Con olle Design o a Single-Phase Two-Cell
Mul ile el Cascade H-B idge Con e e
S. Vazquez; J.I. Leon; J.M. Ca asco; L.G. F anquelo; E. Gal an; J.A. Sanchez; E. Domínguez
A da. De los descub imien os s/n; Escuela Supe io de Ingenie os; Uni e si y o Se ille; Se ille 41092; SPAIN
Email: s azquez@g e.esi.us.es; gal an@g e.esi.us.es; ca asco@g e.esi.us.es; lg [email protected] g; egal [email protected];
shanshe@g e.esi.us.es; buge@g e.esi.us.es
Abs ac - In his pape is s udied he single-phase wo-cell
mul ile el cascade H-b idge powe con e e connec ed o he
g id, ac ing as a synch onous ec i ie . The powe exchange
p ocess be ween he cells o he con e e and he g id is analyzed.
Based on his analysis and on he powe con e e model he
s ages o he con olle design p ocess a e shown. A new
con olle o he cascade powe con e e is p oposed, achie ing
he egula ion o each DC-Link capaci o ol age owa ds i s
e e ence. The p oposed con olle includes a epe i i e scheme in
he cu en acking loop, p o iding low cu en ha monic
con en and almos uni y powe ac o . Simula ion esul s ha e
been ca ied ou in a 10 kVA single-phase wo-cell mul ile el
cascade H-b idge powe con e e model o illus a e he good
pe o mance o he p oposed con olle .
Index Te ms— Mul ile el con e e , powe quali y, non-linea
con ol.
I. INTRODUCTION
Mul ile el cascade con e e s, also named cascaded H-
b idge con e e s, we e i s p esen ed in 1988 [1]. Since hen
hey ha e been a ocus o esea che s because hey p esen
se e al ad an ages compa ed wi h o he mul ile el con e e
opologies in e ms o modula i y, simplici y and numbe o
le els wi h minimum numbe o powe semiconduc o s [2]-[4].
Di e en applica ions ha e been de eloped using he
mul ile el cascade con e e : Synch onous ec i ie s [5],
enewable ene gy in eg a ion sys ems [6], in e e s [7],
S a coms [8] and ac i e il e s [9]. Fo each applica ion,
speci ic con ol s a egies ha e been designed, being he DC-
Link ol ages con ol he mos impo an challenge in his
powe con e e opology.
The DC-Link ol ages con ol p oblem is no a i ial issue
in he cascaded mul ile el opology. As in o he mul ile el
con e e s, he ol ages con ol ask can be app oached
h ough modula ion o as a pa o he sys em con olle . When
he modula ion is used o con ol he ou pu ol ages, he
edundan ou pu s a es o he con e e a e used. In [10] his
ac is used o egula e he ou pu s ol ages o he same
e e ence alue. When he con ol app oach is used, a speci ic
con ol has o be designed o ca y ou he ol ages con ol
ask. Due o his mul iple signals a e needed, one o each H-
b idge, making he con olle design mo e complex. Howe e
he ad an age is ha he ou pu ol age e e ences can be se
independen ly. Se e al s a egies o achie e he ol age
balance can be ound in he li e a u e such as a passi i y
con ol s a egy [11], non-linea con ol s a egy [12], and
s a egies based on PI con olle s [13].
In his pape he con olle app oach will be conside ed. To
de elop he con olle design he powe exchange p ocess
be ween he cells o he cascade con e e and he g id is
analyzed. F om his analysis, he powe low limi s as a
unc ion o he ou pu ol age alues will be poin ed ou , and
inally he con olle exp ession is de i ed.
II. SYSTEM DESCRIPTION
A single-phase wo-cell mul ile el cascade H-b idge powe
con e e (CHB) is depic ed in Fig. 1. The sys em is connec ed
o he g id h ough a smoo hing induc o L, and i is assumed
ha pu e esis i e loads R1 and R2 a e connec ed o each DC-
Link capaci o C1 and C2 espec i ely. The sys em pa ame e s
and a iables a e desc ibed in TABLE I, whe e he con inuous
con ol signals d1 and d2, which ep esen he swi ching
unc ions ha e been de ined.
