A Review of Multilevel Selective Harmonic Elimination PWM: Formulations, Solving Algorithms, Implementation and Applications

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2 A Revew of Multlevel Selectve Harmonc Elmnaton PWM: Formulatons, Solvng Algorthms, Implementaton and Applcatons Mohamed S. A. Dahdah, Senor Member IEEE, Georgos Konstantnou, Member IEEE, and Vasslos G. Agelds, Senor Member IEEE Abstract : Selectve harmonc elmnaton pulse-wdth modulaton (SHE-PWM) offers tght control of the harmonc spectrum of a gven voltage and/or current waveform generated by a power electroncs converter. Owng to ts formulaton and focus on elmnaton of low-order harmoncs, t s hghly benefcal for hgh-power converters operatng wth low swtchng frequences. Over the last decade, the applcaton of SHE-PWM has been extended to nclude multlevel converters. Ths paper provdes a comprehensve revew of the SHE-PWM modulaton technque, amed at ts applcaton to multlevel converters. Ths revew focuses on varous aspects of multlevel SHE-PWM, ncludng dfferent problem formulatons, solvng algorthms, and mplementaton n varous multlevel converter topologes. An overvew of current and future applcatons of multlevel SHE-PWM s also provded. Keywords: Selectve harmonc elmnaton, pulse-wdth modulaton, dc-ac converson, modulaton technques, multlevel converters; LIST OF ABBREVIATIOS A CHB CSC DE DSP FACTS FC GA HVDC HW MMC MPC PC PWM PSO PMSM QW SHE STATCOM THD : artfcal neural networ : cascaded H-brdge : current source converter : dfferental evoluton : dgtal sgnal processng : flexble ac transmsson system : flyng capactor : genetc algorthm : hgh voltage drect current : half wave : modular multlevel converter : model predctve control : neutral pont clamped : pulse wdth modulaton : partcle swarm optmzaton : permanent magnet synchronous motor : quarter wave : selectve harmonc elmnaton : statc synchronous compensator : total harmonc dstorton Mohamed S. A. Dahdah s wth the School of Electrcal and Electronc Engneerng, ewcastle Unversty,ewcastle Upon Tyne, E 7RU, UK. (Emal: mohamed.dahdah@ncl.ac.u) Georgos Konstantnou and Vasslos G. Agelds are wth the Australan Energy Research Insttute and School of Electrcal Engneerng and Telecommuncatons, USW Australa, Sydney, SW, 5, Australa. (Emal: g.onstantnou@unsw.edu.au, vasslos.agelds@unsw.edu.au). VSC ZSCC OMECLATURE: a a n b n f Vdcm L l(ωt) M m a m T V V n V dcm α ε θ φ ω : voltage source converter : zero sequence crculatng current : dc component of the output waveform : sne Fourer coeffcent : cosne Fourer coeffcent : fundamental frequency : order of swtchng angle n the multlevel waveform : level transton parameter : normalzed dc voltage of the m-th brdge : number of levels n the waveform : lower level envelope : number of CHBs per converter : modulaton ndex : number of swtchng angles (per quarter-wave) : number of swtchng angles n the m-th level of the waveform : perod of fundamental frequency : ampltude of fundamental frequency component : ampltude of the n-th harmonc component : dc voltage of the m-th level brdge : -th swtchng angle : swtchng angle devaton : load phase angle : harmonc phase angle : angular frequency I. ITRODUCTIO The performance characterstcs of nverter/rectfer converson systems largely depend on the choce of the partcular pulse wdth modulaton (PWM) technque [], []. PWM technques can be broadly classfed as carrer-based snusodal PWM (SPWM), space vector modulaton (SVM) or selectve harmonc elmnaton (SHE-PWM). Hstorcally, SHE was proposed n the early 96s, when t was found that low order harmoncs could be suppressed by addng several swtchng angles n a square wave voltage [3]. Years later [],[5] the dea was extended usng Fourer seres to mathematcally express the harmonc contents of a PWM waveform by a group of non-lnear and transcendental equatons. Transtons were then calculated n such a way that the low-order harmoncs are set to zero whle eepng the fundamental at a predefned value. SHE-PWM demonstrates several characterstcs ncludng []:. hgh performance wth low rato of swtchng frequency to fundamental frequency.

3 . hgh voltage gan and wde converter bandwdth. smaller flterng requrements. v. elmnaton of low-order harmoncs, resultng n no harmonc nterference such as resonance wth external lne flterng networs, typcally employed n nverter power supples. v. low swtchng losses wth tght control of harmoncs and ablty to leave trplen harmoncs uncontrolled to tae advantage of crcut topology n three-phase system. v. performance ndces that can also be optmzed for dfferent qualty aspects, such as voltage/current total harmonc dstorton (THD). Snce ts ntroducton, SHE-PWM has drawn tremendous research nterest and has also been developed for varous applcatons, prncpally for hgh-voltage and hgh-power converters where swtchng losses are a major concern and ther reducton s of prme mportance. The concept of SHE-PWM technques s based on decomposton of the PWM voltage/current waveform usng Fourer theory and merely depends on the formulaton of the gven waveform and ts propertes. Dfferent waveform formulatons have been consdered and analyzed n the techncal lterature, ncludng: bpolar, unpolar [] [5], and stepped or PWM multlevel waveforms [59] [5]. Waveform propertes such as symmetry [], [], [6], [65] and the number and ampltude of voltage levels [66] [7] are equally mportant factors n the analyss and play an essental role n determnng the form and complexty of the soluton space. These wll be dscussed n detal n the followng sectons of ths paper. Fndng the analytcal soluton of the SHE-PWM waveform s the man challenge, and selecton of a sutable solvng algorthm or method reles heavly on the formulaton of the waveform. umerous solvng technques, such as teratve approaches []-[7], optmzaton technques [9] [] and resultant theory [], [9] [95], have been proposed for obtanng the swtchng angles for dfferent SHE-PWM waveforms. SHE-PWM was ntally studed for conventonal two- and three-level converters [] [5]. It has snce been then extended to varous multlevel [59] [5] and hybrd multlevel [5], [6], [] converters for numerous applcatons. The number and varety of multlevel converters requres dfferent mplementaton for each ndvdual topology and can maxmze the potental benefts that SHE-PWM can offer to a partcular converter. The am of ths paper s to provde an analytcal revew of progress n the feld of SHE-PWM for multlevel converters and defne the state of the art and outstandng ssues wth the SHE-PWM technque. Addtonally, the paper ams to serve as a comprehensve resource on SHE-PWM and facltate understandng of the features, benefts and lmtatons of ths modulaton technque. A thorough revew of the wellestablshed solvng methods s also reported n ths paper, wth the am of helpng prospectve researchers to dentfy approprate algorthms for a gven crcut