Novel Unidirectional Hybrid Three-Phase Rectifier
System Employing Boost Topology
Ricardo Luiz Alves, Carlos Henrique Illa Font, IEEE Student Member and Ivo Barbi, IEEE Senior Member
Power Electronics Institute – INEP
Department of Electrical Engineering
Federal University of Santa Catarina – UFSC
P. O. Box 5119 – Fax +55-48-234-5422
88040-970 Florianópolis, SC – BRAZIL
E-mail: alves@inep.ufsc.br, illa_font@ieee.org, ivobarbi@inep.ufsc.br
The paper presents a brief overview of some high power
rectifier topologies and the mathematical analysis, the control
scheme and the simulation results of the proposed hybrid
rectifier.
Abstract — This paper presents a new hybrid rectifier
composed by the parallel association of a single-switch threephase Boost rectifier with a PWM three-phase unidirectional
rectifier. According to this proposal, each rectifier processes
about a half of the output rated power. Thus, it allows to
improve the robustness and to provide a high efficiency to the
system. The hybrid rectifier is capable of providing output
voltage regulation and power factor correction. An overview of
some high power rectifier topologies and the mathematical
analysis, the control scheme and the simulation results of the
proposed hybrid rectifier are also presented in this paper.
I.
II. OVERVIEW OF SOME HIGH POWER RECTIFIER
TOPOLOGIES
Power converters systems have a high variety of
topologies with different complexity. The line commutedrectifiers are very simple and robust due to be composed by
non controlled and/or semi-controlled switches, as diodes and
thyristors. However, these structures present the inherent
characteristic of high harmonic distortion in input currents.
In the other hand, the self-commuted rectifiers are
composed by active switches (as power MOSFETs, IGBTs
and GTOs) and are capable to produce reduced effects on the
mains. However, the complexity and the cost are increased.
A basic overview of some high power rectifiers are
performed in the sequence.
INTRODUCTION
Before the semiconductor invention, the use of rectifiers in
industrial applications was made with the electromechanical
contact converters (an AC motor coupled with a DC
generator) and with the mercury converters [1].
A new stage started to high power converters when, in
1960, the first diode rectifier above 100kA was placed to the
market, and, ten years later, the first thyristor plant of this
rating was operational.
The capability of to dissipate the internal losses is the
restriction factor of semiconductor element usage. This way,
to medium and high power converters, forced-cooled
heatsinks are frequently used. However, depending on the
application area and the required operational behavior some
switches can not be applied.
The concerns regarding restrictions in the harmonic
content generated by the power converters, above all the
framing in the standards IEEE 519 and IEC 61000-3-4, has
been objective of many recently studies.
Nevertheless, to obtain low THD (Total Harmonic
Distortion) in high power converters can be quite a complex
task. Some technological limitations restrict the use of
certain topologies in pre-established power levels. The latest
advances in high-power semiconductor devices have
introduced newer solutions for high power conversion
systems, however, the degree of acceptance of each
technology vary in according with various industries and
applications.
The aim of this paper is to propose a new hybrid rectifier
topology capable of providing sinusoidal input currents and
output voltage regulation.
0-7803-9033-4/05/$20.00 ©2005 IEEE.
A. Diode Rectifiers
Diode rectifiers are the simplest of all rectifier topologies.
Robustness and low cost are main attractive characteristics
that allow these structures to be applied in high power
applications. However, due to not allow, by it self, to control
the output voltage, these converters are rarely applied in
industrial applications, only in the cases when the output
voltage control is not required. Other important factor that
reduce the acceptance of this converters is the high THD
observed in input currents.
To compensate the harmonic distortion generated by the
standards diode rectifiers, passive linear filters or power
factor correction structures can be employed. Multipulse
techniques are frequently found in high power applications.
In these cases, special winding connections are used in
transformers and, for this reason, they become, as the linear
filters, heavy and bulky, however are extremely robust. A
significant reduction in the final weight and volume can be
achieved replacing the transformers by autotransformers with
differential connections. However, for the 12-pulse structure
six secondary windings and four interphase reactors are
required. For the 18-pulse structure, twelve secondary
487
correction structures are employed, but, the complexity and
the cost obtained are significantly increased.
