Ci a ion: Gada, S.; Fekik, A.; Mahdal,
M.; Vaidyana han, S.; Maidi, A.;
Bouhedda, A. Imp o ing Powe
Quali y in G id-Connec ed
Pho o ol aic Sys ems: A
Compa a i e Analysis o Model
P edic i e Con ol in Th ee-Le el and
Two-Le el In e e s. Senso s 2023,23,
7901. h ps://doi.o g/10.3390/
s23187901
Academic Edi o : Fabio Leccese
Recei ed: 11 Augus 2023
Re ised: 11 Sep embe 2023
Accep ed: 12 Sep embe 2023
Published: 15 Sep embe 2023
Copy igh : © 2023 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
senso s
A icle
Imp o ing Powe Quali y in G id-Connec ed Pho o ol aic
Sys ems: A Compa a i e Analysis o Model P edic i e Con ol
in Th ee-Le el and Two-Le el In e e s
Saliha Gada 1, A ezki Fekik 2, Mi osla Mahdal 3, Sunda apandian Vaidyana han 4,* , Ahmed Maidi 1
and Ali Bouhedda 2
1Labo a oi e de Concep ion e Condui e des Sys èmes de P oduc ion, Facul éde Génie Élec ique e
d’In o ma ique, Uni e si éMouloud Mamme i, Tizi-Ouzou 15000, Alge ia; [email p o ec ed] (S.G.);
[email p o ec ed] (A.M.)
2Depa men o Elec ical Enginee ing, Uni e si y Akli Mohand Oulhadj-Bou ia, Rue D issi Yahia Boui a,
Boui a 10000, Alge ia; [email p o ec ed] (A.F.); [email p o ec ed] (A.B.)
3Depa men o Con ol Sys ems and Ins umen a ion, Facul y o Mechanical Enginee ing, VSB-Technical
Uni e si y o Os a a, 17. Lis opadu 2172/15, 70800 Os a a, Czech Republic; mi osla [email p o ec ed]
4Cen e o Con ol Sys ems, Vel Tech Uni e si y, 400 Fee Ou e Ring Road, Vel Naga , A adi,
Chennai 600062, Tamil Nadu, India
*Co espondence: [email p o ec ed]
Abs ac :
The Single-S age G id-Connec ed Sola Pho o ol aic (SSGC-SPV) opology has ecen ly
gained signi ican a en ion, as i o e s p omising ad an ages in e ms o educing o e all losses
and ins alla ion cos s. We p o ide a comp ehensi e o e iew o he sys em componen s, which
include he pho o ol aic gene a o , he in e e , he Inc emen al Conduc ance Maximum Powe
Poin T acking (IC-MPPT) algo i hm, and he PI egula o o DC bus ol age con ol. Mo eo e ,
his s udy p esen s de ailed sys em con igu a ions and con ol schemes o wo ypes o in e e s:
2L
−
3PVSI and 3L
−
3PNPC. In o de o pe o m a compa a i e s udy be ween he wo s uc u es, we
subjec ed hem o he same i adia ion p o ile using he same g id con igu a ion. The Pho o ol aic
A ay (PVA) i adiance is inc eased ins an aneously, in 0.2 s, om 400 W/m
2
o 800 W/m
2
, is kep a
800 W/m
2
o 0.2 s, is hen g adually dec eased om 800 W/m
2
o 200 W/m
2
in 0.2 s, is hen kep a
200 W/m
2
o 0.2 s, and is hen inally inc eased o 1000 W/m
2
o 0.2 s. We explain he ope a ional
p inciples o hese in e e s and desc ibe he a ious swi ching s a es in ol ed in gene a ing ou pu
ol ages. To achie e e ec i e con ol, we adop he Fini e Se –Model P edic i e Con ol (FS-MPC)
algo i hm, due o he bene i s o excellen dynamic esponsi eness and p ecise cu en acking
abili ies. This algo i hm aims o minimise he cos unc ion, while aking in o accoun he dynamic
beha iou o bo h he PV sys em and he in e e , including any associa ed delays. To e alua e
he pe o mance o he FS-MPC con olle , we compa e i s applica ion in he h ee-le el in e e
con igu a ion wi h he wo-le el in e e se up. The DC bus ol age is main ained a 615 V using he
PI con olle . The objec i e is o achie e a To al Ha monic Dis o ion (THD) below 5%, wi h e e ence
o he IEEE s anda ds. The 2L
−
3PVSI in e e is abo e he h eshold a an i adiance o 200 W/m
2
.
The 3L
−
3PNPC in e e o e s a g ea THD pe cen age, meaning imp o ed quali y o he powe
e u ned o he g id.
Keywo ds:
2L
−
3PVSI in e e ; 3L
−
3PNPC in e e ; cos unc ion; ini e se model p edic i e con ol;
inc emen al conduc ance; maximum powe poin acking; pho o ol aic sys ems
1. In oduc ion
Compe ing and su i ing in oday’s challenging wo ld equi es balancing economic
de elopmen wi h en i onmen al conse a ion. Renewable ene gy sou ces (RESs) play
a c ucial ole in achie ing his balance. People nowadays a e inc easingly in e es ed in
u ilising he as po en ial o a ious RESs, such as sola and wind ene gy. The de elopmen
Senso s 2023,23, 7901. h ps://doi.o g/10.3390/s23187901 h ps://www.mdpi.com/jou nal/senso s
Senso s 2023,23, 7901 2 o 22
o enewable ene gy gene a ion has b ough abou a signi ican change in he ene gy
sec o . A p esen , enewable ene gy sou ces (RESs) mee app oxima ely 17% o he global
ene gy demand, and his igu e is p ojec ed o ise in o de o mi iga e he ad e se e ec s
associa ed wi h con en ional ossil uel-based ene gy sou ces [
1
]. T adi ional ene gy
sou ces, such as pe oleum and na u al gas, a e being deple ed apidly, leading o sca ci y.
As a esul , he e has been an inc easing end owa d he use o non- adi ional ene gy
sou ces. Con en ional ene gy sou ces ha e been deple ed o a g ea ex en due o hei
