High-Performance Torque and Flux Control for ... - IEEE Xplore

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 22, NO. 6, NOVEMBER 2007

High-Performance Torque and Flux Control for Multilevel Inverter Fed Induction Motors Samir Kouro, Student Member, IEEE, Rafael Bernal, Hernán Miranda, Student Member, IEEE, César A. Silva, Member, IEEE, and José Rodríguez, Senior Member, IEEE

Abstract—This paper presents a high-performance torque and flux control strategy for high-power induction motor drives. The control method uses the torque error to control the load angle, obtaining the appropriate flux vector trajectory from which the voltage vector is directly derived based on direct torque control principles. The voltage vector is then generated by an asymmetric cascaded multilevel inverter without need of modulation and filter. Due to the high output quality of the inverter, the torque response presents nearly no ripple. In addition, switching losses are greatly reduced since 80% of the power is delivered by the high-power cell of the asymmetric inverter, which commutates at fundamental frequency. Simulation and experimental results for 81-level inverter are presented. Index Terms—Direct torque control, induction motor, multilevel inverters, switching losses.

I. INTRODUCTION

I

NDUCTION motors are today the most widely used alternative in adjustable speed drives. Field-oriented control (FOC) [1]–[3] and direct torque control (DTC) [4]–[7] have emerged as the standard industrial solutions for high dynamic performance operation of these machines. On the other hand, multilevel inverters have become a very attractive solution for high-power applications, due to higher voltage operation capability, reduced common-mode ’s, and smaller or voltages, near-sinusoidal outputs, low even no output filter [8]. FOC can be naturally extended for multilevel inverter-fed drives, only the modulation method has to be upgraded to multilevel pulsewidth modulation (PWM) (with multiple carrier arrangements) or multilevel space vector modulation (SVM). On the contrary, traditional DTC cannot be extended easily for multilevel inverters, due to the high amount of possible voltage vectors available for selection. Therefore, some contributions have adapted DTC to multilevel topologies

Manuscript received December 1, 2006; revised May 10, 2007. This work was supported by the Chilean National Fund of Scientific and Technological Development (FONDECYT), under Grants 1060423 and 1060436 and by the Industrial Electronics and Mechatronics Millenium Science Nucleus of the Universidad Técnica Federico Santa María. Recommended for publication by Associate Editor A. Consoli. S. Kouro, H. Miranda, C. A. Silva, and J. Rodrígurez are with the Electronics Engineering Department, Universidad Técnica Federico Santa María, Valparaíso, Chile (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). R. Bernal is with the Komatsu Chile S.A., Quilicura, Santiago, Chile (e-mail: [email protected]). 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/TPEL.2007.909189

[9], [10]. However, they are conceived for particular inverter topologies and for a certain amount of levels. A more generalized view is presented in [11] and [12] with good dynamic performance, nevertheless at expense of complicated implementation issues including torque derivatives and prediction. Other recent contributions, for two-level inverter-fed drives, combine DTC principles together with PWM and SVM to reduce torque ripple and fix the switching frequency of the inverter [13]–[20]. Although DTC is known by the absence of modulators and torque linear controllers, this approach has shown significant improvements together with high dynamic performance. This paper presents a load angle control-based DTC to enable the natural incorporation of multilevel inverters. The approach is intended for inverters with high number of levels (over nine levels), more commonly observed in modular structures like the cascaded H-bridge inverter. In particular in this paper, an asymmetric-fed cascaded inverter is used [21]–[24]. The high number of levels and consequently of voltage vectors provided by these inverters makes the modulation stage unnecessary. In addition, the semiconductors of the high-power cells of the inverter only perform few commutations per cycle, reducing the switching losses of the inverter, which is specially attractive for high-power applications. Experimental results obtained for a 81-level inverter-fed induction motor confirm the accuracy and high dynamic performance of the proposed method. II. THE INVERTER A. Power Circuit The power circuit of the Asymmetric Cascaded H-Bridge Inverter is illustrated in Fig. 1. The inverter is composed by the series connection of two or more H-bridge inverters fed by independent dc-sources provided by individual secondaries of a transformer or batteries (if used in electric or hybrid vehicles for example). These sources are not equal, i.e., , for each phase . The use of asymmetric input voltages can reduce, or when properly chosen, eliminate redundant output levels, maximizing the number of different levels generated by the inverter. Therefore this topology can achieve the same output voltage quality with less number of semiconductors. This also reduces volume, costs, losses and improves reliability. When cascading three , 0 and , level inverters like H-bridges (output levels: the optimal asymmetry is obtained by using voltage sources scaled proportional to the power of three. Applying this criteria

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KOURO et al.: HIGH-PERFORMANCE TORQUE AND FLUX CONTROL FOR MULTILEVEL INVERTER FED INDUCTION MOTORS

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TABLE I NINE-LEVEL ASYMMETRIC CASCADED INVERTER SWITCHING STATES

Fig. 1. Asymmetric cascaded H-bridge multilevel inverter.

to the voltage sources illustrated in Fig. 1, optimal design leads to

(1) for phase

, and

the number of cells per phase.