1
S
1
S
2
S
2
S
4
S
4
S
3
S
3
S
Fig. 1 Single-phase wo cell mul ile el cascade H-B idge con e e
TABLE I
SYSTEM PARAMETERS
Pa ame e Desc ip ion
L Induc ance
C1; C2 Capaci ances
R1; R2 Resis i e loads
is( ) G id cu en
s( ) G id ol age
iR1; iR2 Load cu en s
Vdc1; Vdc2 Capaci o ol ages
d1;d2 ò [−1, 1] Con ol signals
The equa ions ha desc ibe he CHB beha io a e well
known and hey ha e been epo ed in se e al p e ious wo ks
[14], hese equa ions a e
m11dc1
V
=d (1)
m22dc2
V
=d (2)
s
sm1m2
di
L
d
=++ (3)
22
dc1dc1
m1s1
1
2
VV
d
iC
d R
æö
=+
ç÷
èø (4)
22
dc2dc2
m2s1
2
2
VV
d
iC
d R
æö
=+
ç÷
èø (5)
In hese equa ions he con ol signals m1 and m2 de ined in
(1) and (2) ha e been in oduced. These signals ep esen he
ol ages ha a e modula ed in each cell. The equa ion ha
ep esen s he inpu cu en dynamic is (3) and he ou pu
capaci o DC ol ages dynamics a e (4) and (5).
To analyze he con olle design s ages, he powe exchange
be ween he cells o a cascade con e e and he g id has o be
s udied. Fo his pu pose he powe con e e ep esen a ion o
Fig. 2 is used. In his ep esen a ion he cells ha e been
eplaced by ol age sou ces wi h alues equal o he
ins an aneous ol ages modula ed by he cells, m1 and m2
espec i ely. The ac i e and eac i e powe consumed o
injec ed by each cell depend on he shi angle be ween he
cu en is, and he modula ed ol age in he cell ( mi). This can
be analyzed using he phaso ial diag am o he cascade powe
con e e ep esen ed in Fig. 3.
Now he ollowing assump ions a e made:
(i) The ol ages dc1 and dc2 a e lowe han he peak alue o
s
(ii) Cell 1 and cell 2 consume ac i e powe , and no eac i e
powe is d awn om he g id.
Fig. 2 CHB ep esen a ion h ough ol age sou ces
Fig. 3 CHB phaso ial diag am o ol ages and cu en
Fo a gi en powe consump ion p1 and p2 in each DC-Link,
he heo e ical e e ence ol ages o each H-b idge can be
de e mined. The o al amoun o ac i e powe ha has o be
d awn om he g id is
T1212
;0;0
ppppp
=+>>
(6)
The necessa y g id cu en and he associa ed induc o d op
( L) can be hen calcula ed and he e o e he ol age ha
should be modula ed be ween he poin s ab o he con e e
can be de e mined.
T
ss
2
sRMS
p
i
= (7)
s
L
d
di
L= (8)
absL
=-
(9)
The ol age ab is composed by he sum o he ou pu ol age
o he cells, m1 and m2. Fo his eason, he DC-Link capaci o
ol age alues a e cons ain s ha should be conside ed when
he load is applied, because only ce ain phaso s composi ions
a e allowed. Fig. 4 shows he phaso s o all ol ages in ol ed.
The se o poin s ha can be eached o a gi en DC-Link
capaci o ol age alues is ep esen ed using a ma ke egion.
An example o alid poin is shown in Fig. 4a. Any poin
ou side o his egion would make he sys em uns able because
he e e ence ol age o one cell o bo h can no be modula ed
wi h he ac ual alues o he DC-Link capaci o ol ages as is
shown in Fig. 4b.
1
>
0
;
2>0
s s
ab
dc1
dc2
m1
m2
ds
d
s s
ab
dc1
dc2
m1
m2
ds
d
a b
Fig. 4 Re e ence ol age be ween poin s ab. a) Solu ion inside he eachable
egion b) Solu ion ou side he eachable egion
Fo a gi en o al amoun o powe pT, he alues o powe
ha can be consumed in each cell can no be chosen eely.
