Control of a Four-Switch Rectifier under
Unbalanced Input Voltage
Saeed Ouni, Vahid Javadian, Mahmoud Shahbazi, and MohammadReza Zolghadri, Member, IEEE
Department of Electrical Engineering, Sharif University of Technology
saeedouni@ee.sharif.edu, javadian@alum.sharif.edu, mahmoudshahbazi@outlook.com ,zolghadr@sharif.edu
Abstract- Nowadays, reduced switch rectifiers are more
interested because of less expense. Control of these rectifiers is
an important part of their designing process. In this paper, a
method is proposed for four-switch rectifier to continue working
under unbalanced input voltage. To achieve this goal, first a
method is introduced to separate positive and negative
sequences of dq components. Also, the necessary condition is
determined. Considering this condition, the control method is
modified and new reference value for the control signals is
calculated. Finally, the system is simulated in Simulink and the
results are provided. These results confirm the accuracy of the
developed model, and also the effectiveness of the proposed
controllers.
Keywords: Four-Switch Rectifier, Power Factor, Positive and
Negative Sequences, and Unbalanced Voltage.
Figure 1. Four switch rectifier
Nomenclature
,
,
,
, ,
, ,0
, ,0
,
,
Standard IEC61000-4-27 [14] with using these components,
defines unbalance index as (2):
Operator as shift by 120 degree
Active power
Reactive power
Input phase voltage
Sequence components of voltage
Sequence components of current
DQ components of voltage
I.
(2)
INTRODUCTION
Nowadays, the semiconductor switches and drivers cost is the
major part of the power converter price. Therefore, some
structures are proposed to reduce the number of switches to
decrease the converter prices [1-4]. Three-phase four-switch
bidirectional converter (B4) is a reduced switch converter,
compared with six-switch converter (B6) shown in Fig. 1.
Some of the applications of this converter are mentioned in
[5-7]. Some switching techniques have been proposed for this
converter [8-11]. In [12] a new SVM switching technique has
been proposed for this converter. Also, in [13] a closed loop
control method has been applied to control of this converter.
In this work, the control signals are controlled in dq
coordinate.
Different definitions have been presented for amount of
unbalance characteristic [14]. In the majority of these
definitions, positive and negative and zero sequence
components which are calculated by (1) are used.
_
1 1
1 a
1 a
1
a
a
(1)
To control a converter that is fed by unbalanced voltages,
there is a method which uses mathematic approach for
converter modeling [15]. But, since in this paper SVM
method is used for controlling of converter, it have been tried
to opt a method which is appropriate for vector control. In
[16-18] similar methods have been used for six-switch
converter with unbalanced input voltages. In these methods, it
is needed to calculate positive and negative dq components of
the currents and voltages. In the section II, existing methods
for calculation of these values will be explained.
In section III, the control method presented in [13] will be
modified so that the converter is able to continue working
under unbalanced voltage condition. Finally, the validity of
the proposed method will be verified by simulation results.
II. CALCULATION OF DQO SEQUENCE COMPONENTS
In unbalance state, parameters of positive and negative
sequence components such as current and voltage should be
available to control of converter. Different methods have
been proposed to calculate these parameters that some of
them are discussed in the following [6-7].
A) Using low pass filter
The frequency of negative (positive) sequence in positive
sequence coordination is two times of fundamental frequency.
Thus, by using a low pass filter which has a bandwidth lower
than mentioned frequency, after of abc/dq0 transformation,
can separate the DC component from second harmonic
component. This method is shown in Fig. 2. In [19-20] this
method is used for calculation of positive and negative
sequence of dq components.
Low pass filter, causes the reduction of stability margin
because of its negative phase. This may even cause the
system instability. Then, to design the controller, the impact
of this filter should be considered.
B) Using notch filter
In this method, by using of notch filter second harmonic
component is separated from the signal transformed by
positive sequence reference. Then positive dq component is
remained. Similarly, this method can be used for negative dq
transformation. In Fig. 3 this method is shown. Same as
previous method, applying negative phase by filter is a
disadvantage of this method.
Using (3) and (4), (5) is deduced that can be used for
calculation of positive and negative components of αβ.