B. Output Voltage Generation Since the power cells are connected in series, the total phase voltages generated by the inverter can be expressed as Fig. 2. Output voltage generation with asymmetric inverter.

(2)

where is the total output voltage of phase (respectively, the is the output voltage of cell of neutral of the inverter ), the switching state associated to cell . phase , and Note how the output voltage of one cell is defined by one of the four binary combinations of the switching state, with “1” and “0” representing the “On” and “Off” states of the corresponding switch, respectively. The voltage levels generated by the inverter can be calculated by replacing (1) into (2), and considering all the possible comdifbinations of the switching states. The inverter generates cells can genferent voltage levels (e.g. an inverter with erate different voltage levels). When using three-phase systems, the number of different voltage vectors is given by , where is the number of levels. For example, for the case with 81 levels there are 19.441 different voltage vectors (huge difference compared to the nine levels and 217 vectors obtained with a 4-cell symmetric-fed cascaded inverter). Table I summarizes the output levels for an asymmetric ninelevel inverter using only cells per phase (only phase is

given). An example of the voltage waveform generation for an asymmetric nine-level inverter is illustrated in Fig. 2. C. Low Power-Cell Regeneration One of the drawbacks of this topology is that the low power cells have an inverse power flow for some voltage levels. This can be appreciated in the nine-level example of Fig. 2. Note that is achieved with the generation of the output voltage level and as individual outputs of the low and high-power cell respectively. This means that the low-power cell is connected in opposite direction to the current flow, and experiments an increase in the dc-link capacitor voltage, eliminating the necessary asymmetry to obtain the output voltage levels of the inverter. This can be corrected using an active frond end (AFE) instead of a diode rectifier. Another solution, but not so efficient, could be the use of a resistive load to dissipate power from the dc-link with a chopper circuit. Nevertheless, the amount of power controlled by the small power cells is less than 15% of the total power managed by the converter [25].

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III. PROPOSED MULTILEVEL DTC A. DTC Basic Principles of an ac machine is reThe stator voltage space vector in a stator fixed coordinate lated to the stator flux vector system by (3) where is the stator resistance and is the stator current space vector [4]. By neglecting the voltage drop in , the stator flux vector is the time integral of the stator voltage vector. Hence, for a small sampling period , the following relation holds:

Fig. 3. DTC operating principle: stator voltage vector influence over the stator flux vector.

(4) This approximation can lead to model errors that affect the operation at low speeds, since the reduction of the voltage becomes comparable to the resistive drop. Nevertheless, this drawback can be compensated, as will be explained later. is related to the On the other hand, the machine torque stator and rotor fluxes by (5) where , known as the load angle, is the angle between stator and , and rotor fluxes, is the number of pole pairs, , with , and the leakage factor as the stator, rotor and mutual inductances, respectively [16]. If both fluxes are kept constant in (5), it is clear that the torque can be controlled directly by changing the load angle. This can be easily achieved, since variations in the stator flux vector change the load angle due to slower rotor flux dynamics. Considering (4) and (5), it follows that the stator voltage vector can be used to manipulate the load angle, and consequently to control the torque.

Fig. 4. Nearest level selection: (a) waveform synthesis and (b) control diagram.

B. Flux and Torque Control by Load Angle Tracking In traditional DTC, the influence over the load angle of each voltage vector generated by the inverter is determined and stored in a lookup table, according to the stator flux position in the complex plane. This is difficult to extend for multilevel inverter-fed drives, where the complexity increases in huge proportions in relation to the levels generated by the inverter, due to the amount of vectors involved for selection. Therefore it is easier to look at the problem in a different way: the torque error can be used to generate a reference load angle necessary to correct the torque behavior. Then the desired load angle can be used to compute the exact voltage vector that will produce the necessary flux . This principle is illustrated in Fig. 3. Note that variation once provided the reference load angle , the reference stator can be computed by flux vector

Fig. 5. Fundamental reference tracking error with nearest voltage level selection (round).

the reference stator flux vector angle . Then the desired stator can be obtained by (4) as voltage vector

(6)

(7)

where is the fixed stator flux amplitude reference, and is the rotor flux vector angle. Note that corresponds to

Finally, has to be generated by the inverter. This is commonly performed with PWM or SVM for two or three level


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Fig. 6. DTC scheme for multilevel inverter-fed induction motor drive.

