] J Van de Vyver J D M De Kooning B MeersmanL Vandevelde and T L Vandoorn ldquoDroop control as analternative inertial response strategy for the synthetic inertiaon wind turbinesrdquo IEEE Transactions on Power Systemsvol 31 no 2 pp 1129ndash1138 2016

16 Mathematical Problems in Engineering

expressed as a percent change in load for 1 deviation infrequency [22] Substituting into equation (26) we can write

ΔPm minus ΔPl 2HdΔfdt

+ DΔf (28)

42 Power System Modelling To investigate the perfor-mances of the proposed control strategies a model of a smallpower system based on the scheme illustrated in Figure 8was designed inMatlabSimulink environment It consists offour identical conventional generating units (n 4 mediumpower hydroelectric generators) [2 22] each has a powerrating of Si 100MVA an inertia constant of Hi 50 s on100 MVA base and a droop for the speed governor δi 02feeding a total load of 220MW For the analysis of frequencyregulation capability we are concerned with the collectivebehaviour of all generators in the power system ampereforein this study all conventional synchronous generators arerepresented by a single equivalent machine driven by themechanical outputs of each turbine [22]ampe power rating ofthe equivalent generator is of Seq nSi and the equivalentdroop δeq and the corresponding inertia constant of thepower system Heq can be determined using the followingequations

Heq nHiSi

Seq

δeq δi

n

(29)

Note that the synchronous generators are operatingwithout automatic generation control (AGC) and onlyprimary frequency regulation is considered in this studywhich is practically sufficient for the research objectives

43 Artificial Inertial Response Evaluation In order to ex-amine the implemented artificial inertial control behaviourwe have compared three simulation scenarios as summa-rized in Table 1

ampe first scenario S1 represents the reference case wherethe first second and third synchronous generation unitsprovide both inertial response and primary frequencycontrol (PFC) while the fourth synchronous generation unitis providing only its inherited inertial reaction withoutprimary frequency response (no PFC) ampus according toequation (29) the system equivalent inertia remains con-stant Heq 50 s but the equivalent droop coefficient is nowδeq 0066 ampe remaining scenarios represent the casewhere the fourth synchronous generation unit is replacedwith a wind farm (WF) with an equivalent power ratingwhere S2 and S3 are respectively the wind farm caseswithout and with inertial control implemented In this casethe wind power penetration rises up to LP 25 thereforethe equivalent inertia constant is decreased to Hrsquoeq Heq(1minus Lp) 375 while the equivalent droop remains constantδrsquoeq 0066 A sudden rise in load by 20MW (005 pu systembase) is introduced to the system at t 300 s

Figure 9 portrays the dynamic reaction of the electricnetwork frequency for the three simulation scenarios Withscenario S1 being the reference case it can be observed that thedeepest frequency nadir the worst case is obtained withscenario S2 where the artificial inertial response of WTs isdisabled ampat is mainly due to the reduction of the systemequivalent inertia caused by the increase of the wind powerpenetration Lp to 25 in the system Meanwhile the narrowfrequency nadir the finest case is obtained with scenario S3where the inertial response is enabled and with an appropriategain KIN choice the inertial support from the WTs could beeven greater than that obtained from the synchronous gen-eration unit Since the wider the range of speed variation thebigger the amount of kinetic energy can be extracted

Figures 10ndash12 show the dynamic behaviour of a singleWT for different operation conditions Initially (before thedisturbance) the rotor speed and the active power output aremaintained to their optimal values corresponding to MPPTAt the event of frequency drop t 120 s and when the windspeed is below rated vw 65ms (partial-load operationmode) the sequence of events that occur can be summarizedas follows

(i) ampe controller adjusts the electromagnetic torquereference causing a deceleration of the rotor speed(Figure 10(a))

(ii) ampe rotor speed is below its maximum value(gt12 pu) therefore the pitch angle is kept at zero(Figure 11(a))

(iii) ampe reduction of the rotor speed causes the ex-traction of a portion of the kinetic energy stored inthe spinning masses (Figure 12(a)) ampis extra activepower will be used to support the power system inrecovering the frequency to 50Hz

(iv) ampe countering spike of the output power(Figure 12(a)) at roughly t 310 s can be explained

++ +++ ndash

WF

n-synchronous generation units

Primary frequency control (δeq)AGC

LpΔPWF

ΔPsyn

ΔPL

ΔfΔPm 12Heqs + D

Figure 8 Electric network frequency regulation control scheme ofa power system

Table 1 Simulation scenarios

Scenarios S1 S2 S3Generation units 1 2 and 3 C C C

Generation unit 4 Cno PFC NC NC

Wind farm NC Cno IC

Conly IC

C connected NC nonconnected PFC primary frequency control ICinertial control

8 Mathematical Problems in Engineering

as follows let us consider that theWTwas operatingat pointA (Figure 4) with the rotor speed reductionthe WTwill move to a suboptimal power extractionoperation point at the end of the inertial reactionamperefore less power will be delivered until fullrecovery of the WT

For a high wind speed vw 15ms (full-load operationmode) the sequence of events that occur can be summarizedas follows

(i) ampe pitch controller (Figure 11(b)) maintains therotor speed at its maximum value (asymp12 pu)(Figure 10(b))

(ii) ampe controller tries to adjust rotor speed but sincethe pitch controller is activated in this mode itcounteracts the action by reducing the pitch anglethus indirectly exploiting the mechanical power thatwas already curtailed by the positive pitch angle tocreate the power surge (Figure 12(b)) Not that thepower response at this mode requires no recoveryprocess since the pitching system is the one re-sponsible for the contribution

In order to highlight the merits of using a backsteppingcontrol algorithm instead of classical controllers it is par-ticularly important to analyse the system performance undersome kind of disturbances amperefore since the machineparameters are usually exposed to many forms of inaccur-acies especially due to the measuring devices identificationmethodology or several natural phenomena a robustnesstest was carried out to compare the performance of theproposed control strategy versus classical PI controllerswhen parametric variations are registered ampe test consistsin purposefully modifying the rotor resistance Rr of theDFIG by 50 and the stator inductance Ls by 10 from theirnormal values

Figures 12 and 13 show respectively the evolution of theDFIG stator active and reactive powers and Figures 14 and15 respectively show the evolution of d and q componentsof the rotor currents ampe test highlights the high sensitivityof classical PI controllers towards parametric variationwhich is notably observed due to the appearance of a sig-nificant static error in all simulation results whereas the

proposed backstepping control algorithm demonstrates anexquisite disturbance rejection being that all the outputsconverge correctly to their designated references Moreoverthe three-phased stator current sinusoidal waveform isshown in Figure 16

44 SpeedDroopControlEvaluation ampe performance of theproposed speed droop control will be evaluated for thefollowing simulation cases

Case 1 partial-load operation mode (wind speedvw 65ms)Case 1 Full-load operation mode (wind speedvw 15ms)

ampe set of results shown in the following figures dem-onstrates the capability of the proposed control strategy torespond to a sudden active power call at t 150 s Before thearrival of the frequency drop the WT is running at a ro-tational speed higher than the optimum (ΩgtΩmppt) inorder to lower the aerodynamic conversion efficiency rep-resented by Cp and therefore to operate following adeloaded operation characteristic with the power reservebeing created For the research objectives this work pre-sumes that the WT is operating with a reserve factorRf 10 while on the practical level the power margins aregenerally specified by the grid codes

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under partial-load operationmode can be summarized as follows

(i) ampe step in the output power reference (by ΔPrscFigure 3) modifies the electromagnetic torque ref-erence Tlowastem causing the rotor speed reduction asshown in Figure 17(a)

(ii) ampe rotor speed is below its maximum value thepitch control is not required in this case andtherefore the pitch angle is maintained at zero(Figure 18(a))

(iii) ampe rotor speed deceleration rises the power coef-ficient Cp to its maximum value (Figure 4) as shownin Figure 19(a) allowing consequently the WT toactivate its full power reserve

(iv) ampe power reserve activation rises the output powerof the WT by ΔPrsc (Figure 20(a)) thereforeallowing it to participate in the frequency recoveryprocess

(v) ampe power peaks induced as shown in Figure 20(a)demonstrate the benefit from creating the powerreserve by acceleration of the rotor speed the leftside of the power curve Figure 4 since now morekinetic energy is at our disposal and it can be usedwhenever the WT is decelerating

(vi) When the frequency recovers at t 400 s the controlstrategy reaccelerates the WT (Figure 17(a)) low-ering the power coefficient (Figure 19(a)) in order

S1S2S3

300 350 400250 Time (sec)

492

494

496

498

50

Fre

quen

cy (H

z)

Figure 9 Electric network frequency deviation for differentscenarios

Mathematical Problems in Engineering 9

to recreate the power reserve (Figure 20(a)) for thenext use

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under full-load operationmode can be summarized as follows

(i) ampe pitch control is now activated as shown inFigure 18(b) to keep the rotor speed at its maxi-mum value (Figure 17(b)) and to create the powerreserve (Figure 19(b)) since the rotor speed can nolonger be accelerated

(ii) ampe active power call (ΔPrsc Figure 4) reduced thepitch angle to make use of the mechanical powercurtailed by the positive β

(iii) β reduction increases the power coefficient CP asshown in Figure 19(b)consequently rising the

output according to the amount of power specifiedby ΔPrsc (Figure 20(b))

(iv) When the frequency recovers at t 400 s the pitchcontrol strategy rises the pitch angle (Figure 18(b))lowering the power coefficient (Figure 19(b)) inorder to recreate the power reserve (Figure 20(b))for the next use

45 Coordinated Control ampe artificial inertial reaction thespeed droop control and the pitch control could be usedaltogether to further enhance the frequency regulationcapability of WTs In this subsection we compared thesimulation scenarios summarized in Table 2 with S1 beingthe reference case where the wind power penetration isLp 0 For the other simulation scenarios the fourthgeneration synchronous is replaced with a WF with an

084

085

086

087

088

089

09

091

092Ro

tor s

peed

(pu)

110 120 130 140 150 160100Time (s)

(a)

116

12

124

Roto

r spe

ed (p

u)

110 120 130 140 150 160100Time (s)

(b)

Figure 10 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

10

Pitc

h an

gle (

deg)

110 120 130 140 150 160100Time (s)

ndash5

0

5

(a)

175

205Pi

tch

angl

e (deg)

110 120 130 140 150 160100Time (s)

18

185

19

195

20

(b)

Figure 11 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

10 Mathematical Problems in Engineering

equivalent power rating and the wind power penetrationrises to Lp 25 with S2 S3 S3 and S4 being respectivelythe cases without any frequency control the inertial reactiononly speed droop control only and all controllers

Figure 21 portrays the dynamic reaction of the frequencyfor each scenario All simulations were performed for amedium wind speed of vw 9ms and a sudden rise in loadby 005 pu system base is introduced to the system att 200 s

ampe results show that the severest case is obtained withthe simulation scenario S2 the case where the WF is

connected with no frequency regulation ability Comparedto the reference case S1 where the wind power penetrationLp 0 the frequency curve for the second simulationscenario S2 falls to a deeper nadir due to the reduction of thesystemrsquos equivalent inertia caused by increasing the windpower penetration Lp 25 On the other hand in the casewhere the inertial control is implemented S3 the WT de-celerates to release a portion of its kinetic energy transientlyimproving the frequency deviation Consequently the fre-quency nadir is lifted up to the level of the reference case S1However the quasi-steady-state frequency does not get any

Pslowast

Ps (PI)Ps (Bs)

ndash034

ndash032

ndash03

ndash028

ndash026

ndash024

ndash022W

T ou

tput

pow

er (p

u)

110 120 130 140 150 160100Time (seconds)

(a)

Pslowast

Ps (PI)Ps (Bs)

ndash105

ndash1

ndash095

ndash09

ndash085

WT

outp

ut p

ower

(pu)

110 120 130 140 150 160100Time (s)

(b)

Figure 12 Active power evolution for partial-load (a) and full-load (b) operation modes

QslowastQs (PI)Qs (Bs)

ndash5000

0

5000

Reac

tive p

ower

Qs (

Var)

110 120 130 140 150 160100Time (s)

(a)

QslowastQs (PI)Qs (Bs)

times104

ndash1

ndash05

0

05

1

Reac

tive p

ower

(Var

)

110 120 130 140 150 160100Time (s)

(b)

Figure 13 Reactive power evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 11

better with only the inertial control being enabled since itprovides only short-term frequency support With the speeddroop controller being enabled simulation scenario S4 itcan be observed that the WTcontribution is higher since themaximum transient and the quasi-steady-state frequencydeviations are both optimised Finally with both controllersbeing simultaneously enabled simulation scenario S5 thefrequency curve will further be improved for both short- andlong-term durations

As mentioned previously with only the inertial controlbeing activated at the event of frequency excursion the

rotor speed deceleration will impose a suboptimal powerextraction and then less power will be delivered until the fullrecovery of theWTto its optimum speed (Figure 10(c))ampisrecovery phase that generally lasts tens of seconds could beavoided when both controllers are simultaneously activatedgiven that the droop speed controller forces the WT tooperate at a higher rotational speed (ΩgtΩmppt) left side ofthe curve (Figure 4)amperefore when theWTdecelerates theoperating point will climb toward the optimum point and asa result there will be no need for the WT to recover at theend of the inertial response

Irqlowast

Irq (PI)Irq (Bs)

500

600

700

800

900

1000

1100Irq

110 120 130 140 150 160100Time (s)

(a)

Irqlowast

Irq (PI)Irq (Bs)

2600

2700

2800

2900

3000

3100

Irq

110 120 130 140 150 160100Time (s)

(b)

Figure 14 Active current Irq evolution for partial-load (a) and full-load (b) operation modes

Irdlowast

Ird (PI)Ird (Bs)

130

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(a)

Irdlowast

Ird (PI)Ird (Bs)

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(b)

Figure 15 Reactive current Ird evolution for partial-load (a) and full-load (b) operation modes

12 Mathematical Problems in Engineering

110 11005 1101 11015 1102

ndash1000

ndash500

0

500

1000

Is (A

)

110 120 130 140 150 160100Time (s)

(a)

ndash2000

ndash1000

0

1000

2000

Is (A

)

110 120 130 140 150 160100Time (s)

110 11005 1101 11015 1102

(b)

Figure 16 Stator current evolution for partial-load (a) and full-load (b) operation modes

08

09

1

11

12

Roto

r spe

ed (p

u)

200 300 400 500100Time (s)

(a)

11

115

12

125

13Ro

tor s

peed

(pu)

200 300 400 500100Time (s)

(b)

Figure 17 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

ndash5

0

5

10

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(a)

18

19

20

21

22

23

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(b)

Figure 18 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 13

Powerreserve

Cplowast

CpCpopt

200 300 400 500100Time (s)

042

044

046

048

05

Cp

(a)

Powerreserve

Cplowast

CpoptCp

011

012

013

014

015

016

Cp

150 200 250 300 350 400 450 500100 Time (s)

