1
> REPLACE THIS LINE WITH YOUR MANUSCRIPT ID NUMBER (DOUBLE-CLICK HERE TO EDIT) <
Hyb id In e e Ze a-Ćuk o G id-Tied
Pho o ol aic Applica ions
Ande son A. Dionizio, Leona do P. Sampaio, Sé gio A. O. da Sil a, Membe , IEEE, Ví o Mon ei o, Senio
Membe , IEEE, João L. A onso, Senio Membe , IEEE,
1
Abs ac — This pape p oposes a no el single-phase in eg a ed in e e o pho o ol aic (PV) applica ions called Hyb id In e e Ze a-
Ćuk (HIZC). The HIZC ope a es in discon inuous conduc ion mode and employs ou unidi ec ional powe swi ches, which a e achie ed
by associa ing se ies powe diodes o MOSFETs. In addi ion, du ing he g id's posi i e hal -cycle, he in e e ac s simila ly o he Ze a
con e e . On he o he hand, du ing he nega i e hal -cycle, he in e e ope a es simila ly o he Ćuk con e e . Due o he adop ed
design c i e ia, he Ze a and he Ćuk ope a ion modes show simila beha io . The small-signals analysis conside s he Ze a and Ćuk
ope a ion modes, showing a signi ican simila i y be ween hei equency esponses, p oo ing he simila i y o he HIZC's unc ionali y
in bo h ope a ion modes. The HIZC can boos he ol age o he PV a ay and pe o m he DC-AC con e sion a he same ime. The
maximum powe a ailable a he PV a ay is ha es ed using a mul i-loop con ol in conjunc ion wi h he pe u b-and-obse e
algo i hm, while an AF-αβ-PLL sys em gua an ees synch onism wi h he powe g id. Expe imen al esul s p o e he s uc u e easibili y
o he p oposed opology o PV applica ions. In addi ion, he HIZC p esen s high-e iciency con e sion and also low o al ha monic
dis o ion in he cu en injec ed in o he powe g id.
Index Te ms— Ćuk con e e , In eg a ed In e e , Pho o ol aic Sys em, Powe Elec onics, Ze a Con e e .
I. INTRODUCTION
n ecen yea s, he in es men s in enewable ene gy
sou ces ha e signi ican ly imp o ed [1,2]. This g ow h
is mo i a ed by a necessi y o expand elec ici y
gene a ion and dis ibu ion [3-6]. Among he enewable ene gy
sou ces, pho o ol aic (PV) is widely employed due o i s
modula cha ac e is ics, gua an eeing la ge ol age and cu en
anges [2, 3, 7-9]. Once he PV gene a ion occu s in di ec
cu en (DC), i is necessa y o adop one o mo e powe
con e sion s ages when he PV sys em is used o g id- ied
al e na ing cu en (AC) applica ions [6,9].
Con en ionally, a PV sys em uses a double powe
con e sion s age, whe e a s ep-up con e e , usually a boos
con e e , is associa ed wi h a ol age sou ce in e e (VSI),
commonly a ull-b idge in e e . This sys em can con ol bo h
s uc u es once he powe con e e s a e decoupled [10-12].
On he o he hand, his sys em can use many elec ical
componen s, p esen ing lowe e iciency and highe weigh and
olume when compa ed o he in eg a ed in e e [5, 6, 10, 11].
The in eg a ed in e e s a e buil in dis inc ways, wi h
di e en con ol s a egies o each s uc u e. Usually, hese
s uc u es can s ep up he ol age ac oss he PV a ay and injec
a sinusoidal cu en in o he u ili y g id h ough a single DC-AC
powe con e sion s age [5, 9].
A modula g id-connec ed single-phase in e e is p esen ed
1
This wo k was suppo ed in pa by he Na ional Council o Scien i ic and
Technological De elopmen (CNPq) unde G an 308620/2021-6 and G an
304707/2021-0; in pa by he Coo denação de Ape eiçoamen o de Pessoal de
Ní el Supe io - B azil (CAPES) - Financing Code 001, and in pa by he
Na ional Funds h ough he Po uguese unding agency FCT unde G an
SAICTPAC/0004/2015-POCI01-0145-FEDER-016434
A. A. Dionizio is wi h he Elec ical Enginee ing Depa men , Fede al
Uni e si y o Technology - Pa aná, Co nélio P ocópio-PR 86300-000, B azil
(e-mail: [email protected] p .edu.b ).
in [13]. The module can ob ain he indi idual maximum powe
in each panel. The opology is based on he Ćuk and SEPIC
con e e s and employs a high- equency ans o me ,
gua an eeing he necessa y gain and gal anic isola ion.
In [14], a Ćuk in e e opology wi h a high- equency
ans o me is also used, whe e a epe i i e con ol is
associa ed. An expe imen al 500 W se up p o es he easibili y
o he sys em. The main esul s show high e iciency and
injec ed cu en wi h low o al ha monic dis o ion (THD).
Simila ly, [5] has p oposed a b idgeless in e e based on he
Ze a con e e . The s uc u e can ope a e in con inuous
conduc ion mode (CCM) o discon inuous conduc ion mode
(DCM), using a eedback con olle o iden i y he conduc ion
mode bounda ies. Bo h pape s, [5] and [14] use epe i i e
con olle s, gua an eeing a sa is ac o y esponse.
A opology based on he DC-DC Ze a con e e named
Modi ied Ze a In e e (MZI) is p esen ed in [6], whe e he
MZI s uc u e ope a es in DCM. Howe e , i s unc ionali y
di e s om he con en ional Ze a con e e , which deli e s a
nega i e cu en h ough he magne iza ion induc o in he hi d
ope a ion s age. The magne iza ion induc o s o he MZI a e
se ies associa ed wi h powe diodes. Thus, hese induc o s'
powe low is unidi ec ional once he diodes p e en nega i e
cu en s.
An in eg a ed in e e based on he Ze a con e e o PV
applica ions has been p oposed in [9]. The opology named
L. P. Sampaio is wi h he Elec ical Enginee ing Depa men , Fede al
Uni e si y o Technology - Pa aná, Co nélio P ocópio-PR 86300-000, B azil
(e-mail: sampaio@u p .edu.b ).
S. A. O. Da Sil a is wi h he Elec ical Enginee ing Depa men , Fede al
Uni e si y o Technology - Pa aná, Co nélio P ocópio-PR 86300-000, B azil
(e-mail: augus@u p .edu.b ).
V. Mon ei o wi h he Depa men o Indus ial Elec onics, Uni e si y o
Minho, 4800-058 Guima aes, Po ugal (e-mail: mon e[email p o ec ed]inho.p ).
J. L. A onso is wi h he Depa men o Indus ial Elec onics, Uni e si y o
Minho, 4800-058 Guima aes, Po ugal (e-mail: jla@ dei.uminho.p ).
I
This a icle has been accep ed o publica ion in IEEE Open Jou nal o Powe Elec onics. This is he au ho 's e sion which has no been ully edi ed and
con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/OJPEL.2025.3576296
This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by/4.0/
2
> REPLACE THIS LINE WITH YOUR MANUSCRIPT ID NUMBER (DOUBLE-CLICK HERE TO EDIT) <
Single-Phase In eg a ed Ze a In e e (SP-IZI) ope a es in
DCM and p esen s h ee ope a ion s ages in each swi ching
pe iod. The s uc u e combines wo modi ied Ze a modules,
whe e one is esponsible o he unc ionali y du ing he
posi i e hal -cycle, and he o he is esponsible o ope a ing in
he nega i e hal -cycle.
