ene gies
A icle
In eg a ed Con ol and Modula ion o Th ee-Le el
NPC Rec i ie s
An onio Ven osa-Cu illas 1,* , Pablo Mon e o-Robina 1, F ancisco Umb ía 2,
Fede ico Cues a 1and F ancisco Go dillo 1
1Depa amen o de Sis emas y Au omá ica, Escuela Técnica Supe io de Ingenie ía, Uni e sidad de Se illa,
41092 Se illa, Spain; [email p o ec ed] (P.M.-R.); [email p o ec ed] (F.C.); [email p o ec ed] (F.G.)
2ASM Assembly Sys ems GmbH & Co. KG, 81379 Munich, Ge many; [email p o ec ed]
*Co espondence: [email p o ec ed]; Tel.: +34-95-448-2292
Recei ed: 8 Ap il 2019; Accep ed: 26 Ap il 2019; Published: 30 Ap il 2019


Abs ac :
This pape uses a no el app oach o he con ol o h ee-le el neu al-poin -clamped
(NPC) ec i ie s in o de o ackle he capaci o ol age balance p oblem. A dis inc i e ea u e o he
new con ol app oach is ha i is based on a model which is w i en in e ms o he du y a ios o each
phase a each le el. Hence, he sys em model p esen s nine du y cycle a iables. Despi e he ac ha
his o mula ion is di e en om he usual ones, i is shown ha he con ol p oblem o cu en s and
dc-link ol age can be o mula ed in a simila way o con en ional me hods. Fu he mo e, he con ol
o he capaci o ol age balance can be exp essed by means o equa ions ha a e decoupled om he
cu en s and dc-link ol age dynamics, which esul s in a speci ic con olle o he ol age balancing
ha does no a ec he p e ious dynamics. A key poin o he p oposed app oach is ha pa o he
modula ion s age is implici in he o mula ion. Two pa icula con olle s a e compa ed in his pape .
The i s one ul ills he di e en con ol objec i es a he expense o a la ge numbe o commu a ions.
This p oblem is o e come in a new p oposed con olle , which p esen s simila pe o mance and a
sa is ac o y numbe o commu a ions. Expe imen al esul s a e pe o med showing he e ec i eness
compa ed wi h a modi ied i ual space ec o modula ion wi h capaci o ol age balance capabili ies.
Keywo ds:
synch onous ec i ie applica ion; neu al-poin -clamped (NPC) con e e ; ol age balancing;
in eg a ed con ol and modula ion (ICM); G id-connec ed powe con e e ; mul ile el con e e s
1. In oduc ion
In he ield o ene gy con e sion sys ems, he ad an ages ha mul ile el powe elec onic
con e e s o e a e well known. Bidi ec ional powe low, inc ease o he ou pu ol age magni ude,
obus ness, e c. a e only some o he ad an ages ha ha e made mul ile el con e e s popula
in medium and high powe applica ions in he indus y [
1
–
3
]. Some o he di e en ypes o
opologies o hese con e e s a e neu al-poin -clamped, cascaded H-b idge o lying-capaci o [
1
,
2
,
4
].
A Neu al-poin -clamped (NPC) con e e , which was p oposed o he i s ime in [
5
], is one o he
mos used mul ile el con e e opologies. Du ing no mal ope a ion, he ol age ha d ops ac oss
each capaci o mus be balanced o he wise, i can esul in poo ou pu ol age quali y, a ec ing he
pe o mance o he con ol o e en damaging he semiconduc o de ices. The e o e, NPC con e e s
p esen an addi ional objec i e apa om he usual con ol objec i es in powe con e e s [
6
] ha is
he ol age balance be ween capaci o s, which is he main ocus in his pape .
O e he las ew yea s, nume ous echniques ha e been de eloped o co ec he ol age
unbalance. Some o hem use addi ional ci cui y [
7
–
9
], bu his would lead o an inc ease in cos ,
losses and complexi y in ha dwa e. O he au ho s use di e en con ol echniques wi h algo i hms o
a ying di icul y [
10
–
15
]. One o hese con ol echniques [
13
] uses a modi ica ion o i ual space
Ene gies 2019,12, 1641; doi:10.3390/en12091641 www.mdpi.com/jou nal/ene gies
Ene gies 2019,12, 1641 2 o 15
ec o [
16
] (deno ed as mVSVPWM in his pape ). In [
13
], he ol age e e ence ec o is ob ained
by c ea ing i ual ec o s whe e he possible swi ching s a es a e weigh ed o gene a e cu en s ha
bene i he ol age balance.
