Influence of Covariance-Based ALS Methods in the Performance of Predictive Controllers With Rotor Current Estimation
Abstract
The use of online rotor current estimators with predictive current controllers has been very recently stated in five-phase induction motor drives, where the closed-loop performance of the system is improved by using suboptimal estimators based on Kalman filters. In this paper, the interest of using optimization methods in the definition of the Kalman filter, like the covariance technique, is analyzed. Obtained system performances using optimal and suboptimal rotor current estimators are experimentally compared.
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Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published by IEEE: J. Rodas, C. Martín, M. R. Arahal, F. Barrero and R. Gregor, "Influence of Covariance-Based ALS Methods in the Performance of Predictive Controllers With Rotor Current Estimation," in IEEE Transactions on Industrial Electronics, vol. 64, no. 4, pp. 2602-2607, April 2017, DOI: 10.1109/TIE.2016.2636205 “© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.”
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Influence of Covariance-Based ALS Methods in the Performance of Predictive Controllers with Rotor Current Estimation Jorge Rodas, Member,IEEE, Cristina Mart´ ın, Manuel R. Arahal, Member,IEEE, Federico Barrero, Senior Member,IEEE, and Ra´ ul Gregor Abstract—The use of on-line rotor current estimators with predictive current controllers has been very recently stated in five-phase induction motor drives, where the closed-loop performance of the system is improved using sub-optimal estimators based on Kalman filters. In this work, the interest of using optimization methods in the definition of the Kalman filter, like the covariance technique, is analyzed. Obtained system performances using optimal and sub-optimal rotor current estimators are experimentally compared. Index Terms—Kalman filter, multiphase drives, optimal covariance estimation, predictive current control. I. INTRODUCTION THE interest in model predictive control like an alternative in power converters and drives to field oriented or direct torque controllers has been growing up in the last decade [1]. In the multiphase drives’ research field the predictive current control (PCC) technique represents the most popular case study [2]. PCC uses a state-space representation of the drive to optimize the control action. The estimation of non-measurable state components, typically rotor currents, is a complex problem that has been recently solved using different methods for the on-line estimation of the rotor variables [3, 4]. These studies illustrate the benefits in using rotor current observers like Kalman filters (KF), although sub-optimal techniques were applied during the necessary tuning process of these observers. Manuscript received May 5, 2016; revised September 1, 2016 and October 17, 2016; accepted November 15, 2016. This work was supported by the Paraguayan Government through the CONACYT grant 14-INV-101 (research Project) in the framework of the program “Programa Paraguayo para el Desarrollo de la Ciencia y Tecnolog´ ıa,” PROCIENCIA. This work was also funded by the Spanish Ministry of Science and Innovation under Project DPI2013-44278-R, the University of Seville, Spain (V Research Plan, action II.2). J. Rodas and R. Gregor are with the Laboratory of Power and Control Systems, Facultad de Ingenier´ ıa, Universidad Nacional de Asunci´ on, 2060 Luque, Paraguay (e-mail: [email protected]y; [email protected]y). C. Mart´ ın and F. Barrero are with the Department of Electronic Engineering, University of Seville, 41004 Seville, Spain (e-mail: cmar[email protected]; [email protected]). M. R. Arahal is with the Department of Systems Engineering and Automatic Control, University of Seville, 41004 Seville, Spain (e-mail: [email protected]). In this paper, a rotor current observer based on KF is included in the conventional PCC technique, being a remarkable contribution of the work the optimal design of the KF by means of a robust covariance estimation method. In [4] the KF gains are tuned based on trial and error strategies, using some prior expert