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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],

    [email protected],

    [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.

    REFERENCES

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    for asymmetrical cascade multilevel converters, InternationalConference on ElectricalMachines and Systems, Korea, 2007,

    pp. 74-79.

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    University of Stellenbosch, Stellenbosch, South-Africa, Dec.

    2005

    [3] E. Babaei, A caccade multilevel converter topology withreduced number of switches, IEEE Trans.Power Electron.,

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