Microsoft Word - 36-3007_s_ETASR_V9_N5_pp4775-4782 Engineering, Technology & Applied Science Research Vol. 9, No. 5, 2019, 4775-4782 4775 www.etasr.com Louarem et al.: An Efficient Active and Reactive Power Control of DFIG for a Wind Power Generator An Efficient Active and Reactive Power Control of DFIG for a Wind Power Generator Sabah Louarem Department of Electrical Engineering, Laboratory DAC HR, Ferhat Abbas University Setif 1, Algeria slouarem@univ-setif.dz Tarek Bouktir Department of Electrical Engineering, Ferhat Abbas University Setif 1, Algeria tbouktir@univ-setif.dz Djamel Eddine Chouaib Belkhiat Department of Physics, Laboratory DAC HR, Ferhat Abbas University Setif 1, Algeria djamel.belkhait@univ-setif.dz Saad Belkhiat Department of Electrical Engineering, Laboratory DAC HR, Ferhat Abbas University Setif 1, Algeria sbelkhiat@univ-setif.dz Abstract—During the last decade, wind energy gained much importance as an energy source in power systems. DFIG energy is one of the most widely accepted types of renewable energy generation because of its several benefits. This paper presents a comparative study on the performance of different control strategies for DFIG wind turbines: proportional––––integral (PI), Artificial Neural Networks (ANN), ��, and adaptive Fuzzy PI controller. Simulation results show that DFIG’s performance, dynamic response, and robustness against machine parameter variations are improved with ��control technique. Keywords-wind energy; DFIG; PI controller; ANN controller; �� controller; adaptive fuzzy PI controller I. INTRODUCTION In the last few years, severe environmental problems attracted the world’s attention to renewable energy utilization [1]. Renewable energy sources, safe and reliable for the environment, are locally available energy sources [2]. Among them, wind power has received considerable attention [3]. Wind energy conversion systems (WECS) can be classified in two categories: variable and fixed-speed WECS. Among these techniques, variable speed wind generators are frequently used compared to fixed-speed systems because of their efficient energy production, improved power quality and dynamic performance during grid faults [4]. In this context, the doubly- fed induction generator (DFIG) has proved its worth as a powerful solution to improve the power rating of wind [4-5]. Several control algorithms have been proposed to improve DFIG-based wind turbine system’s behavior during normal operation [6]. Most of these control laws were generally based on the vector control concept. For instance, decoupled control of active and reactive power in a DFIG-based wind energy conversion system with conventional PI controllers has been proposed in [7]. The main disadvantage of this kind of controllers is that they require accurate knowledge of machine’s parameters [8]. To address this issue, several studies focused on advanced and robust controllers have been conducted. For example, Predictive Functional Control (PFC) [9] was proposed in order to reduce the incidence of machine’s parameter variations. In the same context, a predictive power controller synthesized by using a linearized state-space model of DFIG has been proposed in [10]. The design of an Adaptive Fuzzy Gain Scheduling of Proportional Integral controller (AFGPI) has been performed in [11] to address the issue of parameter changes and satisfactory power response was obtained, compared to the conventional PI controller. A neuronal controller has been designed in [12] to control the rotor currents of DFIG. The robustness of the proposed controller has been tested when the stator and the rotor self- inductances increased by 20%. Another robust H� control design, based on a vector control strategy, has been carried out in [13] for the purpose of controlling active and reactive power flow between DFIG and the grid. The tracking control performance of the proposed controller was evaluated by modifying the machine's parameters. The obtained simulation results were satisfactory, showing the robustness of the H� compared to the conventional PI controller. Recently, a robust power command based on the Active Disturbance Rejection Control (ADRC) for