con inued use, which has also con ibu ed signi ican ly o pollu ion and global wa ming.
The e o e, scien is s a e emphasising he use o RESs. Non- adi ional enewable ene gy
sou ces a e ene gy sou ces ha a e na u ally eplenished and do no un ou [2].
In he pas en yea s, he e has been a no able su ge in he adop ion o dis ibu ed
ene gy esou ces, including sola pho o ol aic sys ems (SPVSs) and ene gy s o age sys ems
(ESSs), in elec ical powe g ids. In eg a ing hese dis ibu ed ene gy esou ces in o he
powe g id has b ough se e al bene i s, such as suppo du ing hea y loads and imp o ed
powe quali y. Fo example, u ili y-scale sola in e e s ha e he abili y o injec eac i e
powe in o he sys em o enhance he ol age p o ile, while ESSs can main ain he g id’s
ol age and equency du ing aul s, allowing mic og ids o con inue p o iding powe o
loads [
3
,
4
]. O all he sola echnologies a ailable, SPVSs a e conside ed a p omising op ion.
Such sys ems can be managed ei he h ough a s o age sys em o by being connec ed
o he g id [
5
,
6
]. SPVSs a e one o he mos apidly g owing RESs. Mul ile el in e e s
ha e gained in e es o use in g id-in e ac i e SPVSs because o hei widesp ead use and
s ic g id codes [
7
]. Fo g id- ied SPVSs, a ious mul ile el in e e opologies ha e been
p esen ed [
7
,
8
]. These in e e s’ main goals a e o eed he g id wi h as much ac i e powe
as possible ha has been ex ac ed om he PVA. Fo he in e e o unc ion p ope ly,
he speci ic goals o he a ious opologies o mul ile el in e e s (challenges a ise in
achie ing DC-link ol age balancing in a ious opologies, such as neu al-poin -clamped
(NPC), cascaded H-b idge, and lying capaci o con igu a ions) a e also c ucial [
9
]. Va ious
adi ional con ol me hods, along wi h modula ion echniques, ha e been discussed in he
li e a u e. Howe e , con olling mul iple objec i es wi h classical con olle s can be qui e
complica ed [10].
Recen ly, Fini e Se –Model P edic i e Con ol (FS-MPC) has become widely popula
in he ield o powe con e e con ol, owing o i s nume ous bene i s. I o e s apid
dynamic esponse, s abili y, and p ecise con ol du ing s eady-s a e ope a ion. Mo eo e ,
FS-MPC allows o he in eg a ion o sys em nonlinea i ies and cons ain s in o he con ol
algo i hm [
11
,
12
]. FS-MPC ollows a unique app oach ha in ol es u ilising a sys em
model o p edic he u u e beha iou o s a es wi hin a speci ic ime in e al [
11
]. These
p edic ions a e hen e alua ed using a cos unc ion, and he sequence ha bes minimises
he cos unc ion is selec ed o de e mine u u e con ol ac ions. Only he i s alue in he
sequence is implemen ed, and he algo i hm is ecalcula ed o each sampling pe iod.
Fini e Se –Model P edic i e Con ol (FS-MPC) possesses se e al ad an ages, such as
i s abili y o e ec i ely handle nonlinea i ies and cons ain s. Howe e , i also has limi a-
ions due o he ex ensi e compu a ional equi emen s o sol ing he online op imisa ion
p oblem, making i imp ac ical when using he sho sampling imes ypically employed in
con e e con ol. To mi iga e his challenge, a po en ial solu ion is o sol e he op imisa ion
p oblem o line, as has been demons a ed in p e ious s udies [13,14].
In his pape , we in oduce a simpli ied con igu a ion known as he Single-S age
G id-Connec ed Sola Pho o ol aic Sys em (SSGC-SPVS). The sys em consis s o a PVA,
which can be con igu ed in pa allel o se ies depending on he desi ed ol age and powe ,
connec ed o he g id h ough an in e e . The in e e can ei he be a h ee-le el, h ee-
phase neu al poin clamped in e e (3L-3PNPC) o a wo-le el, h ee-phase ol age sou ce
in e e (2L
−
3PVSI). To op imise powe ex ac ion, we employ an inc emen al conduc ance
algo i hm (IC-MPPT) along wi h PI con ol o egula e he DC-bus ol age. A e e ence
cu en is gene a ed o he FS-MP con olle , and he magni ude and equency o he
cu en s a e de e mined using he FS-MPC algo i hm.
Senso s 2023,23, 7901 3 o 22
The assessmen o powe quali y being ed back in o he g id is de e mined by
analysing he THD o he g id cu en s. In p e ious esea ch, when he i adiance ell unde
500 W/m
2
, he THD o he g id cu en s go close o he pe missible h eshold. Fo he
3L
−
3PNPC con igu a ion, in e e ence [
15
], he THD was epo ed o be app oxima ely
3.2% when exposed o an i adiance o 400 W/m
2
; meanwhile, in e e ence [
16
], unde an
i adiance o 800 W/m
2
, he THD eached 3.52%, and in e e ence [
17
], a an i adiance o
1000 W/m
2
, i d opped o 1.57%. Fo he 2L
−
3PVSI s uc u e, in [
18
], a an i adiance o
1000 W/m
2
, he THD was epo ed o be 2.54%, while in [
19
], i was epo ed o be 1.4% a
1000 W/m2.
In his s udy, we p opose he use o p edic i e con ol o supe ise he in e e , wi h
he aim o minimising he cos unc ion while aking in o conside a ion he dynamics
