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.
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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.