A Novel SVPWM Scheme for Vienna Rectifier without
Current Distortion at Current Zero-crossing Point
Wenxi Yao, Zhengyu Lv, Ming Zhang, Zhuang Lin
Electrical Engineering College, Zhejiang University, Hangzhou, China
Email: ywxi@zju.edu.cn
Abstract—Vienna rectifier is one of the most popular topologies
for three-phase PFC converter. DC voltage, grid current double
loop controller and three-level SVPWM are normally used to
control the Vienna rectifier. Accurately detecting the current
zero-crossing point is required to achieve the correct SVPWM
signals since the output level of Vienna rectifier is also decided
by the direction of the phase current. The error of the duty ratio
is decided by the error time of the current zero-crossing point
detecting and the duty ratio before and after the current
zero-crossing point. It can be concluded that the impact of
current zero-crossing will be eliminated if the switches near
current zero-crossing point are kept “on”. To achieve this goal, a
novel SVPWM scheme is proposed by using the certain state
combinations of short vectors in each sector. In this method, the
calculation of duty ratio will not be affected by the direction of
phase current near the zero-crossing point, and therefore the
distortion of current caused by current zero-crossing detection
error will be eliminated. Simulations and experiments are
conducted to verify the presented method.
Key words: Vienna rectifier, SVPWM, Current zero-crossing
I. INTRODUCTION
Recently, power electronic techniques are widely used
for power conversion, energy saving, renewable energy
generation, and so on. However conventional power
electronic equipment has the shortages of low power factor
and serious current distortion which deteriorate the energy
quality and degrade the transmission efficiency of the power
system[1]. Therefore the power factor correction (PFC)
technique becomes an important research interesting in power
electronics.[2] Vienna rectifier is one of the most popular
topologies for three-phase PFC due to its good performance
and relatively low costs[3][4]. The sinusoid pulse width
modulation (SPWM) [5] and space vector PWM (SVPWM) [6]
are the two basic control methods for the Vienna rectifier. But
in essential the two methods can be proved equivalent[7]. In
general the direction of the current is required to achieve the
PWM of Vienna rectifier, and the PWM error may appear
when the direction of current is detected incorrect which will
lead to a current distortion at current zero-crossing time,
especially at light load.[8]
zero-crossing point detection. The principle to avoid the
distortion is analyzed, and a control scheme based on
SVPWM is proposed. The simulations and experiments are
conducted to verify the method.
II STRUCTURE AND CONTROL OF VIENNA RECTIFIER
The Vienna rectifier is a three-level converter. The main
circuit is illustrated in Fig.1, includes a three-phase filter in
grid side, two DC link capacitors connected in series in DC
side, and a three-phase commutation circuit which composes
of 6 diodes, 3 bidirectional switches. The bidirectional switch
can be comprised by two MOSFETs or one MOSFET
companying with four diodes connected as show in the below
of fig.1.
Generally, the control scheme with double control loop
is employed in Vienna rectifier as illustrated in fig.2. The
outer loop is DC voltage regulator which is used to control
the output DC voltage. The inner loop is current regulator
which is used to control both the amplitude and the quality of
grid current. The current regulators can be configured in
synchronous frame(DQ), and the synchronous angle is
obtained by a phase lock loop (PLL). The reference voltages
outputted from current regulators are then used to generate
the PWM signals by a PWM scheme.
This paper addresses on the current distortion problem at
the commutation time of the phase current due to the error of
or
Figure 1 Topology of Vienna rectifier
This work was supported by National Natural Science Foundation of China (51177148) and Zhejiang Key Science and Technology Innovation
Group Program (2010R50021)
978-1-4799-2399-1/14/$31.00 ©2014 IEEE
2349
θ
Figure 2 Diagram of control scheme
Suppose the points A, B, C are the three-phase AC side
terminals of the commutation circuit which can be connected
to three voltage levels by controlling the bidirectional
switches and the direction of phase currents. Taking phase A
as an example, when the switch S1 is turn on the point A is
connected to the neutral point of DC bus; when the switch S1
is turn off the potential of point A is decided by the direction
of phase current A, the point A is connected to the positive
point of DC bus if the phase current ia is positive, and
connected to the negative point of DC bus if the phase current
ia is negative.
