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ADVANCED FIVE LEVEL - FIVE PHASE CASCADED MULTILEVEL INVERTER WITH SVPWM ALGORIT

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ADVANCED FIVE LEVEL - FIVE PHASE CASCADED MULTILEVEL INVERTER WITH SVPWM ALGORIT Powered By Docstoc
					INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING &
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –
6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 4, July-August (2013), © IAEME
                             TECHNOLOGY (IJEET)

ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
                                                                                   IJEET
Volume 4, Issue 4, July-August (2013), pp. 144-158
© IAEME: www.iaeme.com/ijeet.asp                                               ©IAEME
Journal Impact Factor (2013): 5.5028 (Calculated by GISI)
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     ADVANCED FIVE LEVEL - FIVE PHASE CASCADED MULTILEVEL
              INVERTER WITH SVPWM ALGORITHM

                    Rajasekharachari k 1, K.Shalini 2, Kumar .k 3, S.R.Divya 4
                         1
                           M.Tech (PEED) student, S.V.C.E.T, Chittoor, India
                         2
                           M.Tech (PEED) student, S.V.C.E.T, Chittoor, India
                         3
                           M.Tech (PEED) student, S.V.C.E.T, Chittoor, India
                           4
                             M.Tech (PEED) student, S.V.C.E.T, Chittoor, India


ABSTRACT

        An Advanced five level five phase multi level inverter with space vector pulse width
modulation control has been discussed here. The detailed working principles, operation, control
schemes, design and the performance were presented. The dc-link capacitor voltages of various types
of multi level inverter and design and the performance is presented. The performance of the diode
clamped multi level inverter and flying capacitor multi level inverter are presents and the five phase,
five level inverter with full bridge cascaded multi level inverter has been discussed. Multi-phase
machines and drives is a topic of growing relevance in recent years, and it presents many challenging
issues that still need further research. This is the case of multi-phase space vector pulse width
modulation (SVPWM), which shows not only more space vectors than the standard three-phase case,
but also new subspaces where the space vectors are mapped. A recent multilevel multiphase space
vector PWM with switching state redundancy is particularized for multilevel converters. Finally, the
new algorithm is implemented in a low-cost field-programmable gate array and it is tested with a
five-level cascaded full-bridge inverter. The proposed implemented circuit of five-level five phase
cascaded full bridge inverter simulation and its results of output voltages are discussed.

Keywords: cascaded full bridge inverter, dc-link capacitor, multi-phase, multi level voltages, and
SVPWM algorithm.

I.     INTRODUCTION

        Inverter is power electronic circuit that converts a direct current into an alternative frequency.
The inverters find their application in modern ac motor and uninterrupted power supplies and static,
inverters have no moving parts and are used in a wide range of applications, from small switching

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power supplies in computers, to large electric utility high-voltage direct current applications that
transport bulk power. Inverters are commonly used to supply AC power from DC sources such as
solar panels or batteries. The electrical inverter is a high-power electronic oscillator. It is so named
because early mechanical AC to DC converters was made to work in reverse, and thus was
"inverted", to convert DC to AC.

1.1     Conventional Two-Level and Three-Level Voltage Source Inverter
        Switch-mode dc-to-ac inverters used in ac power supplies and ac motor drives where the
objective is to produce a sinusoidal ac output whose magnitude and frequency can both be
controlled. Practically, we use an inverter in both single-phase and three phase ac systems. A half-
bridge is the simplest topology, which is used to produce a two level square-wave output waveform.
A center-tapped voltage source supply is needed in such a topology. It may be possible to use a
simple supply with two well-matched capacitors in series to provide the center tap. The full-bridge
topology is used to synthesize a three-level square-wave output waveform. The half-bridge and full-
bridge configurations of the single-phase voltage source inverter are shown in Fig. 1.1 and 1.2,
respectively.




