International Journal of Energetica (IJECA) https://www.ijeca.info ISSN: 2543-3717 Volume 4. Issue 2. 2019 Page 42-53 IJECA-ISSN: 2543-3717. December 2019 Page 42 VOLTAGE SENSORLESS BASED VIRTUAL FLUX CONTROL OF THREE LEVEL NPC BACK-TO-BACK CONVERTER DFIGUNDER GRID FAULT Imad Merzouk 1 , Mohamed Mounir Rezaoui 1 , Noureddine Bessous 2* , Abdsalem Gafazi1 1LAADI, Faculty of Science and Technology, University of Djelfa 17000 DZ, ALGERIA 2Faculty of Science and Technology, University of El Oued 39000 DZ, ALGERIA Email*: nbessous@yahoo.fr Abstract – In this paper, a harmonic elimination of grid and stator currents of doubly fed induction generator (DFIG) in case of grid fault without line voltage sensors is proposed . This can be achieved by compensating power based on virtual flux voltage sensorless technique. Direct power control with space vector modulation (DPC-SVM) is used to control both grid-side (GSC)and rotor-side converters (RSC). To achieve the control objective, compensated active and reactive powers are calculated based on virtual flux technique with balanced and harmonic free current as a control target. A theoretical analysis of active and reactive powers under unbalanced voltage source is clearly demonstrated and the effect of grid fault on the performance of DFIG is profoundly discussed. Simulation results verified the effectiveness of the modified control strategy. Keywords: DFIG,DPC-SVM, virtual flux, compensating power, grid fault Received: 17/10/2019 – Accepted: 25/11/2019 NOMENCLATURE 1.1 Subscript �:Mutual. �, �: Two axis stationary reference frame. �, �:Two-axis direct and quadrature synchronous reference frame. �, �:Stator and rotor reference frame. +, −, 5: Positive, negative sequence and harmonic component. 1.2 Superscript �, �: Angle and angular speed. �, �:Time constant and leakage factor. �: Source voltage. �: Converter terminals voltage. �: Line current. �, �: Input filter inductance and resistance. �, �: Apparent, active and reactive powers. �: Machine flux. � : Virtual flux. 1.3 abbreviation DFIG: Doubly fed induction Generator. DPC : Direct power control GSC: Grid side converter. RSC: Rotor side converter. PNSC:Positive-negative-sequence calculator. PWM: Pulse width modulation. SOGI: Second order general integrator. SVM: Space vector modulation. Abder Image placée Imad Merzouk et al IJECA-ISSN: 2543-3717. December 2019 Page 43 2. INTRODUCTION Doubly fed induction generator (DFIG) connected to three level NPC back-to-back converter has been widely used in recent years due to its several advantages. Some of its advantages are speed operation, controllable power factor, improved system efficiency, very low harmonic distortion, low electromagnetic interferenceand most importantly, reduced converter rating, which is typically 30% of the generation rating , therefore, decreased cost and power loss [1-4]. One drawback of DFIG is its sensitivity to any grid distortion because the stator is directly connected to the grid. This fact may limit the use of DFIG especially in wind energy generation due to imposed electricity code. Hence the power injected in the grid must be performed [5-8]. The control of two level GSC under grid fault was firstly studied in the works of [9-12].Based on power analysis under grid unbalance, the referencing currents were calculated and then used in classical voltage oriented control. After that [13] generalized the study to GSC and RSC for DFIG. But the control became more complex when the grid is unbalanced and harmonically distorted.In addition, the tuning of PI gains constitutes a barrier to the use of this method. In [13-16 ] a modified DPC for GSC and RSC was proposed to achieve one of three selective control targets: obtaining sinusoidal and symmetrical grid current, removing reactive power ripplesor removing active power ripples under unbalanced supply. The results obtained were good,but