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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 23, NO. 1, JANUARY 2008 19

A Five-Level Symmetrically Defined SelectiveHarmonic Elimination PWM Strategy:Analysis and Experimental Validation

Vassilios G. Agelidis, Senior Member, IEEE, Anastasios I. Balouktsis, Member, IEEE, andMohamed S. A. Dahidah, Member, IEEE

Abstract—A five-level symmetrically defined multilevel selectiveharmonic elimination pulsewidth modulation (MSHE–PWM)strategy is reported in this paper. It is mathematically expressedusing Fourier-based equations on a line-to-neutral basis. Anequal number of switching transitions when compared againstthe well-known multicarrier phase-shifted sinusoidal PWM(MPS–SPWM) technique is investigated. For this paper, it isassumed that the four triangular carriers of the MPS–SPWMmethod have nine per unit frequency resulting in seventeenswitching transitions for every quarter period. For the proposedMSHE–PWM method, this allows control of sixteen harmonics andthe fundamental. It is confirmed that the proposed MSHE–PWMoffers significantly higher converter bandwidth in the standardrange of the modulation indices. Moreover, when the bandwidth isreduced to be equal with the one offered with the MPS–PWM, themodulation index can be increased resulting in a higher gain andat a reduced switching frequency overall. Selected solutions for theswitching transitions are presented and verified experimentally inorder to confirm the effectiveness of the proposed technique.

Index Terms—Multilevel Converter, optimization, phase-shiftedsinusoidal pulsewidth modulation (PS–PWM), pulsewidth modu-lation (PWM), selective harmonic elimination (SHE).

I. INTRODUCTION

SELECTIVE harmonic elimination pulse-width modulation(SHE–PWM) techniques have been mainly developed for

two or three-level schemes [1]–[12]. The main challenge asso-ciated with such techniques is to obtain the analytical solutionsof the non-linear transcendental equations that contain trigono-metric terms which naturally exhibit multiple sets of solutions[5]. There have been many approaches to this problem reportedin the technical literature including: sequential homotopy-basedcomputation [6], resultants theory [7], optimization search [8],

Manuscript received April 20, 2006; revised April 25, 2007. This paper waspresented in part at the IEEE PESC’05, Recife, Brazil, June, 2005. Recom-mended for publication by Associate Editor A. Trzynadlowski.

V. G. Agelidis is with the School of Electrical and Information Engineering,The University of Sydney, Sydney NSW 2006, Australia (e-mail: [email protected]).

A. I. Balouktsis is with the Department of Informatics and Communications,Technological Institution of Serres, Terma Magnesias, Serres 62124, Greece(e-mail: [email protected]).

M. S. A. Dahidah was with the Faculty of Engineering, Multimedia Univer-sity, Selangor, Malaysia. He is now with the School of Electrical and ElectronicEngineering, The University of Nottingham (Malaysia Campus), Selangor,Malaysia (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2007.911770

Fig. 1. Generalized staircase waveform suitable for multilevel systems and re-lated angles of transition between the various voltage levels.

Walsh functions [9], [10] and other optimal methods [11] in-cluding genetic algorithms (GAs) [12], [13]. The bipolar wave-form when symmetry is requested through the definition of theproblem has been treated in detail in [14] where a minimizationtechnique is employed along with a biased optimization searchmethod [8] to get the multiple sets as predicted in [6]. Inter-estingly, symmetry, which was widely assumed in the past inall reported methods and solutions, can be relaxed and this re-sults in different solutions and a more generic way to define theproblem as reported in [11], [15]. Recently, solutions trajecto-ries of the harmonic elimination problem were mathematicallyaddressed in [16].

On the other hand, multilevel converters based on solid-statetechnologies have been investigated for more than threedecades. Initially, when the switching frequency was restrictedto line frequency, the generic question associated with theSHE–PWM approach has mainly been the way the staircasemultilevel waveform is generated in order to control the ampli-tude of the fundamental frequency and eliminate the maximumnumber of harmonics from the waveform [17]. A generalizedstaircase waveform suitable for a multilevel converter is shownin Fig. 1, where the transition angles are linked with the levelchange. In a generic definition this does include equal andnon-equal dc levels [13], [18].