Suppose the SVPWM is adopted, it is well known that
the vectors are used to describe the states of three-phase
converter in SVPWM methods. The vector is defined as:
U x = U A + U B e−2π /3 + U C e2π /3
(1)
⎧Ts Ur = t1U 7 + t2 U 8 + t3 U1
⎨
⎩t1 + t2 + t3 = Ts
(2)
Step 3. Decide the duty ratio of the bidirectional switch
of each phase. The duty ratio of each phase can be obtained
by the state combinations and the duration time of these
vectors. Still suppose the reference vector is located at area A,
the duty ratios of each phase are expressed in (3), where Dx1
represent the duty ratio of positive level and Dx2 represent the
duty ratio of negative level, k is the percentage of state
combination [1 0 0] used in short vector U1, which is
normally used to balance the voltage of DC capacitors. The
curve of duty ratio with time is called modulating waveform.
There are two modulating waveforms each phase work
alternatively in Vienna rectifier, which also can be unified to
where UA, UB, UC are the states of the AC side terminals A B
C. In three-level converter, each phase has three states, so
totally there are 27 vectors, of which 19 vectors are different,
as show in fig.3, where the state combination [UA UB UC] is
used to express the vector Ux, and the numbers -1, 0, 1
represent the states (or levels) of the corresponding phase.
Level ‘-1’ is the negative level which means the phase
terminal (A, B or C) connecting to the negative point;
correspondingly the levels ‘0’ and ‘1’ are the zero level and
positive level, which means the phase terminal connected to
the neutral point and the positive point of DC bus respectively.
Among the 19 vectors, there are six long vectors, six middle
vectors, 6 short vectors and 1 zero vector based on the
amplitude of the vectors.
The basic principle to achieve the SVPWM is using the
nearest three vectors to combine the reference vector, so the
steps for SVPWM are generalized as following[7]:
β
[ −1 1 −1]U
11
U12
[ −1
1 1]
[ −1
U 3 [0
[ −1
1 0]
U13
[ −1
1 0]
U2
1 1]
U 0 [1
[ −1
0 0]
[0
[ 0 0 1]
[ −1 −1 0]
0 1]
−1 1] U
15
1 −1]
1 1]
[0
U16 [ 0
1 0]
0 −1]
U1[1
0 0]
[0
−1 −1]
0 0]
[1
U5
U 9 [1
[1
[0
0 −1]
U 4 [0
U14
[ −1
U10 [ 0
0 1] U
6
U8
[1
[1
U17 [1
0 −1]
−1 −1]
[1
U18
−1 0]
−1 1]
1 −1]
U7
α
−1 0]
−1 1]
(a) Sectors division
Step 1. Find the nearest three vectors. That is to find the
triangle which the reference vector located at. First to find the
sector that the reference vector belong to, as show in fig.3(a),
and then find the triangle area that the reference vector at, as
show in fig.3(b). The three point of the triangle are the
nearest three vectors of the reference vector.
Step 2. Calculate the duration time of the three vectors.
As an example, the reference vector is at sector I, area A as
show in fig.3(b). The duration time of each vector can be
calculated by (2), where Ts is the PWM cycle.
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(b) Areas division
Figure 3 Map of three-phase three-level vectors.
one unified modulating waveform. Suppose the unified
modulating waveform is Dx expressed as (4).
1
⎧ Da1 = t1 + t2 + kt3 ⎧ Da 2 = 0
⎪
⎪
, ⎨ Db 2 = t1 + (1 − k )t3
(3)
⎨ Db1 = 0
⎪ D = t + t + (1 − k )t
⎪D = 0
3
⎩ c2 1 2
⎩ c1
Dx = Dx1 − Dx 2
x=a, b, c
(4)
It should be noted that only the state combination [0 0 -1]
for vector U2 and the state combination [0 -1 0] for vector U6
can be selected in sector I due to the current direction of
phase B and phase C are both negative.
