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482 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 8, NO. 3, AUGUST 2012 Instantaneous Reactive Power Minimization and Current Control for an Indirect Matrix Converter Under a Distorted AC Supply Marco Rivera, Member, IEEE, Jose Rodriguez, Fellow, IEEE, Jose R. Espinoza, Member, IEEE, and Haitham Abu-Rub, Senior Member, IEEE Abstract—This paper presents a current control scheme with instantaneous reactive power minimization for an indirect matrix converter. The strategy uses the commutation state of the converter in the subsequent sampling time according to an optimization algorithm given by a simple cost function and the discrete system model. Using this strategy, harmonics in the input current generated by the resonance of the input filter are strongly reduced. Simulation and experimental results with a laboratory prototype are provided in order to validate the control scheme, and the effects of a distorted source voltage and filter resonance are analyzed. Index Terms—AC–AC power conversion, current control, matrix converter, predictive control. NOMENCLATURE Source current . Source voltage . Input current . Input voltage Load current . . Load voltage Output current reference . . DC-link voltage. DC-link current. Filter capacitor. Filter inductor. Manuscript received December 30, 2011; revised February 27, 2012; accepted March 06, 2012. Date of publication April 09, 2012; date of current version July 23, 2012. This work was supported in part by the Centro Científico-Tecnológico de Valparaíso (CCTVal) NFB0821, the Universidad Técnica Federico Santa María, FONDECYT, under Project 1110794, and by the NPRP under Grant 4-077-2-028 from the Qatar National Research Fund (a member of Qatar Foundation). Paper no. TII-11-1086. M. Rivera and J. Rodriguez are with the Electronics Engineering Department, Universidad Técnica Federico Santa María, Valparaíso 2390123, Chile (e-mail: marco.rivera@usm.cl; jrp@usm.cl). J. R. Espinoza is with the Department of Electrical Engineering, Universidad de Concepción, Concepción 160–C, Chile (e-mail: jose.espinoza@udec.cl). H. Abu-Rub is with Texas A&M University at Qatar, Doha, Qatar (e-mail: haitham.abu-rub@qatar.tamu.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TII.2012.2194159 Filter resistor. Load resistance. Load inductance. Stationary coordinates. I. INTRODUCTION ITHIN the family of ac–ac converters, it is possible to distinguish two main groups: the converters with energy storage or dc-link and those without. In the first group are the current and voltage source topologies, with which it is possible to obtain ac–ac conversion taking into consideration the presence of a capacitive or inductive dc-link, respectively. These structures have been widely studied, and they are the converters used in the industry today. In the group of ac–ac circuits without dc-link, different topologies have been reported in the literature and are classified into three main groups: the cycloconverter in a wide power variety, the direct matrix converter (DMC), and the indirect matrix converter (IMC), both in the low-power range [1]. The cycloconverter is very common in high-power applications such as ball mills in mineral processing and cement kilns. However, it is severely limited in terms of output frequency with respect to the input, because of the presence of a high harmonic content caused by the commutations, which cannot be filtered by the load inductance. The IMC [2], [3] has been the subject of investigation for some time. One of the favorable features of an IMC is the absence of a dc-link capacitor, which allows for the construction of compact converters capable of operating under adverse atmospheric conditions such as extreme temperatures and pressures. These features have been explored and are the main reasons why the matrix converter family has been investigated for decades [4]. Compared with a DMC [1], the IMC features an easier-to-implement and more secure commutation technique: the dc-link zero current commutation [5]. Moreover, the conventional IMC has bidirectional power flow capabilities and can be designed to have small-sized reactive elements in its input filter. These characteristics make the IMC a suitable technology for high-efficiency converters for specific applications such as military, aerospace, wind turbine generator systems, external elevators for building construction, and skin pass mills, as reported in [6]–[12]. Therefore, these advantages make up for the additional cost of an IMC compared with conventional converters. IMC uses complex pulsewidth modulation (PWM) and space vector W 1551-3203/$31.00 © 2012 IEEE RIVERA et al.: INSTANTANEOUS REACTIVE POWER MINIMIZATION AND CURRENT CONTROL FOR AN IMC UNDER A DISTORTED AC SUPPLY 483 Fig. 1. General topology of the IMC. modulation (SVM) schemes to achieve the goal of unity power factor and sinusoidal output current [4], [13]–[32]. The subject of harmonics control in current waveforms of three-phase converters is a very important and timely topic. In effect, in [33], the