Selective Harmonic Mitigation Technique for High-Power Converters

Selec i e Ha monic Mi iga ion Technique o High Powe Con e e s J. Napoles, J. I. Leon, Membe ,IEEE, R. Po illo, Membe ,IEEE, L. G. F anquelo, Fellow Membe ,IEEE, and M. A. Agui e, Membe ,IEEE Abs ac —In high powe applica ions he maximum swi ching equency is limi ed due o he mal losses. This leads o highly dis o ed ou pu wa e o ms. In such applica ions, i is necessa y o il e he ou pu wa e o ms using bulky passi e il e ing sys ems. The ecen ly p esen ed selec i e ha monic mi iga ion echnique (SHMPWM) p oduces ou pu wa e o ms whe e he ha monic dis o ion is limi ed ul illing speci ic g id codes when he numbe o swi ching angles is high enough. The ela ed ech- nique has been p e iously p esen ed using a swi ching equency equal o 750Hz. In his pape , a special implemen a ion o he SHMPWM echnique op imized o e y low swi ching equency is s udied. Expe imen al esul s ob ained applying SHMPWM o a h ee-le el neu al poin clamped con e e using a swi ching equency equal o 350Hz a e p esen ed. The ob ained esul s show ha he SHMPWM echnique imp o es he esul s o p e ious selec i e ha monic elimina ion (SHEPWM) echniques o e y low swi ching equencies. This ac highligh s ha he SHMPWM echnique is e y use ul in high powe applica ions leading i s use an impo an educ ion o he bulky and expensi e il e ing elemen s. Index Te ms—Mul ile el sys ems, Ha monic dis o ion, Fil e s. I. INTRODUCTION IN HIGH powe applica ions, he ha monic con en o he ou pu wa e o ms has o be educed as much as possible in o de o a oid dis o ion in he g id and o each he maximum ene gy e iciency. On such applica ions, he he mal losses in he powe semiconduc o s limi he maximum swi ching equency o a ew hund eds o He z and mul ile el con e e s a e he mos sui able powe sys ems o be used. Many ecen wo ks wi h di e en mul ile el con e e opologies ha e been ecen ly p esen ed showing hei good pe o mance o high powe applica ions [1]–[3]. In addi ion, i is necessa y o use special modula ion ech- niques and il e ing sys ems in o de o ul il he g id codes in he poin o common coupling. Usually g id codes es ablish speci ic limi s o ha monics up o 50 h and o he o al ha monic dis o ion (THD). The passi e il e s used o educe ha monic dis o ion in o he g id a e e y bulky and expensi e. On he o he hand, he use o an e icien modula ion me hod is e y con enien o ob ain ou pu wa e o ms wi h accep able ha monic con en . One o he mos in e es ing Manusc ip ecei ed Feb ua y 5, 2009. Accep ed o publica ion June 11, 2009. Copy igh c °2009 IEEE. Pe sonal use o his ma e ial is pe mi ed. Howe e , pe mission o use his ma e ial o any o he pu poses mus be ob ained om he IEEE by sending a eques o [email p o ec ed]. J. Napoles, J. I. Leon, L. G. F anquelo, R. Po illo and M. A. Agui e a e wi h he Elec onic Enginee ing Depa men , Uni e si y o Se ille (Spain), (e-mail: [email p o ec ed]). modula ion echniques o high powe applica ions is he well known selec i e ha monic elimina ion pulse wid h modula ion (SHEPWM) echnique o iginally p esen ed in [4]. This ech- nique is able o ob ain ou pu signals wi h lowe ha monic con en han o he echniques because makes ze o a limi ed numbe o low o de ha monics. On he o he hand, he ecen ly p esen ed selec i e ha monic mi iga ion pulse wid h modula ion (SHMPWM) echnique [5] is able o elax he cons ain s used in he SHEPWM echnique o ob ain ou pu wa e o ms wi h be e ha monic pe o mance aking in o ac- coun ac ual g id egula ions. In [5] i was shown ha using he SHMPWM echnique wi h he swi ching equency equal o 750Hz, i is possible o ul il bo h he CIGRE WG 36-05 and EN 50160 g id code equi emen s wi hou using any addi ional il e ing sys em. In his pape , a e y low swi ching equency equal o 350 Hz is conside ed using only 7 swi ching angles which leads o new designs o he objec i e unc ion (OF) o he SHMPWM echnique. This is a big di e ence wi h e e ence [5] whe e he high numbe o swi ching angles achie ed he ul illmen o he g id code wi hou using il e ing sys ems. In his pape i is shown ha using 7 swi ching angles, some ha monics a e abo e he maximum limi s o he g id code e en