(b)

Figure 19 Power coefficient evolution for partial-load (a) and full-load (b) operation modes

Powerreserve

Power peaks

PrefPoptP

ndash03

ndash028

ndash026

ndash024

ndash022

ndash02

WT

outp

ut p

ower

(pu)

150 200 250 300 350 400 450 500100 Time (s)

(a)

Powerreserve

PrefPoptP

ndash105

ndash1

ndash095

ndash09

ndash085

ndash08

ndash075

ndash07

WT

outp

ut p

ower

(pu)

200 300 400 500100 Time (s)

(b)

Figure 20 WR output power evolution for partial-load (a) and full-load (b) operation modes

Table 2 Simulation scenarios

Scenarios S1 S2 S3 S3 S4Generation units 1 2 and 3 C C C C CGeneration unit 4 C NC NC NC NCWind farm NC C no control C only IC C only PFC C IC and PFCC connected NC nonconnected PFC primary frequency control IC inertial control

14 Mathematical Problems in Engineering

5 Conclusion

ampis paper explores different control approaches thatallow DFIG-based WTs to engage actively in frequencyregulation via coordinating the rotor speed and the pitchangle controllers In a short-term duration the inertialcontrol permits the WT to emulate the synchronousgenerator natural behaviour Accordingly at the event offrequency excursion the controller decelerates the WTin order to extract a portion of its kinetic energy shortlyproviding extra active power support for the powersystem However the inertial reaction alone is heavilydependent on the initial point of operation and a goodtuning of the controller gain is required since for in-stance at low wind speeds the rotor speed should notexceed its minimum value 06 pu for the stable operationof the WT ampe speed droop controller enables the WT toprovide active power assistance over an extended periodimproving the robustness of the system It forces the WTto operate following a deloaded characteristic creating acertain power reserve that can be automatically triggeredat the event of frequency deviations Moreover an in-novative pitch angle control is utilized to protect the WTagainst over speeding and to maintain the frequencyregulation capability under various operationconditions

Finally a study case considering an isolated powersystem that consists of synchronous generators DFIG-basedwind farm and static loads was examined to compare theperformance of each controller ampese simulation resultsshow that the coordination of the controllers improves boththe dynamic and the quasi-steady-state frequency deviationand brings the frequency nadir up to a far superior level thanthat obtained with the wind farm being disconnected (0wind power penetration)

Appendix

Wind turbine parameters

Rated power P 2MW blade radius R 45m gearboxG 90 WT inertia HWT 435 s damping coefficientf 0017Nmiddotmmiddotsrd and air density ρ 12 kgm3

DFIG parameters

Rated power P 2MW rated torque 127 kNm gridrated voltage and frequency Vs 690V and fs 50Hz polepair p 2 generator inertia HG 05 s stator and rotorresistances Rs 26mΩ and Rr 29mΩ stator and rotorinductance Ls 20mH and Lr 20mH and mutual in-ductance M 3253mH

Power coefficient expression

Cp X1X2

λ + 0008βminus00035 middot X2

β3 + 11113888 1113889 minus X3β minus X41113888 1113889

middot expX5

λ + 0008βminus00035 middot X5

β3 + 11113888 1113889 + X6λ

X1 05109

X2 116

X3 04

A4 5

X5 21

X6 00068

(A1)

Data Availability

No data were used to support this study

Disclosure

ampis paper is an expanded version of a paper entitled ldquoIn-ertial Response using Backstepping Control from DFIGbased Wind Power Plant for Short-Term Frequency Regu-lationrdquo presented at 2019 International Conference onControl Decision and Information Technologies held inParis France from 23 to 26 April 2019

Conflicts of Interest

ampe authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] Y Li Z Xu J Zhang and K P Wong ldquoVariable gain controlscheme of DFIG-based wind farm for over-frequency sup-portrdquo Renewable Energy vol 120 pp 379ndash391 2018

[2] N R Ullah T ampiringer and D Karlsson ldquoTemporaryprimary frequency control support by variable speed windturbines- potential and applicationsrdquo IEEE Transactions onPower Systems vol 23 no 2 pp 601ndash612 2008

[3] A Molina-Garcia I Munoz-Benavente A D Hansen andE Gomez-Lazaro ldquoDemand-side contribution to primaryfrequency control with wind farm auxiliary controlrdquo IEEE

S4S5

S1

S3S2

492

494

496

498

50

Freq

uenc

y (H

z)

150 200Time (s)

250 300

Figure 21 Deviation of the frequency for each simulation scenario

Mathematical Problems in Engineering 15

Transactions on Power Systems vol 29 no 5 pp 2391ndash23992014

[4] F Poitiers T Bouaouiche and M Machmoum ldquoAdvancedcontrol of a doubly-fed induction generator for wind energyconversionrdquo Electric Power Systems Research vol 79 no 7pp 1085ndash1096 2009

[5] Z-S Zhang Y-Z Sun J Lin and G-J Li ldquoCoordinatedfrequency regulation by doubly fed induction generator-basedwind power plantsrdquo IET Renewable Power Generation vol 6no 1 pp 38ndash47 2012

[6] R Chakib M Cherkaoui and A Essadki ldquoInertial responseused for a short term frequency control for DFIG windturbine controlled by ADRCrdquo ARPN Journal of Engineeringand Applied Sciences vol 11 no 5 2016

[7] Y-K Wu S-M Chang and P Mandal ldquoGrid-connectedwind power plants a survey on the integration requirementsin modern grid codesrdquo in Proceedings of the 2019 IEEEIAS55th Industrial and Commercial Power Systems TechnicalConference (IampCPS) pp 1ndash9 Canada Canada May 2019

[8] L Ruttledge and D Flynn ldquoEmulated inertial response fromwind turbines gain scheduling and resource coordinationrdquoIEEE Transactions on Power Systems vol 31 no 5pp 3747ndash3755 2015

[9] A I Estanqueiro J M F De Jesus J Ricardo A dos Santosand J A P Lopes ldquoBarriers (and solutions) to Very HighWind Penetration in Power Systemsrdquo in Proceedings of the2007 IEEE Power Engineering Society General Meetingpp 1ndash7 Tampa FL USA June 2007

[10] Y Wang G Delille H Bayem X Guillaud and B FrancoisldquoHigh wind power penetration in isolated power systems-assessment of wind inertial and primary frequency re-sponsesrdquo IEEE Transactions on Power Systems vol 28 no 3pp 2412ndash2420 2013

[11] P-K Keung P Li H Banakar and B T Ooi ldquoKinetic energyof wind-turbine generators for system frequency supportrdquoIEEE Transactions on Power Systems vol 24 no 1 pp 279ndash287 2008

[12] H Ye W Pei and Z Qi ldquoAnalytical modeling of inertial anddroop responses from a wind farm for short-term frequencyregulation in power systemsrdquo IEEE Transactions on PowerSystems vol 31 no 5 pp 3414ndash3423 2015

[13] H Liu and Z Chen ldquoContribution of VSC-HVDC to fre-quency regulation of power systems with offshore windgenerationrdquo IEEE Transactions on Energy Conversion vol 30no 3 pp 918ndash926 2015

[14] R M Kamel A Chaouachi and K Nagasaka ldquoampree controlstrategies to improve the microgrid transient dynamic re-sponse during isolated mode a comparative studyrdquo IEEETransactions on Industrial Electronics vol 60 no 4pp 1314ndash1322 2012

[15] S Wang J Hu X Yuan and L Sun ldquoOn inertial dynamics ofvirtual-synchronous-controlled DFIG-based wind turbinesrdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1691ndash1702 2015

[16] H T Ma and B H Chowdhury ldquoWorking towards frequencyregulation with wind plants combined control approachesrdquoIET Renewable Power Generation vol 4 no 4 pp 308ndash3162010

[17] I A Gowaid A El-Zawawi and M El-Gammal ldquoImprovedinertia and frequency support from grid-connected DFIGwind farmsrdquo in Proceedings of the Power Systems Conferenceand Exposition (PSCE) pp 1ndash9 Phoenix AZ USA March2011

[18] M Nadour A Essadki and T Nasser ldquoComparative analysisbetween PI amp backstepping control strategies of DFIG drivenby wind turbinerdquo International Journal of Renewable EnergyResearch vol 7 no 3 pp 1307ndash1316 2017

[19] M Nadour A Essadki M Fdaili and T Nasser ldquoAdvancedbackstepping control of a wind energy conversion systemusing a doubly-fed induction generatorrdquo in Proceedings of the2017 International Renewable and Sustainable Energy Con-ference (IRSEC) pp 1ndash6 Tangier Morocco December 2017

[20] Y Rebours A Comprehensive Assessment of Markets forFrequency and Voltage Control Ancillary Services PhD thesisUniversity of Manchester Manchester England 2008

[21] P Venne X Guillaud R Teodorescu and J MahseredjianldquoGeneralized gain scheduling for deloaded wind turbineoperationrdquo Wind Engineering vol 34 no 2 pp 219ndash2392010

[22] P Kundur N J Balu andM G Lauby Power System Stabilityand Control Vol 7 McGraw-Hill New York NY USA 1994

[23] J Van de Vyver J D M De Kooning B MeersmanL Vandevelde and T L Vandoorn ldquoDroop control as analternative inertial response strategy for the synthetic inertiaon wind turbinesrdquo IEEE Transactions on Power Systemsvol 31 no 2 pp 1129ndash1138 2016

16 Mathematical Problems in Engineering

as follows let us consider that theWTwas operatingat pointA (Figure 4) with the rotor speed reductionthe WTwill move to a suboptimal power extractionoperation point at the end of the inertial reactionamperefore less power will be delivered until fullrecovery of the WT

For a high wind speed vw 15ms (full-load operationmode) the sequence of events that occur can be summarizedas follows

(i) ampe pitch controller (Figure 11(b)) maintains therotor speed at its maximum value (asymp12 pu)(Figure 10(b))

(ii) ampe controller tries to adjust rotor speed but sincethe pitch controller is activated in this mode itcounteracts the action by reducing the pitch anglethus indirectly exploiting the mechanical power thatwas already curtailed by the positive pitch angle tocreate the power surge (Figure 12(b)) Not that thepower response at this mode requires no recoveryprocess since the pitching system is the one re-sponsible for the contribution

In order to highlight the merits of using a backsteppingcontrol algorithm instead of classical controllers it is par-ticularly important to analyse the system performance undersome kind of disturbances amperefore since the machineparameters are usually exposed to many forms of inaccur-acies especially due to the measuring devices identificationmethodology or several natural phenomena a robustnesstest was carried out to compare the performance of theproposed control strategy versus classical PI controllerswhen parametric variations are registered ampe test consistsin purposefully modifying the rotor resistance Rr of theDFIG by 50 and the stator inductance Ls by 10 from theirnormal values

Figures 12 and 13 show respectively the evolution of theDFIG stator active and reactive powers and Figures 14 and15 respectively show the evolution of d and q componentsof the rotor currents ampe test highlights the high sensitivityof classical PI controllers towards parametric variationwhich is notably observed due to the appearance of a sig-nificant static error in all simulation results whereas the

proposed backstepping control algorithm demonstrates anexquisite disturbance rejection being that all the outputsconverge correctly to their designated references Moreoverthe three-phased stator current sinusoidal waveform isshown in Figure 16

44 SpeedDroopControlEvaluation ampe performance of theproposed speed droop control will be evaluated for thefollowing simulation cases

Case 1 partial-load operation mode (wind speedvw 65ms)Case 1 Full-load operation mode (wind speedvw 15ms)

ampe set of results shown in the following figures dem-onstrates the capability of the proposed control strategy torespond to a sudden active power call at t 150 s Before thearrival of the frequency drop the WT is running at a ro-tational speed higher than the optimum (ΩgtΩmppt) inorder to lower the aerodynamic conversion efficiency rep-resented by Cp and therefore to operate following adeloaded operation characteristic with the power reservebeing created For the research objectives this work pre-sumes that the WT is operating with a reserve factorRf 10 while on the practical level the power margins aregenerally specified by the grid codes

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under partial-load operationmode can be summarized as follows

(i) ampe step in the output power reference (by ΔPrscFigure 3) modifies the electromagnetic torque ref-erence Tlowastem causing the rotor speed reduction asshown in Figure 17(a)

(ii) ampe rotor speed is below its maximum value thepitch control is not required in this case andtherefore the pitch angle is maintained at zero(Figure 18(a))

(iii) ampe rotor speed deceleration rises the power coef-ficient Cp to its maximum value (Figure 4) as shownin Figure 19(a) allowing consequently the WT toactivate its full power reserve

(iv) ampe power reserve activation rises the output powerof the WT by ΔPrsc (Figure 20(a)) thereforeallowing it to participate in the frequency recoveryprocess

(v) ampe power peaks induced as shown in Figure 20(a)demonstrate the benefit from creating the powerreserve by acceleration of the rotor speed the leftside of the power curve Figure 4 since now morekinetic energy is at our disposal and it can be usedwhenever the WT is decelerating

(vi) When the frequency recovers at t 400 s the controlstrategy reaccelerates the WT (Figure 17(a)) low-ering the power coefficient (Figure 19(a)) in order

S1S2S3

300 350 400250 Time (sec)

492

494

496

498

50

Fre

quen

cy (H

z)

Figure 9 Electric network frequency deviation for differentscenarios

Mathematical Problems in Engineering 9

to recreate the power reserve (Figure 20(a)) for thenext use

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under full-load operationmode can be summarized as follows

(i) ampe pitch control is now activated as shown inFigure 18(b) to keep the rotor speed at its maxi-mum value (Figure 17(b)) and to create the powerreserve (Figure 19(b)) since the rotor speed can nolonger be accelerated

(ii) ampe active power call (ΔPrsc Figure 4) reduced thepitch angle to make use of the mechanical powercurtailed by the positive β

(iii) β reduction increases the power coefficient CP asshown in Figure 19(b)consequently rising the

output according to the amount of power specifiedby ΔPrsc (Figure 20(b))

(iv) When the frequency recovers at t 400 s the pitchcontrol strategy rises the pitch angle (Figure 18(b))lowering the power coefficient (Figure 19(b)) inorder to recreate the power reserve (Figure 20(b))for the next use

45 Coordinated Control ampe artificial inertial reaction thespeed droop control and the pitch control could be usedaltogether to further enhance the frequency regulationcapability of WTs In this subsection we compared thesimulation scenarios summarized in Table 2 with S1 beingthe reference case where the wind power penetration isLp 0 For the other simulation scenarios the fourthgeneration synchronous is replaced with a WF with an

084

085

086

087

088

089

09

091

092Ro

tor s

peed

(pu)

110 120 130 140 150 160100Time (s)

(a)

116

12

124

Roto

r spe

ed (p

u)

110 120 130 140 150 160100Time (s)

(b)

Figure 10 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

10

Pitc

h an

gle (

deg)

