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International Journal of Enhanced Research Publications, ISSN: XXXX-XXXX Vol. 2 Issue 4, April-2013, pp: (1-4), Available online at: www.erpublications.com Control of Three Phase PWM Rectifier Using Virtual Flux Based Predictive Direct Power Control and SVM under Harmonic Conditions Vahid Eskandari-Torbati3 Hamid Eskandari-Torbati1, Davood Arab Khaburi2 3 Fiber Optic Project Manager Moniran Consultant Co., Mashhad, Iran 3 1,2 department of electrical engineering Iran University of Science and Technology, Tehran, Iran 1,2 Abstract: – In this paper a new predictive direct power control algorithm to control the PWM rectifier based on Virtual Flux is presented. In this algorithm supply voltage and the line inductance are assumed as an induction machine and so Virtual Flux space vectors are assumed corresponding to the space vectors of the voltages. Instantaneous active and reactive powers and finally convertor average voltage in both stationary and reference frames are calculated by the Virtual Flux space vector components. Main advantages of the proposed method is low Total Harmonic Distortion (THD) of the input current and low ripple in the instantaneous active and reactive powers and DC-bus voltage under harmonic distorted condition of the supply voltage in comparison with Voltage based predictive direct power control. Proposed VF- predictive direct power control with SVM switching strategy was tested in simulations and compared with the voltage based predictive direct power control. Keywords: PWM rectifier, direct power control, space vector modulation (SVM), dead beat control, predictive control Introduction Most of industrial process and domestic applications that need to rectify the electrical energy drawn from AC network, use full bridge diode rectifiers. The most important advantages of these rectifiers are: simple configuration and low cost and furthermore they don’t need any kind of control unit. Against these benefits, diode rectifiers have some disadvantages that most important of them are: large amount of passive elements such as capacitive filter in DC side, high THD in the AC side Currents, consumption of reactive power and so low power factor at the terminal of the network and high value in the DC side voltage ripple [1]. These problems of the diode rectifiers and the attempts of researchers to eliminate them resulted in presentation of PWM rectifiers. Main advantages of PWM rectifiers are: low THD in the input AC currents, low DC side voltage ripple, unity power factor at the terminal of the network and no need to reactive power, but in return some cost should be paid such as more complex control algorithms and more switching loss [1]. Idea of PWM rectifier firstly was proposed in [1], [2]. Development of power electronic switches such as IGBT and their capability to operate under higher switching frequencies, made it possible for researchers to use more complex control algorithms for these rectifiers in order to improve their performance. A better control algorithms results a lower value for DC side capacitor, a lower THD in the input currents and lower ripple in the DC side voltage. In the past years different control algorithms have