International Journal of Energetica (IJECA) https://www.ijeca.info ISSN: 2543-3717 Volume 6. Issue 2. 2021 Page 13-20 IJECA-ISSN: 2543-3717. December 2021 Page 13 Performance study and analysis between vector control and direct power control for DFIG based wind energy system Gufran Nurettin * , Ata Sevinç Department of Electrical and Electronic Engineering, Kırıkkale University, Kırıkkale, TURKEY Email* : ahghby@gmail.com Abstract – This paper concentrates on analyzing the performance of the two most important techniques of independent active and reactive power control of the doubly-fed induction generator used in a variable speed wind power conversion system. In the first technique, the independent control of the active and reactive power is based on the vector control technique by the orientation of the stator voltage space vector using PI controllers; the decoupling components are deduced along with the d, q axes; and the PI controllers' parameters are calculated from the mathematical model of the doubly-fed induction generator. Hysteresis controllers are utilized to designing a direct power control technique. The performances of the studied control methods are tested and compared via simulation results. Keywords: Voltage Oriented Control, Direct Power Control, DFIG Received: 13/07/2021 – Accepted: 05/12/2021 I. Introduction The main reason for the popularity of doubly-fed induction generators (DFIGs) in wind power implementations is the requirement for relatively small power converters. (Usually, 30% from the rated power of the machine) [1-2]. The Scherbius scheme was introduced by the 20th- century German engineer Arthur Scherbius that provides bidirectional power flow in the rotor circuit. Cycloconverter-based power converter topologies joined between the stator and the rotor was informed [3-4]. However, these converters produce high harmonics in the rotor current returned to the stator. These disadvantages can be overcome by employing two separated converters, a Rotor Side Converter (RSC) and a Grid Side Converter (GSC), which are attached back-to-back in the rotor side [5]. To achieve control of the DFIG system, the RSC and GSC can be commanded independently. In practical applications, the RSC can operate in complete separation from the GSC provided that a steady DC bus voltage is supplied by the GSC. Also, in most schemes, the RSC operates commands are completely independent of the GSC by a separate control unit for each converter. One of the conventional control methods in the literature is the vector control that was utilized in the DFIG system [6]. The vector control method employing PI controllers provides a less harmonic distortion and reduces the power ripple [7]. But it might be hard to set the PI gains correctly and its performance depends significantly on machine parameters. The vector control technique according to orientation frame can be classified as the stator flux-oriented control (FOC) [8] or grid voltage-oriented control (VOC) [9]. FOC techniques depend on the accuracy of the stator resistance values, integration problems also exist and extra low-pass filters are applied to precisely determine the stator flux [10]. The influence of the value of stator resistance in the flux calculation can be neglected using the VOC technique by adding a 90-phase variation to the voltage angle which can be obtained using a Phase- Locked Loop (PLL). This can produce an added coupling impact in Active and Reactive Power (ARP) control, which can be recompensed by applying extra controllers https://www.ijeca.info/ Gufran Nurettin et al IJECA-ISSN: 2543-3717. December 2021 Page 14 in the external loop [11-12]. Another control technique in the literature is direct torque control (DTC). The RSC provides the necessary magnetizing current in the rotor windings to produce the needed ARP at the stator terminals. Furthermore, since the electromagnetic torque is concerning to the active power, it is reported that the electromagnetic torque and stator flux reference values are replaced by ARP reference values [13-14]. The direct power control (DPC) technique directly controls the ARP of the stator by applying the suitable voltage vector to the rotor. The errors between the reference ARPs and the estimated ARPs are handled by hysteresis controllers [15-18]. The DPC is distinguished by its simple structure, fast dynamic response and robustness to parameter changes, and not need to use rotor current control loops, but its disadvantages are the highly variable switching frequency. In this study, first, the dynamic model of the DFIG is proffered. Then the vector control and direct power control techniques are studied. At last, the detailed simulation results are presented and discussed using MATLAB/SIMULINK for both techniques. II. The Dynamic Model of DFIG The dynamic model of the DFIG in the synchronous reference frame dq can be described by the following equations: sd sd s sd s sq sq sq s sq s sd d V R i dt d V R i dt                  (1)     rd rd r rd s r rq rq rq r rq s r rd d V R i dt d V R i dt                      (2) The stator and rotor fluxes are related to the current by: sd s sd m rd sq s sq m rq L i L i L i L i          (3) rd r rd m sd rq r rq m sq L i L i L i L i          (4) Whereas the electromagnetic torque, produced by the machine, can be defined by the next equation:  em 3 2 m rd sq rq sd r s PL T L L        (5) where P is the pole pair number of the motor; sR and rR are the stator and rotor phase resistances, respectively; sL , rL and mL are the stator, rotor and mutual inductances, respectively; and  