PEDS 2007
Compensation of DC-Link Oscillations of
Cascaded H-Bridge Converters
*
M. Tavakoli Bina* and B. Eskandari*
Faculty of Electrical Engineering, K. N. Toosi University of Technology, P. 0. Box 16315-1355, Tehran 16314, Iran,
E-mail: tavakoli@,ieee.org
Abstract-Single-phase AC applied voltage of an Hbridge converter produces second harmonic on top of the
DC-link voltage. Three-phase unbalanced voltages make
similar effects on the DC-link voltages, as well.
Nevertheless, for applications that need higher voltages,
series connection of H-bridges could lower the amplitude of
the oscillations. Low-frequency oscillations are considerable
when the number of cascaded H-bridges is less than four,
introducing the worst case oscillations for a single H-bridge
converter. This paper proposes various external DC active
filter circuits, aiming at cancelling these oscillations of
cascaded H-bridges up to three. Proposed circuits are
simulated, and their performances on compensation of
oscillations are compared to select the best choice.
Simulation results confirm that the proposed methods limit
the DC-link oscillations on DC-link of H-bridges. Also, the
presented methods are compared in terms of both their
advantages and disadvantages.
magnitudes of the two H-bridge converters can affect the
balancing of the two capacitor voltages.
Index Terms-Active-filtering, auxiliary compensation,
DC-link Oscillations, H-bridge, S-bridge.
I. INTRODUCTION
CASCADED H-bridge multilevel converters can
potentially be used as an alternative to the series
connection of semiconductor switches to increase the
system voltage [1]-[4]. Figure 1 shows a typical cascade
H-bridge converter in which the harmonic performance is
expected to be improved compared to the converters with
series connected switches. This topology has found highvoltage high-power applications such as modular
multilevel AC-AC converters (M2LC) [5]-[6]. The
M2LC includes four modules of cascaded H-bridge
converters of type shown by Fig. 1. However, each Hbridge sub-module of Fig. 1 exchanges active power
between the electrical network and the load through the
other H-bridge converters. This power exchange depends
on the magnitude of the fundamental voltage of each Hbridge converter as well as the magnitudes of low order
harmonics. The exchanged power would influence
considerably on the DC-link voltage of the H-bridge
converter, causing low frequency oscillations. Further,
when H-bridge converters introduce different power
exchanges from each other, then balance of capacitor
voltages is a major concern that could possibly lead to
instability. Figure l(b) depicts the SPWM technique that
is used to modulate two cascaded H-bridge converters
[7]. It can be seen that the difference in the output voltage
This work was performed in the Research Laboratory of K. N. Toosi
University of Technology.
1-4244-0645-5/07/$20.00©2007 IEEE
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(b)
Figure 1 (a) General topology of Cascade H-bridge converters, and (b)
the effect of difference in fundamental voltage magnitudes of two Hbridge converters on the DC-link voltage balancing.
This paper examines various methods to compensate
the low-frequency oscillations that appear on top of the
DC-link voltages of H-bridge multilevel converters.
Different passive/active filtering circuits are proposed
that is connected to the DC-link capacitor, resulting in
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1&2
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(a)
1
1.5
(b)
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te
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1451441431422.6
2.7
(c)
2.8
2.9
oscillati.ons
3
3.1
3.2
x
(d)
10
Figure 2: (a) Cascaded two H-brige converter without any compensators, (b) DC-link
excluding any DC-link filters, (c) a
tuned passive LC filter compensates the DC-link oscillations, and (d) simulation results when DC capacitor oscillations are absorbed by the passive
filter.
compensation
are
oscillations. All DC-filters
similarly.
Figure
variations
when
of the
performances along
their
H-bridge
DC
voltage
examined and simulated with MATLAB to compare
converters.
with
suitability
for the cascade
Simulation results confirm that the
active-filtering proposals compensate
oscillations
much
effective
than
the DC-link
other
introduced
oscillations.
various
A.
11.
