maximum power extraction strategy for variable speed wind

Received December 17, 2019, accepted December 30, 2019, date of publication January 13, 2020, date of current version July 23, 2020.

Digital Object Identifier 10.1109/ACCESS.2020.2966053

Maximum Power Extraction Strategy for VariableSpeed Wind Turbine System via Neuro-AdaptiveGeneralized Global Sliding Mode ControllerIZHAR UL HAQ1, QUDRAT KHAN 2, (Member, IEEE), ILYAS KHAN3, RINI AKMELIAWATI4,KOTTAKKARAN SOOPY NISAR5, AND IMRAN KHAN61Department of Electrical and Computer Engineering, COMSATS University Islamabad, Islamabad 45550, Pakistan2Center for Advanced Studies in Telecommunications (CAST), COMSATS University Islamabad, Islamabad 45550, Pakistan3Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam4School of Mechanical Engineering, The University of Adelaide, Adelaide, SA 5005, Australia5Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdul aziz University, Wadi Al-Dawaser 11991, Saudi Arabia6Department of Electrical Engineering, College of Engineering and Technology, University of Sargodha, Sargodha 40100, Pakistan

Corresponding author: Ilyas Khan ([email protected])

ABSTRACT The development and improvements in wind energy conversion systems (WECSs) are inten-sively focused these days because of its environment friendly nature. One of the attractive developmentis the maximum power extraction (MPE) subject to variations in wind speed. This paper has addressedthe MPE in the presence of wind speed and parametric variation. This objective is met by designing ageneralized global sliding mode control (GGSMC) for the tracking of wind turbine speed. The nonlineardrift terms and input channels, which generally evolves under uncertainties, are estimated using feed forwardneural networks (FFNNs). The designed GGSMC algorithm enforced sliding mode from initial time withsuppressed chattering. Therefore, the overall maximum power point tracking (MPPT) control is very robustfrom the start of the process which is always demanded in every practical scenario. The closed loop stabilityanalysis, of the proposed design is rigorously presented and the simulations are carried out to authenticatethe robust MPE.

INDEX TERMS Feed forward neural networks (FFNNs), generalized global sliding mode controller(GGSMC), maximum power point tracking (MPPT), permanent magnet synchronous generator (PMSG),wind energy conversion systems (WECSs).

I. INTRODUCTIONDue to industrialization and increasing usage of electricaldevices, the energy demand is increasing every day. Fossilfuels, which are becoming scarce nowadays are the maincause of global warming. Therefore the world energy expertsinvestigate an alternate efficient and environment friendlyenergy resources. Wind energy, which is one of the investi-gated resource, attracted great attention because of its safetyand cleanliness [1]. At the end of 2017, 52 giga watt (GW) ofwind energy was added to the global installed capacity, andmade a total of 539 GW [2].

The WECSs, based on speed, are categorized as fixedspeed and variable speed WECs. In the fixed speed WECSs,the generator speed remains constant and they are connectedto the grid without using power converters. In variable speed

The associate editor coordinating the review of this manuscript andapproving it for publication was Ding Zhai.

WECSs, the speed of the generator is continuously adoptedand controlled in such a manner that the turbine alwaysoperates at its maximum efficiency. Consequently, the MPEphenomena occurs which increased the annual product by5-10% [3]. Note that, the operating region of wind turbineis divided into four regions as depicted in Fig. 4. Region 1covers operation from the startup to the cut-in speed. Thesub operated region, called Region 2, is from cut-in to ratedspeed. In Region 3, the speed regulation region, the goalis speed regulation at rated levels because the wind speedremains high enough to drive the generator at its rated outputpower. Region 4 occurs after the cut-out speed in which theturbine is shut down to avoid any damage because of highwind speed [4]. It is worthy to note that maximum power canbe extracted from the WECSs by operating the turbine in thestarting and rated wind speed.

WECSs, equipped with variable speed permanent magnetsynchronous generator (VS-PMSG), are becoming popular

128536 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 8, 2020

https://orcid.org/0000-0002-9051-5627

I. U. Haq et al.: Maximum Power Extraction Strategy for Variable Speed Wind Turbine System

day by day because of its higher efficiency, low weight,less maintenance, easy to control and no need for reactiveand magnetizing current [5], [6]. The PMSG are generallyoperated by using a drive train technology [7] which buildscoupling between the wind turbine and PMSG. In WECSsdifferent power electronic converter with different topologieshave been used to connect the generator (i.e PMSG) to thegrid. These power interfaces, work as control unit for theMPE and build grids connection capability [8].