1 0
1 0 1
2 1 0
0 1
(3)
cos
sin
(5)
Finally, positive and negative sequence of dq components can
be derived as bellow:
sin
.
sin
(6)
.
C) Delay cancellation method
In this method [19], without using filter, sequences are
separated just based on mathematic calculation.
Firstly, αβ components are calculated by applying Clark
transformer and these components are divided in to positive
and negative parts.
cos
sin
v t
1
v t
0
1 v t T⁄4
0 v t T⁄4
0
1
0
1
sin
.
sin
.
(7)
In Fig. 4 the block diagram for this method is shown.
III.
MODIFICATION OF CONTROL METHOD UNDER
UNBALANCED VOLTAGE CONDITION
Then, by a shift equal to T/4 for αβ components, similar
terms as following are obtained:
⁄4
⁄4
v sin ω t
v
ω t
Transform to
positive
synchronous
reference
φ
φ
(4)
v sin ω t φ
v cos ω t φ
Positive dq
Refernce
LPF
dq
Negative dq
Refernce
LPF
dq
+
abc
Transform to
negative
synchronous
reference
−
Figure 2. Decomposition of positive and negative dq components using low
pass filter
Notch
dq
Notch
dq
+
The rectifier should correct the input power factor under
unbalanced voltage. Nevertheless it is required to define
power factor in this situation. There are different definitions
in the unbalanced condition that each of them can be referred
in a specific field [21-22].
One method to determine the reference current values in
unbalance state of input voltage is that current phase should
be in phase with voltage for each phase. In other words,
positive sequence of current will be in phase with the positive
sequence of voltage and the negative sequence of them will
be in phase as well. Investigation of this method can be done
by presenting the relation between input power components
which consist of average value of active power, average value
of reactive power and second harmonic values of them, based
on dq components of positive and negative sequence of
voltage and current as bellow:
sin 2
cos 2
(8)
−
Figure 3. Decomposition of positive and negative dq components using notch
filter
3
2
T (θ ) dq
+
dq
αβ
T (−θ )
dq
−
dq
Figure 4. Decomposition of positive and negative dq components using delay
cancellation method
For reactive power, second harmonic components can be
defined as (5) but the effect of them can be neglected.
sin 2
cos 2
3
2
(9)
In this method, iq+ and uq+ must be zero. Then, equation (8)
can be simplified to (10):
positive sequence of that phase voltage. Whereas, in negative
sequences they must have 180 degrees phase difference.
For calculation of reference power value, block diagram of
Fig. 5 can be used [16, 18]. This means that if reference value
of output voltage is determined, a control loop with PI
controller can be used. In order to have zero steady state
error, output of this loop must be the reference value of the
power. After determination of voltage reference value, by
using (13), reference values of dq currents for positive and
negative sequence can be obtained. Then, by using the control
loop which was designed in section III, the required vector
for positive and negative sequence, for control of SVM
controller can be determined, so that the time of each vector
and switching state is calculable. Fig. 6 shows the control
method of the rectifier under unbalanced input voltage.
It must be mentioned that, in unbalance condition the aim is
construction of two sinusoidal voltages. Thus, according to
Fig. 6 the control vector should not be in over modulation.
This condition can be presented as (14):
(14)
3
2
sin 2
cos 2
(10)
In this state, in addition to active power, input power contains
reactive power and second harmonic components. Therefore,
output voltage contains second harmonic component. Thus,
this method is not appropriate to determine the currents
reference values.
According to (11) which is obtained from (8) for active power
and other power components equal to 0, positive and negative
components of current can be deduced by (12).
3
2
0
0
0
2
3
.
.
However, this condition is conservative and is not required.
This is just sufficient.
Figure 5. Control loop to determine reference power value
(11)
0
0
0
(12)
After simplification of (12), this equation will be obtained:
2
3
(13)
This is obvious that matrix operations which need calculation
of inverse matrix, led to a simple equation that can be used
easily for calculation of reference values of currents [18, 23].
