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A New Algorithm to Determine the Magnitudes of dc
Voltage Sources in Asymmetric Cascaded Multilevel
Converters Capable of Using Charge Balance Control
MethodsSara Laali
1, Karim Abbaszadeh
2, Hamid Lesani
3
1Member of Young Researchers Club, Islamic Azad University, Tabriz Branch, Tabriz, Iran
2Islamic Azad University, South Tehran Branch, Tehran, Iran
2Department of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran
3School of Electrical & Computer Engineering, University of Tehran, Tehran, Iran
E-mails:[email protected],
Abstract In this paper, a new algorithm is proposed to
determine the magnitudes of dc voltage sources used inasymmetric cascaded multilevel converters. Using this
algorithm, it is possible to generate the maximum number of
output voltage levels and maximum output voltage amplitude
using the minimum number of dc voltage sources. The
magnitudes of dc voltage sources are determined in a way
considering which it is possible to use charge balance control
methods to all dc sources except the minimum amplitude dc
voltage source (first bridge). Therefore, the lifetime of dc voltage
sources used in different bridges of cascaded asymmetric
multilevel converter except the first bridge are the same,
considering which the systems low maintenance cost can be
noted as a result. The simulation results in PSCAD/EMTDC
confirm the abilities of the proposed method.
Keywords Multilevel converter, Symmetric cascaded
multilevel converter, Asymmetric cascaded multilevel converter,
Charge balance control methods
I. INTRODUCTION
The multilevel converters were first introduced in 1975.The interest of using multilevel converters is increased due to
the growing demand for high power, high voltage converters
and considering the limitations; exist in the voltage and
current ranges of semiconductor-based switches. High
efficiency, low electromagnetic interference, providingdesirable output waveform, possessing lower harmonic
components and ability of using low speed semiconductorswitches are some of other advantages of this kind of
converters, which results in paying more attentions to these
converters in recent years. In these converters, some small-
scale dc voltage sources considered as the input sourcesgenerate the desired voltage. As the number of dc voltage
sources increases in input side, the sinusoidal like waveform
can be generated at the output of converter. The power
switches suffer lower dtdv / stress due to low dc voltage
source amplitude [1]-[4].
Several topologies have been presented for multilevel
converters. Fig. 1 shows the basic topologies of multilevelconverters. Among these several topologies, the cascaded
multilevel converter is under more attention due to its
structure simplicity. There are several methods for controllingmultilevel converters that are summarized in Fig. 2 [5]. One
of the most practical control methods of the multilevel
converters is fundamental frequency control method. This is
due to considerably low switching losses in this control
method in compare with the other control methods. In
fundamental frequency control method, the power extractedfrom dc voltage sources in each bridge, differs from other
bridges during a single cycle. In other words, the power
extracted from the dc voltage sources in bridges becomes
time variable and therefore dc voltage sources would possessdifferent charges [1]. In result, the lifetime of used dc voltage
sources will differ and the maintenance cost of system will
increase.
In this paper, the cascaded multilevel converters are
briefly reviewed initially and a new algorithm is proposed in
continuous to determine the value of dc voltage sources used
in cascaded multilevel converters in a way that the charge
balance control methods [6] can be applied to control the
converter. Finally, the capability of the proposed method
would be confirmed by presenting the simulation results in
PSCAD/EMTDC and comparing them to the results of
method presented in [1], which is almost one of the last
activities accomplished in this field.
Fig. 1. The basic topologies of multilevel converters
Converters
ClampedDiode
SourcesDC
Common
Converters
Multilevel
SourcesDC
Isolated
Converters
Cascaded
Converters
CapacitorFlying
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Fig. 2. Different control methods of multilevel converters
II. A REVIEW ON CASCADED MULTILEVEL
CONVERTERS
As shown in Fig. 3 the single-phase cascaded multilevelconverter consists of a few numbers of series connected full
bridge levels. The output voltage of converter equals to sum
of the output voltages of all bridges and is mentioned asfollows:
)()()()( ,2,1, tvtvtvtv Noooo +++= (1)
where N is the number of bridges used in cascaded
converter.