DFIG used in a WECS system has been designed in [14]. Simulation results showed that the proposed ADRC controller had the best performance in terms of robustness against machine's parameter variations. In the DFIGs, the stator is directly connected to the grid and the rotor is connected to the grid via the machine’s and grid’s inverters. In this paper, a comparative study of four kinds of controllers (PI, ANN, H� and adaptive fuzzy PI controllers) is performed for the purpose of driving the power flowing between the stator of the DFIG and the grid. Corresponding author: Sabah Louarem Engineering, Technology & Applied Science Research Vol. 9, No. 5, 2019, 4775-4782 4776 www.etasr.com Louarem et al.: An Efficient Active and Reactive Power Control of DFIG for a Wind Power Generator II. MODELING OF THE WIND TURBINE CONVERSION SYSTEM The diagram of the DFIG-based wind turbine is shown in Figure 1, where RSC and GSC are respectively the rotor side converter and the grid side converter. Fig. 1. Basic configuration of a DFIG wind turbine A. Wind Turbine Model The fraction of power extracted from the wind by a wind turbine is usually referred by the symbol � , which stands for the coefficient of performance or power coefficient. The actual mechanical power output � of a wind turbine is given as [15- 16]: � � � . �. �. ��� ��, �������� (1) where, � is the mechanical output power of the turbine �� , � is the air density �!" #�⁄ , � is the rotor radius �# , and � is the blade pitch angle �%&" . The power coefficient expresses the rotor aerodynamics as a function of both tip speed ratio � and pitch angle of the rotor blades �. The tip speed ratio is defined as the ratio between the blade tip speed and the wind speed, expressed as [17]: � � '()*+,- (2) where . is the rotor speed �/0% and ����� is the wind speed �#/2 . In order to determine � , the following generic equation is used [18-19]: � � 30.5 6 0.0167. �� 6 2�;. 2<= > ?.�@AB. � C.DEB.��FE��G 6 0.00184. �� 6 3�. �� 6 2� (3) B. Modeling of the Doubly-Fed Induction Generator Concordia and Park’s transformation will be applied to the three-phase model of the IG. Dynamic voltages equations in an arbitrary %– L reference frame are following [20-21]. The stator voltage equations are: MN� � �NON� P ��Q �RN�� 6 .NRNSMNS � �NONS P ��Q 3RNS; 6 .NRN� (4) The rotor voltage equations are T MU� � �UOU� P ��Q �RU�� 6 �.N 6 .U�RUSMUS � �UOU� P ��Q 3RUS; 6 �.N 6 .U�RU� (5) The stator current of DFIG was decomposed into active and reactive component via the coordinate transformation and the field-oriented vector transformation. In order to regulate the power of the DFIG based wind turbine system, the vector control strategy is used. It consists of using the flux orientation, such as stator flux orientation (SFO) [7-22]: MN� � 0 and MNS � MN � .NRN. The active and reactive powers at the stator side and rotor side of the DFIG are given as: T N � 6MN VWVX OUSYN � Z[ \XVX 6 ZXVWVX OU� (6) ]̂̂ _ ^̀̂ MU� � �U. OU� P abU 6 VWcVX d �ef-�Q 6".N abU 6 VWcVX d OUS MUS � �U. OUS P abU 6 VWcVX d �efg�Q P ".N abU 6 VW cVX d OU� P ".h VW.iXVX (7) In steady state, the second derivative terms in (7) are neglected and the third term constitutes cross-coupling tams. T MU� � �U. OU� 6 ".N abU 6 VW c VX d OUS MUS � �U. OUS P ".N abU 6 VW cVX d OU� P ".h VW.iXVX (8) III. CONTROLLER SYNTHESIS A. PI Controller Synthesis Figure 2 shows the block diagram of the system controlled with the PI controller. The terms ! and !� represent the proportional and integral gain respectively. The ratio B/A represents the transfer function to be controlled, where j and k are presently defined as follows: j � bN�U P lbN abU 6 VW cVX d and k � 6b�MN (91) The response time of the controlled system will be fixed to 10ms. This value is sufficient for our application, while a lower value could involve transients with important overshoots. The calculated terms are given in [7-23]. Fig. 2. System with PI controller The transfer function of the open loop becomes: m�l� � 6 no pWqXapfpXrpWcds (10) Engineering, Technology & Applied Science Research Vol. 9, No. 5, 2019, 4775-4782 4777 www.etasr.com Louarem et al.: An Efficient Active and Reactive