the study is in case of unbalance grid only. [17] Investigated the method of grid connected three level NPC converter and generalized the study to unbalanced and harmonically polluted grid. Thus, the introduction of voltage sensorless is a good alternative for robust and economic operation [18]. Virtual flux technique is the most responding technique for voltage sensorless control of GSC. In general, filters are used to estimate virtual flux [19- 21]. But under unbalanced conditions, where the separating positive and negative sequences are needed, cascading filter must be used [22]. However, it creates more time delay and reduces the accuracy. Double second order generalized integrator (DSOGI) is a good alternative to remove the drawback of cascading filter, it could estimate the virtual flux and separate sequences of virtual flux and grid current [23]. This paper proposes a voltage sensorless control scheme for three level NPC back-to-back converter DFIG under unbalanced and harmonically polluted grid in order to get sinusoidal and symmetrical grid and stator currents. To achieve that, the referencing current is calculated by the instantaneous power theory. The virtual flux isestimated using DSOGI method which is proposed by [23]. The effectiveness of the proposed method is verified by simulation in MATLAB environment. The electrical circuit of the studied system is ullistrated in Figure1 3. MODELING OF DFIG DFIG voltage and flux equations, expressed in the rotating reference frame, are given by: ⎩ ⎪ ⎨ ⎪ ⎧��� = ����� + � �� ��� − ����� ��� = ����� + � �� ��� + ����� ��� = ����� + � �� ��� − ����� ��� = ����� + � �� ��� + ����� � (1) ⎩ ⎨ ⎧ ��� = ����� + ����� ��� = ����� + ����� ��� = �����+����� ��� = �����+����� � (2) Stator active and reactive powers are given by: � �� = ������ + ������ �� =������ − ������ � (3) Setting the stator flux vector aligned to d-axis and neglicting the per phase stator resistance [15]. � ��� = �� ��� = 0 � (4) � ��� = 0 ��� = �� = ���� � (5) Substuting in (2). � �� = ����� + ����� 0 = ����� + ����� � (6) The relation between the stator and rotor currents is set from equation(6): � ��� = − �� �� ��� + �� �� ��� = − �� �� ��� � (7) Imad Merzouk et al IJECA-ISSN: 2543-3717. December 2019 Figure.1. Simplified electrical circuit of a 3L-NPC back-to-back DFIG Stator active and reactive powers in (3) can be written as: � �� = −����� = − ���� �� ��� �� = −����� = − ���� �� ��� + �� � ���� � (8) Rotor voltages can be expressed by: � ��� = ����� − ��� ��� − �� � �� � ��� ��� = ����� + ��� ��� − �� � �� � ��� + � ���� �� � (9) Figure.2 shows the detailed model of DFIG. 1 ��� − �� 2 �� � � + �� − �� �� �� 1 ��� − �� 2 �� �� + �� − �� �� �� ��� ��� − �� 2 �� � ��� ��� − �� 2 �� � � �� �� �� �� 2 ���� − − ��� ��� ���� ���� Figure.2. Simplified model of DFIG 4. CLASSICAL CONTROL STRATEGY 4.1. RSC control If we neglect the coupling terms in equation (9), and replace (8) in (9) we can control the stator active and reactive powers. The measured statoricactive and reactive powers are compared with the referencing one, and then PI regulators are used as controllers. The output of PI regulators addedtocompensating terms provide the required rotor voltage as illustrated in Figure 3. ��� ��� ��. �� �� ��. �� ���� Figure.3. Direct active and reactive powerscontrol of DFIG 4.2. GSC control For the GSC, the well known DPC-SVM is chosen as control algorithm which details is summarized in Figure 4. The outer control loop provide the required active power to obtain the desired dc-link voltage level.The measured active and reactive powers are compared with the referencing one, and then PI regulators are used as controllers instead look-up-table[24]. The two regulators provide the reference voltage applied to the input of the converter, after that the switching signals are generated by SVM block [25, 26]. Figure.4. DPC-SVM control of GSC