In cascaded multilevel converters, each bridge requires an
independent dc source which can be batteries, super
capacitors and renewable energy sources such as fuel cells,
solar cells and etc [3], [8]. The similarity of required control
method and protection devices, which enables packing eachbridge in a single package, is the advantageous of such
topology [1].
Fig. 3. Cascaded Multilevel Converter
Cascaded multilevel converters are classified in two
Symmetric and Asymmetric groups. The converter is called
symmetric if the magnitudes of dc sources in all bridges are
similar. The converter is called asymmetric if at least the
magnitude of one of the dc sources differs from others [7].
Each bridge used in a cascaded multilevel converter is
comprised of 4 power switches and a dc voltage source in a
way that provides a squared shaped waveform with different
duty cycles. In this converter, each switch is comprised of an
IGBT and an anti-parallel connected diode. There is no need
for diode application if the load of converter is pureresistance. Each used bridge in this converter is able to
generate three voltage levels ( dcV , 0 and dcV+ ) at its output
terminals. Fig. 4 shows an example of output voltage of a
symmetric 7-level cascaded converter. As illustrated in Fig.4,
switching frequency of each switch exists in each level of
converter equals to the frequency of related output voltageand in result the switching losses considerably decreases. This
switching method is known as fundamental frequency
method. As shown in Fig. 4, the operation interval of each
voltage source differs from others and consequently, the dc
voltage sources charge will not be similar. Since the energy
values provided for load by different sources is not the same,the lifetime of sources would not be similar which leads to an
increase in maintenance costs.
Fig. 4. The output waveform of different levels for a 7-level cascadedconverter
High number of switches utilized in cascaded multilevelconverter is one of the disadvantageous of this converter, inwhich the losses, required space for installation, cost and
converter control complexity, increase as the number of
switches and dc voltage sources increase.
According to the fact that the industrial loads are generally
resistance-inductance loads and they show low pass filter
behavior, the output current can be considered as follows:
)sin(max += tIio (2)
where maxI is the output current peak value and is theangle between output voltage and output current of cascadedconverter.
If the value of all dc voltage sources of Fig. 3 equals to
dcV , the number of output voltage levels )( setpn can be
expressed as follows in terms of the number of used bridges
)(N :
12 += Nnstep (3)
1,dcV 2,dcV NdcV ,1,1S
1,3S
1,2S1,4S
2,1S
2,2S
2,3S
2,4S
NS,1
NS ,2
NS ,3
NS ,4
ov
1,ov 2,ov Nov ,
+
1,dci 2,dci Ndci ,
oi
TechniquesModulationMultilevel
PWMFrequencylFundamenta
PWMSinusoidal
PWMVectorSpace
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The maximum amplitude of generated output voltage
)( max,oV for this kind of converters is as follows:
dco VNV =max, (4)
The asymmetric cascaded multilevel converter is proposed
to create more levels at output without any increase in thenumber of bridges. In [10, 11], the dc voltages sources areproposed to be chosen according to a geometric progressionwith a factor of 2 or 3 In this case, the number of output
voltage levels for Nseries connected bridge is as follows:
NjVVifn dcj
jdc
N
step ,,2,12121
,1
=== + (5)
NjVVifn dcj
jdc
N
step ,,2,1331
, === (6)
For these cases, the maximum generated output voltageequals with follows:
NjVVifVV dcj
jdcdcN
o ,,2,12)12(1
,max, === (7)
NjVVifVV dcj
jdcdc
N
o ,,2,132
13 1,max, ==
=
(8)
Comparing (3), (4), (7) and (8), it can be seen that theasymmetrical multilevel converters can generate more voltagelevels and higher maximum output voltage with the same
number of bridges.
