Adv Syst Sci Appl 2022; 01:15–34 Published online at https://ijassa.ipu.ru. Direct Torque Control-Fuzzy Type 2 for Direct Current Link Voltages Balancing of the Five-Level Cascade Converters Used in a Wind Energy Conversion System Abdelhafidh Moualdia1*, Saleh Boulkhrachef1, Patrice Wira2 1LREA Laboratory, Faculty of Technology, University of Medea, Ain d’heb Medea, Algeria 2IRIMAS Laboratory, University of Haute Alsace, Mulhouse, France Abstract: The available power of a wind system depends mainly on the wind speed. In addition, the wind system will give a power output that varies according to the speed of its generator which is a double feed asynchronous machine in our case. In other words, there is an optimal operating point that makes the most of the power available. In this work an innovative technique of capturing maximum power based on type-2 fuzzy systems. The principle of this Maximum Power Point Tracking algorithm is to look for an optimal operating relationship at maximum power and then track the maximum power based on this relationship. As part of the variable speed conversion of wind energy, this article proposes a simplified power electronics for injecting the energy produced in the network, the conversion chain includes a variable speed double feed asynchronous generator, two (back-to-back) converters five-level Neutral Point Clamped type operating in grid side rectifier and rotor-side inverter mode. The main objective of this article is to develop a new stabilization strategy of direct control compatible with voltage inverters at five levels, more particularly Neutral Point Clamped structure. This strategy allows flow and torque control of the double feed asynchronous machine and stabilizes the input capacitor voltages of the inverter. The response of the system obtained with this algorithm makes it possible to validate the soft solution proposed and show, during variation of the wind speed, a fast and precise adaptation of the speed of the double fed induction generator. Keywords: double fed induction generator, direct current link voltage, fuzzy type 2, direct torque control, wind energy, five level converter cascade 1. INTRODUCTION From a general point of view, regardless of the topology, multilevel conversion structures offer huge advantages over a conventional solution, based on a two-level converter [1, 2]. These advantages are visible, on the one hand from a technological point of view and on the other hand from a functional point of view. First of all, the quality of the output signal of the inverter can be improved thanks to the additional degree of freedom which is the number of voltage level [3–6]. The switched voltage is of reduced amplitude and the switching is therefore easier to manage. Despite the advantages of multi-level inverters, the instability of capacitor voltages on the DC side remains the major disadvantage of multi-level NPC (Neutral Point Clamped) inverters [7, 8]. As a result, the imbalance of these voltages leads to the failure of power components and deformation of the output voltage. For this, several solutions are proposed. These solutions include methods based on vector modulation techniques, where the concept of redundant ∗Corresponding author: amoualdia@gmail.com 16 A. MOUALDIA, S. BOULKHRACHEF, P. WIRA voltage vectors has been applied to balance the electrical charge between capacitors [9–11]. However, for high levels, the number of voltage vectors increases considerably and thus the control becomes complex. Other solutions, based on the addition of auxiliary circuits for the balancing of these DC voltages of the inverter, are proposed in the literature . To be able to replace the DC drive and enjoy the advantages of the asynchronous motor, the control must be more and more efficient. DTC (Direct Torque Control) control strategy has emerged as competitive with vector control techniques. This DTC command was invented by I. Takahashi in themid− 1980s. It is based on the separate regulation of the rotor flux and the electromagnetic torque of the double-feed asynchronous generator. In order to provide better control of NPC-structured five-level inverter voltages