using he SHMPWM echnique. An analy ical way o de ine he OF has been in oduced in his pape de ining ac o s such as he sa e y ma gin ρand he penal y ac o λp. Depending on he speci ic applica ion o he high powe con e e , wo possible solu ions o de ine he OF ha e been in oduced. The di e en solu ions (s a egies S1 and S2) a e ocused on he imp o emen o di e en ha monics as is explained in sec ion IV. A compa ison wi h he SHEPWM echnique in he same low swi ching equency condi ions is included. A h ee-phase h ee-le el diode clamped con e e is used as expe imen al se up o illus a e he bene i s ob ained by he SHMPWM echnique. Using SHEPWM i is possible o make ze o a limi ed numbe o ha monics bu he non canceled ha monics a e no conside ed in he algo i hm and could each e y high ampli udes. This leads o he ac ha i is no possible o keep hem below a desi ed alue ha ing a g ea impac in he size and cos o he il e ing sys em. Howe e , he lexibili y o SHMPWM can be used o apply di e en c i e ia o low and high o de ha monics conside ed in he g id code. Low o de ha monics can be educed o alues below he limi s speci ied in he g id code. High o de ha monics, whe e he e is no any con ol using SHEPWM, can be educed using SHMPWM. In his pape , he compu ing e o o he SHMPWM echnique is E -E 0 Vao ω π 2π α1 α0α2 π 2 α3 α4 α0 ≤ α1 ≤ ... ≤ αk-1 ≤ π/2 Fig. 1. Th ee-le el p e-p og ammed PWM swi ching pa e n wi h i e swi ching angles (α0,α1,α2,α3,α4). ocused on educing as much as possible he ha monic con en which has o be il e ed o ul il he g id code. The main goal is o educe he il e ing equi emen s in o de o dec ease he size, weigh and cos o he il e ing elemen s. This pape is o ganized as ollows; in sec ion II he SHM- PWM p inciple is b ie ly summa ized. Nex sec ion desc ibes he il e design p oblem and he mos commonly used solu- ion. In sec ion IV, he di e ences be ween SHEPWM and SHMPWM echniques a e de ailed and a compa ison using he ob ained simula ion esul s is ca ied ou in sec ion V. Expe imen al esul s alida ing he imp o emen s ob ained using he SHMPWM me hod a e p esen ed in sec ion VI. Finally, he conclusions o he pape a e de ailed in he las sec ion. II. SHMPWM PRINCIPLE The Fou ie analysis o he ypical h ee-le el p e- p og ammed PWM swi ching pa e n (Fig. 1) conside ing kswi ching angles αi(i=0,...,k-1) gene a es he ollowing equa ions whe e Hjis he ha monic ampli ude o j h o de : Hj=4 jπ k−1 X i=0 h(−1)isin(jαi)i, whe e j= 1,2, . . . , n. (1) These equa ions can be sol ed in o de o ob ain he ha monic ampli udes H1,H2,..., Hndesi ed alues. Classic SHEPWM echnique ixes he alue o H1(which is no mally called modula ion index (Ma)) o a ce ain alue and also elim- ina es k-1 ha monics. Usually, he mos in e es ing ha monic o de s o be elimina ed a e he odd non- iplen ones because using h ee-phase opologies wi hou neu al connec ion he iplen ha monics do no appea in he line- o-line ol ages. The e o e, he applica ion o he SHEPWM echnique leads o sol e he ollowing exp essions: H1=4 π k−1 X i=0 h(−1)isin(αi)i 0 = 4 jπ k−1 X i=0 h(−1)isin(jαi)i, whe e j= 5,7,11, . . . , q. (2) The SHMPWM echnique is based on he idea ha i is no necessa y o educe o ze o he ha monics while hey a e kep below accep able le els. Those le els a e de ined by he g id codes which es ablish maximum allowed limi s o each ha monic o de and THD in o de o main ain he quali y o he g id. The SHMPWM echnique is based on sol ing he ollowing inequali ies sys em whe e Liis he maximum allowed le el imposed by he applied g id code. |Ma−H1| ≤ L1 1 |H1| 4 jπ k−1 X i=0 h(−1)isin(jαi)i≤Lj, whe e j= 5,7,11,...,49.