Recently, a number of technical papers have appeared ad-dressing the multilevel waveform using similar theories usedpreviously for the bipolar (two-level) and unipolar (three-level)waveforms. Specifically, the theory of resultants and its perfor-mance for a multilevel staircase waveform was reported in [18].A unified approach was presented in [19]. More recently, theuse of symmetric polynomials is combined with the resultanttheory for a multilevel converter [20]. Previous work [18] has

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20 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 23, NO. 1, JANUARY 2008

shown that the transcendental equations characterizing the har-monic content can be converted to polynomial equations whichare then solved using the method of resultants from elimina-tion theory. A difficulty with this approach [18], as suggestedin [20], is that when there are several dc sources, the degrees ofthe polynomials are quite large, thus making the computationalburden of their resultant polynomials (as required by elimina-tion theory) quite high. An interesting method to overcome thepreviously mentioned drawbacks was reported in [20], wherethe theory of symmetric polynomials is exploited to reduce thedegree of the polynomial equations that must be solved whichin turn greatly reduces the computational burden. The use ofoptimization techniques [8] including GAs [12], [13] has beenshown to overcome all known obstacles of previous approaches.On the topic of optimization techniques, interesting theoreticalideas were reported in [31]–[34]. Specifically, reference [31]deals with the single-phase inverter optimal PWM where thestandard mathematical formulation of the problem can be refor-mulated and that the sought solution can be found by computingthe roots of a single invariable polynomial for which algorithmsare readily available. The approach is similar to the one usingpolynomial approximation reported in [7]. In reference [32] asimplex homotopic fixed-point algorithm for the computation ofoptimal PWM pattern was reported. Regarding computationalalgorithms, in [33], an algorithm was proposed that searchessolutions so that two consecutive angles are placed way apartto allow easy implementation. The approach used in [33] is asfollows; the problem is first transformed inot a constraint opti-mization problem and then used differential evolution algorithmto find the roots with the necessary distance separation. A newalgorithm was presented in [34] for pushing the first crest of thesurplus harmonics backwards, ameliorating the amplitude fre-quency spectrum distribution of the output waveform and there-fore reducing the impact of surplus harmonics in programmedPWM techniques. Looking at the SHE–PWM problem as an op-timization problem rather than an elimination one naturally cre-ates new opportunities to extend SHE–PWM methods to a newterritories and the method reported here is one example. Finally,an interesting hybrid method between a carrier based modula-tion and SHE is proposed where the harmonic content and theswitching angles are both controlled through the control of thefrequency of the carrier waveform avoiding the need for solvingthe transcendental equations all together and obtaining at thesame time the required switching angles [35].

On the other hand, multilevel SHE–PWM systems have beencontrolled using the unipolar approach, where the waveformtakes a positive, a negative and a zero value, and phase-shiftedtechniques are used to build multilevel systems [21]. Otherapproaches have also been reported including one where theharmonic elimination is combined with a programmed method[22] and another where a criterion based on power equalizationbetween various cascaded connected H-bridge multilevel con-verters is used to obtain the angles of the harmonic eliminationmethod [23].

The multicarrier phase-shifted sinusoidal PWM(MPS–SPWM) has been used to increase the bandwidth ofmultiple connected converters. This can be traced back inthe 1980s in a conference paper [24] and then in a journalpublication which appeared in [25]. It was then used in manyother works reported in the technical literature as it provided an

Fig. 2. Five-level symmetrically defined (line-to-neutral) MSHE–PWM wave-form shown for a distribution ratio of 5/12 (k = 5,m = 12, andN = k+m =

17).

opportunity to cancel a number of harmonics if the phase-shiftbetween the numerous carriers within the same converter andamong the carriers controlling the other converters is chosencarefully [28].

However, although the MPS–SPWM technique has been ex-tensively used for multilevel systems, no comparison with aMSHE–PWM technique has been reported to clarify the perfor-mance of each method against each other. For instance, highergain and improved bandwidth for the programmed SHE–PWMtechniques have been reported but these gains were analyzedonly for the two-level systems [4]. So far, there exists limited in-formation reported if such superior performance can also be at-tributed to the MSHE–PWM methods. Moreover, thus far therehas been limited documentation regarding a complete set of an-gles for relatively high frequency multilevel waveform for allmodulation indices, except references [22], [26], [27].

The objective of this paper is to propose a symmetrically de-fined MSHE–PWM strategy for a five-level waveform as shownin Fig. 2. The various switching transitions as a function of themodulation index are also presented for the standard modula-tion range, and in the overmodulation region where the band-width of the strategy is reduced to be able to obtain higher ampli-tude for the fundamental component. The proposed technique isthen compared against the well-known MPS–SPWM techniqueusing four carriers in order to create a five-level line-to-neutralswitching pattern [26]. Selected experimental results are alsopresented to confirm the validity of the proposed method.

