96
IEEE POWER ELECTRONICS LETTERS, VOL. 3, NO. 3, SEPTEMBER 2005
Low-Harmonic, Three-Phase Rectifier That Applies
Current Injection and a Passive Resistance Emulator
Predrag Pejović, Predrag Božović, and Doron Shmilovitz
Abstract—A new three-phase diode bridge rectifier that provides low harmonic distortion of the input currents applying
current injection technique is proposed in this paper. The rectifier
applies a novel passive resistance emulator consisting of four
diodes and a transformer with the volt-ampere rating of 3.57% of
the rectifier-rated power. Optimization of the transformer turns
ratio is performed in order to minimize the input current total
harmonic distortion (THD). It is shown that with the optimal turns
ratio the input current THD equals 3.72%. Dependence of the
input current THD on the load current is analyzed, and it is shown
that at low load currents the rectifier operates in the discontinuous
conduction mode with the THD of 7.79%. The analytical results
are experimentally verified on a 2 kW rectifier, indicating that the
input current THD lower than 8% is provided within a wide range
of the load current variations applying simple circuitry.
Index Terms—AC–DC power conversion, converters, harmonic
distortion, power conversion harmonics, power quality, rectifiers.
I. INTRODUCTION
T
HE third-harmonic current injection is a method to reduce
harmonic content of input currents in three-phase diode
bridge rectifiers. The method became popular after simple circuits proposed in [1] and [2] appeared. A detailed theoretical
analysis of the method is given in [3], where it is shown that a
part of the input power has to be taken by the current injection
network in order to improve the input current THD. That power
could be dissipated on resistors, as it is done explicitly in [1],
or restored applying resistance emulation techniques. Another
result of [3] is a comparison of the circuits proposed in [1] and
[2], which showed that the circuit of [1] provides lower input
current THD values than the circuit proposed in [2], due to the
harmonic components at sixth multiples of the line frequency
that flow between the diode bridge output terminals. In the case
of the circuit proposed in [2], this harmonic content is significantly higher, resulting in the higher THD values. On the other
hand, the circuit proposed in [2] requires only one inductor, in
contrast to the circuit proposed in [1] that requires two inductors. To overcome the problem with the harmonic components
at the sixth multiples of the line frequency, an application in the
current injection network of a 1:1 transformer that completely
Manuscript received January 15, 2005; revised August 8, 2005. This paper
was recommended by Associate Editor V. G. Agelidis.
P. Pejović is with the Faculty of Electrical Engineering, University of Belgrade, 11120 Belgrade, Serbia and Montenegro (e-mail: peja@el.etf.bg.ac.yu).
P. Božović is with the Pupin Telecom DKTS, 11080 Belgrade, Serbia and
Montenegro (e-mail: pbozovic@dkts.co.yu).
D. Shmilovitz is with the Faculty of Engineering, Tel Aviv University, Tel
Aviv, 69978 Israel (e-mail: shmilo@eng.tau.ac.il).
Digital Object Identifier 10.1109/LPEL.2005.858411
removes the harmonic components at sixth multiples of the line
frequency is proposed in [4]. Volt-ampere rating of the introduced transformer is only 0.16% of the rectifier-rated power,
and besides a significant reduction of the input current THD, it
allows design of the current injection network applying only one
inductor. The approach of [4] is applied in [5], where recovery of
the power taken by the current injection network is focused. The
result of [5] is a current injection network with a passive resistance emulator that provides self adjustment to the load current.
The circuit proposed in [5] suffers from complexity, since the
current injection network is a system of the fourth order, and it
has to satisfy two resonance constraints. The power taken by the
current injection network is restored at the rectifier output by increasing the output voltage. This requires circuitry to be added
in series with the load, where a huge output current flows.
In this paper, another approach to restore the power taken
by the current injection network is analyzed. The current injection network proposed in [4] is applied, but in contrast to [5],
the power taken by the current injection network is restored at
the rectifier output by increasing the output current. This results
in lower current ratings of applied semiconductor components,
and even more important, the current injection network is of the
second order, and only one resonance constraint has to be satisfied. Although self adjustment to the load current variations is
not as straightforward as in [5], even better results are obtained
experimentally.
II. RECTIFIER TOPOLOGY
The rectifier proposed in this paper is presented in Fig. 1.