Fig. 5a and Fig. 5b show he minimum alue o ac i e powe
ha should be consumed in cell 1 and cell 2 espec i ely, o
main ain he sys em s abili y.
Among he possible solu ions, only hose poin s whe e he
ac i e powe consumed by each cell co esponds wi h p1 and p2
espec i ely a e alid solu ions o he sys em. Fo ins ance,
om p1 i is possible o calcula e he p ojec ion o m1 o e is as
1
m1p
s
RMS
p
i
= (10)
1
>
0
;
2>0
s s
ab
dc1
dc2
m1p m2p
ds
d
s s
ab
dc1
dc2
m1p m2p
ds
d
a b
Fig. 5 Minimum alues o ac i e powe mus be consumed by he cells o a
consumed o al amoun o ac i e powe pT. a) Minimum alue o p1. b)
Minimum alue o p2
This ac leads o calcula e he alue o he p ojec ion o m2
o e is, and o de e mine he possible poin s o ob ain a alid
solu ion. These poin s a e loca ed o e he line o hogonal o s
placed a dis ance m1p om he o igin. The alid solu ions a e
he poin s which simul aneously belong o ha line and a e
inside he se o poin s ha can be eached wi h he DC ol age
alues in cell 1 and 2. Fig. 6 shows he se o possible solu ions
o powe consump ion p1 and p2, which a e loca ed be ween
he poin s MN.
m1p m2p
M
N
1>0 ;
2>0
ds
d
ab
s s
dc1
dc2
Fig. 6 Se o possible solu ions o p1 and p2
I is wo h poin ing ou ha he e is no a single solu ion o
he sys em. The only es ic ion is ha he solu ion has o be
loca ed be ween poin s MN, and he e o e he e is one deg ee
o eedom which can be used o op imize he con e e
beha io and design. Fig. 7 shows wo possible solu ions o
he sys em. Bo h solu ions lead o he same esul d awing
ac i e powe p1 and p2. The only di e ence is he eac i e
powe alue deli e ed o consumed by each cell.
III. CONTROLLER DESIGN
To design he con olle wo ac s mus be conside ed, he
o al ol age egula ion and he ol ages a io. The o al ol age
egula ion is ela ed wi h he sum o he DC-link capaci o
ol ages, and he ol ages a io is de ined as he a io be ween
he DC-link capaci o ol ages o he cells o he con e e ,
meaning o ins ance ha i DC ol age a io is k:1 in a wo-
cell CHB, hen dc1=k· dc2.
1
>
0
;
2>0
s s
ab
dc1
dc2
m1p m2p
m1
m2
ds
d
s s
ab
dc1
dc2
m1p m2p
m1
m2
ds
d
a b
Fig. 7 Two possible solu ions o achie e he same ac i e powe consump ion p1
and p2 in each cell espec i ely.
Fo he con ol law design, i is assumed ha he swi ching
equency is high enough o conside he con ol signal as a
con inuous signal. Due o his ac he a e aged model o he
sys em can be used o de elop he con olle . Also i is
assumed ha he cu en dynamic is as e han he ol age
egula ion and a io dynamics o a CHB con e e . Finally he
con ol design is spli in h ee s ages:
(i) Vol age egula ion con ol loop, which ensu es capaci o
ol age egula ion owa ds i s e e ence. The ou pu o his
loop is he cu en e e ence.
(ii) Cu en con ol loop, which ensu es induc o cu en
acking owa ds i s e e ence. The ou pu o his con olle is
he con ol signal u= m1+ m2.
(iii) Vol age a io con ol loop, which ensu es capaci o ol age
a io owa ds i s e e ence. The ou pu o his con olle a e he
con ol signals m1 and m2.
The con ol objec i es a e:
(i) Regula e he capaci o ol ages o he desi e alues V*
dc1
and V*
dc2
(ii) Achie e induc o cu en wi h high quali y ha monic
con en and main ain he powe ac o as close o uni y as
possible.
A. Vol age egula ion con ol loop
The a e aged pa o equa ions (4) and (5) can be used o
ob ain he necessa y inpu ac i e powe o egula e he DC-
Link ol ages.
2
dc1
1
2
dc2
2
2
2
V
z
V
z
=
=
(11)
In oducing he a iables z1 and z2, equa ions (4) and (5) a e
ans o med in
11
11
1
2
dzz
pC
d R
=+ (12)
22
22
2
2
dzz
pC
d R
=+
(13)
Equa ions (12) and (13) a e well-known LTI sys ems, hus
he alues o p1 and p2 can be calcula ed h ough a PI con olle
as in [15], yielding o he ollowing exp essions
p1 i1
111
s1
kk
pzz
ss
=+
+
%%
(14)
p2 i2
222
s2
kk
pzz
ss
=+
+
%%
(15)
Con olle s (14) and (15) include a low pass il e in he
p opo ional e m o educe he high equency noise, he
pa ame e s kp1, 1, ki1, kp2, 2 and ki2 a e design posi i e non-
ze o cons an s and he e o and he e e ences alues a e
calcula ed as
( )
( )
1
2
*
111
*
222
2
*
dc1
*
2
*
dc2
*
2
2
zzz
zzz
V
z
V
z
=-
=-
=
=
%
%
(16)
The o al amoun o ac i e powe ha he ol age sou ce
should p o ide is he sum o p1 and p2, and hen he cu en
e e ence can be calcula ed as
(
)
12
*
RMS
RMS
** s
RMS
RMS
pp
i
ii
+
=
=
(17)
B. Cu en con ol loop
Equa ion (3) ep esen s he induc o cu en dynamic, o
simpli y he con ol design p ocess he con ol signal u is
de ined as
m1m2
u
=+ (18)
Thus he induc o cu en dynamic is ans o med in
s
s
di
Lu
d
=+
(19)
Equa ion (19) is equal han he cu en dynamic equa ion o
he single-phase H-B idge con e e and he h ee-phase wo-
le el powe con e e . Se e al linea and non-linea con olle s
ha e been p oposed o achie e he cu en acking in hose
powe con e e s, in [16]-[17] a epe i i e con ol scheme is
p oposed o he cu en acking p ocess, and in his wo k he
same solu ion is adop ed.
spcs s
1
1
s
s
Ke
u kiki
Ke
p
-
w
p
-
w
æö
-×
ç÷
=+×+
ç÷
ç÷
+×
èø
%%
(20)
*
sss
iii
=-
%
(21)
The pa ame e s kpc, k and K a e posi i e non-ze o design
cons an s. Equa ion (20) is he exp ession o he con ol signal
u and (21) is he cu en e o de ini ion. In (20) he
p opo ional e m adds damping o he con olle o ensu e
s abili y and he epe i i e e m ep esen s an es ima ion o *
L.
*
*
L
s
di
L
d
= (22)
C. Vol age a io con ol loop
As i is shown in sec ion II, he ol age modula ed by each
cell ( mi) oge he wi h he g id cu en mus p o ide he ac i e
powe and he eac i e powe demanded by he cell. The ac i e
powe demand is sa is ied when he p ojec ion o m1 and m2
o e is a e de ined espec i ely as
s
1
m1p *
RMS
RMS
p
i
=× (23)
s
2
m2p *
RMS
RMS
p
i
=× (24)
Besides, o achie e uni y powe ac o he eac i e powe
deli e ed by he cells mus be equal o he eac i e powe
demanded by he smoo hing induc o . In addi ion, o ensu e
cu en acking (20) mus be sa is ied. To ca y ou all hese
cons ain s he e e ence ol ages in each cell a e de ined as
m1m1ppc1s1 s
1
1
s
s
Ke
kikki
Ke
p
-
w
p
-
w
æö
-×
ç÷
=+×+
ç÷
ç÷
+×
èø
%%
(25)
m2m2ppc2s2 s
1
1
s
s
Ke
kikki
Ke
p
-
w
p
-
w
æö
-×
ç÷
=+×+
ç÷
ç÷
+×
èø
%%
(26)
whe e he ollowing es ic ion mus be sa is ied
12
1
kk
+=
(27)
pc1pc2pc
kkk
+=
(28)
whe e he pa ame e s kpc1, k
pc2, k1 and k2 a e posi i e non-
ze o design cons an s. The cons ans k1 and k2 ep esen how he
eac i e powe is sha ed be ween he cells.