Rega ding he modelling, i is usual o wo k wi h a e aged models whe e he disc e e alues
o he ga ing elemen s a e conside ed as con inuous signals [
1
,
17
]. In o de o implemen he con ol
laws ob ained wi h such models, a disc e iza ion s age, usually called modula ion, needs o be
accomplished [
18
]. Modula ion plays an impo an ole in he o e all sys em pe o mance since
p ope ies such as numbe o commu a ions and ha monic dis o ion o cu en s and ol ages a e
a ec ed by he way modula ion is ca ied ou . Modula ion me hods can be classi ied in o h ee main
g oups [
19
]: pulse wid h modula ion (PWM) [
20
,
21
], pseudo-modula ion [
22
] and closed-loop con ol
me hods wi h implici modula o [23–25].
This pape p esen s a new app oach o deal wi h he con ol o h ee-le el NPC con e e s, which
is based on [
26
]. In his pape , he ci cui model is o mula ed in e ms o he du y a ios o each phase
a each le el. In his way, he e a e nine du y cycle a iables ( h ee du y cycles pe phase) ins ead o
jus h ee (one du y cycle pe phase). This o mula ion is no new, e.g., a simila model, based on d–q
ans o ma ion, was p esen ed in [
27
] o design an LQR con olle o an NPC in e e by linea iza ion
using a small-signal model. In [
26
], i is shown ha his o mula ion allows o explici ly conside ,
in he con ol design s age, he ex a deg ee o eedom associa ed wi h he injec ion o homopola
componen . The inc ease in he numbe o a iables does no make he design signi ican ly mo e
di icul since, wi h an app op ia e change o a iables, he dc-link ol age and ac i e and eac i e
powe con ol p oblems can be o mula ed in a simila way o o he usual app oaches. As a esul ,
he ol age balance con olle can be easily designed a he same ime ha an impo an pa o
modula ion is no needed. Fo his, he p oposed app oach can be conside ed as a con ol me hod wi h
pa o he modula ion s age included in he con ol o mula ion, he e o e, in wha ollows i would
be called “In eg a ed Con ol and Modula ion” (ICM). The main ad an age o he p oposed con ol
law is i s simplici y in implemen a ion compa ed o modi ied e sions o space ec o modula ion
(SVM) [
16
] ha also ackle he capaci o ol age unbalance bu i s ill p esen s some ad an ages
wi h espec o CB-PWM app oaches. This is due o he ac ha he modula ion s age is simpli ied
wi hou losing pa o he lexibili y o SVM [
28
,
29
]. Once he nine du ies a e compu ed, he way
hey a e sequenced can be chosen eely, spli ing hem up o shi ing hem among he di e en
phases. This eedom allows he use o achie e seconda y con ol objec i es simila ly o SVM such
as common-mode ol age educ ion o a oidance o ex a swi ching losses. Fo he sake o a ai
compa ison, his a icle will use a simple iangula -shaped sequence simila o ha o CB-PWM
app oaches. Fu he mo e, he p oblem o mula ion o powe , cu en and dc-link ol age con ol is
he same as when using o he con en ional app oaches, such as model-based di ec powe con ol
(DPC) [30–33] o p opo ional- esonan con olle (PR) o cu en s [34,35].
The d awback o he p oposed app oach in [
26
] is ha i may lead o an unnecessa y inc ease
in he numbe o commu a ions. This is due o he ac ha , unless some o he du y cycle a iables
u n ou o be ze o, he esul an swi ching signals will commu e among all he le els o he h ee
phases e e y sampling pe iod. This is he case o he i s con ol law conside ed in his pape (ICM1),
whe eas wi h he dc-link ol age, cu en o powe con ol can be accomplished by swi ching each
phase be ween wo le els [
36
] when he ol age balance p oblem is no conside ed. In his pape ,
by using a emaining deg ee o eedom associa ed wi h he injec ion o homopola componen ,
some commu a ions a e a oided compa ed o ICM1 p esen ing a second con olle (ICM2) who
explodes his capabili y. The ou pu wa e o m o ICM2, as i will be shown la e on in expe imen s,
is simila o hose app oaches which injec a hi d ha monic signal in o he ou pu ol age o inc ease
he undamen al signal ange wi hou o e modula ing [
37
]. The e o e, ICM2 also has his p ope y
inhe en wi hou he need o ex a compu a ions.
