A Synergetic Sliding Mode Controller Applied to Direct Field-Oriented Control of Induction Generator-Based Variable Speed Dual-Rotor Wind Turbines

energies

Article A Synergetic Sliding Mode Controller Applied to Direct Field-Oriented Control of Induction Generator-Based Variable Speed Dual-Rotor Wind Turbines

Habib Benbouhenni 1 and Nicu Bizon 2,3,*

1 Department of Electrical and Electronics Engineering, Faculty of Engineering and Architecture, Nisantasi University, 34481742 Istanbul, Turkey; [email protected] 2 Faculty of Electronics, Communication and Computers, University of Pitesti, 110040 Pitesti, Romania 3 Doctoral School, Polytechnic University of Bucharest, 060042 Bucharest, Romania * Correspondence: [email protected]

Abstract: A synergetic sliding mode (SSM) approach is designed to address the drawbacks of the direct ﬁeld-oriented control (DFOC) of the induction generators (IGs) integrated into variable speed dual-rotor wind power (DRWP) systems with the maximum power point tracking (MPPT) technique. Using SSM controllers in the DFOC strategy, the active power, electromagnetic torque, and reactive power ripples are reduced compared to traditional DFOC using proportional-integral (PI) controllers. This proposed strategy, associated with SSM controllers, produces efﬁcient state estimation. The effectiveness of the designed DFOC strategy has been evaluated on variable speed DRWP systems with the MPPT technique.

Keywords: synergetic sliding mode; direct field-oriented control; induction generators; variable speed dual-rotor wind power; maximum power point tracking Citation: Benbouhenni, H.; Bizon, N. A Synergetic Sliding Mode Controller Applied to Direct Field-Oriented Control of Induction Generator-Based 1. Introduction Variable Speed Dual-Rotor Wind Turbines. Energies 2021, 14, 4437. Induction generators have many advantages including low maintenance, high dy- https://doi.org/10.3390/en14154437 namic response, easy control, better speed versus torque characteristics, high efficiency, minimized weight, and more compact construction. Due to their mechanical features Academic Editor: Frede Blaabjerg and favorable electricals, induction generators are widely used in the industrial sector, pumps, the military, automotive applications, and wind power [1]. Consequently, many Received: 3 June 2021 works have been developed to enhance the effectiveness of induction generators [2–4]. Accepted: 16 July 2021 Various control techniques for induction generators have been proposed in [5]. The most Published: 22 July 2021 common methods are based on DC-link voltage control [6], space vector control in [7], and direct torque control (DTC) [8]. Most of the presented techniques for power control of Publisher’s Note: MDPI stays neutral induction generators are based on pulse-width modulation (PWM) and use proportional- with regard to jurisdictional claims in integral (PI) regulators. There is another strategy similar to DTC control that relies on direct published maps and institutional affil- control of the reactive and active power of the induction generator, and this is by using iations. two hysteresis controllers and one lookup table [9]. In [10], the reactive and active power ripple minimization is achieved by using neural algorithms. In this proposed method, both the lookup table and the hysteresis comparators were replaced by neural networks. The simulation results show the performances of the designed strategy. For controlling Copyright: © 2021 by the authors. induction generators, two converters should be used. One such converter is the rotor side Licensee MDPI, Basel, Switzerland. converter (RSC), which controls the reactive and active power exchanged between the This article is an open access article induction generator stator and the network. The grids side converter (GSC) which controls distributed under the terms and the voltage and reactive power exchanged between the rotor and the network. Generally, conditions of the Creative Commons the induction generators are driven by a rectifier and a classical inverter each containing Attribution (CC BY) license (https:// six thyristors type inductors. Two different methods can be used or the same method creativecommons.org/licenses/by/ to control both the classical inverter (RSC) and the rectifier (GSC). In [11], a three-switch 4.0/).

Energies 2021, 14, 4437. https://doi.org/10.3390/en14154437 https://www.mdpi.com/journal/energies Energies 2021, 14, 4437 2 of 17