topology and applcaton. Specal consderaton s devoted to the mplementaton of SHE-PWM n the dfferent multlevel converter topologes and ther role n varous ndustral and utlty applcatons. The paper s organzed as follows. Secton II provdes an overvew of multlevel SHE-PWM (MSHE-PWM) formulatons and presents a sngle equaton defnton for the problem, whch s extendable to any number of levels. In Secton III, varous solvng algorthms developed for acqurng the solutons to the trgonometrc and transcendental set of MSHE-PWM equatons are revewed. The requrements and mplementaton aspects of MSHE-PWM n varous multlevel converter topologes are dscussed n Secton IV. Current applcatons are reported n Secton V, whle selected soluton trajectores and llustratve expermental results are provded n Secton VI. Conclusons of the wor are summarzed n Secton VII. II. MULTILEVEL SHE-PWM FORMULATIOS SHE-PWM s based on the Fourer seres decomposton of the perodc PWM voltage waveform generated by a power electroncs converter, as gven by (), and calculaton of the swtchng angles (α ) that elmnate/control the selected loworder harmoncs. a nt nt f ( t) ancos bnsn n T T () There are several ways to defne a gven SHE-PWM problem, as llustrated n Fg.. The smplest formulaton of the SHE-PWM problem for both two-level and multlevel waveforms assumes QW symmetrcal waveforms [59]. Ths greatly smplfes the formulaton and soluton process, snce the dc-component, even harmoncs and the sne coeffcents of odd harmoncs are all equal to zero, resultng n the least number of equatons requrng soluton. Programmed PWM technques Harmonc elmnaton Mnmzaton / Optmzaton Quarter wave symmetry Half wave symmetry onsymmetrcal Unequal and varable levels Harmonc mnmzaton THD mnmzaton Harmonc mtgaton Fg.. Classfcaton of SHE-PWM formulatons

4 The component l(ωt) s not related to the fundamental frequency waveforms [6], [65]. It s always one level lower than the maxmum level of the waveform and equals zero n three level waveforms. Dstrbuton of angles at the dfferent levels s an mportant aspect of MSHE-PWM [66], [67]. Ths can be ncorporated nto the problem formulaton, creatng multple sums for transtons wthn the same level of the waveform. The proposed generalzed formulaton utlzes the lower level envelope functon so that all the level transton nformaton s ncluded n the functon l(ωt), enablng dervaton of a sngle equaton formulaton, albet wth complcated l(ωt) functons. α α α α α + (a) Lower level envelope l(ωt) (b) α ωt ωt Fg.. Multlevel SHE-PWM. (a) Generalzed multlevel waveforms, (b) lower level envelope. A. Quarter-wave symmetry formulaton Based on the prevous assumptons and the waveform analyss of Fg., the generalzed form of a QW-symmetrcal multlevel PWM waveform can be defned by a sngle equaton as: bn n ()cos( n ), () where the parameter s calculated from the modulo operaton of the swtchng angle order and the level waveform as: mod l( t),. (3) The parameter defnes each transton of the waveform and assumes the values of: for the rsng edge, for the fallng edge. To ensure a QW-symmetrcal, physcally correct and mplementable waveform, the swtchng angles wthn the quarter-perod are constraned as. () The normalzed fundamental frequency component s a functon of the modulaton ndex (V ) gven by ˆ V m a, n L. where m a s lmted between and B. Half-wave symmetry formulaton A half-wave (HW) symmetrcal formulaton consders transtons dstrbuted over the half-perod of the waveform. In two-level waveforms, HW symmetry extends the number of avalable solutons[9], [] and can potentally mprove the harmonc performance compared to QW-symmetrcal solutons. Smlar benefts can be ganed n multlevel waveforms [6]. Although HW symmetry elmnates the dc component as well as the even harmoncs, both the sne and cosne terms of an odd harmonc need to be controlled. Usng the defntons of Secton II-A for the parameter, the Fourer coeffcents can be wrtten as: an ( ) sn( n ) n bn ( ) cos( n ) n (6) In ths formulaton, the modulaton ndex s defned as m a b and t s agan restrcted between zero and a L b. The harmonc phasng tan of the a fundamental frequency component can be omtted and the term a can be set to zero, smplfyng the acquston of solutons. The followng constrant ensures that the waveform s physcally correct and follows the HW symmetry requrements:. (7) C. on-symmetrcal formulaton Complete abolshment of all symmetry requrements n twolevel waveforms [], [3] s equally applcable to multlevel waveforms. All odd and even harmoncs as well as the dc component need to be elmnated/controlled [65] n the same way as n two-level waveform [], hence + swtchng angles are requred over the whole perod. Owng to the ncreased complexty of ths formulaton, as well as ts suboptmal harmonc and computatonal performance [3], non-symmetrcal multlevel SHE-PWM remans the least attractve opton among all formulatons. The Fourer coeffcents of the dc component and sne and cosne terms of each harmonc n the waveform are: 3 (5)

5 a ( ) an n n bn n n ( ) cos( ) ( ) cos( ) () These terms have to be evaluated over the whole perod of the waveform. The defnton of the lower level functon l(ωt) becomes sgnfcantly more complcated whle the followng constrant restrcts the angles between zero and :. (9) D. Unequal / varable voltage levels The formulatons of Sectons II-A, B and C are derved based on the assumpton that the voltage levels of the output voltage waveform are equal n ampltude. Whle ths s vald for most multlevel converter topologes, hybrd confguratons of CHB converters [93], [] and CHB converters for PV applcatons [] can operate wth unequal or varable voltage levels, generatng voltage waveforms wth dfferent ampltudes for each voltage level. Several dfferent SHE-PWM formulatons are possble, dependng on the characterstcs of each voltage source. These formulatons nclude: ) Unequal and constant voltage levels [6], [69], [93]. In ths case, the formulaton consders the dfferent voltage levels but the number of harmoncs that are controlled and/or elmnated s equal to the number of swtchng angles n the multlevel waveform, smlar to the three prevous formulatons. The unequal voltage levels are ncluded n the equatons as multplers ( Vdcm ) of the transtons wthn each level and also normalzed to the ampltude of the hgher dc voltage (< Vdcm <). b n ( n Vdc ( ) cos n ( ) cos n () Vdc Vdcm... m ( ) cos n The number of varables and equatons does not change and the calculaton complexty of acqurng the requred solutons remans unaltered. ) Unequal and varable voltage levels [7], [3] [5]. In ths case, the ampltude of each voltage level s consdered as a varable wthn the equatons, allowng more degrees of freedom and elmnatng/controllng a hgher number of harmoncs compared to constant voltage levels. The Fourer coeffcents of a QW waveform are: ) b V n ( n dc ( ) cos n V ( ) cos n V dc dcm... m ( ) cos n ) () The number of harmoncs that can be elmnated/controlled from such a formulaton ncreases from to +M. As all voltage levels are varable, solutons can be acqured for a sngle m a. The swtchng angles reman constant whle the voltage of each level s lnearly vared to change the ampltude of the fundamental frequency component. The ampltudes of all non-elmnated harmoncs ncrease lnearly wth the fundamental frequency component and the %THD of the voltages and currents s constant throughout the whole modulaton ndex range. However, the extra degrees of freedom and soluton smplcty come at the expense of ncreased complexty n the power crcut confguraton, regulaton of ndvdual dc voltages to the requred level, and poor dynamc performance. ) A combnaton of constant and varable voltages [7]. The formulaton s smplfed and the number of harmoncs that can be elmnated s equal to the number of varable dc sources and swtchng angles. The Fourer coeffcents can be derved from () by settng the voltage of the constant dc-sources (V dcm ) equal to. Solutons derved from ths formulaton demonstrate varaton of both dc-voltage levels and swtchng angles [7]. Formulatons wth unequal or varable voltage levels can be extended to any of the possble symmetres, but the benefts from such an extenson cannot be easly dentfed. Another characterstc of all of the above methods s that changng the order of the voltage levels results n a dfferent output voltage waveform; dervaton of complete solutons requres evaluaton for all possble voltages and angles, whch ncrease n a combnatoral manner as the number of CHBs ncreases. An addtonal drawbac, common to all of the formulatons addressed n ths secton, s that as one transton s drectly lned to one of the CHBs, lmtng varatons n the swtchng patterns of the converter and lmtng both power and loss equalzaton among the brdges. Complcaton also arses from the lac of a generalzed formulaton for ths nd of multlevel waveform. However, ther onlne mplementaton s smpler [7], manly because of the lnear soluton patterns they exhbt. The dfferent waveforms of multlevel SHE-PWM and the effect of varable and unequal voltage levels on the output voltage waveform at varous operatng ponts are summarzed n Fg. 3. For constant and equal voltage levels (Fg. 3(a)), a change n the operatng pont wll lead to a change n the PWM pattern, whle for unequal and varyng voltages (Fg. 3(b)), the PWM pattern wll reman the same whle the

6 ampltude of each voltage level wll vary accordngly. Fnally, when there s a combnaton of constant and varyng voltages (Fg. 3(c)), changes n both the PWM pattern and voltage levels are requred, based on the pre-calculated solutons [7]. Change n m a Change n m a Change n m a (a) (b) (c) Fg. 3. Multlevel SHE-PWM waveforms. (a) QW symmetrcal wth equal and constant voltage levels, (b) QW symmetrcal wth unequal and varable voltage levels, and (c) QW symmetrcal wth combnaton of constant and varable voltages. E. Mnmzaton and mtgaton technques A number of alternatve approaches to the complete elmnaton of hgher order harmoncs for SHE-PWM have been proposed n the lterature. These approaches nclude: ) Harmonc mnmsaton [75] [7], [], where the problem s reformulated as a mnmsaton functon seeng local mnma of harmoncs rather than ther complete elmnaton. The fundamental frequency component must agan be controlled to the requred ampltude. Real tme mplementaton becomes easer as convergence to a local optmum can be acheved wthn a reasonable tme step, but at the expense of low-order harmoncs, mang the applcaton of such formulaton unfeasble for certan applcatons. ) Voltage THD mnmsaton [], [3], where the goal s to mnmse the THD rather than elmnate ndvdual harmoncs. The number of harmoncs n the formulaton s not lmted by the number of swtchng angles n the waveform and formulatons may typcally nclude more harmoncs than the number of avalable varables (swtchng angles). The complexty of ths approach enables a global THD mnmum to be found whle loworder harmoncs do not exceed the lmts set by grd codes [6]. t t t ) Harmonc mtgaton [], [], [], whch ncorporates harmonc lmts set by grd codes [6], [7] to provde PWM patterns wth acceptable ampltudes for ndvdual harmoncs rather than complete elmnaton of low-order harmoncs. Harmonc mtgaton does not set explct values for each harmonc but searches for solutons that satsfy the condton of Vn Vn,lmt () The fundamental frequency component s the only component that needs to be accurately controlled to the requred level. Ths approach facltates convergence to solutons and hgher contnuty of solutons at the expense of low-order harmoncs n the spectra. In all cases, the requrement for a complete elmnaton of harmoncs s abolshed, generally allowng easer convergence of the solvng algorthms and ncreased contnuty n the soluton space [76], [], []. Alternatvely, when complete elmnaton of low-order harmoncs s requred, reducng the number of elmnated harmoncs from a gven number of swtchng angles yelds smlar results [9], []. Therefore, a tradeoff between harmonc content and soluton contnuty s vald for all multlevel waveforms, eventually convergng to SPWM- or SVM-equvalent technques. III. SOLVIG ALGORITHMS AD TECHIQUES Great efforts have been made by researchers over the past few decades to develop and enhance numerous algorthms and solvng technques for obtanng the optmal and/or multple sets of solutons for a range of SHE-PWM formulatons. Ths secton s dedcated to the state of the art of these algorthms (as categorzed n Fg. ), hghlghtng ther features and mplcatons. A. umercal approaches Intal approaches to the soluton of the equaton system were based on teratve numercal methods such as ewton Raphson []-[6]. An mportant characterstc of these technques s that convergence reles heavly on good estmaton of the ntal values and, although predcton of these ntal values mght be possble for smple waveforms wth a small number of swtchng angles [6], [7], [], ths may not be achevable for waveforms wth a large number of angles or for multlevel waveforms. evertheless, methods have been reported n the lterature for determnng these ntal values, such as predctve algorthms [], [], whch calculate the ntal values and then apply a ewton algorthm to obtan the exact soluton wthn one or two teratons. An equal area algorthm [3], [] was also used to ntalze the startng pont. The Chebyshev functon [5] was used to transform the trgonometrc equaton of SHE nto ts equvalent n algebrac form, enablng excellent convergence and less processng tme. L et al. [59] utlzed phase-shft technque to provde a startng pont for the non-constraned optmzaton process. Mrror surplus harmonc method s also proposed n ths wor to reduce the computatonal burden of the harmonc suppresson n fve-level nverter. 5