reduction of current harmonics is achieved using the theory of instantaneous active and reactive power. Since power converters have a discrete nature, the application of predictive control constitutes a promising and better-suited approach, as compared with standard schemes that use mean values of the variables. Model-based predictive strategy is a powerful kind of control due to the simplicity and effectiveness of its control algorithm [34]. Using an accurate model of the system to be controlled, expressed in terms of space state equations, an optimal switching state from a power electronics converter can be determined to achieve the best response relative to a control variable reference input [35]–[40]. As the IMC is a finite commutation states machine, the predictive control algorithm is simplified to the prediction of every possible switching state and the application of the best suited one to follow certain references. Until today, most of the predictive techniques applied to matrix converters have been validated by considering a programmable ac supply [5], [41], [42], but, in the following pages, a more realistic behavior will be presented by considering an ac supply with low-order harmonics that introduce distortion in both source voltage and currents. II. IMC MODEL A conventional IMC is shown in Fig. 1. For the rectifier side, the dc-link voltage is obtained as a function of the rectifier switches and the input voltages as and, finally, output voltages are synthesized as a function of the as inverter switches and the dc-link voltage (4) These equations correspond to the nine and eight valid switching states for the rectifier and the inverter stages of a conventional IMC, respectively, as reported in [5]. To comply with the restrictions, the equations have no short circuits in the input and no open lines in the output. Also mandatory for a conventional IMC is to always have a positive dc-link voltage; consequently, the nine rectifier states reduce to only three valid states in every sampling time . In addition, the rectifier includes an filter on the input side which is needed to prevent over-voltages and to provide filtering of the high-frequency components of the input currents produced by the commutations and the inductive nature of the load. The filter consists of a second-order system described by (5) (6) The load model is obtained similarly. Assuming an inductive-resistive load, as shown in Fig. 1, the following equation describes the behavior of the load: (7) (1) III. CONTROL SCHEME FOR THE IMC and input currents are defined as a function of the rectifier switches and the dc-link current as (2) For the inverter side, dc-link current is determined as a function of the inverter switches and the output currents as (3) The control scheme for the IMC is represented in Fig. 2. The approach pursues the selection of the switching state of the converter that leads the output currents closest to their respective references at the end of the sampling period. In addition, the instantaneous reactive power on the line side of the rectifier must be minimized. Finally, the dc-link voltage must always be positive [43]. First, the control objectives are determined and the variables necessary to obtain the prediction model are measured and calculated. The model of the system and the measurements are used 484 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 8, NO. 3, AUGUST 2012 in sampling time. Hence, if the dynamic model is accurate, the control algorithm will always give the best performance. This very simple and intuitive technique is also highly precise in achieving its goal. A cost function is then defined in order to be able to measure the error between the reference and the predicted load current response. Then, every sample period, this cost function is computed for each possible commutation state on the converter. The one with the smallest error is selected and applied at the beginning of the next sample period. The cost function can be as simple as (13) and denote the load current in coordinates for sample time, and and are their respective references. An extra term can be added to this cost function to minimize other parameters that should be subject to control, such as the instantaneous reactive power consumed by the IMC input along with the filter, the common-mode voltage, the commutation losses, the positive voltage in the dc link, and so forth. The cost function used to validate the control scheme in this paper is given by where Fig. 2. Predictive current control scheme. to predict the behavior of the variables that will be controlled in the subsequent sampling time, for each of the valid switching states. The predicted values are then used to evaluate a cost function which deals with the control objectives. After that, the valid switching state that produces the lowest value of the cost function is selected for the next sampling period. In order to compute the differential equations shown in –(7), the general forward-difference Euler formula is used as the derivative approximation to estimate the value of