and achieve better performance, the wind energy conversion system is connected to the power grid using rectifiers controlled by the width modulation. Pulse (PWM). These rectifiers can provide a low harmonic distortion in the input currents, a grid-side adjustable power factor, and a constant DC output voltage. Control of rectifiers based on fuzzy systems is also possible [12]. In particular, the fuzzy controller methodology appears useful when information sources are considered unclear or uncertain. In an ordinary fuzzy system, the membership functions, once determined, are completely precise, and therefore unable to take into account the uncertainty of the linguistic terms used in the premises and consequences of the rules. To solve this limitation, the fuzzy set type-2 was introduced as an extension of the fuzzy set type-1, where each degree of membership of each element is itself a fuzzy set in [0, 1]. [13–15]. First, we first present a description of the DFIG-based wind energy conversion system. The second part of this work will be dedicated to the synthesis of innovative technique of maximum power capture based on type-2 fuzzy systems. The principle of this Maximum Power Point Tracking (MPPT) algorithm is to look for an optimal operating relationship at maximum power and then track the maximum power based on this relationship. In the third step, the development of a stabilizing DTC control, to Fig. 1.1. Wind energy conversion system based on five-level NPC cascaded converters solve the problem of the imbalance of the input voltages of the 5-level converter with NPC structure on the rotor side. Taking advantage of the redundancies of the state of the rotor side converter, producing the same voltage vector, but opposite effects on the voltages of the capacitors, an algorithm is developed. This allows us to balance the capacitor voltages in addition to controlling the torque and flux of the double feed asynchronous generator. The Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) DTC-FUZZY TYPE 2 FOR DC LINK VOLTAGES BALANCING OF THE FIVE-LEVEL CASCADE 17 wind energy conversion system description based on five-level NPC cascaded converters is shown in Figure 1.1. NOMENCLATURE β blade pitch angle; V wind speed (m/s); ρ air density; λ speed ratio; Cp power coefficient; Pm mechanical power (kW); Tm mechanical Torque ; Vsdq, Vrdq dq axis stator and rotor voltages ; isdq, irdq, dq axis stator and rotor current ; ωs, ωr, stator and rotor pulsation (rd/s) ; Φsdq,Φrdq, dq axis stator and rotor flux ; M, mutual inductance ; Ps, Qs generator active and reactive powers ; P1,P2 logical function ; J, f moment of inertia and coefficient of friction ; E1,E2,E3 load conditions ; k Phase number (k=1, 2, 3); C1; C2; C3; C4 DC-link capacitors; UC1; UC2; UC3; UC4 DC bus voltages; IC1; IC2; IC3; IC4 Capacitors currents; Irec1; Irec2; Irec3; Irec4 Output rectifier currents; Iref netk Reference network phase current; Iref rec Reference network phase current; Vsk; isk Stator phase voltage and current; Vsαβ, isαβ Stator voltage and current in the stationary α− β plane Ω,Ωn Rotor speed and speed nominal value; Tem,Tref Electromagnetic torque and reference value; Φs Stator flux magnitude; Φsα,Φsβ Stator flux magnitude in α− β plane fnet Network frequency; VDi Discrete voltage level of vector Vs; Cfl Output Hysteresis flux controller; Ctr Output Hysteresis Torque controller; ABBREVIATIONS USED NPC : Neutral Point Clamped HVDC : high voltage direct current DC : Direct Current DTC : Direct Torque Control PWM : Pulse Width Modulation CSR : Current Source Rectifier IM : Induction machine SVM : Space-Vector Modulation FLC : Fuzzy Logic Controller T1FLS : Type-1 Fuzzy Sets T2FLS : Type-2 Fuzzy Sets PI : Proportional Integral Controller DFIG : Double Fed Induction Generator MPPT : Maximum Power Point Tracking RSC : rotor-side Converter GSC : Grid-side Converter Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 18 A. MOUALDIA, S. BOULKHRACHEF, P. WIRA 2. DESCRIPTION OF THE WIND CONVERSION SYSTEM 2.1. Wind turbine model The mechanical power available on the shaft of a wind turbine can be expressed as [22, 26]: Pm = 0.5Cp (λ) πρR2V 3 1 , (2.1) For the variables speed wind turbines, approximate expression of the power coefficient can be described by the following expression: Cpf (λ, β) = C1 ( C2 λi − C3 − C4 ) exp ( −C5 λi ) +C6λ, (2.2) Where: 1 λi = 1 λ+ 0.08β − 0.035 β3 + 1 (2.3) Where, C1 = 0.5176, C2 = 116, C3 = 0.4, C4 = 5, C5 = 21, C6 = 0.0068.The torque pro- duced by the turbine is expressed in the following way: Tm = Pm Ωm = ( 0.5πρR3V 2 1 ) Cp(λ, β)) λ (2.4) No wind turbine could convert more than 59 of the kinetic energy of the wind into mechanical energy turning the rotor [16]. This is known as the Betz limit and it’s the Cpmax theoretical maximum coefficient of power (for any wind turbine): Cpmax = 16/27 ≈ 0.593. In practice, for the good turbines it’s in the range of 0.45 to about 0.50. The tip speed ratio (λ) for wind (a) (b) Fig. 2.2. (a): for Pitch angle effect on the aerodynamic coefficient of power and (b): for mechanical power output. turbines is the ratio between the rotational speed of the tip of a blade and the actual velocity of the wind, see Figure 2.2. Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) DTC-FUZZY TYPE 2 FOR DC LINK VOLTAGES BALANCING OF THE FIVE-LEVEL CASCADE 19 Table 2.1. Inference matrix de\e NG NM NP EZ PP PM PG NG NG NG NM NM NP NP EZ NM NG NM NM NM NP EZ PP NP NG NM NP NP EZ PP PM EZ NG NM NP EZ PP PM PG PP NM NP EZ PP PP PM PG PM NP EZ PP PM PM PM PG PG EZ PP PP PM PG PG PG Fig. 2.3. Tip speed ratio control (MPPT). 2.2. Maximum power tracking via fuzzy-type 2 systems At a given wind speed, the maximum turbine energy conversion efficiency occurs at an optimal TSR Figure 2.3. Therefore, as wind speed changes the turbine’s rotor speed needs to change accordingly in order to maintain the optimal tip speed ratio TSR and thus to extract the maximum power from the available wind resources. The structure of the fuzzy type-2 regulator is shown in Figure 2.4. In order to have the desired performances, the normalization gains at the input and at the output of the regulator are determined by adjustment. For input and output variables consisting of seven fuzzy sets type-2 interval, the conventional anti-diagonal inference matrix of a fuzzy system is given in Table 2.1. Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 20 A. MOUALDIA, S. BOULKHRACHEF, P. WIRA Fig. 2.4. Structure of the fuzzy type-2 controller. (a) (b) Fig. 2.5. membership functions.(a):membership functions of input variables,(b):membership functions of output variables 2.3. Modelling of the double fed induction generator In the rotating field reference frame of Park, the model of the DFIG is given by the following equations [30, 31]: Vsd = Rsisd + d dt Φsd − ωsΦsq Vsq = Rsisq + d dt Φsq + ωsΦsd Vrd = Rrird + d dt Φrd − ωrΦrq Vrq = Rrirq + d dt Φrq + ωrΦrd, (2.5) Stator and rotor voltages components: Φsd = Lsisd +Mird Φsq = Lsisq +Mirq Φrd = Lrird +Misd Φrq = Lrirq +Misq. (2.6) Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) DTC-FUZZY TYPE 2 FOR DC LINK VOLTAGES BALANCING OF THE FIVE-LEVEL CASCADE 21 Double fed induction generator electromagnetic torque: Cem = Cr + J dΩ dt + fΩ, (2.7) Generator active and reactive powers at the grid side are:{ Ps = Vsdisd + Vsqisq Qs = Vsqisd − Vsdisq. (2.8) 2.4. Five-Level NPC converter Multilevel converters are power-conversion systems composed by an array of power semiconductors and capacitive voltage sources that, when properly connected and controlled, can generate a multiple-step voltage waveform with variable and controllable frequency, phase, and amplitude. The stepped waveform is synthesized by selecting different voltage levels. The numbers of levels of a converter is defined as the number of steps that can be generated by the converter between the output terminal and any reference node within the converter, is usually denoted by N and called neutral. To be called a multilevel converter, each phase of the converter has to generate at least three different voltage levels. This differentiates the classic tw o-level voltage source converter (2L− V SC) from the multilevel family. The neutral clamped inverter, also known as diode clamped inverter. The basic architecture of this inverter discussed