Power Control of DFIG for a Wind Power Generator The transfer function of the closed loop is expressed by: t�l� � Asuf (11) where vU is the response time. Now, we express the controller gains correction based on the settings of the machines and the response time as follows: ]_ `w � 6 uf VXxVfEpWcpX yVWZXw� � 6 uf (fVXVWZX (12) B. ANN Controller Synthesis ANN models are inspired from the basic framework of the brain [24-25]. In this study, the ANN controller was performed by using the nftool of Matlab. The DFIG-based wind turbine is simulated with the PI controller. The data, before and after the controller are computed and saved. After that, the network training was done for 10 iterations. The hidden layers contained 40 neurons. Fig. 3. Neural network structure C. Design of the t� Controller In this section, we present the t� mixed-sensitivity synthesis method for robust tracking control design. The main idea consists of synthesizing the controller by minimizing t�’s performance. As mentioned above, the quotient B/A represents the transfer function to be controlled. Thus, we can define the tracking error, the input control and the output as: &�2� � z�2�{/&|�2� (13) }�2� � !�2�z�2�{/&|�2� (14) {�2� � ~�2�{/&|�2� (15) where z�2� � xO P ��N���N� !�2�y E is the sensitivity function and ~�2� � ��N���N� !�2� xO P ��N���N� !�2�y E is the closed-loop transfer function. We are interested in designing the controller !�2�. For that, we will consider the t� mixed-sensitivity design problem illustrated in Figure 4, where, � �2� and ���2� are selected as loop-shaping weights. Hence, the tracking control design is considered as an optimization problem which consists of finding a stabilizing controller !�2� to minimize the following cost function: �� � �2�z�2����2�!�2�z�2���� (16) Fig. 4. S/KS mixed-sensitivity minimization The design weights � �2� and ���2� were selected as: � �2� � �BBBNA�B (17) ���2� � B.BB�DNcB.BBBDNcADNA BB (18) By using the robust control toolbox of Matlab, we obtain the following controller: ( ) 4 3 8 2 10 11 4 6 3 10 2 11 12 2.98 10 3.00 10 2.7 10 4.20 10 1.25 10 1.23 10 6.19 10 7.34 10 s s s K s s s s s − × − × − × − × = + × + × + × + × (19) D. Adaptive Fuzzy O Controller Synthesis The adaptive fuzzy O controller scheme is given in Figure 5. The FLS inputs are the errors (e) in active, reactive, and rate of change in active and reactive power error �%&�. The output of the fuzzy controller is %}. In contrast to the controller where controller parameters ( w and w� gains) are tuned in a predefined way [30], FLS is used to tune the w and w� parameters of the PI so that the controller can keep up with parametric changes and reference signals can be tracked. Fig. 5. PI control system with fuzzy gain adapter The fuzzy sets are defined as: NB is Negative Big, NM is Negative Medium, NS is Negative Small, ZR is Zero, PS is Positive Small, PM is Positive Medium, PB is Positive Big, B is Big and S is small. The max-min reasoning method and the center of gravity defuzzification method are used [31]. The values of ! � and !�� are determined by a set of fuzzy rules of the form designed fuzzy gain scheduling controller has two inputs and two outputs. ! � � �oE�oW+,�oW��E�oW+, (20) !�� � �+E�+W+,�+W��E�+W+, (21) IV. SIMULATION RESULTS Comparative simulations of the controllers were performed in Matlab. The proposed control algorithm’s nominal parameters are indicated in the Appendix. It was first tested in ideal mode and driven to 1500rpm. The different controllers Engineering, Technology & Applied Science Research Vol. 9, No. 5, 2019, 4775-4782 4778 www.etasr.com Louarem et al.: An Efficient Active and Reactive Power Control of DFIG for a Wind Power Generator were tested and compared by two different criteria, namely reference tracking performance, and robustness by varying the system parameters. A. Reference Tracking in Ideal Conditions Mode Simulation results of active and reactive power using the classical PI controller, an ANN controller, the proposed H� controller and the proposed adaptive fuzzy PI controller are shown in Figure 6. As expected, both active and reactive powers have been produced with good accuracy. Moreover, they