knowledge or hypothesis about the noise. The proposed method is based on the estimation of true covariances in the control system, which has not been previously tested in the multiphase electrical drives’ field. A five-phase induction machine (IM) is used as a case example, but the obtained results can be extrapolated to different electrical machines. II. PREDICTIVE CURRENT CONTROL WITH OPTIMAL ROTOR CURRENT ESTIMATION A five-phase IM drive with distributed windings equally displaced #=2⇡/5and powered by a five-phase two-level voltage source inverter (VSI) is used. A block diagram of the conventional PCC technique detailed in [2] is shown in Fig. 1(a) together with a schematic representation of the five-phase IM drive. This PCC controller utilizes a discrete model of the system, named predictive model, to predict (at time k) the future values (time k+1) of the machine’s stator currents, bis(k+1|k), for each possible stator voltage, u(k). Thus, the predictive model relies on the knowledge of some variables such as the measured stator currents is(k)and electrical speed !r(k), as it is shown in the following equation: bi(k+1|k)=Ai(k)+Bu(k)(1) where i=(i↵s,i s,i xs,i ys,i ↵r,i r),u=(u↵s,u s,u xs,u ys), and Aand Bare matrices that depend on the electrical parameters of the machine and the sampling time Ts. Matrix Aalso depends on the actual value of !r(k), and it must be calculated every sampling time. A detailed explanation of the machine model is not included here for the sake of conciseness and can be found in [3]. It is worth stating that, according to the well-known vector space decomposition approach [4], the electromechanical energy conversion variables are mapped into the ↵subspace, meanwhile the current components in the xysubspace in the analyzed electrical machine are related to harmonic losses. In conventional PCC the computation of the control signal takes a significant amount of time which is comparable with
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS &RVWIXQFWLRQ (T 0LQLPL]HU PLQ-N_N 3UHGLFWLYHPRGHO (TVDQG 7DEOHRISRVVLEOH YROWDJHYHFWRUV )LYHSKDVH,0 96, 3&& (a) &RVWIXQFWLRQ (T 0LQLPL]HU PLQ-N_N 3UHGLFWLYHPRGHO (TVDQG 7DEOHRISRVVLEOH YROWDJHYHFWRUV HVWLPDWRU (T DQG HVWLPDWRUV 4U5Q )LYHSKDVH,0 96, 3&& .) $/6 (b) Fig. 1. Schematic diagram of the five-phase IM drive and blok diagram of (a) the conventional PCC technique applied in [2] for the regulation of five-phase IM drives, and (b) the proposed PCC technique that uses a KF-based optimum rotor current estimator. Ts, so a second-step ahead prediction of the stator currents bis(k+2|k)is required [3]. In the existing literature this term is obtained iteratively using the predictive model. Regarding the rotor quantities that appear in (1), most research works rely on aggregating all unmeasurable quantities into one term that is tracked, although the use of estimators for rotor quantities has been recently proposed in [4], at the expense of a remarkable increment of the computational cost of the implemented controller (by 36 % of the total). Once the second-step ahead prediction is obtained, an optimization process is applied every sampling period, where a cost function Jis calculated for all 32 (25) possible stator voltages to obtain a desired reference trajectory i⇤ s(k). The voltage vector that minimizes the cost function is selected and applied to the system during the next sampling period. The cost function can be defined in different ways, although the deviation between reference and predicted stator currents is normally used as follows: J(k+2|k)=kbe↵ k2+xy kbexy k2(2) being bethe second-step ahead predicted error computed as be=i⇤ s(k+ 2) bis(k+2|k), and xy a tuning parameter that allows to put more emphasis on ↵or xysubspaces [1, 5]. A. Influence of Rotor Current in Prediction As commented before, the predictive model given by (1) cannot be used for producing predictions if rotor currents are not measurable (as it is the normal case) unless some estimation of rotor currents is provided. PCC methods have overcome this problem by aggregating all non-measurable terms in one factor that is later tracked and updated (G). For this purpose, the stator current vector is divided into a measurable