(3) The SHMPWM me hod elaxes he es ic ions o (2) and is able o gene a e ou pu signals wi h low ha monic con en ap- plying (3). This ac allows o conside mo e ha monic o de s han he SHEPWM echnique as can be obse ed om (2) and (3). This lexibili y is e y use ul in high powe sys ems due o he il e ing sys em equi emen s will be elaxed which leads an impo an educ ion in he cos , olume and weigh o he il e ing componen s. Hence, i is possible o choose he mos app op ia e il e ing shape o each applica ion p e iously o he compu ing p ocess. The inequali ies sys em (3) can be syn hesized in an objec- i e unc ion (OF) which has o be minimized: OF(α0, . . . , αk−1) = X i=1,5,...,49 ciE2 i+cT HDTHD. (4) The cicoe icien s o he OF a e modeled as non linea unc ions and, in gene al, ha e been implemen ed as ollows: i (Ei< ρLi)ci= 1; else ci=λp; (5) Whe e ρ²(0,1] is he sa e y ma gin o he maximum allowed le el Liand λpis de ined as he penal y ac o (λpÀ1). The Li alues co espond o he maximum allowed le els shown in (3). As can be obse ed om exp ession (5), i he ob ained ha monic dis o ion o o de i h (Ei) is below he 80% (assuming ha ρ=0.8) o i s co esponding Li alue, he associa ed ciis equal o 1. In o he case, as he dis o ion is close o he maximum allowed alue Li, a penal y is imposed in he cicoe icien in o de o ocus he op imiza ion sea ch educing he dis o ion in his speci ic ha monic o de . This penal y is de ined as he weigh ac o λp. In [5], whe e he SHMPWM echnique was in oduced using 15 swi ching angles, a sa e y ma gin ρequal o 0.8 and a cons an a io penal y ac o λpequal o 1000 was used. The Li alues we e equal o he maximum alues de ined by he applied g id code. As was shown in [5], using 15 swi ching angles pe qua e o pe iod gi es enough lexibili y o comple ely ul ill he g id code. Howe e , o e y high powe applica ions, a low numbe o swi ching angles has o be used. In his pape , 7 swi ching angles ha e been applied ( his co esponds o swi ching equency equal o 350Hz) and his does no allow enough ma gin o mee he g id codes wi hou any addi ional il e ing sys em. In his way, as examples o he lexibili y o he SHMPWM echnique, di e en pa icula iza ions o he exp ession (5) ha e been applied in o de o achie e se e al op imiza ion c i e ia. I mus be no iced ha he de ini ion o he ci unc ions is he base o he SHMPWM echnique because hey mus be adap ed o he conc e e condi ions o he applica ion. In his pape wo di e en s a egies ha e been s udied and he de ails o each implemen a ion will be discussed in sec ion IV. The whole sys em desc ibed by (3) and (4) can be sol ed using an op imiza ion me hod. Di e en algo i hms ha e been es ed bu he well known simula ed annealing op imiza ion me hod [6], [9] has been inally used in he p esen pape because i easily allows new o mula ions o he p oblem. O he me hods such as pa icle swa m, abu sea ch, gene ic algo i hms, an colony sys ems, s ochas ic e olu ion, e ce e a would ob ain simila esul s [7], [8], [10]. III. FILTER DESIGN High powe con e e s ha e o wo k a e y low swi ching equency leading o ou pu signals wi h undesi ed ha monic dis o ion. These ha monics ha e o be il e ed in o de o main ain he quali y in he powe supply. The ob ained expe i- men al esul s p esen ed in his pape show ha he SHMPWM echnique is a powe ul ool o be applied in o de o elax he inal il e ing equi emen s. Any o he elemen which educes he ha monic con en as he coupling ans o me can also be conside ed in o de o elax he equi emen s o he il e . The e a e di e en possible il e ing s a egies o educe he ha monic con en gene a ed by powe con e e s. The mos commonly used a e passi e il e s, ac i e il e s and hyb id il e s mixing bo h passi e and ac i e modules [11]–[13]. In high powe applica ions, passi e il e s a e no mally he mos sui able solu ion. The il e opology mos commonly used in high powe applica ions is he LCL il e wi h ha monic aps (Fig. 2). The il e design is a e y impo an opic because in high powe applica ions he eac i e elemen s a e e y bulky and expensi e. Some impo an design guides can be ound in [14] and [15]. The mos impo an p oblem ela ed o passi e il e s is he exis ence o possible esonances wi h he g id [16]. Di e en echniques ha e been epo ed in o de o a oid his phenomenon when passi e il e s a e used [17]. IV. SHMPWM VS SHEPWM As i has been commen ed abo e, he SHEPWM echnique has been widely used o high powe applica ions [18]–[21]. 