WECSs observe low cost installation with environmentfriendly nature, but suffer from low-efficiency due to varyingwind speed. To increase the efficiency, they must be operatedat the maximum power point (MPP). Thus MPP performsas an important part of a WECS. Sufficient work is donein the development of efficient MPPT controllers. Numer-ous MPPT control techniques are used for VS-PMSG whichmake it possible to continuously adapt the rotational speedof VS-PMSG relative to the wind speed. This resulted inenhanced efficiency of wind turbine with decreased powerfluctuations [9], [10]. In MPPT one search for the maximumcoefficient of performance (Cp) subjected to varying windspeed. Two broad categories i.e conventional design and softcomputing design strategy, for theMPPT design, one focusedextensively in the existing literature.

Among the conventional techniques, perturbation andobservation (P&O) or hill climbing search (HCS) is the sim-plest (see for details [11]). The drawbacks of this methodis that it does not work well for fast varying wind speed aswell as for large inertia wind turbines [12]. The selection ofoptimum step size is also a difficult job in this method.

Thus researchers were fascinated by soft computing tech-niques which are classified as Bio-inspired methods and arti-ficial intelligence (AI) methods. The Bio-inspired techniquesincludes particle swarm optimization (PSO) [13], ant colonyoptimization (ACO) [14] and genetic algorithms (GA) [15].These MPPT controllers under varying wind speed, showedfast convergence as compared to conventional methods. How-ever these methods need many parameters such as populationsize, mutation, selection of chromosomes and crossover rate.In addition, the estimation of these parameters is itself a com-plex job. Under varying wind speed, all these parameters needto be readjusted, otherwise one cannot track MPP correctly.

The AI strategies, for the MPPT of WECSs, include fuzzylogic (FL) based [16], [17] controllers and artificial neuralnetworks (ANN) [18], [19]. These techniques work withvariable inputs, without exact mathematical modelling alongwith self convergence and self learning capabilities. On addi-tion they have adaptive nature for nonlinear behavior ofthe systems. The FL method [16], [17] harvested maximumpower from the wind but the dependency of the trackingperformance and output efficiency on the engineer’s technicalknowledge and the rules base table reduces its applicability.It also needs a lot of theoretical knowldge and may notguarantee an optimal response. The ANN [18] was employedfor pitch controller design for a grid connected wind turbinesystem to harvest maximum power from available wind.

Its performance was superior to conventional controllers. TheANN based MPPT controllers have better performance andeffectiveness than the conventional and bio-inspired tech-niques. However, this requires months for training because oflarge memory size. In addition, it needs periodic tuning withthe passage of time.

Other control techniques like proportional integral(PI) [20], quantitative feedback theory (QFT) [21] andLinear-quadratic-Gaussian (LQG) control technique [22] arealso used for the MPPT of WECSs. All these techniquesrequired a lot of computational and graphical analysis andhave oscillating output power due to its non-robust nature.

Sliding mode control (SMC), introduced in 1950s,is famous for its versatile nature because it can be employedto both linear and nonlinear systems. It is also famous forits robust nature which is always claimed in sliding modewith reduced order dynamics. The order reduction, in slid-ing mode, provides insensitivity to parametric variations anddisturbance of matched kind. It also demonstrates finite timeconvergence with good dynamic behavior and simple imple-mentation [23], [24]. In order to deal with the unmatcheduncertainties effects, an SMC strategy was synthesized withan uncertainty observer in [25] which showed very goodresults. In the context of intelligent designs, an SMC alongwith fuzzy logic was presented for uncertain descripter sys-tems in [26]–[28]. It is important to report here that veryimpressive but summarized developments in SMC, technicalresearch issues and future perspectives regarding the SMC,are presented in [29], [30]. Having witnessed very appelaingdevelopments, the theory of SMC and its applications arestill focused areas among the researchers. In the context ofapplications to power systems, a direct power control (DPC)based on SMC was proposed for the grid connected WECSin [31]. When the grid voltages becomes unbalanced thenthe SMC controller regulate the instantaneous active andreactive powers directly in stator stationary reference frame.To improve the control efciency and performance of SMCused in PMSG-based WECS an exponential reaching law,a necessary part of the sliding mode controller, was proposedin [32]. Since, the dynamics of the wind power system is verystochastic and uncertain, therefore, an adaptive second-orderSMC was presented in [33]. This work dealt efectively thepresence of model uncertainties and the intrinsic nonlinearbehavior of WECS. A proportional integral type sliding sur-face based SMC was proposed for renewable energy conver-sion systems and the electric motor drives in [34], [35]. At thisstage, in the context of SMC applications to power systems,we want to attract the focuss of the readers to an impor-tant point that conventional SMC experiences reaching phasewhich reduces the robustness property of the SMC and it alsocauses chattering across the sliding constraint. Different tech-niques have been used to eliminate the reaching phase andto reduce the chattering effects (see for instance [36]). Sincethe amplitude of chattering phenomena is generally propor-tional to the amplitude of unknown dynamics e.g drift terms,input channels and disturbances. Therefore, in this work,

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FIGURE 1. Wind energy conversion system.