been proposed in literatures to control and improve PWM rectifier performance. According to the condition of the network voltage, these control methods can be classified in two groups; first are those which consider the network voltage ideally and without any harmonic distortion or unbalance conditions and the second are those which try to control and improve the rectifier performance under non-ideal condition of supply network. The literatures in the second groups mostly investigate the effect of the unbalanced supply network on the rectifier and propose methods to improve it [3]–[5]. On the other hand, various control algorithms presented in the literatures can be classified in two groups according to their use of current control loop or active/reactive power control loop [6]. A well-known algorithm among indirect power control that uses current controller is the method that called Voltage Oriented Control (VOC) which is the duality of Field Oriented Control in the control of electrical machines by DC/AC inverters. The main idea of this method is to control space vector of input AC current according to the position of space vector of the network voltage. Also to satisfy unity power factor (UPF) Page | 1 International Journal of Enhanced Research Publications, ISSN: XXXX-XXXX Vol. 2 Issue 4, April-2013, pp: (1-4), Available online at: www.erpublications.com at the terminal of the network, reference value of the current on the quadrature axis is set to zero while reference of the current on the direct axis comes from a PI controller which the input is the tracking error of DC side voltage [7]–[9]. Over past decade a new method has been emerged which is based on direct control of active and reactive powers of the rectifier and is called Direct Power Control (DPC). It is duality of a well-known method called Direct Torque Control (DTC) in driving machines by DC/AC inverters. This method calculates instantaneous active and reactive power of the rectifier drawn from the terminal of the network and compares them with their references to produce the tracking errors. These errors are entered into two fixed band hysteresis controllers separately. At last, status of the switches will be indicated according to the digital output of the controllers and the position of the space vector of input voltage by a predefined switching table. Unity power factor (UPF) operation will be satisfied when the reference value of the reactive power is set to zero. On the other hand the reference of the active power is generated by multiplying the DC side voltage and output signal of a PI controller which its input is tracking error of DC voltage [10]–[12]. This algorithm needs to high sampling frequency which is the main drawback [18]. VOC and DPC algorithms which are based on the position of the space vector of voltage have not good performance under distorted condition of the network. So Malinowski et al. proposed an algorithm that uses Virtual Flux (VF) instead of Voltage as base space vector [12]–[16]. This idea significantly improves the performance of rectifier just under harmonic distorted supply voltage, but the requirement of high sampling frequency remains still with it. So after that, Malinowski et al. used Space