The paper is organized as follows. Section II presents in detailthe proposed symmetrically defined five-level MSHE–PWM inboth the standard modulation index region and in the overmod-ulation one as well. In Section III the MPS–SPWM techniquesuitable for the five-level system is also briefly presented. Thecomparison between the two techniques along with selected ex-perimental results taken from a low power laboratory prototypeare presented and discussed in Section IV. Finally, conclusionsare summarized in Section V.

II. PROPOSED FIVE-LEVEL MSHE–PWM STRATEGY

The proposed symmetrical five-level MSHE–PWM strategyis defined according to the waveform shown in Fig. 2 and repre-sents the line-to-neutral waveform of the three-phase multilevelconverter. The number of levels of the waveform is assumed tobe five, i.e., 1 p.u., 2 p.u., 0 p.u., 1 p.u. and 2 p.u. Let be

AGELIDIS et al.: FIVE-LEVEL SYMMETRICALLY DEFINED SELECTIVE HARMONIC ELIMINATION PWM STRATEGY 21

the number of total switching transitions (angles) of the wave-form sought within the quarter of the period of the waveform.This number can be either odd or even. However, there are re-strictions once it is chosen. For this paper, is chosen to bean odd number. Let be the number of the switching transi-tions placed between the 0 p.u. level and the 1 p.u. This numbercan only be an odd number since the first switching transition ischosen to be from 0 p.u. to 1 p.u. level. Let be the number ofthe remaining switching transitions placed between 1 p.u. and2 p.u. levels. This number can be either even or odd dependingupon . In this case, since has chosen to be odd and is onlyodd, can only be even.

Then, for the proposed MSHE–PWM strategy, can only bean odd number

1,3 (1)

can only be an even number since has been chosen to bean odd number, hence

(2)

and the total sum of both and must always be equal to themaximum number of switching transitions, hence

(3)

For any ratio of then a different set of transcendentalequations describing the Fourier equations linked to the am-plitude of the harmonics that can be eliminated needs to bewritten down. The idea here is the classic SHE–PWM methodthat tries to find switching angles in order to eliminate a numberof harmonics and control simultaneously the fundamental com-ponent. The challenge of the proposed method is that it is ap-plied to a “true” multilevel waveform, i.e., five-level waveform(Fig. 2). The typical half-wave and quarter-wave symmetriesare respected for the waveform, i.e., simply when the switchingangles for all modulation indices are obtained for the anglesbetween zero and 2, the usual reflection occurs to find therest of the angles. Since there are switching angles (i.e.,

, where ), 1 harmonics can be elim-inated if solutions can be found. For a three-phase inverter, thenon-triplen odd harmonics can be eliminated from the wave-form (i.e., fifth, seventh, 11th, 13th, -th where 3 2)and then the strategy relies on the structure of the power circuitin order to remove the triplen ones from the line-to-line voltagewaveforms.

In a generalized form, the set of equations that need to besolved is as follows:

(4)

TABLE ISUMMARY OF STANDARD MODULATION RANGE REGION WHERE SOLUTIONS

FOR ALL SWITCHING ANGLES EXIST AS A RELATIONSHIP TO THE VARIABLE

RATIO OF DISTRIBUTION OF THE SWITCHING ANGLES

BETWEEN THE MULTIPLE LEVELS (k=m) N = 17

(5)

(6)

where

(7)

(8)

If is the amplitude of the fundamental component to begenerated, then

(9)

when 2 the square-waveform of 2 p.u. amplitude can gen-erate 8 per unit maximum value at fundamental frequency.

The minimization technique proposed in [8] has been ap-plied and software is used to investigate the proposed method[29]. The distribution ratio varies for each case where anew set of equations describing the new waveform are written.The equations relating to the minimization of the transcendentalequations describing the Fourier coefficients are then solved.The standard modulation regions where solutions exist for agiven distribution ratio are summarized in Table I. For thispaper, 17. However, this number and the various ratios canbe changed as desired and the minimization method [8] wouldprovide the respective solutions provided they exist. The over-modulation range is also discussed later.

