IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 3, JUNE Juan Dixon, Senior Member, IEEE, and Luis Morán, Senior Member, IEEE IEEE

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1 TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 3, JUNE A Clean Four-Quadrant Sinusoidal Power Rectifier Using Multistage Converters for Subway Applications Juan Dixon, Senior Member,, and Luis Morán, Senior Member, Abstract A special 27-level four-quadrant rectifier for subway applications is analyzed. The arrangement uses only three H-bridges per phase, common dc bus, and independent input transformers for each H-Bridge. The transformers allow galvanic isolation and power escalation to obtain high-quality voltage waveforms, with total harmonic distortion of less than 1%. Some advantages of this 27-level rectifier are: 1) only one of the three H-bridges, called the main converter, manages more than 80% of the total active power in each phase and 2) it switches at fundamental frequency, reducing the switching losses at a minimum value. The rectifier analyzed in this paper is a current-controlled voltage-source type, with a conventional feedback control loop. Some simulations in a rectifier substation, including power reversal at full load are displayed (750 Vdc, 1200 A). The rectifier shows the ability to produce clean ac and dc waveforms without any ripple, and fast reversal of power. Some experimental results with a small prototype, showing voltage and current waveforms, are finally displayed. Index Terms <AUTHOR: PLEASE SUPPLY YOUR OWN KEYWORDS OR SEND A BLANK TO KEY- WORDS@.ORG TO RECEIVE A LIST OF SUGGESTED KEYWORDS>. I. INTRODUCTION POWER electronics devices contribute an important part of harmonics in all kinds of applications, such as power rectifiers, thyristor converters, and static var compensators (SVCs). Even pulsewidth-modulation (PWM) techniques used today to control modern rectifiers, power-factor compensators, or active power filters do not give perfect waveforms, which strongly depend on switching frequency of the power semiconductors. Normally, voltage moves to discrete values, forcing the design of transformers to have good isolation, and sometimes with inductances in excess of the required value. In other words, neither voltage nor current are as expected. This also means harmonic contamination, additional power losses, and high-frequency noise that can affect the controllers. All these reasons have generated much research on the topic of PWM [1] [4]. Manuscript received December 30, 2003; revised February 24, Abstract published on the Internet March 14, This work was supportedd by Conicyt under Project Fondecyt J. Dixon is with the Department of Electrical Engineering, Pontificia Universidad Católica de Chile, <AUTHOR: POSTAL CODE?> Santiago, Chile ( jdixon@ing.puc.cl). L. Morán is with the Department of Electrical Engineering, Universidad de Concepción, <AUTHOR: POSTAL CODE?> Concepción, Chile ( lmoran@renoir.die.udec.cl). Digital Object Identifier /TIE New alternatives to classical converters are multilevel converters, which allow the generation of many voltage steps to create a sinusoidal waveform. A multistage rectifier is a special kind of multilevel converter that can produce many levels of voltage with a small number of power components [5] [7]. Various multistage configurations are possible, using different topologies and connections between them [8]. The number of levels can be optimized for a given number of transistors and power supplies, using power escalation on individual converters of the multistage rectifier. In this work, each phase of the rectifier was implemented with three H-bridges in parallel with a common dc link. The H-bridges were connected to the ac supply through power transformers, with primary windings in series and voltages scaled in power of three. This configuration represents an optimum utilization of power components [9]. The H-bridges can generate three levels of ac voltage: Vdc, 0, and Vdc ( 1, 0, and 1). Using only three of these converters (three-stage), with their transformers scaled in power of three, 27 discrete levels of voltage amplitude are obtained [10]. The transformers give the required galvanic isolation and allow power flow in both directions [11]. When multistage rectifiers have a high number of levels, they can be made to work with amplitude modulation rather than pulse modulation, and this fact makes the outputs of these topologies much cleaner. This way of operation allows for almost perfect currents, and very good voltage waveforms, eliminating most of the undesirable harmonics. Even better, the bridges of each converter work at a very low switching frequency, which gives the possibility of working with low-speed semiconductors, and of generating low switching frequency losses. II. BASICS OF MULTI-STAGE RECTIFIERS A. Basic Principle The basic H-bridge converter topology is used in this work for the implementation of a multistage rectifier. The H-bridge is based on the simple four-switch converter used for single-phase inverters or for dual converters. These converters are able to produce three levels of voltage at the ac side: Vdc, 0, and Vdc. Fig. 1 displays the main components of a three-stage rectifier, implemented with three H-bridges, which will be analyzed in this work. The figure only shows one of the three phases of the complete system. As can be seen, the dc bus of the three converters is common, and the input power transformers, which /$