A ou -swi ch single-s age and single-phase in e e has
been p oposed in [15]. The opology is based on he Buck-Boos
DC-DC con e e and can be employed in au onomous
applica ions o on g id- ied. Howe e , he opology needs an
ex a induc o o g id- ied applica ions once he in e e
p esen s discon inui y in he ou pu cu en .
Al hough he in e in [15] uses ewe semiconduc o s han
he p oposed HIZC, he cu en lows h ough h ee
semiconduc o s simul aneously in some ope a ion s ages. The
HIZC p esen s cu en in wo o ewe semiconduc o s in each
ope a ion s age. The ele a ed numbe o semiconduc o s
p esen ing cu en inc eases he conduc ion losses. The in e e
in [15] co obo a es his issue since he s uc u e shows nea ly
2/3 o conduc ion losses.
In [15], only he heo e ical losses a e shown, demons a ing
he maximum alue o 95.7%, which should be lowe when
measu ed. The HIZC achie es a maximum e iciency o nea ly
96% in he expe imen al se up.
This pape p oposes a new in eg a ed in e e based on he
Ze a and he Ćuk con en ional opologies. The s uc u e ac s as
an in e ace con e e be ween he PV a ay and he u ili y g id.
Fig. 1 p esen s he p oposed in e e . The HIZC employs ou
unidi ec ional powe swi ches buil using a se ies o connec ed
diodes. Thus, he HIZC can be used in mic oin e e s as an
in e ace con e e be ween he PV a ay and he elec ical
powe g id.
Fig. 1. HIZC p oposed opology.
The HIZC p oposed opology p esen s some ad an ages o e
o he s uc u es, such as: (i) The HIZC can inc ease he ol age
o he PV a ay and simul aneously pe o m he DC-AC
con e sion o he powe g id using only a single s age; (ii) The
HIZC uses he o al ol age o he PV a ay in he con e sion
s age, wi hou he need o spli capaci o s; (iii) The HIZC does
no employ a high- equency ans o me ; (i ) The
cha ac e is ics o he opology allows simple con ol s a egies,
gua an eeing a sinusoidal ou pu wi h low dis o ion; ( ) The
HIZC is highly e icien ; ( i) The ol ages ac oss all he
semiconduc o s in he HIZC a e ela i ely low when
conside ing he inpu and ou pu ol ages o he in e e .
The HIZC con e e p esen s some ad an ages wi h espec
o he MZI p oposed in [6]: (i) The HIZC uses he o al PV a ay
ol age, while he MZI mus spli he ol age be ween wo
capaci o s equally, and hus, he s a ic gain o he MZI mus be
highe , p o oking mo e losses; (ii) The magne iza ion induc o s
o he MZI ope a e only in hal -cycle, while he magne iza ion
induc o s o he HIZC ope a e du ing he whole cycle, spli ing
he cu en be ween wo induc o s, educing he peak and he
RMS alue o he cu en , and hus educing he conduc ion
losses; (iii) The ol age s ess in he swi ches o he HIZC is
lowe han ha o he MZI, which educes he losses and he
demons able damage o he componen s.
The HIZC o e s some ad an ages wi h espec o he SP-IZI
[9]. The main bene i is he ac ha he HIZC uses he o al
ol age in he PV a ay, while he SP-IZI spli s equally his
ol age ac oss wo capaci o s. In addi ion, he Li induc o in he
HIZC o e s be e inpu cu en il e ing han he SP-IZI.
This pape is o ganized as ollows: Sec ion II p esen s he
ope a ion, unc ionali y, main equa ions, and heo e ical
wa e o ms o he HIZC. Sec ion III desc ibes he modeling
and con ol adop ed. Sec ion IV compa es he expe imen al
esul s wi h hose o o he in eg a ed in e e s. Finally, sec ion
V p esen s he conclusions.
II. OPERATION AND FUNCTIONALITY OF THE HIZC
The p oposed HIZC ac s as an in e ace con e e be ween a
PV a ay and he single-phase AC u ili y g id. The HIZC
ope a es in DCM wi h linea s a ic gain. In DCM, he HIZC
ope a es simila ly o he Ze a con e e , p esen ing h ee
ope a ion s ages du ing he posi i e hal -cycle in each
swi ching pe iod, such as Dz1Ts, Dz2Ts, and Dz3Ts. On he o he
hand, he HIZC ope a es simila ly o he Ćuk con e e du ing
he nega i e hal -cycle o he powe g id, which p esen s he
ollowing h ee ope a ion s ages: Dc1Ts, Dc2Ts, and Dc3Ts.
The HIZC s uc u e employs ou unidi ec ional powe
swi ches deployed by associa ing se ies powe diodes o he
swi ches. Fu he mo e, he in e e equi es wo inpu
induc o s, one ou pu induc o , wo coupling capaci o s, and an
ou pu il e capaci o , as p esen ed in Fig. 1.
The p oposed con ol o he HIZC is designed o ex ac he
maximum a ailable powe a he PV a ay while injec ing his
ene gy in o he u ili y g id as a sinusoidal synch onized cu en .
The HIZC uses he Pe u b and Obse e algo i hm o pe o m
he maximum powe poin acking (MPPT), while he
synch onism o he powe g id is ca ied ou by an adap i e
alpha-be a phase-locked-loop (AF-αβ-PLL) sys em. The
con olle s, MPPT, and PLL algo i hms a e disc e ized and
embedded in a digi al signals p ocesso (DSP), as shown in
Fig. 2.
The modula ion s a egy o he HIZC opology is based on
he high- equency signal ob ained by he employed con olle
and PLL in o ma ion. Thus, wo swi ches (S2 and S4) ope a e a
low- equency and in a complemen a y way. In con as , he
signal o he swi ch S1 occu s in he posi i e hal -cycle o he
powe g id by compa ing he high- equency signal o a
Lo
iLo g
.
.
.
PV
iPV
Cdc
S1D1
Lm
C1
D2
S2
Li
S3
D3
C2
S4
D4
gS3
gS1
gS2
gS4
Ze a
Ćuk
Lm
+
C1
+
Li
++
C2
Lo
+
iC1
iC2
iLi
iLm ig
Co
+Lg g
+
-
-
-
-
-
--
-
+
This a icle has been accep ed o publica ion in IEEE Open Jou nal o Powe Elec onics. This is he au ho 's e sion which has no been ully edi ed and
con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/OJPEL.2025.3576296
This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by/4.0/
3
> REPLACE THIS LINE WITH YOUR MANUSCRIPT ID NUMBER (DOUBLE-CLICK HERE TO EDIT) <
saw oo h wa e a he swi ching equency. Simila ly, i occu s
he same wi h he swi ch S3, du ing he nega i e hal -cycle o
he powe g id.
Fig. 2. HIZC con ol.
A. Ze a Mode
Du ing he posi i e hal -cycle o he powe g id, he HIZC
ope a es in Ze a mode. In his mode, swi ches S1 and S2 a e
commu ed, while swi ches S3 and S4 emain u ned o du ing
his pe iod.
The i s s age o ope a ion, Dz1Ts, s a s when he swi ch S1
u ns on. The ene gy in he PV a ay lows h ough his swi ch
and diode D1, which is o wa d-biased. In his s age, he
induc o Lm is magne ized and ene gized wi h he PV-a ay
ol age, PV, and he ol age ac oss he induc o Li is he
di e ence be ween he coupling capaci o s C2 and C1, i.e., Li =
C2- C1.
A ela ion be ween he PV ol age, capaci o C1, and he g id
ol age gi es he ol age ac oss he ou pu induc o , Lo =
PV+ C1- g. The cu en h ough he coupling capaci o C1 is he
sum o he Lo and Li induc o cu en s, iC1 = iLo+iLi, and he
cu en h ough he capaci o C2 is he same as he induc o Li.