The
development of soft-switching strategies and the design of an
optimal layout are the great challenges that must be overcome
to introduce these topologies in high power applications.
windings and six interphase reactors. The disadvantage is
that the insulation will be lost, but, in the other hand, the
power processed by the autotransformer is only 20% of the
rated power [2, 3].
These techniques improve significantly the quality of input
currents (for the 12-pulse rectifier, the total harmonic
distortion is approximately 14%, while for the 18-pulse
structure, the obtained THD is approximately 9% [1]) but
they do not allow to obtain the output voltage control.
Two techniques can be used to achieve the output voltage
control and increase the acceptance of these structures in
industrial applications. The first one consists in the use of
OLCTs (on-load tap changers), typically installed on the
primary side of the transformers (or autotransformers). The
major inconvenience is the need of a regular and preventive
maintenance of the contact systems due to depreciation of the
mechanical parts.
The second way to obtain a load voltage control is
introducing a variable impedance into the circuit through a
saturable core reactor. This control range is limited in 60-80
volts [1].
E. Hybrid Rectifiers
Hybrid rectifier denotes the series and/or parallel
connection of a line-commuted rectifier and a self-commuted
converter (PWM rectifier) [4, 5]. Moreover, the passive
rectifier operates with low frequency and it handles the
higher output power rating. Therefore, the active rectifier is
designed to operate with small power ratings and with high
switching frequency.
The great attractive characteristic of these structures is that
they combine the robustness and the efficiency of the linecommuted rectifiers with the low harmonic current
production of the self-commuted rectifiers.
Notice that the hybrid rectifiers can not be classified as an
active filter due to the fact that the self-commuted rectifier, in
this case, processes active power while the active filters have
the characteristic of process only reactive power.
B. Thyristor Rectifiers
The thyristor rectifiers present the same robustness of the
diode rectifiers. The complexity and the costs are a little
increased due to gate drive circuit. The harmonic distortion
of input currents is worst if compared with diode rectifiers
but the output voltage regulation is possible with this
structures. Due to the simplicity, reliability and efficiency,
the thyristor rectifier has been, until today, the most
commonly used rectifier configuration for high power
applications.
F. Summary
Traditionally, three-phase AC-to-DC conversions are
performed by diode or phase-controlled rectifiers. These
rectifiers draw non-sinusoidal currents or reactive power
from the source, deteriorating the electrical power system
quality. Multipulse rectifiers can be used to improve the
power factor [1-4]. In these structures special winding
connections are used in transformers and, for this reason, they
become also heavy and bulky, however are extremely robust.
Switching-mode rectifiers are capable of drawing perfect
sinusoidal currents form the power distribution network.
However, they usually have very complicated control and
power stage circuitry, thus the cost and mainly the
implementation complexity of the PWM rectifiers are
proportional to the rated power.
The number of related publications shows that the focus of
researches of rectifiers is in the area of self-commuted and
hybrid rectifiers. The great challenge is to obtain a rectifier
capable to gather the robustness, lightness, simplicity and the
low cost of the passive rectifiers with the efficient reduction
of the harmonic content of input currents obtained with the
PWM rectifiers. This becomes a quite interesting research
field with great possibility of future applications.
C. Diode Rectifiers Cascaded by DC-DC Converters
Uncontrolled diode rectifiers cascaded by DC-DC
converters regulators are frequently used to compose a twostage rectifier. They were spread and consolidated in lowpower DC traction applications. The recent advances in high
power semiconductors technologies, particularly the IGBT
(insulated gate bipolar transistor) and the IGCT (integrated
gate commutated thyristor) semiconductor type, allowed
extend the use of these two-stage rectifier topologies in
industrial applications.
This technique results in lower weight and volume of
magnetic elements, due to their high frequency operation.
However, this structure can not be pushed to high power
levels because its input currents do not meet the IEEE 519
and IEC6100-3-4 standards.
III. THE PROPOSED HYBRID RECTIFIER
As previously mentioned, the term hybrid rectifier refers
to the parallel or series connection of a line-commuted
rectifier and a self-commuted rectifier.
The diagram of the proposed hybrid rectifier is presented
in Fig. 1. It is composed by the parallel association of a
single-switch three-phase Boost rectifier with a PWM threephase unidirectional rectifier.