3 LEVELS FILTER 1 2 3 4 Fig. 2. Typical passi e il e opology o high powe applica ions. This s uc u e is known as LCL il e wi h ha monic aps. Wi h his echnique i is possible o di ec ly elimina e a limi ed numbe o ha monics (being his limi a ion ela ed o he used swi ching equency) educing he uned il e s needed o mee he g id codes. The main d awback o he SHEPWM echnique is ha he alue o he non-ze oed ha monics can no be managed o ge any op imiza ion objec i e. The SHMPWM echnique imp o es he SHEPWM esul s because i is able o educe he il e ing equi emen s gene a ing ou pu signals wi h a highe numbe o ha monics unde he alues speci ied in he g id codes using he same swi ching equency. This ac makes he SHMPWM echnique specially use ul o high powe applica ions. In addi ion, SHMPWM echnique can be used in a la ge ange o Maimp o ing o he p e ious echniques [22]–[24]. In his wo k, g id codes EN 50160 [25] and CIGRE WG 36-05 [26] ha e been conside ed in he compu ing p ocess bu any o he g id code could be chosen. These g id codes de ail speci ic limi s up o ha monic o de 50 h. The THD is also limi ed by hese speci ic g id codes o 8% bu conside ing only he ha monics up o 40 h. Table I summa izes he limi s speci ied by he applied g id codes. In o de o compa e SHEPWM and SHMPWM echniques, i is assumed ha he con ol s a egy o he con e e a oids any possible esonance. The numbe o swi ching angles αiis equal o 7 pe qua e o a 50Hz cycle which co esponds o a swi ching equency o 350Hz using a h ee-le el con e e . Wi h 7 swi ching angles he SHEPWM can ix he Maand elimina e six non-desi ed ha monics, usually he non- iplen lowe o de ha monics, i.e. 5 h,7 h,11 h,13 h,17 h and 19 h. A Ma ange om 0.60 o 1.16 in s eps o 0.01 is applied conside ing bo h he SHEPWM and he SHMPWM echniques. The lexibili y o he SHMPWM can be used in he com- pu ing p ocess in o de o de e mine he swi ching angles αiwhich gene a e he mos app op ia e ha monic spec um depending on he applica ion. In his wo k wo di e en s a egies ha e been s udied: 1) S a egy I (S1): A limi ed numbe o low o de ha - monics mus mee he g id code wi hou any il e ing sys em. The numbe o hese ha monics mus be a leas he same han using SHEPWM. The es o ha monics speci ied in he g id code, which exceed he maximum limi s, a e educed as much as possible independen ly whe he hey a e low o high o de ha monics. This idea can be ansla ed o he OF using a pa icula ized e sion o he exp ession (5). In his case, he penal y ac o λpis equal o 1000. Besides, he Lile els ha e been di ided in wo g oups. Fo ha monics up o 19 h, he Li alues TABLE I GRID CODE EN 50160 REQUIREMENTS + QUALITY GRID CODE CIGRE WG 36-05 Odd non- iplen ha monics Odd iplen ha monics E en Ha monics Ha monic Rela i e Ha monic Rela i e Ha monic Rela i e o de (n) Vol age (Li) o de (n) Vol age (Li) o de (n) Vol age (Li) 5 6% 3 5% 2 2% 7 5% 9 1.5% 4 1% 11 3.5% 15 0.5% 6...10 0.5% 13 3% 21 0.5% >10 0.2% 17 2% >21 0.2% 19 1.5% 23 1.5% 25 1.5% >25 0.2+32.5/n a e he limi s speci ied by he g id code as in [5]. Fo highe ha monics up o 49 h, he maximum ha monic dis o ion ob ained using he SHEPWM echnique in he whole ange o Mahas been used as he Li alues. In his case ρ=0.9. 2) S a egy II (S2): A limi ed numbe o low o de ha - monics mus mee he g id code wi hou any il e ing sys em. The numbe o hese ha monics mus be a leas he same han using SHEPWM as in S1. Fo he es o ha monics conside ed in he g id code, S2 is ocused on educing as much as possible he ha monic con en om o de 23 d o 29 h. In addi ion, S2 is designed o keep, i possible, he highe o de ha monics up o 49 h below he maximum alues ob ained using he SHEPWM modula ion echnique. In his case, he pa icula ized e sion o exp ession (5) is de ined using a penal y ac o λpequal o 5000 o all he ha monics up o 29 h and equal o 1000 o highe ha monics. The Lile els hose de ined o s a egy S1 excep o he ha monics 23 d,25 h and 29 h whe e a cons an alue equal o 15% has been used. Again has been chosen ρ=0.9. S1 ep esen s he mos immedia e way o apply SHMPWM wi h a educed numbe o swi ching angles. On he o he hand, S2 is ocused on educing he g id connec ion il e aking in o accoun ha he eac i e elemen s o il e low o de ha monics a e specially bulky and expensi e. S2 pays special a en ion on lowe o de ha monics a he expense o elaxing he allowed dis o ion o he high o de ha monics. I mus be no iced ha bo h S1 and S2 s a egies a e ob ained de ining he cicos unc ions men