Fig. 3 (a) shows he HIZC in his subin e al.
The second ope a ion s age, in Ze a mode, s a s when he
swi ch S1 u ns o . The ene gy accumula ed in he induc o s
lows h ough he swi ch S2 and he powe diode D2.
The induc o Lm is demagne ized, and i s accumula ed ene gy
is ans e ed o he capaci o C1. The induc o Lm ol age is he
same as he capaci o C1, Lm = - C1. The accumula ed ene gy
in he induc o Li is ans e ed o he coupling capaci o C2. The
ol age ac oss his induc o is he di e ence be ween he PV-
a ay and capaci o C2 ol ages, i.e. Li = PV- C2.
The cu en h ough he coupling capaci o C1 is he same as
he induc o Lm, while he cu en h ough he capaci o C2
equals he Li cu en du ing he whole Ze a mode. This s age is
isualized in Fig. 3 (b).
The hi d ope a ion s age, Dz3Ts, s a s when he cu en
h ough he swi ch S2 and diode D2 is no enough o pola ize he
diode D2, i.e., he sum o he induc o s' cu en s is nea ly ze o.
Thus, he D2 is e e se-biased, and he cu en s do no low
h ough he swi ch S2, al hough his semiconduc o emains
u ned on du ing he Ze a mode.
In his ope a ions s age, he ene gy lows only in he passi e
elemen s. The ou pu induc o cu en is he sum o he Lm and
Li induc o s' cu en s, iLo = iLm+iLi. The ope a ion s age Dz3Ts is
shown in Fig. 3 (c).
(a)
(b)
(c)
Fig. 3. Ope a ion s ages o he Ze a mode: (a) Fi s , Dz1Ts;
(b) Second, Dz2Ts; (c) Thi d, Dz3Ts.
B. Ćuk Mode
In he nega i e hal -cycle o he u ili y g id, he HIZC
opology ope a es in Ćuk mode. The swi ches S3 and S4 a e
d i en in his mode, in which only swi ch S3 is commu ed wi h
a high equency. On he o he hand, he swi ch S4 is commu ed
a a low equency. A he same ime, he swi ches S1 and S2
keep u ned o du ing his mode.
The i s subin e al in Ćuk mode, Dc1Ts, s a s when he
swi ch S3 is u ned on, allowing he ene gy o low h ough he
A/D Con e e
Signal Condi ioning Boa d
iPV
DSC (TMS320F28335)
gS1
gS2
gS3
gS4
PV
PI
Swi ching Logic
giLo
PV iPV
MPPT
PV
*
PLL
g
Sin(θ)
Ip
iLo
iLo
*
PI
P
W
M
d
.
.
.Cdc
S1D1
Lm
C1
D2
S2
Li
S3
D3
C2
D4
gS3
gS1
gS2
gS4
S4
Lo
Co
Lg g
.
.
.Cdc
S1D1
Lm
C1
D2
S2
S3
D3D4
gS3
gS1
gS2
gS4
S4
Lo
Co
Lg g
.
.
.Cdc Lm
D2
S2
Li
S3
D3
C2
D4
gS3
gS1
gS2
gS4
S4
S1D1C1Lo
Co
Lg g
This a icle has been accep ed o publica ion in IEEE Open Jou nal o Powe Elec onics. This is he au ho 's e sion which has no been ully edi ed and
con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/OJPEL.2025.3576296
This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by/4.0/
4
> REPLACE THIS LINE WITH YOUR MANUSCRIPT ID NUMBER (DOUBLE-CLICK HERE TO EDIT) <
associa ed diode D3. The induc o Li is ene gized and
magne ized wi h he powe o he PV a ay, and he ol age
ac oss Li is he PV a ay ol age, Li = PV.
The Lm induc o is magne ized wi h he ol age di e ence
be ween he coupling capaci o s, Lm = C2- C1. The di e ence
be ween he coupling capaci o C2 and he u ili y g id, Lo = C2-
g gi es he ol age ac oss he ou pu induc o . The cu en
h ough S3 and D3 semiconduc o s is he sum o he induc o s'
cu en s, iS3 = iLm+iLi+iLo.
The cu en h ough he coupling capaci o C2 is he sum o
he Lm and Lo cu en s, iC2 = iLm+iLo, while he C1 cu en is he
same as he Lm induc o du ing he whole Ćuk mode. The
ope a ion s age Dc1Ts is isualized in Fig. 4 (a).
The second ope a ion s age in Ćuk mode, Dc2Ts, s a s when
swi ch S3 u ns o , and he ene gy low pola izes de diode D4.
Swi ch S4 is u ned on du ing he whole nega i e hal -wa e
cycle o he u ili y g id.
(a)
(b)
(c)
Fig. 4. Ope a ion s ages o he Ćuk mode: (a) Fi s , Dc1Ts;
(b) Second, Dc2Ts; (c) Thi d, Dc3Ts.
The ene gy accumula ed in he induc o s Lm and Li a e
ans e ed o he capaci o s C1 and C2, espec i ely, and he
ol ages ac oss hese induc o s a e he same as he capaci o s
C1 and C2, whe e Lm = - C1 and Li = - C2. The cu en h ough
he capaci o is he same as he induc o Li. Fig. 4 (b) p esen s
his ope a ion s age.
Simila ly, in he Ze a mode, he hi d ope a ion s age occu s
when he sum o he induc o cu en s h ough he diode D4 is
insu icien o keep i o wa d-biased. Thus, he ene gy lows
only h ough he passi e elemen . Fig. 4 (c) p esen s his
ope a ion s age o he HIZC.
C. Main Theo e ical Wa e o ms
The main heo e ical wa e o ms o he HIZC con e e can
be ob ained by conside ing ideal componen s, making i easie
o unde s and he s uc u e. The inse ion o non-ideali y and
pa asi ic componen s causes a mo e complex unde s anding
wi hou a signi ican gain. Fo he same eason, he HIZC
modeling also conside s all componen s as ideal.
The cu en lows h ough each g oup o med by a swi ch and
a diode only in o an ope a ion s age du ing a swi ching pe iod.
In he o he s ages, he g oup p esen s dis inc ol age le els,
which can be h ough he swi ch o diode. The cu en h ough
hese g oups has he same peak, iSP. The peak cu en depends
on he du y cycle Dz1 o Dc1. Fig 5 shows he heo e ical
ol ages and cu en s o he swi ch S1, S2, and he diodes D1
and D2. The cu en s and ol ages in o he swi ches S3 and S4,
besides he diodes D3 and D4, each he same le els in dis inc
ope a ion s ages.
The ol ages ac oss he h ee induc o s a e ideally he same
le el du ing a swi ching pe iod. In he i s ope a ion s age, he
ol age is he same as he PV a ay ol age. Du ing he second
ope a ion s age, he ol age is he same as he powe g id, and
in he hi d ope a ion s age, he ol ages ac oss all induc o s a e
ideally null.
The cu en h ough he induc o Lm is posi i e du ing he
whole posi i e powe g id hal -cycle. On he o he hand, du ing
he nega i e g id hal -cycle, he cu en h ough he induc o
Lm assumes posi i e and nega i e le els. The induc o Li
p esen s posi i e and nega i e cu en le els du ing he posi i e
g id hal -cycle and nega i e cu en du ing he nega i e g id
hal -cycle. The ou pu induc o , Lo, p esen s cu en s
synch onized wi h he powe g id. Fig. 6 (a) exhibi s he
heo e ical wa e o ms o he induc o s du ing a swi ching
pe iod du ing he posi i e g id hal -cyle, and Fig. 6 (b) shows
he ol ages and cu en s o he induc o s du ing he nega i e
powe g id hal -cycle.