in references [17, 18]. The neutral clamped inverter obtained the Fig. 2.6. The Five-Level NPC converter. staircase output voltage. If m is the number of level, then the number of capacitors required on the DC bus are (m -1), the number of power electronic switches per phase are 2(m -1) and the number of diodes per phase are 2(m− 2). The DC bus voltage has three levels using two capacitors C1 and C2, for five levels using four capacitors C1, C2, C3 and C4 as shown in Figure 2.6. Table 2.2 lists the voltage levels and their corresponding switch states. State 1 means that the switch is on, and 0 means that the switch is off. We suppose that all the DC voltage sources are the same and equal to nominal value . The output voltage vector is defined Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 22 A. MOUALDIA, S. BOULKHRACHEF, P. WIRA Table 2.2. Switching states and output voltage of the first leg of the five-level NPC inverter State V1M S11 S12 S13 S14 S15 S16 S17 S18 +2 +2Uc 1 1 1 0 0 0 0 0 +1 +Uc 1 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 -1 −Uc 0 0 1 1 1 0 0 1 -2 −2Uc 0 0 0 1 1 1 0 0 as: Vs = VaMe j0 + VbMe −j2π/3 + VcMe −j4π/3 = Vα + jVβ. (2.9) It can be observed that 24 vectors can be generated by a unique switching state, 18 vectors can be generated using two switching states each (2 redundancy), 12 vectors can be generated using three switching states each (3 redundancies), 6 vectors can be generated using four switching states each (4redundancies), and one vector can be generated using five switching states (5redundancies). [15, 16] 3. DTC FOR FIVE-LEVEL ROTOR SIDE CONVERTER (RSC) In recent years, a new control strategy based on direct control of flux and torque has been proposed. This technique, known as DTC, enables the induction motor to deliver a very quick and accurate torque response.The instantaneous values of flux and torque are calculated from measured variables (voltages and currents) and then controlled directly by selecting optimum inverter switching modes.The objective of this section is to present the DTC of induction machine fed by a five–level NPC inverter. The schematic diagram of the proposed DTC system is shown in Figure 3.7. As in the original DTC principle the α− β plane will be divided into several sectors [26]. In a five-level inverter the number of discrete voltage vectors is more important than those obtained with a two-level inverter. Thus, the α− β plane will be divided into 12 sectors rather than six. At each one of these sectors, an appropriate voltage vector will be assigned to keep flux and torque references as needed.The speed of the stator flux vector is given by the modulus of the applied space voltage vector. Thus, the space voltage vectors will be chosen according to the rotor speed. Voltage vectors with low amplitude will be chosen for low speeds, and vectors with greater amplitude will be chosen for higher speeds. In the five-level inverter, four tables have been used, according to a specific speed range, as shown in Table 2.2 . Three different states are used to identify torque status and two states for flux. 4. CONTROL STRATEGY OF THE BALANCING CAPACITOR VOLTAGE We will present the proposed DTC algorithm to balance DC bus voltages using redundant configurations of the five-level inverter. The, each discrete voltage level can be obtained by more than one switching state. As the voltage evolution for a given capacitor will be different for each state, this redundancy let’s to control the capacitors voltages while the requested space vector voltage is supplied. Based on this property, a control strategy will be Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) DTC-FUZZY TYPE 2 FOR DC LINK VOLTAGES BALANCING OF THE FIVE-LEVEL CASCADE 23 Fig. 3.7. Schematic diagram of the proposed DTC system. Table 4.3. Six groups of redundant vectors Group 1 Vp1 Vp4 Vp7 Vp10 Vp13 Vp16 Group 2 Vp2 Vp6 Vp8 Vp12 Vp14 Vp18 Group 3 Vp3 Vp5 Vp9 Vp11 Vp15 Vp17 Group 4 Vp19 Vp21 Vp23 Vp25 Vp27 Vp29 Group 5 Vp20 Vp22 Vp24 Vp26 Vp28 Vp30 Group 6 Vp31 Vp32 Vp33 Vp34 Vp35 Vp36 presented and applied to a five-level inverter. To do so, we firstly study the effect of different