The constraint for the solutions sought is as follows:

(10)

A. Standard Modulation Range 17

In this paper, a selected set of solutions for every region arereported although many more might exist. Therefore, it is be-yond the scope of this paper to treat the cases where multiple


TABLE IISUMMARY OF THE OVERMODULATION REGIONS WHERE SOLUTIONS FOR ALL

SWITCHING ANGLES EXIST AS A RELATIONSHIP TO THE VARIABLE RATIO

OF DISTRIBUTION OF THE SWITCHING ANGLES BETWEEN

THE MULTIPLE LEVELS (k=m) N = varies

Fig. 3. Standard modulation region: Switching angles in degrees versus mod-ulation index M for the various ratios of k=m and cases which are also sum-marized in Table I for N = 17. (a) Case I: 17/0 (0 � M � 0.46, Set 1). (b)Case I: 17/0 (0 � M � 0.9, Set 2). (c) Case II: 15/2 (0.63 � M � 0.9). (d)Case III: 13/4 (0.7 � M � 0.91). (e) Case IV: 11/6 (0.92 � M � 0.98). (f)Case V: 9/8 (0.96 � M � 1.04). (g) Case VI: 7/10 (1.04 � M � 1.36). (h)Case VII: 5/12 (1.39 � M � 1.46, Set 1.

sets of solutions can be found, although some overlap and mul-tiple solutions are also reported. The aim here is to find solutionsthat provide PWM waveform realization for the entire region ofmodulation indices.

It should be noted that the result obtained from the proposedmethod when the ratio is chosen to be 17/0 provides solutionsfor all modulation indices up to 0.9, which has been reportedin other cases to be the maximum attainable value for similarapproaches (i.e., the three-level or unipolar waveform) [7]. This

Fig. 3. (Continued) Standard modulation region: Switching angles in degreesversus modulation index M for the various ratios of k=m and cases which arealso summarized in Table I forN = 17. (i) Case VII: 5/12 (1.43 �M � 1.56,Set 2). (j) Case VII: 5/12 (1.29 �M � 1.42, Set 3) (k) Case VII: 3/14 (1.1 �M � 1.31, Set 4). (l) Case VIII: 3/14 (1.38 � M � 1.51, Set 1). (m) CaseVIII: 3/14 (1.46 �M � 1.59, Set 2). (n) Case IX: 1/16 (1.37 �M � 1.6).

implies that a three-level technique covering this region can beimplemented and the result confirms that there are more thanone set of solutions. The first is a discontinuous set and thesecond covers the entire range. Further results for all combina-tions of ratios are plotted in Fig. 3 and summarized in Table I.

The last non-triplen harmonic that can be eliminated ac-cording to (4)–(6) is the 49 p.u. and this is confirmed in Fig. 4where the first non-triplen significant harmonic present is the53 p.u. since the 51 p.u. is a triplen one. Specifically, Fig. 4(b)shows that the spectrum of the line-to-neutral voltage waveformhas only multiple of triplen harmonics which are cancelled outin a three-phase system for the line-to-line waveforms. This isconfirmed and the line-to-line voltage waveform is shown inFig. 4(c). The bandwidth of the normalized line-to-line voltagewaveform is proved to be according to the theory, which isthat the harmonics up to the 49 p.u. are all zero. Since the 51p.u. harmonic is a triplen one, the first significant non-triplenharmonic present turns out to be the 53 p.u. [Fig. 4(d)].

B. Overmodulation

In order to increase the modulation index for the proposedtechnique and since the available bandwidth is higher than theone when compared with the MPS–PWM technique, the over-modulation region is also investigated and solutions are reportedin this paper. It is shown that controlling up to nine non-triplenharmonics results in the first significant non-triplen harmonic tobe the 31 p.u. The ratio of is changed and the same op-timization algorithm is used to seek the switching transitions.Fig. 5 presents the switching transitions in degrees as a functionof the modulation index for various combinations. It should


Fig. 4. Selected waveforms implemented with the switching angle solutionsgiven by the proposed method, N = 17, non-triplen harmonics to be elimi-nated up to 49 p.u. (n = 3N�2), and taken from the case where k=m = 5/12,Set 3). (a) Line-to-neutral voltage waveform (M = 1.5)). (b) Spectrum of theline-to-neutral voltage waveform (M = 1.5). (c) Line-to-line voltage wave-forms (M = 1.5). (d) Spectrum of the line-to-line voltage waveform (M =1.5).

be noted that the number of the overall transitions varies. Thisinvestigation is similar to the pulse-dropping methods reportedin the past as the lower the number of the angles sought thehigher the effective value of the resulting waveform (see Fig. 6).