The posi i e and nega i e hal -cycles o he powe g id
de e mine when he HIZC ope a es in he Ze a o he Ćuk mode,
changing he swi ches' ga e signals. Fig. 7 (a) shows he ideal
and heo e ical signals o each swi ch employed in he HIZC.
Fo he posi i e hal -cycle, he ga e signal o swi ch S1 uses a
sinusoidal pulse wid h modula ion (SPWM). Simila ly, he ga e
signal o swi ch S3 employs an SPWM du ing he nega i e
hal -cycle. On he o he hand, S2 and S4 a e commu ed by he
g id equency, whe e S2 is u ned on du ing he posi i e hal -
cycle, whe eas S4 is u ned on du ing he nega i e hal -cycle.
.
.
.Cdc
S1D1
Lm
C1
D2
S2
Li
S3
D3
C2
D4
gS3
gS1
gS2
gS4
S4
Lo
Co
Lg g
.
.
.Cdc
S1D1
Lm
C1
D2
S2
Li
S3
D3
C2
D4
gS3
gS1
gS2
gS4
S4
Lo
Co
Lg g
.
.
.Cdc Lm
D2
S2
Li
S3
D3
C2
D4
gS1
gS2
gS4
S4
S1D1C1Lo
Co
Lg g
This a icle has been accep ed o publica ion in IEEE Open Jou nal o Powe Elec onics. This is he au ho 's e sion which has no been ully edi ed and
con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/OJPEL.2025.3576296
This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by/4.0/
5
> REPLACE THIS LINE WITH YOUR MANUSCRIPT ID NUMBER (DOUBLE-CLICK HERE TO EDIT) <
Cu en s h ough induc o s p esen dis inc wa eshapes
du ing he posi i e and nega i e hal -cycles. Acco ding o hose
men ioned ea lie , he inpu induc o Li p esen s he same
cu en as he coupling capaci o C2 du ing he posi i e hal -
cycle. Thus, he a e age cu en is ze o o each swi ching
pe iod. Howe e , his induc o is magne ized and
demagne ized, p esen ing a signi ican cu en ipple and RMS
alue.
(a)
(b)
(c)
(d)
Fig. 5. Theo e ical wa e o ms o he HIZC du ing a swi ching
pe iod: (a) S1 and S2 swi ches du ing he g id posi i e hal -
cycle; (b) S1 and S2 swi ches du ing he g id nega i e hal -
cycle;(c) D1 and D2 diodes du ing he g id posi i e hal -cycle;
(d) D1 and D2 diodes du ing he powe g id nega i e hal -cycle.
The ol age ac oss he coupling capaci o s C1 and C2 p esen s
dis inc alues. The C1 ol age is nea he g id ol age,
in oducing a high- equency ipple, while he ol age ac oss
he capaci o C2 exhibi s he g id ol age wi h an o se o he
PV a ay ol age. The e o e, he a e age, RMS, and maximum
ol ages o he capaci o C2 a e highe han he C1.
The ou pu capaci o Co ac s by il e ing he high- equency
ipple. Thus, he ol age ac oss his capaci o is almos he
u ili y g id ol age.
All induc o s p esen he same ol age du ing each ope a ion
s age i he ol age ipples a e neglec ed. Each swi ching pe iod
is di ided in o h ee subin e als, whe e du ing he i s , he
ol age is he same, independen o he g id ol age condi ion.
The ol age ac oss all induc o s du ing he second subin e al
is app oxima ely he powe g id ol age, and du ing he hi d
subin e al, he ol ages ac oss all induc o s a e ideally ze o.
Fig. 8 shows ol ages ac oss he capaci o s and induc o s.
(a)
(b)
Fig. 6. Theo e ical cu en and ol age wa e o ms o he
induc o s o he HIZC du ing a swi ching pe iod: (a) Du ing he
posi i e powe g id hal -cycle; (b) Du ing he nega i e powe
g id hal -cycle.
I he inpu and magne iza ion induc ance a e he same, bo h
induc o s will ha e equal cu en ipples. Thus, he
magne iza ion induc o Lm also p esen s he highes ipple a he
peak o he g id ol age, exhibi ing a sinusoidal shape du ing
he posi i e hal -cycle.
On he o he hand, he cu en h ough he ou pu induc o Lo
p esen s a sinusoidal shape wi h a low ipple a high equency
caused by he swi ching. Fig. 7 (b) shows he cu en
wa e o ms o he h ee induc o s o he HIZC.
(a)
(b)
Fig. 7. Theo e ical wa e o ms o he HIZC du ing a pe iod o
he u ili y powe g id: (a) Ga e signals; (b) Induc o s cu en s.
S1
S2
iS1
iS2
Dz1TSDz2TSDz3TS
TS
PV+ g
PV
0
0
0
0
iSP
iSP
g
S1
S2
iS1
iS2
Dc1TSDc2TSDc3TS
TS
2 PV
0
0
0
0
PV
PV+ g
D1
D2
iD1
iD2
Dz1TSDz2TSDz3TS
TS
-( PV+ g)
- g
0
0
0
0
iSP
iSP
D1
D2
iD1
iD2
Dc1TSDc2TSDc3TS
TS
0
0
0
0
PV+ g
TS
0
0
0
- g
V
PV
Lm
= Li= Lo
iLm
ILmmax
ILmmin
iLi
ILimax
ILimin
0
iLo
ILomax
ILomax
ILo
DZ1
TSDZ2
TSDZ3
TS
TS
0
0
0
Lm
= Li= Lo
iLm
-ILmmax
-ILmmin
iLi
-ILimax
-ILimin
0
iLo
-ILomin
-ILomax
ILo
DC1
TSDC2
TSDC3
TS
V
PV
g
gS1
2π
0
0
0
π 3π/2
π/2
0
0
gS2
gS3
gS4
iLm
iLi
iLo
2π
0
0
0
ILip
ILmp
π 3π/2
π/2
0
This a icle has been accep ed o publica ion in IEEE Open Jou nal o Powe Elec onics. This is he au ho 's e sion which has no been ully edi ed and
con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/OJPEL.2025.3576296
This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by/4.0/
6
> REPLACE THIS LINE WITH YOUR MANUSCRIPT ID NUMBER (DOUBLE-CLICK HERE TO EDIT) <
Fig.8. Theo e ical ol age wa e o ms o he HIZC du ing a
pe iod o he u ili y powe g id.
D. Main Equa ions and S a ic Gain
This sec ion p esen s he main equa ions ela ed o he
s eady-s a e analysis in o de o ob ain he HIZC s a ic gain.
Hence, by analyzing he HIZC ope a ion men ioned in Sec ion
II. A and II.B, he equa ions a e de i ed o a single swi ching
pe iod.
As is well-known, he a e age induc o ol age is null in a
s eady s a e. Thus, analyzing he ol age ac oss he Lm induc o
in Ze a mode, he ollowing ela ion is ob ained:
𝑣𝐿𝑚 =𝑣𝑃𝑉𝐷𝑧1 −𝑣𝐶1𝐷𝑧2
+(𝑣𝑃𝑉 +𝑣𝐶1 −𝑣𝐶2 +𝑣𝐿𝑖)𝐷𝑧3 =0. (1)
The ol age ac oss he induc o Li, in he Ze a mode, is gi en
as:
𝑣𝐿𝑖 =(𝑣𝐶2 −𝑣𝐶1)𝐷𝑧1 +(𝑣𝑃𝑉 −𝑣𝐶2)𝐷𝑧2
+(𝑣𝑃𝑉 +𝑣𝐶1 −𝑣𝐶2 +𝑣𝐿𝑚)𝐷𝑧3 =0. (2)
The ou pu induc o , Lo, p esen s he a e age ol age ela ed
by:
𝑣𝐿𝑜 =(𝑣𝑃𝑉 +𝑣𝐶1 −𝑣𝑔)𝐷𝑧1 −𝑣𝑔𝐷𝑧2
+(𝑣𝐶1 −𝑣𝑔+𝑣𝐿𝑚)𝐷𝑧3 =0. (3)
Some ela ions a e es ablished when equa ing (1)-(3), such
as he ol age ela ion C2 = C1+ PV. The a e age ol age
ac oss he coupling capaci o C2 is highe han he C1 ol age.