Bo h con ol laws a e alida ed by means o expe imen s and compa ed wi h a con ol echnique
based on a modi ied i ual space ec o modula ion (mVSVPWM) [
13
], which includes capaci o
Ene gies 2019,12, 1641 3 o 15
ol age balance capabili ies. The e o e, he main con ibu ions o his pape in compa ison wi h [
26
]
a e he inclusion o a new app oach (ICM2) along wi h expe imen al e i ica ion o bo h app oaches.
The nex sec ion is de o ed o p esen ing he con e e conside ed in his pape , as well as i s
dynamic model. Sec ion 3p esen s he con olle design o ul illing he h ee con ol objec i es:
egula ion o he cu en s and he dc-link ol age and capaci o ol age balance. Sec ion 4p oposes
wo a ian s o he selec ion o he emaining deg ees o eedom esul ing in wo di e en con olle s,
ICM1 and ICM2. Sec ion 5p esen s expe imen al esul s. The pape closes wi h a sec ion o conclusions.
2. Dynamic Model o he Sys em
The con igu a ion o he con e e used in his pape is a h ee-phase h ee-le el NPC con e e
in ec i ie mode wi h a esis i e load, as shown in he scheme o Figu e 1.
Figu e 1. Schema ic diag am o he h ee-phase h ee-le el neu al-poin -clamped (NPC) ec i ie .
The elec ical powe g id is conside ed as a h ee-phase ol age sou ce, whe e he phase ol ages
a e ep esen ed by
sa
,
sb
and
sc
. The con e e is connec ed o he g id h ough an induc i e il e
whe e induc ances ha e he same alue L.
On he dc-link side, capaci o s ha e he same alue
C
and hei ol ages a e deno ed by
c1
and
c2
. Connec ed o he con e e e minals he e is a esis i e load
R
. The o al dc-link ol age is de ined
as dc = c1+ c2.
Conside ed Sys em Model
The model conside ed in his pape is desc ibed in [
26
], which is based on a model p esen ed
in [
27
]. This model uses he equa ions in
αβγ
coo dina es by in oducing he powe -in a ian o m
o he Cla ke T ans o m. Fu he mo e, he swi ching signals ha e been eplaced by hei espec i e
du y a ios in each le el [
27
,
38
],
dij
wi h
i=α
,
β
,
γ
and
j=p
,
o
,
n
, whe e
p
is he posi i e le el when
swi ches
Si
1
and
Si
2
a e closed,
o
is he ze o le el when swi ches
Si
1
and
Si
2
a e closed and
n
is he
nega i e le el when swi ches Si
1and Si
2a e closed. This o mulism yields
Ldiα
d = sα−(dαp−dαn) dc
2−(dαp+dαn) d
2(1)
Ldiβ
d = sβ−(dβp−dβn) dc
2−(dβp+dβn) d
2(2)
Cd dc
d = (dαp−dαn)iα+ (dβp−dβn)iβ−2 dc
R(3)
Cd d
d = (dαp+dαn)iα+ (dβp+dβn)iβ, (4)
Ene gies 2019,12, 1641 4 o 15
whe e
d
is he dc-link capaci o ol age di e ence de ined by
d= c1− c2
. The con ol inpu s
dαp
,
dαn
,
dβp
and
dβn
a e he du y a ios in
αβγ
coo dina es. Con ol inpu s
dγp
and
dγn
do no appea in
he model, as men ioned in [
26
], because hey a e mul iplied by
iγ
, whose alue is ze o o a balanced
sys em. Simila ly, a iables
dio
do no appea in his model bu hei alues can be e ie ed a he
inal s age o he con olle using he ollowing cons ain s:
dap +dao +dan =1 (5)
dbp +dbo +dbn =1 (6)
dcp +dco +dcn =1 (7)
dij ∈[0, 1], o i=a,b,cand j=p,o,n.