is the total leakage factor. Furthermore, the ARPs of the stator and rotor can be determined according to the next equations:     s s 3 2 3 2 sd sd sq sq sq sd sd sq P V i V i Q V i V i         (6)     r r 3 2 3 2 rd rd rq rq rq rd rd rq P V i V i Q V i V i         (7) III. Voltage Oriented Control Technique The principle of the VOC consists of aligning the q- axis with the stator voltage space vector sV , which means that s sqV V and 0sdV  . From equation (1), since the stator is connected directly to the grid at constant AC voltage the stator flux is constant, thus, the term s d dt  is zero. Furthermore, considering that the voltage drop in the stator resistance is slight; consequently, the angle between the stator flux and the voltage vector almost is 90 ,  as demonstrated in Figure 1. Figure 1. The phasor diagram of dq reference frame aligned with the stator voltage space vector Thus, the equations (1,3,5 and 6) become as follows: 0 . sd sq s s V V        (8) 0 sd s sd m rd s sq m rq L i L i L i L i         (9) Gufran Nurettin et al IJECA-ISSN: 2543-3717. December 2021 Page 15  em 3 2 m rq sd r s PL T L L      (10)     s s 3 2 3 2 sq sq sq sd P V i Q V i       (11) From the aforementioned equations, it can be noted that the current rdi is proportional to the stator reactive power sQ and that the current rqi is proportional to the active stator power sP . Accordingly, from the DFIG model by substituting equations (4) and (9) into equation (2), the rotor voltages can obtain as a function of stator flux and the rotor currents. rd rd r rd r r r rq di V R i L L i dt      (12) rq m rq r rq r r r rd r s s di L V R i L L i dt L         (13) Consequently, by adopting similar PI controllers for both loops, and using the decoupling components between the dq axes. The equivalent closed-loop systems for currents can be represented as a second-order system by two poles and zero. Appropriate gains of the PI controllers are chosen as shown in Figure 2. Figure 2. Inner closed-loop of rotor current control by PI controllers Figure 3. Overall block diagram of vector control technique Next, it is possible to inference the external closed-loop of power control with PI controllers by substituting the direct and quadrature rotor currents from equation (9) in equation (11). Gufran Nurettin et al IJECA-ISSN: 2543-3717. December 2021 Page 16 s 3 2 m s s rq p rq s L P i C i L     (14) s 3 2 m s s s s rd Q rd s m m L Q i C i L L L                     (15) It can be observed that the abridged closed-loop systems provide a first-order system that can be set by determining the proper gains of the PI controller. Consequently, the overall diagram of vector control for the DFIG is demonstrated in Figure 3. IV. Direct Power Control Technique In this study, the direct control technique for ARP is carried out based on the stator flux directing. The switching table is defined based on the ARP errors and the instantaneous location of the stator flux. The stator flux orientation method is adopted instead of the rotor flux orientation based on that the electrical components of the stator have less noise and harmonics compared to the electrical components of the rotor due to the discontinuous voltage applied to the rotor from the voltage converter RSC. However, from equation (6), it is not possible to know how the injection of different rotor voltage vectors can affect the creation of desired sP and sQ . The stator voltage is fixed by the grid, whereas the stator current depends on the chosen rotor voltage vectors. Consequently, by substitution of DFIG model equations in equations (6) can be obtained follows the equations:     s _ _ s _ _ 3 sin 2 3 cos 2 xy m s s xy r xy r s s m s xy r s xy s r L P L L L Q L L                           (16) Where   is the phase shift between the stator and the rotor flux space vectors. From equation (16) can notice the stator ARPs can be controlled by modifying the angle between the stator and rotor flux vectors and their amplitudes. Fig. 4 illustrates the terms  _ sinr xy  ,  _ cosr xy  , stator and rotor flux space vector’s locations. Figure 4. Phasor diagram of xy rotating reference frame with stator and rotor fluxes The stator flux space vector position in the rotor reference frame is split into six sectors as shown in Figure 5. Figure 5. Distribution of the six sectors in xy rotating reference frame IV.1. Voltage Vector Selection and Hysteresis Controllers In the DPC technique, the required rotor voltage vector directly is select from sP and sQ errors, using hysteresis controllers. It determines the needed voltage vector to correct the errors in the controlled variables. The sQ controller is based on a two-level hysteresis controller with QH hysteresis band, while the sP controller employs a three-level hysteresis comparator with PH hysteresis band. The schematic representation of these two controllers is shown in Fig. 6. Once the Psu and Qsu signals are defined employing the hysteresis controllers, together with the information about the stator flux vector position (i.e., the sector number), It can choose the rotor voltage vector from the switching table as illustrated in Table 1. Figure 6. Active and reactive powers hysteresis controllers Gufran Nurettin et al IJECA-ISSN: 2543-3717. December 2021 Page 17 Table 1. Switching table for DPC technique Qs u 1 -1 Ps u 1 0 -1 1 0 -1 Sector 1 V5 V7 V3 V6 V0 V2 Sector 2 V6 V0 V4 V1 V7 V3 Sector 3 V1 V7 V5 V2 V0 V4 Sector 4 V2 V0 V6 V3 V7 V5 Sector 5 V3 V7 V1 V4 V0 V6 Sector 6 V4 V0 V2 V5 V7 V1 IV.2. Estimation of stator flux in xy rotating reference frame