FIGURE 2. Equivalent model of WECS.

the uncertain nonlinearities (i.e drift terms and input chan-nel) are accurately estimated via the FFNNs. Consequently,the chattering is suppressed because the uncertainty bound(for a sliding mode) will be a bit smaller in this adaptivecase. In addition, the surface across which the sliding modeis enforced is an integral type which also results in chatteringsuppression along with enhanced robustness. The chatterringsuppression is also targeted via the use of a strong reachabilitylaw. The use of this reachability law gives us fast slidingmode enforcement time. The elimination of reaching phase,which often results in decreased robustness, is also a target inthis work. Therefore, a FFNNs based robust GGSM MPPTcontrol law is developed in this paper which is quite fascint-ing to investigate. The closed loop stability analysis andstates convergence is ensuredmathematically and simulations(inMATLAB environment) are carried out to authenticate theclaim. The developed results are also compared with standardliterature results [37].

The rest of the paper is structured as follow. The detailof WECS is given in Section 2 and input-output form of

the considered system is presented in Section 3. The FFNN,used for the estimation of unknown terms and analysis ofthe proposed control technique, is discussed in Section 4 andsection 5 respectively. Simulation results under varying windspeed is given in Section 6. In Section 7, the performance ofthe proposed controller is compared with standard feedbacklinearization approach. Finally, the conclusion is presented inSection 7.

II. MODELLING OF WECSThe model of WECS which will be studied in this paperis shown in Fig. 1. It mainly consists of a turbine, a gearbox, converters and a variable speed wind turbine which isequipped with a PMSG and is further connected to a grid.The system illustrated in Fig. 2, is an equivalent model of thesystem of Fig. 1. The variable resistance Rl and the constantinductance Ls are the control variables in which Ls is keptfixed and Rl is adjusted to extract maximum power.

Now the detailed presentation of wind turbine model, drivetrain and PMSG will be given in the following study.

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A. WIND TURBINE MODELThe fundamental equation governing the mechanical powercaptured by the turbine from wind is given as [38]:

Pmech =12ρAV 3Cp(λ, β) (1)

where ρ is the air density (kg/m3),Cp is the power coefficient,A is the area of the blades (m2), V is the average windspeed (m/s), λ is the tip speed ratio and β is the pitch angle.As the wind speed increases the mechanical output power ofwind turbine significantly increases as clearly seen in Fig. 3.

FIGURE 3. Wind turbine speed vs output mechanical power.

The tip speed ratio is defined as

λ =ωhRtV

(2)

where Rt is the radius of the turbine(m) and ωh is the angularspeed of the high speed shaft. Note that Cp is a nonlinearfunction of lambda λ and beta β, whose values varies fromsystem to system. The detailed mathematical expression ofCp is given as [39]:

Cp = (0.5− 0.0167(β − 2)sin[π (λ+ 0.1)

18− 0.3(β − 2)]

− 0.00184(λ− 3)(β − 2) (3)

The theoretical upper limit of Cp, also known is Betzcoefficient, is 0.47 [40]. For different values of beta, the Cpcharacteristic curve is shown in Fig. 4. By changing λ and β,the Cp is changing. At a specific λ called lambda optimum(λopt ) the value Cp is maximum which is called Cp max .By following the Cp max curve, the variable speed wind tur-bine gets maximum power from the wind (i.e., by varying therotor speed to keep the system at rated speed and λopt ).

B. DRIVE TRAIN MODELBy neglecting the stiffness and damping factor, the one-massdrive train model [37] is described as.

J∂ωh

∂t= Ta − Tem (4)

where J is the inertia constant of the high speed shaft, Ta is theaerodynamic torque and Tem is the electromagnetic torque.

FIGURE 4. Wind turbine operation regions.

Note that the mechanical power, in term of Ta and ωh, looksas follows

Pmech = Taωh (5)

The ratio between Cp and λ appear as follows

Cq =Cp(λ, β)

λ(6)

Incorporating (1) and (2) in (5), one may get

Ta =12(ρπr3)CqV 2 (7)

For the purposes of optimal control, the Cq in term of λ isapproximated as follows

Cq(λ) = a0 + a1λ+ a2λ2 (8)

Using (2) in (8) and then incorporating it in (7), the aerody-namic torque Ta becomes

Ta = d1v2 + d2vωh + d3ωh2 (9)

where

d1=12πρR3t a0, d2=

12πρR4t a1, d3=

12πρR5t a2 (10)

with

a0 = 0.1253, a1 = −0.0047, a2 = −0.0005 (11)

C. PMSG MODELHaving performed Park’s transformation and eliminating vo,the PMSG model can be described by the followingdynamics [37].

vd = Rid + Lddiddt− Lqiqωs (12)

vq = Riq + Lqdiqdt+ (Ld id + φm)ωs (13)

where R is the stator resistance, vd , vq are d and q statorvoltages, Ld and Lq are the d and q inductances,ωs is the statorpulsation and φm is the flux that is constant due to permanentmagnets.