o bo h he pho o ol aic sys em, which expe iences apid changes in insola ion, and he
in e e , including any po en ial delays his may in oduce. We p o ide a comp ehensi e
o e iew o he o e all sys em, including he wo s uc u es (2L
−
3PVSI and 3L
−
3PNPC),
he PVA model, and he in e e opology. Fu he mo e, we de ail he hie a chical con ol
sys em, s a ing wi h IC-MPPT, DC bus, and MPC design. To e alua e he sys em’s
pe o mance, simula ions a e conduc ed using MATLAB and Simulink o bo h s uc u es.
The THD is assessed a di e en le els o i adia ion—speci ically, a 200 W/m
2
, 400 W/m
2
,
800 W/m
2
, and 1000 W/m
2
o bo h s uc u al con igu a ions (2L
−
3PVSI and 3L
−
3PNPC).
These da a se e as he basis o a compa a i e analysis o he wo s uc u es. The esul s
a e ho oughly analysed and in e p e ed. Finally, he s udy concludes wi h a summa y o
he key esea ch indings.
2. Sys em Desc ip ion
2.1. Global Sys em Con igu a ion
The gene al block diag am adop ed o his s udy is a PVA connec ed h ough a
single-s age g id- ied in e e in wo con igu a ions: 2L
−
3PVSI in e e (Figu e 1) and
3L
−
3PNPC in e e (Figu e 2) con igu a ion. Figu e 1depic s he sugges ed model o
a g id- ied 2L
−
3PVSI sys em. This model includes a PV panel g oup, a PLL ci cui , an
LR il e , and an IC-MPPT. Addi ionally, a block s a egy con olle is employed. The PV
panel g oup is di ec ly linked o he g id h ough he 2L
−
3PVSI in e e . The PLL ci cui
is employed o synch onise he 2L
−
3PVSI in e e ou pu cu en wi h he g id ol age.
Figu e 2depic s a 3L
−
3PNPC in e e con igu a ion wi h wo capaci o s and a neu al
clamped poin . The IC-MPPT echnique’s ou pu es ablishes he e e ence ol age (
Vdc e
).
The measu ed inpu ol age o he NPC (
Vdc
) is compa ed o his ol age, and one o he
ecommended con ol s a egies is employed o gene a e he equi ed e e ence cu en
(i∗
max) in conside a ion o he esul ing e o .
2.2. PVA Con igu a ion
The i e-pa ame e single-diode model is widely ecognised and alued o i s sim-
plici y and accu acy in modelling pho o ol aic (PV) cells. One signi ican aspec o his
model, as depic ed in Figu e 3, is he inclusion o pa allel esis ance (R
p
). This pa ame e is
esponsible o cap u ing he in luence o ac o s such as leakage cu en , impu i ies, and
c ys al impe ec ions wi hin he PV cell s uc u e [20].
The ou pu cu en o a sola cell, which includes he pho ocu en , can be ma hema i-
cally modelled by conside ing componen s such as ligh -gene a ed cu en sou ces, diodes,
and se ies and pa allel esis ances.
Ip =Iph −Idexpq
cBTAVp −1(1)
Iph =G[Isc +Ki(T−T )] (2)
Senso s 2023,23, 7901 4 o 22
Id=IoT
T 3
expqEg
KQA1
T −1
T (3)
He e,
Ip
is he ou pu cu en and
Vp = (A
,
V)
is he ou pu ol age,
T
is he em-
pe a u e,
G
is he sola i adiance (W/m
2)
,
Id
is PV sa u a ion cu en ,
Io
is he sa u a ion
cu en a
T
,
Isc
is he sho cu en unde e e ence condi ions,
T
is he e e ence empe a-
u e,
q
is he elec on cha ge, and
CB
is Bol zmann’s cons an . The cha ac e is ics
I/V
and
P/Vo Sola Wo ld SW220 Poly a e shown in Figu e 4.
Senso s 2023, 23, x FOR PEER REVIEW 4 o 23
Figu e 1. Global sys em con igu a ion and con ol o he 2L−3PVSI s uc u e.
Figu e 2. Global sys em con igu a ion and con ol o he 3L−3PNPC s uc u e.
2.2. PVA Con igu a ion
The i e-pa ame e single-diode model is widely ecognised and alued o i s sim-
plici y and accu acy in modelling pho o ol aic (PV) cells. One signi ican aspec o his
model, as depic ed in Figu e 3, is he inclusion o pa allel esis ance (R
p
). This pa ame e
is esponsible o cap u ing he in luence o ac o s such as leakage cu en , impu i ies,
and c ys al impe ec ions wi hin he PV cell s uc u e [20].
Figu e 1. Global sys em con igu a ion and con ol o he 2L−3PVSI s uc u e.
Senso s 2023, 23, x FOR PEER REVIEW 4 o 23
Figu e 1. Global sys em con igu a ion and con ol o he 2L−3PVSI s uc u e.
Figu e 2. Global sys em con igu a ion and con ol o he 3L−3PNPC s uc u e.
2.2. PVA Con igu a ion
The i e-pa ame e single-diode model is widely ecognised and alued o i s sim-
plici y and accu acy in modelling pho o ol aic (PV) cells. One signi ican aspec o his
model, as depic ed in Figu e 3, is he inclusion o pa allel esis ance (R
p
). This pa ame e
is esponsible o cap u ing he in luence o ac o s such as leakage cu en , impu i ies,
and c ys al impe ec ions wi hin he PV cell s uc u e [20].
Figu e 2. Global sys em con igu a ion and con ol o he 3L−3PNPC s uc u e.
Senso s 2023,23, 7901 5 o 22
Senso s 2023, 23, x FOR PEER REVIEW 5 o 23
Figu e 3. Single-diode model o PVA.
The ou pu cu en o a sola cell, which includes he pho ocu en , can be ma hema -
ically modelled by conside ing componen s such as ligh -gene a ed cu en sou ces, di-
odes, and se ies and pa allel esis ances.
exp 1
p ph d p
B
q
III V
cTA