Imad Merzouk et al IJECA-ISSN: 2543-3717. December 2019 5. POWER ANALYSIS UNDER GRID FAULT 5.1. Virtual flux estimation Virtual flux (VF) concept is the most adopted method to estimate grid voltage for GSC. By integrating ac-voltage we get the virtual flux as follows: ���� = ∫ ����� (10) Replacing ac-voltage by its equivalent value extracted from the ac-side converter model we get: ���� = ����� + ∫������ + ������� (11) ����is estimated from the switching state and dc-link voltage. Under ideal conditions, the VF has only positive-sequence components, but during grid fault, negative and harmonic sequences also appear in the virtual flux. And thus,positive,negative and harmonic sequences have to be separated in order to control the converter.Positive and negative sequence calculator (PNSC) is used to calculate the positive and negative sequences for each order harmonics. As shown in Figure 5-a the PNSC needs the instantaneous values of the VF and its quadratic value. To get these values, Double Second Order Generalized Integrator (DSOGI) is one of the most feasible solutions proposed so far in the literature for its good results in terms of the accuracy and its capability for grid synchronization [23]. The transfer function for the SOGI-QSG is given by: �(�) = �(�)� �(�) = �.��́ ����.�́.���� (12) �(�) = �(�)� �(�) = �.�′ � ����.�́.���′ � (13) The structure of (SOGI) is given in Fig.5-b. where the constant K is the SOGI gain that determines the system dynamics (k is selected as k =√2 for optimum value time response and overshoot). The complete structure of virtual flux estimation with sequences separation is illustrated in Figure 6. 5.2. Powers equations With the virtual flux approach active and reactive powers can be calculated from: � � = � � �(������ − ������) � = − � � �(������ + ������) � (14) Using symmetrical component theory [27]. �� = � � �(��� � ��� � − ��� � ��� � + ��� � ��� � − ��� � ��� � + ��� � ��� � − ��� � ��� � + ��� � ��� � − ��� � ��� � + ��� � ��� � − ��� � ��� � + ��� � ��� � − ��� � ��� � + ��� � ��� � − ��� � ��� � + ��� � ��� � − ��� � ��� � + ��� � ��� � − ��� � ��� � ) (15) �� = − � � �(��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + �� ���� � ) (16) Compared with active and reactive powers obtained under ideal voltages supply, many additional terms appear under grid fault. These terms result from the interaction between each sequence of the voltage (positive, negative and 5 th harmonic) with the sequences of the current separately. These additional terms are responsible of the poor performance of the DFIG, especially the distorted stator currents. According to equations (15) and (16) active and reactive powers can be regrouped in four terms: � = ��� + ��� + ��� + ��� (17) Where: ⎩ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎧��� = 3 2 �(��� � ��� � − ��� � ��� � + ��� � ��� � − ��� � ��� � ) +��� � ��� � − ��� � ��� � ��� = 3 2 �(��� � ��� � − ��� � ��� � + ��� � ��� � − ��� � ��� � ) ��� = 3 2 �(��� � ��� � − ��� � ��� � + ��� � ��� � − ��� � ��� � ) ��� = 3 2 �(��� � ��� � − ��� � ��� � + ��� � ��� � − ��� � ��� � ) � (18) P1 is the average active power delivered to the stator and it is a constant power. P2 represents the interaction between the positive and the negative sequences of the voltages and the currents. P3 represents the interaction between the positive and the 5 th harmonic sequences of the voltages and the currents. P4 represents the interaction between the negative and the 5 th harmonic sequences of the voltages and the currents. The same analysis was carried for the reactive power: Imad Merzouk et al IJECA-ISSN: 2543-3717. December 2019 + + - - 1 1 s s k SOGI � � � �� + + + + + + - - 1/2 1/2 PNSC �αβ � SOGI SOGI �α ��α �β ��β ��� + ��� − Figure.5. PNSC and SOGI structure - + - - + - - + - - + - - + - - + - - + - - + - - + - - + - - + - - + - � � � � � � � � � � � � ���� ���� ���� ���� - + - - + - - + - - + - - + - - + - - + - - + - - + - - + - - + - - + - � � � � � � � � � � � ���� ���� ���� ���� � �SOGI 1 �SOGI2 �SOGI3 �SOGI 1 �SOGI2 �SOGI3 �SOGI n �SOGI n � Resistance voltage compensation Inductor flux compensation ����� � ���� � ����� 3 ���� 3 ���� 2 ����� 2 ����� 1 ���� 1 ���� 1+ ���� 1− ���� 2− ���� 2+ ���� 3+ ���� 3− ���� �− ���� �+ ���� � ���� � ���� � ���� �−1 ���� 3 ���� 3 ���� 2 ���� 2 ���� 2 ���� 1 ���� 1 ���� 1 ���� ���� 1+ ���� 1− ���� 2− ���� 2+ ���� 3+ ���� 3− ���� �− ���� �+ ���� �− ���� �+ ���� 3− ���� 3+ ���� 2+ ���� 2− ���� 1− ���� 1+ ���� 1 ����� 1 ����� 2 ���� 2 ���� 3 ����� 3 ����� � ���� � ���� 1 ���� 1 ���� 1 ���� 2 ���� 2 ���� 2 ���� 3 ���� 3 ���� � ���� � ���� � ���� �−1 ���� Figure.6. Complete structure of virtual flux estimation with sequence separation Imad Merzouk et al IJECA-ISSN: 2543-3717. December 2019 � = ��� + ��� + ��� + ��� (19) ⎩ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎧��� = − 3 2 �(��� � ��� � + ��� � ��� � + ��� � ��� � +��� � ��� � + ��� � ��� � + ��� � ��� � ) ��� = − 3 2 �(��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � ) ��� = − 3 2 �(��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � ) ��� = − 3 2 �(��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � ) � (20) 6. MODIFIED CONTROL STRATEGY Classical DPC shows good performance under ideal voltage supply. But, unbalanced and or harmonically polluted grid voltages will result in significant low-order harmonic components in the grid and stator currents, which are caused by the negative and harmonic components in the voltages. Thus, in this paper,a modified strategy is proposed to improve the behavior of DFIG under grid fault. For symmetrical and harmonic free components of stator/grid current we must make the negative component of current in equations (15) and (16) equal to zero so we get: ⎩ ⎪ ⎨ ⎪ ⎧ �� = � � �(��� � ��� � − ��� � ��� � + ��� � ��� � − ��� � ��� � + ��� � ��� � − ��� � ��� � ) �� = − � � �(��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � + ��� � ��� � ) �(21) omparing equations (21) and (14) we get the compensation power as: ⎩ ⎪ ⎨ ⎪ ⎧ ������ = � � (��� � ��� � − ��� � ��� � +��� � ��� � − ��� � ��� � ) ������ = � � (��� � ��� � + ��� � ��� � +��� � ��� � + ��� � ��� � ) � (22) The same analysis carried out for GSC was used to control RSC, substituting grid current by stator current in all active and reactive power equations. 7. SIMULATION RESULTS Simulation studies of the GSC and RSC under unbalanced and grid fault conditions were carried out using MATLAB/simulink. The system parameters are given in the appendix. The complete structure of the proposed control is shown in Figure7. 7.1 Balanced case The grid is assumed balanced and perfectly sinusoidal with a change in the reference value of the active power of DFIG at instant 0.8 s (from -1.5 to -2MW) and an increase of the reactive power at instant 1s (from 0 to 30KVar) of GSC. The result are shown in Figs.8 to 12. + - - + + - + + - - Vdc 1 Vdc 2 ��� �� � � � � � � �� �� ��� �� + + + + + + + - - - - - �� �� �� �� �� �� �� �scal Qscal �scomp Qscomp �sref Qsref �gref Qgref �gcal Qgcal �gcomp Qgcomp ����� ����� � � ��� +,− ���� +,− � ���� +,− � Figure.7. Control scheme under grid fault Imad Merzouk et al IJECA-ISSN: 2543-3717. December 2019 Figure.8. Dc-link voltage, vdc1and vdc2 Figure.9. Grid current, voltage and current Figure.10. Grid estimated and measured active and reactive powers Figure.11. Stator active and reactive powers Figure.12. Virtual flux components It is noted that DC voltage follows its reference and the balancing of continuous sources is always ensured as shown in Fig.8. Grid currents are sinusoidal and balanced with a unit power factor that shifts with the change in reactive power. The change of the stator power causes a proportional variation in the power of GSC but does not affect the value of the continuous