three-phase inverter controlled by field-oriented control (FOC) strategy using traditional PI regulators for an induction generator-based wind turbine is presented. In [12], the direct FOC strategy of induction generators is proposed, this strategy controls the reactive and active power through a simple modulation technique of a three-phase inverter. Direct FOC technique is a control strategy in which is indirectly selected output voltage vector states based on the active and reactive power fluctuations using PI regulators and with using the current loop. The indirect FOC strategy is presented in [13], the principle indirect FOC strategy is to control the active and reactive powers by using four PI regulators. In [14] the indirect FOC strategy reduces a more harmonic distortion (THD) of voltage compared to the direct FOC method of induction generators. In this work, we will focus on applying the direct FOC method to the induction generators and improving their effectiveness. On the other hand, the direct FOC method is a simpler structure and easy to apply. One of the main disadvantages of this technique is that its effectiveness depends highly on accurate induction generator parameters such as rotor, stator inductances, and resistances. Another disadvantage of the direct FOC strategy is the highly active and reactive power ripples [15]. For minimizing active and reactive power ripples, several techniques have been designed for reducing these drawbacks. A novel direct FOC strategy utilizing the fuzzy logic controllers has been proposed in order to control torque, reactive and active power of induction generator in [16]. A novel direct FOC strategy end with neural algorithms has been designed in [17]; the traditional PI controllers were replaced by neural networks, thus lowering the effect of the DC-link voltage on commutation reactive and active power minimization to some extent. The direct FOC method and traditional space vector modulation (SVM) technique is combined to control of the induction generator-based wind power [18]. For effectively reducing the reactive and active power undulations, the sliding mode controllers (SMCs) are used to apply the controlled direct and quadrature rotor voltages from the replaced traditional PI controllers by robust control based on SMC technique [19]. Additionally, commutation active and reactive power ripple minimization by using neuro-fuzzy algorithms is designed in [20]. In the direct FOC strategy, real active and reactive power measurement is variable in practice. The feedback of active and reactive power control is susceptible to many factors, including model accuracy, parameter changes, etc., because the algorithm estimation is mutually exclusive. However, in direct FOC strategy, it is easy to measure the actual values of the control variables by measuring the rotor current and rotor voltage in a real system; therefore, this work proposes induction generators controlled by direct FOC strategy using a new nonlinear control theory for variable speed dual-rotor wind power (DRWP) systems with the maximum power point tracking (MPPT) technique. Direct FOC strategy with synergetic sliding mode controllers minimizes the cost of drive because it decreases the reactive and active power undulations. Moreover, in this work, by reducing the chattering phenomenon and using the modified SVM technique, the cost of an induction generator drive can be more minimized. The main contributions of the work are listed below: 1. This work designed a robust direct FOC method of induction generator-based DRWP systems; 2. A new robust control to reactive and active power ripples minimization for direct FOC method is designed; 3. Synergetic sliding mode controllers to minimize error tracking reactive and active power references of induction generator-based DRWP systems; 4. Using the proposed technique and modified SVM technique minimizes the THD of voltage and torque ripple of the induction generator-based DRWP systems. This work is organized as follows. Section2 points out necessary equations related to the mathematical modeling of the DRWP system. Synergetic sliding mode control theory is presented in Section3. Section4 explains the designed robust direct FOC method for induction generators. Matlab software-based simulation studies is presented in Section5. The conclusion is given in Section6. Energies 2021, 14, 4437 3 of 17

Energies 2021, 14, 4437 for induction generators. Matlab software-based simulation studies is presented in Section 3 of 17 5. The conclusion is given in Section 6.

2. DRWP2. Model DRWP Model DRWP isDRWP a turbine is a turbinewith two with rotors. two It rotors. aims Itto aimsimprove to improve the effectiveness the effectiveness of the ofclassi- the classical cal windwind turbine turbine and andminimize minimize the thepower power generated generated from from traditional traditional sources sources based based on on fossil fossil fuels,fuels, such such as ascoal, coal, oil, oil, and and natural natural gas, gas, even even if if the the wind wind is is highly highly variable variable [21]. [21]. Dou- Double rotor ble rotorwind wind turbines turbines have have two two rotors rotors rotating rotating in oppositein opposite directions directions on theon samethe same axis axis [22]. DRWP [22]. DRWPis a newis a technologynew technology of wind of wind power powe thatr has that been has designedbeen designed to increase to increase the production the of productionmechanical of mechanical energy energy (See Figure (See 1Figure). 1).

Figure 1. Block diagram of DRWP system with an induction generator. Figure 1. Block diagram of DRWP system with an induction generator. The number of mechanical components in DRWP is higher than in the classical wind Theturbine. number This of mechanical new technology components has been in studiedDRWP inis higher several than works in [the23]. classical This new wind technology turbine. hasThis an new excellent technology performance has been studied in regions in several with low works and [23]. high This wind new speeds. technology Among its has an excellentadvantages performance is that it operatesin regions at with lower low tip-speed and high ratios wind compared speeds. Among to the classicalits ad- wind vantagesturbine is that [it24 operates]. This method at lower has tip-speed several drawbacks,ratios compared for example, to the classical high financial wind turbine cost, difficulty [24]. Thisto method control, andhas aseveral risk of subsynchronousdrawbacks, for resonance.example, high It contains financial a large cost, number difficulty of mechanical to control, componentsand a risk of comparedsubsynchronous to SRWP resonanc systems.e. OnIt contains the other a large hand, number we use theof mechanical MPPT technique to componentscontrol compared the DRWP to SRWP system, systems. such as On a traditional the other windhand, turbine. we use Therethe MPPT are several technique methods in to controlorder the DRWP to track system, the maximum such as power a tradit pointional (MPP) wind andturbine. theglobal There MPPare several or the globalmethods maximum in orderefficiency to track the point maximum (GMEP) power [25]. Equationpoint (MPP) (1) representsand the global the aerodynamicMPP or the global mechanical max- power imum efficiencyresulting point from (GMEP) the DRWP [25]. system Equation [26]: (1) represents the aerodynamic mechanical power resulting from the DRWP system [26]: PDRWP = PT = PMR + PAR (1) 𝑃 =𝑃 =𝑃 +𝑃 (1) where PAR,PMR the aerodynamic mechanical power of the auxiliary and main rotors. where PAR, PMRIn the the aerodynamic DRWP system, mechanical the resulting power aerodynamic of the auxiliary torque and is the main sum rotors. of the aerodynamic In thetorques DRWP of thesystem, auxiliary the andresulting main aerody rotor, andnamic is represented torque is the by sum the following of the aerody- equations: namic torques of the auxiliary and main rotor, and is represented by the following equations: TDRWP = TMR + TAR (2) 𝑇 =𝑇 +𝑇 (2) where TAR,TMR the aerodynamic torque of the auxiliary and main rotors. where TAR, TMRThe the aerodynamic aerodynamic torque torque of of the the auxiliary auxiliary and and main main rotor rotors. is given by Equations (3) and The(4), aerodynamic respectively torque [24]. of the auxiliary and main rotor is given by Equations (3) and C (4), respectively [24]. = p · · 5 · 2 TAR 3 ρ π RAR wAR (3) 2λAR C = p · · 5 · 2 TMR 3 ρ π RMR wMR (4) 2λMR