each function one sample time in the future (the variable’s predicted value). A. Input Filter and Load Discrete Equations The predicted values of the input and output side are (14) which allows for control of the load current and the minimization of the instantaneous reactive power on the input side. In denotes the error between (14), is a weighting factor and the reference and predicted value of the instantaneous reactive sampling time, expressed as power in (8) where (9) (10) Matrices and are given as (11) The load current prediction can be obtained using a forward Euler approximation in (7) such as (12) where, and are constants dependent on load parameters and [41]. Note that the currents and depend on the switching state through (2) and (4), respectively. B. Cost Function Definition With the discretized system model, including the load, the input filter, and the IMC, the implementation of the predictive algorithm is very straightforward. The goal of this method is to always apply the IMC switching state that gives the right voltage space vector , in order to produce the lowest error between the desired load current and the predicted load current response (15) where , , , and are the source voltages and curcoordinates, respectively. The instantaneous reacrents in in order to have a tive power reference is established as (for an unity power factor on the input side. Noting that arbitrary ) gives perfect tracking of the load current and unity power factor on the source side, then, by minimizing , the optimum value for commutation state is guaranteed. In practice, by the appropriate selection of the weighting factor , a given THD of the input and output currents is obtained. The principal method for selecting the weighting factors has been presented in [44]. C. Discrete Time Delay Error Compensation Several measured and calculated variables are needed, as well as the knowledge of the nine rectifier-side and the eight inverterside valid switching states, to compute the control scheme algorithm. With these IMC rectifier and inverter side valid states, there are 72 possible switching combinations that must be calculated to select the one resulting in the least error in the cost function. If the three valid rectifier-side switching states giving positive dc-link voltage are calculated before the cost function calculation routine, then only 24 switching combinations must be computed. This results in saved computation time, but the microelectronic controller still carries a large numerical burden, causing an unwanted delay. The variables measured are , , , and , leaving the IMC input current and the IMC output voltage as functions of the th selected switching RIVERA et al.: INSTANTANEOUS REACTIVE POWER MINIMIZATION AND CURRENT CONTROL FOR AN IMC UNDER A DISTORTED AC SUPPLY 485 TABLE I EXPERIMENTAL SETUP PARAMETERS state, and , respectively, to be calculated. In order to counter the delay error due to the discrete time computation, an effective and simple method is implemented: the cost function . First, the variables in are predicted calculation for ; then, the variusing the already applied switching state ables to be controlled are predicted for using the best switching state to get to a minimum. The sample time should be sufficient to begin the data acquisition at . The variables are then computed for using , time is calculated to select the optimum ; and the this is all done in the same time interval so the latter can be ap. is considered equal to due to plied in its very small change in one sample time [5], [45]. Fig. 3. Simulation results of current control without instantaneous reactive power minimization. (a) Source voltage v [V/10] and current i [A]. (b) Output current i and reference i [A]. (c) Instantaneous reactive power q [VAR]. IV. SIMULATION RESULTS Two different simulations were carried out to feasibility probe the control method. Simulations with and without instantaneous reactive power minimization were done in order to evaluate the effect of introducing the instantaneous reactive power minimization in the control scheme. The simulation parameters are established according to the experimental setup available in our laboratory (they are indicated in Table I), and the sampling pe20 s. The outputs riod of the control algorithm was set at of the controller are used to deliver the gate driver signals for the IGBTs. These outputs are directly set by the control algorithm and no modulator is needed. A. Simulation Results Without Instantaneous Reactive Power Minimization First, the control scheme is simulated without including the term that minimizes the instantaneous reactive power on the input side of the system, so in (14). Results show that the input current in Fig. 3(a) has a strong distortion. This is also clearly indicated in the frequency spectrum of Fig. 4(b), where it is shown that the resonance of the input filter is situated in 650 Hz, according to the filter parameters, and with this it is possible to observe 1.1%, 87.2%, and 91.3% of the third, fifth, and seventh harmonics, respectively. On the other hand, the output currents follow the reference accurately as indicated in Fig. 3(b). Fig. 4(c) shows the spectrum of the load current . Fig. 3(c) shows the instantaneous reactive power on the input side. Due to the strong distortion of the source current, an unwanted high reactive power is present on the input side. In this is clean with a sinusoidal waveform and case, the ac supply no harmonic distortion [Fig. 4(a)]. Fig. 4. Simulation results of current control without instantaneous reactive power minimization.