part, is=(i↵s,i s,i xs,i ys), and a non-measured part, ir=(i↵r,i r), and the predictive model takes the following form: bis(k+1|k)=¯ Ai s(k)+¯ Bu(k)+b G(k|k)(3) with appropriate ¯ Aand ¯ Bmatrices obtained from (1) using elemental algebra. The b G(k|k)term is approximated holding its previous value b G(k1|k)computed at time k, using past values of measured variables: b G(k1|k)=is(k)¯ Ai s(k1) ¯ Bu(k1) (4) B. Rotor Current Estimator Based on Kalman Filter Instead of using the tracking and updating technique proposed in conventional PCC methods, a KF is used in [4] as it is shown in Fig. 1(b), where the b Q⇢and b R⌫estimators block were not taken into account. The rotor currents ( bir) are estimated every sampling time using the measured rotor speed !r, stator phase currents isand stator phase voltages u. Considering uncorrelated processes and zero-mean Gaussian measurement noises, the machine’s model (1) can be written as follows: bi(k+1|k)=Ai(k)+Bu(k)+H⇢(k) is(k)=Ci(k)+⌫(k)(5) being ⇢(k)the disturbance vector (process noise), ⌫(k)the measurement noise, and Hthe noise weight matrix. Dividing the current vector in two parts, i↵s=(i↵s,i s) and i↵r=(i↵r,i r), the dynamic of the reduced-order rotor current estimator can be defined in the following way: bi↵r(k+1|k)=(A22 K(k)A12)bi↵r(k) +K(k)bi↵s(k+1|k) +(A21 K(k)A11)i↵s(k) +(B2K(k)B1)u↵(k) (6)
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS where K(k)represents the KF gain matrix and u↵ =(u↵s,u s). This estimation of rotor currents can now be used to produce the second-step ahead prediction for the stator current as: bi↵s(k+2|k)=A11 bi↵s(k+1|k)+A12 bi↵r(k+1|k) +B1u↵(k+ 1) (7) The KF gain matrix is calculated at each sampling time in a recursive manner using an estimation of two covariance matrices of the noises called b Q⇢and b R⌫. These covariances are defined as the expected values of the disturbance and the measurement noise as Q⇢=cov(⇢)=E{⇢·⇢T}and R⌫=cov(⌫)=E{⌫·⌫T}, being the KF gain matrix obtained using the following steps: (k)='(k)'(k)·CT(C·'(k)·CT+b R⌫)1·C·'(k)(8) K(k)=(k)·CTb R1 ⌫(9) '(k+ 1) = A(k)·AT+Hb Q⇢·HT(10) This completes the required relations for the state estimation, where the minimum estimation errors depends on K(k)and it is guaranteed if the estimated noise covariances and the initial condition of the state covariance ('(0)) are known. Notice that the interest of using KF in the context of the stator current prediction and PCC is presented in [4], where the KF was hardly tuned using initial values, but the obtained experimental results encouraged future research towards establishing the KF as a tool of choice for the definition of predictive controllers in electrical drives. C. Proposed optimization procedure The KF optimal implementation is difficult due to the lack of information about the noises. The use of an optimal estimation using KF requires the estimation of b Q⇢and b R⌫, which can be done through Bayesian, maximum likelihood, covariance matching or correlation techniques. Bayesian and maximum likelihood are complex and require much data. Covariance matching uses the residuals of the state estimation problem, but it provides biased estimates of the true covariances, resulting in a non optimal KF tuning. In [6] the Autocovariance Least Squares method (ALS) is proposed to provide unbiased estimates with the lowest variance, guaranteeing optimal KF tuning. The ALS method is done off-line based on data gathered from closed-loop operation. The positive semi-definiteness of the covariance estimation is guaranteed by adding constraints to the ALS problem. Note that without this method, and given the current level of sophistication of the predictive control methods, the use of KF is incomplete, following the Bellman optimality principle. Furthermore, the KF algorithm computational cost is the same whereas the system performance improves. The initial estimation of disturbance covariances ( b Q⇢0and b R⌫0) can be obtained from the residuals of the estimator using (11) and (12), as it is stated in [7]. Then, by solving the optimization problem (13) the estimated covariances ( b Q⇢ and b R⌫) are obtained. The first term in (13) is the residues norm, the second term is the constraint penalization term, the <(6 12 ,QLWLDO9DOXHV 5HDG6WRUHG'DWD ,I RU FRQYHUJHV 3HUIRUP1HZWRQ6WHSIRU DQG(VWLPDWH8SGDWH 2EWDLQHGIURP(T 2EWDLQHGIURP(T 8VHU'H¿QHG Fig. 2. ALS flow chart considering initial covariances (Q⇢0and Rnu0) and number of data points (Nd). 