bus as well as the reactive power on the GSC. The change of the reactive power on the grid causes a change in the power factor on the grid side, however, and all the other quantities remain practically unchanged. The measured and estimated active and reactive powers are coincide as seen in Fig.10, so the DSOGI can estimate the active and reactive powers with infinite precision. Figure12 shows the (α and β) component of the virtual flux. It is clear that the SOGI is able to estimate the virtual flow with a good dynamic and excellent robustness with respect to the changes made. 7.2 Unbalanced case Introducing a voltage drop of 20% in phase 3 at time 0.7s then an overvoltage of 20% in phase 1 at time 0.8s. The compensation powers are injected at the instant 0.9s for GSC and 1s for RSC and the results obtained are shown in the figures above. 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1900 1950 2000 2050 2100 2150 2200 V d c (V ) 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 850 900 950 1000 1050 1100 1150 t(s) V d c 1 ,2 0.75 0.8 0.85 0.9 0.95 1 1.05 -200 -150 -100 -50 0 50 100 150 200 ig a b c (A ) 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 -600 -400 -200 0 200 400 600 t(s) E g a ,3 x ig a 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 -1.5 -1.4 -1.3 -1.2 -1.1 -1 -0.9 -0.8 x 10 5 p g ,p g e 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 -1 0 1 2 3 4 5 6 x 10 4 t(s) q g ,q g e pge pg qge qg 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 -2.5 -2 -1.5 -1 x 10 6 p s (W ) 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 -5 0 5 x 10 5 t(s) q s (V a r) 0.75 0.8 0.85 0.9 0.95 1 1.05 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 t(s) p h ig a lp h a ,p h ig b e ta Imad Merzouk et al IJECA-ISSN: 2543-3717. December 2019 Figure.13. Dc-link voltage, vdc1and vdc2 Figure.14. Grid current, voltage and current Figure.15. Grid estimated and measured active and reactive powers Figure.16. Positive, negative component of virtual flux and positive component of current In Figures. 13~16, the behavior of the GSC has been demonstrated. After the introduction of the compensation powers, the system remained stable and the currents became balanced and sinusoidal with a unit power factor. The estimated and measured active and reactive powers are coincide with each other. In Figure16, we see that the negative sequence of the virtual flux is zero before the instant 0.7s, then we detect a negative sequence with a transient time about 0.02s and its amplitude is amplified at instant 0.8s. Figure.17. Stator active and reactive powers 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1900 1950 2000 2050 2100 v d c (V ) 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 920 940 960 980 1000 1020 1040 1060 1080 t(s) v d c 1 ,2 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 -150 -100 -50 0 50 100 150 ig a b c (A ) 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 -800 -600 -400 -200 0 200 400 600 800 t(s) E a ,3 x ig a 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 -11 -10.5 -10 -9.5 -9 -8.5 -8 -7.5 x 10 4 p g (W ) 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 -2 -1.5 -1 -0.5 0 0.5 1 1.5 x 10 4 t(s) q g (V a r) 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 -2 -1 0 1 2 p h ia lp h a + ,b e ta + (w b r) 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 -0.2 -0.1 0 0.1 0.2 p h ia lp h a -, b e ta -( w b r) 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 -100 -50 0 50 100 t(s) ia lp h a + ,i b e ta + (A ) 0.75 0.8 0.85 0.9 0.95 1 1.05 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 x 10 6 p s (W ) 0.75 0.8 0.85 0.9 0.95 1 1.05 -3 -2 -1 0 1 2 3 x 10 5 t(s) q s (V a r) Imad Merzouk et al IJECA-ISSN: 2543-3717. December 2019 Figure.18. Stator and rotor current The same conclusion can be made for the GSC whose results are shown in Figures.17 and 18. It is observed that the control proposed is capable of improving the waveform of the stator currents by acting on the rotor variables. Stator currents become sinusoidal and balanced and rotor current fluctuations are minimized with the presence of ripples in the stator power. 