IV. SIMULATION RESULTS
In his sec ion simula ion esul s a e shown in o de o es
he p oposed con olle using a p o o ype. Fo his pu pose he
single-phase wo-cell mul ile el cascade H-b idge powe
con e e has been conside ed. The expe imen consis s o a
load s ep om no-load o ull load, including di e en
capaci o ol ages e e ence. To modula e he e e ence ol age
a phase-shi ed PWM s a egy has been used. To assess he
con olle pe o mance, measu emen s o DC-Link capaci o
ol ages, g id ol age and cu en s a e ep esen ed. TABLE II
shows he elec ical pa ame e s o he powe con e e ,
swi ching and sampling equencies ha ha e been used in he
model.
Fig. 8 shows he ob ained esul s o he comple e
expe imen pe iod. The expe imen has h ee s eps. In he i s
s ep, he DC-Link capaci o ol age e e ences a e se o 200V
in bo h cells. Once he e e ence is achie ed, a load s ep is
in oduced connec ing a 20W esis o in each DC-Link.
TABLE II
ELECTRICAL PARAMETERS OF THE SYSTEM
G id Vol age 230 V
G id equency 50 Hz
Smoo hing induc ance 1 mH
DC-Link capaci o C1 4700 µF
DC-Link capaci o C2 4700 µF
Swi ching equency 10 KHz
Sampling equency m 10 kHz
The second s ep is ca ied ou when he s eady s a e is
eached, and hen he DC-Link capaci o ol age e e ence o
he cell 1 is se o 300V. Finally, he hi d s ep is in oduced
when cell 1 achie es i s e e ence, in his momen he DC-Link
capaci o ol age e e ence o cell 2 is se o 100V. As i can be
seen in Fig. 8 he p oposed con ol s a egy is capable o
egula e each DC-Link capaci o ol ages o he desi ed alues,
and o con ol he g id cu en .
F om Fig. 9 and Fig. 10 i is demons a ed ha he p oposed
con olle has good pe o mance in ansien and s eady s a e
condi ions when a load s ep is applied. When a e e ence DC
ol age s ep is applied in any cell he same good beha io is
ob ained as is shown in Fig. 11 and Fig. 12.
Fig. 9a shows he DC-Link capaci o ol ages ansien
esponse when he loads a e connec ed and he ol age
e e ences a e 200V. Fig. 9b shows he co esponding g id
cu en and ol age. Fig. 10a shows he DC-Link capaci o
ol ages in s eady s a e. I can be no iced ha he e e ences a e
achie ed, he 100 Hz ipple in he ol ages is due o he ac i e
powe consump ion. Fig. 10b shows he g id ol age and
cu en in s eady s a e. I can be obse ed ha he g id cu en
has high quali y and is almos in phase wi h he g id ol age.
Fig. 11a shows he DC-Link capaci o ol ages ansien
esponse when he e e ence o cell 1 is changed om 200V o
300V and he e e ence o cell 2 is main ained in 200V. I can
be no iced ha in a ew g id cycles he e e ence is achie ed,
and he ol age in cell 2 is almos no a ec ed by he e e ence
change in cell 1. In Fig. 11b i can be obse ed ha he g id
cu en inc eases un il he DC-Link capaci o ol age is
s abilized in he new e e ence alue.
Fig. 12 shows simila esul compa ed wi h Fig. 11 when he
e e ence o he cell 2 is changed om 200V o 100V and he
e e ence o he cell 1 is main ained in 300V.