III. PROPOSED ALGORITHM
In [1], a new algorithm has been presented to determinethe amplitude of dc voltage sources of asymmetric cascaded
multilevel converters. In this given algorithm, the amplitudesof dc sources are determined as follows:
dcdc VV =1, (9)
NjVV dcjdc ,,3,22, == (10)
Here, the maximum generated level at output voltage)( stepn is as follows:
14 = Nnstep (11)
The maximum amplitude of generated output voltage
)( ,MaxoV is as follows:
dcMaxo VNV )12(, = (12)
If the number of levels and the maximum amplitude of
generated voltage in this given algorithm are compared to thesimilar parameters of symmetric cascaded converters, it isobvious that, for the similar number of bridges, in compare to
the symmetric cascaded multilevel converter, the number oflevels and the maximum amplitude of generated voltage at theoutput of converter are considerably increased in algorithmpresented in [1]. It is important to note that the reason for
which the algorithm presented in [1] is compared to thesymmetric cascaded multilevel converter is the fact that it ispossible to apply charge balance control methods in both of
them.In this paper, a new algorithm is proposed to determine
the magnitudes of dc voltage sources in order to develop the
number of generated levels at the output of converter andincrease the maximum amplitude of generated voltage. Itshould be noted that it is possible to use charge balancecontrol methods in proposed algorithm. It is recommended to
choose the magnitudes of dc voltage sources as follows:
dcdc
VV =1,
(13)
NjVV dcjdc ,,3,23, == (14)
Here, the maximum number of generated levels at outputvoltage is calculated as follows:
36 = Nnstep (15)
In the proposed algorithm, the maximum amplitude of
generated output voltage )( ,MaxoV is given by:
dco VNV )23(max, = (16)
Comparing (11), (12), (15) and (16), it is obvious that, forthe similar number of bridges, the proposed algorithm is able
to provide more number of levels and higher maximumvoltage amplitude in comparison the algorithm presented in[1]. Figs. 5 and 6 show the variation of the maximum numberof levels and maximum amplitude of generated voltage (inper unit) in terms of similar used number of bridges forproposed algorithm and the one presented in [1], respectively.
Fig. 5. Variation of maximum number of levels versus number of bridges
0 2 4 6 8 100
20
40
60
stepn
N
proposed
]1[
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Fig. 5. Variation of maximum amplitude of generated voltage versus number
of bridges
IV. SIMULATION RESULTS
The simulation results in PSCAD/EMTDC are used toprove the correct operation of proposed algorithm in desirableoutput voltage waveform generation and implementation ofcharge balance control methods. The control method used inthis paper is fundamental frequency method. The reason is the
fact that the switching frequency of this switching method isless than the other methods and as a result, the switching
losses are considerably low. The simulation results arepresented for classic control method and full wave and halfwave charge balance control methods.
Fig.7 shows the simulated asymmetric cascaded 15-levelconverter which consists of three H-Bridge stages. The value
of used dc voltage sources are VVdc 1001, = and
VVV dcdc 3003,2, == .
Fig. 7. 15-level asymmetric cascaded converter
This converter is able to generate 15 levels at its output
with maximum voltage of V700 and it is designed based on
the proposed algorithm. It is necessary to mention that theconverter could just provide 10 levels at its output with
maximum voltage of V500 if it was designed on the method
presented in [1]. Compared to the method presented in [1], theproposed method shows great advantageous due to more
number of levels and maximum amplitude of generatedoutput voltage. It is important to mention that the othercapabilities of both methods are the same. The load connected
to the converter is a LR load with =100R and
mHL 55= .
Figs. 8 and 9 show the voltage and current waveforms,
respectively. As shown in Fig. 8, this converter is able togenerate step waveform at its output with 15 levels and
V700 maximum voltage. Comparing current waveform with
the voltage waveform shows that the current waveform is
closer to ideal sinusoidal waveform. This is due to applicationof resistive-inductive load, which behaves as a low-pass filter.
Considering the above comparison, it is obvious that there is aphase difference between voltage and current waveform,which is due to inductive characteristics of the load.
0.000 0.020 0.040 0.060 0.080
-800
800Vo
Fig. 8. The output voltage waveform of a 15-level asymmetric cascaded
converter in classic control method
0.000 0.020 0.040 0.060 0.080
-8.0
8.0Io
Fig. 9. The output current waveform of a 15-level asymmetric cascaded
converter in classic control method
The output voltages of different levels of converter usingclassic control method are illustrated in Fig. 10. The outputwaveform of each level is in pulse waveform in a way that thesums of output waveforms of different levels regenerate thesemi-sinusoidal waveform at load side. As shown in Fig. 10,
the width of generated pulses differs in different levels. Inresult, the operation time of different dc voltage sourcesdiffers from each other. The currents passing throughdifferent bridges are similar due to series connection ofbridges outputs. Therefore, the energy extracted from dcvoltage sources of different bridges would differ.Consequently, the dc voltage sources of different bridges
would possess different charges and their lifetime would notbe the same.