Each rectifier is responsible to process about 50% of the
output power. Thus, the robustness is improved and a high
efficiency is achieved.
D. PWM Rectifiers
Active rectification techniques are the most promising
rectifier technology from a power quality viewpoint. A unity
power factor and a very low harmonic distortion can be
achieved. These structures are standard in low and medium
power equipments, however not yet available to high current
applications just due to unavailable of suitable cost-effective
power electronic devices. In applications where the weigh
and volume are decisive factors, active power factor
488
Self-commuted
Rectifier
Boost Converter
LB 2
DB1
D2a
D1a
D1b
D2b
D1c
S1
D1d
D3a
D2c
D3b
D2e
D3d
D2f
D1f
D1
D3e
Co
L1
L2
IA2
D3
SB
Ro
D4
LB
V1(t)
i1(t)
V2(t)
i2(t)
V3(t)
i3(t)
D
C
S
D3f
DB2
IA1
D2
L
D3c
S3
S2
D2d
D1e
Line-commuted
Rectifier
D5
R
gate
D6
2
L3
IA3
IP3
gate
IP2
V1
~
I1
V2
~ I2
V3
~
PWM
Gv(s)
Gi(s)
IP1
I3
V ref
Voltage and current in Phase 1
Fig. 1. Proposed hybrid rectifier.
Harmonic Analysis
0.12
i1(t)
0.10
THD = 32%
0.08
A. Line-commuted Rectifier with DC-DC Stage
The single-switch three-phase Boost rectifier, presented in
Fig. 2, shows a relative high power factor and is
characterized in general by a very high utilization of the
power components [4]. However, this structure can not be
pushed to high power levels because its input currents do not
meet the IEEE 519 and IEC6100-3-4 standards. The singleswitch Boost rectifier imposes a rectangular shape to input
currents waveforms. The current control loop can impose
only the amplitude of these currents, maintaining the output
voltage constant under load variations.
To compose the hybrid rectifier a little modification
should be made in the circuit presented in Fig. 2. The
modification consists in to split the Boost diode and Boost
inductor to ensure the appropriated operation of the hybrid
rectifier.
Power Factor = 0.953
0.06
0.04
0.02
V1 (t)
0
2 3 4 5 6 7 8 9 1011121314151617181920 2122232425
Order n
Fig. 2. Single-switch three-phase Boost rectifier.
D2a
D1a
D3a
Kv
D1b
D2b
D1c
S1
gate 1
D1d
D2c
D3b
D2e
D3d
D3c
S3
S2
gate 2
D2d
D1e
gate 3
D2f
D1f
D3e
L2
+
L3
gate 3
Gi(s)
-
PWM
ref2
+
gate 2
Gi(s)
-
PWM
ref1
V1
~
I1
V2
~
I2
V3
~
+
I3
Line currents Waveforms
-
gate 1
Gi(s)
PWM
Harmonic Analysis
1.6E-02
i2(t)
i1(t)
THD = 3.14%
Power Factor = 0.999
1.2E-02
8.0E-03
4.0E-03
i3(t)
0
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Order n
Fig. 3. Unidirectional PWM three-phase rectifier.
Three-Phase
Diode Bridge
IV. MATHEMATICAL ANALYSIS
Boost
Converter
iop (t)
iP2 (t)
To perform the mathematical analysis to the input current
viewpoint, the output voltage is considered constant. Thus,
the simplified circuit presented in Fig. 4 is adopted.
Input voltages and input currents are supposed perfectly
sinusoidal and expressed by (1).
and
Gv(s)
D3f
iP1 (t)
⎧i1 ( t ) = Ip ⋅ sin ( ω⋅ t )
⎪
⎪
o
⎨i2 ( t ) = Ip ⋅ sin ( ω⋅ t −120 )
⎪
o
⎩⎪i3 ( t ) = Ip ⋅ sin ( ω⋅ t +120 )
Ro
ref3
L1
B. Self-commuted Rectifier
Theoretically any PWM three-phase rectifier can compose
the hybrid rectifier. To assist the unidirectional requirements,
the rectifier presented in Fig. 3 is settled.
This topology allows to obtain a unity power factor and
presents as advantage the reduced number of active switches
[4, 6].