( a) Spectrum of source voltage [pu]. (b) Spectrum of source current [pu]. (c) Spectrum of output current [pu]. B. Simulation Results With Instantaneous Reactive Power Minimization In the second case, the control strategy is evaluated considering in (14). Fig. 5(a) shows an improved input behavior, with sinusoidal current in correct phase with the input phase voltage, fulfilling the condition of unitary power factor, with a reduced harmonic distortion as indicated in Fig. 6(b). In this case, it is possible to observe 0.3%, 2.7%, and 1.2% of the third, fifth, and seventh harmonics, respectively. On the output side, the load current presents a good tracking with respect its reference, Fig. 5(b). Fig. 5(c) shows the improvement in the instantaneous reactive input power minimization, and, thus, the goal of the proposed predictive current control is clearly achieved. It must be acknowledged that the main advantage of the proposed control method is the simplicity of implementation, since the controller does not need a complex modulation unit. This can reduce the overall cost of the entire system. 486 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 8, NO. 3, AUGUST 2012 Fig. 5. Simulation results of current control including instantaneous reactive [V/10] and current i [A]. power minimization. (a) Source voltage v (b) Output current i and reference i [A]. (c) Instantaneous reactive power q [VAR]. Fig. 7. Experimental results of current control without instantaneous reactive power minimization. (a) Source voltage v [V] and current i [A]. (b) output current i [A]. Fig. 8. Experimental results of current control without instantaneous reactive power minimization. (a) Spectrum of source voltage [pu]. (b) Spectrum of source current [pu]. (c) Spectrum of output current [pu]. Fig. 6. Simulation results of current control with instantaneous reactive power minimization. (a) Spectrum of source voltage [pu]. (b) Spectrum of source current [pu]. (c) Spectrum of output current [pu]. V. EXPERIMENTAL RESULTS An IMC laboratory prototype designed and built by Universidad Técnica Federico Santa María, thanks to the support of the Power Electronics Systems Laboratory of ETH, Zurich, Switzerland, was used for the experimental evaluation. The converter features IGBTs of type IXRH40N120 for the bidirectional switch, and standard IGBTs with anti-parallel diodes IRG4PC30UD for the inverter stage. The control scheme was implemented in a dSPACE 1103, which is connected to additional boards that include the field-programmable gate array (FPGA) for the commutation sequence generation and the signal conditioning for the measurement of voltages and currents. The parameters used in the experimental tests are given in Table I. The sampling period of the control algorithm 20 s. was set in A. Experimental Results Without Instantaneous Reactive Power Minimization First, the control strategy is evaluated considering in (14). Fig. 7 shows the input current with a high harmonic distortion, as indicated in Fig. 8(b). There, it is evident that according to the filter parameters, the input filter resonance is situated at 650 Hz. As mentioned before, an input approximately filter must be added to assist the commutation of switching devices and to mitigate against line-current harmonics. However, the filter configuration which is shown in Fig. 1 presents a resonance frequency, and it can be excited by the utility due to the potential 5th and 7th harmonics in the ac-source and also by the converter itself. Due to the available ac-source in our laboratory, the input filter resonance is reflected in the source voltage as seen in Fig. 7(a) and Fig. 8(a). Finally, as reported in [46]–[48], when a distortion is present in the source voltage, the source current is not sinusoidal. For all the aforementioned reasons, it is necessary to include a term in the cost function that can help overcome this problem. A summary of the total harmonic distortion (THD) is presented in Table II. RIVERA et al.: INSTANTANEOUS REACTIVE POWER MINIMIZATION AND CURRENT CONTROL FOR AN IMC UNDER A DISTORTED AC SUPPLY TABLE II EXPERIMENTAL THD RESULTS WITH  487 =0 Fig. 10. Experimental results of current control including instantaneous reactive power minimization. (a) Spectrum of source voltage [pu]. (b) Spectrum of source current [pu]. (c) Spectrum of output current [pu]. TABLE III EXPERIMENTAL THD RESULTS WITH  = 0:003 Fig. 9. Experimental results current control including instantaneous reactive power minimization. (a) Source voltage v [V] and current i [A]. (b) Output current i [A]. B. Experimental