7 Algorthms & Methods Iteratve approaches Walsh functons As SHE equvalent Algebrac Optmsaton Resultant theory GAs PSO DE Hybrd Fg.. Classfcaton of SHE-PWM algorthms and solvng technques. B. Algorthms wth multple solutons capabltes Despte the varatons n the abovementoned technques, one caveat assocated wth all of them s that they all gnore (or are unable to fnd) multple solutons to the SHE problem. Transformaton steps to the nonlnear transcendental equatons have been ntensvely nvestgated, amng to ensure convergence and fndng all sets of solutons. Analyss based on Walsh functons was ntroduced to two-level [6] [9] and multlevel waveforms [6] n order to convert these equatons nto a set of lnear algebrac equatons that can easly be solved whle reducng the computaton tme. The harmonc ampltudes are expressed drectly as a functon of swtchng angles, allowng dgtal mplementaton usng a straght-lne curve-fttng method. The global soluton, however, s searched among all possble swtchng patterns, mang the approprate ntal condton an essental condton to guarantee the optmal soluton. The acquston of any soluton s restrcted by varyng only one angle wthn a gven nterval []. Therefore, f a soluton exsts that requres two angles n the same selected nterval, such a soluton cannot be detected. Hence the accuracy of ths technque s a factor of the samplng ponts of the PWM sgnal (.e. the number of ntervals), whch n turn ncreases the computaton complexty f hgher accuracy s requred. Ths was allevated wth the use of a pulse-bloc functon, allowng more than one angle to be vared wthn a selected nterval [3]. evertheless, a powerful algorthm to carry out the requred converson between Walsh seres and Fourer seres representatons s deemed essental [9]. C. Theory of resultants Convertng the transcendental equatons of the SHE problem nto an equvalent set of polynomal equatons usng trgonometrc denttes s well-documented and studed for both two-level and multlevel waveforms [], [9] [97]. Eq. () s converted nto an equvalent polynomal system wth the assumpton of x cos, x cos,, x cos The theory of resultants s then appled to compute the resultant system of polynomal equatons and then wor bacwards to fnd all sets of solutons of the swtchng angles for a gven SHE-PWM waveform [], [9], [93]. Later, the degree of polynomal equatons s reduced by usng symmetrc polynomals [9], [95] or power sums [96] to reduce the computatonal burden. The man lmtatons of the resultant theory are:. The order of polynomals ncreases as the number of harmoncs to be elmnated also ncreases; therefore t can only be easly appled when such number s low.. When there are several dc sources, the degrees of the polynomals are qute large, thus mang the computatonal burden of ther resultant polynomals (as requred by the elmnaton theory) qute hgh [9].. If multlevel nverters wth non-equal dc voltage sources are consdered, the set of the transcendental equatons to be solved then becomes no longer symmetrcal and requres the soluton of a set of hgh-degree equatons, whch s beyond the capablty of contemporary computer algebra [93]. D. Optmzaton based technques SHE-PWM can be reformulated nto an optmzaton problem where trgonometrc equatons for each harmonc, descrbed by (), are represented n the followng cost functon. The cost functon of (3) s mnmzed wth the constrant mposed by (), and modern stochastc search technques are employed to fnd all multple sets of solutons. The transcendental equatons of SHE-PWM are transformed nto a constrant optmzaton problem [], [3], [96] and then a DE algorthm s appled to fnd the optmal swtchng angles. Another approach based on a mnmzaton technque combned wth a random search was ntally appled to twoand three-level waveforms [9] [3] and then extended to varous multlevel waveforms [5], [6], [9] []. The method s appled drectly to the set of transcendental equatons, resultng n all solutons of a SHE problem beng obtaned n one relatvely smple step, even when there s a large number of harmoncs to be elmnated. Genetc algorthms (GAs) have also been appled to fnd solutons to the SHE-PWM problem n a number of research artcles [3] [], [65] [69]. Although GAs were ntally ntroduced as an optmzaton technque for obtanng the optmal swtchng angles that reduce the lne current harmonc n a PWM ac-dc nverter [7], they were later extended to varous SHE-PWM output waveforms (.e. two-, three- and mult-level) ether for selected harmonc elmnaton or THD mnmzaton. PSO s another promsng optmzaton method for the SHE-PWM problem that has been recently appled for varous waveforms [9], [7], []. 6

8 Vdc ( ) cos ( ) Vdc ( ) cos ( )... Vdcm ( ) cos ( ) V... m mn Vdc ( ) cos (5 ) Vdc ( ) cos (5 )... Vdc m ( ) cos (5 ) m Vdc ( ) cos (n ) Vdc ( ) cos (n )... Vdc m ( ) cos (n )... m (3) Furthermore, PSO was used to fnd the soluton of the swtchng angles that mnmze the THD of the multlevel waveform rather than a complete elmnaton of low order harmoncs for cases of both equal [] and non-equal [7] dc sources. E. Methods that facltate onlne mplementaton Owng to the complexty of the resultant system of equatons, on-the-fly soluton s consdered a challengng tas [], [], and most of the prevously-mentoned solvng technques are based on off-lne calculaton. evertheless, onlne (real-tme) mplementaton can be acheved va nterpolatng the off-lne calculated swtchng angles by smple functons (models) [] or an analytcal expresson []. A pecewse lnear representaton [6] and a curvefttng model [3] were also ntroduced to represent the nonlnear curves of the soluton of the optmal swtchng angles as straght-lne segments, whch can be easly mplemented usng modern DSP boards. However, the accuracy of such technques largely reles on locatons of the brea-ponts connectng the lnear segments together, as well as the number of segments. The other challenge s the contnuty of the soluton set, whch s not the case for many multlevel waveforms. An nterestng representaton of the optmal swtchng angles, usng the well-nown regular-sampled PWM technques to am for easer mplementaton n real-tme usng a mcroprocessor, was frst ntroduced n [3]. However, t has been shown that reproducng optmzed PWM exactly usng samplng technques requres a rather complcated nonlnear samplng process [35]. Therefore, t s only possble to approxmately reproduce optmzed PWM usng regularsampled technques [3] [37]. On the other hand, mcroprocessor-based technques necesstate large memory, whereas most of the computatonal efforts of the mcroprocessor are spent on tedous tmng tass assocated wth generaton of the swtchng sgnals for ndvdual phases of the nverter. The applcaton of Abased methods facltates mplementaton of a smple mcroprocessor-less PWM that realzes optmal swtchng angles of the nverters and for any value of the modulaton ndex [3], [39], [], [6]. However, complete and detaled pror nowledge of the swtchng angles s requred to tran the neural networ off-lne before t can be used on-lne [3], []. Soluton methods based on model predctve control (MPC) [], [] were recently used to calculate harmonc components n real tme n order to elmnate unwanted harmoncs from the output voltage waveform wth relatvely low swtchng frequency. In addton to the ncreased computatonal tme, MPC methods are typcally mplemented onlne and generate non-symmetrcal SHE-PWM waveforms requrng elmnaton of the dc-component as well as of even harmoncs, smlarly to Subsecton II-C. An analytcal model asssted wth Chebyshev polynomals, descrbng pattern generaton of the SHE waveform [3] was developed to allow for a smple onlne mplementaton usng dgtal sgnal controllers or FPGA boards. However, the method was only appled for two swtchng angles and ts ablty to deal wth greater number of swtchng angles s stll unclear as the complexty mght become a constrant. Hence, onlne mplementaton of SHE-PWM could be acheved on the expenses of ncreasng the complexty and the need for very advanced computatonal tools and memory capabltes to accommodate the looup tables or compromsng the accuracy through approxmatng the soluton of SHE-PWM. Ths always could mpose lmtatons on the applcaton of SHE-PWM to one crcut or another. IV. SHE-PWM IMPLEMETATIO O MULTILEVEL COVERTERS The solutons of the MSHE-PWM equatons descrbed n Secton II, as acqured usng the algorthms dscussed n Secton III, are completely ndependent of the converter topology and only depend on the number of voltage levels and swtchng angles. However, each converter has ts own operatonal requrements and requres a dfferent mplementaton n order to produce the requred waveform at the output termnals of the power crcut. Ths secton revews the ey features of mplementng MSHE-PWM n varous multlevel converter topologes. A. CHBs and hybrd multlevel converters Implementaton of MSHE-PWM for CHB converters and hybrd converters based on CHBs s the most straghtforward, and has found numerous applcatons [65] [73], [] []. One brdge can be swtched at any of the pre-calculated 7

9 angles; dstrbuton of the swtchng angles to the brdges s performed based on addtonal crtera such as balancng of the dc-ln voltages and/or loss equalzaton. Fg. 5(a) shows an example of angle dstrbuton between two H-brdges of a fve-level CHB converter. The angles can be dstrbuted n an arbtrary manner or n accordance wth level-shfted carrers (Fg. 5(b) [99]) or phase-shfted carrers (Fg. 5(c) [97]). CHB and hybrd multlevel converters can also be operated wth unequal or varable voltage levels [7], n whch case the flexblty of selectng brdges for each transton s lmted. Addtonally, n hybrd converters, the dstrbuton of angles to the brdges should tae nto account the voltage level of the floatng capactor [] and the devaton of the voltage from ts reference value. A method for equalzng small varatons n the dc-voltages for cascaded H-brdge converters when operaton wth equal voltages s requred was presented n [73], [7]. α Output Voltage α Waveform (a) ωt - Brdge Brdge - Brdge Brdge - - (b) (c) Fg. 5. Multlevel waveforms and angle dstrbuton. (a) Fve-level waveform, (b) LSC-PWM equvalent dstrbuton and (c) PSC-PWM equvalent dstrbuton. B. PC and FC converters Three-level PC and FC converters requre balancng of capactor voltages (ether dc-ln capactors or FCs). In a 3L- PC converter, voltage balancng of the dc-ln capactor can be acheved wth a longer tme constant through the passve, self-balancng propertes of the topology. Accelerated convergence requres actve methods based on the selecton of redundant swtchng states [5]. Actve selecton of redundant states s also necessary for FC converters. Further mprovements of the voltage balancng characterstcs can also be acheved by ntroducng a slght varaton (ε) to the pre-calculated swtchng angles (Fg. 6); ether by extendng or lmtng the conducton tme of each capactor dependng on the voltage devaton and the current drecton as: () The varaton n conducton tmes asssts n algnng the capactor voltage wth the set reference value. The tmng of transtons s also altered, and ths mght have a nondetrmental effect on the harmonc content. evertheless, ths s nsgnfcant compared to the dstorton caused by the unbalanced capactor voltages as shown n [5], [6]. The method s equally applcable to PC and actve PC (APC) converters [5], [6], as well as FC topologes [7], []. The man concept behnd ths method s llustrated n Fg. 6(b). α α Modulaton Index (M) Phase Angle (θ) Capactor Voltage Measurements Load current () α -ε Angle Loo-up Table α α +ε (a) α Capactor Voltage Control ωt / (b) Fg. 6. Small varatons n the swtchng angles facltate voltage balancng of PC, APC and FC converters. (a) Voltage waveform and angle modfcaton, and (b) calculaton of angle varaton ε and PWM generaton. ± ε + + PWM Generaton Gate Sgnals C. Mult-module converters A mult-module converter [9] uses a cascaded connecton of three-phase, two-level converters and a summng multwndng transformer at the phase output. The am of angle dstrbuton to the ndvdual two-level modules s to lmt the varaton of the ndvdual dc-lns, whle controllng the overall dc-ln voltage. Ths can be acheved by pre-selectng the sngle-phase swtchng patterns of each module [] from the optmzed multlevel waveform and rotatng the derved patterns to provde the necessary balancng. The dc-ln capactors n a mult-module converter do not carry the full load current of the converter and the devaton on the ndvdual dc-ln capactors s sgnfcantly smaller than the capactor voltage rpple of other modular converters. Pattern rotaton can be mplemented over a number of perods nstead of every swtchng nstant, so t does not actvely ncrease the swtchng frequency of the converter modules or the assocated swtchng losses. D. Modular multlevel converters MMCs are the state-of-the-art multlevel converter topology. A unque feature of PWM n MMCs s that the dervaton of the swtchng pattern s not drectly related to the swtchng of a partcular sub-module (SM) [7], [] but s typcally handled by an SM capactor-voltage balancng algorthm. Multlevel SHE-PWM technques can be drectly mplemented as long as the requrements for capactor voltage balancng of the MMC SMs are satsfed. Typcal mplementatons of PWM for MMCs separate the modulaton nto two dstnct stages. The frst stage uses the pre-calculated swtchng angles and an nput from external controllers to defne the multlevel waveform as well as the number of sub-modules that wll be connected to the upper and lower arm of each phase-leg. These patterns can be ether