 




(1)

ph sc i
IGIKTT



(2)
3
11
exp
g
do
qE
T
II
TKQATT

  




  

(3)
He e,
p
I
is he ou pu cu en and (,)
p
VAV
is he ou pu ol age,
T
is he
empe a u e, Gis he sola i adiance (W/m
2
󰇜, d
I
is PV sa u a ion cu en , o
I
is he sa -
u a ion cu en a
,
T
s
c
I
is he sho cu en unde e e ence condi ions,
T
is he e -
e ence empe a u e,
q
is he elec on cha ge, and B
C
is Bol zmann’s cons an . The
cha ac e is ics /IV
and /PV
o Sola Wo ld SW220 Poly a e shown in Figu e 4.
(a)
(b)
Figu e 4. Cha ac e is ic o Sola Wo ld SW220 Poly and (a) Cha ac e is ic I/V and (b) Cha ac e is-
ic P/V.
Figu e 3. Single-diode model o PVA.
Senso s 2023, 23, x FOR PEER REVIEW 5 o 23
Figu e 3. Single-diode model o PVA.
The ou pu cu en o a sola cell, which includes he pho ocu en , can be ma hema -
ically modelled by conside ing componen s such as ligh -gene a ed cu en sou ces, di-
odes, and se ies and pa allel esis ances.
exp 1
p ph d p
B
q
III V
cTA


 




(1)

ph sc i
IGIKTT



(2)
3
11
exp
g
do
qE
T
II
TKQATT

  




  