can track the desired reference after a finite time interval and the answers are without overshoots for different controllers. Fig. 6. Active and reactive power behavior Fig. 7. Zoom in active and reactive power behavior Figure 7 shows a zoom view of active and reactive power behavior from 0 to 0.005s to compare the response times of all controllers. We can notice a quicker response time for ANN and H� controllers. In the same context, we notice that the system controlled by the PI controller evolved to a steady state with an important response time in comparison with the other controllers. Fig. 8. Evolution of cumulative tracking error functions In order to show which controller has the best steady state accuracy, we graph the evolution of the following cumulative tracking error functions: �~�� � � � N 6 NU���%�, � ∈ �0 22 QB (22) �~�� = � �YN − YNU���%�, � ∈ �0 22 Q B (23) As shown in Figure 8, the H� controller has the best steady state accuracy in comparison with the other controllers. In contrast to the H� controller, the conventional PI controller has low steady state accuracy. B. Robustnes We are interested in evaluating the robustness of the different controllers against parameter variation for parameters such as the inductances bN, bU, the mutual inductance b� and the resistance �U. The controllers’ performances are compared according to rise time, maximum peak overshoot and settling time. We test the robustness of the controllers against mutual inductance variations. Figure 9 and Table I present the simulation results for a parametric variation in the order of -10%. Unlike the adaptive fuzzy PI controller and the H� controller, we can remark that the ANN and PI controllers lose their performance regarding maximum overshoot. Fig. 9. Active and reactive power behavior with -10% mutual inductance variation Engineering, Technology & Applied Science Research Vol. 9, No. 5, 2019, 4775-4782 4779 www.etasr.com Louarem et al.: An Efficient Active and Reactive Power Control of DFIG for a Wind Power Generator TABLE I. COMPARISON OF THE RESPONSE PARAMETERS �b� − 10%� Active power Controller Rise time (s) Maximum overshoot (%) Settling time (s) PI 0.0102 29.43 0.0541 ANN 0.0018 7.62 0.0023 �� 0.0023 0.77 0.001 Adaptive Fuzzy PI 0.0024 0.01 0.0042 Reactive power PI 0.0102 19.20 0.0252 ANN 0.0005 7.62 0.0021 �� 0.0005 1.20 0.0010 Adaptive Fuzzy PI 0.0024 0.14 0.0042 In order to refine our study, we tested the robustness of the proposed controllers against a mutual inductance variation in the order of -25%. The simulation results are presented in Figure 10 and Table II. We can note that the PI and ANN controllers lose their performance in response time with undesirable maximum overshoots and only adaptive fuzzy PI controller and H� controller can resist this parametric variation with a slight superiority for H� controller in terms of response time. Fig. 10. Active and reactive power behavior using H� and adaptive fuzzy PI controllers with -25% mutual inductance variation TABLE II. COMPARISON OF THE RESPONSE PARAMETERS �b� − 25%� Controller Rise time (s) Maximum overshoot (%) Settling time (s) Active power �� 0.0014 1.95 0.0057 Adaptive Fuzzy PI 0.0060 0.61 0.0104 Reactive power �� 0.0015 2.96 0.0058 Adaptive Fuzzy PI 0.0060 0.70 0.0106 In the same way, the robustness of the proposed controllers against rotor inductance variations was tested. Two deep simulations have been performed (Figures 11 and 12). The first one concerns a variation in the order of +10% and the second a variation in the order of +25%. The results are shown in Tables III and IV respectively. Note that only two controllers have resisted the second test with slight superiority regarding response time for the H� controller. Regarding stator inductance variations, the simulation results are shown in Tables V and VI. As in the preceding cases, only the H� and the adaptive fuzzy PI controllers can resist the high stator inductance variation. Fig. 11. Active and reactive power behavior with 10% rotor inductance variation TABLE III. COMPARISON OF THE RESPONSE PARAMETERS �bU + 10%� Active power Controller Rise time (s) Maximum overshoot (%) Settling time (s) PI 