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where ρ: the air density, RMR,RAR: Blade radius of the auxiliary and main rotors, λAR, λMR: the tip-speed ratio of the main and auxiliary rotors, and wAR, wMR: the mechanical speed of the auxiliary and main rotors. The Cp is given:

1 0.035 Cp(λ, β) = − (5) λ + 0.08.β β3 + 1

where β is pitch angle. Equation (6) represents the tip-speed ratios of the auxiliary rotor.

wAR.RAR λAR = (6) V1

with V1 is the wind speed on an auxiliary rotor. Equation (7) represents the tip-speed ratios of the main rotor.

wMR·RMR λMR = (7) VMR

where VMR is the speed of the uniﬁed wind on main rotor. Equation (8) represents the wind speed in the main turbine. The distance between the auxiliary and the main rotors is 15 m [26]. p ! 1 − (1 − CT) 2x Vx = V1· 1 − (1 + √ ) (8) 2 1 + 4x2

where x: the non-dimensional distance from the auxiliary rotor disk, Vx: is the velocity of the disturbed wind between rotors at point x, and CT: the trust coefﬁcient (CT = 0.9).

3. Synergetic Sliding Mode Control Theory In this part, we proposed a new technique based on the combination of synergistic control and sliding mode control (SMC), intending to create a more robust method and reducing the chattering phenomenon. The proposed technique is to improve the performance of the sliding mode control by replacing the control equivalent portion (ueq(t)) with the synergetic control. The structure of a sliding mode control consists of two sections, one concerning the exact linearization (ueq) and the other stabilizing (un). Equation (9) represents the principle of the SMC method [27]. u = ueq(t) + un(t) (9) with: un(t) = −K·sign(S) (10) where S is the linear sliding surface. Synergistic control is a type of variable structure control. It differs from sliding mode control in the way it forces the sliding surface to fall to zero. Equation (11) represents the principle of the synergetic control theory [26–29].

dS S + N· = 0 (11) dt N is the convergence speed (N > 0). Substituting the exact linearization into the SMC method using Equation (11), we obtain a new nonlinear method called synergetic sliding mode control (SSMC). This proposed strategy is a simpler algorithm and more robust compared to the classical SMC method. On Energies 2021, 14, 4437 5 of 17

Substituting the exact linearization into the SMC method using Equation (11), we obtain a new nonlinear method called synergetic sliding mode control (SSMC). This proposed strategy is a simpler algorithm and more robust compared to the classical SMC method. On the other hand, this proposed strategy does not need the mathematical model of the system. Equation (12) represents the principle of the proposed SSMC control theory (see Figure 2): Energies 2021, 14, 4437 𝑑𝑆 5 of 17 𝑢(𝑡) =𝑆+𝑁∙ − 𝐾 ∙ 𝑠𝑖𝑔𝑛(𝑆) (12) 𝑑𝑡 where K is the positive gain. the otherThe following hand, this will proposed ensure strategy the stability does not of needthe SSMC the mathematical controller based model on of Lyapunov the system. theorem:Equation S (12)(0) = represents 0 and S(x the)∙x principle> 0 for all of x the ≠ 0. proposed The dynamics SSMC controland stability theory of (see the Figure system2): controlled by the proposed method can be ensured by appropriately setting the values for dS parameters N and K. The reachingu(t) = conditionS + N· is− givenK·sign by(S the) following equation: (12) dt 𝑆(𝑥) ∙ 𝑆(𝑥) ≤ 0 (13) where K is the positive gain.