Here
DC ACTIVE -FILTERING OF OSCILLATIONS
we
passive/active
examine
filtering
connection
circuits
across
of
the DC
DC
capacitor
to
compensate the low-frequency oscillations imposed by
the
exchange
these
is
100/120
Hz
operates at 50/60 Hz. Figure 2(a)
H-bridge converter, excluding any
when
shows
phase
power
a
of
system
cascaded two
DC-link compensator,
which is simulated with SIMULINK. A
employed
frequency
of active power. Predominant
oscillations
PI
controller is
H-bridges output
voltages such that the average DC-voltage remains fixed
at 150 V [8]-[9]. Switching pulses are swapped between
the two
to
control the
H-bridges
to force both
topologies
efficiently
Passive
of the
capacitor voltages
the
designed
is
clear that the
DC
to
oscillations
capacitor
absorb
the
cannot
be
that
use
passive/active
filters to
damp
the oscillations.
LC-filtier compensation
(PLC): proposition
can be
low-frequency
using a tuned LC passive filter that its natural
frequency is 100 Hz. Figure 2(c) shows a cascade
converter consisting of two H-bridges as well as two LC
passive filters, which is simulated by SIMULINK. This
would effectively reduce the oscillations, needs no extra
The
various
is
illustrates
filter
damped (peak-to-peak variation is about 8V or 5.330o).
Hence, the following sub-sections suggest and examine
more
methods.
It
2(b)
no
oscillations of the DC-link
filtered
semiconductor
switches
and
Nevertheless, the disadvantage of the
vary
856
circuits.
passive LC filter needs big parameters
occupying huge space [10].
the 100 Hz
as
control
PLC method is that
as
well
(a)
1 54
-
50
--
148
146 _
+
A-
-
+
A-
-
2.8
2.9
144 _
142 _
140 _
(b)
3
3.2
3.1
3.3
3.4
3.5
x
lo'
Figure 3: (a) The DC-links of two cascaded H-bridge converters are compensated using two auxiliary H-bridge
converters, and (b) the compensated oscillations of the two DC-link capacitor voltages.
B. Auxiliary H-brige compensation (AHC): proposition 2
Here an H-bridge converter (with DC capacitor Cf ) is
connected across the DC-link capacitor C of each main
H-bridge converter through the inductance L like it is
shown by Fig. 3(a) [11]. Capacitance Cf is much bigger
than that of C while the average voltage of both
capacitors is considered identical. The two H-bridges
operate in a way that when the voltage of capacitorC
starts rising, the capacitor Cf is charged by its H-bridge
converter. When voltage of capacitor C starts getting
lower, then the capacitor Cf is discharged to prevent the
decrease in voltage of capacitorC It is noticeable that
the voltage variations in capacitor Cf is lower than
,
.
capacitor C because Cf is bigger than C
Any oscillations on the capacitor C is transferred to
the capacitor Thus, the low-frequency oscillations on the
capacitor voltage Vc are sampled from the capacitor
A PI controller is used to regulate the
voltage VC
.
.
average voltage of the capacitor Cf. Also, the capacitor
voltage is considered to be slightly bigger than Vc. This
would prevent the flow of current from Cf through the
parallel diodes to the capacitor C.
It should also be mentioned that the switching signals
are swapped between the two H-bridge converters of Fig.
3(a) symmetrically. This implies that the two capacitors
(Cf) have similar variations. Hence, taking sample from
one of the capacitors is compared to a reference voltage,
and the resultant error is sent to a PI controller.
One disadvantage over the AHC is the big
capacitance Cf, which causes dynamically slow tracking
of the DC-link voltage. Also, since the average DC
voltages of both C and Cf are identical, a voltage
difference between these two capacitors is needed to
control the current exchange through the inductance L
Therefore, the AHC is unable to damp completely the
oscillations of the DC-links. Figure 3(b) provides
simulated oscillations of the two DC-links using the
AHC, which is much lower than those of the
uncompensated case.
.