It consists of a three-phase diode bridge (diodes D1 to D6,
the diodes not being labeled according to their conduction sequence), a current injection device which is realized as a zigzag
autotransformer, a current injection network (consisting of two
capacitors, an inductor , and a 1:1 transformer), and
transformer and diodes
a passive resistance emulator (
DR1 to DR4). Resistor models losses in the current injection
network and the current injection device. The current injection
network is the same as the one proposed in [4], but the resistance
emulator is completely different in comparison to the one proflows through the primary
posed in [5]. The injected current
of the
transformer, which is applied to adjust the voltage
level. The transformer secondary is connected to the ac side of a
single-phase diode bridge, which is supplied by a current originating from transformed . This current, after being rectified, is
added to the output current. In this manner, the power taken by
the current injection network is restored at the rectifier output.
1540-7985/$20.00 © 2005 IEEE
PEJOVIĆ et al.: LOW-HARMONIC, THREE-PHASE RECTIFIER
Fig. 1.
97
The rectifier.
III. OPERATION OF THE RECTIFIER
The rectifier presented in Fig. 1 differs from the rectifier proposed in [4] in the resistance emulator section. Its function is to
restore the power taken by the current injection network. The
waveforms relevant to describe operation of the resistance emulator are presented in Fig. 2. The resistance emulator provides
a link between the injected current , presented in Fig. 2(a),
and the rectifier output voltage, whose waveform is presented
in Fig. 2(b). Since the resistance emulator diode bridge (diodes
DR1 to DR4) is current-fed, states of the diodes are determined
by the direction of , such that DR1 and DR4 conduct when
is positive, while DR2 and DR3 conduct when
is negative.
at the
transThis results in the waveform of the voltage
former primary, as presented in Fig. 2(c). The power is restored
, presented in Fig. 2(d). This
at the rectifier output by current
current contains spectral components at sixth multiples of the
line frequency, and it modifies the current that loads the threephase diode bridge.
Applying the same nomenclature as in [5], spectral compoand
at the triple of the line frequency are the
nents of
same, equal to
(1)
as given by (4) and (5) of [5]. Assume that the injected current
is
(2)
Since the spectral component of
at the triple of the line frequency, derived by applying Fourier analysis of the waveform
of Fig. 2(c), is
(3)
and the resonance of the reactive elements of the current injection network is tuned to the triple of the line frequency, i.e.,
Fig. 2. Waveforms of the rectifier voltages and currents, n = 10.
, applying the method of equivalent circuits of
[3], we obtain
(4)
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IEEE POWER ELECTRONICS LETTERS, VOL. 3, NO. 3, SEPTEMBER 2005
Fig. 3. Waveform of the input current for n = 10 and k = 30=(7 ).
Fig. 4. Experimentally obtained waveforms of the input voltage and the input
current at the first phase.
Thus,
(5)
, gives the turns ratio of the reand, in the ideal case of
. Volt-ampere rating of
sistance emulator transformer
of the input
this transformer is computed as
power. The diodes DR1 to DR4 are exposed to the maximum
blocking voltage equal to the maximum instantaneous value of
, the same as for the diodes in the
the output voltage, 1.73
main three-phase diode bridge. Average current of each of these
, presented
diodes is equal to one half of the average value of
in Fig. 2(d), and equals 4.34%
. This is significantly lower
than the current rating for the diodes in the three-phase bridge.
In this manner, applying one small transformer and four moderately-sized diodes, the resistance emulation is realized without
a requirement for high frequency switching.
of the injected current affects the input curAmplitude
rent THD. Analyzing the waveform of the input current, as, negligible losses (
,
suming constant output current
), and the injected current waveform specified by (2),
dependence of the input current THD on the amplitude of the
injected current is obtained as
(6)
where is normalized amplitude of the injected current, as defined by (2). This result is negligibly dependent on in the area
of interest.
The minimum of the THD is reached for
(7)
in comparison to 1.5 obtained in [3], and results in the THD
value of
(8)
in comparison to 5.12% in [3]. These results are different from
[3], since the current
alters the waveform of the diode bridge
, and thus affects the input current.
load current, now
This technique is similar to the one utilized in [6] to completely
remove harmonics of the input currents. The obtained waveform
of the input current for the optimal value of is presented in
Fig. 3.
The optimal amplitude of the injected current can be obtained
precisely by adjusting the turns ratio of the resistance emulator
transformer according to (5), but this can provide the optimal
current injection for only one value of the output current. At low
loads, the injected current amplitude is limited by the discontinuous conduction of the diode bridge [7], while at high output
currents the injected current amplitude will be independent on
the load current, being determined by (4). Thus, it is of vital importance for the rectifier applicability to analyze the dependence
of the input current THD on the output current in the suboptimal
modes.