Results With Instantaneous Reactive Power Minimization C. Problem With a Weak AC Supply It is known that most industrial applications require unity power factor in the grid side. For this reason, through the instantaneous reactive power minimization, the system is forced to work with a unity power factor on the input side. Fig. 9(a) shows the measured source current and voltage of phase , and Fig. 9(b) shows the reference and measured output current of phase . As expected, the source current fulfills the condition of unitary power factor showing an almost sinusoidal waveform and, as a consequence, the instantaneous reactive power is minimized. This is achieved by increasing the value of the weighting to which has been empirifactor from cally adjusted as explained in [44]. There, first it is established as a value equal to zero in order to prioritize the control of the output current; later it is slowly increased with the aim to obtain unity power factor in the input currents while maintaining a good behavior on the output side. In Fig. 9(b), a very good tracking of the load current with respect to its reference can be seen. The improvement in the quality of the source current is remarkable, because, due to the mitigation of the input filter resonance, a significant reduction of distortion is apparent in Fig. 10(b) compared with Fig. 8(b). The same effect is observed in the source voltage of Fig. 10(a). As evident in Fig. 9(a), the source currents show a ripple corresponding to the resonance frequency of the input filter and the harmonic distortion of the ac supply, as observed in the spectrum of Fig. 10(a). The THD of the source voltage and current and the output current are indicated in Table III. In Figs. 8(a) and 10(a), the spectrum of the source voltage is shown in both cases, when [Fig. 8(a)] and [Fig. 10(a)]. In the first case, the ac-source was highly distorted due to the high input current distortion and the low-order harmonics of the grid. This phenomenon occurs because a three-phase variac as the ac-supply is used. The variac behaves like a weak ac-source for the system, due to the associated inductance with the autotransformer connection. Thanks to the minimization of the instantaneous reactive power, the harmonic distortion of the source voltage is decreased from a THD of 36.48% to 14.82%. In Fig. 7(a), a distorted source current with a THD of 66.07% was observed, but when the instantaneous reactive power is minimized, a THD of 21.03% is obtained. The load current THD was 8.80% in the first case, but, when the weighting factor is considered as , an output current with a THD of 8.54% is observed. The resonance of the input filter is still a major concern that directly affects the selection of the design parameters and the modulation method. In Fig. 11, the predictive controller is enhanced by including an active damping scheme in order to mitigate the potential resonances in the input filter. The method is resonance, imbased on a virtual resistor that damps the proving the performance of the system as indicated in [49]–[51]. By considering this method, the source voltage and current THD are 13.67% and 22.81%, respectively, with a THD of 7.49% in the load current. 488 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 8, NO. 3, AUGUST 2012 Fig. 11. Experimental results with active damping implementation. (a) Source voltage v [V] and current i [A]. (b) Output current i [A]. VI. CONCLUSION A current control with instantaneous reactive power minimization for an IMC has been presented in this paper. The control scheme uses the predicted values of the input and output currents to evaluate the best-suited converter state considering the output current error and the input power factor. Our experimental results indicate that the presented strategy provides good tracking of the output current to its reference and at the same time minimizes the instantaneous reactive power on the input side. In addition, the strategy presented in this paper produces a drastic reduction in the input current harmonics generated by the resonance of the input filter, which is usually a major problem in matrix converters. The method also presents drawbacks, as the cost function is explicitly solved for each switching state. This can be a problem if a slow controller is used, as a higher sampling time could increase the harmonic distortion in the currents. The ac supply and the filter resonance have an important influence on the behavior of the source current, and better results can be expected by optimizing the input filter, by adding active damping but also with a clean ac supply. REFERENCES [1] P. Wheeler, J. Rodriguez, J. Clare, L. Empringham, and A. Weinstein, “Matrix converters: A technology review,” IEEE Trans. Ind. Electron., vol. 49, no. 2, pp. 276–288, Apr. 2002. [2] T. Wijekoon, C. Klumpner, P. Zanchetta, and P. Wheeler, “Implementation of a hybrid ac-ac direct power converter with unity voltage transfer,” IEEE Trans. Power Electron., vol. 23, no. 4, pp. 1918–1926, Jul. 2008. [3] J. Kolar, T. Friedli, J. Rodriguez, and