III. MPS–SPWM TECHNIQUE

The MPS–SPWM technique has been used in many appli-cations in order to increase the bandwidth of the system [24],[25]. The harmonics are controlled through the separate SPWMcontrolled systems but due to the phase-shift effect between thevarious modulators the overall harmonic spectrum is further im-proved as the number of carrier waveforms is increased [28].

In this paper, the MPS–SPWM technique with four carrierwaveforms is considered. This way a five-level (line-to-neutral)PWM voltage waveform is generated so that to accommodateits comparison with the MSHE–PWM technique, presented inSection II. The carrier frequency is chosen to be 9 p.u. Fig. 7presents this technique. Specifically, Fig. 7(a) shows the ref-erence signal (sinusoidal) with the four triangular signals witheach having the same frequency (9 p.u.). Each carrier is phase-shifted by 1/4 of its period. This ensures that the line-to-neutralvoltage waveform generated and shown in Fig. 7(b) has an in-creased bandwidth which is equal to four times the per unit fre-quency. This is the result of the phase-shift introduced which al-lows the cancellation of the switching frequency harmonics andthe associated sidebands. Closer observation of the line-to-neu-tral waveform reveals that the switching transitions of the wave-form for the modulation index shown 1.5 5 (from 0 p.u.level to 1 p.u.) and 12 (from 1 p.u. level to 2 p.u.), respectively.

When looking at the spectrum, as the theory of PWM sug-gests, the first significant harmonics will be centered around the4 9 36 p.u. frequency. For the 50-Hz system shown in Fig. 7,the first point of interest in the spectrum becomes the 36 p.u. fre-quency which is 1800-Hz frequency although this frequency isnot present in the spectrum. The sidebands are present and theseinclude harmonics of 35 p.u., 33 p.u., 31 p.u., and 29 p.u. This

Fig. 5. Overmodulation region: Switching angles in degrees versus modulationindex M for various ratios of k=m and cases which are also summarized inTable II. N also varies, and the method results in reduced switching frequencyand reduced bandwidth and higher modulation index value when compared withthe standard modulation range. (a) Case I: 1/9N = 10, 1.42 �M � 1.56 (Set1). (b) Case I: 1/9N = 10, 1.6 �M � 1.7 (Set 2). (c) Case II: 1/10,N = 11,1.54 � M � 1.63 (Set 1). (d) Case II: 1/10, N = 11, 1.54 � M � 1.68 (Set2). (e) Case III: 1/11, N = 12, 1.56 �M � 1.68. (f) Case IV: 1/12, N = 13,1.18 � M � 1.47 (Set 1). (g) Case IV: 1/12, N = 13, 1.4 � M � 1.55 (Set2). (h) Case IV: 1/12, N = 13, 1.57 � M � 1.67 (Set 3). (i) Case V: 1.13,N = 14, 1.58 � M � 1.64. (j) Case VI: 1/14, N = 15, 1.42 � M � 1.6.(k) Case VII: 1/15, N = 16, 1.52 � M � 1.62 (Set 1). (l) Case VII: 1/15,N = 16, 1.21 � M � 1.62 (Set 2).

implies that the most significant sideband harmonic which is noteliminated due to the PWM switching is the 29 p.u. or 1450 Hz.


Fig. 6. Implementation of the proposed MSHE–PWM strategy in the over-modulation region where M = 1.7 (Set 2) and k=m = 1/9, N = 10. (a)Line-to-neutral voltage waveform. (b) Spectrum of the line-to-neutral voltagewaveform (9 non-triplen harmonics eliminated with the first non-triplen har-monic present being the 31 p.u.). (c) Line-to-line voltage waveform. (d) Spec-trum of the line-to-line voltage waveform (the first non-triplen harmonic presentbeing the 31 p.u.).

Fig. 7. Multicarrier phase-shifted sinusoidal PWM technique for five-levelline-to-neutral switching pattern using four carriers (M = 1.5). (a) Referenceand four carrier triangular signals with 9 p.u. frequency. (b) Line-to-neutralswitching pattern directly controlled by the comparison of the signals. (c) Spec-trum of the line-to-neutral waveform showing the bandwidth being almost fourtimes the 9 p.u. as the theory suggests (around 36 p.u. minus the sidebands).