110 120 130 140 150 160100Time (s)

ndash5

0

5

(a)

175

205Pi

tch

angl

e (deg)

110 120 130 140 150 160100Time (s)

18

185

19

195

20

(b)

Figure 11 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

10 Mathematical Problems in Engineering

equivalent power rating and the wind power penetrationrises to Lp 25 with S2 S3 S3 and S4 being respectivelythe cases without any frequency control the inertial reactiononly speed droop control only and all controllers

Figure 21 portrays the dynamic reaction of the frequencyfor each scenario All simulations were performed for amedium wind speed of vw 9ms and a sudden rise in loadby 005 pu system base is introduced to the system att 200 s

ampe results show that the severest case is obtained withthe simulation scenario S2 the case where the WF is

connected with no frequency regulation ability Comparedto the reference case S1 where the wind power penetrationLp 0 the frequency curve for the second simulationscenario S2 falls to a deeper nadir due to the reduction of thesystemrsquos equivalent inertia caused by increasing the windpower penetration Lp 25 On the other hand in the casewhere the inertial control is implemented S3 the WT de-celerates to release a portion of its kinetic energy transientlyimproving the frequency deviation Consequently the fre-quency nadir is lifted up to the level of the reference case S1However the quasi-steady-state frequency does not get any

Pslowast

Ps (PI)Ps (Bs)

ndash034

ndash032

ndash03

ndash028

ndash026

ndash024

ndash022W

T ou

tput

pow

er (p

u)

110 120 130 140 150 160100Time (seconds)

(a)

Pslowast

Ps (PI)Ps (Bs)

ndash105

ndash1

ndash095

ndash09

ndash085

WT

outp

ut p

ower

(pu)

110 120 130 140 150 160100Time (s)

(b)

Figure 12 Active power evolution for partial-load (a) and full-load (b) operation modes

QslowastQs (PI)Qs (Bs)

ndash5000

0

5000

Reac

tive p

ower

Qs (

Var)

110 120 130 140 150 160100Time (s)

(a)

QslowastQs (PI)Qs (Bs)

times104

ndash1

ndash05

0

05

1

Reac

tive p

ower

(Var

)

110 120 130 140 150 160100Time (s)

(b)

Figure 13 Reactive power evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 11

better with only the inertial control being enabled since itprovides only short-term frequency support With the speeddroop controller being enabled simulation scenario S4 itcan be observed that the WTcontribution is higher since themaximum transient and the quasi-steady-state frequencydeviations are both optimised Finally with both controllersbeing simultaneously enabled simulation scenario S5 thefrequency curve will further be improved for both short- andlong-term durations

As mentioned previously with only the inertial controlbeing activated at the event of frequency excursion the

rotor speed deceleration will impose a suboptimal powerextraction and then less power will be delivered until the fullrecovery of theWTto its optimum speed (Figure 10(c))ampisrecovery phase that generally lasts tens of seconds could beavoided when both controllers are simultaneously activatedgiven that the droop speed controller forces the WT tooperate at a higher rotational speed (ΩgtΩmppt) left side ofthe curve (Figure 4)amperefore when theWTdecelerates theoperating point will climb toward the optimum point and asa result there will be no need for the WT to recover at theend of the inertial response

Irqlowast

Irq (PI)Irq (Bs)

500

600

700

800

900

1000

1100Irq

110 120 130 140 150 160100Time (s)

(a)

Irqlowast

Irq (PI)Irq (Bs)

2600

2700

2800

2900

3000

3100

Irq

110 120 130 140 150 160100Time (s)

(b)

Figure 14 Active current Irq evolution for partial-load (a) and full-load (b) operation modes

Irdlowast

Ird (PI)Ird (Bs)

130

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(a)

Irdlowast

Ird (PI)Ird (Bs)

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(b)

Figure 15 Reactive current Ird evolution for partial-load (a) and full-load (b) operation modes

12 Mathematical Problems in Engineering

110 11005 1101 11015 1102

ndash1000

ndash500

0

500

1000

Is (A

)

110 120 130 140 150 160100Time (s)

(a)

ndash2000

ndash1000

0

1000

2000

Is (A

)

110 120 130 140 150 160100Time (s)

110 11005 1101 11015 1102

(b)

Figure 16 Stator current evolution for partial-load (a) and full-load (b) operation modes

08

09

1

11

12

Roto

r spe

ed (p

u)

200 300 400 500100Time (s)

(a)

11

115

12

125

13Ro

tor s

peed

(pu)

200 300 400 500100Time (s)

(b)

Figure 17 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

ndash5

0

5

10

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(a)

18

19

20

21

22

23

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(b)

Figure 18 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 13

Powerreserve

Cplowast

CpCpopt

200 300 400 500100Time (s)

042

044

046

048

05

Cp

(a)

Powerreserve

Cplowast

CpoptCp

011

012

013

014

015

016

Cp

150 200 250 300 350 400 450 500100 Time (s)

(b)

Figure 19 Power coefficient evolution for partial-load (a) and full-load (b) operation modes

Powerreserve

Power peaks

PrefPoptP

ndash03

ndash028

ndash026

ndash024

ndash022

ndash02

WT

outp

ut p

ower

(pu)

150 200 250 300 350 400 450 500100 Time (s)

(a)

Powerreserve

PrefPoptP

ndash105

ndash1

ndash095

ndash09

ndash085

ndash08

ndash075

ndash07

WT

outp

ut p

ower

(pu)

200 300 400 500100 Time (s)

(b)

Figure 20 WR output power evolution for partial-load (a) and full-load (b) operation modes

Table 2 Simulation scenarios

Scenarios S1 S2 S3 S3 S4Generation units 1 2 and 3 C C C C CGeneration unit 4 C NC NC NC NCWind farm NC C no control C only IC C only PFC C IC and PFCC connected NC nonconnected PFC primary frequency control IC inertial control

14 Mathematical Problems in Engineering

5 Conclusion

ampis paper explores different control approaches thatallow DFIG-based WTs to engage actively in frequencyregulation via coordinating the rotor speed and the pitchangle controllers In a short-term duration the inertialcontrol permits the WT to emulate the synchronousgenerator natural behaviour Accordingly at the event offrequency excursion the controller decelerates the WTin order to extract a portion of its kinetic energy shortlyproviding extra active power support for the powersystem However the inertial reaction alone is heavilydependent on the initial point of operation and a goodtuning of the controller gain is required since for in-stance at low wind speeds the rotor speed should notexceed its minimum value 06 pu for the stable operationof the WT ampe speed droop controller enables the WT toprovide active power assistance over an extended periodimproving the robustness of the system It forces the WTto operate following a deloaded characteristic creating acertain power reserve that can be automatically triggeredat the event of frequency deviations Moreover an in-novative pitch angle control is utilized to protect the WTagainst over speeding and to maintain the frequencyregulation capability under various operationconditions

Finally a study case considering an isolated powersystem that consists of synchronous generators DFIG-basedwind farm and static loads was examined to compare theperformance of each controller ampese simulation resultsshow that the coordination of the controllers improves boththe dynamic and the quasi-steady-state frequency deviationand brings the frequency nadir up to a far superior level thanthat obtained with the wind farm being disconnected (0wind power penetration)

Appendix

Wind turbine parameters

Rated power P 2MW blade radius R 45m gearboxG 90 WT inertia HWT 435 s damping coefficientf 0017Nmiddotmmiddotsrd and air density ρ 12 kgm3

DFIG parameters

Rated power P 2MW rated torque 127 kNm gridrated voltage and frequency Vs 690V and fs 50Hz polepair p 2 generator inertia HG 05 s stator and rotorresistances Rs 26mΩ and Rr 29mΩ stator and rotorinductance Ls 20mH and Lr 20mH and mutual in-ductance M 3253mH

Power coefficient expression

Cp X1X2

λ + 0008βminus00035 middot X2

β3 + 11113888 1113889 minus X3β minus X41113888 1113889

middot expX5

λ + 0008βminus00035 middot X5

β3 + 11113888 1113889 + X6λ

X1 05109

X2 116

X3 04

A4 5

X5 21

X6 00068

(A1)

Data Availability

No data were used to support this study

Disclosure

ampis paper is an expanded version of a paper entitled ldquoIn-ertial Response using Backstepping Control from DFIGbased Wind Power Plant for Short-Term Frequency Regu-lationrdquo presented at 2019 International Conference onControl Decision and Information Technologies held inParis France from 23 to 26 April 2019

Conflicts of Interest

ampe authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] Y Li Z Xu J Zhang and K P Wong ldquoVariable gain controlscheme of DFIG-based wind farm for over-frequency sup-portrdquo Renewable Energy vol 120 pp 379ndash391 2018

[2] N R Ullah T ampiringer and D Karlsson ldquoTemporaryprimary frequency control support by variable speed windturbines- potential and applicationsrdquo IEEE Transactions onPower Systems vol 23 no 2 pp 601ndash612 2008

[3] A Molina-Garcia I Munoz-Benavente A D Hansen andE Gomez-Lazaro ldquoDemand-side contribution to primaryfrequency control with wind farm auxiliary controlrdquo IEEE

S4S5

S1

S3S2

492

494

496

498

50

Freq

uenc

y (H

z)

150 200Time (s)

250 300

Figure 21 Deviation of the frequency for each simulation scenario

Mathematical Problems in Engineering 15

Transactions on Power Systems vol 29 no 5 pp 2391ndash23992014

[4] F Poitiers T Bouaouiche and M Machmoum ldquoAdvancedcontrol of a doubly-fed induction generator for wind energyconversionrdquo Electric Power Systems Research vol 79 no 7pp 1085ndash1096 2009

[5] Z-S Zhang Y-Z Sun J Lin and G-J Li ldquoCoordinatedfrequency regulation by doubly fed induction generator-basedwind power plantsrdquo IET Renewable Power Generation vol 6no 1 pp 38ndash47 2012

[6] R Chakib M Cherkaoui and A Essadki ldquoInertial responseused for a short term frequency control for DFIG windturbine controlled by ADRCrdquo ARPN Journal of Engineeringand Applied Sciences vol 11 no 5 2016

[7] Y-K Wu S-M Chang and P Mandal ldquoGrid-connectedwind power plants a survey on the integration requirementsin modern grid codesrdquo in Proceedings of the 2019 IEEEIAS55th Industrial and Commercial Power Systems TechnicalConference (IampCPS) pp 1ndash9 Canada Canada May 2019

[8] L Ruttledge and D Flynn ldquoEmulated inertial response fromwind turbines gain scheduling and resource coordinationrdquoIEEE Transactions on Power Systems vol 31 no 5pp 3747ndash3755 2015

[9] A I Estanqueiro J M F De Jesus J Ricardo A dos Santosand J A P Lopes ldquoBarriers (and solutions) to Very HighWind Penetration in Power Systemsrdquo in Proceedings of the2007 IEEE Power Engineering Society General Meetingpp 1ndash7 Tampa FL USA June 2007

[10] Y Wang G Delille H Bayem X Guillaud and B FrancoisldquoHigh wind power penetration in isolated power systems-assessment of wind inertial and primary frequency re-sponsesrdquo IEEE Transactions on Power Systems vol 28 no 3pp 2412ndash2420 2013

[11] P-K Keung P Li H Banakar and B T Ooi ldquoKinetic energyof wind-turbine generators for system frequency supportrdquoIEEE Transactions on Power Systems vol 24 no 1 pp 279ndash287 2008

[12] H Ye W Pei and Z Qi ldquoAnalytical modeling of inertial anddroop responses from a wind farm for short-term frequencyregulation in power systemsrdquo IEEE Transactions on PowerSystems vol 31 no 5 pp 3414ndash3423 2015

[13] H Liu and Z Chen ldquoContribution of VSC-HVDC to fre-quency regulation of power systems with offshore windgenerationrdquo IEEE Transactions on Energy Conversion vol 30no 3 pp 918ndash926 2015

[14] R M Kamel A Chaouachi and K Nagasaka ldquoampree controlstrategies to improve the microgrid transient dynamic re-sponse during isolated mode a comparative studyrdquo IEEETransactions on Industrial Electronics vol 60 no 4pp 1314ndash1322 2012

[15] S Wang J Hu X Yuan and L Sun ldquoOn inertial dynamics ofvirtual-synchronous-controlled DFIG-based wind turbinesrdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1691ndash1702 2015

[16] H T Ma and B H Chowdhury ldquoWorking towards frequencyregulation with wind plants combined control approachesrdquoIET Renewable Power Generation vol 4 no 4 pp 308ndash3162010

[17] I A Gowaid A El-Zawawi and M El-Gammal ldquoImprovedinertia and frequency support from grid-connected DFIGwind farmsrdquo in Proceedings of the Power Systems Conferenceand Exposition (PSCE) pp 1ndash9 Phoenix AZ USA March2011

[18] M Nadour A Essadki and T Nasser ldquoComparative analysisbetween PI amp backstepping control strategies of DFIG drivenby wind turbinerdquo International Journal of Renewable EnergyResearch vol 7 no 3 pp 1307ndash1316 2017

[19] M Nadour A Essadki M Fdaili and T Nasser ldquoAdvancedbackstepping control of a wind energy conversion systemusing a doubly-fed induction generatorrdquo in Proceedings of the2017 International Renewable and Sustainable Energy Con-ference (IRSEC) pp 1ndash6 Tangier Morocco December 2017

[20] Y Rebours A Comprehensive Assessment of Markets forFrequency and Voltage Control Ancillary Services PhD thesisUniversity of Manchester Manchester England 2008

[21] P Venne X Guillaud R Teodorescu and J MahseredjianldquoGeneralized gain scheduling for deloaded wind turbineoperationrdquo Wind Engineering vol 34 no 2 pp 219ndash2392010

[22] P Kundur N J Balu andM G Lauby Power System Stabilityand Control Vol 7 McGraw-Hill New York NY USA 1994

[23] J Van de Vyver J D M De Kooning B MeersmanL Vandevelde and T L Vandoorn ldquoDroop control as analternative inertial response strategy for the synthetic inertiaon wind turbinesrdquo IEEE Transactions on Power Systemsvol 31 no 2 pp 1129ndash1138 2016

16 Mathematical Problems in Engineering

to recreate the power reserve (Figure 20(a)) for thenext use

At the arrival of frequency excursion (t 150 s) thesequence of events that occur under full-load operationmode can be summarized as follows

(i) ampe pitch control is now activated as shown inFigure 18(b) to keep the rotor speed at its maxi-mum value (Figure 17(b)) and to create the powerreserve (Figure 19(b)) since the rotor speed can nolonger be accelerated

(ii) ampe active power call (ΔPrsc Figure 4) reduced thepitch angle to make use of the mechanical powercurtailed by the positive β

(iii) β reduction increases the power coefficient CP asshown in Figure 19(b)consequently rising the

output according to the amount of power specifiedby ΔPrsc (Figure 20(b))