Phase cu en s iαand iβcan be exp essed in e ms o powe s as
iα=1
2
sα+ 2
sβ sαp− sβq(8)
iβ=1
2
sα+ 2
sβ sβp+ sαq, (9)
whe e
p
and
q
a e he ins an aneous ac i e and eac i e powe s o he sys em, espec i ely. In his
way, (3) and (4) could be exp essed as
Cd dc
d =1
2
sα+ 2
sβdαp−dαn sαp− sβq+1
2
sα+ 2
sβdβp−dβn sβp+ sαq−2 dc
R(10)
Cd d
d =1
2
sα+ 2
sβdαp+dαn sαp− sβq+1
2
sα+ 2
sβdβp+dβn sβp+ sαq, (11)
whe e a iables dc and da e exp essed in e ms o he ins an aneous powe pand q.
3. Con olle Design
Wi h he pu pose o dealing wi h he h ee con ol objec i es (cu en s, dc-link ol age and
capaci o ol age balance con ol), he sys em dynamic model
(1)
–
(4)
p esen ed p e iously is
conside ed o design he con olle s in his sec ion. I can be seen ha he p oposed modeling allows
o cope wi h he capaci o ol age balance p oblem while i does no a ec he cu en and dc-link
ol age con olle s.
3.1. To al DC-Link Vol age Con olle
In o de o main ain cons an he dc-link ol age and close o i s e e ence (
dc
), as usual, a PI
con olle is used [26,30,39],
p =kdc
p
dc
2− 2
dc+kdc
iZ
0
dc
2− 2
dcdτ, (12)
whe e cons an s kdc
pand kdc
ia e con olle uning pa ame e s.
Ene gies 2019,12, 1641 5 o 15
3.2. Cu en Con olle
Obse ing Equa ions (1) and (2), wo i ual con ol a iables can be de ined as
u1˙=dαp−dαn(13)
u2˙=dβp−dβn. (14)
In oducing hese a iables in o he cu en s dynamic model and assuming ha he alue o a iable
dis small enough o be neglec ed,
Ldiα
d = sα−u1
dc
2(15)
Ldiβ
d = sβ−u2
dc
2. (16)
These exp essions a e equi alen o hose cu en dynamics o he con en ional wo-le el
con e e [
26
]. The e o e, by he use o he change o a iables (13) and (14), he added di icul y
inhe en o he adop ed o mula ion disappea s, a leas a his s age. Addi ionally, in oducing
he e e ences o he ac i e (
p
) and eac i e powe (
q
) in o
(8)
and
(9)
, he cu en e e ences can
be e ie ed (
i
α
,
i
β
). Once hese alues a e known, a non-ideal p opo ional- esonan con olle [
35
],
uned a he g id equency, is used o make he phase cu en s o ack hei e e ences. In his
way, he acking e o
(i
α−iα
,
i
β−iβ)
inpu s he esonan con olle , p o iding he alue o con ol
a iables (u1,u2).
GPRω(s) = kp+2k ωcs
s2+2ωcs+ω2
u1=2
dc
(−GPRωg(i
α−iα) + sα)(17)
u2=2
dc
(−GPRωg(i
β−iβ) + sβ)(18)
whe e
kp
and
k
a e he p opo ional and esonan con ol pa ame e s;
ωc
is he cu -o equency o
he low-pass il e implemen ed in o he esonan pa ; and
ω
is he esonan equency— uned a he
g id equency ωg.
3.3. Vol age Balance Con olle
The objec i e o he ol age balance con olle is o keep he s a e a iable
d
close o ze o, a oiding
he unbalance o he dc-link capaci o ol ages, and i is based on he de ini ion o wo new i ual
con ol a iables
u3˙=dαp+dαn(19)
u4˙=dβp+dβn. (20)
In oduc ion o (19) and (20) in o (11) yields
Cd d
d = sαp− sβq
2
sα+ 2
sβ
u3+ sβp+ sαq
2
sα+ 2
sβ
u4. (21)
I is impo an o highligh ha he de ini ion o
u3
and
u4
causes a decoupling o he i ual con ol
a iables o con ol pu poses. No e ha
u1
and
u2
a e designed o egula e he s a e a iables
p
and
q
, whe eas
u3
and
u4
can be used o egula e
d(21)
. This is an impo an bene i o he p oposed
con ol app oach.