       Fig: 1.1 Half Bridge Configuration                     Fig: 1.2 Full Bridge Inverter

        In a single-phase half-bridge inverter, only two switches are needed. To avoid shoot-through
fault, both switches are never turned on at the same time. S1 is turned on and S2 is turned off to give
a load voltage, AO V in Fig. 1.1, of 2 / s V+. To complete one cycle, S1 is turned off and S2 is
turned on to give a load voltage, AO V, of 2 / s V-. In full bridge configuration, turning on S1 and S4
and turning off S2 and S3 give a voltage of VS between point A and B ( AB V ) in Fig. 1.2, while
turning off S1 and S4 and turning on S2 and S3 give a voltage of Vs - . Figure 1.2.2 Full-bridge
configuration. To generate zero level in a full-bridge inverter, the combination can be S1 and S2 on
while S3 and S4 off or vice versa. The three possible levels referring to above discussion are shown
in Table 1.1

                     Conducting switches                        Load voltages
                            S1, S4                                   +Vs
                            S2, S4                                    -Vs
                      S1,S2 or S3&S4                          0
               Table 1.1 Load Voltages with Corresponding Conducting Switches

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        Conducting Switches Load Voltage AB V S1, S4 s V + S2, S3 s V - S1, S2 or S3, S4 0 Note
that S1 and S3 should not be closed at the same time, nor should S2 and S4. Otherwise, a short
circuit would exist across the dc source. The output waveform of half bridge and full-bridge of
single-phase voltage source inverter are shown in Fig. 1.3 and 1.4, respectively.




                      Fig: 1.3 Output waveform of half-bridge configuration




                      Fig: 1.4 Output waveform of full-bridge configuration

        Multilevel inverters are ideal for connecting renewable energy sources such as photovoltaic
to the grid. They have been developed in such to overcome shortcomings in solid-state switching
device ratings by using a series connected semiconductors devices to block the higher voltage levels
involved. The desired high ac voltage is synthesized from several of smaller dc voltages levels. For
this reason, additional applications of multilevel inverters include such uses as medium voltage
adjustable, speed motor drives, static VAR compensation.

The main advantages of this approach are summarized as follows
    • The semiconductors are wired in a series-type connection, which allows operation at higher
        voltage.
    • The voltage capacity of the existing devices can be increased many times without the
        complications of static and dynamic voltage sharing that occur in series connected devices.
    • The smaller voltage steps lead to the production of higher power quality waveforms with low
        distortion harmonics without the use of transformers
    • Spectral performance of multilevel waveforms is superior to that of their two level
        counterparts.
      The selection of the best multilevel topology and the best control strategy for each given
application is often not clear and is subject to various engineering tradeoffs. By narrowing this study

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to the DC/AC multilevel power conversion technologies that do not require power regeneration,
several attractive topological, modulation and power semiconductor device choices present
themselves. The most actively developed of these multilevel topologies are listed in figure 1.5.




                             Fig: 1.5 Multilevel Converter Topologies

II.   INTRODUCTION TO MULTI LEVEL INVERTERS

        Inverters are expected to play an essential role in the field of power production, especially in
the rural areas where over two billion people today have no access to electricity. As a result of the
variety of inverters applications, a number of inverter topologies have been developed ranging from
single-phase half-bridge to three-phase multilevel inverters.
        The concept of multilevel converters has been introduced since 1975. The term multilevel
began with the three-level converter. Subsequently, several multilevel converter topologies have
been developed. However, the elementary concept of a multilevel converter to achieve higher power
is to use a series of power semiconductor switches with several lower voltage dc sources to perform
the power conversion by synthesizing a staircase voltage waveform. Capacitors, batteries, and
renewable energy voltage sources can be used as the multiple dc voltage sources.
         The commutation of the power switches aggregate these multiple dc sources in order to
achieve high voltage at the output; however, the rated voltage of the power semiconductor switches
depends only upon the rating of the dc voltage sources to which they are connected. A multilevel
converter has several advantages over a conventional two-level converter that uses high switching
frequency pulse width modulation (PWM). The attractive features of a multilevel converter can be
briefly summarized as follows.
           Staircase waveform quality:
           Multilevel converters not only can generate the output voltages with very low distortion,
        but also can reduce the dv/dt stresses; therefore electromagnetic compatibility (EMC)
        problems can be reduced.
           Common-mode (CM) voltage:
           Multilevel converters produce smaller CM voltage; therefore, the stress in the bearings of a
        motor connected to a multilevel motor drive can be reduced. Furthermore, CM voltage can be
        eliminated by using advanced modulation strategies.
           Input current:
           Multilevel converters can draw input current with low distortion.
           Switching frequency:
           Multilevel converters can operate at both fundamental switching frequency and high
        switching frequency PWM. It should be noted that lower switching frequency usually means
        lower switching loss and higher efficiency.