In full-wave and half-wave charge balance control
methods, the load voltage and current waveforms are the
1,ov
+
V100
1,1S 1,3S
1,4S 1,2S
2,1S 2,3S
2,4S 2,2S
3,1S 3,3S
3,4S 3,2S
2,ov+
3,ov+
ov
V300
V300
dc
o
V
V max,
N
0 2 4 6 8 100
10
20
30
]1[
proposed
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same as the waveforms of classic method (Figs. 8 and 9).
However, the output waveforms of different bridges differfrom each other. For full-wave charge balance controlmethod, the output voltage waveforms of different bridges are
illustrated in Fig. 11. In this converter, the full-wave chargebalance control method is not used for the first bridge while itis used to control the second and third bridges. As shown inFig. 11, the output voltages of second and third bridges are
substituted between these bridges in a way that the operationperiod of them are equalized after two periods and in result,the sources used in these two bridges are charged or
discharged equally and their lifetime would be similar if theirinitial charges are equal.
For full-wave charge balance control method, the output
voltage waveforms of different bridges are illustrated in Fig.12. In this converter, the full-wave charge balance controlmethod is not used for the first bridge while it is used tocontrol the second and third bridges. As this figure shows, the
output voltages of second and third bridges are substitutedbetween these bridges in a way that the operation period ofthem are equalized after two periods and in result, the sources
used in these two bridges are charged or discharged equallyand their lifetime would be similar if their initial charges areequal. It is necessary to mention that the operation period ofthe dc voltage source used in the first bridge differs fromothers in both full-wave and half-wave charge balance controlmethods. In result, the charge balance control methods are notapplicable for the first bridge.
Charge Balance (15-Level)
0.000 0.020 0.040 0.060 0.080
-400
-200
0
200
400Vo2
Charge Balance (15-Level)
0.000 0.020 0.040 0.060 0.080
-400
-200
0
200
400Vo3
0.000 0.020 0.040 0.060 0.080
-150
-100
-50
0
50
100
150Vo1
Fig. 10. The output voltage waveforms of different bridges of a 15-level
asymmetric cascaded converter in classic method
0.000 0.020 0.040 0.060 0.080
-150
-100
-50
0
50
100
150Vo1
Charge Balance (15-Level)
0.000 0.020 0.040 0.060 0.080
-400
-300
-200
-100
0
100
200
300
400Vo2
Charge Balance (15-Level)
0.000 0.020 0.040 0.060 0.080
-400
-300
-200
-100
0
100200
300
400Vo3
Fig. 11. The output voltage waveforms of different bridges of a 15-level
asymmetric cascaded converter in full-wave charge balance control method
0.000 0.020 0.040 0.060 0.080
-150
-100
-50
0
50
100
150Vo1
Charge Balance (15-Level)
0.000 0.020 0.040 0.060 0.080
-400
-300
-200
-100
0
100
200
300
400Vo2
Charge Balance (15-Level)
0.000 0.020 0.040 0.060 0.080
-400
-200
0
200
400Vo3
Fig. 12. The output voltage waveforms of different bridges of a 15-level
asymmetric cascaded converter in half-wave charge balance control method
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V. CONCLUSION
In this paper, the advantageous of asymmetric cascadedmultilevel inverters were clarified by a brief review on
cascaded multilevel converters. However, in spite of theiradvantageous, it is not possible to use charge balance controlmethods to control them properly. Therefore, a newmathematical algorithm is proposed initially to determine the
magnitudes of dc voltage sources used in asymmetricmultilevel converters in a way that the maximum number oflevels and the maximum amplitude can be provided for the
output voltage using the minimum number of dc voltagesources and there would be the possibility of using chargebalance control methods. The results of the proposed method
are compared to the results of [1], which is the one of the lastactivities accomplished in this field, doing which the bettercapabilities of proposed method are proved in compare to theconventional methods. The simulation results in
PSCAD/EMTDC reconfirm the abilities of proposed method.
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