(iv) When the frequency recovers at t 400 s the pitchcontrol strategy rises the pitch angle (Figure 18(b))lowering the power coefficient (Figure 19(b)) inorder to recreate the power reserve (Figure 20(b))for the next use

45 Coordinated Control ampe artificial inertial reaction thespeed droop control and the pitch control could be usedaltogether to further enhance the frequency regulationcapability of WTs In this subsection we compared thesimulation scenarios summarized in Table 2 with S1 beingthe reference case where the wind power penetration isLp 0 For the other simulation scenarios the fourthgeneration synchronous is replaced with a WF with an

084

085

086

087

088

089

09

091

092Ro

tor s

peed

(pu)

110 120 130 140 150 160100Time (s)

(a)

116

12

124

Roto

r spe

ed (p

u)

110 120 130 140 150 160100Time (s)

(b)

Figure 10 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

10

Pitc

h an

gle (

deg)

110 120 130 140 150 160100Time (s)

ndash5

0

5

(a)

175

205Pi

tch

angl

e (deg)

110 120 130 140 150 160100Time (s)

18

185

19

195

20

(b)

Figure 11 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

10 Mathematical Problems in Engineering

equivalent power rating and the wind power penetrationrises to Lp 25 with S2 S3 S3 and S4 being respectivelythe cases without any frequency control the inertial reactiononly speed droop control only and all controllers

Figure 21 portrays the dynamic reaction of the frequencyfor each scenario All simulations were performed for amedium wind speed of vw 9ms and a sudden rise in loadby 005 pu system base is introduced to the system att 200 s

ampe results show that the severest case is obtained withthe simulation scenario S2 the case where the WF is

connected with no frequency regulation ability Comparedto the reference case S1 where the wind power penetrationLp 0 the frequency curve for the second simulationscenario S2 falls to a deeper nadir due to the reduction of thesystemrsquos equivalent inertia caused by increasing the windpower penetration Lp 25 On the other hand in the casewhere the inertial control is implemented S3 the WT de-celerates to release a portion of its kinetic energy transientlyimproving the frequency deviation Consequently the fre-quency nadir is lifted up to the level of the reference case S1However the quasi-steady-state frequency does not get any

Pslowast

Ps (PI)Ps (Bs)

ndash034

ndash032

ndash03

ndash028

ndash026

ndash024

ndash022W

T ou

tput

pow

er (p

u)

110 120 130 140 150 160100Time (seconds)

(a)

Pslowast

Ps (PI)Ps (Bs)

ndash105

ndash1

ndash095

ndash09

ndash085

WT

outp

ut p

ower

(pu)

110 120 130 140 150 160100Time (s)

(b)

Figure 12 Active power evolution for partial-load (a) and full-load (b) operation modes

QslowastQs (PI)Qs (Bs)

ndash5000

0

5000

Reac

tive p

ower

Qs (

Var)

110 120 130 140 150 160100Time (s)

(a)

QslowastQs (PI)Qs (Bs)

times104

ndash1

ndash05

0

05

1

Reac

tive p

ower

(Var

)

110 120 130 140 150 160100Time (s)

(b)

Figure 13 Reactive power evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 11

better with only the inertial control being enabled since itprovides only short-term frequency support With the speeddroop controller being enabled simulation scenario S4 itcan be observed that the WTcontribution is higher since themaximum transient and the quasi-steady-state frequencydeviations are both optimised Finally with both controllersbeing simultaneously enabled simulation scenario S5 thefrequency curve will further be improved for both short- andlong-term durations

As mentioned previously with only the inertial controlbeing activated at the event of frequency excursion the

rotor speed deceleration will impose a suboptimal powerextraction and then less power will be delivered until the fullrecovery of theWTto its optimum speed (Figure 10(c))ampisrecovery phase that generally lasts tens of seconds could beavoided when both controllers are simultaneously activatedgiven that the droop speed controller forces the WT tooperate at a higher rotational speed (ΩgtΩmppt) left side ofthe curve (Figure 4)amperefore when theWTdecelerates theoperating point will climb toward the optimum point and asa result there will be no need for the WT to recover at theend of the inertial response

Irqlowast

Irq (PI)Irq (Bs)

500

600

700

800

900

1000

1100Irq

110 120 130 140 150 160100Time (s)

(a)

Irqlowast

Irq (PI)Irq (Bs)

2600

2700

2800

2900

3000

3100

Irq

110 120 130 140 150 160100Time (s)

(b)

Figure 14 Active current Irq evolution for partial-load (a) and full-load (b) operation modes

Irdlowast

Ird (PI)Ird (Bs)

130

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(a)

Irdlowast

Ird (PI)Ird (Bs)

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(b)

Figure 15 Reactive current Ird evolution for partial-load (a) and full-load (b) operation modes

12 Mathematical Problems in Engineering

110 11005 1101 11015 1102

ndash1000

ndash500

0

500

1000

Is (A

)

110 120 130 140 150 160100Time (s)

(a)

ndash2000

ndash1000

0

1000

2000

Is (A

)

110 120 130 140 150 160100Time (s)

110 11005 1101 11015 1102

(b)

Figure 16 Stator current evolution for partial-load (a) and full-load (b) operation modes

08

09

1

11

12

Roto

r spe

ed (p

u)

200 300 400 500100Time (s)

(a)

11

115

12

125

13Ro

tor s

peed

(pu)

200 300 400 500100Time (s)

(b)

Figure 17 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

ndash5

0

5

10

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(a)

18

19

20

21

22

23

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(b)

Figure 18 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 13

Powerreserve

Cplowast

CpCpopt

200 300 400 500100Time (s)

042

044

046

048

05

Cp

(a)

Powerreserve

Cplowast

CpoptCp

011

012

013

014

015

016

Cp

150 200 250 300 350 400 450 500100 Time (s)

(b)

Figure 19 Power coefficient evolution for partial-load (a) and full-load (b) operation modes

Powerreserve

Power peaks

PrefPoptP

ndash03

ndash028

ndash026

ndash024

ndash022

ndash02

WT

outp

ut p

ower

(pu)

150 200 250 300 350 400 450 500100 Time (s)

(a)

Powerreserve

PrefPoptP

ndash105

ndash1

ndash095

ndash09

ndash085

ndash08

ndash075

ndash07

WT

outp

ut p

ower

(pu)

200 300 400 500100 Time (s)

(b)

Figure 20 WR output power evolution for partial-load (a) and full-load (b) operation modes

Table 2 Simulation scenarios

Scenarios S1 S2 S3 S3 S4Generation units 1 2 and 3 C C C C CGeneration unit 4 C NC NC NC NCWind farm NC C no control C only IC C only PFC C IC and PFCC connected NC nonconnected PFC primary frequency control IC inertial control

14 Mathematical Problems in Engineering

5 Conclusion

ampis paper explores different control approaches thatallow DFIG-based WTs to engage actively in frequencyregulation via coordinating the rotor speed and the pitchangle controllers In a short-term duration the inertialcontrol permits the WT to emulate the synchronousgenerator natural behaviour Accordingly at the event offrequency excursion the controller decelerates the WTin order to extract a portion of its kinetic energy shortlyproviding extra active power support for the powersystem However the inertial reaction alone is heavilydependent on the initial point of operation and a goodtuning of the controller gain is required since for in-stance at low wind speeds the rotor speed should notexceed its minimum value 06 pu for the stable operationof the WT ampe speed droop controller enables the WT toprovide active power assistance over an extended periodimproving the robustness of the system It forces the WTto operate following a deloaded characteristic creating acertain power reserve that can be automatically triggeredat the event of frequency deviations Moreover an in-novative pitch angle control is utilized to protect the WTagainst over speeding and to maintain the frequencyregulation capability under various operationconditions

Finally a study case considering an isolated powersystem that consists of synchronous generators DFIG-basedwind farm and static loads was examined to compare theperformance of each controller ampese simulation resultsshow that the coordination of the controllers improves boththe dynamic and the quasi-steady-state frequency deviationand brings the frequency nadir up to a far superior level thanthat obtained with the wind farm being disconnected (0wind power penetration)

Appendix

Wind turbine parameters

Rated power P 2MW blade radius R 45m gearboxG 90 WT inertia HWT 435 s damping coefficientf 0017Nmiddotmmiddotsrd and air density ρ 12 kgm3

DFIG parameters

Rated power P 2MW rated torque 127 kNm gridrated voltage and frequency Vs 690V and fs 50Hz polepair p 2 generator inertia HG 05 s stator and rotorresistances Rs 26mΩ and Rr 29mΩ stator and rotorinductance Ls 20mH and Lr 20mH and mutual in-ductance M 3253mH

Power coefficient expression

Cp X1X2

λ + 0008βminus00035 middot X2

β3 + 11113888 1113889 minus X3β minus X41113888 1113889

middot expX5

λ + 0008βminus00035 middot X5

β3 + 11113888 1113889 + X6λ

X1 05109

X2 116

X3 04

A4 5

X5 21

X6 00068

(A1)

Data Availability

No data were used to support this study

Disclosure

ampis paper is an expanded version of a paper entitled ldquoIn-ertial Response using Backstepping Control from DFIGbased Wind Power Plant for Short-Term Frequency Regu-lationrdquo presented at 2019 International Conference onControl Decision and Information Technologies held inParis France from 23 to 26 April 2019

Conflicts of Interest

ampe authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] Y Li Z Xu J Zhang and K P Wong ldquoVariable gain controlscheme of DFIG-based wind farm for over-frequency sup-portrdquo Renewable Energy vol 120 pp 379ndash391 2018

[2] N R Ullah T ampiringer and D Karlsson ldquoTemporaryprimary frequency control support by variable speed windturbines- potential and applicationsrdquo IEEE Transactions onPower Systems vol 23 no 2 pp 601ndash612 2008

[3] A Molina-Garcia I Munoz-Benavente A D Hansen andE Gomez-Lazaro ldquoDemand-side contribution to primaryfrequency control with wind farm auxiliary controlrdquo IEEE

S4S5

S1

S3S2

492

494

496

498

50

Freq

uenc

y (H

z)

150 200Time (s)

250 300

Figure 21 Deviation of the frequency for each simulation scenario

Mathematical Problems in Engineering 15

Transactions on Power Systems vol 29 no 5 pp 2391ndash23992014

[4] F Poitiers T Bouaouiche and M Machmoum ldquoAdvancedcontrol of a doubly-fed induction generator for wind energyconversionrdquo Electric Power Systems Research vol 79 no 7pp 1085ndash1096 2009

[5] Z-S Zhang Y-Z Sun J Lin and G-J Li ldquoCoordinatedfrequency regulation by doubly fed induction generator-basedwind power plantsrdquo IET Renewable Power Generation vol 6no 1 pp 38ndash47 2012

[6] R Chakib M Cherkaoui and A Essadki ldquoInertial responseused for a short term frequency control for DFIG windturbine controlled by ADRCrdquo ARPN Journal of Engineeringand Applied Sciences vol 11 no 5 2016

[7] Y-K Wu S-M Chang and P Mandal ldquoGrid-connectedwind power plants a survey on the integration requirementsin modern grid codesrdquo in Proceedings of the 2019 IEEEIAS55th Industrial and Commercial Power Systems TechnicalConference (IampCPS) pp 1ndash9 Canada Canada May 2019

[8] L Ruttledge and D Flynn ldquoEmulated inertial response fromwind turbines gain scheduling and resource coordinationrdquoIEEE Transactions on Power Systems vol 31 no 5pp 3747ndash3755 2015

[9] A I Estanqueiro J M F De Jesus J Ricardo A dos Santosand J A P Lopes ldquoBarriers (and solutions) to Very HighWind Penetration in Power Systemsrdquo in Proceedings of the2007 IEEE Power Engineering Society General Meetingpp 1ndash7 Tampa FL USA June 2007

[10] Y Wang G Delille H Bayem X Guillaud and B FrancoisldquoHigh wind power penetration in isolated power systems-assessment of wind inertial and primary frequency re-sponsesrdquo IEEE Transactions on Power Systems vol 28 no 3pp 2412ndash2420 2013

[11] P-K Keung P Li H Banakar and B T Ooi ldquoKinetic energyof wind-turbine generators for system frequency supportrdquoIEEE Transactions on Power Systems vol 24 no 1 pp 279ndash287 2008

[12] H Ye W Pei and Z Qi ldquoAnalytical modeling of inertial anddroop responses from a wind farm for short-term frequencyregulation in power systemsrdquo IEEE Transactions on PowerSystems vol 31 no 5 pp 3414ndash3423 2015

[13] H Liu and Z Chen ldquoContribution of VSC-HVDC to fre-quency regulation of power systems with offshore windgenerationrdquo IEEE Transactions on Energy Conversion vol 30no 3 pp 918ndash926 2015

[14] R M Kamel A Chaouachi and K Nagasaka ldquoampree controlstrategies to improve the microgrid transient dynamic re-sponse during isolated mode a comparative studyrdquo IEEETransactions on Industrial Electronics vol 60 no 4pp 1314ndash1322 2012

[15] S Wang J Hu X Yuan and L Sun ldquoOn inertial dynamics ofvirtual-synchronous-controlled DFIG-based wind turbinesrdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1691ndash1702 2015

[16] H T Ma and B H Chowdhury ldquoWorking towards frequencyregulation with wind plants combined control approachesrdquoIET Renewable Power Generation vol 4 no 4 pp 308ndash3162010

[17] I A Gowaid A El-Zawawi and M El-Gammal ldquoImprovedinertia and frequency support from grid-connected DFIGwind farmsrdquo in Proceedings of the Power Systems Conferenceand Exposition (PSCE) pp 1ndash9 Phoenix AZ USA March2011

[18] M Nadour A Essadki and T Nasser ldquoComparative analysisbetween PI amp backstepping control strategies of DFIG drivenby wind turbinerdquo International Journal of Renewable EnergyResearch vol 7 no 3 pp 1307ndash1316 2017

[19] M Nadour A Essadki M Fdaili and T Nasser ldquoAdvancedbackstepping control of a wind energy conversion systemusing a doubly-fed induction generatorrdquo in Proceedings of the2017 International Renewable and Sustainable Energy Con-ference (IRSEC) pp 1ndash6 Tangier Morocco December 2017

[20] Y Rebours A Comprehensive Assessment of Markets forFrequency and Voltage Control Ancillary Services PhD thesisUniversity of Manchester Manchester England 2008

[21] P Venne X Guillaud R Teodorescu and J MahseredjianldquoGeneralized gain scheduling for deloaded wind turbineoperationrdquo Wind Engineering vol 34 no 2 pp 219ndash2392010

[22] P Kundur N J Balu andM G Lauby Power System Stabilityand Control Vol 7 McGraw-Hill New York NY USA 1994

[23] J Van de Vyver J D M De Kooning B MeersmanL Vandevelde and T L Vandoorn ldquoDroop control as analternative inertial response strategy for the synthetic inertiaon wind turbinesrdquo IEEE Transactions on Power Systemsvol 31 no 2 pp 1129ndash1138 2016