3UHGLFWLYH0RGHO(T 3UHGLFWLYH0RGHO(T &RVW)XQFWLRQ(YDOXDWLRQ(T <(6 12 <(6 12 5RWRU&XUUHQW(VWLPDWLRQ (T .)*DLQ0DWUL[ (YDOXDWLRQ (TV Fig. 3. Proposed PCC algorithm in a flow chart diagram. term |·|denotes the determinant of the matrix, Aand bbare defined in [6] as Eqs. (11) and (12), respectively, and µis the barrier parameter for the semi-definite constraint (Q⇢0and R⌫0). By using a Newton-based optimization procedure, the covariances are obtained after a predefined number of iterations (n) or when the results converge as shown in Fig. 2.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 6SHHG(QFRGHU )LYH3KDVH,0 '&0RWRU'&0RWRU 3RZHU(OHFWURQLF&RQYHUWHU &RPSXWHU '&/LQN Fig. 4. Scheme of the experimental test rig. b Q⇢0=cov{bi(k+1|k)Abi(k|k1) Bu(k)H⇢(k|k1)}(11) b R⌫0=cov{is(k)Ci(k|k1) I⇢(k|k1)}(12) minQ⇢ R⌫A(Q⇢)s (R⌫)sbb 2 2 µlog Q⇢0 0R⌫(13) Note that b Q⇢and b R⌫are constant values during the proposed PCC algorithm. To make things clearer, a flow chart of the proposed PCC control algorithm is presented in Fig. 3. In general, tuning parameters of the predictive controllers is not easy as many studies focusing on this area have shown [5, 8]. Although the use of KF improves the modeling of complex electrical systems and consequently the better performance of the PCC controller, the optimal parameters of the filter was still a problem to be solved, and the proposed method covers this part of the problem by an optimal estimation of b Q⇢and b R⌫. The contribution of this paper analyzes the obtained improvement when this optimal rotor current estimator is applied. III. EXPERIMENTAL RESULTS To validate the proposed control method, an experimental evaluation has been conducted. A diagram of the test rig is shown in Fig. 4. The principal element is a three pairs of poles five-phase IM whose nominal parameters have been experimentally determined as Rs= 19.45 ⌦,Rr=6.77 ⌦, Lls = 100.7mH, Llr = 38.06 mH, M= 656.5mH, !n= 1,000 rpm and Pn=1kW. Two 2-level three-phase power converters from Semikron (SKS22F) are used to drive the five-phase IM, where the DC-link voltage is set to 300 V using a DC power supply system. The control system is based on a MSK28335 board and a TMS320F28335 DSP, being the rotor mechanical measured using a GHM510296R/2500 digital encoder and the eQEP peripheral of the DSP. A DC motor is also used to introduce a variable load torque in the system. Different tests were carried out to validate the current controller performance using the conventional PCC method (C1), the PCC method with KF detailed in [4] (C2) and the PCC with the proposed optimum-KF (C3). A sampling TABLE I EXPERIMENTAL RESULTS AT DIFFERENT OPERATING POINTS ![rpm] Figures of merit C1 C2 C3 400 MSEi⇤ ↵s0.1068 0.0972 0.0954 MSE b i⇤ ↵s0.1468 0.1390 0.1382 MSEi⇤ xs 0.1217 0.1199 0.1176 THD(%) 14.15 13.29 13.47 500 MSEi⇤ ↵s0.1075 0.0950 0.0907 MSE b i⇤ ↵s0.1411 0.1343 0.1267 MSEi⇤ xs 0.1284 0.1051 0.0963 THD(%) 16.86 15.07 14.07 550 MSEi⇤ ↵s0.1227 0.1044 0.0879 MSE b i⇤ ↵s0.1526 0.1363 0.1247 MSEi⇤ xs 0.1408 0.1354 0.1260 THD(%) 16.08 14.63 13.18 600 MSEi⇤ ↵s0.1177 0.0924 0.0860 MSE b i⇤ ↵s0.1469 0.1318 0.1234 MSEi⇤ xs 0.1435 0.1355 0.1203 THD(%) 16.42 12.50 12.96 700 MSEi⇤ ↵s0.1266 0.0875 0.0835 MSE b i⇤ ↵s0.1579 0.1300 0.1285 MSEi⇤ xs 0.1524 0.1433 0.1430 THD(%) 17.34 14.81 14.70 frequency of 15 kHz and half of the nominal load are considered, as well as the cost function defined in (2) with xy =0.1(the torque and flux production are promoted by the controller over the harmonic losses). Four figures of merit are used to compare the efficiency of the different rotor current estimators in terms of control performance and prediction accuracy. These are mean squared values of the current control error in ↵and xaxis, defined in (14), the model prediction error in ↵axis (15), and a total harmonic distortion measurement (THD) of the stator phase (15). MSEi⇤ (↵,x)s=v u u tPN j=1 ⇣i(↵,x)s(j)i⇤ (↵,x)s(j)⌘2 N(14) MSEbi↵s=v u u tPN j=1 ⇣i↵s(j)bi↵s(j)⌘2 N(15)