FigureFigure 2. 2. ProposedProposed SSMC SSMC controller. controller. The following will ensure the stability of the SSMC controller based on Lyapunov 4. Direct FOC Method with SSMC Controllers theorem: S(0) = 0 and S(x)·x > 0 for all x 6= 0. The dynamics and stability of the system controlledFOC is by one the of proposed the most methodpopular canmethods be ensured applied by to appropriately rotating electrical setting machines, the values and for thisparameters is becauseN andof itsK characteristics. The reaching compared condition isto givensome byof the the controls. following The equation: principle of the FOC technique is to orient the stator flux along the axis of the rotating frame. There are . several applications to this method, forS(x ex)· Sample,(x) ≤ the0 asynchronous motor [30], the syn- (13) chronous motor [31], and multiphase machines [32]. There are two types of this method: the4. Directdirect FOC Methodmethod and with the SSMC indirect Controllers FOC method. The direct FOC method is simpler (usingFOC simple is one calculations) of the most and popular can be methods accomplished applied easily to rotating compared electrical to the machines, indirect FOC and method.this is because However, of its despite characteristics these advantages, compared the to somedirect of FOC the controls.method gives The principle the most offluc- the tuationsFOC technique in the reactive is to orient andthe active stator powers. flux along On the the other axis of hand, the rotating the direct frame. FOC There method are givesseveral more applications THD of stator to this voltage method, and forcurrent example, compared the asynchronous to the indirect motor FOC control [30], the tech- syn- niquechronous [33]. motor The principle [31], and of multiphase operation machines of the di [rect32]. method There are is twoillustrated types of in this the method: following the scientificdirect FOC works method [34–39]. and theIn indirect[35], the FOC indire method.ct FOC The (IFOC) direct method FOC method improved is simpler the perfor- (using mancesimple of calculations) the induction and generator can be accomplished compared with easily the compared direct FOC to (DFOC) the indirect strategy. FOC method.In [36], theHowever, DFOC strategy despite thesewas designed advantages, based the on direct the super FOC methodtwisting givesalgorithms the most to regulate fluctuations the torquein the reactiveand speed and of active the six-phase powers. Oninduction the other motor. hand, The the experimental direct FOC method result givesshows more the superiorityTHD of stator of the voltage designed and currentDFOC strategy. compared In to [37], the the indirect DFOC FOC technique control techniquewas designed [33]. basedThe principle on an intelligent of operation SVM method of the direct to minimi methodze the is active illustrated power in and the torque following undulations scientific ofworks ASG-based [34–39]. SRWP In [35 ],systems. the indirect In [38], FOC the (IFOC) FOC methodtechnique improved was designed the performance based on maxi- of the muminduction torque generator per ampere compared to minimize with the the direct cope FOCr losses (DFOC) of the strategy. system of In the [36], permanent the DFOC magnet-assistedstrategy was designed synchronous based onreluctance the super motor. twisting FOC algorithms method and to flatness regulate approach the torque were and combinedspeed of the to control six-phase the induction permanent motor. synchronous The experimental motor using result the showsdSPACE the controller superiority [39]. of Thethe designedexperimental DFOC and strategy. simulation In [37 ],results the DFOC show technique the superiority was designed of the based proposed on an FOC intel- method.ligent SVM To ensure method the to minimizedecoupling the between active power control and axes, torque a DFOC undulations strategy ofwas ASG-based applied [23]SRWP by aligning systems. the In [stator38], the flux FOC with technique the direct was axis designed d. based on maximum torque per ampere to minimize the coper losses of the system of the permanent magnet-assisted synchronous reluctance motor. FOC method𝜓 =𝜓 and and flatness 𝜓 =0 approach were combined to control(14) the permanentThe stator voltage synchronous can be motorexpressed using by: the dSPACE controller [39]. The experimental and simulation results show the superiority of the proposed FOC method. To ensure the decoupling between control axes, a DFOC strategy was applied [23] by aligning the stator flux with the direct axis d. ψds = ψs and ψqs = 0 (14) The stator voltage can be expressed by:

V = 0 ds (15) Vqs = Vs = ws·ψs Energies 2021, 14, 4437 6 of 17

The expressions of stator current are deﬁned by: ( I = − M I + ψs ds Ls dr Ls (16) I = − M I qs Ls qr

The reactive and active powers is achieved through the control of the induction generator rotor currents  P = − 3 ωsψs M I  s 2 Ls qr 2 (17) Q = − 3 ωsψs M I − ωsψs  s 2 Ls dr Ls

The electromagnetic torque equation is:

3 M Tem = − p Iqrψds (18) 2 Ls The direct and quadrature rotor voltages can be expressed [23]:

 2 2 V = R ·I + L − M p·I − g·w L − M I  dr dr dr r Ls dr s r Ls qr 2 2 (19) V = R ·I + L − M p·I − g·w L − M I + g M·Vs  qr dr qr r Ls qr s r Ls dr Ls

Equation (20) represents the relationship between the rotor voltages and the rotor currents [12].  2 V = R ·I − g·w L − M I  dr dr dr s r Ls qr 2 (20) V = R ·I − g·w L − M I + g M·Vs  qr dr qr s r Ls dr Ls The rotor current has the expression:  M2 1  Idr = Vdr − g·ws(Lr − )Iqr 2  Ls R + L − M p r r Ls 2 (21) M M·Vs 1  Iqr = Vqr − g·ws Lr − Iqr − g 2  Ls Ls R + L − M p  r r Ls

Energies 2021, 14, 4437 Figure3 depicts the induction generator active and reactive powers control based7 of on 17

direct FOC technique, where two independent PI controllers are used for each control axis.

Figure 3. Classical direct FOC technique. Figure 3. Classical direct FOC technique.