Vector Modulation (SVM) switching strategy with Virtual Flux based Direct Power Control in order to eliminate this drawback (VF-DPC SVM) [17]. In this method hysteresis controllers are replaced by PI controller and the outputs of them are transferred to stationary reference frame. After that, switching states will be indicated by using a SVM algorithm instead of switching table. This method has the advantages of VOC and DPC simultaneously but the disadvantage is the tuning of the PI controller. In [16] some ways for tuning the PI controllers is proposed. P. Antoniewicz and also the authors used predictive algorithms based on Model Predictive Control (MPC) in order to control PWM rectifiers [17-19]. A. Bouafia et al. proposed a new Predictive Direct Power Control in the sense of Dead Beat Control that uses SVM switching algorithm to control PWM rectifier [20]. D. A. Khaburi et al. used VF-DPC algorithm and hysteresis controllers to design and control a PWM rectifier which is connected to a micro turbine generator and hence it can work under high frequency supply voltage [21]. Furthermore, some of the works have focused on the multilevel PWM rectifiers and some other has incorporated different control theories, such as Fuzzy Logic, with conventional control methods in the PWM rectifiers in order to improve them. Presented method in [18] is based on the space vector of the network voltage and therefore has not good performance under harmonic conditions of the supply voltage. This paper uses Virtual Flux instead of Voltage space vector in order to estimate the value of active and reactive power of the system at the beginning of the next switching step and after that indicates the space vector of the convertor voltage in beginning of the present switching step. By using this method the performance of the system will be improved under harmonic conditions of the supply voltage. Theoretical discussion of the method in both stationary (α-β) and rotating (d-q) reference frame has been presented and simulation studies have been performed in MATLAB/SIMULINK. Finally simulation results of the method based on the both space vectors (Voltage and Virtual Flux) have been presented and compared with each other’s. Principles of Virtual Flux Based Predictive Direct Power Control (VF-PDPC) In Virtual Flux based Direct Power Control using SVM that has been presented in [15], the rectifier average voltage vector vαβ, comes from PI controllers of active and reactive powers errors after a coordinate transformation. Fig. 1 shows the block diagram of VF-DPC with SVM switching strategy. As can be seen in Fig. 1, inputs of the PI controllers are instantaneous errors of the active and reactive powers of the rectifier. Thus the switching states at each switching period are generated so that the tracking errors could be canceled at the end of that switching period. While in the proposed method, the rectifier average voltage vector at the start of the switching period is computed so that to cancel the instantaneous tracking errors of active and reactive powers at the end of the switching period as shown in Fig. 2. Therefore the reference value of the active and reactive powers at the end of each switching period should be estimated. In