C. Auxiliary S-bridge compensation (ASC): proposition
3
This proposal uses two identical capacitors
(Cfl and Cf 2)
along with three switches for each DClink like it is illustrated by Fig. 4(a). Capacitances
Cf1 and Cf 2 do not have to be big, while their average
DC voltages are equal to three quarters of the DC-link
voltage of capacitor C. Three switches are operated in a
way that when the DC-link voltage is increased beyond
than a positive band (AV ), the two vertical switches are
turned on and the horizontal switch is turned off. This
makes both capacitances Cfl and Cf2 to operate in
857
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(a)
1 51 5
151 _
111te
1505
150 _
149-5
149
148-5-=
3-2
(b)
3-3
3-4
3-5
3-6
x 10
Figure 4: (a) The DC-links of two cascaded H-bridge converters are regulated using the second suggested topology, (b) simulation results concerned
with voltages of the two DC-link capacitors.
parallel, asorbing chaging curre ts Ihog
parallel, absorbing charging currents through the
inductance L from the DC-link C by the following slope:
diL
VL
Idt
L
VDC
4 VDC
L
VDC
4L
Where the voltage VL is the drop on inductance L and
iL is the absorbed current. This relatively big slope
forces the main DC-link voltage to come down more
rapidly. Accordingly, when the DC-link voltage is
dropped below a negative band (-AV), the two vertical
switches are turned off and the horizontal switch is turned
on. The two capacitors Cfl and Cf 2 operate in series,
injecting current to the DC-link C through the inductance
L as follows:
diL
Idt
VL
L
VDC
4
L
VDC
2L
Here the negative slope reverses the current from
ithes
and Cf 2 to charge the DC-link capacitor C. Note
that here the positive slope is different from the negative
one as it is illustrated by Fig. 4(b). Simulation results
show that peak-to-peak of the oscillations is smaller than
IV (or 0.6%). In practice, the hysteresis band could limit
the performance of the proposal because the switching
frequency could be very high when the chosen AV is
small.
Like the PI controller of the AHC, the controller of the
ASC takes DC-voltage sample from either Cfi or Cf2;
because voltage variations of the two capacitors are
identical. Table I summarizes the simulation results
obtained by all suggested methods, including the AHC,
the ASC, the PLC, and the uncompensated case.
It can be seen from the results gathered in Table I that
while the uncompensated case contains considerable loworder oscillations, other suggested methods lower the
oscillations from 11.1I% well below 3.5%. Amongst the
analyzed methods, the ASC introduces the lowest level of
oscillations (smaller than 0.6%). Then, the AHC achieves
2.6% maximum oscillations, and the PLC up to 3.3%.
Since the proposed circuits use low-power elements, total
cost of the added device could be reasonable enough to
apply the suggested methods to the H-bridge converters.
Cf
858
TABLE I: SIMULATION RESULTS CONCERNED WITH THE PEAK-TO-PEAK OSCILLATIONS OF THE DC-LINK OF H-BRIDGE CONVERTERS ALONG WITH THE
ADVANTAGES AND DISADVANTAGES OF ALL SUGGESTED METHODS
Compensation Method
AHC
ASC
PLC
Uncompensated
Oscillations (maximum Peak-to-Peak)
2.6%
0.6%
3.13%
11.1%0
Oscillations (average Peak-to-Peak)
2.6%
0.6%
1.82%
8.9%0
III. CONCLUSIONS
The DC-link oscillations related to the H-bridge
cascade converters is significant when the number of Hbridges is smaller than four. This situation is worse when
the three-phase applied voltages are unbalanced. The
oscillations on the DC-link are modulated through the Hbridge converter, and enter the AC system. This has
considerable impacts on harmonic performance as wellas
the efficiency of the converter. While an uncompensated
simulation with two H-bridges show considerable
oscillations on the DC-links, three methods are proposed
and examined to lower the peak-to peak oscillations.
These methods are the passive LC-filter compensation
(PLC), the auxiliary H-bridge compensation (AHC) and
the auxiliary S-bridge compensation (ASC). These
methods are also simulated with SIMULINK to compare
their effectiveness on lowering the DC-link oscillations.
Simulation results show that these three methods
successfully control the oscillations, amongst them the
ASC performs as the best solution. Nevertheless, there
are both advantages and disadvantages for each method
that are needed to be taken into account in practical
implementations.
ACKNOWLEDGEMENT
The authors would like to thank the support of the
research Laboratory of power quality and reactive power
control in K. N. Toosi University of Technology.
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