2 2 TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 3, JUNE 2005 Fig. 1. One phase of the three-stage 27-level rectifier, implemented with H modules. Fig. 2. Rectifier voltage v using a three-stage 27-level rectifier. (a) 100% amplitude. (b) 75% amplitude. give the necessary galvanic isolation, are scaled with levels of voltage in power of three. The scaling of voltages in power of three allows having, with only three converters, 27 different levels of voltage: 13 levels of positive values, 13 levels of negative values, and 0. The H-bridge located at the bottom of the figure has the bigger voltage, and is called the main converter (M). This converter, which manages most of the power (80%), works at the fundamental switching frequency, which is an additional advantage of this topology, because it can be implemented with slow gate-turn-off thyristors (GTOs) for very-high-power applications. The optimum number of levels is given by (1) (1) where is the number of levels, is the number of H-bridges in the chain, and is the number of levels of each individual converter. In this case, the H-bridges have only three levels: 1, 0, and 1. B. Voltage Modulation and Power Distribution With 27 levels of voltage, a three-stage rectifier can follow a sinusoidal waveform in a very precise way, as shown in Fig. 2. It can control the ac voltage as an amplitude modulation (AM) device. Fig. 2 shows two different levels of amplitude: 100% and 75%, which are obtained through the control of the gates of the power transistors in each one of the three converters. However, it is important to mention that the voltage amplitude in a power

3 DIXON AND MORÁN: CLEAN FOUR-QUADRANT SINUSOIDAL POWER RECTIFIER 3 Fig. 3. (a) voltage modulation and (b) active power distribution in each one of the three converters of Fig. 1, for 100% output voltage and unity power factor. TABLE I ACTIVE POWER DISTRIBUTION FOR cos ' =1 rectifier fluctuates very little, because the control is mainly by voltage phase shift rather than voltage amplitude. Subsequently, the voltage can be controlled always near the 100% level, where more steps of voltage are available. Fig. 3(a) shows the modulation required by each one of the three converters of Fig. 1, to get a sinusoidal voltage waveform. In this case, the figure shows

4 4 TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 3, JUNE 2005 Fig. 4. Fig. 5. Power substation for a metropolitan railway application. Closed-loop rectifier transfer function. the modulation of the H-bridges for 100% input voltage. As was already mentioned, another advantage of the multistage strategy is that most of the power delivered comes from the main converter, as shown in Fig. 3(b), where more than 80% of the real power is carried by this converter, and only 20% for the other two converters, which are called auxiliary converters (A1 and A2). Due to the symmetry of the sinusoidal waveforms, the percentage of power distribution between converters can be calculated taking only a quarter of a cycle. Table I shows the active power distribution between the three H-bridges of the chain, for unity-power-factor operation, which is the normal power factor of this rectifier. Column 1 shows the level of the voltage (assuming level one as the highest), columns 2, 3, and 4 show the input state of M, A1, and A2, respectively ( 1, 0, or 1), and column 5 gives the instantaneous voltage amplitude of the rectifier. On the other hand, column 6 shows the percentage of time that one particular level of instantaneous voltage stays active (100% of time corresponds to a quarter of a cycle). Columns 7, 8, and 9 show the percentage of voltage (positive, zero, or negative) in M, A1, and A2, respectively (because voltage escalation is in power of three, is three times and nine times ). Continuing with the explanation of Table I, columns 10, 11, and 12 display the instantaneous power in each H-bridge (M, A1, or A2), related to the maximum power at level one. Finally, columns 13, 14, and 15 show the average active power given for each converter. These last results have to be corrected because the steps give a fundamental with amplitude times the value of the last step. In addition, as the power is proportional to the rms values of voltage and current, the percentage of on each converter is: As a result, it can be seen from Table I that the main converter (M) gives more than 80% of the total power to the dc load, A1 gives a little more than 16%, and the H-bridge called A2 transfers a little more than 3%. The assumption of unity power factor is the most common in current-controlled voltage-source rectifiers. III. CONTROL OF THE MULTISTAGE RECTIFIER This rectifier has reversal of power capability, can correct power factor, and work as an active power filter. In particular, this paper shows the application of this rectifier in a substation for a metropolitan railway. In this application, the reversal of power is required for regenerative braking, and also good power-factor operation is desirable. In addition, if the multistage rectifier is adequately connected, it can work as an active power filter for other contaminating loads connected at the same source. (2)