P. Wheeler, “Review of threephase pwm ac-ac converter topologies,” IEEE Trans. Ind. Electron., vol. 58, no. 11, pp. 4988–5006, Nov. 2011. [4] J. Kolar, T. Friedli, F. Krismer, and S. Round, “The essence of threephase ac-ac converter systems,” in Proc. Power Electron. Motion Control Conf., Poznan, Poland, 2008. [5] P. Correa, J. Rodriguez, M. Rivera, J. Espinoza, and J. Kolar, “Predictive control of an indirect matrix converter,” IEEE Trans. Ind. Electron., vol. 56, no. 6, pp. 1847–1853, Jun. 2009. [6] P. Zanchetta, P. Wheeler, J. Clare, M. Bland, L. Empringham, and D. Katsis, “Control design of a three-phase matrix-converter-based ac-ac mobile utility power supply,” IEEE Trans. Ind. Electron., vol. 55, no. 1, pp. 209–217, Jan. 2008. [7] S. Lopez Arevalo, P. Zanchetta, P. Wheeler, A. Trentin, and L. Empringham, “Control and implementation of a matrix-converter-based ac ground power-supply unit for aircraft servicing,” IEEE Trans. Ind. Electron., vol. 57, no. 6, pp. 2076–2084, Jun. 2010. [8] E. Yamamoto, T. Kume, H. Hara, T. Uchino, J. Kang, and H. Krug, “Development of matrix converter ans its applications in industry,” in Proc. Annu. Conf. IEEE Ind. Electron. Soc., Porto, Portugal, 2009. [9] R. Bucknall and K. Ciaramella, “On the conceptual design and performance of a matrix converter for marine electric propulsion,” IEEE Trans. Power Electron., vol. 25, no. 6, pp. 1497–1508, Jun. 2010. [10] R. Gupta, K. Mohapatra, A. Somani, and N. Mohan, “Direct-matrixconverter-based drive for a three-phase open-end-winding ac machine with advanced features,” IEEE Trans. Ind. Electron., vol. 57, no. 12, pp. 4032–4042, Dec. 2010. [11] R. Cardenas, R. Pena, J. Clare, and P. Wheeler, “Analytical and experimental evaluation of a WECS based on a cage induction generator fed by a matrix converter,” IEEE Trans. Energy Conversion, vol. 26, no. 1, pp. 204–215, Jan. 2011. [12] C. Ortega, A. Arias, C. Caruana, J. Balcells, and G. Asher, “Improved waveform quality in the direct torque control of matrix-converter-fed PMSM drives,” IEEE Trans. Ind. Electron., vol. 57, no. 6, pp. 2101–2110, Jun. 2010. [13] J. Rodriguez, M. Rivera, J. Kolar, and P. Wheeler, “A review of control and modulation methods for matrix converters,” IEEE Trans. Ind. Electron., vol. 59, no. 1, pp. 58–70, Jan. 2012. [14] X. Lu, K. Sun, G. Li, and L. Huang, “Analysis and control of input power factor in indirect matrix converter,” in Proc. Annu. Conf. IEEE Ind. Electron. Soc., Porto, Portugal, 2009. [15] S. Ahmed, A. Iqbal, and H. Abu-Rub, “Generalized duty-ratio-based pulsewidth modulation technique for a three-to-k phase matrix converter,” IEEE Trans. Ind. Electron., vol. 58, no. 9, pp. 3925–3937, Sep. 2011. [16] J. Kang, E. Yamamoto, M. Ikeda, and E. Watanabe, “Medium-voltage matrix converter design using cascaded single-phase power cell modules,” IEEE Trans. Ind. Electron., vol. 58, no. 11, pp. 5007–5013, Nov. 2011. [17] S. Ahmed, A. Iqbal, H. Abu-Rub, J. Rodriguez, C. Rojas, and M. Saleh, “Simple carrier-based PWM technique for a three-to-nine-phase direct ac-ac converter,” IEEE Trans. Ind. Electron., vol. 58, no. 11, pp. 5014–5023, Nov. 2011. [18] P. Kiatsookkanatorn and S. Sangwongwanich, “A unified PWM method for matrix converters and its carrier-based realization using dipolar modulation technique,” IEEE Trans Ind. Electron., vol. 59, no. 1, pp. 80–92, Jan. 2012. [19] Z. Yan, M. Jia, C. Zhang, and W. Wu, “An integration SPWM strategy for high-frequency link matrix converter with adaptive commutation in one step based on de-re-coupling idea,” IEEE Trans. Ind. Electron., vol. 59, no. 1, pp. 116–128, Jan. 2012. [20] M. Jussila and H. Tuusa, “Comparison of simple control strategies of space-vector modulated indirect matrix converter under distorted supply voltage,” IEEE Trans. Power Electron., vol. 22, no. 1, pp. 139–148, Jan. 2007. [21] R. Pena, R. Cardenas, E. Reyes, J. Clare, and P. Wheeler, “A topology for multiple generation system with doubly fed induction machines and indirect matrix converter,” IEEE Trans. Ind. Electron., vol. 56, no. 10, pp. 4181–4193, Oct. 2009. [22] M. Y. Lee, P. Wheeler, and C. Klumpner, “Space-vector modulated multilevel matrix converter,” IEEE Trans. Ind. Electron., vol. 57, no. 10, pp. 3385–3394, Oct. 2010. [23] R. Cardenas-Dobson, R. Pena, P. Wheeler, and J. Clare, “Experimental validation of a space vector modulation algorithm for four-leg matrix converters,” IEEE Trans. Ind. Electron., vol. PP, no. 99, pp. 1–1, 2010. [24] T. Friedli and J. Kolar, “Comprehensive comparison of three-phase ac-ac matrix converter and voltage dc-link back-to-back converter systems,” in Proc. Int. Power Electron. Conf., Sapporo, Japan, 2010. [25] J. Kolar, F. Schafmeister, S. Round, and H. Ertl, “Novel three-phase ac-ac sparse matrix converters,” IEEE Trans. Power Electron., vol. 22, no. 5, pp. 1649–1661, Sep. 2007. [26] H. Hojabri, H. Mokhtari, and L. Chang, “A generalized technique of modeling, analysis, and control of a matrix converter using SVD,” IEEE Trans. Ind. Electron., vol. 58, no. 3, pp. 949–959, Mar. 2011. [27] R. Pena, R. Cardenas, E. Reyes, J. Clare, and