Fig. 7. Estimators: (a) flux and (b) torque.

TABLE II MOTOR PARAMETERS

inverters [13], [14]. The inclusion of the modulation stage is considered a drawback in comparison to classic DTC and can

Fig. 8. Asymmetric cascaded inverter (four cells per phase, 81 levels).

also introduce considerable switching losses, specially in highpower applications, due to the high-frequency carriers used in PWM strategies. Since asymmetric multilevel inverters can generate a large amount of different voltage vectors, no modulation is really necessary. The closest vector that can be generated by the inverter to the reference can be directly synthesized. This inverter control technique is known as space vector control [26]. However, the determination of the closest vector, although conceptually very simple, demands in practice some extra computational resources. Instead of choosing the closest vector, the reference voltage vector can be transformed into three-phase coordinates giving three voltage references , and in time domain. Now the problem is reduced to finding the closest voltage level. This is function. The nearest ineasily performed using the teger function or round function, is defined such that is the integer closest to . Since this definition is ambiguous for half-integers, the additional convention is that half-integers are

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Fig. 9. Speed step response: (a) simulation results and (b) experimental results.

always rounded to even number, for example, . Fig. 4(a) shows a qualitative example of the working principle. The inverter output level will be the closest possible to the refer. The imence. The largest possible error is then limited by plementation of the nearest voltage level generation is presented in Fig. 4(b). Note that the inverter switching table corresponds to Table I of this paper. It is worth to mention that this method is not a modulation technique, since there are no duty cycles involved, the stepped waveform is naturally generated and the number of commutations are reduced. The drawback is that no exact mean value tracking of the reference is possible since there are no average value calculations. Nevertheless, the introduced error can be neglected due to the high amount of levels generated by the inverter, and also because the involved variables are included in the inner control loop, hence the outer loop will compensate the differences if a proper bandwidth is designed. In addition this error is reduced to almost zero when using three or four cells with asymmetric-fed sources, this is shown in Fig. 5 where clearly can be appreciated errors below 1% for 3-cell (27-level) inverters across all the modulation indexes. The complete control diagram of the proposed multilevel DTC strategy is shown in Fig. 6. Note that a coordinates into the three-phase transformation is necessary to convert voltage references so the nearest level can be selected and generated. In addition, for a practical implementation, the necessary to implement (7) can be a block with the gain problem, since it is a dead-beat controller that with the practical implementation delay can lead to instability [20]. In addition, since can be very small leading to a very high gain. This will produce large control actions and also noise introduction in the loop, which can result in system stability problems. Therefore, as shown in this gain can be replaced by a linear controller

the diagram, in this work a PI controller has been used. In addiby a controller, more degrees tion, by changing the gain of freedom are available to compensate the approximation of (3) to (4), to avoid problems at low speeds. Its worth noticing that the resistive drop is not neglected in the flux estimation used for feedback due to the use of the rotor equation for this estimation. This is possible because the control scheme is not sensorless and the speed measurement is available for flux estimation. However, at higher frequencies (higher speed) the low-pass nature of the controller (PI) does not provide an adequate compensation leaving stationary error. This is not relevant, since at high-speed operation the approximation error of neglecting the resistive drop is not significant, and its effect on the torque production is compensated by outer the torque loop controller. If necessary, the approximation can be avoided by the use of the measured current and the resistance value , by using (3) rather than (4). Finally, the flux and torque estimators used in this particular work are illustrated in Fig. 7(a) and (b), respectively. The first is based on the rotor flux equation and the latter on the torque equation [20]. The flux-weakening operation can be easily implemented by the stator flux control [19]. The overmodulation in the voltage reference required in the field weakening zone for PWM inverters can be achieved by adding a zero sequence to each phase and ), to maximize the use of the voltage reference ( , available dc-link voltage. In this case, the new phase voltage and ) can be calculated by references ( , (8) (9)


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Fig. 10. Speed reversal: (a) simulation results and (b) experimental results.