5 DIXON AND MORÁN: CLEAN FOUR-QUADRANT SINUSOIDAL POWER RECTIFIER 5 Fig. 6. Fig. 7. Control block for a multistage current-controlled rectifier, and lookup table. Power substation with active filtering capability. A. Rectifier Configuration The Fig. 4 shows a three-stage configuration for a 750-Vdc 1200-Adc power substation for a metropolitan railway application. A feedback control loop that compares the dc voltage with a reference voltage, generates an error signal, which defines the magnitude of the ac currents to be controlled from the mains supply. The CONTROL BLOCK executes the following operation: However, one problem arises with the rectifier, because the feedback control loop on the voltage can produce instability. Therefore, it is necessary to take into account this problem (3) during the design of the rectifier. Upon introducing the voltage feedback, and the controller, the control of the rectifier can be represented in a block diagram in the Laplace dominion, as shown in Fig. 5. This block diagram represents a linearization of the system around an operating point, given by the rms value of the ac input current,. The blocks and of Fig. 5 represent the transfer function of the rectifier (around the operating point), and the transfer function of the dc-link capacitor, respectively, (4) (5)

6 6 TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 3, JUNE 2005 Fig. 8. Reversal of power capability of multistage rectifier. (a) Voltages and currents at ac side. (b) Voltages and currents at dc side. Fig. 9. Unity-power-factor operation. (a) Voltages and currents at ac side (rectifier operation). (b) Phase shift between mains and rectifier (rectifier operation). (c) Same as (a) but inverter operation. (d) Same as (b) but inverter operation. and represent the input and output power of the rectifier in the Laplace dominion, the rms value of the mains voltage supply (phase-to-neutral), the input current being controlled by the template, the input inductance, and the resistance between the converter and power supply.

7 DIXON AND MORÁN: CLEAN FOUR-QUADRANT SINUSOIDAL POWER RECTIFIER 7 Fig. 10. Active power filter operation. (a) Source current. (b) Filter (27-level rectifier) current. (c) Diode rectifier current. According to stability criteria, and assuming a proportional integral (PI) controller, the following relations are obtained: These two relations are useful for the design of the current-controlled rectifier. They relate the values of dc-link capacitor, dc-link voltage, rms voltage supply, input resistance and inductance, and input power factor, with the rms value of the input current. With these relations the proportional and integral gains and can be calculated to ensure stability of the rectifier. These relations only establish limitations for rectifier operation, because negative currents always satisfy the inequalities. With these two stability limits satisfied, the rectifier will keep the dc capacitor voltage at the value of (PI controller), for all load conditions, by moving power from the ac to the dc side. Under inverter operation (regenerative braking), the power will move in the opposite direction. The phase shift of the currents ( ) can be fully controlled (power factor control), and is defined inside the CONTROL BLOCK, which takes the mains voltage as a phase reference. The angle is normally chosen to be zero for unity-power-factor operation. Once the sinusoidal current template has been created with their magnitude and phase shift, it is compared, in each phase, with the real current, forcing this current to follow the template. To follow the current, a Lookup Table defines which one of the three H-bridges have to be positive, zero, or negative. Fig. 6 explains in more detail the CONTROL BLOCK of the rectifier, and shows the 27 levels stored in the Lookup Table. The control algorithms and lookup (6) (7) Fig. 11. Voltage waveform generated at the experimental 27-level rectifier. tables inside the CONTROL BLOCK are easily implemented using digital signal processors (DSPs), which will give the corresponding ON OFF signals to each one of the four transistors in each H-bridge. The rectifier can also be controlled without current sensors, by shifting and adjusting the amplitude of the scaled voltage of the rectifier. These adjustments are made through mathematical calculations executed by a digital controller [12]. B. Rectifier Operating as Active Filter The multistage rectifier can also work as an active power filter [13]. If some contaminating load is connected, keeping the current sensors at the source side, the multistage rectifier will force the source currents to remain sinusoidal. Fig. 7 shows the way the contaminating load must be connected with respect to the current sensors and the multistage rectifier, to get the filtering of harmonics. One drawback of this configuration is that the dc voltage can become distorted, because the harmonic compensation is generated by the multistage rectifier.