In order to improve the effectiveness of the traditional direct FOC technique, the standard PI controllers will be replaced by two robust controls based on the SSMC controller. The reactive and active power estimation block keeps the same shape as that established for the traditional direct FOC method, described in the previous work [35]. In this robust direct FOC technique, the reactive and active power are controlled by two SSMC controllers, while the modified SVM technique replaces the traditional PWM strategy. This control by direct FOC-SSMC has the advantages of vector control and conventional direct FOC method to overcome the problem of fluctuations in power and is generated by the induction generators. SSMC controllers and the MSVM technique are used to obtain a fixed switching frequency and less pulsation of the powers. The principle of the direct FOC-SSMC control technique is the direct regulation of the reactive and active powers of the induction generator-based DRWP system, by using two SSMC controllers. The two controlled variables are active and reactive powers, which are usually regulated by the proposed SSMC method. The idea is to keep the reactive and active power quantities within these sliding surfaces. The direct FOC with the SSMC method (FOC-SSMC) is a modification of the traditional direct FOC strategy, where the PI controllers have been replaced by the SSMC method, as shown in Figure 4.

Figure 4. Structure of the direct FOC-SSMC technique.

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Energies 2021, 14, 4437 7 of 17 Figure 3. Classical direct FOC technique.

In order to improve the effectiveness of the traditional direct FOC technique, the In order to improve the effectiveness of the traditional direct FOC technique, the stan- standard PI controllers will be replaced by two robust controls based on the SSMC con- dard PI controllers will be replaced by two robust controls based on the SSMC controller. troller. The reactive and active power estimation block keeps the same shape as that es- The reactive and active power estimation block keeps the same shape as that established fortablished the traditional for the traditional direct FOC direct method, FOC describedmethod, described in the previous in the previous work [35 work]. In this[35]. ro-In bustthis robust direct FOCdirect technique, FOC technique, the reactive the reacti andve active and poweractive power are controlled are controlled by two by SSMC two controllers,SSMC controllers, while while the modified the modified SVM SVM technique technique replaces replaces the traditionalthe traditional PWM PWM strategy. strat- Thisegy. controlThis control by direct by direct FOC-SSMC FOC-SSMC has the has advantages the advantages of vector of vector control control and conventional and conven- directtional FOCdirect method FOC method to overcome to overcome the problem the problem of fluctuations of fluctuations in power in power and is generatedand is gener- by theated induction by the induction generators. generators. SSMC controllers SSMC cont androllers the and MSVM the MSVM technique technique are used are to used obtain to aobtain fixed a switching fixed switching frequency frequency and less and pulsation less pulsation of the powers.of the powers. The principle The principle of the directof the FOC-SSMCdirect FOC-SSMC control control technique technique is the directis the direct regulation regulation of the of reactive the reactive and active and active powers pow- of theers of induction the induction generator-based generator-based DRWP DRWP system, system, by using by using two SSMC two SSMC controllers. controllers. The twoThe controlledtwo controlled variables variables are activeare active and and reactive reactive powers, powers, which which are usuallyare usually regulated regulated by the by proposedthe proposed SSMC SSMC method. method. The The idea idea is is to to keep keep the the reactive reactive and and active active powerpower quantitiesquantities within these sliding surfaces.surfaces. The directdirect FOCFOC with with the the SSMC SSMC method method (FOC-SSMC) (FOC-SSMC) is a is modification a modification of the of traditional the tradi- directtional FOCdirect strategy, FOC strategy, where thewhere PI controllersthe PI controllers have been have replaced been replaced by the SSMC by the method, SSMC asmethod, shown as in shown Figure in4. Figure 4.

Figure 4. Structure of the direct FOC-SSMC technique.

The SSMC method was proposed to force the controlled dynamics towards manifolds and keeps them there. To force the induction generator reactive and active powers to track their corresponding references, the linear sliding surfaces are selected to equal the error between the real and desired dynamics by Equations (22) and (23):

∗ Sa = Ps − Ps (22)

∗ Sr = Qs − Qs (23)

where the surfaces are the reactive power error Sr = Qs* − Qs and the active power error Sa = Ps* − Ps. The linear sliding surfaces shown in (22) and (23) are used as input to the SSMC controller method control law. Stator reactive and active power SSMC method are used to inﬂuence, respectively, the direct and quadrature rotor voltage components as in (24) and (25): dS V∗ = S + N· a − K·sign(S ) (24) qr a dt a dS V∗ = S + N· r − K·sign(S ) (25) dr r dt r Energies 2021, 14, 4437 8 of 17

The SSMC method was proposed to force the controlled dynamics towards manifolds and keeps them there. To force the induction generator reactive and active powers to track their corresponding references, the linear sliding surfaces are selected to equal the error between the real and desired dynamics by Equations (22) and (23):

∗ 𝑆 =𝑃 −𝑃 (22) ∗ 𝑆 =𝑄 −𝑄 (23)

where the surfaces are the reactive power error Sr = Qs*−Qs and the active power error Sa = Ps*−Ps. The linear sliding surfaces shown in (22) and (23) are used as input to the SSMC controller method control law. Stator reactive and active power SSMC method are used to influence, respectively, the direct and quadrature rotor voltage components as in (24) and (25):