It can be resulted from this equation that in unbalance state,
positive sequence of each phase current must be in phase with
Figure 6. Block diagram of control process unbalance condition
IV. SIMULATION RESULTS
Figure 7. Input unbalanced voltage
TABLE I
POSITIVE AND NEGATIVE SEQUENCE OF DQ COMPONENTS
Parameter
Value
Parameters
Value
Simulation is carried out to investigate the converter
operation under application of unbalanced voltage. Methods
of [12, 13] are used for switching, control and balancing
capacitor voltages. Two different type of unbalance condition
are considered.
A) In first condition, the values of positive and negative
components are considered as following:
220√2 0
(15)
44√2 60
(16)
Base on (2) unbalance indicator is equal to:
(17)
20%
Acceptable unbalance value for voltage of 380 Volts L-Lrms is
equal to 2 % [14]. Fig. 7 shows the input voltage.
Table I shows the dq components of current that are
calculated by (13) and voltage components for positive and
negative sequence for rectifier power of 6 kW and output
voltage of 1200 Volts.
Based on:
342.2
346.4
53.9
322.7
(18)
It can be deduced that:
0
-31.12 V
1.326 A
53.9 V
-2.296 A
380
360
(19)
400
200
0
340
V(V)
Fig. 8 shows the value of voltage vector that can be made. It
is obvious that the vector magnitude is not constant and it has
a main frequency component that its peak value is larger than
amplitude of sinusoidal voltage. According to Fig. 9 which
shows the time of application of each voltage vector, it is
shown that each time span is a portion of switching period
that is equal to 50 µsec. If control method of SVM works
under over modulation conditions, some of calculated time
spans are negative which are not acceptable. Therefore,
according to the obtained values for these parameters during
the simulation time that are positive and below 50 µsec, it can
be resulted that SVM works in normal condition without over
modulation.
Input Voltage (V)
13.255 A
0
In Fig. 10, 11 and 12 waveforms of input current, positive
sequence of current and negative sequence of current are
shown respectively. In waveform of negative sequence
current, switching ripple is clearer because the magnitude of
current is smaller.
In Fig 13 reference values of dq components for positive and
negative sequences are shown. As it is clear, the results are in
accordance with the values calculated in Table I.
Waveform of output voltage and capacitor voltages are
presented in Fig. 14. It is obvious that voltage of capacitors is
symmetric and output voltage that is equal to 1200 Volts has
an acceptable ripple.
For more investigation, main component and DC component
of input current and also positive and negative sequences,
output voltage and capacitors’ voltage are shown in Table II.
According to this table, it can be said that as it was expected
positive sequence currents have the same phase as positive
sequence voltages and also, negative sequence currents are in
the opposite phase of negative sequence voltages.
320
300
280
260
240
220
0.44
0.45
0.46
0.47
time(s)
0.48
0.49
0.5
Figure 8. Value of voltage vector
5
Vectors Modulation time(s)
44
220
I
311.12 V
x 10
-5
3
t3
t1
4
t2
t4
2
1
0
-200
0.48
0.485
0.49
time(s)
0.495
Figure 9. The time of application of each voltage vector
-400
0.44
0.45
0.46
0.47
time(s)
0.48
0.49
0.5
0.5
TABLE II
20
FUNDAMENTAL AND DC VALUE OF POSITIVE AND NEGATIVE
SEQUENCE OF DQ COMPONENTS
Input Currents (A)
10
0
-10
-20
0.44
0.45
0.46
0.47
0.48
0.49
0.5
time(s)
Figure 10. Waveforms of input current
Positive Sequence Currents (A)
15
10
5
0
-5
-10
-15
0.44
0.45
0.46
0.47
0.48
0.49
0.5
time(s)
B) In the following, the simulation is accomplished for the
conditions in which unbalanced voltage leads the SVM to
work in over modulation region.
So, the input voltage is determined for positive and negative
sequences, as below:
Negative Sequence Currents (A)
Figure 11. Positive sequence of current
(20)
44√2 0
(21)
4
2
In this state, unbalance indicator is again 20 %.
According to Fig. 15 which shows the time span of applying
vectors, it can be said that vector controller is in the over
modulation state. Nevertheless, output voltage in Fig. 16,
shows that the output voltage waveform and capacitors
voltages are as expected.