This is shown in Fig. 7(c). Finally, the line-to-line voltage wave-form for a three-phase system is shown in Fig. 7(d) and its spec-trum in Fig. 7(e).

TABLE IIICOMPARISON BETWEEN THE TWO TECHNIQUES:

MPS–SPWM AND MSHE–PWM

IV. DISCUSSION OF RESULTS—EXPERIMENTAL VALIDATION

A. MSHE–PWM and MPS–SPWM Techniques: A Comparison

In this paper, the two techniques have been compared inorder to identify any potential benefits from using the proposedMSHE–PWM. The MPS–SPWM technique is obviously easierto implement as the switching transitions are directly controlledby the comparison of signals which can be easily varied tocontrol the modulation index.

The MSHE–PWM offers a challenge from the calculationpoint of view since the system of equations that needs tobe solved is not an easy one. However, in this paper, it isshown that when the two techniques are studied, the proposedMSHE–PWM technique offers significant benefits which canjustify the extra effort involved in solving the equations. TheSPWM provides switching angles that are not optimum andmathematically are not calculated in order to eliminate themaximum number of possible harmonics from the spectrum.When the mathematical approach is followed, the maximum at-tainable modulation index increases to 1.7 p.u. when comparedwith the 1.57 p.u. possible with the MPS–SPWM technique. Ifovermodulation is desired for the SPWM, low-order harmonicsare introduced. This was resolved in two-level PWM systemswith the introduction of third harmonic into the referencesignal to increase the gain before bandwidth deteriorates [30].In the multilevel case however, the most significant harmonicin the case of the MPS–SPWM is the 29 p.u. frequency. Thisgain can be increased if a third harmonic is also introducedin the reference waveform. With the proposed approach, theharmonic is tightly controlled for all modulation indices andthe switching angles available can eliminate up to 49 p.u. The51 p.u. happens to be a triplen harmonic therefore the firstsignificant non-triplen harmonic becomes the 53 p.u. Thisresults in an increased bandwidth without any further need toincrease the switching transitions.

These benefits are summarized in Table III confirming thatthe mathematical approach to harmonic control in a multilevelsystem is a beneficial approach although the way the angles arecalculated requires effort and computing time.

B. Experimental Results

A low-power laboratory five-level inverter prototype based onthe two IGBT (IRG4BC20FD) H-bridges configuration shownin Fig. 8 was developed and tested to verify the feasibilityand the validity of the theoretical and the simulation findings.Each dc bus voltage is approximately 50 V. High-voltagehigh-speed drivers (IR2112) were used along with opticallycoupled isolators (SFH610). The pre-calculated PWM signals


Fig. 8. Schematic diagram of the converter topology used to verify the pro-posed five-level (line-to-neutral) MSHE–PWM method.

Fig. 9. Experimental results for an operating point within the standardmodulation index range (a) Proposed five-level MSHE–PWM line-to-neu-tral (M = 1.5) (b) Spectrum of the proposed five-level MSHE–PWMline-to-neutral voltage waveform. (c) Line-to-neutral voltage waveform ofthe MPS–SPWM technique (M = 1.5, four carriers, 9 p.u. frequency each)(d) Spectrum of the line-to-neutral voltage waveform of the MPS–SPWMtechnique.

are implemented using low-cost high-speed Texas InstrumentsTMS320F2812 digital signal processor (DSP) board with anaccuracy of 20 s. A digital real-time oscilloscope (TektronixTDS210) was used to display and capture the output waveformsand using the feature of the fast Fourier transformer (FFT), thespectrum of each of the output voltage was obtained.

Specifically, Fig. 9(a) shows the line-to-neutral voltage wave-form of the proposed five-level MSHE–PWM method for1.5 and the associated spectrum is presented in Fig. 9(b). It isconfirmed that only triplen harmonics are present in the wave-form and the first significant non-triplen harmonic is the 53 p.u.as predicted. For completeness, the same five-level waveformis presented when the MPS–SPWM technique is used also for

1.5. Clearly, the method controls the bandwidth at the

Fig. 10. Experimental results for an operating point within the overmodula-tion index range (a) proposed five-level MSHE–PWM line-to-neutral (M = 1.7(Set 2) and k=m = 1/9, N = 10) and (b) spectrum of the proposed five-levelMSHE–PWM line-to-neutral voltage waveform.

output placing the most significant harmonics at 29 p.u. as thetheory predicts.