∗ 𝑑𝑆 𝑉 =𝑆 +𝑁∙ − 𝐾 ∙ 𝑠𝑖𝑔𝑛(𝑆) (24) Energies 2021, 14, 4437 𝑑𝑡 8 of 17 𝑑𝑆 𝑉∗ =𝑆 +𝑁∙ − 𝐾 ∙ 𝑠𝑖𝑔𝑛(𝑆 ) (25) 𝑑𝑡

This designed strategyThis designed is implemented strategy is implemented for a direct FOC for a techniquedirect FOC basedtechnique on thebased SSMC on the SSMC method to obtain the minimum reactive power ripple and to reduce the chattering phe- method to obtain the minimum reactive power ripple and to reduce the chattering phenomenon. nomenon. The basic structure of the direct FOC-SSMC control method of the induction genera- The basic structuretor-based of variable the direct speed FOC-SSMC DRWP system control using method the MPPT of the strategy induction is generator-shown in Figure 5. based variable speedThis designed DRWP system control using technique the MPPTis robust, strategy simple, is and shown has ina small Figure response5. This time. de- On the signed control techniqueother hand, is this robust, designed simple, control and technique has a small minimized response the active time. and On reactive the other power rip- hand, this designedples compared control technique to the traditional minimized direct theFOC, active direct andpower reactive control, power and indirect ripples FOC meth- compared to theods. traditional direct FOC, direct power control, and indirect FOC methods.

Figure 5. Direct FOC-SSMCFigure 5. Direct control FOC-SSMC of the IG-based control of DRWPthe IG-based system. DRWP system.

5. Numerical Simulation5. Numerical Simulation The proposed SSMCThe proposed controllers SSMC as applied controllers for theas applied induction for generatorthe induction active generator and reac- active and tive powers havereactive been implemented powers have been using implemented Matlab software using Matlab (from MATLABsoftware (from & Simulink MATLAB® & Sim- ® of MathWorks).ulink In addition, of MathWorks). a comparison In addition, study betweena comparison the SSMCstudy between controllers the withSSMC the controllers traditional PI controllerswith the traditional was carried PI controllers out in terms was ofcarried torque, out current,in terms activeof torque, and current, reactive active and reactive power ripple minimization, wind speed changing, trajectory tracking, and ro- power ripple minimization, wind speed changing, trajectory tracking, and robustness to bustness to induction generator parameter variations. induction generator parameter variations. 5.1. First Test 5.1. First Test The simulations are carried out with a 1.5 MW induction generator attached to a 398 The simulationsV/50 Hz are grid. carried The outparameters with a 1.5of the MW machine induction are given generator in Table attached 1. to a 398 V/50 Hz grid. The parameters of the machine are given in Table1.

Table 1. Parameters of the simulated induction generator.

Parameter Value Pn 1.5 MW Vn 380 V p 2 Rs 0.012 Ω Rr 0.021 Ω Ls 0.0137 H Lr 0.0136 H Lm 0.0135 H J 1000 Kg.m2 fr 0.0024 Nm.s/rad f 50 Hz

The two direct FOC methods, direct FOC method with PI controllers and proposed direct FOC method, are simulated and compared in terms of torque, stator current, reactive and active power ripples, reference tracking, and THD value of current. Figures6–14 show the obtained simulation results. As it is shown in Figures6–9, for the two direct FOC methods, the reactive and active powers track almost perfectly their reference values. On the other hand, Figure9 shows the current of both direct FOC Energies 2021, 14, 4437 9 of 17

methods. It therefore conﬁrms that the amplitudes of the currents depend on the state of the drive system and the value of the load active power. Figures 13 and 14 show the THD value of current of the induction generator-based variable speed DRWP system with MPPT for both direct FOC methods. It can be clearly observed through these ﬁgures that the THD Energies 2021,, 1414,, 44374437 value is minimized for the proposed direct FOC method (0.50%) when compared10 to of the 17

traditional direct FOC method (1.45%).

Figure 6. ActiveActive power. power.

Figure 7. ReactiveReactive power. power.

Figure 8. Torque.Torque.

Figure 9. Stator current.

Energies 2021, 14, 4437 10 of 17

Figure 6. Active power.

Figure 7. Reactive power.

Energies 2021, 14, 4437 10 of 17

Figure 8. Torque.

Energies 2021, 14, 4437 11 of 17 Energies Energies 2021 2021, 14, 14, 4437, 4437 1111 of of 17 17 FigureFigure 9.9. StatorStator current.current.

Figure 10. Zoom (Active power). FigureFigure 10. 10. Zoom Zoom (Active (Active power). power).

Figure 11. Zoom (Torque). FigureFigureFigure 11. 11.11. Zoom ZoomZoom (Torque). (Torque).(Torque).

2400 24002400 2200 22002200 2000 Ias (PI) 2000 Ias (PI) 2000 IasIas (PI) (SSMC) Ias (SSMC) Stator current Ias (A) 1800 Ias (SSMC)

Stator current Ias (A) 1800 Stator current Ias (A) 1800 0.0835 0.084 0.0845 0.085 0.0855 0.086 0.0865 0.0835 0.084 0.0845 0.085 0.0855 0.086 0.0865 0.0835 0.084 0.0845 Time0.085 (s) 0.0855 0.086 0.0865 Time (s) Time (s) Figure 12. Zoom (Current). FigureFigureFigure 12. 12.12. Zoom ZoomZoom (Current). (Current).(Current).