Ene gies 2019,12, 1641 6 o 15
Taking in o accoun (21), he p oposed con ol laws [26] a e de ined as ollows
u3=kd
sαp− sβq
p2+q2(
d− d)+kdi
sαp− sβq
p2+q2Z
0
(
d− d)dτ(22)
u4=kd
sβp+ sαq
p2+q2(
d− d)+kdi
sβp+ sαq
p2+q2Z
0
(
d− d)dτ, (23)
whe e posi i e cons an s
kd
and
kdi
a e cus oma y uning pa ame e s. The e e ence o
d
is deno ed
by
d
, which is se o ze o o ensu e a balanced dis ibu ion o he dc-link ol age ac oss capaci o s
C1
and C2.
By in oducing (22) and (23) in o (21), he ol age balance dynamics become linea :
Cd2(
d− d)
d 2+kd
d(
d− d)
d +kdi(
d− d) = 0, (24)
whose s abili y is assu ed p o ided ha pa ame e s
kd
and
kdi
a e posi i e. A comple e schema ic
block diag am o all con olle s is illus a ed in Figu e 2.
Figu e 2. Comple e schema ic block diag am o he con olle s.
Ene gies 2019,12, 1641 7 o 15
4. Modula ion S a egy
The con olle p esen ed in he p e ious sec ion p o ides, a each sampling ime, he alues o
u1
,
u2
,
u3
and
u4
. The co esponding alues o
dαp
,
dαn
,
dβp
and
dβn
can be ob ained sol ing he sys em
o Equa ions (13), (14), (19) and (20) yielding
dαp=1
2(u1+u3)(25)
dαn=1
2(−u1+u3)(26)
dβp=1
2(u2+u4)(27)
dβn=1
2(−u2+u4)(28)
In o de o compu e he ac ual du y a ios
dij
,
i=a
,
b
,
c
;
j=p
,
n
, he Cla ke ans o ma ion can be used



daj
dbj
dcj


= 2
3








1 0 1
√2
−1
2
√3
2
1
√2
−1
2−√3
2
1
√2











dαj
dβj
dγj


,j=p,n. (29)
whe e
dγp
and
dγn
a e emaining deg ees o eedom. Ob iously, he emaining du y a ios,
dao
,
dbo
and dco can be compu ed using (5)–(7).
4.1. Fi s P oposal, ICM1
The i s a ian , ICM1, was p oposed in [
26
]. In his a ian ,
dγp
and
dγn
a e chosen o be cons an
and can be conside ed as uning pa ame e s. In [
26
], guidelines a e gi en in o de o a oid sa u a ion
p oblems. This app oach is a simple way o accomplish he modula ion bu i p esen s an impo an
d awback: excep by chance, none o he
dij
will esul in ze o. This implies ha , in each sampling
ime, each phase commu es among he h ee le els, which can be conside ed oo many commu a ions
compa ed wi h o he con olle s, e en hose including ol age balancing. This ac could yield la ge
swi ching losses.
4.2. Second P oposal, ICM2
In o de o a oid he la ge numbe o commu a ions, a new a ian is p oposed. This a ian akes
ad an age o he wo deg ees o eedom associa ed wi h
dγp
and
dγn
by imposing, a each sampling
pe iod, one
dip
and one
din
o be ze o. The wo phases o which one o he du y a ios has o be ze o
need o be chosen ca e ully, as i is explained below, aking in o accoun ha he du y cycles in
abc
coo dina es ha e o be in he in e al
[
0, 1
]
. The esul is ha hese wo phases only swi ch be ween
wo le els while he emaining phase commu es among he h ee le els.
In o de o selec hese phases, he p ocedu e checks i se ing one o he dij,i=a,b,c;j=p,n o
ze o yields o he ul illmen o he cons ain s 0
≤dij ≤
1 o he es o du y cycle a iables. S a ing
wi h he case
dap =
0, Equa ion (29) o
j=p
can be conside ed as a se o equa ions, whe e
dαp
,
dβp
a e known,
dap =
0 and
dbp
,
dcp
and
dγp
a e he unknowns. The esul an sys em o equa ions can be
sol ed in o de o check i his case is easible, ha is, i
dbp
and
dcp
a e in he in e al
[
0, 1
]
. Repea ing
o he o he phases, h ee di e en cases ha e o be analyzed o
j=p
and o he h ee cases o
j=n
.