16 Mathematical Problems in Engineering

equivalent power rating and the wind power penetrationrises to Lp 25 with S2 S3 S3 and S4 being respectivelythe cases without any frequency control the inertial reactiononly speed droop control only and all controllers

Figure 21 portrays the dynamic reaction of the frequencyfor each scenario All simulations were performed for amedium wind speed of vw 9ms and a sudden rise in loadby 005 pu system base is introduced to the system att 200 s

ampe results show that the severest case is obtained withthe simulation scenario S2 the case where the WF is

connected with no frequency regulation ability Comparedto the reference case S1 where the wind power penetrationLp 0 the frequency curve for the second simulationscenario S2 falls to a deeper nadir due to the reduction of thesystemrsquos equivalent inertia caused by increasing the windpower penetration Lp 25 On the other hand in the casewhere the inertial control is implemented S3 the WT de-celerates to release a portion of its kinetic energy transientlyimproving the frequency deviation Consequently the fre-quency nadir is lifted up to the level of the reference case S1However the quasi-steady-state frequency does not get any

Pslowast

Ps (PI)Ps (Bs)

ndash034

ndash032

ndash03

ndash028

ndash026

ndash024

ndash022W

T ou

tput

pow

er (p

u)

110 120 130 140 150 160100Time (seconds)

(a)

Pslowast

Ps (PI)Ps (Bs)

ndash105

ndash1

ndash095

ndash09

ndash085

WT

outp

ut p

ower

(pu)

110 120 130 140 150 160100Time (s)

(b)

Figure 12 Active power evolution for partial-load (a) and full-load (b) operation modes

QslowastQs (PI)Qs (Bs)

ndash5000

0

5000

Reac

tive p

ower

Qs (

Var)

110 120 130 140 150 160100Time (s)

(a)

QslowastQs (PI)Qs (Bs)

times104

ndash1

ndash05

0

05

1

Reac

tive p

ower

(Var

)

110 120 130 140 150 160100Time (s)

(b)

Figure 13 Reactive power evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 11

better with only the inertial control being enabled since itprovides only short-term frequency support With the speeddroop controller being enabled simulation scenario S4 itcan be observed that the WTcontribution is higher since themaximum transient and the quasi-steady-state frequencydeviations are both optimised Finally with both controllersbeing simultaneously enabled simulation scenario S5 thefrequency curve will further be improved for both short- andlong-term durations

As mentioned previously with only the inertial controlbeing activated at the event of frequency excursion the

rotor speed deceleration will impose a suboptimal powerextraction and then less power will be delivered until the fullrecovery of theWTto its optimum speed (Figure 10(c))ampisrecovery phase that generally lasts tens of seconds could beavoided when both controllers are simultaneously activatedgiven that the droop speed controller forces the WT tooperate at a higher rotational speed (ΩgtΩmppt) left side ofthe curve (Figure 4)amperefore when theWTdecelerates theoperating point will climb toward the optimum point and asa result there will be no need for the WT to recover at theend of the inertial response

Irqlowast

Irq (PI)Irq (Bs)

500

600

700

800

900

1000

1100Irq

110 120 130 140 150 160100Time (s)

(a)

Irqlowast

Irq (PI)Irq (Bs)

2600

2700

2800

2900

3000

3100

Irq

110 120 130 140 150 160100Time (s)

(b)

Figure 14 Active current Irq evolution for partial-load (a) and full-load (b) operation modes

Irdlowast

Ird (PI)Ird (Bs)

130

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(a)

Irdlowast

Ird (PI)Ird (Bs)

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(b)

Figure 15 Reactive current Ird evolution for partial-load (a) and full-load (b) operation modes

12 Mathematical Problems in Engineering

110 11005 1101 11015 1102

ndash1000

ndash500

0

500

1000

Is (A

)

110 120 130 140 150 160100Time (s)

(a)

ndash2000

ndash1000

0

1000

2000

Is (A

)

110 120 130 140 150 160100Time (s)

110 11005 1101 11015 1102

(b)

Figure 16 Stator current evolution for partial-load (a) and full-load (b) operation modes

08

09

1

11

12

Roto

r spe

ed (p

u)

200 300 400 500100Time (s)

(a)

11

115

12

125

13Ro

tor s

peed

(pu)

200 300 400 500100Time (s)

(b)

Figure 17 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

ndash5

0

5

10

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(a)

18

19

20

21

22

23

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(b)

Figure 18 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 13

Powerreserve

Cplowast

CpCpopt

200 300 400 500100Time (s)

042

044

046

048

05

Cp

(a)

Powerreserve

Cplowast

CpoptCp

011

012

013

014

015

016

Cp

150 200 250 300 350 400 450 500100 Time (s)

(b)

Figure 19 Power coefficient evolution for partial-load (a) and full-load (b) operation modes

Powerreserve

Power peaks

PrefPoptP

ndash03

ndash028

ndash026

ndash024

ndash022

ndash02

WT

outp

ut p

ower

(pu)

150 200 250 300 350 400 450 500100 Time (s)

(a)

Powerreserve

PrefPoptP

ndash105

ndash1

ndash095

ndash09

ndash085

ndash08

ndash075

ndash07

WT

outp

ut p

ower

(pu)

200 300 400 500100 Time (s)

(b)

Figure 20 WR output power evolution for partial-load (a) and full-load (b) operation modes

Table 2 Simulation scenarios

Scenarios S1 S2 S3 S3 S4Generation units 1 2 and 3 C C C C CGeneration unit 4 C NC NC NC NCWind farm NC C no control C only IC C only PFC C IC and PFCC connected NC nonconnected PFC primary frequency control IC inertial control

14 Mathematical Problems in Engineering

5 Conclusion

ampis paper explores different control approaches thatallow DFIG-based WTs to engage actively in frequencyregulation via coordinating the rotor speed and the pitchangle controllers In a short-term duration the inertialcontrol permits the WT to emulate the synchronousgenerator natural behaviour Accordingly at the event offrequency excursion the controller decelerates the WTin order to extract a portion of its kinetic energy shortlyproviding extra active power support for the powersystem However the inertial reaction alone is heavilydependent on the initial point of operation and a goodtuning of the controller gain is required since for in-stance at low wind speeds the rotor speed should notexceed its minimum value 06 pu for the stable operationof the WT ampe speed droop controller enables the WT toprovide active power assistance over an extended periodimproving the robustness of the system It forces the WTto operate following a deloaded characteristic creating acertain power reserve that can be automatically triggeredat the event of frequency deviations Moreover an in-novative pitch angle control is utilized to protect the WTagainst over speeding and to maintain the frequencyregulation capability under various operationconditions

Finally a study case considering an isolated powersystem that consists of synchronous generators DFIG-basedwind farm and static loads was examined to compare theperformance of each controller ampese simulation resultsshow that the coordination of the controllers improves boththe dynamic and the quasi-steady-state frequency deviationand brings the frequency nadir up to a far superior level thanthat obtained with the wind farm being disconnected (0wind power penetration)

Appendix

Wind turbine parameters

Rated power P 2MW blade radius R 45m gearboxG 90 WT inertia HWT 435 s damping coefficientf 0017Nmiddotmmiddotsrd and air density ρ 12 kgm3

DFIG parameters

Rated power P 2MW rated torque 127 kNm gridrated voltage and frequency Vs 690V and fs 50Hz polepair p 2 generator inertia HG 05 s stator and rotorresistances Rs 26mΩ and Rr 29mΩ stator and rotorinductance Ls 20mH and Lr 20mH and mutual in-ductance M 3253mH

Power coefficient expression

Cp X1X2

λ + 0008βminus00035 middot X2

β3 + 11113888 1113889 minus X3β minus X41113888 1113889

middot expX5

λ + 0008βminus00035 middot X5

β3 + 11113888 1113889 + X6λ

X1 05109

X2 116

X3 04

A4 5

X5 21

X6 00068

(A1)

Data Availability

No data were used to support this study

Disclosure

ampis paper is an expanded version of a paper entitled ldquoIn-ertial Response using Backstepping Control from DFIGbased Wind Power Plant for Short-Term Frequency Regu-lationrdquo presented at 2019 International Conference onControl Decision and Information Technologies held inParis France from 23 to 26 April 2019

Conflicts of Interest

ampe authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] Y Li Z Xu J Zhang and K P Wong ldquoVariable gain controlscheme of DFIG-based wind farm for over-frequency sup-portrdquo Renewable Energy vol 120 pp 379ndash391 2018

[2] N R Ullah T ampiringer and D Karlsson ldquoTemporaryprimary frequency control support by variable speed windturbines- potential and applicationsrdquo IEEE Transactions onPower Systems vol 23 no 2 pp 601ndash612 2008

[3] A Molina-Garcia I Munoz-Benavente A D Hansen andE Gomez-Lazaro ldquoDemand-side contribution to primaryfrequency control with wind farm auxiliary controlrdquo IEEE

S4S5

S1

S3S2

492

494

496

498

50

Freq

uenc

y (H

z)

150 200Time (s)

250 300

Figure 21 Deviation of the frequency for each simulation scenario

Mathematical Problems in Engineering 15

Transactions on Power Systems vol 29 no 5 pp 2391ndash23992014

[4] F Poitiers T Bouaouiche and M Machmoum ldquoAdvancedcontrol of a doubly-fed induction generator for wind energyconversionrdquo Electric Power Systems Research vol 79 no 7pp 1085ndash1096 2009

[5] Z-S Zhang Y-Z Sun J Lin and G-J Li ldquoCoordinatedfrequency regulation by doubly fed induction generator-basedwind power plantsrdquo IET Renewable Power Generation vol 6no 1 pp 38ndash47 2012

[6] R Chakib M Cherkaoui and A Essadki ldquoInertial responseused for a short term frequency control for DFIG windturbine controlled by ADRCrdquo ARPN Journal of Engineeringand Applied Sciences vol 11 no 5 2016

[7] Y-K Wu S-M Chang and P Mandal ldquoGrid-connectedwind power plants a survey on the integration requirementsin modern grid codesrdquo in Proceedings of the 2019 IEEEIAS55th Industrial and Commercial Power Systems TechnicalConference (IampCPS) pp 1ndash9 Canada Canada May 2019

[8] L Ruttledge and D Flynn ldquoEmulated inertial response fromwind turbines gain scheduling and resource coordinationrdquoIEEE Transactions on Power Systems vol 31 no 5pp 3747ndash3755 2015

[9] A I Estanqueiro J M F De Jesus J Ricardo A dos Santosand J A P Lopes ldquoBarriers (and solutions) to Very HighWind Penetration in Power Systemsrdquo in Proceedings of the2007 IEEE Power Engineering Society General Meetingpp 1ndash7 Tampa FL USA June 2007

[10] Y Wang G Delille H Bayem X Guillaud and B FrancoisldquoHigh wind power penetration in isolated power systems-assessment of wind inertial and primary frequency re-sponsesrdquo IEEE Transactions on Power Systems vol 28 no 3pp 2412ndash2420 2013

[11] P-K Keung P Li H Banakar and B T Ooi ldquoKinetic energyof wind-turbine generators for system frequency supportrdquoIEEE Transactions on Power Systems vol 24 no 1 pp 279ndash287 2008

[12] H Ye W Pei and Z Qi ldquoAnalytical modeling of inertial anddroop responses from a wind farm for short-term frequencyregulation in power systemsrdquo IEEE Transactions on PowerSystems vol 31 no 5 pp 3414ndash3423 2015

[13] H Liu and Z Chen ldquoContribution of VSC-HVDC to fre-quency regulation of power systems with offshore windgenerationrdquo IEEE Transactions on Energy Conversion vol 30no 3 pp 918ndash926 2015

[14] R M Kamel A Chaouachi and K Nagasaka ldquoampree controlstrategies to improve the microgrid transient dynamic re-sponse during isolated mode a comparative studyrdquo IEEETransactions on Industrial Electronics vol 60 no 4pp 1314ndash1322 2012

[15] S Wang J Hu X Yuan and L Sun ldquoOn inertial dynamics ofvirtual-synchronous-controlled DFIG-based wind turbinesrdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1691ndash1702 2015

[16] H T Ma and B H Chowdhury ldquoWorking towards frequencyregulation with wind plants combined control approachesrdquoIET Renewable Power Generation vol 4 no 4 pp 308ndash3162010

[17] I A Gowaid A El-Zawawi and M El-Gammal ldquoImprovedinertia and frequency support from grid-connected DFIGwind farmsrdquo in Proceedings of the Power Systems Conferenceand Exposition (PSCE) pp 1ndash9 Phoenix AZ USA March2011

[18] M Nadour A Essadki and T Nasser ldquoComparative analysisbetween PI amp backstepping control strategies of DFIG drivenby wind turbinerdquo International Journal of Renewable EnergyResearch vol 7 no 3 pp 1307ndash1316 2017

[19] M Nadour A Essadki M Fdaili and T Nasser ldquoAdvancedbackstepping control of a wind energy conversion systemusing a doubly-fed induction generatorrdquo in Proceedings of the2017 International Renewable and Sustainable Energy Con-ference (IRSEC) pp 1ndash6 Tangier Morocco December 2017

[20] Y Rebours A Comprehensive Assessment of Markets forFrequency and Voltage Control Ancillary Services PhD thesisUniversity of Manchester Manchester England 2008

[21] P Venne X Guillaud R Teodorescu and J MahseredjianldquoGeneralized gain scheduling for deloaded wind turbineoperationrdquo Wind Engineering vol 34 no 2 pp 219ndash2392010

[22] P Kundur N J Balu andM G Lauby Power System Stabilityand Control Vol 7 McGraw-Hill New York NY USA 1994

[23] J Van de Vyver J D M De Kooning B MeersmanL Vandevelde and T L Vandoorn ldquoDroop control as analternative inertial response strategy for the synthetic inertiaon wind turbinesrdquo IEEE Transactions on Power Systemsvol 31 no 2 pp 1129ndash1138 2016

16 Mathematical Problems in Engineering

better with only the inertial control being enabled since itprovides only short-term frequency support With the speeddroop controller being enabled simulation scenario S4 itcan be observed that the WTcontribution is higher since themaximum transient and the quasi-steady-state frequencydeviations are both optimised Finally with both controllersbeing simultaneously enabled simulation scenario S5 thefrequency curve will further be improved for both short- andlong-term durations

As mentioned previously with only the inertial controlbeing activated at the event of frequency excursion the

rotor speed deceleration will impose a suboptimal powerextraction and then less power will be delivered until the fullrecovery of theWTto its optimum speed (Figure 10(c))ampisrecovery phase that generally lasts tens of seconds could beavoided when both controllers are simultaneously activatedgiven that the droop speed controller forces the WT tooperate at a higher rotational speed (ΩgtΩmppt) left side ofthe curve (Figure 4)amperefore when theWTdecelerates theoperating point will climb toward the optimum point and asa result there will be no need for the WT to recover at theend of the inertial response