0
-2
-4
0.44
0.45
0.46
0.47
0.48
0.49
0.5
time(s)
5
Vectors Modulation time(s)
Figure 12. Negative sequence of current
20
Currents Reference Value (A)
220√2 0
Idp
Iqp
Idn
Iqn
15
10
5
x 10
-5
t1
4
t3
t2
3
t4
2
1
0
0
0.48
-5
0.44
0.45
0.46
0.47
time(s)
0.48
0.49
0.5
0.485
0.49
time(s)
0.495
0.5
Figure 15. The time of application of each voltage vector
Output and
Capasitors Voltage (V)
1200
1000
800
600
400
0.44
0.45
0.46
0.47
time(s)
0.48
0.49
0.5
Figure 14. Waveform of output voltage and capacitor voltages
Capacitors Voltage and output Voltage (V)
Figure 13. Reference values of dq components
1300
1200
1100
1000
900
800
700
600
500
0.44
0.45
0.46
0.47
time(s)
0.48
0.49
Figure 16. Waveform of output voltage and capacitor voltages
0.5
20
[3]
Input Currents (A)
15
10
[4]
5
0
-5
-10
[5]
-15
-20
0.44
0.45
0.46
0.47
time(s)
0.48
0.49
0.5
Figure 17. Input current waveform
[6]
[7]
[8]
[9]
[10]
Figure 18. Frequency spectrum of input current
According to Fig. 17 and 18 which show the input current and
its frequency spectrum, the quality of input current is not
suitable and magnitude of the low order harmonics are
significant.
Finally, it can be said that if the designed controller doesn’t
work in over modulation state, designed rectifier has a
suitable operating state for unbalanced voltage. Nevertheless,
if the controller works in over modulation, the output voltage
is as expected but the quality of input current is unacceptable
and also magnitude of low order harmonics are noticeable.
V. CONCLUSION
In this paper an appropriate control method was proposed for
four-switch rectifier under unbalanced input voltage
condition. First a useful method for decomposition of positive
and negative sequences of dq component was introduced.
After that, the criteria that converter must support under
unbalancing condition such as reactive power and second
order component of power omitting, was determined. Finally
the controller was modified to improve the converter
performance. To show designed controller and decomposition
method effectiveness, the rectifier was simulated in
SIMULINK for various operational conditions. Simulation
results confirm that using the proposed control method, the
rectifier works well under unbalanced input voltage, if no
over-modulation occurs. In case of over-modulation, the
rectifier can produce the desired output voltage, but with
considerable low-order harmonics in the input current.
REFERENCES
[1]
[2]
C. B. Jacobina, I. S. de Freitas, E. R. C. da Silva, A. M. N. Lima, and
R. L. D. A. Ribeiro, "Reduced Switch Count DC-Link AC-AC FiveLeg Converter," IEEE Transactions on Power Electronics, vol. 21, pp.
1301-1310, 2006.
R. Srinivasan, and R. Oruganti, “A unity power factor converter using
half-bridge boost topology,” IEEE Trans. Power Electron.,vol. 13, no.
3, pp. 487-500, May 1998.
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
B. K. Lee, B. Fahimi, and M. Ehsani, “Overview of reduced parts
converter topologies for AC motor drives,” in Proc. 2001 IEEE PESC,
pp. 2019-2024.
M. Shahbazi, P. Poure, S. Saadate and M. R. Zolghadri, “Fault Tolerant
Five-Leg Converter Topology with FPGA-based Reconfigurable
Control”, IEEE Trans. Ind. Electron., vol. 60, no. 6, pp. 2284-2294,
June 2013.
P. N. Enjeti, and A. Rahman, “A new single-phase to three-phase
converter with active input current shaping for low cost ac motor
drives,” IEEE Trans. Ind. Applicat., vol. 29, no. 4, pp. 806-813,
July/Aug. 1993.
C. B. Jacobina, I. S. de Freitas, and A. M. N. Lima, “DC-link Threephase-to-three-phase four-leg converters,” IEEE Trans. Ind. Electron.,
vol. 54, no. 4, pp. 1953-1961, Aug. 2007.