Fundamental (50Hz) = 3027 , THD= 1.45% FundamentalFundamental (50Hz) (50Hz) = =3027 3027 , THD=, THD= 1.45% 1.45% 1 11 0.8 0.80.8 0.6 0.60.6 0.4 0.40.4 Mag (% of Fundamental) 0.2 Mag (% of Fundamental) Mag (% of Fundamental) 0.20.2 0 0 500 1000 1500 2000 00 00 500500 Frequency10001000 (Hz) 15001500 20002000 FrequencyFrequency (Hz) (Hz)

Figure 13. THD (direct FOC method). FigureFigure 13. 13. THD THD (direct (direct FOC FOC method). method).

Energies 2021, 14, 4437 11 of 17

Figure 10. Zoom (Active power).

Figure 11. Zoom (Torque).

2400

2200

2000 Ias (PI) Ias (SSMC)

Stator current Ias (A) 1800

0.0835 0.084 0.0845 0.085 0.0855 0.086 0.0865 Energies 2021, 14, 4437 11 of 17 Time (s) Figure 12. Zoom (Current).

Fundamental (50Hz) = 3027 , THD= 1.45%

0.8

0.6

0.4

Mag (% of Fundamental) 0.2

0 0 500 1000 1500 2000 Frequency (Hz)

Energies 2021, 14, 4437 12 of 17

FigureFigure 13. 13. THDTHD (direct (direct FOC FOC method). method).

Fundamental (50Hz) = 3045 , THD= 0.50%

0.6

0.5

0.4

0.3

0.2 Mag (% of Fundamental) 0.1

0 0 500 1000 1500 2000 Frequency (Hz)

FigureFigure 14. 14. THDTHD (direct (direct FOC-SSMC FOC-SSMC control). control).

5.2. SecondThe zoom Test in the active power, torque, and stator current is shown in Figures 10–12, respectively.In this part, It can we be changed seen that the the values proposed of parameters direct FOC Ls method, Lr, Rs, minimizes Rr, and M the, to ripplesfind out in whichtorque, control stator technique current, and is not active affected power by compared a change toof the parameters. traditional The direct obtained FOC method.results areBased shown on the in resultsFigures above, 15–23. it Note can be that said there that is the a proposedchange in direct active FOC power, method stator has current, proven its efﬁciency in reducing ripples and chattering phenomena in addition to keeping the torque, and reactive power because both torque and current are related to the changing same advantages of the traditional direct FOC method. On the other hand, this designed values of parameters. On the other hand, the classical method was greatly affected by the control scheme minimized the THD value of stator current compared to other techniques change of parameters compared to the proposed control scheme (Figures 19–21), and this (see Table2, where VFDPC is the virtual ﬂux direct power control). is evident in the value of THD (Figures 22 and 23). Thus, it can be concluded that the direct FOC technique with proposed SSMC controllers is more robust than the traditional direct FOC technique with PI regulators.

Figure 15. Active power.

Figure 16. Reactive power.

EnergiesEnergies 2021 2021, ,14 14, ,4437 4437 1212 ofof 1717

FundamentalFundamental (50Hz) (50Hz) = = 3045 3045 , ,THD= THD= 0.50% 0.50%

Energies 2021, 14, 4437 12 of 17 0.60.6

0.50.5

Table 2. 0.4Comparison0.4 of the obtained results with other methods.

0.30.3Reference Technique THD (%) VFDPC 4.19 0.20.2 Ref. [40] Mag (% of Fundamental) Mag (% of Fundamental) DPC 4.88 0.10.1 Ref. [41] FOC 3.7 00 Ref.00 [42]500500 10001000 SMC15001500 20002000 3.05 Frequency (Hz) Ref. [43] RobustFrequency DTC (Hz) control 0.98 Proposed DFOC 1.45 techniques FigureFigure 14.14. THDTHD (direct(direct FOC-SSMCFOC-SSMC control).control).DFOC-SSMC 0.50

5.2.5.2. Second Second Test Test InInIn this thisthis part, part,part, we wewe changed changedchanged the thethe values valuesvalues of ofof parameters parametersparameters LsLs,, LrLr,, RsRs,,, Rr,Rr, andand MM,,, to toto find ﬁndfind out out whichwhich controlcontrol technique techniquetechnique is isis not notnot affected affectedaffected by byby a changeaa changechange of of parameters.of parameters.parameters. The TheThe obtained obtainedobtained results resultsresults are areshownare shownshown in Figures inin FiguresFigures 15–23 15–23.15–23.. Note NoteNote that therethatthat therethere is a change isis aa changechange in active inin active power,active power,power, stator current, statorstator current,current, torque, torque,andtorque, reactive andand reactivereactive powerbecause powerpower because bothbecause torque bothboth and torquetorque current andandare currentcurrent related areare to relatedrelated the changing toto thethe changing valueschanging of valuesparameters.values ofof parameters.parameters. On the other OnOn thehand,the otherother the hand, classicalhand, thethe method classicalclassical was methodmethod greatly waswas affected greatlygreatly by affectedaffected the change byby thethe of changeparameterschange ofof parametersparameters compared comparedcompared to the proposed toto thethe proposcontrolproposeded scheme controlcontrol (Figures schemescheme 19 (Figures(Figures–21), and 19–21),19–21), this is andand evident thisthis isinis evident evident the value in in the the of THDvalue value (Figures of of THD THD 22(Figures (Figures and 23 22 22). and Thus,and 23). 23). it Thus, Thus, can be it it concludedcancan be be concluded concluded that the that that direct the the direct FOCdirect FOCtechniqueFOC techniquetechnique with with proposedwith proposedproposed SSMC SSMCSSMC controllers controllerscontrollers is more isis moremore robust robustrobust than thethanthan traditional thethe traditionaltraditional direct directdirect FOC FOCtechniqueFOC techniquetechnique with with PIwith regulators. PIPI regulators.regulators.