ioned in sec ion II in a sui able way. The wo king condi ions a e comple ely di e en compa ed wi h [5] and an heu is ic sea ch is needed o ansla e he desc ip ions o he s a egies p esen ed abo e o he g oup o ci unc ions. This sea ch is an impo an no el y p esen ed in his pape . V. SIMULATION RESULTS SHEPWM echnique and SHMPWM echnique applying S1 and S2 ha e been es ed i s ly by simula ions. A h ee-le el con e e has been conside ed o compa e he echniques. Fig. 3 and Fig. 4 show a compa ison be ween he ob ained simula- ion esul s using he SHEPWM and SHMPWM echniques conside ing he s a egies S1 and S2 espec i ely. In bo h igu es a e ep esen ed he wo s THD and he wo s alue Exp I 0.60<Ma<1.16 0 10 20 30 40 50 60 5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 THD40 SHMPWM SHEPWM G id Code S a egy S1 0.6<M <1.16 a Maximum Dis o ion Le els (%) Ha monics and THD Fig. 3. Simula ion esul s compa ing SHEPWM and SHMPWM echniques conside ing he s a egy S1 wi h swi ching equency equal o 350Hz. Wo s case in he in e al 0.6< Ma<1.16. 0 10 20 30 40 50 60 5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 THD40 SHMPWM SHEPWM G id Code S a egy S2 0.6<M <1.16 a Maximum Dis o ion Le els (%) Ha monics and THD Fig. 4. Simula ion esul s compa ing SHEPWM and SHMPWM echniques conside ing he s a egy S2 wi h swi ching equency equal o 350Hz. Wo s case in he in e al 0.6< Ma<1.16. o dis o ion o each ha monic ob ained o a speci ic ange o he modula ion index Ma( om 0.60 o 1.16). In Fig. 3, i is clea ha using he SHMPWM echnique wi h s a egy S1, he maximum dis o ion le els o he non-elimina ed ha monics a e unde he maximum alues ob ained using he SHEPWM echnique. This ac is especially ele an o ha monics 23 d o 31s whe e he esul s ob ained using he SHEPWM echnique nea ly double hose ob ained using he SHMPWM me hod. Fig. 4 shows a compa ison be ween he simula ion e- sul s ob ained using he SHEPWM echnique and SHMPWM me hod wi h s a egy S2. In his case, he maximum dis o ion le els in he ange 23 d o 29 h ha e been educed as much as possible compa ed wi h he SHEPWM esul s and wi h SHMPWM using S1. This is e y in e es ing because he il e ing elemen s needed in he uned il e s a e mo e bulky, hea y and expensi e in low o de ha monics. This ad an age is achie ed a he expense o he ac ha ha monics 35 h and 37 h a e highe han he maximum alues ob ained using SHEPWM. S2 could be a e y in e es ing s a egy in hose cases whe e is be e o educe he maximum powe suppo ed by he eac i e elemen s o low o de ha monics han in high o de ha monics because he cos , weigh and size g ow mo e han linea ly. These esul s demons a e ha he lexibili y o he SHMPWM me hod can be e y use ul and le s he designe o choose he mos app op ia e il e ing shape acco ding o each applica ion. In S2, he main goal is o educe as much as possible ha monics 23 d o 29 h bu any o he s a egy could be chosen. Using SHMPWM echnique wi h S1 o S2, i can be no iced ha he e y low o de ha monics (up o ha monic 19 h) he dis o ion le els a e unde he limi s speci ied by he g id codes. Using SHEPWM and SHMPWM echniques i is no necessa y any uned il e in he low o de ha monics. In he highe o de ha monics, i S1 is applied, he ob ained dis o ion is much highe using SHEPWM me hod han using he SHMPWM echnique. This means ha he uned il e s ha e o suppo highe powe s which deal wi h mo e bulky and expensi e il e ing elemen s. On he o he hand, i S2 is ap- plied, he mos impo an ad an age o SHMPWM compa ed wi h SHEPWM is ocused on he educ ion o he uned il e s dedica ed o he lowe o de ha monics. I mus be no iced ha his is a e y impo an ad an age because he cos in bo h, induc o s and capaci o s, g ow mo e han linea ly when he maximum cu en (o ol age) is inc eased keeping he induc ance o eac ance alue. VI. EXPERIMENTAL RESULTS All he esul s p esen ed in he p e ious sec ions ha e been expe imen ally es ed using he 150kVA IGBT-based back- o- back h ee-le el h ee-phase diode-clamped con e e shown in Fig. 5. This p o o ype is a scale down model o high powe con e e s and bo h he modula ion echniques and expe imen al esul s ob ained wi h i can be ex ended o any h ee-le el highe powe con