The overmodulation region for the proposed method is alsoexperimentally verified and results presented in Fig. 10. Specif-ically, Fig. 10(a) shows the five-level SHE–PWM waveform for

1.7 (Set 2) and 1/9, 10. The spectrum of thewaveform shown in Fig. 10(b) confirms that only triplen har-monics exist and the first non-triplen one is the 31 p.u. as thetheory suggests.

V. CONCLUSION

A symmetrically defined five-level multilevel SHE–PWMtechnique has been proposed in this paper. The variousswitching transitions are calculated using a minimizationtechnique with a biased search optimization approach. Thisapproach results in an efficient method to obtain the switchingtransitions. It is shown that these angles can be computedfor all modulation indices by using a distribution ratio andsearch for solutions. When compared with the conventionalMPS–SPWM technique and keeping the number of transitionsthe same, the proposed method offers significant benefits forincreased modulation index and higher bandwidth tightlycontrolled throughout the entire range. Extending its operatingrange to the overmodulation region where a higher gain can beobtained while compromising some of the bandwidth is alsopossible. Selected simulation and experimental results havebeen presented to confirm the theoretical findings.

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Vassilios G. Agelidis (SM’00) was born in Serres,Greece. He received the B.S. degree in electricalengineering from Democritus University of Thrace,Thrace, Greece, in 1988, the M.S. degree in appliedscience from Concordia University, Montreal, QC,Canada, in 1992, and the Ph.D. degree in electricalengineering from the Curtin University of Tech-nology, Perth, Australia, in 1997.

From 1993 to 1999, was with the School of Elec-trical and Computer Engineering, Curtin Universityof Technology. In 2000, he joined the University of

Glasgow, Glasgow, U.K., as a Research Manager for the Centre for EconomicRenewable Power Delivery. In addition, he has authored/coauthored severaljournal and conference papers as well as Power Electronic Control in Elec-trical Systems (2002). From January 2005 to December 2007, he was the in-augural Chair in Power Engineering in the School of Electrical, Energy andProcess Engineering, Murdoch University, Perth, Australia. Since January 2007,he has held the EnergyAustralia Chair of Power Engineering at the Universityof Sydney, Australia.

Dr. Agelidis received the Advanced Research Fellowship from the UnitedKingdom’s Engineering and Physical Sciences Research Council (EPSRC-UK)in 2004. He was the Vice President Operations within the IEEE Power Elec-tronics Society for 2006–2007. He was an Associate Editor of the IEEE POWER

ELECTRONICS LETTERS from 2003 to 2005, and served as the PELS ChapterDevelopment Committee Chair from 2003 to 2005. He is currently an AdCommember of IEEE PELS for 2007–2009. He will be the Technical Chair of the39th IEEE PESC’08, Rhodes, Greece.

Anastasios I. Balouktsis (M’99) was born in Serres,Greece, in 1955. He received the Dipl.-Eng. degreein electrical and mechanical engineering and the B.S.degree in mathematics from Aristotle Universityof Thessaloniki, Thessaloniki, Greece, in 1978 and1982, respectively, and the Ph.D. degree in electricalengineering from Democritus University of Thrace,Xanthi, Greece, in 1986.

From 1981 to 1986, he was a scientific collaboratorand from 1987 to 1990 a Lecturer with the Depart-ment of Electrical Engineering, Democritus Univer-

sity of Thrace. Since 1990, he has been a Professor with the Technological Edu-cational Institution (T.E.I.), Serres, Greece. He has been elected as the Head ofSchool of Applied Technology and has been Vice President and President of theInstitution (TEI). He is the author/coauthor of many scientific papers in variousdisciplines and his technical interests include renewable energy sources, powersystems, power electronics, digital electronics, and mathematics.

Mohamed S. A. Dahidah (M’03) was born inTripoli, Libya. He received the B.S. degree in elec-trical and electronic engineering from the Bright StarUniversity of Technology, Briga, Libya, in 1998, theM.S. degree in applied science from Universiti PutraMalaysia, Malaysia, in 2002, and is currently pur-suing the Ph.D. degree in the Faculty of Engineeringand Technology, Multimedia University, Selangor,Malaysia.

In November 2007, he was appointed Lecturer inthe School of Electrical and Electronic Engineering,

The University of Nottingham (Malaysia Campus), Selangor. He has authoredor co-authored a number of refereed journal and conference papers. His researchinterests include power electronics, selective harmonic elimination techniques,and PWM converter control.