8 8 TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 3, JUNE 2005 Fig. 12. Voltages v at the three phases and current phase shift for cos ' =1. IV. SIMULATION RESULTS The following results show the quality of waveforms obtained with a multilevel rectifier, designed for a traction substation. The substation is intended for a metropolitan railway using distributed consumption. The rating of the rectifier is 750 Vdc, 1200 Adc, line voltage 860 V, line impedance, and mh, and dc-link capacitor mf. The displayed results have been obtained using software called PSIM [14], which has demonstrated its reliability for almost ten years of simulations. The first group of oscillograms shows the reversal of power capability of the rectifier (regenerative braking), and its ability to keep a constant power factor. In this case, the CONTROL BLOCK ensures unity power factor at the ac side for all load conditions. The second group of oscillograms shows the rectifier working as a shunt active power filter, where the contaminating load is around 25% of the rated load of the rectifier. A. Reversal of Power Fig. 8 shows the reversal of power capability of the rectifier. The load dc current has changed from 0 to 1200 Adc, and later on, from 1200 Adc to 1200 Adc. The control block, which uses PI controllers in these simulations, keeps and recovers the normal conditions of operation in only one cycle. It is important to mention that these conditions are very extreme and, hence, under normal operation, the rectifier will be able to work in both quadrants, positive and negative dc currents, with negligible effects in the power system. In this case the capacitor of the rectifier (see Figs. 4, 5, or Fig. 6) is a F unit. The system also works with smaller capacitors, but the system takes more time in reaching steady-state condition. It is important to mention that reversal of power (regenerative braking) works automatically when the dc-link voltage tries to go higher than (750 V ). B. Control of Input Power Factor It is also interesting to see the phase-shift between voltage and current at the ac side. The control has been adjusted to keep the power factor at unity under all load conditions. Fig. 9 shows two situations under unity power factor operation: 1) rectifier operation and 2) inverter operation (regenerative braking). In these two cases, the in-phase condition between current and source voltage and the phase shift between source voltage and rectifier voltage are displayed. The rectifier is under steady state for both cases: positive and negative dc current ( 1200 and 1200 Adc). It can be observed that the rectifier voltage (the one with small steps) lags the source voltage under rectifier operation and vice versa. The phase shift between these two voltages is adjusted automatically through the feedback control loop. The control loop measures the ac currents and forces them to be sinusoidal and to remain in phase with the source voltage. The control can also be adjusted to operate at lagging or leading power factor, by the adequate choice of the angle. C. Multistage Rectifier Operating as Active Power Filter The active filtering capability of the multistage converter was already mentioned in Section III-B, and displayed in Fig. 7. A simulation of ac currents for one phase of this system is shown in Fig. 10. A diode rectifier, connected to the same grid as the multistage rectifier, is feeding a 300-A dc load. The phase-to-phase voltage of the ac source is 860 V, and the multistage rectifier is feeding a 1200-Adc load (railway). Three oscillograms are displayed in Fig. 10: the source current [Fig. 10(a)]; the multistage rectifier current [Fig. 10(b)]; and the diode rectifier current [Fig. 10(c)]. It can be observed that the source current remains almost sinusoidal, and the harmonics required by the diode rectifier are produced by the multistage rectifier.