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The electromagnetic torque is expressed as

Tem = p[φmiq + (Ld − Lq)id iq] (14)

where p is the number of pole pairs. If the permanant magnetis mounted on the rotor surface, then Ld becomes equal to Lq.Consequently,

Tem = pφmiq (15)

The non linear equations for a PMSG, when connected to agrid, is described as [37]id=−

1Ld + Ls

[(R+ Rl)id + p(Lq + Ls)iqωh]

iq=−1

Lq + Ls[(R+ Rl)iq − p(Ld + Ls)idωh + pφmωh]

ωh=1J(Ta − pφmiq)

(16)

while Rl is the load resistance and Ls is the load inductanceand (ωh = ωl × i and i is the gear ratio).The system (16), in general form, can be expressed as{

x = f (x)+ g(x)uy = h(x)

(17)

where id , iq, and ωh is considered as x1, x2, and x3, respec-tively, and Rl is replaced with u. In addition,

f (x) =

1

Ld+Ls(−Rx1 + p(Lq − Ls)x2x3

1Lq+Ls

(−Rx2 − p(Ld + Ls)x1x3)+ pφmx31J (d1v

2+ d2vx3 + d3x23 − pφmx2)

∈ IR3×1

−g(x) =

1

Ld+Lsx1

1Lq+Ls

x2

0

∈ IR3×1.uand y = h(x) = x3 = ωh is the output of the plant.

(18)

III. INPUT-OUTPUT FORMFor our control strategy, the most suitable form is theinput-output form of the (18) as in [37], [41] which is rep-resented as by defining the following transformation.

z1 = y = h(x) = x3 = ωh

z2 = Lf h(x) =∂h(x)∂x

.f (x) = m1−m2x3−m3x23−m4x2

z3 = L2f h(x) =x1x2

(19)

Since the relative degree, r of the system is one, less thanthe system order n i.e., (r < n), so the input-output formappear as follows

z1 = z2z2 = L2f h(x)+ LgLf h(x)u

}(20)

z3 =m4

m1(−

k1z3m1

m4−k2z1m1

m4−k3z3m1um4

)

− (z3m1

m4)(m24

m21

)(−l1m1

m4−l2m1z3z1m4

+ l3z1 −l4m1um4

)

(21)

The parametric values of the under study model is given intable 1. The values of the derived parameters are calculatedby using the typical parameters given in the table 2 and 3 (seefor more details [37], [41]).

TABLE 1. Parametric values of the under study model.

So, one of the transformed state i.e., z3 is of zero dynam-ics. Now, it is necessary to discuss the stability of thezero-dynamics.

A. ZERO-DYNAMICS STABILITY INVESTIGATIONThe nonlinear system’s dynamics are divided into 2 partsi.e., an internal part and an external (input-output) part, whenperforming the input-output conversion. Since, the externaldynamic states i.e., (z1, z2) are controllable states and aredirectly controlled by u while the stability of the internaldynamic state i.e., (z3) is simply determined by the locationof zeros called zero-dynamics for a nonlinear system [42].To calculate the zero dynamics, the following variablesshould be set to zero i.e., z1 = z2 = u = 0 in (21). By simpli-fying (21), finally one gets

z3 = −z3(k1 − l1) (22)

where k1 > l1, so

z3 = −Kz3 (23)

where K is a positive integer. So the zero-dynamic state z3 isstable as long as k1 > l1.Remark 1: The third order nonlinear system (reported

in (19)) with two visible states i.e., z1, z2 and one internaldynamics state z3, is considered for the controller designwhich will be discussed in details in the control designsection.

IV. UNKNOWN TERMS ESTIMATIONThis section presents the estimation of the nonlinear drift termL2f h(x) and input channel LgLf h(x) for the input-output formdeveloped in the previous section. The estimation is done viaFFNNs which will discussed below.

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FIGURE 5. Characteristics curves of Cp by varying β.

A. ESTIMATION OF DRIFT TERM (L2f h(x)) AND INPUT

CHANNEL (LgLf h(x))In order to estimate the nonlinear mapping between the inde-pendent variables i.e., z1, z2, z3 and V , and the dependingvariables L2f h(x) and LgLf h(x), a FFNN is used [43]. TheNNs learns to create a mapping between these independentvariable and dependent output [44]. The training set in NNsfor this nonlinear approximation will include the states z1,z2, z3 and V . A three layer FFNN is an efficient method forthe non-linear function estimation. The schematic diagram ofunder study procedure is shown in Fig. 6.