This esponse is expec ed because o cha ac e is ics om he
Ze a and Ćuk con e e s. The C1 a e age ol age du ing each
swi ching pe iod is nea he g id ol age, C1 = g.
E alua ing he ol ages du ing he hi d ope a ion s age,
Dz3Ts, he sum o he Lm and Li is an equal ela ion be ween he
PV a ay ol age and he coupling capaci o s ol ages, Lm+ Li
= PV+ C1- C2. As men ioned be o e, C2 = PV+ C1, esul ing in
Lm+ Li = 0. Addi ionally, du ing his ope a ion s age, he
ol age ac oss he ou pu induc o can be exp essed using he
Lm o Li ol age. Thus, he ol ages ac oss he h ee induc o s
a e ideally null in he hi d ope a ion s age.
Conside ing he null ol age du ing he hi d ope a ion s age,
om (1), he HIZC s a ic gain is ob ained as pe :
𝐺𝑠=𝑣𝑔
𝑣𝑃𝑉 =𝐷𝑧1
𝐷𝑧2. (4)
Acco ding o he indica ed ol ages, all induc o s a e cha ged
and magne ized wi h nea ly he PV-a ay ol age du ing he
i s ope a ion s age, eaching he maximum alue a he end o
he i s ope a ion s age, Dz1Ts.
Du ing he i s ope a ion s age, he cu en h ough swi ch
S1 is he sum o he h ee induc o s' cu en s. In he second
ope a ion s age, he cu en h ough semiconduc o s s a s a he
maximum alue and dec eases o ze o. Thus, he cu en peak
in semiconduc o s is ob ained as ollows:
𝑖𝑆𝑃 =𝑣𝑃𝑉𝐷𝑧1𝑇𝑠(1
𝐿𝑚+1
𝐿𝑖+1
𝐿𝑜)= 𝑣𝑃𝑉𝐷𝑧1𝑇𝑠
𝐿𝑒𝑞 , (5)
whe e Leq is he pa allel associa ion be ween he h ee HIZC
induc ances.
The swi ch S1 p esen s cu en only du ing he i s ope a ion
s age. Thus, i s a e age cu en can be de e mined as ollows:
𝑖𝑆𝑎𝑣 =𝑣𝑃𝑉𝐷𝑧12𝑇𝑠
2𝐿𝑒𝑞 . (6)
[16] p esen s an app oach o modeling he sys em in which
he a ailable powe in he con e e 's inpu ans e s o he
swi ch when i is commu ed on. An e ec i e esis ance, Re,
p ocesses his powe . The e ec i e esis ance o he HIZC
opology, using (6), is calcula ed as pe :
𝑅𝑒= 𝑣𝑃𝑉
𝐼𝑠𝑎𝑣 =2𝐿𝑒𝑞
𝐷𝑧12𝑇𝑠. (7)
Dis ega ding he powe losses, he inpu powe is equal o he
ou pu powe . The eby, he a ailable ene gy in he PV a ay is
injec ed in o he powe g id as a sinusoidal and con olled
cu en . The ideal powe balance is ela ed as ollows:
𝑃𝑖𝑛 = 𝑃𝑜𝑢𝑡 =𝑣𝑃𝑉2
𝑅𝑒=𝑣𝑔2𝑃𝑜𝑢𝑡
𝑣𝑔2. (8)
The HIZC maximum s a ic gain is ob ained conside ing he
in e e ope a ion a he peak ol age o he u ili y g id, Vp.
Hence, by manipula ing (7) and (8), he s a ic gain is
de e mined as ollows:
𝐺𝑠= 𝑉𝑝𝐷𝑧1
√4𝐿𝑒𝑞𝑃𝑜𝑢𝑡𝑓𝑠 , (9)
whe e s is he HIZC swi ching equency, and Vp is he ol age
peak o he u ili y g id. F om (4) and (9), he subin e al Dz2 is
calcula ed as:
𝐷𝑧2 =√4𝐿𝑒𝑞𝑃𝑜𝑢𝑡𝑓𝑠
𝑉𝑝. (10)
2π
Vp
0
π 3π/2
π/2
0
-Vp
g
Vp - VPV
0
-Vp - VPV
Vp
0
-Vp
C2
C1
Vp
0
-Vp
VLm = VLi = VLo
VPV
-VPV
This a icle has been accep ed o publica ion in IEEE Open Jou nal o Powe Elec onics. This is he au ho 's e sion which has no been ully edi ed and
con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/OJPEL.2025.3576296
This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by/4.0/
7
> REPLACE THIS LINE WITH YOUR MANUSCRIPT ID NUMBER (DOUBLE-CLICK HERE TO EDIT) <
The same analysis can be pe o med o he Ćuk mode, which
gene a es he same esul s. This equali y be ween Ze a and Ćuk
modes is necessa y o he HIZC co ec ope a ion.
E. A e age and RMS Cu en Equa ions
Due o he DCM cha ac e is ics, RMS cu en alues a e
highe when compa ed wi h he CCM ope a ion o he same
powe a e. Howe e , he e iciency o a con e e ope a ing in
DCM can be as high as ha o a con e e ope a ing in CCM o
highe once o he cha ac e is ics imp o e he e iciency, such
as he ze o cu en swi ching (ZCS), in insic in DCM ope a ion
[17].