V. CONCLUSIONS
In his pape a single-phase wo-cell mul ile el cascade H-
b idge powe con e e connec ed o he g id, ac ing as a
synch onous ec i ie is s udied. F om he analysis o he powe
exchange p ocess be ween he cells o he con e e and he
g id, i is demons a ed ha o a gi en o al ac i e powe
consump ion he ac i e powe sha ing be ween he cells can
no be chosen eely. The con olle design s ages a e shown,
and ollowing hese s ages a con olle is p oposed, using in he
cu en acking loop a epe i i e con ol scheme. Simula ion
esul s ha e been de eloped and i has been e i ied ha he
p oposed con olle p o ides DC-Link capaci o ol ages
egula ion and a io con ol. Besides he p oposed epe i i e
scheme p o ides cu en wi h low ha monic con en and also i
is capable o achie e almos uni y powe ac o , p o iding a
e y good pe o mance o he o e all sys em.
Fig. 8 Cu es o he comple e expe imen pe iod. a) dc1 and dc2 b) is
Fig. 9 Capaci o ol ages and g id cu en ansien s wi h DC ol age
e e ences equal o 200V o bo h cells. a) dc1 and dc2 b) s, and is
Fig. 10 Capaci o ol ages and g id cu en de ails in s eady s a e, wi h DC
ol age e e ences equal o 200 V o bo h cells. a) dc1 and dc2 b) s, and is

Fig. 11 Capaci o ol ages and g id cu en ansien s wi h DC ol age
e e ences equal o 300V o cell 1 and 200 V o cell 2. a) dc1 and dc2 b) s,
and is
Fig. 12 Capaci o ol ages and g id cu en ansien s wi h DC ol age
e e ences equal o 300V o cell 1 and 100 V o cell 2. a) dc1 and dc2 b) s,
and is
ACKNOWLEDGMENT
This wo k has been de eloped hanks o he inancial
suppo o Spanish Go e nmen wi hin he esea ching p ojec
TEC2006-03863.
REFERENCES
[1] M. Ma chesoni, M. Mazzucchelli and S. Tenconi, “A non Con en ional
Powe Con e e o Plasma S abiliza ion,” in Powe Elec onics
Specialis Con e ence 1988 (PESC’88), pp. 122–129, 11-14 Ap il 1988.
[2] J. Rod iguez, Jih-Sheng Lai and Fang Zheng Peng, “Mul ile el in e e s:
a su ey o opologies, con ols, and applica ions”, IEEE T ansac ions on
Indus ial Elec onics, Volume 49, Issue 4, pp. 724 – 738, Augus 2002.
[3] Y. Cheng, C. Qian, M.L. C ow, S. Peka ek and S. A ci y, "A
Compa ison o Diode-Clamped and Cascaded Mul ile el Con e e s o
a STATCOM Wi h Ene gy S o age," IEEE T ansac ions on Indus ial
Elec onics, ol. 53, no. 5, pp. 1512-1521, Oc obe 2006.
[4] M.E. O uza , R.E. Ca mi, J.W. Dixon and L. Mo an, "Vol age-sou ce
ac i e powe il e based on mul ile el con e e and ul acapaci o DC
link," IEEE T ansac ions on Indus ial Elec onics, ol. 53, no. 2, pp.
477- 485, Ap il 2006.