10 of fundamental [7], [] or hgher [7], [] swtchng frequency, dependng on the applcaton. The second stage, based on a sub-module capactor voltage sortng and balancng algorthm, defnes whch sub-modules to connect or bypass n the arms of the converter and generates the swtchng sgnals. The two-stage algorthm for the MMC s outlned n Fg. 7. Alternatvely, under fundamental frequency modulaton, the selecton can be made based on an estmaton of the energy [7], [] n the capactors of each SM. The selecton s facltated by the nowledge of the exact transton ponts and voltage balancng s acheved by averagng the total energy n and out of the SMs to zero over multple perods. MMCs typcally operate wth a hgh number of voltage levels at low swtchng frequences; n such confguratons the benefts of SHE-PWM can be dmnshed. evertheless, modulaton technques for MMCs stll reman under actve research [7], [], [7], []. Modulaton Index (M) Phase Angle (θ) Gatng Sgnals to the SMs Angle Loo-up Table angles Selecton of SMs Target Waveform Generaton Polarty of the arm current ( arm ) Sortng (Ascendng / Descendng) # of requred SMs n arms SM voltage measurements Stage Stage Fg. 7. Two-stage modulaton and SHE-PWM mplementaton for the MMC. V. KEY APPLICATIOS BASED O MSHE-PWM Swtchng losses n medum- and hgh-power converters are of major concern and ther reducton s of prme mportance. SHE-PWM offers a consderably lower equvalent swtchng frequency compared to carrer-based PWM technques, resultng n lower swtchng power losses and good harmonc performance. Ths therefore maes t a compettve and attractve soluton n such applcatons, ncludng grd support and grd-connected converters, as well as medum-voltage drve applcatons. Some of the developed applcatons that employ SHE-PWM as a method of modulaton are revewed and summarzed n ths secton. A. SHE-PWM for motor drve converters Despte the potental dffcultes assocated wth onlne mplementaton of SHE-PWM, the possblty of explotng ts features n motor drve applcatons (.e. medum voltage, hgh power) has been reported by several research artcles. The method effectvely reduces the low-order harmonc dstortons at both the lne and motor sdes, therefore reducng the swtchng losses and mprovng the power factor. In [55], for example, SHE-PWM s appled to a PMSM to elmnate loworder voltage harmoncs, resultng n elmnaton of current harmoncs. SHE-PWM clamed to be sutable for motor drve applcatons such as pumps and fans that do not need fast dynamcs due to swtchng pattern transton problem [55]. In [56], mplementaton of a 6 V/ VA PC converter motor drve based on ICGT was facltated by SHE- PWM. Another study [57] showed that the method outperforms the SVM technque wth equvalent swtchng frequency n terms of system effcency and thermal-loss reducton. A hybrdzaton of the SHE technque wth trapezodal modulaton [5] and SVM [9] were proposed for hgh-power bac-to-bac CSC drve systems, mantanng hgh power factor durng hgh speed operaton wth low swtchng frequency devces. Furthermore, the operaton of a hybrd multlevel converter for electrc vehcles operated wth MSHE-PWM was analyzed n [3]. MSHE-PWM was also used n VSCbased drve applcatons wth the am of reducng both the acoustc nose [3] and common-mode voltage [9]. A capactor-less AC-AC motor drve was recently realzed usng SHE-PWM to prevent the low-order harmoncs from beng fed to the motor [6]. B. SHE-PWM-based actve rectfers SHE-PWM has also recently been extended to medumand hgh-power actve rectfer crcuts [], [], [9], [] [3]. In [] and [9], the lne current THD of the three-level ac-dc converter was sgnfcantly mnmzed by usng the SHE-PWM approach. The method was further able to balance the voltage of the dfferent cells of the cascaded multlevel actve rectfer [9] and the modular currentsource rectfer [3] by controllng the power level of each ndvdual cell whle employng a low swtchng frequency modulaton scheme. In [9], the method s used to elmnate the harmoncs n the twelve-pulse actve front end converter n order to remove or mnmze the flterng requrement, wth the am of complyng wth IEEE Standard [3]. SHE-PWM was also consdered n [9] and [] for an nterleaved four-quadrant tracton rectfer to mprove the harmonc profle of the nput current. C. SHE-PWM-based grd-connected converters VSCs are ncreasngly replacng conventonal passvebased grd-support FACTS devces and flters n modern electrcty networs. However, swtchng losses, whch are drectly lned to hgh-frequency PWM operaton, are one of the most serous and challengng ssues n VSC-based hgh power applcatons such as FACTS and HVDC systems. SHE- PWM has proved to be an effectve modulaton technque n such applcaton converters, owng to ts low swtchng frequency. For nstance, several SHE-PWM-based STATCOM systems have recently been proposed n the techncal lterature [] [6], [7], [9]. SHE-PWM was used n conjuncton wth phase-shft control to elmnate low-order harmoncs from the output voltage of both conventonal [] and multlevel [], [9] VSC-based STATCOM systems, leadng to complance of the nput current wth IEEE Standard 9

11 59-99 [6], as well as better devce utlzaton and hgh system performance. Ths was also extended to a CSC for mne excavators [5], achevng a unty power factor and a lne current complyng wth the relevant standards. In [6], SHE-PWM helped to elmnate the remanng harmoncs (.e. f ±, where f s the fundamental frequency) of an nterphase transformer based large-power FACTS controller. Furthermore, nterestng wor was recently reported n [] and [5] where SHE-PWM was ncorporated n a mult-module converter based HVDC transmsson system that employed seres-connected two-level three-phase converters. Ths provded wder harmonc bandwdth at reduced swtchng frequences, resultng n a reducton of both swtchng losses and flterng requrements. A compensaton method for the bacground harmoncs based on the SHE-PWM approach was recently developed n [7]. The method maes the grd-nterfacng converters, such as hgh-power current-source rectfers; operate as an actve harmonc flter whle mantanng low swtchng frequency. However, the method appears to be mpractcal for smultaneous compensaton of multple harmoncs, necesstatng multdmensonal looup tables wth a demandng memory space requrement. SHE-PWM also provdes benefts for other grd-connected applcatons, such as nterfacng photovoltac (PV) systems wth the grd [5], [6], [5], provdng lower swtchng losses, mproved dc-ln voltages, and better semconductor swtchng utlzaton compared wth conventonal SVM or SPWM technques. The use of SHE-PWM to facltate the ntegraton of dstrbuted energy resources va multlevel converters, to compensate for harmoncs generated by the nonlnear loads, was recently reported n [3]. D. Other applcatons SHE-PWM has been used to address the zero-sequence current ssue n varous VSCs [5] [53]. Partcularly n the case of a mult-modular voltage-source nverter, SHE-PWM elmnates the low-order harmoncs from the output voltage waveform and also ether elmnates [5] or reduces [5] the ZSCC n mult-module paralleled converters by selectve elmnaton of the trplen harmoncs from each converter, or reduces the ZSCC by breang up the ZSCC path [53]. Another nterestng applcaton