Analyzing a u ili y g id pe iod, induc o s Lm and Li p esen
he same a e age and RMS alues. The compu ing o he
a e age cu en h ough hese induc o s using a hal -cycle o
he powe g id is ound as:
𝐼𝐿𝑚,𝑖𝑎𝑣 = 𝐼1+𝐼2
8𝜋𝑉𝑝, (11)
whe e Vp is he peak o he u ili y g id, I1 and I2 a e calcula ed
as ollows:
𝐼1=(2𝑉𝑃𝑉𝐷z1𝑇𝑠
𝐿𝑚− 𝐼𝐿𝑜𝑚𝑖𝑛)𝜋𝐷z1𝑉𝑝−𝐼𝐿𝑜𝑚𝑖𝑛𝜋𝐷z1𝑉𝑝. (12)
𝐼2=−8𝐼𝐿𝑜𝑚𝑖𝑛(𝑉𝑝−𝑉𝑝𝐷z1 −𝑉𝑃𝑉𝐷z1). (13)
The quan i y ILomin is he lowes alue o he ou pu induc o
a he ol age peak o he powe g id and can be exp essed by:
𝐼𝐿𝑜𝑚𝑖𝑛 = 2𝑃𝑜𝑢𝑡
𝑉𝑝−𝑣𝑃𝑉𝐷𝑧1𝑇𝑠(𝐷𝑧1+𝐷𝑧2)
2𝐿𝑜. (14)
The in eg al o each pe iod ob ains he RMS alue o he
cu en h ough he inpu and magne iza ion induc o s
exp essed as ollows:
𝐼𝐿𝑚,𝑖𝑟𝑚𝑠 =2
3√𝐼3+𝐼4+𝐼5
𝐿𝑚
2𝜋, (15)
whe e
𝐼3=24𝜋𝑇𝑠2𝑉𝑃𝑉
3𝐷z1
3−18𝐼𝐿𝑜𝑚𝑖𝑛𝐿𝑚𝜋𝑇𝑠𝑉𝑃𝑉
2𝐷z1
2
𝑉𝑝, (16)
𝐼4=36𝑇𝑠2𝑉𝑃𝑉
2𝐷z1
3−48𝐼𝐿𝑜𝑚𝑖𝑛𝐿𝑚𝑇𝑠𝑉𝑃𝑉𝐷z1
2, (17)
𝐼5=9𝐼𝐿𝑜𝑚𝑖𝑛
2𝐿𝑚
2𝜋. (18)
Using he peak cu en o he semiconduc o s (5), he
espec i e a e age and RMS cu en s h ough he swi ches S1
and S3 ha occu only du ing he i s ope a ion s age (Dz1 and
Dc1), can be ob ained as ollows:
𝐼𝑆1,3𝑎𝑣 =𝐷z1𝑖𝑆𝑃
8, (19)
𝐼𝑆1,3𝑟𝑚𝑠 =√2
3√𝐷z1(𝐼6+𝐼7+𝐼8)
𝐿𝑚
2𝜋, (20)
whe e:
𝐼6=Dz1𝑇𝑠𝑉𝑃𝑉(4𝐷𝑧1𝑇𝑠𝑉𝑃𝑉 +3𝐼𝐿𝑜𝑚𝑎𝑥𝐿𝑚), (21)
𝐼7=3𝐼𝐿𝑜𝑚𝑎𝑥
2𝐿𝑚
2−Dz1𝑇𝑠𝑉𝑃𝑉(6𝐼𝐿𝑜𝑚𝑖𝑛𝐿𝑚), (22)
𝐼8=3𝐼𝐿𝑜𝑚𝑖𝑛
2𝐿𝑚
2−6𝐼𝐿𝑜𝑚𝑎𝑥𝐼𝐿𝑜𝑚𝑖𝑛𝐿𝑚
2. (23)
Simila ly, du ing a u ili y powe g id pe iod, he a e age and
RMS cu en s o he swi ches S2 and S4 can also be achie ed
using (5), as ollows:
𝐼𝑆2,4𝑎𝑣 =𝑉𝑃𝑉𝐷z1𝑖𝑆𝑃
2𝜋𝑉𝑝, (24)
𝐼𝑆2𝑟𝑚𝑠𝐶𝐴 =√3
6√𝑉𝑃𝑉𝐷z1(𝐼6+𝐼7+𝐼8)
𝐿𝑚
2𝜋𝑉𝑝. (25)
III. MODELING AND CONTROL
This sec ion in oduces he main small-signal equa ions
ela ed o he dynamic sys em ope a ion o p o ide bases o
ob aining he HIZC ans e unc ions.
A. Con ol Design
The con ol o he HIZC aims o pe o m he powe
ans e ence om he PV a ay o he u ili y g id h ough a
sinusoidal and synch onized ac i e cu en , ha es ing he
maximum a ailable PV a ay powe .
The HIZC is synch onized o he powe g id by an adap i e
il e AF-αβ-pPLL, which ob ains he angle o he u ili y g id
(θ) used in a sine unc ion. The AF-αβ-pPLL is based on he
ins an aneous ac i e powe heo y and designed o ope a e wi h
ol age dis u bances, such as sags and equency a ia ions,
acco ding o he esul s ob ained in [18].
The P&O algo i hm is used o pe o m he MPPT. Ini ially,
he PV a ay ol age and cu en a e measu ed o calcula e he
ol age e e ence (𝑣𝑃𝑉∗), which is used o each he maximum
powe .
The P&O causes small pe u bances on he ol age e e ence
and analyzes whe he he e is an imp o emen o dec emen in
he PV a ay ol age and powe . Thus, he P&O upda es he
ol age e e ence [19-22].
A P opo ional-In eg al (PI) con olle compa es he
e e ence o he PV-a ay ol age. This con ol gene a es a
cu en peak (Ip) mul iplied by a synch onized sine ec o ,
esul ing in he cu en e e ence.
An inne PI con olle compa es he e e ence cu en o he
ou pu induc o cu en (iLo). The PI esponse mul iplied by a
PWM gain (KPWM) gene a es a du y cycle (d) combined wi h a
swi ching logical con ol, which d i es he powe swi ches. The
swi ching logic uses he PLL in o ma ion o de e mine i he
swi ches S1 and S2 ope a e (Ze a mode) o S3 and S4 (Ćuk mode)
Fig. 9 (a) shows he block diag am, and Fig. 9 (b) ep esen s he
adop ed swi ching logic.
B. Equi alen Ci cui
The HIZC opology ope a es simila ly o he Ze a and he
Ćuk con e e s. In each swi ching pe iod, only wo swi ches
and wo diodes p esen cu en . Howe e , he cu en lows in
This a icle has been accep ed o publica ion in IEEE Open Jou nal o Powe Elec onics. This is he au ho 's e sion which has no been ully edi ed and
con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/OJPEL.2025.3576296
This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by/4.0/
8
> REPLACE THIS LINE WITH YOUR MANUSCRIPT ID NUMBER (DOUBLE-CLICK HERE TO EDIT) <
all passi e componen s du ing bo h modes. Two equi alen
ci cui s can be ob ained, he i s o he ope a ion like he Ze a
con e e and ano he o he Ćuk.
(a)
(b)
Fig. 9. Con ol s uc u e: (a) Block diag am; (b) Swi ching
con ol logic.
As men ioned be o e, he h ee s ages o he ope a ion o he
Ze a and Ćuk modes a e equi alen . By he opology design, he
magne iza ion and demagne iza ion o he induc o s Lm and Li
p esen he same in ensi y. Thus, he HIZC modeling can be
simpli ied using an equi alen ci cui om he Ze a o one o he
om he Ćuk mode. The esponse om bo h equi alen ci cui s
mus be simila o gua an ee he adequa e ope a ion o he
HIZC.
A ep esen a ion o he induc o s Lm and Li is employed in
he equi alen ci cui s and named Le, calcula ed by he pa allel
associa ion o he Lm and Li induc o s, Le = (Lm+Li)/LmLi.
Addi ionally, hese induc ances p esen he same alue so ha
he Le induc ance can be exp essed as Le= Lm/2=Li/2.
The coupling capaci o s, C1 and C2, also p esen cu en low
du ing he en i e HIZC ope a ion. Thus, an equi alen
capaci ance, named Ca, is adop ed. This capaci ance is he
pa allel associa ion be ween C1 and C2, Ca = C1+C2. Fig. 10 (a)
ep esen s he Ze a mode equi alen ci cui , and Fig. 10 (b)
ep esen s he Ćuk mode.
(a)
(b)
Fig. 10. Equi alen ci cui : (a) Ze a mode; (b) Ćuk mode.
C. Inne Loop Modeling
S a e-space a e aging (SSA) is widely employed in
modeling linea sys ems. Commonly, he cu en s h ough
induc o s and he ol ages ac oss capaci o s a e chosen as s a e
a iables in elec ical sys ems, while he ol ages and cu en
sou ces a e adop ed as sys em inpu s [23].
S a ic con e e s can be modeled using he SSA me hod in
bo h CCM and DCM ope a ion modes. When a s a ic con e e
ope a es in CCM, he SSA p esen s a sa is ac o y
ep esen a ion, whe e each subin e al has i s ma ices ela ed,
and he a e age model is quickly ob ained om he ponde ed
meaning. On he o he hand, when a s a ic con e e ope a es in
DCM, he ponde ed meaning in he SSA me hod p esen s e o s
caused by he di e ences be ween he RMS and a e age alues,
mainly in he induc o s' cu en s.