other word, this method needs a predictive model of the instantaneous power behavior, which is described in the following steps. A. Stationary Reference Frame In the stationary reference frame (α-β) by considering the supply voltage as a balanced three phase network, the instantaneous active and reactive powers of the rectifier based on the Virtual Flux are defined as follows [13]: −𝜓𝑙𝛽 𝑃 [ ] = 𝜔[ 𝑞 𝜓𝑙𝛼 𝜓𝑙𝛼 𝑖𝛼 ] [ ] 𝜓𝑙𝛽 𝑖𝛽 where 𝜓𝑙𝛼𝛽 = [𝜓𝑙𝛼 𝜓𝑙𝛽 ]𝑇 is the Virtual Flux vector corresponding to the network voltage vector and 𝑖𝛼𝛽 = [𝑖𝛼 the input current vector of the rectifier and 𝜔 is the angular frequency of the network. 𝑖𝛽 ]𝑇 is As it is shown in Fig. 3 the Virtual Flux vector components can be derived from the integration of the network voltage vector components. In this Figure the feedback loop has been adopted in order to cancel the error that could be caused by assigning a wrong value for the initial condition of the integral process. Page | 2 International Journal of Enhanced Research Publications, ISSN: XXXX-XXXX Vol. 2 Issue 4, April-2013, pp: (1-4), Available online at: www.erpublications.com Figure 1. VF based instantaneous DPC configuration of three phase PWM Rectifier If switching period Ts is small enough so that the value of the Virtual Flux vector components could be considered constant during a switching period (𝜓𝑙𝛼𝛽 (𝑘 + 1) = 𝜓𝑙𝛼𝛽 (𝑘)), the difference between amount of the instantaneous active and reactive powers from the beginning of the switching period to the end can be written as (2): [ −𝜓𝑙𝛽 (𝑘) 𝑃(𝑘 + 1) − 𝑃(𝑘) ] = 𝜔[ 𝜓𝑙𝛼 (𝑘) 𝑞(𝑘 + 1) − 𝑞(𝑘) 𝜓𝑙𝛼 (𝑘) 𝑖𝛼 (𝑘 + 1) − 𝑖𝛼 (𝑘) ][ ] 𝜓𝑙𝛽 (𝑘) 𝑖𝛽 (𝑘 + 1) − 𝑖𝛽 (𝑘) In the above equation, P(𝑘), 𝑞(𝑘), 𝜓𝑙𝛼𝛽 (𝑘) and 𝑖𝛼𝛽 (𝑘) are determined at each sampling instant by measuring, and 𝜔 is obtained from the available data of the supply network. In this step we suppose that the values of P(k+1) and q(k+1) are determined too and we will correct the assumption later. Now as a result of the assumption, the values of 𝑖𝛼𝛽 (𝑘 + 1) could be computed as: [ −𝜓𝑙𝛽 (𝑘) 𝑖𝛼 (𝑘 + 1) 1 ]= 2[ 𝑖𝛽 (𝑘 + 1) 𝜓𝑙𝛼 (𝑘) 𝜔‖𝜓𝑙𝛼𝛽‖ 𝜓𝑙𝛼 (𝑘) 𝑃(𝑘 + 1) − 𝑃(𝑘) 𝑖𝛼 (𝑘) ][ ]+[ ] 𝑖𝛽 (𝑘) 𝜓𝑙𝛽 (𝑘) 𝑞(𝑘 + 1) − 𝑞(𝑘) Differential equation of a PWM rectifier in α-β frame can be expressed as (4): [ 𝑑 𝑖𝛼 (𝑡) 𝑒𝛼 (𝑡) 𝑣𝛼 (𝑡) 𝑖𝛼 (𝑡) ]=[ ]+𝐿 [ ]+𝑅[ ] (𝑡) 𝑒𝛽 (𝑡) 𝑣𝛽 (𝑡) 𝑖 𝑖𝛽 (𝑡) 𝑑𝑡 𝛽 (4) Figure 3. Block diagram of Virtual Flux calculator Page | 3 International Journal of Enhanced Research Publications, ISSN: XXXX-XXXX Vol. 2 Issue 4, April-2013, pp: (1-4), Available online at: www.erpublications.com Figure 2. VF based Predictive DPC-SVM configuration for three phase PWM rectifier By neglecting the effect of the resistance R in the presence of inductance L and taking integral of (4), the relationship between Virtual Flux vector components of the PWM rectifier and input current vector components is obtained as below: 𝜓𝑙𝛼 (𝑡) 𝜓𝑠𝛼 (𝑡) 𝑖𝛼 (𝑡) [ ]=[ ]+𝐿[ ] 𝜓𝑙𝛽 (𝑡) 𝜓𝑠𝛽 (𝑡) 𝑖𝛽 (𝑡) (5) Therefore the values of the Virtual Flux components that corresponds to the converter side voltage at the end of switching period could be computed as: [ 𝜓𝑠𝛼 (𝑘 + 1) 𝜓𝑙𝛼 (𝑘 + 1) 𝑖𝛼 (𝑘 + 1) 𝜓𝑙𝛼 (𝑘) 𝑖𝛼 (𝑘 + 1) ]=[ ]−𝐿[ ]=[ ]−𝐿[ ] 𝜓𝑠𝛽 (𝑘 + 1) 𝜓𝑙𝛽 (𝑘 + 1) 𝑖𝛽 (𝑘 + 1) 𝜓𝑙𝛽 (𝑘) 𝑖𝛽 (𝑘 + 1) Hence substituting (3) in (6) results: [ −𝜓𝑙𝛽 (𝑘) 𝜓𝑠𝛼 (𝑘 + 1) 𝜓𝑙𝛼 (𝑘) 𝐿 ]=[ ]− 2[ 𝜓𝑠𝛽 (𝑘 + 1) 𝜓𝑙𝛽 (𝑘) 𝜓𝑙𝛼 (𝑘) 𝜔‖𝜓𝑙𝛼𝛽‖ 𝜓𝑙𝛼 (𝑘) 𝑃(𝑘 + 1) − 𝑃(𝑘) 𝑖𝛼 (𝑘) ][ ]−𝐿[ ] 𝑖𝛽 (𝑘) 𝜓𝑙𝛽 (𝑘) 𝑞(𝑘 + 1) − 𝑞(𝑘) And also it could be obtained from (5): [ 𝜓𝑠𝛼 (𝑘) 𝜓𝑙𝛼 (𝑘) 𝑖𝛼 (𝑘) ]=[ ]−𝐿[ ] 𝜓𝑠𝛽 (𝑘) 𝜓𝑙𝛽 (𝑘) 𝑖𝛽 (𝑘) On the other hand we know that the convertor side voltage (𝑣𝛼𝛽 ) is the derivative of the corresponding Virtual Flux (𝜓𝑠𝛼𝛽 ) as (9). 