IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 3, JUNE 2005
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A Clean Four-Quadrant Sinusoidal Power Rectifier
Using Multistage Converters for
Subway Applications
Juan Dixon, Senior Member, IEEE, and Luis Morán, Senior Member, IEEE
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KEYWORDS>.
I. INTRODUCTION
P
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.
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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.
OWER 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, 2004. Abstract
published on the Internet March 14, 2005. This work was supportedd by Conicyt
under Project Fondecyt 1020460.
J. Dixon is with the Department of Electrical Engineering, Pontificia Universidad Católica de Chile, <AUTHOR: POSTAL CODE?> Santiago, Chile
(e-mail jdixon@ing.puc.cl).
L. Morán is with the Department of Electrical Engineering, Universidad
de Concepción, <AUTHOR: POSTAL CODE?> Concepción, Chile (e-mail
lmoran@renoir.die.udec.cl).
Digital Object Identifier 10.1109/TIE.2005.843976
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
0278-0046/$20.00 © 2005 IEEE
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 3, JUNE 2005
Fig. 2.
Rectifier voltage v
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Fig. 1. One phase of the three-stage 27-level rectifier, implemented with “H” modules.
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
Fig. 3.
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DIXON AND MORÁN: CLEAN FOUR-QUADRANT SINUSOIDAL POWER RECTIFIER
(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
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 3, JUNE 2005
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Fig. 4. Power substation for a metropolitan railway application.
Fig. 5. 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 escais three times
and nine times
lation is in power of three,
). 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 1.041 times
the value of the last step. In addition, as the power is proportional to the rms values of voltage and current, the percentage
on each converter is:
of
(2)
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.
DIXON AND MORÁN: CLEAN FOUR-QUADRANT SINUSOIDAL POWER RECTIFIER
5
Fig. 7.
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Fig. 6. 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
, generates an error signal, which
with a reference voltage
of the ac currents to be controlled
defines the magnitude
from the mains supply. The CONTROL BLOCK executes the
following operation:
during the design of the rectifier. Upon introducing the voltage
controller, the control of the rectifier can
feedback, and the
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, .
and
of Fig. 5 represent the transfer
The blocks
function of the rectifier (around the operating point), and the
transfer function of the dc-link capacitor , respectively,
(3)
However, one problem arises with the rectifier, because the
can produce instafeedback control loop on the voltage
bility. Therefore, it is necessary to take into account this problem
(4)
(5)
6
Reversal of power capability of multistage rectifier. (a) Voltages and currents at ac side. (b) Voltages and currents at dc side.
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Fig. 8.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 3, JUNE 2005
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
the rms value of
of the rectifier in the Laplace dominion,
the input curthe mains voltage supply (phase-to-neutral),
the input inductance,
rent being controlled by the template,
and
the resistance between the converter and power supply.
Fig. 10.
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DIXON AND MORÁN: CLEAN FOUR-QUADRANT SINUSOIDAL POWER RECTIFIER
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:
(6)
(7)
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
, and input power factor, with
resistance and inductance
the rms value of the input current . With these relations the
and
can be calculated
proportional and integral gains
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
(PI controller), for
the dc capacitor voltage at the value of
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
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
at the three phases and current phase shift for cos ' = 1.
Voltages v
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Fig. 12.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 3, JUNE 2005
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
mH, and dc-link capacitor
mF. The disand
played 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 10 000- 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
[Fig. 10(c)]. It can be observed that the source curcurrent
rent remains almost sinusoidal, and the harmonics required by
the diode rectifier are produced by the multistage rectifier.
DIXON AND MORÁN: CLEAN FOUR-QUADRANT SINUSOIDAL POWER RECTIFIER
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
[9] K. Corzine and Y. Familiant, “A new cascaded multilevel H-bridge
drive,” IEEE Trans. Power Electron., vol. 17, no. 1, pp. 125–131, Jan.
2002.
[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. IEEE 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. IEEE 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,” IEEE Trans.
Ind. Electron., vol. 35, no. 4, pp. 508–515, Nov. 1988.
[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,” IEEE Trans. Power Electron., vol. 14, no.
4, pp. 724–729, Jul. 1999.
[14] (<AUTHOR: DATE?>) PSIM Version 4.1, for “Power Electronics
Simulations, User Manual”. Powersim Technologies, Vancouver, BC,
Canada. [Online]. Available: http://www.powersimtech.com
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.
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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.
9
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Sep./Oct. 1993.
[3] D. Chung, J. Kim, and S. Sul, “Unified voltage modulation technique for
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[5] A. Draou, M. Benghanen, and A. Tahri, “Multilevel converters and
VAR compensation,” in Power Electronics Handbook, M. H. Rashid,
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[6] F. Z. Peng, “A generalized multilevel inverter topology with self
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[7] K. Matsui, Y. Kawata, and F. Ueda, “Application of parallel connected
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[8] J. Rodríguez, J.-S. Lai, and F. Z. Peng, “Multilevel inverters: A survey of
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49, no. 4, pp. 724–736, Aug. 2002.
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 1990.
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 IEEE TRANSACTIONS
ON INDUSTRIAL ELECTRONICS during 1995. From 1997 to 2001, he was an Associate Editor of the IEEE TRANSACTIONS ON POWER ELECTRONICS. In 1998,
he received the City of Concepción Medal of Honor for achievement in applied
research.