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 7LPHV &XUUHQW$ (a) 7LPHV &XUUHQW$ (b) 7LPHV &XUUHQW$ (c) Fig. 5. Experimental comparison of obtained stator currents in ↵and xaxis using (a) C1, (b) C2 and (c) C3 techniques at 550 rpm and half nominal torque load. THDbis=sMSEbi2 ↵s+MSE bi2 xys i↵s peak/2(16) Table I and Fig. 5 summarize the obtained results in steady-state operation, where it is quantified the obtained improvement when the proposed rotor current estimator is used. It is observed that all mean squared values are improved (lower values) if the proposed optimum KF rotor current estimator (C3) is used. For instance, the obtained MSEi⇤ ↵s value at 550 rpm using C3 is reduced in 28.36 % and 15.80 % when it is compared with those obtained using C1 and C2, respectively. Similarly, the obtained MSEbi↵svalue at 600 rpm is also reduced in 16.00 % and 6.37 % when C3 is employed instead of C1 and C2, respectively. Note that similar results are obtained at different operating points. Fig. 5 details the performance of the system using C1, C2 and C3 at 550 rpm, where the current tracking characteristics in ↵and xaxis are plotted, showing that the closed-loop performance of the system using C3 technique offers better tracking characteristics than others. Regarding the harmonic content of the stator current, the obtained value is lower if the rotor current estimator is used, being C3 the best in most cases. The dynamic performance using the C3 method is finally analyzed, and the obtained results are shown in Fig. 5. The qstator current reference (i⇤ qs) is varied according to a step profile, while the dstator current reference is set to a constant value (i⇤ ds=0.57 A); see Fig. 5 (upper plot). The measured stator currents in synchronous (dand qaxis, upper plot of Fig. 5) and stationary (↵xyaxis, middle plot of Fig. 5) frames follow the impressed references, which confirms that the proposed controller works well at different mechanical speed and during transient states. Note that the outer speed controller is not used in the test and the mechanical speed is not regulated, hence it varies as it is shown in the lower plot of Fig. 5. It is also worth mentioning that a sampling frequency of 15 kHz (sampling time of about 67 µs) is used, which still enables the implementation of the KF-based rotor estimator in the C2 and C3 controllers. Note also that the proposed ALS method does not affect the computational cost (the proposed 7LPHV 6SHHGUSP DQG&XUUHQWV$ &XUUHQWV$ Fig. 6. Transient response using the C3 controller. From top to bottom: dqstator currents ids and iqs, and their references i⇤ ds and i⇤ qs;↵and xcurrents i↵sand ixs, with the imposed reference i⇤ ↵s, and mechanical speed !m. optimization procedure is performed off-line, prior to starting the normal operation of the multiphase drive). IV. CONCLUSION This work addresses the application of KF in the design of rotor current observers when PCC methods are used in IM drives. In particular, a procedure for the design of an optimal KF is presented. Experimental results in a five-phase IM drive show the interest of the proposed procedure, which improves stator current prediction and tracking, comparing with other conventional or KF-based PCC methods. Notice that all the obtained conclusions for a particular case example based on five phase IM can be extended to different multiphase and conventional IM. REFERENCES [1] S. Kouro, M.A. Perez, J. Rodriguez, A.M. Llor, and H.A. Young, “Model Predictive Control: MPC’s Role in the Evolution of Power Electronics,” IEEE Ind. Electron. Mag., vol. 9, DOI 10.1109/MIE.2015.2478920, no. 4, pp. 8–21, Dec. 2015.