Irqlowast

Irq (PI)Irq (Bs)

500

600

700

800

900

1000

1100Irq

110 120 130 140 150 160100Time (s)

(a)

Irqlowast

Irq (PI)Irq (Bs)

2600

2700

2800

2900

3000

3100

Irq

110 120 130 140 150 160100Time (s)

(b)

Figure 14 Active current Irq evolution for partial-load (a) and full-load (b) operation modes

Irdlowast

Ird (PI)Ird (Bs)

130

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(a)

Irdlowast

Ird (PI)Ird (Bs)

140

150

160

170

180

190

Ird

110 120 130 140 150 160100Time (s)

(b)

Figure 15 Reactive current Ird evolution for partial-load (a) and full-load (b) operation modes

12 Mathematical Problems in Engineering

110 11005 1101 11015 1102

ndash1000

ndash500

0

500

1000

Is (A

)

110 120 130 140 150 160100Time (s)

(a)

ndash2000

ndash1000

0

1000

2000

Is (A

)

110 120 130 140 150 160100Time (s)

110 11005 1101 11015 1102

(b)

Figure 16 Stator current evolution for partial-load (a) and full-load (b) operation modes

08

09

1

11

12

Roto

r spe

ed (p

u)

200 300 400 500100Time (s)

(a)

11

115

12

125

13Ro

tor s

peed

(pu)

200 300 400 500100Time (s)

(b)

Figure 17 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

ndash5

0

5

10

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(a)

18

19

20

21

22

23

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(b)

Figure 18 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 13

Powerreserve

Cplowast

CpCpopt

200 300 400 500100Time (s)

042

044

046

048

05

Cp

(a)

Powerreserve

Cplowast

CpoptCp

011

012

013

014

015

016

Cp

150 200 250 300 350 400 450 500100 Time (s)

(b)

Figure 19 Power coefficient evolution for partial-load (a) and full-load (b) operation modes

Powerreserve

Power peaks

PrefPoptP

ndash03

ndash028

ndash026

ndash024

ndash022

ndash02

WT

outp

ut p

ower

(pu)

150 200 250 300 350 400 450 500100 Time (s)

(a)

Powerreserve

PrefPoptP

ndash105

ndash1

ndash095

ndash09

ndash085

ndash08

ndash075

ndash07

WT

outp

ut p

ower

(pu)

200 300 400 500100 Time (s)

(b)

Figure 20 WR output power evolution for partial-load (a) and full-load (b) operation modes

Table 2 Simulation scenarios

Scenarios S1 S2 S3 S3 S4Generation units 1 2 and 3 C C C C CGeneration unit 4 C NC NC NC NCWind farm NC C no control C only IC C only PFC C IC and PFCC connected NC nonconnected PFC primary frequency control IC inertial control

14 Mathematical Problems in Engineering

5 Conclusion

ampis paper explores different control approaches thatallow DFIG-based WTs to engage actively in frequencyregulation via coordinating the rotor speed and the pitchangle controllers In a short-term duration the inertialcontrol permits the WT to emulate the synchronousgenerator natural behaviour Accordingly at the event offrequency excursion the controller decelerates the WTin order to extract a portion of its kinetic energy shortlyproviding extra active power support for the powersystem However the inertial reaction alone is heavilydependent on the initial point of operation and a goodtuning of the controller gain is required since for in-stance at low wind speeds the rotor speed should notexceed its minimum value 06 pu for the stable operationof the WT ampe speed droop controller enables the WT toprovide active power assistance over an extended periodimproving the robustness of the system It forces the WTto operate following a deloaded characteristic creating acertain power reserve that can be automatically triggeredat the event of frequency deviations Moreover an in-novative pitch angle control is utilized to protect the WTagainst over speeding and to maintain the frequencyregulation capability under various operationconditions

Finally a study case considering an isolated powersystem that consists of synchronous generators DFIG-basedwind farm and static loads was examined to compare theperformance of each controller ampese simulation resultsshow that the coordination of the controllers improves boththe dynamic and the quasi-steady-state frequency deviationand brings the frequency nadir up to a far superior level thanthat obtained with the wind farm being disconnected (0wind power penetration)

Appendix

Wind turbine parameters

Rated power P 2MW blade radius R 45m gearboxG 90 WT inertia HWT 435 s damping coefficientf 0017Nmiddotmmiddotsrd and air density ρ 12 kgm3

DFIG parameters

Rated power P 2MW rated torque 127 kNm gridrated voltage and frequency Vs 690V and fs 50Hz polepair p 2 generator inertia HG 05 s stator and rotorresistances Rs 26mΩ and Rr 29mΩ stator and rotorinductance Ls 20mH and Lr 20mH and mutual in-ductance M 3253mH

Power coefficient expression

Cp X1X2

λ + 0008βminus00035 middot X2

β3 + 11113888 1113889 minus X3β minus X41113888 1113889

middot expX5

λ + 0008βminus00035 middot X5

β3 + 11113888 1113889 + X6λ

X1 05109

X2 116

X3 04

A4 5

X5 21

X6 00068

(A1)

Data Availability

No data were used to support this study

Disclosure

ampis paper is an expanded version of a paper entitled ldquoIn-ertial Response using Backstepping Control from DFIGbased Wind Power Plant for Short-Term Frequency Regu-lationrdquo presented at 2019 International Conference onControl Decision and Information Technologies held inParis France from 23 to 26 April 2019

Conflicts of Interest

ampe authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] Y Li Z Xu J Zhang and K P Wong ldquoVariable gain controlscheme of DFIG-based wind farm for over-frequency sup-portrdquo Renewable Energy vol 120 pp 379ndash391 2018

[2] N R Ullah T ampiringer and D Karlsson ldquoTemporaryprimary frequency control support by variable speed windturbines- potential and applicationsrdquo IEEE Transactions onPower Systems vol 23 no 2 pp 601ndash612 2008

[3] A Molina-Garcia I Munoz-Benavente A D Hansen andE Gomez-Lazaro ldquoDemand-side contribution to primaryfrequency control with wind farm auxiliary controlrdquo IEEE

S4S5

S1

S3S2

492

494

496

498

50

Freq

uenc

y (H

z)

150 200Time (s)

250 300

Figure 21 Deviation of the frequency for each simulation scenario

Mathematical Problems in Engineering 15

Transactions on Power Systems vol 29 no 5 pp 2391ndash23992014

[4] F Poitiers T Bouaouiche and M Machmoum ldquoAdvancedcontrol of a doubly-fed induction generator for wind energyconversionrdquo Electric Power Systems Research vol 79 no 7pp 1085ndash1096 2009

[5] Z-S Zhang Y-Z Sun J Lin and G-J Li ldquoCoordinatedfrequency regulation by doubly fed induction generator-basedwind power plantsrdquo IET Renewable Power Generation vol 6no 1 pp 38ndash47 2012

[6] R Chakib M Cherkaoui and A Essadki ldquoInertial responseused for a short term frequency control for DFIG windturbine controlled by ADRCrdquo ARPN Journal of Engineeringand Applied Sciences vol 11 no 5 2016

[7] Y-K Wu S-M Chang and P Mandal ldquoGrid-connectedwind power plants a survey on the integration requirementsin modern grid codesrdquo in Proceedings of the 2019 IEEEIAS55th Industrial and Commercial Power Systems TechnicalConference (IampCPS) pp 1ndash9 Canada Canada May 2019

[8] L Ruttledge and D Flynn ldquoEmulated inertial response fromwind turbines gain scheduling and resource coordinationrdquoIEEE Transactions on Power Systems vol 31 no 5pp 3747ndash3755 2015

[9] A I Estanqueiro J M F De Jesus J Ricardo A dos Santosand J A P Lopes ldquoBarriers (and solutions) to Very HighWind Penetration in Power Systemsrdquo in Proceedings of the2007 IEEE Power Engineering Society General Meetingpp 1ndash7 Tampa FL USA June 2007

[10] Y Wang G Delille H Bayem X Guillaud and B FrancoisldquoHigh wind power penetration in isolated power systems-assessment of wind inertial and primary frequency re-sponsesrdquo IEEE Transactions on Power Systems vol 28 no 3pp 2412ndash2420 2013

[11] P-K Keung P Li H Banakar and B T Ooi ldquoKinetic energyof wind-turbine generators for system frequency supportrdquoIEEE Transactions on Power Systems vol 24 no 1 pp 279ndash287 2008

[12] H Ye W Pei and Z Qi ldquoAnalytical modeling of inertial anddroop responses from a wind farm for short-term frequencyregulation in power systemsrdquo IEEE Transactions on PowerSystems vol 31 no 5 pp 3414ndash3423 2015

[13] H Liu and Z Chen ldquoContribution of VSC-HVDC to fre-quency regulation of power systems with offshore windgenerationrdquo IEEE Transactions on Energy Conversion vol 30no 3 pp 918ndash926 2015

[14] R M Kamel A Chaouachi and K Nagasaka ldquoampree controlstrategies to improve the microgrid transient dynamic re-sponse during isolated mode a comparative studyrdquo IEEETransactions on Industrial Electronics vol 60 no 4pp 1314ndash1322 2012

[15] S Wang J Hu X Yuan and L Sun ldquoOn inertial dynamics ofvirtual-synchronous-controlled DFIG-based wind turbinesrdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1691ndash1702 2015

[16] H T Ma and B H Chowdhury ldquoWorking towards frequencyregulation with wind plants combined control approachesrdquoIET Renewable Power Generation vol 4 no 4 pp 308ndash3162010

[17] I A Gowaid A El-Zawawi and M El-Gammal ldquoImprovedinertia and frequency support from grid-connected DFIGwind farmsrdquo in Proceedings of the Power Systems Conferenceand Exposition (PSCE) pp 1ndash9 Phoenix AZ USA March2011

[18] M Nadour A Essadki and T Nasser ldquoComparative analysisbetween PI amp backstepping control strategies of DFIG drivenby wind turbinerdquo International Journal of Renewable EnergyResearch vol 7 no 3 pp 1307ndash1316 2017

[19] M Nadour A Essadki M Fdaili and T Nasser ldquoAdvancedbackstepping control of a wind energy conversion systemusing a doubly-fed induction generatorrdquo in Proceedings of the2017 International Renewable and Sustainable Energy Con-ference (IRSEC) pp 1ndash6 Tangier Morocco December 2017

[20] Y Rebours A Comprehensive Assessment of Markets forFrequency and Voltage Control Ancillary Services PhD thesisUniversity of Manchester Manchester England 2008

[21] P Venne X Guillaud R Teodorescu and J MahseredjianldquoGeneralized gain scheduling for deloaded wind turbineoperationrdquo Wind Engineering vol 34 no 2 pp 219ndash2392010

[22] P Kundur N J Balu andM G Lauby Power System Stabilityand Control Vol 7 McGraw-Hill New York NY USA 1994

[23] J Van de Vyver J D M De Kooning B MeersmanL Vandevelde and T L Vandoorn ldquoDroop control as analternative inertial response strategy for the synthetic inertiaon wind turbinesrdquo IEEE Transactions on Power Systemsvol 31 no 2 pp 1129ndash1138 2016

16 Mathematical Problems in Engineering

110 11005 1101 11015 1102

ndash1000

ndash500

0

500

1000

Is (A

)

110 120 130 140 150 160100Time (s)

(a)

ndash2000

ndash1000

0

1000

2000

Is (A

)

110 120 130 140 150 160100Time (s)

110 11005 1101 11015 1102

(b)

Figure 16 Stator current evolution for partial-load (a) and full-load (b) operation modes

08

09

1

11

12

Roto

r spe

ed (p

u)

200 300 400 500100Time (s)

(a)

11

115

12

125

13Ro

tor s

peed

(pu)

200 300 400 500100Time (s)

(b)

Figure 17 Rotor speed evolution for partial-load (a) and full-load (b) operation modes

ndash10

ndash5

0

5

10

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(a)

18

19

20

21

22

23

Pitc

h an

gle (

deg)

200 300 400 500100Time (s)

(b)

Figure 18 Pitch angle evolution for partial-load (a) and full-load (b) operation modes

Mathematical Problems in Engineering 13

Powerreserve

Cplowast

CpCpopt

200 300 400 500100Time (s)

042

044

046

048

05

Cp

(a)

Powerreserve

Cplowast

CpoptCp

011

012

013

014

015

016

Cp

150 200 250 300 350 400 450 500100 Time (s)

(b)

Figure 19 Power coefficient evolution for partial-load (a) and full-load (b) operation modes

Powerreserve

Power peaks

PrefPoptP

ndash03

ndash028

ndash026

ndash024

ndash022

ndash02

WT

outp

ut p

ower

(pu)

150 200 250 300 350 400 450 500100 Time (s)

(a)

Powerreserve

PrefPoptP

ndash105

ndash1

ndash095

ndash09

ndash085

ndash08

ndash075

ndash07

WT

outp

ut p

ower

(pu)

200 300 400 500100 Time (s)

(b)

Figure 20 WR output power evolution for partial-load (a) and full-load (b) operation modes

Table 2 Simulation scenarios

Scenarios S1 S2 S3 S3 S4Generation units 1 2 and 3 C C C C CGeneration unit 4 C NC NC NC NCWind farm NC C no control C only IC C only PFC C IC and PFCC connected NC nonconnected PFC primary frequency control IC inertial control

14 Mathematical Problems in Engineering

5 Conclusion

ampis paper explores different control approaches thatallow DFIG-based WTs to engage actively in frequencyregulation via coordinating the rotor speed and the pitchangle controllers In a short-term duration the inertialcontrol permits the WT to emulate the synchronousgenerator natural behaviour Accordingly at the event offrequency excursion the controller decelerates the WTin order to extract a portion of its kinetic energy shortlyproviding extra active power support for the powersystem However the inertial reaction alone is heavilydependent on the initial point of operation and a goodtuning of the controller gain is required since for in-stance at low wind speeds the rotor speed should notexceed its minimum value 06 pu for the stable operationof the WT ampe speed droop controller enables the WT toprovide active power assistance over an extended periodimproving the robustness of the system It forces the WTto operate following a deloaded characteristic creating acertain power reserve that can be automatically triggeredat the event of frequency deviations Moreover an in-novative pitch angle control is utilized to protect the WTagainst over speeding and to maintain the frequencyregulation capability under various operationconditions

Finally a study case considering an isolated powersystem that consists of synchronous generators DFIG-basedwind farm and static loads was examined to compare theperformance of each controller ampese simulation resultsshow that the coordination of the controllers improves boththe dynamic and the quasi-steady-state frequency deviationand brings the frequency nadir up to a far superior level thanthat obtained with the wind farm being disconnected (0wind power penetration)

Appendix

Wind turbine parameters

Rated power P 2MW blade radius R 45m gearboxG 90 WT inertia HWT 435 s damping coefficientf 0017Nmiddotmmiddotsrd and air density ρ 12 kgm3