Fig. 11. Zoom to the estimated torque response at speed step change (experimental).

where is the zero sequence signal computed directly from the original phase voltage references given by the flux controller. IV. RESULTS The method was tested using an 81-level asymmetric inverter-fed induction motor drive. The inverter prototype is shown in Fig. 8 and the motor parameters are given in Table II. The dynamic response of the rotor speed , Estimated torque , and the stator flux magnitude for a 2500 [rpm] speed change are shown in Fig. 9. The same variables during a speed reversal are presented in Fig. 10. A zoom to the estimated torque step response is presented in Fig. 11. Note there is a strong reduction of torque ripple compared to traditional DTC schemes due to the quality of the inverter output voltages, which can be appreciated in Fig. 12(a), and absence of hysteresis comparators. The steady-state error of the flux magnitude is due to the approximation made in (4), that is not compensated by the PI controller for higher frequencies, hence it appears at high speed (due to the PI bandwidth). However, this is not relevant, since this error is compensated by the outer loop torque controller.

Fig. 12. (a) 81-level three-phase output voltages (experimental). (b) Voltage synthesis phase a (experimental).

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V. CONCLUSION

Fig. 13. Motor currents during speed reversal: (a) simulation and (b) experimental.

A high-performance torque and flux control strategy for highpower induction motor drives is presented. The main achievements of the proposed control method are: significant reduction in the torque ripple, sinusoidal output voltages and currents, lower switching losses and a high-performance torque and flux regulation. In addition, this approach simplifies the application of DTC principles to multilevel inverters-fed drives. Particularly, there is no need of multiple hysteresis comparators, particular sector divisions and more complex lookup tables, which are too difficult to extended to inverters with a higher number of levels. The asymmetric multilevel inverter enables a DTC solution for high-power motor drives, not only due to the higher voltage capability provided by multilevel inverters, but mainly due to the reduced switching losses and the improved output voltage ’s and common mode voltages), which proquality (small vides sinusoidal current without output filter. Future work on this topic can be the extension of this method to grid inverter interfaces. In this case, the direct power angle control should replace the torque angle control, and the inverter should be considered as an active filter for reactive power compensation. REFERENCES

Fig. 14. Comparison of the number of commutations per fundamental cycle between multilevel PWM (2-kHz carriers) and nearest voltage level (round) for a nine-level asymmetric cascaded inverter.

To review the 81-level stepped waveform synthesis, the output voltages of each cell of phase are shown in Fig. 12(b), including the total phase output voltage , which corre. Note that the sponds to the sum of the four cells high-power cell switches at fundamental frequency, reducing the switching losses. The motor currents during the speed reversal are shown in Fig. 13. The currents appear completely sinusoidal due to the high quality of the inverter output voltage and the low-pass filtering nature of the load. In addition, Fig. 14 compares the number of commutations per fundamental cycle for a range of different operating frequencies, obtained with traditional multicarrier PWM techniques and with the nearest level method (round) used in this work. It is clear that a significant improvement is obtained in terms of switching losses. Considering that the PWM results of Fig. 14 are with 2 kHz carriers and for a nine-level inverter (only 8 switches per phase), it is clear that the difference will be greater for higher frequency carriers and for inverters with more cells.