In [24], a co ec ion ma ix called M adequa es he s a e's
ma ix, p esen ing good esul s o second-o de con e e s,
such as Buck, Boos , and Buck-Boos . Howe e , he app oach
p esen ed in [24] is inadequa e o ou h-o de con e e s. On
he o he hand, [17] p oposes a gene alized me hod o ou h-
o de powe con e e s, which is used in [9] o model an
in eg a ed in e e based on Ze a opology. This app oach
esul s in good modeling o ou h-o de con e e s, such as
Ze a, Ćuk, and SEPIC. Thus, he p oposed HIZC can be
modeled simila ly.
Using he co ec ion app oach o DCM ope a ion and he
SSA me hod ini ially, he modeling o he HIZC is desc ibed as
pe :
𝑥=𝑀𝐴𝑚𝑥+𝐵𝑚𝑢, (26)
𝑦=𝐶𝑥. (27)
The ec o 𝑥 ep esen s he a e age s a es a iables
(induc o s cu en s and capaci o ol ages), Am, is he a e age
s a es ma ix du ing he h ee ope a ion s ages, Bm is he a e age
inpu ma ix, and 𝑢 ec o ep esen s he inpu sys em, in his
case, PV a ay and u ili y g id ol ages.
The M ma ix is exp essed as [17]:
𝑀=
[
1−𝐷𝑏
𝐷𝑎00 0 0
0 1 0 0 0
0
0
0
0
0
0
1 0 0
0 1 0
0 0 1
]
. (28)
F om he HIZC equi alen ci cui du ing Ze a mode [see
Fig. 8 (a)] and i s ope a ion p esen ed in Sec ion II and in Fig. 1
and Fig. 3, he SSA model conside ing he co ec ion app oach
is de e mined as ollows:
[
𝑖𝐿𝑒
𝑖𝐿𝑜
𝑣𝐶𝑎
𝑣𝐶𝑜
𝑖𝐿𝑔
]
=
[
0 0 𝑎13 𝐷z3
𝐿𝑒+𝐿𝑜0
0 0 𝑎23 𝑎24 0
𝐷𝑧2−𝐷𝑧2
2
𝐶𝑎𝐷𝑎𝐷𝑧2−1
𝐶𝑎0 0 0
01
𝐶𝑜0 0 −1
𝐶𝑜
0 0 1
𝐿𝑔0−𝑟𝑔
𝐿𝑔
]
[
𝑖𝐿𝑒
𝑖𝐿𝑜
𝑣𝐶𝑎
𝑣𝐶𝑜
𝑖𝐿𝑔
]
KPWM
d
iLo
Ip
Sin(θ)
MPPT
PV
iPV PV
*
PLL
iLo
*
g
Kpi
Kii /s
Kp
Ki /s
gS1
gS2
gS3
gS4
PWM
>0
sin(θ)
d
>
PV
S1D1
S2
D2
Cdc
Lo
Le
Ca
Cdc gS2
gS1 Co g
iLe
Le iLo
+
-
+-
Lo
+-
Ca
iCa
.
.
.
Lg
iLg
+-
Lg
g
+
-
Co
+
-
+
-
PV
S1
D1
S2
D2
Cdc
Lo
LeCa
Cdc gS2
gS1
Co g
iLe
Le
iLo
+-
+-
Lo
+-
Ca
iCa
.
.
.
Lg
iLg
+-
Lg
g
+
-
Co
+
-
+
-
This a icle has been accep ed o publica ion in IEEE Open Jou nal o Powe Elec onics. This is he au ho 's e sion which has no been ully edi ed and
con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/OJPEL.2025.3576296
This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by/4.0/
9
> REPLACE THIS LINE WITH YOUR MANUSCRIPT ID NUMBER (DOUBLE-CLICK HERE TO EDIT) <
+
[
𝐷𝑧1
𝐿𝑒0
𝐷𝑧1
𝐿𝑜0
0 0
0 0
0−1
𝐿𝑔
]
[𝑣𝑃𝑉
𝑣𝑔], (29)
𝑦=[0 1 0 0 0]
[
𝑖𝐿𝑒
𝑖𝐿𝑜
𝑣𝐶𝑎
𝑣𝐶𝑜
𝑖𝐿𝑔
]
, (30)
whe e 𝑦 ep esen s he ou pu ec o ; 𝑎13 =−(𝐿𝑒+𝐿𝑜)𝐷z1−𝐿𝑒𝐷z3
𝐿𝑒(𝐿𝑒+𝐿𝑜);
𝑎23 =(𝐿𝑒+𝐿𝑜)𝐷z1−𝐿𝑜𝐷z3
𝐿𝑜(𝐿𝑒+𝐿𝑜), and 𝑎24 =−(𝐷𝑧1+𝐷𝑧2)(𝐿𝑒+𝐿𝑜)−𝐿𝑜𝐷z3
𝐿𝑜(𝐿𝑒+𝐿𝑜).
I he con e e ac s in CCM, he hi d subin e al is
elimina ed. Howe e , elimina ing his ope a ion s age (29) will
be adequa e o he a e age model, and (30) will no be al e ed.
When HIZC ac s in he Ćuk mode, i s unc ionali y is
equi alen o he Ze a mode. The a e age ol age ac oss he
capaci o Ca is dis inc because o cha ac e is ics om he Ze a
and Ćuk con e e s. The o he s a es' a iables and inpu s a e
unal e ed.
In he equi alen ci cui o he Ze a mode, he PV a ay
supplies ene gy o HIZC only du ing he i s ope a ion s age.
Howe e , in he equi alen ci cui o he Ćuk mode, he PV
a ay p o ides ene gy o HIZC du ing he whole s uc u e
unc ionali y. Thus, each case's inpu ma ix, Bm, mus be
dis inc .
Equalizing he ope a ion s ages, i.e., Dz1Ts = Dc1Ts, Dz2Ts =
Dc2Ts, and Dz3Ts = Dc3Ts, and using he equi alen ci cui o
his mode [see Fig. 10(b)], a SSA ep esen a ion can be ound
as ollows:
[
𝑖𝐿𝑒
𝑖𝐿𝑜
𝑣𝐶𝑎
𝑣𝐶𝑜
𝑖𝐿𝑔
]
=𝐴𝑚
[
𝑖𝐿𝑒
𝑖𝐿𝑜
𝑣𝐶𝑎
𝑣𝐶𝑜
𝑖𝐿𝑔
]
+
[
𝑏11 0
𝐷𝑐3
𝐿𝑜0
0 0
0 0
0−1
𝐿𝑔
]
[𝑣𝑃𝑉
𝑣𝑔], (31)
whe e b11 = (𝐷𝑐1+𝐷𝑐2)(𝐿𝑒+𝐿𝑜)+𝐷𝑐3𝐿𝑒
𝐿𝑒(𝐿𝑒+𝐿𝑜)
The Am ma ix is he same in bo h HIZC modes, esul ing in
he same poles om (29) and (31). This conclusion indica es
ha Ze a and Ćuk modes ha e simila dynamics and
compo men .
[16] p oposed a gene alized swi ch a e aging (GSA) o
modeling DCM con e e s. The GSA app oach di ides he
con e e in o wo subsys ems: i) one linea , o med by he
passi e elemen s, which can be ep esen ed o he SSA model;
ii) one non-linea , o med by he semiconduc o s.
[9] models an in eg a ed in e e based on a Ze a con e e
o g id- ied applica ions using his associa ion, p esen ing a
high simila i y be ween he ma hema ical model and a
simula ed ci cui .