[5] Lin, B.-R.; Lu, H.-H.; “New mul ile el ec i ie based on se ies
connec ion o H-b idge cell” Elec ic Powe Applica ions, IEE
P oceedings- ol 147, no 4, pp 304 – 312 July 2000
[6] Alonso, O.; Sanchis, P.; Gubia, E.; Ma oyo, L.; “Cascaded H-b idge
mul ile el con e e o g id connec ed pho o ol aic gene a o s wi h
independen maximum powe poin acking o each sola a ay” in
Powe Elec onics Specialis Con e ence 2003 (PESC’03), ol 2, pp 731
– 735, 15-19 June 2003
[7] Lezana, P.; Sil a, C.A.; Rod iguez, J.; Pe ez, M.A.; “Ze o-S eady-S a e-
E o Inpu -Cu en Con olle o Regene a i e Mul ile el Con e e s
Based on Single-Phase Cells” IEEE T ansac ions on Indus ial
Elec onics, ol 54,no 2, pp 733 – 740,Ap il 2007
[8] Ba ena, Jon Andoni; Ma oyo, Luis; Rod iguez, Miguel Angel; Alonso,
Osca ; To ealday, Jose Ramon; “DC Vol age Balancing o PWM
Cascaded H-B idge Con e e Based STATCOM”; in IEEE Indus ial
Elec onics Con e ence(IECON06), pp 1840 – 1845, No embe . 2006
[9] Escoba , G.; Ma inez-Mon ejano, M.F.; Ma inez-Rod iguez, P.R.;
He nandez-Gomez, M.; “A model-based con olle o he cascade h-
b idge mul ile el con e e used as a shun ac i e il e ”; in Powe
Elec onics Specialis Con e ence 2006 (PESC’06), pp 1-5, 18-22 June
2006
[10] Ceca i, C.; Dell'Aquila, A.; Lise e, M.; Monopoli, V.G.; “Design o H-
b idge mul ile el ac i e ec i ie o ac ion sys ems” IEEE T ansac ions
on Indus y Applica ions, Vol 39,no 5,, pp 1541-1550, Sep embe .-Oc
2003
[11] Dell'Aquila, A.; Lise e, M.; Monopoli, V.G.; Ro ondo, P.; “Two
passi i y-based app oaches o he con ol o he H-b idge-based
mul ile el ec i ie ”; in IEEE Indus ial Elec onics Con e ence 2003
(IECON03) Vol 2, pp 1191 – 1196, 2-6 No embe . 2003
[12] So o, D.; Pena, R.; “Nonlinea con ol s a egies o cascaded mul ile el
STATCOMs”; IEEE T ansac ions on Powe Deli e y, Vol 19, no 4, pp
1919 – 1927, Oc obe . 2004
[13] Dell'Aquila, A.; Lise e, M.; Monopoli, V.G.; Ro ondo, P.; “O e iew o
PI-based solu ions o he con ol o he dc-buses o a single-phase H-
b idge mul ile el ac i e ec i ie ”; Applied Powe Elec onics
Con e ence and Exposi ion, 2004 (APEC04). Vol 2, pp 836 – 842, 22-26
Feb ua y 2004
[14] Dell'Aquila, A.; Lise e, M.; Monopoli, V.G.; Ro ondo, P.; “An Ene gy-
Based Con ol o an n-H-B idges Mul ile el Ac i e Rec i ie ”, IEEE
T ansac ions on Indus ial Elec onics, Volume 52, 3, pp. 670 – 678,
June 2005.
[15] G. Escoba , A.M. S anko ic, J.M. Ca asco, E. Gal an and R. O ega,
“Analysis and design o di ec powe con ol (DPC) o a h ee phase
synch onous ec i ie ia ou pu egula ion subspaces”, IEEE
T ansac ions on Powe Elec onics, Vol. 18, Issue 3, pp. 823-830, May
2003
[16] Escoba , G.; O ega, R.; As ol i, A.; Ma inez, M.F.; Ley a-Ramos, J,
“A epe i i e based con olle o a shun ac i e il e o compensa e o
eac i e powe and ha monic dis o ion”, Con e ence on Decision and
Con ol, 2005 and 2005 Eu opean Con ol Con e ence. (CDC-ECC '05),
pp. 6480 – 6485, 12-15 Decembe . 2005
[17] J.A. Sanchez, S. Vazquez, G. Escoba , J.M. Ca asco, E. Gal an, E.
Dominguez, M. Reyes, “Digi al Implemen a ion Issues o a Th ee-
Phase Powe Con e e De elopmen Using a Repe i i e Con ol
Scheme”, in In e na ional Symposium on Indus ial Elec onics 2007
(ISIE07), pp 1-6, 4-7 June 2007