P. Wheeler, “Control of a doubly fed induction generator via an indirect matrix converter with changing dc voltage,” IEEE Trans. Ind. Electron., vol. 58, no. 10, pp. 4664–4674, Oct. 2011. [28] X. Wang, H. Lin, H. She, and B. Feng, “A research on space vector modulation strategy for matrix converter under abnormal input-voltage conditions,” IEEE Trans. Ind. Electron., vol. 59, no. 1, pp. 93–104, Jan. 2012. [29] X. Lie, J. Clare, P. Wheeler, L. Empringham, and L. Yongdong, “Capacitor clamped multilevel matrix converter space vector modulation,” IEEE Trans. Ind. Electron., vol. 59, no. 1, pp. 105–115, Jan. 2012. RIVERA et al.: INSTANTANEOUS REACTIVE POWER MINIMIZATION AND CURRENT CONTROL FOR AN IMC UNDER A DISTORTED AC SUPPLY [30] H. She, H. Lin, B. He, X. Wang, L. Yue, and X. An, “Implementation of voltage-based commutation in space-vector-modulated matrix converter,” IEEE Trans. Ind. Electron., vol. 59, no. 1, pp. 154–166, Jan. 2012. [31] H. Nguyen, H.-H. Lee, and T.-W. Chun, “Input power factor compensation algorithms using a new direct-SVM method for matrix converter,” IEEE Trans. Ind. Electron., vol. 58, no. 1, pp. 232–243, Jan. 2011. [32] M. Hamouda, H. Blanchette, K. Al-Haddad, and F. Fnaiech, “An efficient DSP-FPGA-based real-time implementation method of SVM algorithms for an indirect matrix converter,” IEEE Trans. Ind. Electron., vol. 58, no. 11, pp. 5024–5031, Nov. 2011. [33] S. Mikkili and A. Panda, “Instantaneous active and reactive power and current strategies for current harmonics cancellation in 3-PH 4WIRE SHAF with both PI and fuzzy controllers,” Energy Power Eng., 2011. [34] S. Kouro, P. Cortes, R. Vargas, U. Ammann, and J. Rodriguez, “Model predictive control, a simple and powerful method to control power converters,” IEEE Trans. Ind. Electron., vol. 56, no. 6, pp. 1826–1838, Jun. 2009. [35] P. Correa, J. Rodriguez, I. Lizama, and D. Andler, “A predictive control scheme for current-source rectifiers,” IEEE Trans. Ind. Electron., vol. 56, no. 5, pp. 1813–1815, May 2009. [36] P. Cortes, G. Ortiz, J. Yuz, J. Rodriguez, S. Vazquez, and L. Franquelo, “Model predictive control of an inverter with output LC filter for UPS applications,” IEEE Trans. Ind. Electron., vol. 56, no. 6, pp. 1875–1883, Jun. 2009. [37] H. Miranda, P. Cortes, J. Yuz, and J. Rodriguez, “Predictive torque control of induction machines based on state-space models,” IEEE Trans. Ind. Electron., vol. 56, no. 6, pp. 1916–1924, Jun. 2009. [38] M. Preindl, E. Schaltz, and P. Thπgersen, “Switching frequency reduction using model predictive direct current control for high power voltage source inverters,” IEEE Trans. Ind. Electron., vol. PP, no. 99, pp. 1–1, 2010. [39] J. Rodriguez, J. Kolar, J. Espinoza, M. Rivera, and C. Rojas, “Predictive torque and flux control of an induction machine fed by an indirect matrix converter with reactive power minimization,” in Proc. Int. Symp. Ind. Electron., Bari, Italy, 2010. [40] M. Rivera, J. Rodriguez, P. Wheeler, C. Rojas, A. Wilson, and J. Espinoza, “Control of a matrix converter with imposed sinusoidal source currents,” IEEE Trans. Ind. Electron., vol. 59, no. 4, pp. 1939–1949, Apr. 2012. [41] S. Muller, U. Ammann, and S. Rees, “New time-discrete modulation scheme for matrix converters,” IEEE Trans. Ind. Electron., vol. 52, no. 6, pp. 1607–1615, Dec. 2005. [42] R. Vargas, J. Rodriguez, U. Ammann, and P. Wheeler, “Predictive current control of an induction machine fed by a matrix converter with reactive power control,” IEEE Trans. Ind. Electron., vol. 55, no. 12, pp. 4362–4371, Dec. 2008. [43] J. Rodriguez, J. Kolar, J. Espinoza, M. Rivera, and C. Rojas, “Predictive current control with reactive power minimization in an indirect matrix converter,” in Proc. Int. Conf. Ind. Technol., Viña del Mar, Chile, 2010. [44] P. Cortes, S. Kouro, B. La Rocca, R. Vargas, J. Rodriguez, J. Leon, S. Vazquez, and L. Franquelo, “Guidelines for weighting factors design in model predictive control of power converters and drives,” in Int. Conf. Ind. Technol. (ICIT), Gippsland, Australia, 2009. [45] P. Cortes, J. Rodriguez, C. Silva, and A. Flores, “Delay compensation in model predictive current control of a three-phase inverter,” IEEE Trans. Ind. Electron., vol. 59, no. 2, pp. 1323–1325, Feb. 2012. [46] D. Casadei, G. Serra, and A. Tani, “A general approach for the analysis of the input power quality in matrix converters,” IEEE Trans. Power Electron., vol. 13, no. 5, pp. 882–891, May 1998. [47] F. Blaabjerg, D. Casadei, C. Klumpner, and M. Matteini, “Comparison of two current modulation strategies for matrix converters under unbalanced input voltage conditions,” IEEE Trans. Ind. Electron., vol. 49, no. 2, pp. 289–296, Feb. 2002. [48] A. Timbus, P. Rodriguez, R. Teodorescu, M. Liserre, and F. Blaabjerg, “Control strategies for distributed power generation systems operating on faulty grid,” in Proc. Int. Symp. Ind. Electron., Montreal, QC, Canada, 2006. [49] M. Rivera, P. Correa, J. Rodriguez, I. Lizama, and J. Espinoza, “Predictive control of the indirect matrix converter with active damping,” in Proc. Int. Power Electron. Motion Control Conf., Wuhan, China, 2009. [50] M. Rivera, C. Rojas, J. Rodriguez, P. Wheeler, B. Wu, and J. Espinoza, “Predictive current control with input filter resonance mitigation for a direct matrix converter,” IEEE Trans. Power Electron., vol. 26, no. 10, pp. 2794–2803, Oct. 2011. 