The main objective to be reached with the proposed hybrid
rectifier is to employ the structures presented in Fig. 2 and
Fig. 3 to obtain perfectly sinusoidal input currents and load
sharing characteristic.
⎧v1 ( t ) = Vp ⋅ sin ( ω⋅ t )
⎪
⎪
o
⎨v2 ( t ) = Vp ⋅ sin ( ω⋅ t −120 )
⎪
o
⎩⎪v3 ( t ) = Vp ⋅ sin ( ω⋅ t +120 )
Vref
Co
iP3 (t)
V1 (t)
i1(t)
V2 (t)
i2(t)
V3 (t)
(1)
i3(t)
io(t)
(passive)
+
Vo
iA1 (t)
(ative)
ioa (t)
iA2 (t)
iA3 (t)
Three-Phase PWM
Rectifier
Fig. 4. Simplified hybrid rectifier block diagram.
489
-
To simplify the analysis, the system is considered lossfree. This way, the input active power Pin can be expressed
by (2).
Pin =3⋅
Vp ⋅ Ip
2
= Po = Vo ⋅ Io
i L(t)
(2)
i 1(t)
Where:
- Peak value of input voltage;
Vp
Ip
- Peak value of input current;
Po
- Output power;
Vo
- DC output voltage;
Io
- DC output current.
Therefore, substituting (2) in (1):
⎧
2 Po
⎪i1 ( t ) = ⋅ ⋅ sin(ωt)
3 Vp
⎪
⎪⎪
2 Po
o
⎨i 2 ( t ) = ⋅ ⋅ sin(ωt − 120 )
3
V
p
⎪
⎪
2 P
⎪i3 ( t ) = ⋅ o ⋅ sin(ωt + 120o )
3 Vp
⎪⎩
30°
Pop ≤
(3)
330°
3
⋅ Po ≈ 0.552 ⋅ Po
π
(8)
(9)
Where:
Poa - Active power processed by the PWM rectifier.
The expression (8) is very important to define the active
power sharing between the two converters. If this relation is
not satisfied, the input currents will be distorted as depicted
in Fig. 6. The shaded areas denote the intervals were the
relation is not satisfied.
(4)
V. CONTROL STRATEGY
The control loop scheme is presented in Fig. 7. The
currents on the mains must be sampled and compared with
their respective sinusoidal references. These references
signals should be synchronized with the mains voltages. A
good practical way to obtain these signals is through
synchronization transformers. The errors produced by the
comparisons between the sampled signal and reference signal
are applied in their respective compensators and the PWM
modulators generate the gate signals to the active rectifier.
The Boost inductor current is also sampled and compared
with a constant reference to generate the gate signal of the
Boost switch in a similar manner.
To compensate load variations, a single voltage control
loop can be used. As can be observed in Fig. 7, the output
voltage is compared with a constant reference and the error
signal is applied in the voltage compensator.
The load sharing pre-established by (8) is guaranteed by
the gains k1 e k2 that must be settled to satisfy the expression
(10).
(5)
Where:
- Boost inductor current;
IL
Pop
- Active power processed by the passive
rectifier.
Substituting (6) in (5) and analyzing the waveform of Fig.
5:
if 30 o ≤ ω t ≤ 150 o
270°
Poa ≥ (1 − 0.552 ) ⋅ Po ≈ 0.448 ⋅ Po
Vp 3 ⋅ 3
Pop
⎧ 2 Po
π
⎪ 3 ⋅ V ⋅ sin( ω t) − V ⋅
⋅
3
3
p
p
⎪
i A1 ( t ) = ⎨
⎪ 2 ⋅ Po ⋅ sin( ω t)
⎪3 V
p
⎩
210°
Therefore, the active power rectifier operation limit is:
Analyzing the passive rectifier current on phase 1, witch is
depicted in Fig. 5, the relation (6) can be written:
P
π
(6)
I = op ⋅
L
150°
Due to unidirectional characteristic of PWM rectifier, the
instantaneous input power should have only positive values.
Analyzing (7), the solution that satisfies this condition is
presented in (8):
Where:
iA1(t), iA2(t), iA3(t) - Active rectifier input currents;
iP1(t), iP2(t), iP3(t) - Passive rectifier input currents.