V. F. Pires, J. F. Silva, “Three-Phase Single-Stage Four-Switch PFC
Buck–Boost-Type Rectifier,” IEEE Trans. Ind. Electron., vol. 52, no. 2,
2, April. 2005.
A. W. Green, and J. T. Boys, “hysteresis current-forced three-phase
voltage-sourced reversible rectifier,” in Proc. IEE, vol. 136,no. 3, pp.
113-120, May 1989.
K. Thiyagarajah, V. T. Ranganathan, and B. S. Ramakrishna Iyengar,
“A high switching frequency IGBT pwm rectifier/inverter system for ac
motor drives operating from single phase supply,” IEEE Trans. Power
Electron., vol. 6, no. 4, pp. 576-584, Oct. 1991.
M. B. de R. Correa, C. B. Jacobina, E. R. C. da Silva, and A. M.N.
Lima, “A general PWM strategy for four-switch three-phase inverters,”
IEEE Trans. Power Electron., vol. 21, no. 6, pp. 1618-1627, Nov.
2006.
F. Blaabjerg, S. Freysson, H. H. Hansen, and S. Hansen, “A new
optimized space-vector modulation strategy for a component minimized
voltage source inverter,” IEEE Trans. Power Electron, vol. 12, no. 4,
pp. 704-714, July 1997.
S. Ounie, M.R. Zolghadri, “Space Vector Modulation for Four Switch
Rectifier with Compensating Capacitors Voltage Ripple Effect”, in
Proc. EPECS 2009, pp. 1-6, Sharjah, 2009.
Ouni, S.; Shahbazi, M.; Zolghadri, M., "Modeling, control and voltage
unbalance compensation in a four-switch rectifier with input power
factor correction," Power Electronics, Drive Systems and Technologies
Conference (PEDSTC), 2013 4th, pp.148,152, 13-14 Feb. 2013.
“Testing and measurement techniques - Unbalance, immunity test,”
IEC 61000-4-27 ed 1.02 2008-08.
J. Klima, J. Skramlik, and V. Valouch, “An Analytical Modeling of
Three-Phase Four-Switch PWM Rectifier Under Unbalanced Supply
Conditions,” IEEE Trans. Circuit and systems, vol. 54, no. 12,
December 2007.
Bo YIN, Ramesh ORUGANTI, Sanjib Kumar PANDA and Ashoh K. s.
BHAT “A Novel Instantaneous Power Control Strategy for a PWM
Rectifier under Unbalanced Input Voltage Conditions,” The 30th
Annual Conference of the IEEE Industrial Electronics Society,
November 2 - 6,2004, Busan, Kore.
S. Xiaofeng; W. Weiyang; W. Baocheng; M. Qiang; W. Kun, “Control
of a Three-Phase Converter Under Unbalanced Input Voltage
Conditions Using Invert Sequence d-q Representation,” IPEMC 2004.
vol. 3, pp. 1340 – 1345.
H. Song and K. Nam, “Dual Current Control Scheme for PWM
Converter Under Unbalanced Input Voltage Conditions,” IEEE Trans.
Ind. Electron., vol. 46, NO. 5, October 1999.
Y. Zhou, P. Bauer, J. A. Ferreira and J. Pierik , “Operation of GridConnected DFIG Under Unbalanced Grid Voltage Condition, ” IEEE
Trans. Energy Conversion, vol. 24, NO. 1, March 2009.
Giuseppe Saccomando, Jan Svensson, “Transient Operation of Gridconnected Voltage Source Converter under Unbalanced Voltage
Conditions,” Industry Applications Conference, Thirty-Sixth IAS
Annual Meeting, vol. 4, pp. 2419 - 2424 Chicago, IL, USA, 2001.
“Definitions for the measurement of electric power quantities under
sinusoidal, nonsinusoidal, balanced, or unbalanced conditions”, IEEE
Std 1459-2000, January 2000.
A. E. Emanuel, “Summary of IEEE Standard 1459: Definitions for the
measurement of electric power quantities under sinusoidal,
nonsinusoidal, balanced, or unbalanced conditions”, IEEE Trans.
Industry Applications, Vol. 40, No. 3, May/June 2004, pp. 869-876.