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        One particular disadvantage is the greater number of power semiconductor switches needed.
Although lower voltage rated switches can be utilized in a multilevel converter, each switch requires
a related gate drive circuit. This may cause the overall system to be more expensive and complex.
        Plenty multilevel converter topologies have been proposed during the last two decades.
Contemporary research has engaged novel converter topologies and unique modulation schemes.
Moreover, three different major multilevel converter structures have been reported in the literature:
cascaded H-bridges converter with separate dc sources, diode clamped (neutral-clamped), and flying
capacitors (capacitor clamped). Moreover, abundant modulation techniques and control paradigms
have been developed for multilevel converters such as sinusoidal pulse width modulation (SPWM),
selective harmonic elimination (SHE-PWM), space vector modulation (SVM), and others. In
addition, many multilevel converter applications focus on industrial medium-voltage motor drives,
utility interface for renewable energy systems, flexible AC transmission system (FACTS), and
traction drive systems.
        Three different major multilevel converter structures have been applied in industrial
applications: cascaded H-bridges converter with separate dc sources, diode clamped, and flying
capacitors. Before continuing discussion in this topic, it should be noted that the term multilevel
converter is utilized to refer to a power electronic circuit that could operate in an inverter or rectifier
mode.

2.1     Diode Clamped Inverters
        The most commonly used multilevel topology is the diode clamped inverter, in which the
diode is used as the clamping device to clamp the dc bus voltage so as to achieve steps in the output
voltage. Figure shows the circuit for a diode clamped inverter for a three-level and a four-level
inverter. The key difference between the two-level inverter and the three-level inverter are the diodes
D1a and D2a.
        These two devices clamp the switch voltage to half the level of the dc-bus voltage. In general
the voltage across each capacitor for an N level diode clamped inverter at steady state is
vdc/(n-1) Although each active switching device is only required to block V, the clamping devices
have different ratings. The diode-clamped inverter provides multiple voltage levels through
connection of the phases to a series of capacitors. Due to capacitor voltage balancing issues, the
diode-clamped inverter implementation has been limited to the three levels. Because of industrial
developments over the past several years, the three level inverter is now used extensively in industry
applications. Although most applications are medium-voltage, a three-level inverter for 480V is on
the market.




 Fig:2.1 Topology of the diode-clamped inverter (I) two-level inverter, (II) three-level inverter,
                                   (III) four-level inverter

        In general for a N level diode clamped inverter, for each leg 2 (N-1) switching devices, (N-1)
* (N-2) clamping diodes and (N-1) dc link capacitors are required. When N is sufficiently high, the
number of diodes and the number of switching devices will increase and make the system

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impracticable to implement. If the inverter runs under pulse width modulation (PWM), the diode
reverse recovery of these clamping diodes becomes the major design challenge.

2.2     Flying Capacitor Multilevel Inverter
        Meynard and Foch introduced a flying-capacitor-based inverter in 1992. The structure of this
inverter is similar to that of the diode-clamped inverter except that instead of using clamping diodes,
the inverter uses capacitors in their place. The circuit topology of the flying capacitor multilevel
inverter is shown in Fig2.2. This topology has a ladder structure of dc side capacitors, where the
voltage on each capacitor differs from that of the next capacitor. The voltage increment between two
adjacent capacitor legs gives the size of the voltage steps in the output waveform.
       One advantage of the flying-capacitor-based inverter is that it has redundancies for inner
voltage levels; in other words, two or more valid switch combinations can synthesize an output
voltage.




            Figure: 2.2 Three-phase six-level structure of a flying capacitor inverter

        Moreover, the flying-capacitor inverter has phase redundancies, whereas the diode-clamped
inverter has only line-line redundancies. These redundancies allow a choice of charging/discharging
specific capacitors and can be incorporated in the control system for balancing the voltages across
the various levels.
        In addition to the (m-1) dc link capacitors, the m-level flying-capacitor multilevel inverter
will require (m-1) × (m-2)/2 auxiliary capacitors per phase if the voltage rating of the capacitors is
identical to that of the main switches. One application proposed in the literature for the multilevel
flying capacitor is static var generation.