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS [2] F. Barrero and M.J. Duran, “Recent Advances in the Design, Modeling, and Control of Multiphase Machines – Part I,” IEEE Trans. Ind. Electron., vol. 63, DOI 10.1109/TIE.2015.2447733, no. 1, pp. 449–458, Jan. 2016. [3] C. Martin, M.R. Arahal, F. Barrero, and M.J. Duran, “Multiphase Rotor Current Observers for Current Predictive Control: a Five-Phase Case Study,” Control Eng. Pract., vol. 49, DOI 10.1016/j.conengprac.2016.01.011, pp. 101–111, Apr. 2016. [4] J. Rodas, F. Barrero, M.R. Arahal, C. Martin, and R. Gregor, “On-Line Estimation of Rotor Variables in Predictive Current Controllers: a Case Study Using Five-Phase Induction Machine,” IEEE Trans. Ind. Electron., vol. 63, DOI 10.1109/TIE.2016.2559420, no. 9, pp. 5348–5356, Sept. 2016. [5] C.S. Lim, E. Levi, M. Jones, N.A. Rahim, and W.P. Hew, “FCS-MPC based Current Control of a Five-Phase Induction Motor and its Comparison with PI-PWM Control,” IEEE Trans. Ind. Electron., vol. 61, DOI 10.1109/TIE.2013.2248334, no. 1, pp. 149–163, Jan. 2014. [6] B.J. Odelson, M.R. Rajamani, and J.B. Rawlings, “A New Autocovariance Least-Squares Method for Estimating Noise Covariances,” Automatica, vol. 42, DOI 10.1016/j.automatica.2005.09.006, no. 2, pp. 303–308, Feb. 2006. [7] T. Soderstrom, M. Mossberg, and M. Hong, “A Covariance Matching Approach for Identifying Errors-in-Variables Systems,” Automatica, vol. 45, DOI 10.1016/j.automatica.2009.05.010, no. 9, pp. 2018–2031, Sept. 2009. [8] S.A. Davari, D.A. Khaburi, and R. Kennel, “An Improved FCS–MPC Algorithm for an Induction Motor With an Imposed Optimized Weighting Factor,” IEEE Trans. Power Electron., vol. 27, DOI 10.1109/TPEL.2011.2162343, no. 3, pp. 1540–1551, Mar. 2012. Jorge Rodas (S’08–M’12) was born in Asuncion, Paraguay, in 1984. He received his B.Eng. degree in Electronic Engineering from the National University of Asuncion, Paraguay, in 2009. He received his M.Sc. degrees from the University of Vigo, Spain, in 2012 and from the University of Seville, Spain, in 2013. He received his Ph.D. degrees from the National University of Asuncion, in 2016 and from the University of Seville, in 2016. In 2011, Prof. Rodas joined the Engineering Faculty at the National University of Asuncion, where he is currently a Full Professor. His main research areas are predictive control, multiphase drives, matrix converters and control of power converters for renewable energy applications. Cristina Mart´ın was born in Seville, Spain, in 1989. She received the Industrial Engineer degree from the University of Malaga, Spain, in 2014. In 2015, she joined the Electronic Engineering Department of the University of Seville, where she is currently working toward the Ph.D. degree. Her current research interests include modeling and control of multiphase drives, microprocessor and DSP device systems, and electrical vehicles. Manuel R. Arahal (M’06) was born in Seville, Spain, in 1966. He received the M.Sc. and Ph.D. degrees in Industrial Engineering from the University of Seville, Spain, in 1991 and 1996, respectively. He is currently a Professor at the Systems Engineering and Automation Department at the University of Seville. He has been distinguished with the Best Paper Awards from the IEEE Transactions on Industrial Electronics for 2009, and from the IET Electric Power Applications for 2010–2011. Federico Barrero (M’04–SM’05) received the M.Sc. and Ph.D. degrees in Electrical and Electronic Engineering from the University of Seville, Spain, in 1992 and 1998, respectively. In 1992, he joined the Electronic Engineering Department at the University of Seville, where he is currently an Associate Professor. He received the Best Paper Awards from the IEEE Transactions on Industrial Electronics for 2009 and from the IET Electric Power Applications for 2010–2011. Ra´ul Gregor was born in Asuncion, Paraguay, in 1979. He received his B.Eng. degree in Electronic Engineering from the Catholic University of Asuncion, Paraguay, in 2005. He received the M.Sc. and Ph.D. degrees in Electronic, Signal Processing and Communications from the Higher Technical School of Engineering (ETSI), University of Seville, Spain, in 2008 and 2010, respectively. Since March 2010, Prof. Gregor is Head of the Laboratory of Power and Control System of the Engineering Faculty in the National University of Asuncion, Paraguay. He received the Best Paper Awards from the IEEE Transactions on Industrial Electronics for 2009 and from the IET Electric Power Applications for 2010–2011. His research interests include; multiphase drives, advanced control of power converters topologies, quality of electrical power, renewable energy, modelling, simulation, optimization and control of power systems, smart metering & smart grids and predictive control.