DFIG parameters

Rated power P 2MW rated torque 127 kNm gridrated voltage and frequency Vs 690V and fs 50Hz polepair p 2 generator inertia HG 05 s stator and rotorresistances Rs 26mΩ and Rr 29mΩ stator and rotorinductance Ls 20mH and Lr 20mH and mutual in-ductance M 3253mH

Power coefficient expression

Cp X1X2

λ + 0008βminus00035 middot X2

β3 + 11113888 1113889 minus X3β minus X41113888 1113889

middot expX5

λ + 0008βminus00035 middot X5

β3 + 11113888 1113889 + X6λ

X1 05109

X2 116

X3 04

A4 5

X5 21

X6 00068

(A1)

Data Availability

No data were used to support this study

Disclosure

ampis paper is an expanded version of a paper entitled ldquoIn-ertial Response using Backstepping Control from DFIGbased Wind Power Plant for Short-Term Frequency Regu-lationrdquo presented at 2019 International Conference onControl Decision and Information Technologies held inParis France from 23 to 26 April 2019

Conflicts of Interest

ampe authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] Y Li Z Xu J Zhang and K P Wong ldquoVariable gain controlscheme of DFIG-based wind farm for over-frequency sup-portrdquo Renewable Energy vol 120 pp 379ndash391 2018

[2] N R Ullah T ampiringer and D Karlsson ldquoTemporaryprimary frequency control support by variable speed windturbines- potential and applicationsrdquo IEEE Transactions onPower Systems vol 23 no 2 pp 601ndash612 2008

[3] A Molina-Garcia I Munoz-Benavente A D Hansen andE Gomez-Lazaro ldquoDemand-side contribution to primaryfrequency control with wind farm auxiliary controlrdquo IEEE

S4S5

S1

S3S2

492

494

496

498

50

Freq

uenc

y (H

z)

150 200Time (s)

250 300

Figure 21 Deviation of the frequency for each simulation scenario

Mathematical Problems in Engineering 15

Transactions on Power Systems vol 29 no 5 pp 2391ndash23992014

[4] F Poitiers T Bouaouiche and M Machmoum ldquoAdvancedcontrol of a doubly-fed induction generator for wind energyconversionrdquo Electric Power Systems Research vol 79 no 7pp 1085ndash1096 2009

[5] Z-S Zhang Y-Z Sun J Lin and G-J Li ldquoCoordinatedfrequency regulation by doubly fed induction generator-basedwind power plantsrdquo IET Renewable Power Generation vol 6no 1 pp 38ndash47 2012

[6] R Chakib M Cherkaoui and A Essadki ldquoInertial responseused for a short term frequency control for DFIG windturbine controlled by ADRCrdquo ARPN Journal of Engineeringand Applied Sciences vol 11 no 5 2016

[7] Y-K Wu S-M Chang and P Mandal ldquoGrid-connectedwind power plants a survey on the integration requirementsin modern grid codesrdquo in Proceedings of the 2019 IEEEIAS55th Industrial and Commercial Power Systems TechnicalConference (IampCPS) pp 1ndash9 Canada Canada May 2019

[8] L Ruttledge and D Flynn ldquoEmulated inertial response fromwind turbines gain scheduling and resource coordinationrdquoIEEE Transactions on Power Systems vol 31 no 5pp 3747ndash3755 2015

[9] A I Estanqueiro J M F De Jesus J Ricardo A dos Santosand J A P Lopes ldquoBarriers (and solutions) to Very HighWind Penetration in Power Systemsrdquo in Proceedings of the2007 IEEE Power Engineering Society General Meetingpp 1ndash7 Tampa FL USA June 2007

[10] Y Wang G Delille H Bayem X Guillaud and B FrancoisldquoHigh wind power penetration in isolated power systems-assessment of wind inertial and primary frequency re-sponsesrdquo IEEE Transactions on Power Systems vol 28 no 3pp 2412ndash2420 2013

[11] P-K Keung P Li H Banakar and B T Ooi ldquoKinetic energyof wind-turbine generators for system frequency supportrdquoIEEE Transactions on Power Systems vol 24 no 1 pp 279ndash287 2008

[12] H Ye W Pei and Z Qi ldquoAnalytical modeling of inertial anddroop responses from a wind farm for short-term frequencyregulation in power systemsrdquo IEEE Transactions on PowerSystems vol 31 no 5 pp 3414ndash3423 2015

[13] H Liu and Z Chen ldquoContribution of VSC-HVDC to fre-quency regulation of power systems with offshore windgenerationrdquo IEEE Transactions on Energy Conversion vol 30no 3 pp 918ndash926 2015

[14] R M Kamel A Chaouachi and K Nagasaka ldquoampree controlstrategies to improve the microgrid transient dynamic re-sponse during isolated mode a comparative studyrdquo IEEETransactions on Industrial Electronics vol 60 no 4pp 1314ndash1322 2012

[15] S Wang J Hu X Yuan and L Sun ldquoOn inertial dynamics ofvirtual-synchronous-controlled DFIG-based wind turbinesrdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1691ndash1702 2015

[16] H T Ma and B H Chowdhury ldquoWorking towards frequencyregulation with wind plants combined control approachesrdquoIET Renewable Power Generation vol 4 no 4 pp 308ndash3162010

[17] I A Gowaid A El-Zawawi and M El-Gammal ldquoImprovedinertia and frequency support from grid-connected DFIGwind farmsrdquo in Proceedings of the Power Systems Conferenceand Exposition (PSCE) pp 1ndash9 Phoenix AZ USA March2011

[18] M Nadour A Essadki and T Nasser ldquoComparative analysisbetween PI amp backstepping control strategies of DFIG drivenby wind turbinerdquo International Journal of Renewable EnergyResearch vol 7 no 3 pp 1307ndash1316 2017

[19] M Nadour A Essadki M Fdaili and T Nasser ldquoAdvancedbackstepping control of a wind energy conversion systemusing a doubly-fed induction generatorrdquo in Proceedings of the2017 International Renewable and Sustainable Energy Con-ference (IRSEC) pp 1ndash6 Tangier Morocco December 2017

[20] Y Rebours A Comprehensive Assessment of Markets forFrequency and Voltage Control Ancillary Services PhD thesisUniversity of Manchester Manchester England 2008

[21] P Venne X Guillaud R Teodorescu and J MahseredjianldquoGeneralized gain scheduling for deloaded wind turbineoperationrdquo Wind Engineering vol 34 no 2 pp 219ndash2392010

[22] P Kundur N J Balu andM G Lauby Power System Stabilityand Control Vol 7 McGraw-Hill New York NY USA 1994

[23] J Van de Vyver J D M De Kooning B MeersmanL Vandevelde and T L Vandoorn ldquoDroop control as analternative inertial response strategy for the synthetic inertiaon wind turbinesrdquo IEEE Transactions on Power Systemsvol 31 no 2 pp 1129ndash1138 2016

16 Mathematical Problems in Engineering

Powerreserve

Cplowast

CpCpopt

200 300 400 500100Time (s)

042

044

046

048

05

Cp

(a)

Powerreserve

Cplowast

CpoptCp

011

012

013

014

015

016

Cp

150 200 250 300 350 400 450 500100 Time (s)

(b)

Figure 19 Power coefficient evolution for partial-load (a) and full-load (b) operation modes

Powerreserve

Power peaks

PrefPoptP

ndash03

ndash028

ndash026

ndash024

ndash022

ndash02

WT

outp

ut p

ower

(pu)

150 200 250 300 350 400 450 500100 Time (s)

(a)

Powerreserve

PrefPoptP

ndash105

ndash1

ndash095

ndash09

ndash085

ndash08

ndash075

ndash07

WT

outp

ut p

ower

(pu)

200 300 400 500100 Time (s)

(b)

Figure 20 WR output power evolution for partial-load (a) and full-load (b) operation modes

Table 2 Simulation scenarios

Scenarios S1 S2 S3 S3 S4Generation units 1 2 and 3 C C C C CGeneration unit 4 C NC NC NC NCWind farm NC C no control C only IC C only PFC C IC and PFCC connected NC nonconnected PFC primary frequency control IC inertial control

14 Mathematical Problems in Engineering

5 Conclusion

ampis paper explores different control approaches thatallow DFIG-based WTs to engage actively in frequencyregulation via coordinating the rotor speed and the pitchangle controllers In a short-term duration the inertialcontrol permits the WT to emulate the synchronousgenerator natural behaviour Accordingly at the event offrequency excursion the controller decelerates the WTin order to extract a portion of its kinetic energy shortlyproviding extra active power support for the powersystem However the inertial reaction alone is heavilydependent on the initial point of operation and a goodtuning of the controller gain is required since for in-stance at low wind speeds the rotor speed should notexceed its minimum value 06 pu for the stable operationof the WT ampe speed droop controller enables the WT toprovide active power assistance over an extended periodimproving the robustness of the system It forces the WTto operate following a deloaded characteristic creating acertain power reserve that can be automatically triggeredat the event of frequency deviations Moreover an in-novative pitch angle control is utilized to protect the WTagainst over speeding and to maintain the frequencyregulation capability under various operationconditions

Finally a study case considering an isolated powersystem that consists of synchronous generators DFIG-basedwind farm and static loads was examined to compare theperformance of each controller ampese simulation resultsshow that the coordination of the controllers improves boththe dynamic and the quasi-steady-state frequency deviationand brings the frequency nadir up to a far superior level thanthat obtained with the wind farm being disconnected (0wind power penetration)

Appendix

Wind turbine parameters

Rated power P 2MW blade radius R 45m gearboxG 90 WT inertia HWT 435 s damping coefficientf 0017Nmiddotmmiddotsrd and air density ρ 12 kgm3

DFIG parameters

Rated power P 2MW rated torque 127 kNm gridrated voltage and frequency Vs 690V and fs 50Hz polepair p 2 generator inertia HG 05 s stator and rotorresistances Rs 26mΩ and Rr 29mΩ stator and rotorinductance Ls 20mH and Lr 20mH and mutual in-ductance M 3253mH

Power coefficient expression

Cp X1X2

λ + 0008βminus00035 middot X2

β3 + 11113888 1113889 minus X3β minus X41113888 1113889

middot expX5

λ + 0008βminus00035 middot X5

β3 + 11113888 1113889 + X6λ

X1 05109

X2 116

X3 04

A4 5

X5 21

X6 00068

(A1)

Data Availability

No data were used to support this study

Disclosure

ampis paper is an expanded version of a paper entitled ldquoIn-ertial Response using Backstepping Control from DFIGbased Wind Power Plant for Short-Term Frequency Regu-lationrdquo presented at 2019 International Conference onControl Decision and Information Technologies held inParis France from 23 to 26 April 2019

Conflicts of Interest

ampe authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] Y Li Z Xu J Zhang and K P Wong ldquoVariable gain controlscheme of DFIG-based wind farm for over-frequency sup-portrdquo Renewable Energy vol 120 pp 379ndash391 2018

[2] N R Ullah T ampiringer and D Karlsson ldquoTemporaryprimary frequency control support by variable speed windturbines- potential and applicationsrdquo IEEE Transactions onPower Systems vol 23 no 2 pp 601ndash612 2008

[3] A Molina-Garcia I Munoz-Benavente A D Hansen andE Gomez-Lazaro ldquoDemand-side contribution to primaryfrequency control with wind farm auxiliary controlrdquo IEEE

S4S5

S1

S3S2

492

494

496

498

50

Freq

uenc

y (H

z)

150 200Time (s)

250 300

Figure 21 Deviation of the frequency for each simulation scenario

Mathematical Problems in Engineering 15

Transactions on Power Systems vol 29 no 5 pp 2391ndash23992014

[4] F Poitiers T Bouaouiche and M Machmoum ldquoAdvancedcontrol of a doubly-fed induction generator for wind energyconversionrdquo Electric Power Systems Research vol 79 no 7pp 1085ndash1096 2009

[5] Z-S Zhang Y-Z Sun J Lin and G-J Li ldquoCoordinatedfrequency regulation by doubly fed induction generator-basedwind power plantsrdquo IET Renewable Power Generation vol 6no 1 pp 38ndash47 2012

[6] R Chakib M Cherkaoui and A Essadki ldquoInertial responseused for a short term frequency control for DFIG windturbine controlled by ADRCrdquo ARPN Journal of Engineeringand Applied Sciences vol 11 no 5 2016

[7] Y-K Wu S-M Chang and P Mandal ldquoGrid-connectedwind power plants a survey on the integration requirementsin modern grid codesrdquo in Proceedings of the 2019 IEEEIAS55th Industrial and Commercial Power Systems TechnicalConference (IampCPS) pp 1ndash9 Canada Canada May 2019

[8] L Ruttledge and D Flynn ldquoEmulated inertial response fromwind turbines gain scheduling and resource coordinationrdquoIEEE Transactions on Power Systems vol 31 no 5pp 3747ndash3755 2015

[9] A I Estanqueiro J M F De Jesus J Ricardo A dos Santosand J A P Lopes ldquoBarriers (and solutions) to Very HighWind Penetration in Power Systemsrdquo in Proceedings of the2007 IEEE Power Engineering Society General Meetingpp 1ndash7 Tampa FL USA June 2007

[10] Y Wang G Delille H Bayem X Guillaud and B FrancoisldquoHigh wind power penetration in isolated power systems-assessment of wind inertial and primary frequency re-sponsesrdquo IEEE Transactions on Power Systems vol 28 no 3pp 2412ndash2420 2013

[11] P-K Keung P Li H Banakar and B T Ooi ldquoKinetic energyof wind-turbine generators for system frequency supportrdquoIEEE Transactions on Power Systems vol 24 no 1 pp 279ndash287 2008

[12] H Ye W Pei and Z Qi ldquoAnalytical modeling of inertial anddroop responses from a wind farm for short-term frequencyregulation in power systemsrdquo IEEE Transactions on PowerSystems vol 31 no 5 pp 3414ndash3423 2015

[13] H Liu and Z Chen ldquoContribution of VSC-HVDC to fre-quency regulation of power systems with offshore windgenerationrdquo IEEE Transactions on Energy Conversion vol 30no 3 pp 918ndash926 2015

[14] R M Kamel A Chaouachi and K Nagasaka ldquoampree controlstrategies to improve the microgrid transient dynamic re-sponse during isolated mode a comparative studyrdquo IEEETransactions on Industrial Electronics vol 60 no 4pp 1314ndash1322 2012

[15] S Wang J Hu X Yuan and L Sun ldquoOn inertial dynamics ofvirtual-synchronous-controlled DFIG-based wind turbinesrdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1691ndash1702 2015

[16] H T Ma and B H Chowdhury ldquoWorking towards frequencyregulation with wind plants combined control approachesrdquoIET Renewable Power Generation vol 4 no 4 pp 308ndash3162010