9 DIXON AND MORÁN: CLEAN FOUR-QUADRANT SINUSOIDAL POWER RECTIFIER 9 V. EXPERIMENTAL RESULTS A small 27-level prototype with three H-bridges connected through isolation transformers is implemented. The rating of this prototype is 1 kw and gives an idea of the quality of voltages that can be obtained. The isolation between power and control has been implemented with optocouples, and the drive IR-2113 switches the insulated gate bipolar transistors (IGBTs). Fig. 11 shows the voltage waveform in one phase where it is possible to see the 27 levels. The steps are very clean and the resultant THD is less than 1%. Fig. 12(a) shows the voltages at the three phases, and Fig. 12(b) shows the phase shift between current and voltage for unity-power-factor operation. This figure can be compared with the simulation in Fig. 9(b) where current also leads the voltage generated by the rectifier for operation at. VI. CONCLUSION A three-stage 27-level power rectifier using three-state H-bridges has been analyzed. The H-bridges are connected through power transformers with their input voltages scaled in power of three, allowing the generation of voltage waveforms almost perfectly sinusoidal. One of the H-bridges, called the main converter, manages more than 80% of the total active power in each phase, and switches at fundamental frequency. The configuration uses a common dc bus and input transformers for each converter. The rectifier analyzed in this work is a current-controlled voltage-source type with conventional feedback control loop. Some simulations for a particular application in a four-quadrant rectifier substation for a metropolitan subway were presented. The rectifier shows the ability to produce clean ac and dc waveforms without any ripple, and fast reversal of power. Some experimental results with a small prototype, showing voltage and current waveforms, were finally displayed. REFERENCES [1] H. Akagi, The state-of-the-art power electronics in Japan, Trans. Power Electron., vol. 13, no. 2, pp , Mar [2] B. Bose, Power electronics and motion control-technology status and recent trends, Trans. Ind. Appl., vol. 29, no. 5, pp , Sep./Oct [3] D. Chung, J. Kim, and S. Sul, Unified voltage modulation technique for real time three-phase power conversion, Trans. Ind. Appl., vol. 34, no. 2, pp , Mar./Apr [4] J. Holtz and B. Beyer, Fast current trajectory tracking control based on synchronous optimal pulse width modulation, Trans. Ind. Appl., vol. 31, no. 5, pp , Sep./Oct [5] A. Draou, M. Benghanen, and A. Tahri, Multilevel converters and VAR compensation, in Power Electronics Handbook, M. H. Rashid, Ed. New York: Academic, 2001, ch. 25, pp [6] F. Z. Peng, A generalized multilevel inverter topology with self voltage balancing, Trans. Ind. Appl., vol. 37, no. 2, pp , Mar./Apr [7] K. Matsui, Y. Kawata, and F. Ueda, Application of parallel connected NPC-PWM inverters with multilevel modulation for AC motor drive, Trans. Power Electron., vol. 15, no. 5, pp , Sep [8] J. Rodríguez, J.-S. Lai, and F. Z. Peng, Multilevel inverters: A survey of topologies, controls and applications, Trans. Ind. Electron., vol. 49, no. 4, pp , Aug [9] K. Corzine and Y. Familiant, A new cascaded multilevel H-bridge drive, Trans. Power Electron., vol. 17, no. 1, pp , Jan [10] J. W. Dixon, A. Bretón, F. Ríos, and L. Morán, High power machine drive, based on three-stage connection of H converters, and active front end rectifiers, in Proc. IECON 03, Roanoke, VA, Nov. 2003, CD-ROM. [11] M. E. Ortúzar, R. Carmi, J. W. Dixon, and L. A. Morán, Voltage source active power filter, based on multi-stage converter and ultracapacitor DC-link, in Proc. IECON 03, Roanoke, VA, Nov. 2003, CD-ROM. [12] J. W. Dixon and B. T. Ooi, Indirect current control of a unity power factor sinusoidal current boost type three-phase rectifier, Trans. Ind. Electron., vol. 35, no. 4, pp , Nov [13] J. W. Dixon, J. Contardo, and L. A. Morán, A fuzzy-controlled active front-end rectifier with current harmonic filtering characteristics and minimum sensing variables, Trans. Power Electron., vol. 14, no. 4, pp , Jul [14] (<AUTHOR: DATE?>) PSIM Version 4.1, for Power Electronics Simulations, User Manual. Powersim Technologies, Vancouver, BC, Canada. [Online]. Available: Juan Dixon (M 90 SM 95) was born in Santiago, Chile. He received the Degree in Electrical Engineering from the Universidad de Chile, Santiago, Chile, in 1977, and the M.S. Eng. and Ph.D. degrees from McGill University, Montreal, QC, Canada, in 1986 and 1988, respectively. In 1976, he was with the State Transportation Company in charge of trolleybus operation. In 1977 and 1978, he was with the Chilean Railways Company. Since 1979, he has been with the Electrical Engineering Department, Pontificia Universidad Catolica de Chile, Santiago, Chile, where he is currently a Professor. He has authored more than 25 published papers related to power electronics. His main areas of interests are electric traction, power converters, PWM rectifiers, active power filters, power-factor compensators, and multilevel and multistage converters. His consulting work has been related to trolleybuses, traction substations, machine drives, hybrid electric vehicles, and electric railways. He founded an electric vehicle laboratory, where he has built state-of-the-art vehicles using brushless dc machines with ultracapacitors and high-specific-energy batteries. Recently, he has begun research on distributed generation and power generation using renewable energy sources. Luis Morán (M 78 SM 94) was born in Concepción, Chile. He received the Degree in Electrical Engineering from the University of Concepción, Concepción, Chile, in 1982, and the Ph.D. degree from Concordia University, Montreal, QC, Canada, in Since 1990, he has been with the Electrical Engineering Department, University of Concepción, where he is a Professor. He has authored more than 25 published papers on active power filters and static var compensators. He has extensive consulting experience in the mining industry, in particular, in the application of medium-voltage ac drives, large power cycloconverter drives for SAG mills, and power quality issues. His main areas of interest are ac drives, power quality, active power filters, FACTS, and power protection systems. Prof. Morán was the principal author of the paper that received the Outstanding Paper Award for the best paper published in the TRANSACTIONS ON INDUSTRIAL ELECTRONICS during From 1997 to 2001, he was an Associate Editor of the TRANSACTIONS ON POWER ELECTRONICS. In 1998, he received the City of Concepción Medal of Honor for achievement in applied research.