This way:
⎧
2 Po
⋅ sin( ω t) − i P1 ( ω t )
⎪ i A1 ( t ) = ⋅
3 Vp
⎪
⎪⎪
2 Po
⋅ sin( ω t − 120 o ) − i P 2 ( ω t )
⎨i A 2 ( t ) = ⋅
3 Vp
⎪
⎪
2 P
⎪ i A 3 ( t ) = ⋅ o ⋅ sin( ω t + 120 o ) − i P 3 ( ω t )
3 Vp
⎪⎩
90°
Fig. 5. The relevant currents waveforms of the six-pulse diode bridge
rectifier cascaded by Boost converter.
However, the mains currents are composed by two parts;
the first one originated by the active rectifier and the other
one by the passive structure. This statement leads to (4).
⎧i1 ( t ) = iA1 ( t ) + iP1 ( t ) = Ip ⋅ sin ( ω⋅ t )
⎪
⎪
o
⎨i2 ( t ) = iA2 ( t ) + iP2 ( t ) = Ip ⋅ sin ( ω⋅ t −120 )
⎪
o
⎪⎩i3 ( t ) = iA3 ( t ) + iP3 ( t ) = Ip ⋅ sin ( ω⋅ t + 120 )
i P1(t)
IL
0≤
k2
≤ 0.50
k1
(10)
It is extremely important that the gains ratio established by
(10) has been adjusted quite close to 0.5, but never greater
than this value. If the ratio is grater than 0.5, the imposed
line currents will be distorted. Otherwise, if the ratio is close
to 0, the active rectifier will assume the output rated power.
(7)
o
o
⎪⎧ 0 ≤ ω t ≤ 30 or
if ⎨
o
o
⎪⎩150 ≤ ω t ≤ 180
490
IL
TABLE I
i P1(t)
Variable
(a) SIX-PULSE DIODE BRIDGE INPUT CURRENT
Ip
i A1(t)
I p- I L
(b) PWM IDEAL INPUT CURRENT
Ip
SPECIFICATIONS USED IN SIMULATION
Description
Value
Vp
Peak of line voltage
311V
Vin
RMS input voltage
220V
Vo
Output voltage
650V
Po
Output power
20kW
Lp
Passive rectifier filter inductor
1.5mH
L1 , L2 , L3
Active rectifier input inductors
2.5mH
Co
Output capacitor
4500µF
fs
Switching frequency
10kHz
In Fig. 9 the main current and the input currents on phase
1 of passive and active rectifiers are depicted. As expected,
the main current presents a sinusoidal shape. It must be
observed that the power processed by passive and active
rectifiers (proportional to the amplitudes of the passive and
the active input currents) is about 50% of the total output
power.
i A1(t)
(c) PWM REAL INPUT CURRENT
Ip
i 1(t)
400V
0V
(d) TOTAL INPUT CURRENT
Fig. 6. Currents on phase 1.
-400V
Lp1
i2p (t)
i3p (t)
V1 (t)
i1(t)
V2 (t)
i2(t)
V3 (t)
i3(t)
LINE VOLTAGES
50A
i1p (t)
Lp2
Dp1
Mp
Dp2
0A
+
(passive)
Co
Ro
-
i1a (t)
L1
-50A
(ative)
0s
i2a (t)
5ms
10ms
15ms
20ms
25ms
LINE CURRENTS
M1
Fig. 8. Input voltages and input currents.
L2
M2
i3a (t)
sen(wt)
Voltage control loop
Ha1 (s) PWM
Gate M1
k1
Hv(s)
Gate M2
0A
-
Sum
Ha2 (s) PWM
+
Vref
+
Mult
Sum
k2
Mult
sen(wt-120°)
-
-40A
Sum
+
sen(wt+120°)
40A
M3
Sum
+
-
L3
Ha3 (s) PWM
Gate M3
Mult
Iref
Mult
PWM Current Control Loop
+
Sum
-
Hp(s)
PWM
INPUT CURRENT OF THE PASSIVE RECTIFIER
Gate Mp
40A
Boost current control loop
Fig. 7. Control loop.
0A
VI. SIMULATION RESULTS
-40A
The specifications used in simulation are presented in
Table I.
The line voltages and the line currents are presented in
Fig. 8. The power factor correction is achieved, due the
sinusoidal line currents with low THD and the absence of
displacement factor.