2.3     Cascaded H-Bridges Inverter
        A single-phase structure of an m-level cascaded inverter is illustrated in Figure 2.3. Each
separate dc source (SDCS) is connected to a single-phase full-bridge, or H-bridge, inverter. Each
inverter level can generate three different voltage outputs, +Vdc, 0, and –Vdc by connecting the dc
source to the ac output by different combinations of the four switches, S1, S2, S3, and S4. To obtain

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+Vdc, switches S1 and S4 are turned on, whereas –Vdc can be obtained by turning on switches S2 and
S3.
        By turning on S1 and S2 or S3 and S4, the output voltage is 0. The ac outputs of each of the
different full-bridge inverter levels are connected in series such that the synthesized voltage
waveform is the sum of the inverter outputs.
        The number of output phase voltage levels m in a cascade inverter is defined by m = 2s+1,
where s is the number of separate dc sources. The phase voltage

                                van = va1 + va2 + va3 + va4 + va5    …… (1)

       For a stepped waveform such as the one depicted in Figure 2.4.1 with s steps, the Fourier
Transform for this waveform follows

                               )+            ) +…+              )]     , where n=1, 3, 5, 7,…….(2)




   Fig: 2.3 Single-phase structure of a             Fig: 2.3.1 Output phase voltage waveform
  Multilevel cascaded H-bridges inverter                  of an 11-level cascade inverter


III.   MULTI LEVEL MULTIPHASE SVPWM

        In order to solve the multilevel modulation problem various pulse-width modulation (PWM)
strategies have been developed and studied in detail such as multilevel sinusoidal PWM, multilevel
selective harmonic elimination and space vector modulation. Among these strategies, the space
vector PWM (SVPWM) stands out because it offers significant flexibility to optimize switching
waveforms and it is well suited for digital implementation. Complexity and computational cost of
traditional SVPWM techniques increase with the number of levels of the converter, and most of them
use trigonometric functions or precomputed tables. A two-dimensional (2D) SVPWM algorithm that
calculates the switching vectors and the switching times without using angles, trigonometric func-
tions or precomputed tables was proposed. A tree-dimensional (3D) SVPWM algorithm that
generalizes this 2D algorithm for systems with neutral wire was presented. Due to their low
computational cost both techniques are suitable for real time hardware implementation in low cost-
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devices. A generalized direct PWM method in which the switching states and the pulse-width of each
phase are directly determined in terms of the normalized reference voltage vector is proposed. It is
proved that the modulation outputs of the direct algorithm and the previous 3D SVPWM generalized
algorithm are equivalent.
        Recently, a new multiphase SVPWM technique with low computational complexity, that
makes it suitable for real-time implementation in low-cost devices, was presented. This new
technique can be used with the standard multilevel topologies such us diode-clamped, flying
capacitor, cascaded full-bridge or even hybrid converters. That new modulation algorithm is valid for
any number of phases and consequently it can be applied to three-phase converters

3.1     MULTILEVEL MULTIPHASE SVPWM ALGORITHM
        In multiphase converters the space vector PWM is a multidimensional problem where the
vector selection can be carried out directly in a multidimensional space. In the modulation problem
of a P-phase converter is formulated in a P-dimension space and it is solved for multilevel
topologies in which the output level of every phase is an integer multiple of a fixed voltage step Vdc
, such as flying capacitor, diode-clamped, cascaded full- bridge or hybrid converters. The solution is
an algorithm based on a displacement plus a two-level multiphase SVPWM modulator that is valid
for any number of levels and phases. This multiphase modulation technique is able to handle all
switching states of the inverter, without discard any one, and it provides a sorted switching vector
sequence that minimizes the number of switching. In addition, the algorithm proves suitable for real-
time implementation due to its low computational complexity.
        Since the switching states of any power converter topology stay at discrete states, the
multilevel multiphase SVPWM technique is used to synthesize a reference voltage vector Vr by
means of a sequence of space vectors during each modulation cycle. Each space vector vsj must be
applied during an interval tj in accordance with the following modulation law.

                       Vr =                                      --------> (3.1)
       Where

                                  = 1

In which

               Vr =Vr/Vdc = [      ,    ........         ]   -------- > (3.1.1)

Is the normalized reference vector, which belongs to the P-dimension real space ,
 vsj = [     ,     ........        ] are the switching vectors, which belongs to the integer space ,
and tj are the normalized switching times that correspond to each switching vector.
         If expressions in (3.1) are rewritten in matrix format the following system of linear equations.
Which must be solved by the multilevel multiphase SVPWM algorithm is obtained.