s hgh- or medum-voltage four-leg three-phase nverters where SHE-PWM agan elmnates the zero-sequence current and allows the converter to operate wth low swtchng frequency, whle smultaneously dealng wth an unbalance condton. VI. SOLUTIO TRAJECTORIES AD SHE-PWM WAVEFORMS: ILLUSTRATIVE EXAMPLES The dfferent ways of formulatng the SHE-PWM problem depend on the number of voltage levels and swtchng angles, creatng an nfnte number of possble combnatons and, hence, results. Ths secton provdes selected SHE-PWM soluton trajectores and expermental results, demonstratng the most wdely used presentaton method n the avalable lterature- that of swtchng angles versus modulaton ndex. Fg. llustrates a varety of SHE-PWM solutons, ncludng fundamental frequency swtchng for seven-, 5- and 9-level waveforms (Fg. (a) (c)), as well as waveforms wth hgher swtchng frequences (Fg. (d) (f)). Increasng the number of levels reduces the modulaton ndex range of the calculated solutons, but solutons tend to retan ther lnearty over the range that they are calculated, whch s an advantage for onlne mplementaton. Extendng the technques to nclude varable and unequal voltages, the constant swtchng pattern wth lnearly varyng voltages for both unequal and varable voltages formulatons s observed n Fg. (g), for a seven-level waveform wth angles per quarter perod. When voltage levels are assumed constant, both angles and voltages change as the modulaton ndex changes, as llustrated n Fg. (h) and () for sevenlevel waveforms wth angles and ether two or one varable voltages. Correspondng operatng ponts from the solutons of Fg. are expermentally demonstrated n Fg. 9 for llustraton purposes. VII. COCLUSIO Selectve harmonc elmnaton pulse-wdth modulaton s an attractve modulaton technque for a wde range of low swtchng frequency applcatons owng to ts unque features, ncludng drect control of the harmonc spectrum and reducton of the swtchng frequency. A comprehensve revew of the development and research trends of the SHE- PWM technque, wth specal focus on multlevel waveforms and converters (MSHE-PWM), was presented n ths paper. The man outcomes of ths revew can be summarzed n the followng ponts: The formulaton and the propertes of the SHE-PWM waveform play an mportant role n determnng the complexty of the problem, acqurng the avalable solutons and defnng the soluton space. The number of output voltage levels and swtchng angles are other essental factors that nfluence the defnton of relevant equatons. Dfferent symmetres, ncludng QW, HW and non-symmetrcal waveforms, can be mplemented, wth QW offerng the smplest formulaton and easer expanson to hgher number of levels. A generalzed formula for representng any multlevel SHE-PWM waveform wth a sngle equaton can easly facltate problem defnton. The complexty of the formulaton s drectly nfluenced by the symmetry requrements and, unle two-level waveforms, nonsymmetrcal multlevel SHE-PWM becomes ncreasngly complex wthout clear benefts. The objectve functon s another mportant aspect, and elmnaton of low-order harmoncs can be relaxed to consder mnmsaton of THD or adherence to the harmonc lmts of grd codes. Removng the need for complete harmonc elmnaton or reducng the number of elmnated harmoncs extends the avalable solutons at the cost of low-order harmoncs and suboptmal harmonc performance.

12 Angles (rad) Angles (rad) Angles (rad) Modulaton Index, m a (d) 3 Angles (rad) Modulaton Index, m a Modulaton Index, m a (a) (b) (c) Vdcl (p.u.) Angles (rad) Angles (rad) Modulaton Index, m a.95 3 (e) 3 Angles (rad) Angles (rad) Modulaton Index, m a Modulaton Index, m a (f) Modulaton Index, m a Modulaton Index, m a Modulaton Index, m a (g) (h) () Fg.. Swtchng angles (sold lnes ) and dc-ln voltages (dashed lnes) of SHE-PWM solutons. (a) Seven-level fundamental frequency, (b) 5-level fundamental frequency, (c) 9-lev el fundamental frequency, (d) Seven-level, angles, dstrbuton, (e) ne-level, angles, dstrbuton, (f) -level, 5 angles, dstrbuton, (g) Seven-level, angles, three varable voltages, dstrbuton, (h) Seven-level, angles, two varable voltages, dstrbuton, and () Seven-level, angles, one varable voltage, --9 dstrbuton. SHE-PWM defnes the requred transtons of the multlevel waveform. However, mplementaton of the technque depends on the multlevel converter topology, and addtonal aspects, such as capactor voltage balancng and loss dstrbuton and equalsaton, should be consdered, focusng on a gven converter topology SHE-PWM demonstrates sgnfcant potental for varous ndustral applcatons. The technque s largely accepted n utlty power converters owng to ts lower swtchng frequency compared to SPWM or SVM. It has also ganed wde acceptance n other applcatons such as motor drves and renewable energy condtonng converters, although the dynamc response should be carefully evaluated n such applcatons. Fnally, SHE-PWM s a very promsng approach for future advanced power converson systems, and there s a wde range of research opportuntes across dfferent aspects that should be nvestgated to mprove ts features and practcalty. REFERECES []. P.. Enjet, P. D. Zogas and J. F. Lndsay, Programmed PWM technques to elmnate harmoncs: a crtcal evaluaton, n IEEE Trans. Ind. Appl., vol. 6, no., pp. 3 36, Mar./Apr. 99. Vdcl (p.u.) Angles (rad) []. T. A. Lpo and D. G. Holmes, Pulse-wdth modulaton for power converters prncples and practce, IEEE Press Seres on Power Engneerng, 3. [3]. F. G. Turnbull, Selected harmonc reducton n statc dc-ac nverters, IEEE Trans. Communcaton and Electroncs, vol. 3, no. 73, pp , Jul. 96. []. H. S. Patel and R. G. Hoft, Generalzed technques of harmonc elmnaton and voltage control n thyrstor nverters: Part I- harmonc elmnaton, n IEEE Trans. Ind. Appl., vol. IA-9, no. 3, pp. 3 37, May/Jun [5]. H. S. Patel and R. G. Hoft, Generalzed technques of harmonc elmnaton and voltage control n thyrstor nverters: Part IIvoltage control technques, n IEEE Trans. Ind. Appl., vol. IA-, no. 5, pp , Sep./Oct. 97. [6]. P. Enjet and J. F. Lndsay, Solvng nonlnear equatons of harmonc elmnaton PWM n power control, n IEE Electroncs Letters, vol. 3, no., pp , Jun. 97. [7]. T. Kato, Sequental homotopy-based computaton of multple solutons for selected harmonc elmnaton n PWM nverters, n IEEE Trans. Crcuts Syst., vol. 6, no. 5, pp , May 999. []. J. R. Wells, B. M. ee, P. L. Chapman and P. T. Kren, Selectve harmonc control: A general problem formulaton and selected solutons, IEEE Trans. Power Electron., vol., pp , 5. [9]. G. Konstantnou and V. G. Agelds, Bpolar swtchng waveform: ovel soluton sets to the selectve harmonc elmnaton problem, n Proc. IEEE ICIT,, pp []. G. Konstantnou and V. G. Agelds, On re-examnng symmetry of two-level selectve harmonc elmnaton PWM: ovel formulatons, solutons and performance evaluaton, Electrc Power Systems Research, vol., pp. 5 97,. Vdcl (p.u.)