e e . The chosen semiconduc o s a e he IGBT modules SKM 300 GB 123 D o 300A and 1200V om Semik on. A ha dwa e pla o m based on a TMS320VC33 DSP is used o con ol he ec i ie and he in e e sides o he con e e . The ec i ie side is con olled o es ablish a DC-link ol age equal o 800V. The in e e side is used o eed a passi e RL load wi h R=120Ωand L=15mH. Bo h SHMPWM and SHEPWM echniques ha e been applied o he in e e in o de o compa e hei pe o mances. In he compu ing p ocess eal powe semiconduc o s ha e been conside ed o keep a sa e y ma gin o 32µs be ween wo consecu i es swi ching angles as in [22]. The SHMPWM echnique in a closed loop con ol scheme was p esen ed in [27] whe e he swi ching equency was equal o 750Hz. Howe e , in his case, he e e ence wa e o ms o be gene a ed by he in e e side a e de e mined in open loop co esponding o a 50Hz pu ely sinusoidal signal. In addi ion, in his pape , he same g id codes a e applied bu only se en Fig. 5. 150 kVA IGBT-based back- o-back h ee-le el diode-clamped in e e . The DC-Link ol age is 800V. Fig. 6. Expe imen al phase o middle poin ol age using 7 swi ching angles o a h ee-le el con e e ob ained using a 1:5 ol age a io oscilloscope p obe. TABLE II SIMULATION AND EXPERIMENTAL RESULTS USING SHEPWM AND SHMPWM TECHNIQUES CONSIDERING STRATEGIES S1 AND S2 Ha monic Maximum SHEPWM(%) SHMPWM-S1(%) SHMPWM-S2(%) o de (n) Limi (Li) simula ions expe imen s simula ions expe imen s simula ions expe imen s 5 6 0.00 0.26 5.40 5.54 5.40 5.50 7 5 0.00 0.26 4.50 4.48 4.50 4.47 11 3.5 0.00 0.22 3.15 3.21 3.15 3.19 13 3 0.00 0.18 2.70 2.74 2.68 2.73 17 2 0.00 0.20 1.80 1.93 1.80 1.82 19 1.5 0.00 0.33 1.35 1.45 1.35 1.37 23 1.5 34.52 32.03 20.16 20.48 7.60 7.75 25 1.5 30.08 28.07 16.80 16.71 13.93 12.02 29 1.32 32.49 33.05 17.64 17.93 15.20 15.06 31 1.25 29.30 27.02 15.12 15.05 25.32 25.14 35 1.13 13.76 13.09 12.45 12.57 22.82 22.40 37 1.08 15.45 15.15 9.45 9.95 23.26 22.85 41 0.99 12.22 12.09 7.56 7.68 12.06 12.21 43 0.96 12.12 12.07 7.56 7.32 11.14 10.97 47 0.89 16.72 17.02 8.82 8.88 8.18 8.02 49 0.86 15.77 15.23 8.32 8.03 8.24 7.84 THD40 8 48.21 49.84 32.31 34.03 34.87 34.12 swi ching angles a e conside ed leading o a low swi ching equency equal o 350Hz as can be obse ed in Fig. 6. Fig. 7 shows he cu en o one phase in he load and he line ol age o Ma=1.20 using he SHMPWM echnique wi h s a egy S2. An oscilloscope ol age p obe wi h an a enua ion a io o 1:5 and a 10mV/A cu en p obe we e used o ob ain bo h cap u es. The SHMPWM echnique allows o ob ain solu ions wi h good pe o mance wi h Maup o 1.20. Howe e , a modula ion index ange om 0.6 o 1.16 is chosen in o de o make a ai compa ison wi h he well-known SHEPWM echnique. In Fig. 8, he ends o he magni udes o he ha monics (23 d,25 h,29 h and 31s ) using he di e en echniques s udied in his pape ha e been ep esen ed. Fig. 8a, Fig. 8b and Fig. 8c co espond o he esul s ob ained using he Fig. 7. Expe imen al cu en and line ol age o Ma=1.20 ob ained using a 1:5 ol age a io oscilloscope p obe and 10mV/A o he cu en p obe . SHEPWM echnique, using he SHMPWM wi h s a egy S1 and using he SHMPWM wi h s a egy S2 espec i ely. In all he cases, he e ical scale has been adjus ed om 0% o 35% o he undamen al ha monic ampli ude. The ho izon al scale is he simula ion ime. In he expe imen , he modula ion index Mais changing con inuously om 0.60 o 1.16 using s eps equal o 0.01. Each speci ic modula ion index alue is applied du ing 1 second and he expe imen al esul s ha e been aken du ing 1 minu e in o de o show he esul s o all he modula ion index ange. All he expe imen al esul s a e summa ized in Table II o expe imen s E1 and E2. F om le o igh a e shown he ha monic o de , he maximum le els speci ied by he g id codes and he esul s ob ained wi h SHEPWM and SHMPWM echniques. The shown esul s co espond wi h he maximum ha monic dis o ion ob ained in he whole ange o Ma. All he ha monic dis o ion alues a e speci ied as a pe cen age espec o he undamen al ha monic alue. F om op o bo om a e s udied all he ha monics o in e es (odd non- iplen) and in he inal ow is de ailed he THD ob ained conside ing up o ha monic 40 h. The esul s om Table II show