7.3 Distorted case To verify the wide validity of the proposed method, a test of the cascade under harmonically polluted grid was performed. In our case, the disturbance is the superposition of 20% of the 5 th harmonic on the fundamental of the grid voltage. The system parameters and operating point are always kept the same as before. The presence of the 5 th harmonic in the grid creates pulsating terms in the DC voltage, their frequency is six times that of the grid frequency. The reflected pulses combined with the SVM fundamentals generate the 7 th order harmonic in the grid currents. These harmonics can be eliminated by applying the proposed command as shown in Figuress.19~22. The THD of the grid currents of the proposed control is only 1.19%, contrary to conventional methods which have a THD of 20.56%. Figure.19. Dc-link voltage, vdc1and vdc2 Figure.20. Grid current, voltage and current Figure.21. Grid estimated and measured active and reactive powers 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 -3000 -2000 -1000 0 1000 2000 3000 is a b c (A ) 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 -3000 -2000 -1000 0 1000 2000 3000 t(s) ir a b c (A ) 0.8 0.85 0.9 0.95 1 1.05 1900 1950 2000 2050 2100 v d c (v ) 0.8 0.85 0.9 0.95 1 1.05 900 950 1000 1050 1100 t(s) v d c 1 ,2 0.85 0.9 0.95 1 -150 -100 -50 0 50 100 150 ig a b c (A ) 0.85 0.9 0.95 1 -800 -600 -400 -200 0 200 400 600 800 t(s) E a ;3 x ig a 0.85 0.9 0.95 1 1.05 -12 -11 -10 -9 -8 -7 -6 x 10 4 p g (W ) 0.85 0.9 0.95 1 1.05 -3 -2 -1 0 1 2 x 10 4 t(s) q g (V a r) Imad Merzouk et al IJECA-ISSN: 2543-3717. December 2019 Figure ig.22. Positive, 5th harmonic component of virtual flux and positive component of current Likewise, the grid fault has a harmful impact on the stator and rotor currents of the DFIG as shown in Figures.23 and 24. But after the injection of the compensation powers at the instant 1s, we observe a significant improvement in the waveform of the stator currents where the THD is decreased from 20.56 % to 3.94% driven by a minimization of the fluctuations in the rotor currents. Figure.23. Stator active and reactive powers Figure.24. Grid current, voltage and current 7.4 Unbalanced and distorted case Finally the system is tested under a very severe case where the imbalance and the harmonic are introduced together. As shown inFigures.25,26 and 27, the control technique proposed with the virtual flux always proves its validity under all conditions. The SOGI is capable of estimating and decomposing the virtual flux with precession and with good dynamics. The target objective is achieved and, in our case, we were able to have sinusoidal and balanced currents on the grid and stator. The stability of the system is always assured in the different passages from the ideal to the abnormal. Figure.25. From the top to the bottom: dc-link voltage, grid current, grid active and reactive powers 0.75 0.8 0.85 0.9 0.95 1 -2 -1 0 1 2 p h ig a lp h a + ,b e ta + (w b r) 0.75 0.8 0.85 0.9 0.95 1 1.05 -200 -100 0 100 200 p h ig a lp h a 5 ,b e ta 5 (w b r) 0.75 0.8 0.85 0.9 0.95 1 1.05 -200 -100 0 100 200 t(s) ig a lp h a + ,b e ta + (A ) 0.75 0.8 0.85 0.9 0.95 1 1.05 -2 -1.8 -1.6 -1.4 -1.2 -1 x 10 6 p s (W ) 0.75 0.8 0.85 0.9 0.95 1 1.05 -5 0 5 x 10 5 t(s) q s (v a r) 0.85 0.9 0.95 1 1.05 -3000 -2000 -1000 0 1000 2000 3000 is a b c (A ) 0.85 0.9 0.95 1 1.05 -3000 -2000 -1000 0 1000 2000 3000 t(s) E a ,i s a 0.75 0.8 0.85 0.9 0.95 1 1.05 1800 1900 2000 2100 v d c (V ) 0.75 0.8 0.85 0.9 0.95 1 1.05 -100 0 100 ig a b c (A ) 0.75 0.8 0.85 0.9 0.95 1 1.05 -1.5 -1 -0.5 x 10 5 p g (W ) 0.75 0.8 0.85 0.9 0.95 1 1.05 -5 0 5 x 10 4 t(s) q g (V a r) Imad Merzouk et al IJECA-ISSN: 2543-3717. December 2019 Figure. 