𝑣𝛼𝛽 = 𝑑 𝑑𝑡 𝜓𝑠𝛼𝛽 By using a discrete first order approximation of (9), the value of the components of the convertor voltage at the beginning of the switching period can be obtained as (10): 𝑣𝛼 (𝑘) = { 𝑣𝛽 (𝑘) = 𝜓𝑠𝛼 (𝑘+1)−𝜓𝑠𝛼 (𝑘) 𝑇𝑠 𝜓𝑠𝛽 (𝑘+1)−𝜓𝑠𝛽 (𝑘) 𝑇𝑠 Now we discuss about the values of the P(K+1) and q(K+1). The desired conditions are achieved when the active and reactive powers of the PWM rectifier reach to their reference values. Thus the average of the convertor voltage vector should be adopted so that to cancel the power errors as below: [ 𝑃𝑟𝑒𝑓 (𝑘 + 1) 𝑃(𝑘 + 1) ]=[ ] 𝑞(𝑘 + 1) 𝑞𝑟𝑒𝑓 (𝑘 + 1) Approximately in all DPC schemes, the reference value of the active power is derived from the output of a PI controller for DC-bus voltage that is multiplied by the DC bus voltage. If the tracking error of DC side voltage is assumed constant during switching period from start to end, the instantaneous active power command at the beginning of the next switching period P(k+1) can be estimated using a linear extrapolation as shown in Fig. 4. While the reference value of the reactive power is given directly from the outside of the control unit and usually is equal to zero for unity power factor operation. Therefore the equation (12) can be expressed: Page | 4 International Journal of Enhanced Research Publications, ISSN: XXXX-XXXX Vol. 2 Issue 4, April-2013, pp: (1-4), Available online at: www.erpublications.com [ 𝑃𝑟𝑒𝑓 (𝑘 + 1) 2𝑃𝑟𝑒𝑓 (𝑘) − 𝑃𝑟𝑒𝑓 (𝑘 − 1) ]=[ ] 𝑞𝑟𝑒𝑓 (𝑘 + 1) 𝑞𝑟𝑒𝑓 (𝑘) Finally the equation (7) can be rewritten as below: Figure 4. Estimation of the predictive value for active power command [ −𝜓𝑙𝛽 (𝑘) 𝜓𝑠𝛼 (𝑘 + 1) 𝜓𝑙𝛼 (𝑘) 𝐿 ]=[ ]− 2[ 𝜓𝑠𝛽 (𝑘 + 1) 𝜓𝑙𝛽 (𝑘) 𝜓𝑙𝛼 (𝑘) 𝜔‖𝜓𝑙𝛼𝛽‖ 𝜓𝑙𝛼 (𝑘) Δ𝑃𝑟𝑒𝑓 (𝑘) + 𝜀𝑃 (𝑘) 𝑖𝛼 (𝑘) ][ ]−𝐿[ ] 𝑖𝛽 (𝑘) 𝜓𝑙𝛽 (𝑘) 𝜀𝑞 (𝑘) Where 𝜀𝑃 (𝑘) and 𝜀𝑞 (𝑘) are the actual active and reactive powers tracking errors, respectively and Δ𝑃𝑟𝑒𝑓 (𝑘) is the actual variation of active power command, defined as Δ𝑃𝑟𝑒𝑓 (𝑘) = 𝑃𝑟𝑒𝑓 (𝑘) − 𝑃𝑟𝑒𝑓 (𝑘 − 1). B. Rotating Reference Frame Virtual Flux based predictive control, represented in the stationary reference frame, can be expressed in the rotating reference frame d-q using the following equations: 𝑖𝑞 𝑃 [ ] = 𝜔𝜓𝑙𝑑 [ ] 𝑞 𝑖𝑑 Under purely sinusoidal and balanced condition of the supply network, the amount of the 𝜓𝑙𝑑 is exactly constant in the steady state condition and can be expressed as 𝜓𝑙𝑑 (𝑘 + 1) = 𝜓𝑙𝑑 (𝑘) = 𝜓𝑙𝑑 (𝑚𝑎𝑥). As a result, the difference between active and reactive powers during a switching period can be expressed as [ 𝑖𝑞 (𝑘 + 1) − 𝑖𝑞 (𝑘) 𝑃(𝑘 + 1) − 𝑃(𝑘) ] = 𝜔𝜓𝑙𝑑 [ ] 𝑞(𝑘 + 1) − 𝑞(𝑘) 𝑖𝑑 (𝑘 + 1) − 𝑖𝑑 (𝑘) What mentioned in the stationary reference frame about the left side of the equation (2), remains true in the rotating reference frame i.e. in (15). Hence the amount of the 𝑖𝑞 and 𝑖𝑑 at the start of the next switching period can be computed using (15). On the other hand the differential equations of a PWM rectifier