[17] I A Gowaid A El-Zawawi and M El-Gammal ldquoImprovedinertia and frequency support from grid-connected DFIGwind farmsrdquo in Proceedings of the Power Systems Conferenceand Exposition (PSCE) pp 1ndash9 Phoenix AZ USA March2011

[18] M Nadour A Essadki and T Nasser ldquoComparative analysisbetween PI amp backstepping control strategies of DFIG drivenby wind turbinerdquo International Journal of Renewable EnergyResearch vol 7 no 3 pp 1307ndash1316 2017

[19] M Nadour A Essadki M Fdaili and T Nasser ldquoAdvancedbackstepping control of a wind energy conversion systemusing a doubly-fed induction generatorrdquo in Proceedings of the2017 International Renewable and Sustainable Energy Con-ference (IRSEC) pp 1ndash6 Tangier Morocco December 2017

[20] Y Rebours A Comprehensive Assessment of Markets forFrequency and Voltage Control Ancillary Services PhD thesisUniversity of Manchester Manchester England 2008

[21] P Venne X Guillaud R Teodorescu and J MahseredjianldquoGeneralized gain scheduling for deloaded wind turbineoperationrdquo Wind Engineering vol 34 no 2 pp 219ndash2392010

[22] P Kundur N J Balu andM G Lauby Power System Stabilityand Control Vol 7 McGraw-Hill New York NY USA 1994

[23] J Van de Vyver J D M De Kooning B MeersmanL Vandevelde and T L Vandoorn ldquoDroop control as analternative inertial response strategy for the synthetic inertiaon wind turbinesrdquo IEEE Transactions on Power Systemsvol 31 no 2 pp 1129ndash1138 2016

16 Mathematical Problems in Engineering

5 Conclusion

ampis paper explores different control approaches thatallow DFIG-based WTs to engage actively in frequencyregulation via coordinating the rotor speed and the pitchangle controllers In a short-term duration the inertialcontrol permits the WT to emulate the synchronousgenerator natural behaviour Accordingly at the event offrequency excursion the controller decelerates the WTin order to extract a portion of its kinetic energy shortlyproviding extra active power support for the powersystem However the inertial reaction alone is heavilydependent on the initial point of operation and a goodtuning of the controller gain is required since for in-stance at low wind speeds the rotor speed should notexceed its minimum value 06 pu for the stable operationof the WT ampe speed droop controller enables the WT toprovide active power assistance over an extended periodimproving the robustness of the system It forces the WTto operate following a deloaded characteristic creating acertain power reserve that can be automatically triggeredat the event of frequency deviations Moreover an in-novative pitch angle control is utilized to protect the WTagainst over speeding and to maintain the frequencyregulation capability under various operationconditions

Finally a study case considering an isolated powersystem that consists of synchronous generators DFIG-basedwind farm and static loads was examined to compare theperformance of each controller ampese simulation resultsshow that the coordination of the controllers improves boththe dynamic and the quasi-steady-state frequency deviationand brings the frequency nadir up to a far superior level thanthat obtained with the wind farm being disconnected (0wind power penetration)

Appendix

Wind turbine parameters

Rated power P 2MW blade radius R 45m gearboxG 90 WT inertia HWT 435 s damping coefficientf 0017Nmiddotmmiddotsrd and air density ρ 12 kgm3

DFIG parameters

Rated power P 2MW rated torque 127 kNm gridrated voltage and frequency Vs 690V and fs 50Hz polepair p 2 generator inertia HG 05 s stator and rotorresistances Rs 26mΩ and Rr 29mΩ stator and rotorinductance Ls 20mH and Lr 20mH and mutual in-ductance M 3253mH

Power coefficient expression

Cp X1X2

λ + 0008βminus00035 middot X2

β3 + 11113888 1113889 minus X3β minus X41113888 1113889

middot expX5

λ + 0008βminus00035 middot X5

β3 + 11113888 1113889 + X6λ

X1 05109

X2 116

X3 04

A4 5

X5 21

X6 00068

(A1)

Data Availability

No data were used to support this study

Disclosure

ampis paper is an expanded version of a paper entitled ldquoIn-ertial Response using Backstepping Control from DFIGbased Wind Power Plant for Short-Term Frequency Regu-lationrdquo presented at 2019 International Conference onControl Decision and Information Technologies held inParis France from 23 to 26 April 2019

Conflicts of Interest

ampe authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] Y Li Z Xu J Zhang and K P Wong ldquoVariable gain controlscheme of DFIG-based wind farm for over-frequency sup-portrdquo Renewable Energy vol 120 pp 379ndash391 2018

[2] N R Ullah T ampiringer and D Karlsson ldquoTemporaryprimary frequency control support by variable speed windturbines- potential and applicationsrdquo IEEE Transactions onPower Systems vol 23 no 2 pp 601ndash612 2008

[3] A Molina-Garcia I Munoz-Benavente A D Hansen andE Gomez-Lazaro ldquoDemand-side contribution to primaryfrequency control with wind farm auxiliary controlrdquo IEEE

S4S5

S1

S3S2

492

494

496

498

50

Freq

uenc

y (H

z)

150 200Time (s)

250 300

Figure 21 Deviation of the frequency for each simulation scenario

Mathematical Problems in Engineering 15

Transactions on Power Systems vol 29 no 5 pp 2391ndash23992014

[4] F Poitiers T Bouaouiche and M Machmoum ldquoAdvancedcontrol of a doubly-fed induction generator for wind energyconversionrdquo Electric Power Systems Research vol 79 no 7pp 1085ndash1096 2009

[5] Z-S Zhang Y-Z Sun J Lin and G-J Li ldquoCoordinatedfrequency regulation by doubly fed induction generator-basedwind power plantsrdquo IET Renewable Power Generation vol 6no 1 pp 38ndash47 2012

[6] R Chakib M Cherkaoui and A Essadki ldquoInertial responseused for a short term frequency control for DFIG windturbine controlled by ADRCrdquo ARPN Journal of Engineeringand Applied Sciences vol 11 no 5 2016

[7] Y-K Wu S-M Chang and P Mandal ldquoGrid-connectedwind power plants a survey on the integration requirementsin modern grid codesrdquo in Proceedings of the 2019 IEEEIAS55th Industrial and Commercial Power Systems TechnicalConference (IampCPS) pp 1ndash9 Canada Canada May 2019

[8] L Ruttledge and D Flynn ldquoEmulated inertial response fromwind turbines gain scheduling and resource coordinationrdquoIEEE Transactions on Power Systems vol 31 no 5pp 3747ndash3755 2015

[9] A I Estanqueiro J M F De Jesus J Ricardo A dos Santosand J A P Lopes ldquoBarriers (and solutions) to Very HighWind Penetration in Power Systemsrdquo in Proceedings of the2007 IEEE Power Engineering Society General Meetingpp 1ndash7 Tampa FL USA June 2007

[10] Y Wang G Delille H Bayem X Guillaud and B FrancoisldquoHigh wind power penetration in isolated power systems-assessment of wind inertial and primary frequency re-sponsesrdquo IEEE Transactions on Power Systems vol 28 no 3pp 2412ndash2420 2013

[11] P-K Keung P Li H Banakar and B T Ooi ldquoKinetic energyof wind-turbine generators for system frequency supportrdquoIEEE Transactions on Power Systems vol 24 no 1 pp 279ndash287 2008

[12] H Ye W Pei and Z Qi ldquoAnalytical modeling of inertial anddroop responses from a wind farm for short-term frequencyregulation in power systemsrdquo IEEE Transactions on PowerSystems vol 31 no 5 pp 3414ndash3423 2015

[13] H Liu and Z Chen ldquoContribution of VSC-HVDC to fre-quency regulation of power systems with offshore windgenerationrdquo IEEE Transactions on Energy Conversion vol 30no 3 pp 918ndash926 2015

[14] R M Kamel A Chaouachi and K Nagasaka ldquoampree controlstrategies to improve the microgrid transient dynamic re-sponse during isolated mode a comparative studyrdquo IEEETransactions on Industrial Electronics vol 60 no 4pp 1314ndash1322 2012

[15] S Wang J Hu X Yuan and L Sun ldquoOn inertial dynamics ofvirtual-synchronous-controlled DFIG-based wind turbinesrdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1691ndash1702 2015

[16] H T Ma and B H Chowdhury ldquoWorking towards frequencyregulation with wind plants combined control approachesrdquoIET Renewable Power Generation vol 4 no 4 pp 308ndash3162010

[17] I A Gowaid A El-Zawawi and M El-Gammal ldquoImprovedinertia and frequency support from grid-connected DFIGwind farmsrdquo in Proceedings of the Power Systems Conferenceand Exposition (PSCE) pp 1ndash9 Phoenix AZ USA March2011

[18] M Nadour A Essadki and T Nasser ldquoComparative analysisbetween PI amp backstepping control strategies of DFIG drivenby wind turbinerdquo International Journal of Renewable EnergyResearch vol 7 no 3 pp 1307ndash1316 2017

[19] M Nadour A Essadki M Fdaili and T Nasser ldquoAdvancedbackstepping control of a wind energy conversion systemusing a doubly-fed induction generatorrdquo in Proceedings of the2017 International Renewable and Sustainable Energy Con-ference (IRSEC) pp 1ndash6 Tangier Morocco December 2017

[20] Y Rebours A Comprehensive Assessment of Markets forFrequency and Voltage Control Ancillary Services PhD thesisUniversity of Manchester Manchester England 2008

[21] P Venne X Guillaud R Teodorescu and J MahseredjianldquoGeneralized gain scheduling for deloaded wind turbineoperationrdquo Wind Engineering vol 34 no 2 pp 219ndash2392010

[22] P Kundur N J Balu andM G Lauby Power System Stabilityand Control Vol 7 McGraw-Hill New York NY USA 1994

[23] J Van de Vyver J D M De Kooning B MeersmanL Vandevelde and T L Vandoorn ldquoDroop control as analternative inertial response strategy for the synthetic inertiaon wind turbinesrdquo IEEE Transactions on Power Systemsvol 31 no 2 pp 1129ndash1138 2016

16 Mathematical Problems in Engineering

Transactions on Power Systems vol 29 no 5 pp 2391ndash23992014

[4] F Poitiers T Bouaouiche and M Machmoum ldquoAdvancedcontrol of a doubly-fed induction generator for wind energyconversionrdquo Electric Power Systems Research vol 79 no 7pp 1085ndash1096 2009

[5] Z-S Zhang Y-Z Sun J Lin and G-J Li ldquoCoordinatedfrequency regulation by doubly fed induction generator-basedwind power plantsrdquo IET Renewable Power Generation vol 6no 1 pp 38ndash47 2012

[6] R Chakib M Cherkaoui and A Essadki ldquoInertial responseused for a short term frequency control for DFIG windturbine controlled by ADRCrdquo ARPN Journal of Engineeringand Applied Sciences vol 11 no 5 2016

[7] Y-K Wu S-M Chang and P Mandal ldquoGrid-connectedwind power plants a survey on the integration requirementsin modern grid codesrdquo in Proceedings of the 2019 IEEEIAS55th Industrial and Commercial Power Systems TechnicalConference (IampCPS) pp 1ndash9 Canada Canada May 2019

[8] L Ruttledge and D Flynn ldquoEmulated inertial response fromwind turbines gain scheduling and resource coordinationrdquoIEEE Transactions on Power Systems vol 31 no 5pp 3747ndash3755 2015

[9] A I Estanqueiro J M F De Jesus J Ricardo A dos Santosand J A P Lopes ldquoBarriers (and solutions) to Very HighWind Penetration in Power Systemsrdquo in Proceedings of the2007 IEEE Power Engineering Society General Meetingpp 1ndash7 Tampa FL USA June 2007

[10] Y Wang G Delille H Bayem X Guillaud and B FrancoisldquoHigh wind power penetration in isolated power systems-assessment of wind inertial and primary frequency re-sponsesrdquo IEEE Transactions on Power Systems vol 28 no 3pp 2412ndash2420 2013

[11] P-K Keung P Li H Banakar and B T Ooi ldquoKinetic energyof wind-turbine generators for system frequency supportrdquoIEEE Transactions on Power Systems vol 24 no 1 pp 279ndash287 2008

[12] H Ye W Pei and Z Qi ldquoAnalytical modeling of inertial anddroop responses from a wind farm for short-term frequencyregulation in power systemsrdquo IEEE Transactions on PowerSystems vol 31 no 5 pp 3414ndash3423 2015

[13] H Liu and Z Chen ldquoContribution of VSC-HVDC to fre-quency regulation of power systems with offshore windgenerationrdquo IEEE Transactions on Energy Conversion vol 30no 3 pp 918ndash926 2015

[14] R M Kamel A Chaouachi and K Nagasaka ldquoampree controlstrategies to improve the microgrid transient dynamic re-sponse during isolated mode a comparative studyrdquo IEEETransactions on Industrial Electronics vol 60 no 4pp 1314ndash1322 2012

[15] S Wang J Hu X Yuan and L Sun ldquoOn inertial dynamics ofvirtual-synchronous-controlled DFIG-based wind turbinesrdquoIEEE Transactions on Energy Conversion vol 30 no 4pp 1691ndash1702 2015

[16] H T Ma and B H Chowdhury ldquoWorking towards frequencyregulation with wind plants combined control approachesrdquoIET Renewable Power Generation vol 4 no 4 pp 308ndash3162010

[17] I A Gowaid A El-Zawawi and M El-Gammal ldquoImprovedinertia and frequency support from grid-connected DFIGwind farmsrdquo in Proceedings of the Power Systems Conferenceand Exposition (PSCE) pp 1ndash9 Phoenix AZ USA March2011

[18] M Nadour A Essadki and T Nasser ldquoComparative analysisbetween PI amp backstepping control strategies of DFIG drivenby wind turbinerdquo International Journal of Renewable EnergyResearch vol 7 no 3 pp 1307ndash1316 2017

[19] M Nadour A Essadki M Fdaili and T Nasser ldquoAdvancedbackstepping control of a wind energy conversion systemusing a doubly-fed induction generatorrdquo in Proceedings of the2017 International Renewable and Sustainable Energy Con-ference (IRSEC) pp 1ndash6 Tangier Morocco December 2017

[20] Y Rebours A Comprehensive Assessment of Markets forFrequency and Voltage Control Ancillary Services PhD thesisUniversity of Manchester Manchester England 2008

[21] P Venne X Guillaud R Teodorescu and J MahseredjianldquoGeneralized gain scheduling for deloaded wind turbineoperationrdquo Wind Engineering vol 34 no 2 pp 219ndash2392010

[22] P Kundur N J Balu andM G Lauby Power System Stabilityand Control Vol 7 McGraw-Hill New York NY USA 1994

[23] J Van de Vyver J D M De Kooning B MeersmanL Vandevelde and T L Vandoorn ldquoDroop control as analternative inertial response strategy for the synthetic inertiaon wind turbinesrdquo IEEE Transactions on Power Systemsvol 31 no 2 pp 1129ndash1138 2016

16 Mathematical Problems in Engineering