0
-1
0.01
0.02
0
0.01
0.02
0
-1
Figure 5 Three-level PWM scheme with disposition carrier
In general, the ideal reference vector’s track is a circle in
one line cycle if the three phase line voltages are symmetrical
and have pure sinusoid waveforms. In this condition and
suppose the k in (3) is valued 0.5, the unified modulating
waveform of phase A is shown in fig.4. The sector which the
reference vector located at is noted at the top of the figure. It
can be seen that the duty ratio will step up or down at the
time when the modulating waveform moves from one sector
to another. For example, the duty ratio will step from about
0.8 down to about 0.5 when the modulating waveform moves
from sector VI to sector I.
1
0.5
0
0
0.01
0.02
0.01
0.02
1
0
-1
0
1
Figure 6 principle of PWM scheme of Vienna rectifier
0.5
needs to be reversed after the point of current zero-crossing.
The waveform of output level after modulating is shown in
the below of fig.6 which is the same with the one in fig.5.
0
III THE IMPACT OF CURRENT ZERO-CROSSING
-0.5
-1
0
1
0
0.01
0.02
0.03
0.04
Figure 4 modulating waveform when k=0.5
Step 4. Generate the PWM control signal. The PWM
signals are generated by the duty ratios compare to the
triangle waveform. In regular three-level converter, the PWM
scheme that the modulating waveforms compare to the
disposition carrier waveforms with same phase is used most
widely due to its low harmonics of switching frequency. The
principle of this method is illustrated in fig.5, where there are
two triangle waveforms spanning from -1 to 0 and from 0 to 1
respectively are used to be compared with the modulating
waveform. When the modulating waveform larger than the
upper triangle waveform, the output level is ‘1’; when the
modulate waveform smaller than the lower triangle waveform,
the output level is ‘-1’; otherwise the output level is ‘0’. The
below waveform of fig.5 is the signal of output level.
Unlike the regular three-level converter, the bidirectional
switches in Vienna rectifier is used to control the level ‘0’
which means when the switch is turn on, the corresponding
phase outputs level ‘0’. The level ‘1’ and level ‘-1’ is decide
by the direction of current, therefore the principle of PWM
scheme is illustrated in fig.6. The duty ratio of the switch
equals to 1-Dx when the current is positive and equals to 1+Dx
when the current is negative. The phase of the carrier also
As analyzed above, when the current crosses zero, the
duty ratio will have a step. This is because the selectable state
combinations will change when the reference vector moves
through the sectors edges. For example, in fig. 3(a) when the
reference vector moves from sector I to sector II, the current
of phase B will change from negative to positive, so both the
state combinations of vector U1, [1 0 0] and [0-1-1], are
selectable in sector I, but the state combination [0-1-1] is not
selectable in sector II which will results the duty ratios step
suddenly if the state combination [0-1-1] is used in sector I.
In the same way, the state combination [1 1 0] of vector U2 is
selectable in sector II but not selectable in sector I.
The step of duty ratio will bring a step of common mode
voltage but not a problem when the direction of current is
measured correctly. However, a PWM modulation error will
occur if the direction of current is not accuracy, and
consequently a current spike will be appeared at the time of
current zero-crossing which may distort the grid current and
increase the EMI Interference. Fig.7 shows the impact of
inaccuracy detection of current direction, where fig.7(a) show
the modulation error when the detection of current direction
has one degree’s error and consequently the grid current is
show in fig.8, in which current spike will appear at every
current zero crossing time
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1
1
0.5
0
0.01
-0.5
-1
0
0.01
0.02
0
0.4
0.1
0.01
-0.4
0
0.01
0.02
-1
0
(a) PWM modulation errors
0.01
0.02
(a) Unified modulating waveform
15
15
10
5
5
0
-5
-5
-15
0
0.01
-10
0.02
-15
(b) Three phase grid current
Figure 7 Impact of inaccuracy detection of current direction
The error of modulation waveform is expressed in (5),
where the Dx1o and Dx2o are the duty ratios before and after
the zero-crossing time defined as (3). Δtc is the error time of
current zero-crossing detection. It can be seen that the error of
modulation waveform is decided by the step of duty ratio and
the error of current zero-crossing detection.