in d-q frame can be expressed as [ 𝑒𝑞 (𝑡) 𝑣𝑞 (𝑡) 𝑖𝑞 (𝑡) 𝜔𝐿(𝑡) 𝑑 𝑖𝑞 (𝑡) ]=[ ]+𝐿 [ ]+𝑅[ ]+[ ] 𝑑𝑡 −𝜔𝐿𝑖 (𝑡) (𝑡) (𝑡) (𝑡) 𝑒𝑑 𝑣𝑑 𝑖𝑑 𝑖𝑑 𝑑 (𝑡) In order to decouple the previous differential equation, it could be assumed that 𝑢𝑞𝑑 (𝑡) = 𝑣𝑞𝑑 (𝑡) ± 𝜔𝐿𝑖𝑞𝑑 (𝑡) and by neglecting the influence of the resistance R and taking an integral from the obtained equation the result will be as follows: [ 𝜓𝑙𝑞 (𝑡) 𝜓𝑢𝑞 (𝑡) 𝑖𝑞 (𝑡) ]=[ ]+𝐿[ ] 𝜓𝑙𝑑 (𝑡) 𝜓𝑢𝑑 (𝑡) 𝑖𝑑 (𝑡) By referring to the equations expressed in the α-β frame, following equations can be written in the d-q frame: Page | 5 International Journal of Enhanced Research Publications, ISSN: XXXX-XXXX Vol. 2 Issue 4, April-2013, pp: (1-4), Available online at: www.erpublications.com 𝜓𝑢𝑞 (𝑘) 𝜓𝑙𝑞 (𝑘) 𝑖𝑞 (𝑘) ]=[ ]−𝐿[ ] 𝜓𝑢𝑑 (𝑘) 𝜓𝑙𝑑 (𝑘) 𝑖𝑑 (𝑘) 𝜓𝑢𝑞 (𝑘 + 1) 𝜓𝑙𝑞 (𝑘 + 1) 𝑖𝑞 (𝑘 + 1) ]=[ ]−𝐿[ ] 𝜓𝑢𝑑 (𝑘 + 1) 𝜓𝑙𝑑 (𝑘 + 1) 𝑖𝑑 (𝑘 + 1) [ [ And so { 𝑢𝑞 (𝑘) = 𝑢𝑑 (𝑘) = 𝜓𝑢𝑞 (𝑘+1)−𝜓𝑢𝑞 (𝑘) 𝑇𝑠 𝜓𝑢𝑑 (𝑘+1)−𝜓𝑢𝑑 (𝑘) 𝑇𝑠 And finally the rectifier average voltage vector in the d-q reference frame is given by the following expression: [ 𝑣𝑞 (𝑘) 𝑢𝑞 (𝑘) 𝜔𝐿𝑖𝑞 (𝑘) ]=[ ]+[ ] 𝑣𝑑 (𝑘) 𝑢𝑑 (𝑘) −𝜔𝐿𝑖𝑑 (𝑘) To use SVM switching strategy, it is needed to transform 𝑣𝑞𝑑 to 𝑣𝛼𝛽 i.e. from rotating coordinates in to stationary one. It can be done by using the following transformation matrix: [ 𝑣𝛼 (𝑘) −sin(𝜃) ]=[ 𝑣𝛽 (𝑘) cos(𝜃) cos(𝜃) 𝑣𝑞 (𝑘) ][ ] sin(𝜃) 𝑣𝑑 (𝑘) Simulation Results To study the performance of the VF based Predictive DPC (VF-PDPC) system under different supply voltage conditions, the PWM rectifier with proposed control scheme in both stationary and rotating reference frames has been simulated using MATLAB/Simulink tool. The main electrical parameters and control data of the system are given in Table. I Furthermore, V based predictive DPC (V-PDPC) control scheme has been simulated on the same electrical system in order to compare the operation of it with one of the VF-PDPC under distorted supply voltage conditions. Table 1: Electrical parameters of power circuit Item Value Switching period Ts 65 µS Resistance of reactor R 0.56 [Ω] Inductance of reactor L 19.5 [mH] DC-bus capacitor C 1100 µF Load resistance RL 68.6 [Ω] Line to line AC voltage E 85 V rms Source voltage frequency f 50 Hz DC-bus voltage vdc 180 V Simulation results in steady state and under ideal supply voltage condition obtained with Voltage based P-DPC in α-β reference frame is shown in Fig. 5. Also simulation results with the proposed VF-PDPC in both α-β and d-q reference frames are shown in Fig. 6 and Fig. 7 respectively. In these Figures (vα,vβ) is the components of the convertor average voltage vector which are calculated by the corresponding algorithms. As it can be seen from these results, the proposed Virtual Flux based P-DPC is as good as Voltage based P-DPC under ideal voltage conditions. Furthermore the THD of the input currents is improved just by 0.01% which is very impalpable. Fig. 9 to Fig. 20 show simulation results of the PWM rectifier under harmonic distorted supply voltage (%5 of fifth harmonic have been added to the ideal supply voltage). Simulation results are obtained by both Voltage and Virtual Flux based P-DPC in the stationary and rotating reference frames. Moreover Fig. 8 presents dynamic response and transient behavior of the