FigureFigure 15. 15.15. ActiveActive power. power.

FigureFigure 16. 16.16. ReactiveReactive power. power.

Energies 2021, 14, 4437 13 of 17 EnergiesEnergies 20212021,, 1414,, 44374437 1313 ofof 1717 Energies 2021, 14, 4437 13 of 17

FigureFigure 17.17. Torque.Torque. Figure 17. Torque.

FigureFigure 18.18. Current.Current. Figure 18. Current.

FigureFigure 19.19. ZoomZoom (Active(Active power).power). Figure 19. Zoom (Active power).

FigureFigure 20.20. ZoomZoom (Torque).(Torque). Figure 20. Zoom (Torque).

Energies 2021, 14, 4437 14 of 17 EnergiesEnergies 20212021,,, 141414,,, 443744374437 1414 ofof 1717

IasIasIas (PI)(PI)(PI) 35003500 IasIasIas (SSMC)(SSMC)(SSMC)

30003000

25002500 Stator current Ias (A) Stator current Ias (A) Stator current Ias (A)

0.4230.423 0.4240.424 0.4250.425 0.4260.426 0.4270.427 0.4280.428 TimeTime (((ss))) FigureFigureFigure 21.21. 21. ZoomZoomZoom (Current).(Current). (Current).

FundamentalFundamental (50Hz)(50Hz) == 29932993 ,, THD=THD= 3.89%3.89% 1.61.61.6

1.41.41.4

1.21.21.2

111

0.80.80.8

0.60.60.6

0.40.40.4 Mag(% Fundamental) of Mag(% Fundamental) of Mag(% Fundamental) of 0.20.20.2

000 000 500500500 100010001000 150015001500 200020002000 FrequencyFrequency (Hz)(Hz)

FigureFigureFigure 22.22. 22. THDTHDTHD (direct(direct (direct FOCFOC FOC method).method). method).

FundamentalFundamental (50Hz)(50Hz) == 30313031 ,, THD=THD= 0.62%0.62%

0.60.60.6

0.50.50.5

0.40.40.4

0.30.30.3

0.20.20.2 Mag (% Fundamental) of Mag (% Fundamental) of Mag (% Fundamental) of 0.10.10.1

000 000 500500500 100010001000 150015001500 200020002000 FrequencyFrequency (Hz)(Hz)

FigureFigureFigure 23.23. 23. THDTHDTHD (direct(direct (direct FOC-SSMCFOC-SSMC FOC-SSMC control).control). control).

Energies 2021, 14, 4437 15 of 17

6. Conclusions This work presented two types of FOC method for an induction generator-based variable speed dual-rotor wind power generation system, with detailed simulation investigation and theoretical analysis. The main ﬁndings are as follows: (1) As in the direct FOC-SSMC method, active and reactive power should not be esti- mated; the direct FOC-SSMC method causes ﬁlter design and converter simplicity. It also improves the transient effectiveness of the controller. (2) Direct FOC method gives more THD value and power ripple. There is no improved system effectiveness in comparison with the direct FOC-SSMC method. (3) Although the robustness of the designed method causes the use of the proposed nonlinear controllers, its characteristics, as stated in part six, such as improved dynamic and transient performance, make it a suitable controller for variable speed dual-rotor wind power production. In conclusion, the classical and proposed direct FOC methods analyzed in this paper may differently meet the imposed performance requirements, as shown in Table3.

Table 3. Comparison between proposed strategy and classical method.

Performance Criteria Classical Technique Proposed Technique Simplicity of calculations + + Improvement of transient - + performance Improvement of dynamic - + response Simplicity of converter and + + ﬁlter design Negligible parameter effects - + on system performance Robustness - + Note: Meaning of the signs used: + (meets the performance criteria) and-(does not meet the performance criteria).

Author Contributions: Conceptualization, H.B.; methodology, H.B.; software, H.B.; validation, N.B.; investigation, H.B.; resources, H.B. and N.B.; data curation, N.B.; writing—original draft preparation, H.B.; supervision, N.B.; project administration, N.B.; Formal analysis: N.B.; Funding acquisition: N.B.; Visualization: N.B.; writing—review and editing: N.B. and H.B. Both authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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