Dxe = ( Dx1o + Dx 2o )Δtc
(5)
IV SVPWM SCHEME WITHOUT CURRENT DISTORTION
AT CURRENT ZERO-CROSSING POINT
Obviously, improving the accuracy of detecting the
current zero crossing is the direct way to decrease the impact
of current zero-crossing, which is not easy at all-time due to
the switching frequency harmonics in grid current. Besides,
reducing the duty ratio step also will decrease the impact of
current zero-crossing.
The positive and negative duty ratio Dx1 and Dx2 are
always large than zero, so the impact of current zero-crossing
will be eliminated if Dx1o = Dx2o = 0. It also means that the
switch of the corresponding phase are kept ‘on’ during the
time of phase current zero-crossing, and the output level
maintains ‘0’. A simple way to achieve this goal is using
conventional SPWM. The principle and the performance are
illustrated in fig. 8, where fig.8(a) shows the unified
modulating waveforms of SPWM with third harmonic
injection, from which it can be seen that the duty ratio is zero
at the time of zero crossing of the corresponding phase
current. Consequently, the currents in fig.8(b) are improved
comparing to fig.7(b). But the current distortion still exists
with one degree error of current zero-crossing detecting,
because the duty ratio equals to zero only at the point of
current zero-crossing and does not equal to zero near this
0
0.01
0.02
(b) Three phase grid current
Figure 8 Impact of inaccuracy detection of current direction
with SPWM
point.
The more effective way of reducing the impact of
current zero-crossing is to enlarge the period of zero duty
ratios near the point of current zero-crossing. The proposed
method can be achieved by selecting the certain redundant
vectors in SVPWM scheme. Tab.1 shows the state
combination of short vectors selected in each sector which
can avoid the step of duty ratio when the vector moves
through the sector edges. Using this method the state
combinations which may lead to the step of duty ratios are
given up.
Tab.1 State combination of short vectors in each sector
Sectors
State combination
I
II
III
IV
V
VI
100
00-1
010
-100
001
0-10
The unified modulating waveforms of the proposed
method are illustrated in fig.9 (a) which shows that sufficient
time of zero duty ratios is achieved when the reference vector
moves from one sector to another sector, therefore the output
levels of three-phase will not affect by the direction of the
current which nears zero-crossing. Using this SVPWM
scheme, the grid currents of simulation are shown in fig.9(b)
which shows that the distortions of current at current
zero-crossing point are removed thoroughly with one degree
error of current zero-crossing detecting.
V EXPERIMENT VERIFICATION
An experimental prototype of Vienna rectifier is
developed to verify the proposed method. The main circuit
and the control diagram are shown in fig.1 and fig.2
2352
this purpose, a novel SVPWM scheme is proposed in this
paper. Both the simulation and experiments verify that the
control performance of this method will not be affected by
the accuracy of zero-crossing point detecting.
1
0
-1
0
1
0.02
(a) Grid current with conventional SVPWM (2A/div 10ms/div)
(a) Unified modulating waveform
15
10
5
0
(b) Grid current with proposed SVPWM(2A/div 10ms/div)
-5
-10
-15
0
0.01
0.02
(b) Three phase grid current
Figure 9 the proposal method
respectively. The parameters of the experiment are listed in
tab.2. The result waveforms are shown in fig.10. Fig.10(a) is
the waveform of phase current A using conventional SVPWM,
of which the duty ratios have steps at the current
zero-crossing point, therefore a current spike will appear at
zero-crossing point of each phase. Fig.10(b) shows the one
using the proposed method. It can be seen there is no obvious
distortion at the current zero-crossing point. Fig.10(c) shows
the waveform of grid voltage.
Tab.2 Parameters of experiments
Filter inductor
380uH
DC capacitor
220uF
Input voltage
AC 30V
Output voltage
DC 100V
Load
150Ω
VI CONCLUSION
This paper analyzes the current distortion caused by
detecting error of current zero-crossing point. Vienna rectifier
is a three-level converter, but only the zero level can be
controlled by switches completely, the positive and negative
levels are also decided by the direction of current. Thus the
accuracy of detecting the current zero-crossing point will
significant affects the quality of grid current. Let the duty
ratio of the switches equal to 1 near the zero-crossing time,
the impact of the direction of current will be eliminated. For
(c) Grid voltage (50V/div 10ms/div)
Figure 10 Experimental results
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