redundant vectors on capacitor voltages. In Table 5.4, all the redundant vectors of the space vector diagram and the corresponding capacitors currents according to the load (i1, i2, i3) are presented. Depending on the forms of relationships (Equation 2.9, 4.10 and 4.11 in Table 4.3), we distinguish six groups of redundant vectors: 4.1. Effect of redundant vectors on capacitor voltages Redundant vectors of each group can increase or decrease capacitor voltages, depending on load conditions sign of (Equation 2.9, 4.10 and 4.11. For groups with one Equation 2.9 (groups 1, 4 and 6), we have two possibilities of load conditions, each one is associated with a logical function: P1 = 1 if E1 > 0 else P1 = 0 P2 = 1 if E1 ≤ 0 else P2 = 0. (4.10) Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 24 A. MOUALDIA, S. BOULKHRACHEF, P. WIRA For groups with three (Equation 2.9, 4.10 (groups 2, 3 and 5), we have six possibilities of load conditions, associated with six logical functions: P1 = 1 if E1 < 0, E2 < 0, and E3 > 0, else P1 = 0; P2 = 1 if E1 < 0, E2 > 0, and E3 < 0, else P2 = 0; P3 = 1 if E1 < 0, E2 > 0, and E3 > 0, else P3 = 0; P4 = 1 if E1 > 0, E2 < 0, and E3 < 0, else P4 = 0; P5 = 1 if E1 > 0, E2 < 0, and E3 > 0, else P5 = 0; P6 = 1 if E1 > 0, E2 > 0, and E3 < 0, else P6 = 0. (4.11) 4.2. Choice of redundancies For each case of redundancy, the vector which reduces the fluctuation voltages in capacitors will be selected. The diagram of the control algorithm is shown in Figure 4.8. We select the vector which charge the undercharged capacitors, and discharge the overcharged ones. To do so, we must measure capacitor voltages and calculate their deviation case. Each deviation case is characterized by a logical function Cj (Table 5.4.). For example, the first case : Uc1 k, then set dIrefr ′′ = dIrefr . • step 4 :If dIrefr ′′ 6= dIrefr ′, then go to step 5. If dIrefr ′′ = dIrefr ′ then set dIrefr = dIrefr ′′ and go to step 6. • step 5 :set dIrefr ′ = dIrefr ′′ and return to step 2. • step 6 : End The procedure for computing dIrefl is very similar, only two changes need to be made: In step 2, we need to find k (1 ≤ k′ ≤M − 1) such that uml ≤ dIrefl ′ ≤ uml , m=k’+1 and in step 3, let F i l = F i for i ≤ k′ and F i l = F i for i > k′ . From the type-reduction stage, we have for each output a type-reduced set. The crisp output of the type-2 fuzzy controller can be obtained by using the average value of dIrefr and dIrefl . Hence, the defuzzified crisp output becomes: dIrefk = dIrefkl + dIrefkr 2 (5.18) Fig. 5.11. Wind speed profile 6. SIMULATION RESULTS In order to demonstrate the feasibility of the proposed control method, simulation testing are undertaken on the structure shown in Figure 1.1. The most commonly encountered disturbances in drive applications are changes in the load torque or changes in the speed. It is important thereby to show if the proposed cascade is able to handle aforementioned transients and ensure the stability of DC-bus voltages. The wind speed profile applied to energy conversion system is shown with in Figure 5.11. The multilevel DTC strategy has been tested by simulation in different level of speed control loop.The reference speed is obtained by the MPPT block. The control objective in this section is to show the performance in both interest operation regions (I and III) of the turbine characteristic. In the region III, one can see that the stator power is limited at its Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) DTC-FUZZY TYPE 2 FOR DC LINK VOLTAGES BALANCING OF THE FIVE-LEVEL CASCADE 29 Fig. 6.12. MPPT result maximum value by the pitch angle control,as shows Figure 6.12. This is approved by the waveforms illustrated in Figure 6.17 of the tip speed ratio (λ) and the power coefficient (Cp). The mechanical speed is kept constant, at its limit value, as plotted in Figure 6.12. Fig. 6.13. Response of electromagnetic torque and rotor flux However, in region I the power is maximized by the MPPT algorithm. In this case, as expected, tip speed ratio and the power coefficient are maintained at constant values see Figure 6.12 (β = 0,λ = λopt = 8.1, Cp = Cp−max = 0.49). The reference tracking