[1] F. Blaschke, “The principle of field orientation as applied to the transvector closed-loop control system for rotating-field machines,” Siemens Rev., vol. 34, pp. 217–220, 1972. [2] K. Hasse, “Drehzahl geber fahren fur schnelle umkehrantriere mit stromrichtergespiesten asynchron-kurzschluss läufermotoren,” Reglungstechnik, vol. 20, pp. 60–66, 1972. [3] M. Imecs, A. M. Trzynadlowski, I. I. Incze, and C. Szabo, “Vector control schemes for Tandem-converter fed induction motor drives,” IEEE Trans. Power Electron., vol. 20, no. 2, pp. 493–501, Mar. 2005. [4] I. Takahashi and T. Noguchi, “A new quick-response and high-efficiency strategy of an induction motor,” IEEE Trans. Ind. Appl., vol. IA-22, no. 7, pp. 820–827, 1986. [5] M. Depenbrock, “Direct self control (DSC) of inverter fed induction machine,” IEEE Trans. Power Electron., vol. 3, no. 4, pp. 420–429, Jul. 1988. [6] V. Ambrozic, M. Bertoluzzo, G. Buja, and R. Menis, “An assessment of the inverter switching characteristics in DTC induction motor drives,” IEEE Trans. Power Electron., vol. 20, no. 2, pp. 457–465, Mar. 2005. [7] Z. Sorchini and P. T. Krein, “Formal derivation of direct torque control for induction machines,” IEEE Trans. Power Electron., vol. 21, no. 5, pp. 1428–1436, Sep. 2006. [8] J. Rodríguez, J. S. Lai, and F. Z. Peng, “Multilevel inverters: A survey of topologies, controls and applications,” IEEE Trans. Ind. Electron., vol. 49, no. 4, pp. 724–738, Jul./Aug. 2002. [9] M. Escalante, J.-C. Vannier, and A. Arzondé, “Flying capacitor multilevel inverters and dtc motor drive applications,” IEEE Trans. Ind. Electron., vol. 49, no. 4, pp. 805–815, Jul./Aug. 2002. [10] A. Sapin, P. Steimer, and J. Simond, “Modeling, simulation and test of a three-level voltage source inverter with output lc filter and direct torque control,” in Proc. 38th IEEE Industry Application Society Annu. Meeting (IAS 03), Oct. 2003. [11] C. Martins, X. Roboam, T. Meynard, and A. Carvalho, “Switching frequency imposition and ripple reduction in DTC drives by using a multilevel converter,” IEEE Trans. Power Electron., vol. 17, no. 2, pp. 286–297, Mar. 2002. [12] J. Rodríguez, J. Pontt, S. Kouro, and P. Correa, “Direct torque control with imposed switching frequency in an 11-level cascaded inverter,” IEEE Trans. Ind. Electron., vol. 51, no. 4, pp. 827–833, Aug. 2004, Special Section on DTC. [13] T. Habetler, F. Profumo, M. Pastorelli, and L. Tolbert, “Direct torque control of induction machines using space vector modulation,” IEEE Trans. Ind. Electron., vol. 28, no. 5, pp. 1045–1053, Sep./Oct. 1992.


[14] L. Tang, L. Zhong, M. Rahman, and Y. Hu, “A novel direct torque controlled interior permanent magnet synchronous machine drive with low ripple in flux and torque and fixed switching frequency,” IEEE Trans. Power Electron., vol. 19, no. 2, pp. 346–354, Mar. 2004. [15] J. Rodríguez, J. Pontt, C. Silva, S. Kouro, and H. Miranda, “A novel direct torque control scheme for induction machines with space vector modulation,” in Proc. Power Electronics Specialist Conf. (PESC04), Aachen, Germany, Jun. 2004, pp. 1392–1397. [16] G. S. Buja and M. P. Kazmierkowski, “Direct torque control of PWM inverter-fed AC motors—A survey,” IEEE Trans. Ind. Electron., vol. 51, no. 4, pp. 744–757, Aug. 2004. [17] A. Tripathi, A. M. Khambadkone, and S. K. Panda, “Torque ripple analysis and dynamic performance of a space vector modulation based control method for ac-drives,” IEEE Trans. Power Electron., vol. 20, no. 2, pp. 485–492, Mar. 2005. [18] I. Boldea, C. Pitic, C. Lascu, G. Andreescu, L. Tutelea, F. Blaabjerg, and P. Sandholdt, “DTFC-SVM motion-sensorless control of a PM-assisted reluctance synchronous machine as starter-alternator for hybrid electric vehicles,” IEEE Trans. Power Electron., vol. 21, no. 3, pp. 711–719, May 2006. [19] A. Tripathi, A. M. Khambadkone, and S. k. Panda, “Dynamic control of torque in overmodulation and in the field weakening region,” IEEE Trans. Power Electron., vol. 21, no. 4, pp. 1091–1098, Jul. 2006. [20] H. Miranda, C. Silva, and J. Rodriguez, “Torque regulation by means of stator flux control for induction machines,” in Proc. 32nd Annu. Conf. IEEE Industrial Electronics Society (IECON’2006), Paris, France, Nov. 2006, pp. 1218–1222. [21] O. M. Mueller and J. N. Park, “Quasi-linear IGBT inverter topologies,” in APEC’94 Conference Proc., Feb. 1994, pp. 253–259. [22] A. Damiano, M. Fracchia, M. Marchesoni, and I. Marongiu, “A new approach in multilevel power conversion,” in Proc. 7th European Conf. Power Electronics and Applications (EPE ’97), Trondheim, Norway, Sep. 8–10, 1997, pp. 4216–4221. [23] T. Lipo and M. Manjrekar, “Hybrid Topology for Multilevel Power Conversion,” US Patent 6 005 788, Dec. 1999. [24] C. Rech and J. R. Pinheiro, “Impact of hybrid multilevel modulation strategies on input and output harmonic performances,” IEEE Trans. Power Electron., 2007, available at IEEEXplore. [25] J. Dixon, M. Ortuzar, and L. Moran, “Drive system for traction applications using 81-level converter,” Proc. IEEE Vehicular Power Propulsion Conf. (VPP 2004), Oct. 6–8, 2004. [26] J. Rodríguez, L. Morán, P. Correa, and C. Silva, “A vector control technique for medium-voltage inverters,” IEEE Trans. Ind. Electron., vol. 49, no. 4, pp. 882–888, Aug. 2002. Samir Kouro (S’04) was born in Valdivia, Chile, in 1978. He received the Eng. and M.Sc. degrees in electronics engineering in 2004 from the Universidad Técnica Federico Santa María (UTFSM), Valparaíso, Chile, where he is currently pursuing the Ph.D. degree. In 2004 he joined the Electronics Engineering Department UTFSM as Research Assistant. In 2004, he was distinguished as the youngest researcher of Chile in being granted with a governmental-funded research project (FONDECYT) as Principal Researcher. His research interests include power converters and adjustable speed drives.