                                                                      ---------- > (3.1.2)




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        The modulation problem solving requires searching a set of integer numbers for the
coefficients matrix that permit to solve the linear system in order to calculate the switching times.
        As fig 3.1 shows, if the reference vector vr, is decomposed in the sum of an integer, vi, and a
fractional part , vf, as

               vi = integ(vr) ε               --------- > (3.1.3)

               vf = vr – vi ε                 ---------- > (3.1.4)

then the modulation law in (3.1.2) can be solved by means of a two – level multiphase modulator
where the reference vector is vf



                                                               --------- > (3.1.5)



        The solution of this new system of equations is the sequence of displaced switching vectors,
vdj = [    ,      ........         ] that approximate the reference vf. The elements of the multilevel
switching sequence, vsj, can be obtained from this two level switching sequence by adding the
integer part of the reference to the displaced vectors.

               vsj = vi + vdj         ---------------- > (3.1.6)

       The switching times tj of the multilevel algorithm are the same as the switching times of the
two –level algorithm.




    Fig: 3.1 Block diagram of the multi level                  Fig 3.1.2 Block diagram of the two
            Multi phase SVPWM                                      level multiphase SVPWM


Fig 3.1.2 shows the block diagram of the two level multiphase space vector PWM algorithm. This
algorithm searches a coefficient matrix


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                       D=                                              ------------ > (3.1.7)



       That permits to solve the linear system in (3.1.5) in order to calculate the switching time. This
matrix can be calculated by means of

                             D=        D                      --------------- > (3.1.8)

Where

                        D=                                           ------------- > (3.1.9)



And P is a permutation matrix that sorts the elements of the reference vector               in descending order.


                        P       =                                  ------------- > (3.1.10)

Where vf = [       ,        ........       ]   is the sorted vector in which

          1>           ≥...........≥              ≥     ≥........         ≥0      ----------> (3.1.11)

Finally, the switching times can be calculated from vf as


            tj =                                                                  -------     (3.1.12)




               Fig 3.1.3 Multi level multiphase SVPWM ALGORITHM flow chart


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Steps Involved In the Algorithm
   Which are summarized in the flow chart fig 3.1.3 are
   1) Calculate normalized reference vr. from the reference voltage vector using the expression in
       (3.1.1)
   2) Decompose the normalized reference into the sum of its integer part vi and its fractional part
       vf by means of(3.1.3) and (3.1.4) respectively
   3) Calculate the permutation matrix P that sorts the vector vf in descending order in accordance
       with (3.1.10) and (3.1.11)
   4) Rearrange the row of the triangular matrix D in order to obtain the matrix D by means of
       (3.1.8)
   5) Extract the displaced switching vector. vdj from the matrix D by taking into account the
       expression in (3.1.7)
   6) Obtain the final switching vector, vsi by adding the integer part of the reference, vi to the
       displaced switching vector vdj according to (3.1.6)
   7) Calculate the time corresponding to each switching vector from components of the vector vf
       by means of expression in (3.1.12).
       Finally, trigger signals have to be generated from the switching vectors and the switching
times. The relationship between switching states and the particular trigger signals of transistors
depends on the multilevel topology.

3.2      FIVE PHASE FIVE LEVEL CASCADED MULTI LEVEL INVERTER
        Multiphase multilevel inverters are controlled by this hybrid modulation (SVPWM) to
provide multiphase variable voltage and variable frequency supply. The proposed modulation
inherits the features of fundamental frequency modulation and carrier based space vector modulation
strategies. The main characteristics of this hybrid modulation are the reduction in power losses, and
effectively improve harmonic performance. This algorithm can be applied to cascaded multilevel
inverter topologies. It has low computational complexity and it is suitable for hardware
implementations. Theoretical considerations are detailed using a five phase multilevel inverter. The
performance of this hybrid modulation (SVPWM) is analyzed based on power loss, weighted total
harmonic distortion, the linearity and it is compared with standard modulation strategies.