FIGURE 6. FFNN for L2f h(x) and LgLf h(x) generation.

The informations in the input layer are multiplied by scalarweighted, Vij, with a biased value bjo. This input layer com-putes its net activation as

aj =n∑i=1

Vjipi + bjo (24)

where j = 1, 2, 3 . . . ., lo represents the number of neuronsin the hidden layer, pi is the input of the input node i, bjo isthe respective reconstruction error or bias. The output of thehidden layer is given by

yi = f (aj) (25)

where f is the activation function which is chosen to be tanh.

The output layer computes its net activation as follow

ak =lo∑j=1

ωkjyi + bko, (26)

where k is the number of neuron in the output layer, ωkj isscalar called weight between the k th output layer node and thejth hidden layer node. The output layer produces an outputsL2f h(x) and LgLf h(x) as a function of its net activation asfollows {

L2f h(x) = f1(ak )LgLf h(x) = f2(ak )

(27)

The outputs of the estimated model can be expressed as thefunction of the inputs, the weights between input and hiddenlayer and the weights between the hidden and the output layerwhich is described as follows

L2f h(x)= f1

(∑lo

j=1ωkjf

(∑n

i=1Vjipi+bjo

)+bk0

)LgLf h(x)= f2

(∑lo

j=1ωkjf

(∑n

i=1Vjipi+bjo

)+bk0

)(28)

For two layer the FFNN, as shown in Fig. 6, considerlo and k1 are the number of neurons in layer1 and layer2,respectively. So, the above equations can also be presentedin the vectors form as

L2f h(x) or LgLf h(x) = f (W T f (V T p+ bv)+ bw) (29)

More explicitly, this expression can be expressed asfollows

L2f h(x) or LgLf h(x) = (Wtanh(V p+ bv)+ bw) (30)

After selection of the network structure, the network train-ing is done byminimizing the cost function. The cost functionis generally characterized as follows

J (Vji, ωkj) =12

lo∑i=1

(tk − zk )2 (31)

where tk is the target output at the k th output node andJ (Vji, ωkj) is the mean square error (MSE).

Levenberg-Marquardt training algorithm is used for updat-ing the weights of the FFNN. The MSE criterion or themaximum number of iterations decide the termination of theiterative process. A range of values of the network parametershas been varied systematically to achieve a good estimateof the training data. The varying network parameters are thenumber of hidden neurons in the hidden layers, with learningrate range and the number of iterations are used for theestimation of L2f h(x) and LgLf h(x).The final FFNN structure for L2f h(x) and LgLf h(x) has

three layer and the learning rate is 0.1. The first layer consistsof the inputs. The second layer which is the hidden layerconsists of ten neurons with sigmoid function as an activationfunction. The third layer is an output layer which gives us

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L2f h(x) and LgLf h(x) as an estimates of the plant drift termsand input channel, respectively. This choice of the networkparameters yields a good match between the actual and thepredicted values.

FIGURE 7. Performance plot.

1) SIMULATION RESULTS OF FFNNThe performance in terms of MSE, during the estimation ofL2f h(x) and LgLf h(x), is shown in Fig. 7. It the start thereis considerable amount of error. However, with the increasein epoches, the error reduces to its minimum value. Theirregression plots, depicted in Fig. 8, are plotted against thetarget values. The regression parameter R decides the successrate of estimation. If R = 1, it mean good estimates are madeand as R decreases the true estimation decreases.

FIGURE 8. Regression plot.

The estimation error histogram associated with L2f h(x) andLgLf h(x) shown in Fig. 9. It reveals a very small error withan average very close to zero.

FIGURE 9. Mean squared error histogram.

This estimation provides the estimates (L2f h(x) andLgLf h(x)) which will be used in control algorithm outlinedin next section.

V. GENERALIZED GLOBAL SLIDING MODE CONTROLIn this section the GGSMC based control law is designed toextract maximum power from the WECS. This job can bedone by steering ωh to ωopt by logically varying the controlinput u (i.e.,Rl). Now, by considering the output based nor-mal form (20) subject to uncertainties. Thus one may have{

z1 = z2z2 = L2f h(x)+ LgLf h(x)u+1(z1, z2, t)

(32)

where z1 = x3 and z2 = 1J (d1v

2+d2vx3+d3x23 −pφmx2) and

1(z1, z2, t) is the uncertainty which is assumed to be matchedand bounded by a positive constant K i.e., |1(z1, z2, t)| ≤ K .