reflecting the robustness of the proposed control under random behavior of wind speed. Figure 6.13 shows the rotor flux waveform, it is circular and kept constant at 1.6 Wb. The random evolution of the rotor current magnitude is related to the electromagnetic torque variations and their pulsation is depending on the slip variations. The operation as a generator is illustrated by the negative sign of the electromagnetic torque Cem < 0, with a variable amplitude, which depends on the wind speed evolution, as presented in Figure 6.13 where we can see that the operation with constant power is clear within the over-speed zone. In Figure 6.14, the Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 30 A. MOUALDIA, S. BOULKHRACHEF, P. WIRA capacitor voltages with the proposed DTC balancing strategy are shown . It can be seen that the balancing of the capacitor voltages is achieved sufficiently over the full speed state and for all load torque of induction machine, which prove that the stability of DC voltages with proposed strategy is independent of machine operating points. In the study- state condition, the maximum of each capacitor voltage ripple is less than 4V (2%) , which shows the effectiveness of the DTC balancing strategy. Consequently, the different between the voltages capacitor tends to zero, as shown in Figure 6.15. Fig. 6.14. Response of DC-link voltages with proposed DTC control strategy. Fig. 6.15. Error DC-link voltages. 7. CONCLUSION In this work, the application of direct torque control in a wind energy conversion system supplied by a five level NPC back-to-back converter has been presented. The choice of this Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) DTC-FUZZY TYPE 2 FOR DC LINK VOLTAGES BALANCING OF THE FIVE-LEVEL CASCADE 31 Fig. 6.16. Response of stator and rotor currents structure allows a bidirectional flow of power, and provides regeneration capability.Another advantage of the back-to-back system is that it can control easily the input power factor. The effectiveness of the proposed DTC-based voltage balancing strategy it demonstrated under various operating conditions of double fed induction generator. Is may therefore be concluded that the proposed multilevel direct torque control not only has the advantage of reducing the undesirable torque ripple, but also has the additional advantage of preventing the voltage drift phenomen on of the DC-link capacitors of the back-to-back system, longer life of DC-link capacitors can be achieved. Furthermore, the employment of multilevel topology improves the stator voltage quality, reducing electromagnetic interference and isolation stress problems of windings. This results in the reduction of radiated emissions, which makes this kind of drives a less polluting system than the traditional two-level drive. In addition, this study has successfully demonstrated the application of type-2 fuzzy systems to control the DC-link voltage, and the maximization of power tracking. It found that the type-2 fuzzy control scheme could achieve good performance in terms of overshoot, steady-state error, torque disturbance, and variable speed tracking. Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 32 A. MOUALDIA, S. BOULKHRACHEF, P. WIRA Fig. 6.17. Response of stator active and reactive power ACKNOWLEDGEMENTS The research is part of a project PRFU’2020, realized respectively in the laboratory of electrical engineering and automatic LREA research, University of Medea, and IRIMAS Laboratory, University of Haute Alsace, Mulhouse, France. REFERENCES 1. Polinder, H., F. F. A. Van Der Pijl, G. J.de Vilder and P. J. 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Adv Syst Sci Appl (2022) Introduction Description of the wind conversion system Wind turbine model Maximum power tracking via fuzzy-type 2 systems Modelling of the double fed induction generator Five-Level NPC converter DTC for five-level rotor side converter (RSC) Control strategy of the balancing capacitor voltage Effect of redundant vectors on capacitor voltages Choice of redundancies Control of five-level grid side converter (GSC) Type-2 Fuzzy Logic Controller Design Simulation Results Conclusion