(3)
He e,
p
I
is he ou pu cu en and (,)
p
VAV
is he ou pu ol age,
T
is he
empe a u e, Gis he sola i adiance (W/m
2
󰇜, d
I
is PV sa u a ion cu en , o
I
is he sa -
u a ion cu en a
,
T
s
c
I
is he sho cu en unde e e ence condi ions,
T
is he e -
e ence empe a u e,
q
is he elec on cha ge, and B
C
is Bol zmann’s cons an . The
cha ac e is ics /IV
and /PV
o Sola Wo ld SW220 Poly a e shown in Figu e 4.
(a)
(b)
Figu e 4. Cha ac e is ic o Sola Wo ld SW220 Poly and (a) Cha ac e is ic I/V and (b) Cha ac e is-
ic P/V.
Figu e 4.
Cha ac e is ic o Sola Wo ld SW220 Poly and (
a
) Cha ac e is ic I/V and (
b
) Cha ac e is-
ic P/V.
PV cells a e placed in o PV modules, which a e o ganised in o la ge PV a ays.
Achie ing high e iciency om PV cells is c ucial, bu is o en limi ed by inancial con-
s ain s, esul ing in an e iciency ange o 9–20% [
21
]. PVA elec ici y gene a ion depends
on a mosphe ic condi ions, wi h he I-V cu e being nonlinea and in luenced by sola
i adiance changes, as shown in Figu e 4a. Only he knee ope a ion poin in Figu e 4b
p o ides maximum powe , and so i is essen ial o ope a e he PV gene a o a his poin .
2.3. In e e Con igu a ion
The g id- ied in e e s ha we employed o ou in es iga ion ha e ypical se ups.
The swi ching sequences and he unc ional schemes a e de ined o he wo con igu a ions.
2.3.1. 2L-3PVSI Con igu a ion
The con igu a ion o he 2L-3PVSI con e e is illus a ed in Figu e 5. One c ucial
equi emen o he con e e ’s op imal ope a ion is o ensu e ha he swi ches in each leg
ope a e in a complemen a y manne . This complemen a y mode o ope a ion is essen ial
o p e en ing any po en ial sho ci cui s in he DC sou ce. As a esul , he con e e
is limi ed o a o al o eigh pe missible swi ching s a es. Each o hese swi ching s a es
gene a es speci ic line- o-line ou pu ol ages and he DC-link cu en [22,23].

Senso s 2023,23, 7901 6 o 22
Senso s 2023, 23, x FOR PEER REVIEW 6 o 23
PV cells a e placed in o PV modules, which a e o ganised in o la ge PV a ays.
Achie ing high efficiency om PV cells is c ucial, bu is o en limi ed by inancial con-
s ain s, esul ing in an efficiency ange o 9–20% [21]. PVA elec ici y gene a ion depends
on a mosphe ic condi ions, wi h he I-V cu e being nonlinea and in luenced by sola
i adiance changes, as shown in Figu e 4a. Only he knee ope a ion poin in Figu e 4b
p o ides maximum powe , and so i is essen ial o ope a e he PV gene a o a his poin .
2.3. In e e Con igu a ion
The g id- ied in e e s ha we employed o ou in es iga ion ha e ypical se ups.
The swi ching sequences and he unc ional schemes a e de ined o he wo con igu a-
ions.
2.3.1. 2L-3PVSI Con igu a ion
The con igu a ion o he 2L-3PVSI con e e is illus a ed in Figu e 5. One c ucial
equi emen o he con e e ’s op imal ope a ion is o ensu e ha he swi ches in each
leg ope a e in a complemen a y manne . This complemen a y mode o ope a ion is essen-
ial o p e en ing any po en ial sho ci cui s in he DC sou ce. As a esul , he con e e
is limi ed o a o al o eigh pe missible swi ching s a es. Each o hese swi ching s a es
gene a es speci ic line- o-line ou pu ol ages and he DC-link cu en [22,23].
Figu e 5. 2L−3PVSI con igu a ion.
Figu e 6 shows he eigh swi ching s a es in he ol age ec o opology on a complex
plane.
Figu e 6. Vol age ec o s in he complex plane o 2L−3PVSI in e e .
Figu e 5. 2L−3PVSI con igu a ion.
Figu e 6shows he eigh swi ching s a es in he ol age ec o opology on a com-
plex plane.
Senso s 2023, 23, x FOR PEER REVIEW 6 o 23
PV cells a e placed in o PV modules, which a e o ganised in o la ge PV a ays.
Achie ing high efficiency om PV cells is c ucial, bu is o en limi ed by inancial con-
s ain s, esul ing in an efficiency ange o 9–20% [21]. PVA elec ici y gene a ion depends
on a mosphe ic condi ions, wi h he I-V cu e being nonlinea and in luenced by sola
i adiance changes, as shown in Figu e 4a. Only he knee ope a ion poin in Figu e 4b
p o ides maximum powe , and so i is essen ial o ope a e he PV gene a o a his poin .
2.3. In e e Con igu a ion
The g id- ied in e e s ha we employed o ou in es iga ion ha e ypical se ups.
The swi ching sequences and he unc ional schemes a e de ined o he wo con igu a-
ions.
2.3.1. 2L-3PVSI Con igu a ion
The con igu a ion o he 2L-3PVSI con e e is illus a ed in Figu e 5. One c ucial
equi emen o he con e e ’s op imal ope a ion is o ensu e ha he swi ches in each
leg ope a e in a complemen a y manne . This complemen a y mode o ope a ion is essen-
ial o p e en ing any po en ial sho ci cui s in he DC sou ce. As a esul , he con e e
is limi ed o a o al o eigh pe missible swi ching s a es. Each o hese swi ching s a es
gene a es speci ic line- o-line ou pu ol ages and he DC-link cu en [22,23].
Figu e 5. 2L−3PVSI con igu a ion.
Figu e 6 shows he eigh swi ching s a es in he ol age ec o opology on a complex
plane.
Figu e 6. Vol age ec o s in he complex plane o 2L−3PVSI in e e .
Figu e 6. Vol age ec o s in he complex plane o 2L−3PVSI in e e .
The ol age ec o s in Figu e 6can be desc ibed as ollows.