Since the ultimate objective is the tracking of the optimumspeed of the generator named as ωopt . Therefore, the mis-match between the actual and reference speed is defined by

e = z1 − ωref (33)

where ωref = ωopt Based on this error, a new variable σ isdefined as follows

σ = e+ ae− f (t) (34)

where the function f (t), called the forcing function, mustbe designed (according to [45]) to meet the following threeconditions so that σ = 0 is satisfied for all t ≥ 0.1) f (0)=e0 + ae02) f (t)→ 0 as t →∞3) f (t) has a bounded first time derivativeHere e0 and e0 are the velocity and position errors respec-

tively, at t = 0. The detailed mathematical expression of f (t)in GGSMC is chosen as follows

f (t) = [(e0 + ae0)cosbt − be0sinbt] exp(−at) (35)

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where a and b are positive constants. Note that, this forcingfunction satisfy all the above three conditions.

when σ = 0 is met, then the solution of the closedloop system will be governed by the following differentialequation e + ae − f (t) = 0. The solution of this equationappears as follows

e(t) = (e0cosbt +e0 + ae0

bsinbt) exp(−at) (36)

It is worthy to mention that this solution can also beobtained by solving the forthcoming second order system

e+ 2ae+ (a2 + b2)e = 0 (37)

with initial conditions e(0) = e0 and e(0) = e0.The poles of this system are lying at−a±bj. This gives the

indication that the dynamics of the system, in sliding mode,does not reduces which implies that the system experiencesintegral sliding mode for all t ≥ 0.

The time derivative of (34) along system (32) becomes

σ = z2 − ωopt + c(z1 − ωopt )− f (t) (38)

At this stage, the main interest is that the system shouldevolves with full states. Thus, a proportional integral surfacein term of σ can be defined as follows

ξ = σ + c∫ t

0σ (τ )dτ (39)

The choice of such proportional integral surface carriesvery interesting meaning. This is actually a PI type mani-fold which provides us no order reduction (to the order ofsystem’s dynamics) in sliding mode. Consequently, the sys-tem evolves with full states in sliding mode from the verystart which results in enhanced robustness. In addition, thistype of surface accompanied by the strong reachability law(reported in equation (43)) results in the suppressed chatter-ing phenomenon.

The time derivative of ξ becomes

ξ = σ + cσ (40)

Now incorporating the values of σ and σ and then posingξ = 0 and then calculating for the input u, one may get

uequ =1

lglf h[−a(z2 − ωopt )− l2fh+ ωopt + f (t)] (41)

Since the practical system always operates under uncer-tainties therefore, the equivalent control alonewill be nomorecapable to enforce sliding mode. So, the overall sliding modeenforcement law appear as follows

u = uequ + udis (42)

where

udis = −k1(ξ +Wsign(ξ )); 0 <W < 1. (43)

The schematic diagram of the designed control techniqueis shown in Fig. 10.

FIGURE 10. Control design for WECS equipped with PMSG.

Theorem 1: The sliding mode will be enforced along themanifold (39) by the control law of the (43) and hence thetracking will happen if the switching gain of the discontinu-ous control component (i.e, udis) chosen larger than the boundof the uncertainty i.e.,

K > |1(z1, z2, t)| + η

Proof:Now, at this stage we are ready to confirm slidingmode establishment. A lyapunove function, in term of thesliding variable, is defined as follows.

V =12ξ2 (44)

The time derivative of this function along (41) becomes

V = ξ ξ = ξ (σ + cσ ) (45)

Using (38) and (42) (with components given in (41)and (43)), one may get

V = ξ (−k1(ξ +Wsign(ξ ))+1)

or

V ≤ −k1ξ2 − k1W |ξ | + |ξ ||1| (46)

V ≤ −k1ξ2 − |ξ |(k1W − |1|) (47)

This expression remains true, i.e., negative definite, if

k1W − |1| ≥ η > 0

k1W ≥ η + |1| (48)

The inequality (47) can also be written as

V ≤ −k12V −√2ηV

12 (49)

or

V + k12V +√2ηV

12 ≤ 0 (50)

The differential inequality is a fast finite time convergingequation, which confirms that V approaches to zero in finitetime. It means that ξ approaches to zero. As ξ −→ 0,the equation (40) becomes

σ + cσ = 0 (51)

The homogeneous equation has a solution

σ (t) = σ (0)exp(−at) (52)

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It means that σ will approach to zero. The σ convergenceto zero certify the equation (37) with solution reported in(36). Thus, the tracking error converges to zero which in turnprovide us the reference tracking. This proves the theorem.Having tracked the reference, the maximum power will beextracted via the equation (1).

VI. SIMULATION RESULTS AND DISCUSSIONSIn this section, the closed loop simulation results of the aforesaid process are displayed. In the first subsection the robusttracking performance in an uncertain scenario is performedwhile in the second subsection the comparison to standardliterature results is shown.

FIGURE 11. Wind speed profile.

TABLE 2. Parameters of wind turbine.