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17 a cascaded multlevel rectfer, IEEE Trans. Ind. Electron., vol. 5, no. 6, pp , Dec., 7. [5]. J. I. Guzman, P. E. Meln, J. R. Espnoza, L. A. Moran, C. R. Baer, J. A. Munoz and G. A. Gunez, Dgtal mplementaton of selectve harmonc elmnaton technques n modular current source rectfer, IEEE Trans. Ind. Informat., vol. 9, no., pp , May, 3. [6]. IEEE Recommended Practces and Requrements for Harmonc Control n Electrcal Power Systems, Std. IEEE-59-9, Jun., 99. [7]. Voltage Characterstcs of Electrcty Suppled by Publc Dstrbuton Systems, E 56,. []. B. Gulten and M. Erms, Cascaded multlevel converterbased transmsson STATCOM: System desgn methodology and development of a V ±MVAr power stage, IEEE Trans. Power Electron., vol., no., pp , ov. 3. [9]. B. Gulten, C. O. Gerçe, T. Atal, M. Denz,. Bçer, M. Erms, K.. Kose, C. Erms, E. Koç, I. Çadrc, A. Aç, Y. Aaya, H. Toygar and S. Bdec, Desgn and mplementaton of a 5-V ±5-Mvar transmsson STATCOM based on - level cascaded multlevel converter, IEEE Trans. Ind. Appl., vol., no. 3, pp. 3 5, May/Jun.. [3]. Y. W. L, M. Pande,. R. Zatgar and B. Wu, An nput power factor control strategy for hgh-power current-source nducton motor drve wth actve front-end, IEEE Trans. Power Electron., vol. 5, no., pp , Feb.. [3]. A. R. Bahsha, H. Jn and G. Joos, Reducton of harmonc concentraton and acoustc noses usng varable selectve harmonc elmnaton technque, n Proc. IEEE ICIT 996, 5 Aug. 996, Tape, Chna, vol., pp. 7. [3]. D. Ahmad and J. Wang, Onlne selectve harmonc compensaton and power generaton wth dstrbuted energy resources, IEEE Trans. Power Electron., vol. 9, no. 7, pp , Jul.. Mohamed S. A. Dahdah (M SM ) receved hs Ph.D. degree n Electrcal Engneerng from Multmeda Unversty, Malaysa, n 7. In ovember 7, he was apponted Assstant Professor n the School of Electrcal and Electronc Engneerng, The Unversty of ottngham, Malaysa Campus. He s currently wth the School of Electrcal and Electronc Engneerng, ewcastle Unversty, UK. He has authored or co-authored a number of refereed journal and conference papers. Hs research nterests nclude multlevel converters, SHE modulaton technques, PWM converter control and renewable energy. Dr. Dahdah s the Deputy Edtor-n- Chef for IET Power Electroncs and has been a regular revewer for both IEEE and IET journals. Georgos Konstantnou (S M 3) receved the B.Eng. degree n electrcal and computer engneerng from the Arstotle Unversty of Thessalon, Thessalon, Greece, n 7 and the Ph.D. degree n electrcal engneerng from the Unversty of ew South Wales (USW), Sydney, Australa, n. He s currently a Senor Research Assocate wth the Australan Energy Research Insttute and the School of Electrcal Engneerng and Telecommuncatons, USW. Hs research nterests nclude hybrd and modular multlevel converters, pulse wdth modulaton, and selectve harmonc elmnaton technques for power electroncs. Dr. Konstantnou s an Assocate Edtor of IET Power Electroncs. Vasslos G. Agelds (SM ) was born n Serres, Greece. He receved the B.Eng. degree n electrcal engneerng from the Democrtus Unversty of Thrace, Thrace, Greece, n 9; the M.S. degree n appled scence from Concorda Unversty, Montreal, QC, Canada, n 99; and the Ph.D. degree n electrcal engneerng from Curtn Unversty, Perth, Australa, n 997. He has wored wth Curtn Unversty ( ); the Unversty of Glasgow, Glasgow, U.K. ( ); Murdoch Unversty, Perth, Australa (5 6); and the Unversty of Sydney, Sydney, Australa (7 ). He s currently the Drector of the Australan Energy Research Insttute, School of Electrcal Engneerng and Telecommuncatons, Unversty of ew South Wales, Sydney. Dr. Agelds was the recpent of the Advanced Research Fellowshp from the U.K. s Engneerng and Physcal Scences Research Councl n. He was the Vce Presdent for Operatons wth the IEEE Power Electroncs Socety (PELS) from 6 to 7. He was an AdCom Member of IEEE PELS from 7 to 9 and the Techncal Char of the 39th IEEE Power Electroncs Specalsts Conference n held n Rhodes, Greece. 6