The non-linea subsys em ob ains h ee gains: one o he
du y cycle, one o he ol age ac oss he swi ch, and ano he
o he diode cu en [16]. In he HIZC, he ol age ac oss he
swi ch is conside ed he ol age ac oss he associa ion o S1 and
D1. Fo he cu en diode, he cu en is adop ed h ough he
diode D2. The h ee gains a e p esen ed as ollows:
𝑘𝑐= 2𝐷𝑧2
(𝐷𝑧1+𝐷𝑧3)2, (32)
𝑘𝑣𝑠 = 𝐷𝑧1𝐷𝑧2
𝑣𝑃𝑉(𝐷𝑧1+𝐷𝑧3)2, (33)
𝑘𝑖𝑑 = −𝑅𝑒𝐷𝑧12
𝑣𝑃𝑉(𝐷𝑧1+𝐷𝑧3)2. (34)
The ans e unc ion ha ela es he ou pu induc o , Lo, o
he du y cycle o he HIZC opology is de e mined as ollows:
𝐺𝑖𝑑(s)=𝑖𝐿𝑜(𝑠)
𝑑
(𝑠) =𝐶(𝑠−𝑀𝐴𝑚+𝐵𝑑𝑘𝑠𝑀𝐶𝑚
1−𝑘𝑠𝐸𝑑)−1 𝐵𝑑𝑘𝑐
1−𝑘𝑠𝐸𝑑, (35)
whe e 𝑘𝑠=[𝑘𝑖𝑑 𝑘𝑣𝑠], and he ma ices 𝐵𝑑 and 𝐸𝑑 a e de ined
as ollows:
𝐸𝑑=[𝐶1−𝐷𝑧2
1−𝐷𝑧1𝐶2−𝐷𝑧3
1−𝐷𝑧1𝐶3]
[
𝑖𝐿𝑒
𝑖𝐿𝑜
𝑣𝐶𝑎
𝑣𝐶𝑜
𝑖𝐿𝑔
]
+[𝐸1−𝐷𝑧2
1−𝐷𝑧1 𝐸2−𝐷𝑧3
1−𝐷𝑧1 𝐸3][𝑣𝑃𝑉
𝑣𝑔], (36)
𝐵𝑑=[𝐴1−𝐷𝑧2
1−𝐷𝑧1 𝐴2−𝐷𝑧3
1−𝐷𝑧1 𝐴3]
[
𝑖𝐿𝑒
𝑖𝐿𝑜
𝑣𝐶𝑎
𝑣𝐶𝑜
𝑖𝐿𝑔
]
+[𝐵1−𝐷𝑧2
1−𝐷𝑧1 𝐵2−𝐷𝑧3
1−𝐷𝑧1 𝐵3][𝑣𝑃𝑉
𝑣𝑔], (37)
whe e he ma ices A1, A2, A3, B1, B2, and B3 a e he s a es' and
inpu s' ma ices o he SSA du ing he h ee ope a ion s ages
Dz1Ts, Dz2Ts, and Dz3Ts. Ma ices C1, C2, and C3 a e he ou pu
ma ices o he GSA, while E1, E2, and E3 a e he di ec
ansi ion ma ices. The ma ix Cm is ob ained by he ope a ion
a e aging, i.e., Cm = C1Dz1 + C2Dz2 + C3Dz3.
Using he modeling o he equi alen ci cui o he Ćuk
mode ge s a close esponse. The ans e unc ion exhibi s he
same s uc u e shown in (20), wi h only some dis inc ma ices.
The high simila i y be ween bo h models is co obo a ed by
plo ing he equency esponse o he ans e unc ions and
he swi ched con e e , as demons a ed in Fig. 11.
Fig. 11. F equency esponses o nominal ope a ing alues.
Ćuk mode
Ze a mode
Swi ched con e e
Ćuk mode
Ze a mode
Swi ched con e e
Magni ude (dB)
Phase (deg)
F equency (Hz)
This a icle has been accep ed o publica ion in IEEE Open Jou nal o Powe Elec onics. This is he au ho 's e sion which has no been ully edi ed and
con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/OJPEL.2025.3576296
This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by/4.0/
16
> REPLACE THIS LINE WITH YOUR MANUSCRIPT ID NUMBER (DOUBLE-CLICK HERE TO EDIT) <
[20] S. K. Kollimalla and M. K. Mish a, "Va iable Pe u ba ion Size
Adap i e P&O MPPT Algo i hm o Sudden Changes in I adiance,"
in IEEE T ansac ions on Sus ainable Ene gy, ol. 5, no. 3, pp. 718-
728, July 2014.
[21] J. Ahmed and Z. Salam, "An Enhanced Adap i e P&O MPPT o Fas
and E icien T acking Unde Va ying En i onmen al Condi ions," in
IEEE T ansac ions on Sus ainable Ene gy, ol. 9, no. 3, pp. 1487-
1496, July 2018.
[22] S. Bha acha yya, D. S. Kuma P, S. Saman a and S. Mish a, "S eady
Ou pu and Fas T acking MPPT (SOFT-MPPT) o P&O and InC
Algo i hms," in IEEE T ansac ions on Sus ainable Ene gy, ol. 12, no.
1, pp. 293-302, Jan. 2021.
[23] I. Ba bi, "Modelagem de con e so es CC-CC emp egando modelo
médio de espaço de es ados" 1s ed. 2014.
[24] J. Sun, D. M. Mi chell, M. F. G euel, P. T. K ein, and R. M. Bass,
"A e aged modeling o PWM con e e s ope a ing in discon inuous
conduc ion mode," IEEE T ans. Powe Elec on., ol. 16, no. 4, pp.
482–492, 2001.
[25] IEEE S anda d o In e connec ion and In e ope abili y o Dis ibu ed
Ene gy Resou ces wi h Associa ed Elec ic Powe Sys ems In e aces,
IEEE S d. 1547-2018, 2018.
[26] IEC 61727- Pho o ol aic (PV) Sys ems - Cha ac e is ics o he U ili y
In e ace, IEC S d. 61727:2004, 2004.
[27] A. Anu ag, N. Deshmukh, A. Magulu i and S. Anand, "In eg a ed DC–
DC Con e e Based G id-Connec ed T ans o me less Pho o ol aic
In e e Wi h Ex ended Inpu Vol age Range," in IEEE T ansac ions
on Powe Elec onics, ol. 33, no. 10, pp. 8322-8330, Oc . 2018.
[28] J. Roy, Y. Xia and R. Ayyana , "High S ep-Up T ans o me less
In e e o AC Module Applica ions Wi h Ac i e Powe
Decoupling," in IEEE T ansac ions on Indus ial Elec onics, ol. 66,
no. 5, pp. 3891-3901, May 2019.
[29] B. Han, J. S. Lee and M. Kim, "Repe i i e Con olle Wi h Phase-
Lead Compensa ion o Cuk CCM In e e ," in IEEE T ansac ions on
Indus ial Elec onics, ol. 65, no. 3, pp. 2356-2367, Ma ch 2018.
[30] X. Hu, P. Ma, B. Gao and M. Zhang, "An In eg a ed S ep-Up In e e
Wi hou T ans o me and Leakage Cu en o G id-Connec ed
Pho o ol aic Sys em," in IEEE T ansac ions on Powe Elec onics,
ol. 34, no. 10, pp. 9814-9827, Oc . 2019.
[31] A. Fallahzadeh, S. A., Abjadi, N. R., Ka ga , A., and Blaabje g, F.
"Applying sliding-mode con ol o a double-s age single-phase g id-
connec ed PV sys em," in Jou nal o Renewable Ene gy and
En i onmen , ol. 18, no. 1, pp. 1-12, 2021.
This a icle has been accep ed o publica ion in IEEE Open Jou nal o Powe Elec onics. This is he au ho 's e sion which has no been ully edi ed and
con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/OJPEL.2025.3576296
This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by/4.0/