A. ROBUST TRACKING PERFORMANCEThe VS-WECS equipped with PMSG has been build basedon equations (1) to (16). The power rating of the VS-WECSequipped with PMSG is 3 kilo Watt (kW). The windspeed profile is generated through Kaimal spectra is shownin Fig. 11 reported in [46]. The simulations has been per-formed using variable step ode45 solver. Different param-eters of the wind turbine and PMSG are shown in table 2and table 3 of Appendix, respectively. These parameters areadapted from [37]. In order to verify the tracking perfor-mances of the investigated controller, the simulation resultsare shown in Fig. 12-14. In Fig. 12, the tracking performanceof the reference generator speed by the actual speed of thegenerator is ensured by GGSMC. In Fig. 13 and Fig. 14,power coefficient Cp and the tip speed ratio λ are displayed,respectively. The actual variations in Cp and λ can be seen inthe zoomed sections of the Fig. 13 and 14. The Cp value wasfound very close to its optimum value of 0.47 where as the λwas found very closed to its optimum value 7.

TABLE 3. Parameters of PMSG.

FIGURE 12. Reference speed tracking via shaft speed.

FIGURE 13. Power coefficient evolution.

FIGURE 14. Tip speed ratio vs time.

It is important to mentioned that the wind speed trackingwas performed in uncertain scenarios. The uncertainties ofmatched kind were 0.5sin(t) while the plant parameters werevaried with a change of 5%. The performance is quit good

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and the maximum power is nicely extracted by keeping thepower coefficient Cp and the tip speed ratio λ close to theiroptimum values. Hence the NNs base GGSMC displays itsself as an appealing candidate for such power systems.

FIGURE 15. GGSMC tracking performance in comparison with resultsof [37].

FIGURE 16. Comparison of power coefficient Cp.

FIGURE 17. Comparison of tip speed ratio λ.

B. COMPARISON WITH STANDARD LITERATURE RESULTSTo highlight the performance of the NNs based GGSMC,its results are compared with the feedback linearized con-troller [37]. Both the controllers are simulated and comparedwith varying wind speed. Simulation results from Fig. 15-17shows the fast tracking and better performance of the newly

investigated controller as compared to the conventional feed-back linearized controller. In Fig. 15, it is clearly shownthat the GGSMC tracks the reference speed of the rotor insmall time and have low oscillations around the referencespeed as compared to the feedback linearized controller [37].The tracking performance of both the controllers, in the fasttransients, are also shown in zoomed views in the Figure. Thepower coefficient has its optimum value near to 0.47 whichis ensured the best by GGSMC with no oscillations as com-pared to feedback linearized controller (one may see thenin Fig. 16). The GGSMC have tip speed ratio almost aroundoptimal tip speed ratio as compared to feedback linearizedcontroller, as shown in Fig. 17, which guarantees maximumpower extraction from the wind at the given wind speed.

Having observed the comparative results, its very clearthat the FFNN based GGSMC proves its self an appealingcandidate for MPPT designs in wind power systems.

VII. CONCLUSIONIn this paper NNs based GGSMC MPPT law have beeninvestigated for a variable wind speed turbine which is con-nected a PMSG. The unknown nonlinear dynamics (i.e., driftterms and input channels) are estimated via the FFNN anda robust GGSMC law is developed which maintain the Cpand λ at it required values and confirms maximum powerextraction. The sliding mode enforcement stability is alsopresented in details. To highlight the benefits of the FFNNbased GGSMC, its results are compared with standard litera-ture results (i.e., feedback linearized controllers [37]). At theend it is confirmed that the newly investigated FFNN baseGGSMC is an appealing candidate for such tasks in powersystems.

APPENDIXSee Tables 2 and 3.

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IZHAR UL HAQ received the B.S. degree inelectrical electronics engineering fromCOMSATSUniversity Islamabad (Abbottabad campus),Pakistan, in 2016, and the M.S. degree in elec-trical engineering from COMSATS UniversityIslamabad, Pakistan, in 2019. His research inter-ests include maximum power extraction fromrenewable energy systems, integration of renew-able energy systems, hybrid power systems, andintelligent control of hybrid power systems.

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http://dx.doi.org/10.1109/TFUZZ.2019.2930036


QUDRAT KHAN (Member, IEEE) received theB.Sc. degree in mathematics and computer sci-ence from the University of Peshawar, in 2003,the M.Sc. and M.Phil. degrees in mathemat-ics from Quaid-i-Azam University, Islamabad,in 2006 and 2008, respectively, and the Ph.D.degree in nonlinear control systems from M. A.Jinnah University, Islamabad, in November 2012.He was postgraduate scholarship holder duringPh.D., from 2008 to 2011, and IRSIP scholarship

holder during PhD (as a Visiting Research Scholar at the University of Pavia,Italy). He has been working as an Assistant Professor with COMSATS,Islamabad, since July 2013. He worked as a Postdoctoral Fellow at theDepartment of Mechatronics Engineering, International Islamic University,Malaysia, from September 2015 to August 2016. He was selected for YoungAuthor Support Program, IFAC, World Congress, 2011, Milan, Italy. He haspublished more than 50 research articles (with impact factor more than 40)in referred international journals and conference proceedings. His researchinterests include robust nonlinear control design, observers design, faultdetection in electromechanical systems and multiagent system’s control.He is listed in the young productive scientists of Pakistan in 2017 and 2018.