Rafael Bernal was born in Viña del Mar, Chile, in 1978. He received the Eng. and M.Sc. degrees in electronics engineering from the Universidad Técnica Federico Santa María (UTFSM), Valparaíso, Chile, in 2005 and 2006, respectively. Between 2003 and 2004, he was an exchange student at the Institut für Stromrichtertechnik und Elektrische Antriebe (ISEA), Rheinisch-Westfälische Technische Hochschule, Aachen, Germany. In 200,7 he joined Komatsu Chile S.A., where he is a Project Engineer. Currently, he is with the Autonomous Haulage System project. His interests include power converters and drives.

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Hernán Miranda (S’06) was born in Valparaíso, Chile, in 1979. He received the Elect. Eng. degree in 2004 from the Universidad Técnica Federico Santa María (UTFSM), Valparaíso, Chile, where he is currently pursuing the MSc. degree in electronics engineering. Since 2002, he has been with the Power Electronics Research Group, Departamento de Electrónica, UTFSM, where he is a Scientific Assistant. His main research interests are in advanced motion control and adjustable-speed drives.

César A. Silva (S’02–M’04) was born in Temuco, Chile, in 1972. He received the Civ. Electron. Eng. degree from the Universidad Técnica Federico Santa María (UTFSM), Valparaiso, Chile, in 1998 and the Ph.D. degree from The University of Nottingham, Nottingham, U.K., in 2003. In 1999, he was granted the Overseas Research Students Awards Scheme (ORSAS) to join the Power Electronics Machines and Control Group at the University of Nottingham, Nottingham, U.K. as a postgraduate research student. There, he developed his doctoral thesis on “Sensorless Vector Control of Surface Mounted Permanent Magnet Machines Without Restriction of Zero Frequency”. Since 2003, he has been a Lecturer at the Department of Electronic Engineering, UTFSM, where he teaches basic electric machines theory, power electronics, and ac machine drives. His main research interests include sensorless vector control of ac machines and control of static converters. He has authored and co-authored more than ten refereed journal and conference papers on these topics.

José Rodríguez (M’81–S’83–SM’94) received the Eng. degree from the Universidad Técnica Federico Santa María (UTFSM), 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 a Professor since 1977 at the UTFSM. From 2001 to 2004, he was appointed as Director of the Electronics Engineering Department. From 2004 to 2005, he served as Vice-Rector of Academic Affairs, and in 2005 he was elected Rector of the same university, a position he holds today. During his sabbatical leave in 1996, he was responsible for the Mining Division of the Siemens Corporation in Chile. He has extensive consulting experience in the mining industry, especially in the application of large drives like cycloconverter-fed synchronous motors for SAG mills, high-power conveyors, controlled ac drives for shovels, and power quality issues. His main research interests include multilevel inverters, new converter topologies, and adjustable speed drives. He has directed over 40 R&D projects in the field of industrial electronics, has coauthored over 50 journal and 130 conference papers, and contributed one book chapter. His research group has been recognized as one of the two centers of excellence in Engineering in Chile in the years 2005 and 2006. Dr. Rodriguez is an active Associate Editor of the IEEE Power Electronics and Industrial Electronics Societies since 2002. He has served as Guest Editor of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS in four opportunities (Special Section on: Matrix Converters (2002), Multilevel Inverters (2002), Modern Rectifiers (2005), and High Power Drives (2007)).