he ad an ages ob ained using he SHMPWM echnique in compa ison wi h SHEPWM due o he lexibili y o he me hod. As can be obse ed om Table II, he simula ion esul s a e in acco dance wi h he ob ained expe imen al esul s. F om he expe imen al esul s, o ha monics up o 19 h, using SHEPWM and SHMPWM i is no necessa y any il e ing sys em because he maximum ou pu alues a e always unde he limi speci ied in he g id codes. Fo he es o ha monics conside ed by he g id code, om 23 d o 49 h, he esul s ob ained using he SHMPWM echnique depend on he selec ed s a egy du ing he compu a ion p ocess (S1 o S2). Conside ing E1, he maximum alues ob ained using SHM- PWM a e always below he maximum alues ob ained using a) b) c) 35% 0% 35% 0% 35% 0% 35% 0% 35% 0% 35% 0% 35% 0% 35% 0% 35% 0% 35% 0% 35% 0% 35% 0% Fig. 8. Expe imen al alues in he whole Ma ange ob ained using: a) SHEPWM, b) SHMPWM-S1 and c) SHMPWM-S2. F om op o bo om, ha monics 23 d,25 h,29 h and 31s . The scales ha e been adjus ed om 0 o 35% o he undamen al ha monic ampli ude. SHEPWM in he whole Ma ange. This esul ep esen a g ea ad an age o SHMPWM espec o he SHEPWM because he g id connec ion il e equi emen s will be clea ly educed. Fo ins ance, ha monic dis o ions om 23 d o 31s a e imp o ed educing he maximum le el nea ly o he hal alue. Conside ing E2, o ha monics om 23 d o 49 h, om da a o Table II i can be no iced ha ha monics 23 d o 29 h a e g ea ly educed compa ed wi h hose ob ained using SHEPWM. This was he p ima y objec i e o s a egy S2 o de e mine he swi ching angles o be applied o he SHMPWM echnique. In ac , he dis o ion o ha monics om 23 d o 29 h using S2 is also lowe han ha achie ed by s a egy S1. This imp o emen is achie ed a he expense o he ac ha ha monics 35 h and 37 h ha e dis o ion abo e he le el ob ained using he SHEPWM echnique. S2 was de ined in his way because he il e ing elemen s needed o mee he g id codes a e bigge and mo e expensi e whils he ha monics conside ed ha e lowe o de s. VII. CONCLUSIONS In his pape , a compa ison be ween he SHEPWM and SHMPWM o e y low swi ching equency (350Hz) o a h ee-le el con e e is p esen ed. In high powe applica ions, he he mal losses limi he maximum swi ching equency o a ew hund eds o He z ( s<500Hz). In his con ex , i is necessa y o elimina e he undesi ed ha monics using il e ing sys ems. The SHEPWM has been adi ionally used in high powe applica ions because i is able o gene a e ou pu wa e o ms wi h a limi ed numbe o elimina ed ha monics. In his pape i is demons a ed ha using e y low swi ching equency, he SHMPWM echnique is able o gene a e ou pu signals wi h be e ha monic pe o mance compa ed o he SHEPWM echnique in a wide ange o he modula ion index. In he pape , he lexibili y o he SHMPWM echnique has been exploi ed conside ing di e en c i e ia o de e mine he swi ching angles o be applied o he h ee-le el con e e . One o he s a egies (S1) was de ined o imp o e he esul s o he SHEPWM o all he ha monics ha a e no ze oed. A second s a egy (S2), has been also in oduced in o de o educe as much as possible he il e equi emen s o low o de ha monics abo e he maximum limi imposed by he g id code. The simula ion and expe imen al esul s show ha he maximum ou pu alues o he ha monics using he SHMPWM echnique up o 19 h a e below he limi s imposed by he applied g id codes. These ha monics a e elimina ed using SHEPWM. The e o e, hese ha monics do no need o be il e ed using bo h echniques. On he o he hand, he non- elimina ed ha monics ob ained using SHEPWM ha e much highe alues compa ed wi h hose ob ained using he SHM- PWM echnique using S1. This ac leads o a educ ion in he maximum powe suppo ed by he elemen s o he uned il e s o be used. The consequence is a signi ican educ ion in cos , size and weigh o he il e ing sys em equi ed o ul il he g id codes. Finally, he esul s ob ained o s a egy S2 show ha any il e ing shape can be applied o de e mine he swi ching angles o he SHMPWM echnique. S2 objec i e was o achie e a g ea educ ion o non-elimina ed low o de ha monics and his goal has been eached. Expe imen al esul s alida ing he p oposed concep s a e included. ACKNOWLEDGMENT The au ho s g a e ully acknowledge inancial suppo p o- ided by he Spanish Minis y o Science and Technology unde p ojec TEC2006-03863 and by he Andalusian Go e n- men Resea ch Council unde p ojec EXC/2005/TIC-1172. REFERENCES [1] J. Rod iguez, S. Be ne , B. Wu, J. O. Pon and S. Kou o, “Mul ile el Vol age-Sou ce-Con e e Topologies o Indus ial Medium-Vol age D i es,” IEEE T ans. Ind. Elec on., ol. 54, no. 6, pp. 2930–2945, Dec. 2007. [2] L. G. F anquelo, J. Rod iguez, J. I. Leon, S. Kou o, R. Po illo and M. M. 