The associa ed equa ions a e
Ene gies 2019,12, 1641 8 o 15
Case 1: daj =0
dbj =−√6
2dαj+√2
2dβj(30)
dcj =−√6
2dαj−√2
2dβj(31)
Case 2: dbj =0
daj =√6
2dαj−√2
2dβj(32)
dcj =−√2dβj(33)
Case 3: dcj =0
daj =√6
2dαj+√2
2dβj(34)
dbj =√2dβj, (35)
whe e
j
=
p
,
n
. The esul an du y a ios o he conside ed sampling ins an a e he co esponding ones
o he easible cases, ha is, cases whe e all he du y cycles a e in he in e al
[
0, 1
]
. I will be shown
below ha , a e e y ins an , he e exis s a leas one (and apa om some bo de cases, only one)
easible case.
Rega ding he compu a ion bu den o his app oach, a e e ie ing (25)–(28), he calcula ion
o he du y a ios
dij
can be achie ed by checking he cons ain s
dij ∈[
0, 1
]
o he 3
×
2
=
6 cases.
Fo his, (30)–(35) ha e o be used wice ( o le els
p
and
n
). This las s age implies he compu a ion o
20 mul iplica ions and 8 sums as well as 24 compa isons.
Al e na i ely, a di e en app oach can be used o choose he co ec case a e e y sampling
ins an wi h he help o Figu e 3. This igu e depic s he s aigh lines ha a e he bounda ies o
cons ain s 0
≤dij ≤
1 using exp essions
(30)
–
(35)
. Consequen ly, he shaded egions ep esen he
ul illmen o hese cons ain s o each one o he h ee cases abo e. As o each le el
j=p
,
n
he e
is one
dij
ha i is equal o ze o, he e a e ou o such lines o each case, ins ead o six. I can be
seen ha he h ee shadowed a eas do no o e lap (excep a hei bo de s) and ha hey co e a
whole hexagon. An in e es ing ac is ha his hexagon is ela ed o he well-known hexagon o Space
Vec o Modula ion (SVM), bu in his case, he e a e wo such hexagons (one o
j=p
and one o
j=n
). The in e es o Figu e 3is wo old: (1) i shows ha , p o ided he con e e does no wo k in
o e modula ion egion, one o he h ee cases is always easible, and (2) Figu e 3can be used as an
al e na i e me hod o choose he co ec case: he wo king sec o can be compu ed as usual in SVM
and once he app op ia e case is selec ed, he co esponding o mulae can be applied.
In summa y, he ICM2 algo i hm, whose da a inpu and ou pu a e depic ed in Figu e 4, can be
implemen ed in wo al e na i e and equi alen ways ha only di e in he compu a ional bu den,
which in al e na i e B depends on he me hod used o he compu a ion o he sex an :
Al e na i e A:
•Compu a ion o u3and u4using (22) and (23).
•Compu a ion o dαp,dαn,dβp,dβnusing (25)–(28).
•Fo le els pand n:
–
Compu a ion o Equa ions (30)–(35) and selec ion o he case ha ul ills he cons ain s
0≤dij ≤1. This p ocedu e gi es di ec ly he esul an du y cycles.
Ene gies 2019,12, 1641 9 o 15
Al e na i e B:
•Compu a ion o u3and u4using (22) and (23).
•Compu a ion o dαp,dαn,dβp,dβn(25)–(28).
•Fo le els pand n:
–
Compu a ion o he sex an inside he hexagon o Figu e 3. This s ep is simila o he
co esponding one in SVM (bu i mus be compu ed wice, one o le el
p
and one o le el
n). The sex an gi es he co esponding case.
–Compu a ion o he du ies using he co esponding Equa ions o (30)–(35).
I can be no ed ha he compu a ional complexi y is lowe in bo h ICM1 and ICM2 wi h espec
o SVM s a egies ha include con ol o he ol age balance, such as [13].
Figu e 3. G aphical ep esen a ion o he limi s o each case.
Figu e 4. Da a inpu and ou pu o ICM1 and ICM2.
5. Expe imen al Ve i ica ion
This sec ion p esen s he expe imen al esul s ob ained in he labo a o y o he wo app oaches
p esen ed in his pape and he one used as a compa a i e (mVSVPWM) [
13
]. To his end, he h ee-le el
NPC con e e shown in Figu e 5has been used. I has been con igu ed as ec i ie and i has he
ci cui and con ol pa ame e s p o ided in Table 1. A i s -o de low-pass il e has also been added
o he p opo ional pa o he o al dc-link ol age con olle , as i is ecommended in [
33
], uned a
5 KHz in o de o educe he ha monics p esence.