V1=0, V2=2
3Vdc,V3=1
3+j√3
3Vdc,
V4=−1
3+j√3
3Vdc,V5=−2
3Vdc,V6=−1
3Vdc −j√3
3Vdc,
V7=1
3Vdc,V8=0
(4)
2.3.2. 3L-3PNPC Con igu a ion
NPC mul ile el in e e s a e designed o gene a e a s epped ou pu ol age wa e-
o m by u ilising di e en le els o DC capaci o ol age [
24
]. Fo example, an m-le el
NPC in e e comp ises (m
−1
) capaci o s connec ed o he DC bus, 2
×
(m
−1
) swi ching
de ices pe phase, and 2
×
(m
−2
) clamping diodes pe phase. Figu e 7p o ides a isual
ep esen a ion o a h ee-le el NPC in e e . To achie e his con igu a ion, he DC bus
ol age is di ided in o h ee dis inc le els using wo DC capaci o s, namely, C1 and C2.
Each capaci o main ains a ol age o V
DC⁄
2 ol s, and he ol age dis ibu ion is limi ed o
speci ic capaci o le els [24].
Senso s 2023,23, 7901 7 o 22
Senso s 2023, 23, x FOR PEER REVIEW 7 o 23
The ol age ec o s in Figu e 6 can be desc ibed as ollows.
⎩
⎪
⎪
⎨
⎪
⎪
⎧
𝑉0, 𝑉2
3𝑉,𝑉󰇧1
3
𝑗
√
3
3󰇨𝑉,
𝑉󰇧−1
3𝑗√3
3󰇨𝑉,𝑉−2
3𝑉,𝑉−1
3𝑉−𝑗√3
3𝑉,
𝑉1
3𝑉,𝑉0
(4)
2.3.2. 3L-3PNPC Con igu a ion
NPC mul ile el in e e s a e designed o gene a e a s epped ou pu ol age wa e-
o m by u ilising diffe en le els o DC capaci o ol age [24]. Fo example, an m-le el
NPC in e e comp ises (m
−1
) capaci o s connec ed o he DC bus, 2 × (m
−1
) swi ching de-
ices pe phase, and 2 × (m
−2
) clamping diodes pe phase. Figu e 7 p o ides a isual ep-
esen a ion o a h ee-le el NPC in e e . To achie e his con igu a ion, he DC bus ol -
age is di ided in o h ee dis inc le els using wo DC capaci o s, namely, C1 and C2. Each
capaci o main ains a ol age o V
DC
⁄2 ol s, and he ol age dis ibu ion is limi ed o spe-
ci ic capaci o le els [24].
The u ilisa ion o NPC mul ile el in e e s allows o he gene a ion o ou pu ol -
ages wi h enhanced esolu ion and educed ha monic dis o ion. By employing mul iple
capaci o le els, he s ai case wa e o m can app oxima e a sinusoidal wa e o m wi h in-
c eased p ecision. This imp o ed ol age quali y is pa icula ly ad an ageous in a a ie y
o applica ions, including enewable ene gy sys ems and mo o d i es, as i helps mini-
mise powe losses and mi iga e undesi able effec s on connec ed de ices.
Figu e 7. 3L−3PNPC con igu a ion.
The swi ching s a es o 3L-3PNPC a e p esen ed in Table 1.
Figu e 7. 3L−3PNPC con igu a ion.
The u ilisa ion o NPC mul ile el in e e s allows o he gene a ion o ou pu ol -
ages wi h enhanced esolu ion and educed ha monic dis o ion. By employing mul iple
capaci o le els, he s ai case wa e o m can app oxima e a sinusoidal wa e o m wi h
inc eased p ecision. This imp o ed ol age quali y is pa icula ly ad an ageous in a a ie y
o applica ions, including enewable ene gy sys ems and mo o d i es, as i helps minimise
powe losses and mi iga e undesi able e ec s on connec ed de ices.
The swi ching s a es o 3L-3PNPC a e p esen ed in Table 1.
Table 1. Swi ching s a es o an 3L−3PNPC in e e (x=a,b,c).
SxSx1Sx2Sx3Sx4Sx0
+ 1 1 0 0 VDC/2
001100
−0011−VDC/2
In equa ion o m, he ollowing can be exp essed:
Vxn =