489 [51] M. Rivera, J. Rodriguez, B. Wu, J. Espinoza, and C. Rojas, “Current control for an indirect matrix converter with filter resonance mitigation,” IEEE Trans. Ind. Electron., vol. 59, no. 1, pp. 71–79, Jan. 2012. Marco Rivera (S’09–M’10) received the B.Sc. degree in electronics engineering and M.Sc. degree in electrical engineering from the Universidad de Concepción, Concepción, Chile, in 2007 and 2008, respectively, and the Ph.D. degree in electronics engineering from Universidad Técnica Federico Santa María, Valparaíso, Chile, in 2011. During January and February of 2010, he was a Visiting Ph.D. student with the Electrical and Computer Engineering Department, Ryerson University, Canada, where he was involved with predictive control applied on four-leg inverters. He was also a Visiting Ph.D. student with the Departamento de Ingeniería Eléctrica y Computacional, ITESM, Monterrey, Mexico, where he was involved with experimental aspects of a double fed induction generator—indirect matrix converter system. Between September and November 2011, he was a Visiting Researcher with the Laboratoire PLAsma et Conversion d’Energie (LAPLACE), Université de Toulouse, Toulouse, France. Currently, he holds a Post-Doctoral position with the Universidad Técnica Federico Santa María, Valparaíso, Chile. His research interests include direct and indirect matrix converters, predictive and digital controls for high-power drives, four-leg converters, and development of high-performance control platforms based on field-programmable gate arrays. Dr. Rivera was awarded a scholarship from the Marie Curie Host Fellowships for Early Stage Research Training in Electrical Energy Conversion and Conditioning Technology at University College Cork, Ireland, in 2008. Jose Rodriguez (M’81–SM’94–F’10) received the Engineer degree from the Universidad Técnica Federico Santa María, Valparaíso, Chile, in 1977, and the Dr.-Ing. degree from the University of Erlangen, Erlangen, Germany, in 1985, both in electrical engineering. He has been with the Department of Electronics Engineering, Universidad Técnica Federico Santa María, Valparaíso, Chile, since 1977, where he is currently a Full Professor and Rector. He has coauthored more than 300 journal and conference papers. His main research interests include multilevel inverters, new converter topologies, control of power converters, and adjustable-speed drives. Prof. Rodriguez is member of the Chilean Academy of Engineering. He has been an associate editor of the IEEE TRANSACTIONS ON POWER ELECTRONICS and the IEEE TRANSACTIONS ON INDUSTRY ELECTRONICS since 2002. He received the Best Paper Award from the IEEE TRANSACTIONS ON INDUSTRY ELECTRONICS in 2007, the Best Paper Award from the IEEE INDUSTRIAL ELECTRONICS MAGAZINE in 2008, and the Best Paper Award from the IEEE TRANSACTIONS ON POWER ELECTRONICS in 2010. Jose R. Espinoza (S’92–M’97) received the Engineering degree in electronic engineering and M.Sc. degree in electrical engineering from the University of Concepción, Concepción, Chile, in 1989 and 1992, respectively, and the Ph.D. degree in electrical engineering from Concordia University, Montreal, QC, Canada, in 1997. Since 2006, he has been a Professor with the Department of Electrical Engineering, Universidad de Concepción, Concepción, Chile, where he is engaged in teaching and research in the areas of automatic control and power electronics. He has authored and coauthored more than 100 refereed journal and conference papers. Prof. Espinoza is currently an associate editor of the IEEE TRANSACTIONS ON INDUSTRY ELECTRONICS and the IEEE TRANSACTIONS ON POWER ELECTRONICS. 490 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 8, NO. 3, AUGUST 2012 Haitham Abu-Rub (M’99–SM’07) received the M.Sc. degree in electrical engineering from the Gdynia Maritime University, Gdynia, Poland, in 1990, and the Ph.D. degree from Gdansk University of Technology, Gdansk, Poland, in 1995. He then became an Assistant Professor with Gdansk University of Technology, Gdansk, Poland. For eight years, he was an Assistant Professor and an Associate Professor with Birzeit University, Palestine, where he has been the Chairman of the Electrical Engineering Department for four years. He is currently an Associate Professor with Texas A&M University at Qatar, Doha, Qatar. He has authored or coauthored more than 140 journal and conference papers. His main research interests include electric drives and power electronics. Dr. Abu-Rub is the recipient of many prestigious international awards, such as the American Fulbright Scholarship (at Texas A&M University), the German Alexander von Humboldt Fellowship (at the University of Wuppertal), the German DAAD Scholarship (at Bochum University), the British Royal Society Scholarship (at Southampton University), and others.