26. From the top to the bottom: Positive,negative, 5th harmonic component of virtual flux and positive component of current Figure.27. Stator active and reactive powers, stator current, stator current and voltage 8. Conclusion This paper has proposed sensorless compensated control scheme based on improved direct power control with space vector modulation (DPC-SVM) for doubly fed induction generator supplied by distorted grid voltage. In order to obtain sinusoidal grid and stator currents under grid distortion, compensated powers are calculated and added to the original referenced power to achieve balanced and high quality grid/stator current. The positive, negative and harmonic sequences of the virtual flux and the current are extracted using SOGI filter. The proposed method proves its capability of yielding sinusoidal grid and stator currentwith unity power factor under severe unbalanced voltage source. REFERENCES 1. Portillo, R. ; Vazquez, S.; Leon, J.I.; Parts, M.M and Franquelo, L.G." 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Power circuit parameters Items Symbol Value Nominal Power P 2MW Stator resistance �� 12 �Ω Rotor resistance �� 21 �Ω Stator inductance �� 0.0137 H Rotor inductance �� 0.01367 H Mutual inductance �� 0.0135H Number of pole pairs � 2 Input filter inductance L 12�H Input filter resistance � 0.3Ω Dc-bus capacitor ��� 500μ� DC voltage ��� 400� AC source voltage � 690� https://doi.org/10.1049/iet-pel.2010.0160 https://doi.org/10.1109/TIE.2012.2217718 https://doi.org/10.1109/TEC.2011.2180389 https://doi.org/10.1109/TPEL.2013.2258943 https://doi.org/10.1016/j.conengprac.2017.05.002 http://ieeexplore.ieee.org/document/7933126/ http://ieeexplore.ieee.org/document/7933126/ http://ieeexplore.ieee.org/document/7933126/ http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7873788 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7873788 https://doi.org/10.23919/CJEE.2016.7933126 https://doi.org/10.1109/TPEL.2015.2453129 https://ieeexplore.ieee.org/document/8353122/ https://ieeexplore.ieee.org/document/8353122/ https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=28 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=28 https://doi.org/10.1109/TIA.2018.2832122 https://doi.org/10.1109/TIE.2014.2361802 https://doi.org/10.1109/TIE.2010.2042420 http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=%22Authors%22:.QT.Jon%20Are%20Suul.QT.&newsearch=true http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=%22Authors%22:.QT.Alvaro%20Luna.QT.&newsearch=true http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=%22Authors%22:.QT.Pedro%20Rodr%C3%ADguez.QT.&newsearch=true http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=%22Authors%22:.QT.Tore%20Undeland.QT.&newsearch=true http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=%22Authors%22:.QT.Tore%20Undeland.QT.&newsearch=true http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=63 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6200448 https://doi.org/10.1109/TPEL.2012.2190301 https://doi.org/10.1109/TPEL.2014.2387694 https://doi.org/10.1109/TIE.2016.2538208 https://digital-library.theiet.org/content/journals/10.1049/iet-pel.2015.0653 https://digital-library.theiet.org/content/journals/10.1049/iet-pel.2015.0653 https://digital-library.theiet.org/content/journals/10.1049/iet-pel.2015.0653 https://doi.org/10.1049/iet-pel.2015.0653 https://doi.org/10.1109/TPEL.2016.2584385 NOMENCLATURE 1.1 Subscript 1.2 Superscript 2. INTRODUCTION 3. MODELING OF DFIG 4. CLASSICAL CONTROL STRATEGY 4.1. RSC control 4.2. GSC control 5. POWER ANALYSIS UNDER GRID FAULT 5.1. Virtual flux estimation 5.2. Powers equations 6. MODIFIED CONTROL STRATEGY 7. SIMULATION RESULTS 7.1 Balanced case 7.2 Unbalanced case 7.3 Distorted case 7.4 Unbalanced and distorted case 8. Conclusion REFERENCES