PWM rectifier in the startup conditions. This result is obtained with proposed VF-PDPC in the rotating frame. As can be seen in this figure, the DC bus voltage reaches and stays in its reference value in less than 120ms. There is some oscillations in the initial times (before t=120ms) of the response which there is not in the response obtained by V-PDPC; this is because of the estimation process of the Virtual Flux. Page | 6 International Journal of Enhanced Research Publications, ISSN: XXXX-XXXX Vol. 2 Issue 4, April-2013, pp: (1-4), Available online at: www.erpublications.com a) b) c) d) Figure 5. Simulation results of PWM rectifier in steady state for Voltage based P-DPC in stationary (α-β) reference frame. (a): Active/Reactive Powers, qref=0, (b): three phase Currents, THD= 0.65%, (c): DC bus Voltage, Vdcref=180 v, (d): Convertor Average Voltage in α-β frame. a) b) c) d) Figure 6. Simulation results of PWM rectifier in steady state for Virtual Flux based P-DPC in stationary (α-β) reference frame. (a): Active/Reactive Powers, qref=0, (b): three phase Currents, THD= 0.64%, (c): DC bus Voltage, Vdcref=180 v, (d): Convertor Average Voltage in α-β frame. a) b) c) d) Figure 7. Simulation results of PWM rectifier in steady state for Virtual Flux based P-DPC in rotating (d-q) reference frame. (a): Active/Reactive Powers, qref=0, (b): three phase Currents, THD= 0.64%, (c): DC bus Voltage, Vdcref=180 v, (d): Convertor Average Voltage components in d-q frame Page | 7 International Journal of Enhanced Research Publications, ISSN: XXXX-XXXX Vol. 2 Issue 4, April-2013, pp: (1-4), Available online at: www.erpublications.com Figure 8. Dynamic response of DC bus Voltage using proposed VF-PDPC method in d-q frame Figure 9. Instantaneous Active and Reactive Powers in steady state conditions under V-PDPC algorithm in α-β frame Figure 10. Instantaneous Active and Reactive Powers in steady state conditions under VF-PDPC algorithm in α-β frame Figure 11. Instantaneous Active and Reactive Powers in steady state conditions under V-PDPC algorithm in d-q frame Figure 12. Instantaneous Active and Reactive Powers in steady state conditions under VF-PDPC algorithm in d-q frame Figure 13. DC bus Voltage in steady state under harmonic conditions that is controlled by V-PDPC algorithm in α-β frame Figure 14. DC bus Voltage in steady state under harmonic conditions that is controlled by VF-PDPC algorithm in α-β frame Fig. 9 to Fig. 12 present the steady state condition of the active and reactive powers (Fig. 9 and Fig. 11 are obtained by VPDPC in stationary and rotating frames respectively and Fig. 10 and Fig. 12 are obtained by VF-PDPC in stationary and rotating frames respectively). Also Fig. 13 to Fig. 16 present DC-bus voltage in steady state (Fig. 13 and Fig. 15 are obtained by V-PDPC in stationary and rotating frames and Fig. 14 and Fig. 16 are obtained by VF-PDPC in stationary and rotating frames respectively). Page | 8 International Journal of Enhanced Research Publications, ISSN: XXXX-XXXX Vol. 2 Issue 4, April-2013, pp: (1-4), Available online at: www.erpublications.com Figure 15. DC bus Voltage in steady state under harmonic conditions that is controlled by V-PDPC algorithm in d-q frame Figure 16. DC bus Voltage in steady