ILYAS KHAN works atMajmaah University, SaudiArabia. He is currently a Visiting Professor withthe Department ofMathematical Sciences, Facultyof Science, Universiti Teknologi Malaysia, Sku-dai, UTM Johar Bahru, Malaysia, and Faculty ofMathematics and Statistics, Ton Duc Thang Uni-versity, Ho Chi Minh City, Vietnam. He is work-ing on both analytical and numerical techniques.He has published more than 300 articles in variousreputed journals. He is also the author of several

books and book chapters. His research interests are Boundary layer flows,Newtonian and non-Newtonian fluids, heat and mass transfer, renewableenergy, and nanofluids.

RINI AKMELIAWATI received the B.Eng. degree(Hons.) in electrical engineering from the RoyalMelbourne Institute of Technology (RMIT) Uni-versity, Australia, in1997, and the Ph.D. degreein electrical and electronic engineering from theUniversity of Melbourne, Australia, in 2002. Sheis currently an Associate Professor with the Schoolof Mechanical Engineering, The University ofAdelaide, Australia. She was a Full Professorwith the Department of Mechatronics Engineer-

ing, International Islamic University, Malaysia, from 2012 to 2018. Shejoined the Department as an Associate Professor, in 2008. She was a Lecturerwith RMIT University, from 2001 to 2004, and Monash University, from

2004 to 2008. She is a Fellow member of Engineers Australia and amember of International Federation of Automatic Control (IFAC) Tech-nical Committees. She was a Visiting Professor with the University ofMelbourne, in 2012, and Universiti Teknologi Melaka, from 2014-2016.She has published more than 50 peer-reviewed articles in indexed journals,three books and edited books, 20 refereed book chapters, and more than90 conference papers in international refereed conference proceedings. Shehas two patents in Malaysia. Her main research interests include nonlin-ear control systems theory and applications, intelligent and mechatronicssystems, and signal and image processing. She has received more than35 awards inform of Gold, Silver, and Bronze medals, best paper awards,best reviewer award, and other certificates from International and Nationalorganizations as well as from the university. She has been invited to beinvited speaker on her research outcomes in International and National Con-ferences/Symposiums/Colloqiums/Seminars. In recognition of her expertise,she has been invited to review articles in prestigious international journals.She was the Vice President of the Malaysian Society of Automatic ControlEngineers (MACE) (2016–2018). She was the Chair of the IEEE Instrumen-tation andMeasurement SocietyMalaysia Chapter 2007–2009, the Treasurerof the same society, in 2010, and the educational executive committee,in 2016, and a secretary of the IEEEControl Systems SocietyMalaysia Chap-ter, in 2010, the Chair of Intelligent Mechatronics System Research Unit atthe International Islamic University Malaysia (2010–2018). She is also theCo-Editor-In-Chief of International Journal of Robotics and Mechatronics(IJRM), a member of editorial advisory board of International Journal ofIntelligent Unmanned Systems (Emerald Group, UK - since 2012), Journalof Unmanned Systems Technology (UNSYS Publishing, South Korea - since2013).

KOTTAKKARAN SOOPY NISAR is currentlyworking as an Associate Professor with theDepartment of Mathematics, College of Arts andScience, Prince Sattam Bin Abdulaziz Univer-sity, Wadi Al-Dawaser, Saudi Arabia. His areaof specialization is partial differential equations,fractional calculus, and numerical solutions fornonlinear PDEs. He has published more than200 articles. He is also referee of several journals.

IMRAN KHAN received the B.Sc. degree in elec-trical engineering from the Federal Urdu Univer-sity of Arts, Science and Technology, Islamabad,in 2009, the M.S. degree in electronic engineeringfrom Mohammad Ali Jinnah University, Islam-abad, in 2012, and the Ph.D. degree in electricalengineering from the Capital University of Sci-ence and Technology, Islamabad, in 2016. He iscurrently an Assistant Professor with the Electri-cal Engineering Technology Department, National

University of Technology. His research interests include analysis and designof nonlinear control systems, especially sliding mode control, for variousindustrial applications. He has more than six years research and teachingexperience.

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maximum power extraction strategy for variable speed wind

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