Vc1+Vc2i (Sx1,Sx2)a e ON
Vc2i (Sx2,Sx3)a e ON
0 i (Sx3,Sx4)a e ON
(5)
ixn =


i1i (Sx1,Sx2)a e ON
iNi (Sx2,Sx3)a e ON
i2i (Sx3,Sx4)a e ON
(6)
Figu e 8illus a es he po en ial ol age ec o s and co esponding swi ching s a es.
Senso s 2023,23, 7901 8 o 22
Senso s 2023, 23, x FOR PEER REVIEW 8 o 23
Table 1. Swi ching s a es o an 3L−3PNPC in e e 󰇛𝑥𝑎,𝑏,𝑐󰇜.
S
x
S
x1
S
x2
S
x3
S
x4
S
x0
+ 1 1 0 0 VDC/2
0 0 1 1 0 0
− 0 0 1 1 −VDC/2
In equa ion o m, he ollowing can be exp essed:
12 12
223
34
i ( , ) a e ON
i ( , ) a e ON
0 i ( , ) a e ON
cc xx
xn c x x
xx
VV SS
VV SS
SS






(5)
112
23
234
i ( , ) a e ON
i ( , ) a e ON
i ( , ) a e ON
xx
xn N x x
xx
iSS
ii SS
iSS





(6)
Figu e 8 illus a es he po en ial ol age ec o s and co esponding swi ching s a es.
Figu e 8. Vol age ec o s and swi ching s a es in a 3L−3PNPC in e e .
Figu e 8. Vol age ec o s and swi ching s a es in a 3L−3PNPC in e e .
3. Sys em Con ol
The con ol sys em is di ided in o h ee s ages o he wo con igu a ions (i.e., 2L-
3PVSI and 3L
−
3PNPC). The i s is he IC-MPPT, he second is he DC- ol age con ol,
ollowed by, inally, FS-MPC.
3.1. IC-MPPT Algo i hm
In o de o op imise he ene gy ou pu o a pho o ol aic (PV) sys em in a iable
wea he condi ions, i is essen ial o inco po a e a maximum powe poin acking (MPPT)
algo i hm. The IC-MPPT algo i hm is based on he concep o u ilising he inc emen al
conduc ance o he PV panel o de e mine he slope o he powe cu e. By ensu ing ha he
inc emen al conduc ance ma ches i s ins an aneous alue, he MPPT algo i hm e ec i ely
acks he maximum powe poin [
24
,
25
]. Figu e 9p o ides a isual ep esen a ion o he
lowcha o he IC-MPPT algo i hm.
3.2. DC-Bus Vol age Con ol
The DC-bus ol age is main ained a i s e e ence le el o he wo con igu a ions,
i.e., o bo h 2L−3PVSI and 3L−3PNPC in e e s. Fo 3L−3PNPC in e e , he measu ed
DC-bus ol age is he sum o he wo capaci o s.
A simple PI egula o is used in he wo con igu a ions, as shown in Figu e 10. The
ou pu o he PI con olle is he ampli ude e e ence cu en , which cons i u es he inpu
o he model’s p edic i e con olle .
Senso s 2023,23, 7901 9 o 22
Senso s 2023, 23, x FOR PEER REVIEW 9 o 23
3. Sys em Con ol
The con ol sys em is di ided in o h ee s ages o he wo con igu a ions (i.e., 2L-
3PVSI and 3L−3PNPC). The i s is he IC-MPPT, he second is he DC- ol age con ol,
ollowed by, inally, FS-MPC.
3.1. IC-MPPT Algo i hm
In o de o op imise he ene gy ou pu o a pho o ol aic (PV) sys em in a iable
wea he condi ions, i is essen ial o inco po a e a maximum powe poin acking (MPPT)
algo i hm. The IC-MPPT algo i hm is based on he concep o u ilising he inc emen al
conduc ance o he PV panel o de e mine he slope o he powe cu e. By ensu ing ha
he inc emen al conduc ance ma ches i s ins an aneous alue, he MPPT algo i hm effec-
i ely acks he maximum powe poin [24,25]. Figu e 9 p o ides a isual ep esen a ion
o he lowcha o he IC-MPPT algo i hm.
(a)
(b)
Figu e 9. (a) Flowcha o he IC-MPTT algo i hm; (b) block diag am o IC-MPPT using
MATLAB/Simulink.
3.2. DC-Bus Vol age Con ol
The DC-bus ol age is main ained a i s e e ence le el o he wo con igu a ions,
i.e., o bo h 2L−3PVSI and 3L−3PNPC in e e s. Fo 3L−3PNPC in e e , he measu ed
DC-bus ol age is he sum o he wo capaci o s.
Figu e 9.
(
a
) Flowcha o he IC-MPTT algo i hm; (
b
) block diag am o IC-MPPT using MAT-
LAB/Simulink.
Senso s 2023, 23, x FOR PEER REVIEW 10 o 23
A simple PI egula o is used in he wo con igu a ions, as shown in Figu e 10. The
ou pu o he PI con olle is he ampli ude e e ence cu en , which cons i u es he inpu
o he model’s p edic i e con olle .
Figu e 10. PI co ec o o he DC-bus ol age.
3.3. MP Con olle Design
Fini e Se –Model P edic i e Con ol (FS-MPC) is a highly popula app oach em-
ployed in powe elec onic con e e s o effec i ely manage he low o elec ical ene gy.
This echnique is enowned o i s ad an ages, which include i s simple design and e-
ma kable dynamic pe o mance [26,27]. The unde lying p inciple o FS-MPC e ol es
a ound selec ing he mos sui able swi ching s a e o he powe con e e in o de o min-
imise he u u e de ia ion o he con olled a iable [28,29].
Du ing he implemen a ion o Fini e Se –P edic i e Model Con ol (FS-MPC), an im-
po an aspec o conside is he e alua ion o he cos unc ion. This unc ion conside s
diffe en e ms ha a e de i ed om he con olled a iables and ope a ing condi ions.
To achie e he desi ed pe o mance, i is c ucial o de ine weigh ing ac o s ha es ablish
he ela ionship be ween hese e ms. None heless, a signi ican challenge in deploying
FS-MPC is he ca e ul selec ion o app op ia e weigh ing ac o s ha can adequa ely bal-
ance he con ol objec i es. This ask equi es inding he op imal combina ion o weigh s
o assign o a ious e ms in he cos unc ion, which is essen ial o achie ing he desi ed
con ol pe o mance. This issue has been add essed in p e ious s udies [29,30].
The FS-MPC algo i hm o he con ol o he 3L-NPC is ini ialised wi h he disc e i-
sa ion o DC cu en . The equa ions go e ning he dynamic beha iou o he ol age
ac oss he DC-link capaci o can be exp essed as ollows:
1
1
1()
c
c
dV i
d C