The stator flux components are estimated from measured stator voltage and currents’ α and β components according to the following equations:     0 0 t s s s s t s s s s V R i dt V R i dt                   (17) The transformation matrix with the rotor angular position is employed to make the stator flux components rotate in xy rotating reference frame         cos sin sin cos sx s sy s                          (18) Thus, the stator flux space vector angle which determines the sector number is calculated according to Fig. 5 by the following relationship _ arctan 2 s xy sy sx             (19) The control scheme of the DPC technique implemented in this study is demonstrated in Figure7. Figure 7. Block scheme of the DPC technique V. Results and Discussion The validity of the studied schemes was verified by the simulations using Matlab/Simulink. The simulation was carried out under various operating conditions to show the studied techniques' performance. (a) (a) (b) (c) (d) Gufran Nurettin et al IJECA-ISSN: 2543-3717. December 2021 Page 18 Figure 8. VOC technique responses for case 1 Figure 9. DPC technique responses for case 1 The Runge-Kutta method was used to solve differential equations. Sampling time is 𝑇𝑠= 20𝜇𝑠 and the RSC converter switching frequency was set as 5𝐾𝐻𝑧. The nominal parameters of the DFIG are presented in Table 2. Both controls technique VOC and DPC are simulated and compared in the next cases: Case 1: the rotor speed is increased from sub- synchronous to super-synchronous speed with ramp reference change of the active power. Case 2: the rotor speed is set at sub-synchronous with the step reference change of the active power. In both cases, the reactive power is adjusted to zero to get a unity power factor at the grid side. Table 2. Parameters of doubly fed induction generator Pn=1 KW P=2 pairs Un=380 V Rs=7.2 𝛀 Ls=0.28 H Rr=1.35𝛀 Lm=0.118 H Lr=0.075 H J=0.006 kg.m 2 fn=50 Hz TL=6.7 N.m F=0.0046 Nm.s V.1. The performance at sub-synchronous and super- synchronous speed operation with ramp reference change of active power. As shown in Figure 8 and 9, the rotor speed is sub- synchronous (w= 250 rad/s) then at t= 4 s it accelerating to become super-synchronous (w= 350 rad/s), Also, the reference active power demand is increased from 100 to 800 watts at t= 5 s. From Figure 8 (f and d) and Figure 9 (f and d), it can be noticed the supremacy of the DPC technique in terms of response speed and reducing distortion occurring in the active and reactive power. Furthermore, in both techniques, balanced stator currents are obtained by maintaining a constant frequency equal to the grid frequency as illustrated in Figures 8 (b) and 9 (b). (c) (a) (b) (d) (f) (f) Gufran Nurettin et al IJECA-ISSN: 2543-3717. December 2021 Page 19 V.2. Performance at sub-synchronous speed operation with the step reference change of active power. In this test, a step variable reference active power is demanded at a sub-synchronous rotation speed. Figures 10 and 11 show the response of the ARP to both studied techniques. as noticed, the effectiveness and speed response of the DPC technique compared with the VOC technique. It can be seen the overshoot in the active power response with VOC technique and reactive power response variations according to active power variations. In the last comparison test, the total harmonic distortion (THD) of the stator current in each technique is evaluated by employing the Fast Fourier Transform (FFT) as seen in Figure 12. It can be seen that the THD for the DPC technique (THD = 1.01%) is low when compared with the VOC technique, and it’s due to the difference and difficulty in choosing the optimal parameter values for PI controllers in the VOC technique. Figure 10. VOC technique responses for case 2 Figure 11. DPC technique responses for case 2 Figure 12. Stator current FFT analysis, (a) VOC, (b) DPC After presenting the detailed simulation results indicating the superiority of the DPC technique, Table 3 reviews the key differences between the VOC technique and the DPC technique. Table 3. Performance evaluation between DPC and VOC techniques Indicators DPC VOC Dynamic response High Low Dependency on machine parameters Very low High Power ripples Medium High Switching frequency Variable Constant Robustness Medium Low Controllers Tow hysteresis controllers Four PI controllers Control method Directly controlled Indirectly controlled by rotor currents Park and Clark Transformations No need Needed (a) (b) Gufran Nurettin et al IJECA-ISSN: 2543-3717. December 2021 Page 20 VI. Conclusion In this paper, the DPC and VOC techniques of DFIG in energy conversion systems were studied and simulated by MATLAB/SIMULINK. First, the theory of vector control by the stator voltage space vector orientation and how to calculate the parameters of PI controllers for the internal and external loops based on the mathematical model of DFIG was explained. Second, the stator flux orientation method is adopted instead of rotor flux orientation for the DPC technique using hysteresis controllers because the electrical components of the stator have less noise and harmonics compared to the electrical components of the rotor due to the discontinuous voltage applied to the rotor from the voltage converter RSC. Simulation results showed that the DPC technique presents a fast and good dynamic response and less harmonic distortion compared with the VOC technique. Moreover, the implementation of the DPC technique is simple and does not have the inherent complexity of the VOC technique. 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