INPUT CURRENT OF THE PWM RECTIFIER
50A
0A
-50A
0s
5.0ms
10.0ms
15.0ms
20.0ms
LINE CURRENT
Fig. 9. Currents on phase 1.
491
25.0ms
30.0ms
Harmonic Content
2.5
Some peaks can be observed in the line current presented
in Fig. 9. Due the high transitions in the input currents of the
passive rectifier, the current control loop of the active
rectifier can not impose a current which will provide
sinusoidal line current.
If the line impedances were
contemplated in simulation, the passive rectifier input
currents would present slower transitions and, consequently,
the peaks would be minimized. Considering 100µH of line
inductances, the results are presented in Fig. 10.
The total harmonic distortion observed in input currents is
about 3.22%. In Fig. 11 the harmonic content of the input
current and the limits imposed by the IEEE 61000-3-4 are
depicted.
To verify the dynamic response of the system, a load
variation was performed and presented in Fig. 12. Between
0ms and 50ms the converter operates with the rated power.
After this interval, the converter operates with a half of the
rated power through 50ms. In 100ms the converter operates
with full load again.
The output voltage transient is observed in Fig. 13.
As previously mentioned, values greater than 0.5 for the
ratio established by k1 and k2 will result in input currents
distorted. In Fig. 14 the distortion in the line current of phase
1 generated by a 0.68 k1 and k2 ratio can be observed.
In the case presented in Fig. 14, the passive rectifier
processes about 75% of the rated power while the active
rectifier processes the remaining 25% of the output power.
However, according to the Fig. 15, the line currents do not
meet the harmonic content limit imposes by IEC 61000-3-4
standard. Thus, the relation between k1 and k2 must be set up
to 0.5.
THD = 3.22%
2.0
Hybrid Rectifier
IEC 61000-3-4
1.5
1.0
0.5
0
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Order (n)
Fig. 11. Harmonic content of input current.
40A
0A
-40A
INPUT CURRENT OF THE PWM RECTIFIER
40A
0A
-40A
INPUT CURRENT OF THE PASSIVE RECTIFIER
50A
0A
-50A
10ms 20ms
40ms
60ms
80ms
100ms
120ms
140ms
LINE CURRENTS
Fig. 12. Load step response.
30A
700V
0A
650V
-30A
600V
INPUT CURRENT OF THE PWM RECTIFIER
10ms 20ms
30A
40ms
60ms
80ms
100ms
120ms
140ms
Fig. 13. Output voltage transient response.
40A
0A
-30A
0A
INPUT CURRENT OF THE PASSIVE RECTIFIER
50A
-40A
0A
50A
INPUT CURRENTS OF THE PASSIVE RECTIFIER AND THE PWM RECTIFIER
-50A
0s
5ms
10ms
15ms
20ms
25ms
0
LINE CURRENT
Fig. 10. Currents on phase 1 considering 100µH of line inductances.
-50A
25ms
30ms
35ms
LINE CURRENT
40ms
45ms
Fig. 14. Simulation results to k1 and k2 ratio equal to 0.68.
492
50ms
Harmonic Content
5
ACKNOWLEDGMENT
THD = 9.04%
The authors would like to thank CNPq (National Council
of Scientific and Technological Development) for their
contribution to this work in the form of a grant provided to
Carlos Henrique Illa Font and Ricardo Luiz Alves.
Hybrid Retifier
4
IEC 61000-3-4
3
2
1
0
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
REFERENCES
25
Order (n)
[1]
Fig. 15. Harmonic content of input current for k1 and k2 ratio equal to 0.68.
VII. CONCLUSION
[2]
A novel three-phase hybrid rectifier to high power
applications was proposed in this paper. The structure is
composed by the parallel association of a passive and an
active rectifier. The fact that each rectifier is responsible to
process about 50% of the output power allows improving the
robustness and providing a high efficiency of the power
converter.
The adopted control strategy allows the regulation of the
output voltage and the control of the input currents to achieve
high power factor.
The increase of the component count by the use of two
rectifier topologies does not affect strongly the volume,
because the components are designed for the half of the
output power. Moreover, all the magnetic elements are
designed for high frequency operation.
The next step of this work is the assembling of the
prototype to validation of this conception.
[3]
[4]
[5]
[6]
493
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