0.0066 11.94 0.0414 ANN 0.0011 0.37 0.0012 �� 0.0003 0.40 0.0005 Adaptive Fuzzy PI 0.0013 0.0023 Reactive power PI 0.0060 17.76 0.0427 ANN 0.0003 17.16 0.0013 �� 0.0003 0.78 0.0005 Adaptive Fuzzy PI 0.0013 0.25 0.0024 Fig. 12. Active and reactive power behavior using H� and adaptive fuzzy PI controllers with +25% rotor inductance variation Engineering, Technology & Applied Science Research Vol. 9, No. 5, 2019, 4775-4782 4780 www.etasr.com Louarem et al.: An Efficient Active and Reactive Power Control of DFIG for a Wind Power Generator TABLE IV. COMPARISON OF THE RESPONSE PARAMETERS �bU + 25%� Controller Rise time (s) Maximum overshoot (%) Settling time (s) Active power �� 0.0007 0.93 0.0011 Adaptive Fuzzy PI 0.0028 0.31 0.0106 Reactive power �� 0.0007 1.54 0.0038 Adaptive Fuzzy PI 0.0028 0.18 0.0011 Fig. 13. Active and reactive power behavior using the four controllers with +10% variation of bN TABLE V. COMPARISON OF THE RESPONSE PARAMETERS �bN + 10%� Active power Controller Rise time (s) Maximum overshoot (%) Settling time (s) PI 0.0066 11.51 0.0411 ANN 0.0010 0.36 0.0012 �� 0.0003 0.39 0.0005 Adaptive Fuzzy PI 0.0024 0.01 0.0042 Reactive power PI 0.0068 17.11 0.0424 ANN 0.0003 18.86 0.0012 �� 0.0003 0.74 0.0005 Adaptive Fuzzy PI 0.0013 / 0.0023 TABLE VI. COMPARISON OF THE RESPONSE PARAMETERS �bN + 25%� Controller Rise time (s) Maximum overshoot (%) Settling time (s) Active power �� 0.0007 0.90 0.0011 Adaptive Fuzzy PI 0.0028 0.01 0.0049 Reactive power �� 0.0007 1.30 0.0011 Adaptive Fuzzy PI 0.0003 1.80 0.0052 Finally, regarding the rotor resistance variation, which is the result of the rotor heating, a deep simulation was performed by considering a rotor resistance variation in the order of 100%. The simulation results are shown in Figure 15 and the controllers’ performances are summarized in Table VII. Thus, we can see that the different controllers can drive the system to track the reference signals. In other words, the active and reactive powers follow correctly the reference signals. Fig. 14. Active and reactive power behavior using the H�and adaptive fuzzy PI controller with +25% variation of bN. TABLE VII. COMPARISON OF THE RESPONSE PARAMETERS ��U + 100%� Active power Controller Rise time (s) Maximum overshoot (%) Settling time (s) PI 0.00220 1.17 0.02330 ANN 0.00020 0.10 0.00020 �� 0.00003 0.39 0.00007 Adaptive Fuzzy PI 0.0002 / 0.00050 Reactive power PI 0.00240 5.15 0.1500 ANN 0.00005 24.37 0.1498 �� 0.00001 71.37 0.1499 Adaptive Fuzzy PI 0.00004 3.01 0.1500 As far as the active power is concerned, it is clear that the H� controller has the best rise time and settling time when compared with the other controllers. However, concerning reactive power, the controller performances are almost identical to those of the ANN controller with a slight superiority for H� controller. In a nutshell, the simulation results presented in this work have shown that the H� controller has the best steady state accuracy compared with the other controllers. Regarding the robustness against parametric variation, the H� and adaptive fuzzy PI controllers have the best tracking performance and robustness with a slight superiority of the H� controller. V. CONCLUSION In this paper, the control of doubly fed induction generator (DFIG) based wind energy conversion has been studied. The DFIG’s stator was directly connected to the grid and the rotor was connected to the grid via the machine’s and grid’s inverters. The design of four control strategies, namely PI, ANN, adaptive fuzzy PI, and H� controller, has been presented and discussed. The Engineering, Technology & Applied Science Research Vol. 9, No. 5, 2019, 4775-4782 4781 www.etasr.com Louarem et al.: An Efficient Active and Reactive Power Control of DFIG for a Wind Power Generator obtained results showed that the H� controller is the best to drive the DFIG’s stator and to track perfectly the active and reactive power references with very good tracking performance, namely low-rise time, low settling time, and high steady-state accuracy. The H� controller seems more robust than all other controllers against parameter variations. Fig. 15. 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