state under harmonic conditions that is controlled by V-PDPC algorithm in d-q frame Figure 17. Three phase Currents of the rectifier under harmonic conditions that is controlled by V-PDPC algorithm in α-β frame (THD of phase A is 5.32% and THD of phases B,C is 5.77%) Figure 18. Three phase Currents of the rectifier under harmonic conditions that is controlled by VF-PDPC algorithm in α-β frame (THD of phases A, B and C is 1.29%) Figure 19. Three phase Currents of the rectifier under harmonic conditions that is controlled by V-PDPC algorithm in d-q frame (THD of phase A is 5.27% and THD of phases B,C is 5.74%) Figure 20. Three phase Currents of the rectifier under harmonic conditions that is controlled by VF-PDPC algorithm in d-q frame (THD of phases A, B and C is 1.23%) It is obvious in these results that the ripples of the active and reactive powers and also DC-bus voltage in the proposed Virtual Flux based P-DPC are less than in Voltage based P-DPC method. Since the ripples of the mentioned wave forms are negligible in both methods, it cannot be a good reason to use VF-PDPC algorithm instead of V-PDPC. But the main feature of the proposed method reveals itself in the wave form of the input currents. This feature is discussed in the next paragraph and the figures are presented after that. Fig. 17 to Fig. 20 present three phase AC currents of the PWM rectifier in steady state conditions (Fig. 17 and Fig. 19 are obtained by V-PDPC in stationary and rotating frames and Fig. 18 and Fig. 20 are obtained by VF-PDPC in stationary and rotating frames respectively). As can be seen in these results, the main advantage of the proposed method is that the THD of the input currents in the proposed algorithm is about 5 times less than in Voltage based P-DPC (for VF-PDPC: THD in α-β is 1.29% and in d-q is 1.23% and for V-PDPC: THD in α-β is 5.34% and in d-q is 5.27%). This feature is because of the low pass filter nature of the integrator element which exists in the estimation process of the Virtual Flux. There is a negligible problem in the proposed algorithm that reactive power of the PWM rectifier has a small offset in both α-β and d-q reference frame. This offset is caused by the effect of the low pass filter in the Virtual Flux estimator because the estimated Virtual Flux is not exactly lagged by 90 degrees from the corresponding voltage and there is about 3 to 4 degrees error in it. In 2011, a paper has presented a novel Virtual Flux observer that tries to eliminate this problem from the Virtual Flux estimation [22], but it has not been considered in this work. Page | 9 International Journal of Enhanced Research Publications, ISSN: XXXX-XXXX Vol. 2 Issue 4, April-2013, pp: (1-4), Available online at: www.erpublications.com Conclusion This paper presents a new Predictive Direct Power Control (P-DPC) for three phase PWM rectifier which is based on Virtual Flux (VF) space vector instead of Voltage space vector of the network. The proposed algorithm uses space vector modulation (SVM) switching strategy that works with constant switching frequency. The VF P-DPC scheme has been discussed theoretically in both stationary (α-β) and rotating (d-q) reference frames. 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