The discontinuous conduction mode of the diode bridge ocand
reach zero
curs when the diode bridge load currents
[7]. Starting from these conditions and assuming the injected
current waveform given by (2), the amplitude of the injected
current in the discontinuous conduction mode is obtained as
, resulting in
for
and
. This gives the THD value of
(9)
In the case where the resistance emulator is not applied, the dis, resulting
continuous conduction mode occurs at
in the input current THD of 10.43% [7]. It should be noted here
that (9) is an approximation obtained assuming high filtering of
the current injection network and negligible losses, resulting in
waveform given by (2). However, simulation and experthe
imental experience justify these approximations.
IV. EXPERIMENTAL RESULTS
In order to validate the theoretical predictions, an experimental rectifier with rated power of 2 kW was built, applying
mH and
F. The rectifier operated with
V and output current
input voltage amplitude of
up to 10 A. Fixing the turns ratio of the transformer according
, in order to
to (2), (5) and (7), it was chosen to be
A; the
provide the optimal current injection at
parasitic resistance of the current injection system is measured
.
as
Waveforms of the input current and the input voltage at the
A, are presented in Fig. 4.
first phase, recorded for
This situation corresponds to the rectifier operation close to the
optimal current injection. Measured THD of the input current is
4.48%, while the THD of the voltage waveform is 3.59%.
To provide further comparison of the analytical and the experimental results, the waveforms presented in Fig. 2 were recorded
PEJOVIĆ et al.: LOW-HARMONIC, THREE-PHASE RECTIFIER
99
Fig. 6. Dependence of the input current THD on the output current: (a) with
the resistance emulator; (b) without the resistance emulator.
THD. For the output current above 5.5 A, the rectifier operates
in the continuous conduction mode with the injected current
amplitude
A, which no longer depends on the
output current.
To analyze the effects brought by the resistance emulator, dependence of the input current THD on the output current was
measured on the same rectifier with the resistance emulator excluded. These results are presented by curve (b) of Fig. 6. The
curve indicates that application of the resistance emulator improved the input current THD within a wide range of the output
current.
V. CONCLUSIONS
Fig. 5. Experimentally recorded waveforms of the rectifier voltages and
currents, n = 17:6.
on the experimental rectifier for the optimal current injection
case, i.e.,
A, and the recorded waveforms are presented in Fig. 5 in the same form as the theoretical waveforms
of Fig. 2. In the first diagram, Fig. 5(a), slight pollution of the
injected current with the higher order harmonics could be observed. This effect was neglected in the analysis by the assumption of (2). The waveform of the output voltage, presented in
Fig. 5(b), is close to the analytical predictions. A minor discrepancy was caused by commutation effects in the diode bridge
and the distortions of the input voltages. However, the waveform of the voltage at the resistance emulator transformer primary, presented in Fig. 5(c), exposes a significantly lower amplitude than the corresponding waveform of Fig. 2(c), although
the waveform shape matches the theoretical expectations. This
discrepancy is caused by the transformer turns ratio, increased
to
to compensate for the losses in the current injection system. (Compare the lossless case where
, which
is used to generate the waveforms of Fig. 2.) The same situation
applies for the diagram of the resistance emulator output current
presented in Fig. 5(d).
Dependence of the input current THD on the output current is presented in Fig. 6, curve (a). For the output current
lower than 5.5 A, the rectifier operates in the discontinuous
conduction mode. In the output current range from 1 A to
5.5 A, (9) is proven to be a good estimate of the input current
A three-phase diode bridge rectifier that applies the current
injection technique and a novel resistance emulator is proposed
in this paper. The resistance emulator consists only of passive elements, four diodes and a transformer, and it restores the power
taken by the current injection network at the rectifier output. The
output current of the resistance emulator alters the diode bridge
load current, and it contains some amount of harmonic components at sixth multiples of the line frequency. In the case of the
optimal current injection, this results in the input current THD
of 3.72%, a slight improvement over the input current THD of
5.12% obtained by pure third-harmonic current injection. The
rectifier discontinuous conduction mode occurs when the amplitude of the injected current equals 5/3 of the output current,
in comparison to the double of the output current in the case of
pure third-harmonic current injection. In this manner, the THD
of the input current in the discontinuous conduction mode is reduced from 10.43% to 7.79%. The proposed rectifier provides
an input current THD lower than 8% in a wide range of the rectifier load current variations. The volt-ampere rating of the resistance emulator transformer is 3.57% of the rectifier rated power,
while the resistance emulator diodes are exposed to the average
current of 4.34% of the output current. Analytical results are
verified on a 2 kW experimental rectifier.
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