       Fig: 3.2 Schematic diagram of the                Fig: 3.2.1 Power circuit configuration
      Five phase multilevel inverter topology                     For One phase leg


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       The power circuit for a five-phase five-level cascaded inverter topology is shown in Fig 3.2.1.
Modulation control of multiphase multilevel inverter is quite challenging, and much of the reported
research is based on somewhat heuristic investigations. Most of the available work on PWM
schemes for a multiphase voltage source inverter either covers carrier-based PWM or space vector
PWM schemes. By and large, the emphasis has been placed on space vector PWM (SVPWM)
methods. SVPWM offers great flexibility to optimize switching waveforms and is suited for digital
implementation. However, due to constant sampling rate used in SVPWM, the equivalent carrier-
based techniques have been developed. Carrier-based space vector modulation (CBSVM) is
appropriate for inverters with more than five levels, where the computational overhead for
conventional SVPWM is exceeding due to many output states a new hybrid modulation technique is
presented to address the reduction of power losses in multiphase multilevel inverter, with improved
harmonic performance.

IV.    SIMULATION OF FIVE LEVEL FIVE PHASE INVERTER




  Fig: 4.1 simulation diagram for five level five phase cascaded full bridge inverter by using
                                           SVPWM


       The above simulation represents the simulation diagram of five phase five level cascaded full
bridge inverter. The operation of the blocks Multilevel multiphase SVPWM and Two-level
multiphase SVPWM. It includes a five-level five-phase inverter feeding a passive load.


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                         Fig: 4.2 simulation circuit for sequence block

        The above simulation represents the subsystem of the sequence block. The Sequence block
provides the time sequence of switching vectors. The output of the sequence block is connected to
the triggering signal. The Trigger signals generates the proper trigger signals from output levels
specified in each switching vector.




                         Fig: 4.3 simulation circuit for triggering signal


        The above diagram represents the subsystem of the triggering signal. The input of the
triggering signal taken from the sequence block.



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           Fig: 4.4 simulation circuit for 5 level 5 phase cascaded full bridge inverter

        The above diagram represents the subsystem of the five phase five level cascaded full bridge
inverter. The 5-level 5-phase cascaded full-bridge inverter block is the ideal model of the multilevel
voltage-source converter. The loads are resistances with a series connected inductances. Load neutral
is connected to the inverter neutral.




         Fig: 4.5 output waveform of five level five phase cascaded full bridge inverter

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       The above simulation output represents the output waveform of five level five phase
cascaded full bridge inverter. The scope 1 represents the reference voltages Vref of five phases. The
phase shift between each phase is 72˚. The scope 2 represents the filtered output voltage which is
taken from the low pass filter. The filter is used for eliminating the harmonics. The scope 3
represents the inverter output.

V. CONCLUSION

         In this five phase five level we are using the cascaded multilevel inverter topology.
Multilevel technology permits the achievement of high power ratings with voltage limited devices.
With the cascaded multi level inverter reaches the higher output voltage and power levels and higher
reliability due to its modular topology.
         Here a new space vector pulse-width modulation algorithm for multilevel multiphase voltage
source converters with low computational cost has been presented. This algorithm can be used with
any number of phases; therefore it can be also used with classical three-phase topologies. The
SVPWM algorithm provides a sorted switching vector sequence that minimizes the number of
switching’s. The SVPWM algorithm proves suitable for real-time implementation due to its low
computational complexity.

VI.     REFERENCES
  [1]   Oscar Jacobo Alvarez, Jesus Doval-Gandoy and Franciso D.Freijedo “Multilevel Multiphase
        Space Vector PWM algorithm”,IEEE® Transactions on Industrial Electronics, vol. 55, no. 5, pp.
        1933-1942, May 2008, doi:10.1109/TIE.2008.918466
  [2]   L. G. Franquelo, J. Rodriguez, J. I. Leon, S. Kouro, R.Portillo, and M. A. M. Prats, "The age of
        multilevel converters arrives," IEEE Ind.
  [3]   G. S. Perantzakis, F. H. Xepapas, and S. N. Manias, “A new four-level PWMinverter topology
        for high power applications-effect of switching strategies on losses distribution,” in Proc.
        PESC’04, Aachen, Germany, 2004, pp. 4398–4404.
  [4]   G. Carrara, S. Gardella, M. Marchesoni, R. Salutari, and G. Sciutto, “A new multilevel PWM
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