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[25] CENELEC EN 50160, “Vol age cha ac e is ics o elec ici y supplied by public dis ibu ion sys ems,” 2001. [26] CIGRE WG 36-05, “Ha monics, cha ac e is ic pa ame e s, me hods o s udy, es ima es o exis ing alues in he ne wo k,” Elec a no.77, 1981, S.35-54. [27] J. N´ apoles, R. Po illo, J. I. Leon, M. A. Agui e and L. G. F anquelo, “Implemen a ion o a closed loop SHMPWM Technique o Th ee Le el Con e e s,” in he 34 h IEEE Annual Con e ence o he Indus ial Elec onics Socie y (IECON’08), pp. 3260–3265, 10–13 No . 2008, O lando (USA). Ja ie Napoles was bo n in Se ille in 1978. He ob ained he Telecommunica ions Enginee deg ee om he Uni e si y o Se ille, Spain, in 2005. He is cu en ly pu suing he PhD deg ee in elec ical engi- nee ing a he Powe Elec onics G oup, Uni e si y o Se ille. In 2005, he joined o he Depa men o Elec onic Enginee ing, Se ille Uni e si y, wo king on R+D p ojec s. His in e es s include he de elop- men o echniques and algo i hms o imp o e he ene gy quali y om u ili y g id specially ocused o ha monic con en implemen ed on FPGA. Jose I. Leon (S’04, M’07) was bo n in C´ adiz, Spain, in 1976. He ecei ed he B.S. and M.S. and PhD deg ees in elecommunica ions enginee ing om he Uni e si y o Se ille (US), Spain, in 1999, 2001 and 2006 espec i ely. In 2002, he joined he Powe Elec onics G oup, US, wo king in R&D p ojec s. Cu en ly, he is an Associa e P o esso wi h he Depa men o Elec onic Enginee ing, US. His esea ch in e es s include elec onic powe sys ems, modeling, modula ion and con ol o powe con e - e s and indus ial d i es. Ramon Po illo (S’06) was bo n in Se ille, Spain, in 1974. He ecei ed he Indus ial Enginee deg ee om he Uni e si y o Se ille (US), Se ille, Spain, in 2002. He is cu en ly wo king owa d he Ph.D. deg ee in elec ical enginee ing in he Powe Elec- onics G oup, US. In 2001, he joined he Powe Elec onics G oup, US, wo king in R+D p ojec s. Since 2002, he has been an Associa e P o esso wi h he Depa men o Elec onic Enginee ing, US. His esea ch in e es s include elec onic powe sys- ems applied o ene gy condi ioning and gene a ion, powe quali y in enewable gene a ion plan s, applica ions o uzzy sys ems in indus y and wind a ms, and modeling and con ol o powe -elec onic con e e s and indus ial d i es. Leopoldo G. F anquelo (M’84, SM’96, F’05) was bo n in M´ alaga, Spain. He ecei ed he M.Sc. and Ph.D. deg ees in elec ical enginee ing om he Uni e si y de Se ille (US), Se ille, Spain in 1977 and 1980 espec i ely. His cu en esea ch in e es lies on modula ion echniques o mul ile el in e - e s and i s applica ion o powe elec onic sys ems o enewable ene gy sys ems. He was he Vice- P esiden o he Indus ial Elec onics Socie y (IES) Spanish Chap e (2002 - 2003), membe a La ge o he IES AdCom (2002 - 2003). He was he Vice- P esiden o Con e ences o he IES (2004 - 2007), in which he has also been a Dis inguished Lec u e since 2006. He has been an Associa ed Edi o o he IEEE T ansac ions on Indus ial Elec onics since 2007. Since Janua y 2008 he is P esiden Elec o IEEE Indus ial Elec onics Socie y. Miguel A. Agui e (M’97) was bo n in Mad id, Spain in 1963. He ob ained he Mas e deg ee in 1991, in Elec ical and Elec onic Enginee ing by he Uni e si y o Se illa, Spain. He ob ained he PhD deg ee in 1994 in he same Uni e si y. He is cu en ly eaching digi al mic oelec onics in he Elec onic Enginee ing Depa men o he Uni e si y o Se illa, as Assis an P o esso . He is he au ho o mo e han 10 publica ions in he IEEE. He made his hesis in algo i hm and heu is ics o placemen and ou ing in eg a ed, and cu en ly he is wo king in ools o dependable design o in eg a ed ci cui s.