(7)
2
2
1()
c
c
dV i
d C

(8)
He e,
1
C
and
2
C
a e capaci ances ac oss he uppe and lowe DC-link capaci o s,
espec i ely. Addi ionally,
1c
V
and
2c
V
a e DC-link capaci o ol ages. Mo eo e ,
1c
i
and
2c
i
a e cu en s h ough capaci o s
1
C
and
2
,C
espec i ely.
To p edic and an icipa e he dynamics o he a iables in ol ed in he cos unc ion,
i is essen ial o u ilise a disc e e- ime model o he sys em. This disc e e- ime model al-
lows o he o mula ion o ma hema ical equa ions ha desc ibe he sys em’s beha iou
o e disc e e ime in e als. To achie e his, he Eule p e iew echnique is employed due
o i s simplici y and accep able accu acy, which is e y impo an o achie ing imp o ed
pe o mance [23,31]. Using his echnique, he sys em’s disc e e ime o m can be ob-
ained, as shown in he ollowing:
() ( 1) ( )
,
s
di i k i k
d T


(9)
whe e
s
T
is he sampling pe iod.
Figu e 10. PI co ec o o he DC-bus ol age.
3.3. MP Con olle Design
Fini e Se –Model P edic i e Con ol (FS-MPC) is a highly popula app oach employed
in powe elec onic con e e s o e ec i ely manage he low o elec ical ene gy. This
echnique is enowned o i s ad an ages, which include i s simple design and ema kable
dynamic pe o mance [
26
,
27
]. The unde lying p inciple o FS-MPC e ol es a ound selec -
ing he mos sui able swi ching s a e o he powe con e e in o de o minimise he u u e
de ia ion o he con olled a iable [28,29].
Du ing he implemen a ion o Fini e Se –P edic i e Model Con ol (FS-MPC), an
impo an aspec o conside is he e alua ion o he cos unc ion. This unc ion conside s
di e en e ms ha a e de i ed om he con olled a iables and ope a ing condi ions. To
achie e he desi ed pe o mance, i is c ucial o de ine weigh ing ac o s ha es ablish he
Senso s 2023,23, 7901 16 o 22
Figu e 19 p esen s he esul s o ne wo k ol age and phase cu en o wo di e en
s uc u es: (a) 2L−3PVSI and (b) 3L-3PNPC.
Senso s 2023, 23, x FOR PEER REVIEW 17 o 23
(b) 3L−3PNPC s uc u e
Figu e 18. G id ol age.
Figu e 19 p esen s he esul s o ne wo k ol age and phase cu en o wo diffe en
s uc u es: (a) 2L−3PVSI and (b) 3L-3PNPC.
(a) 2L−3PVSI s uc u e
(b) 3L−3PNPC s uc u e
Figu e 19. Phase ol age and g id cu en .
Figu e 20 p esen s he esul s o ac i e and eac i e powe o wo diffe en s uc-
u es: (a) 2L−3PVSI and (b) 3L−3PNPC.
(a) 2L-3PVSI s uc u e
Figu e 19. Phase ol age and g id cu en .
Figu e 20 p esen s he esul s o ac i e and eac i e powe o wo di e en s uc u es:
(a) 2L−3PVSI and (b) 3L−3PNPC.
Senso s 2023, 23, x FOR PEER REVIEW 17 o 23
(b) 3L−3PNPC s uc u e
Figu e 18. G id ol age.
Figu e 19 p esen s he esul s o ne wo k ol age and phase cu en o wo diffe en
s uc u es: (a) 2L−3PVSI and (b) 3L-3PNPC.
(a) 2L−3PVSI s uc u e
(b) 3L−3PNPC s uc u e
Figu e 19. Phase ol age and g id cu en .
Figu e 20 p esen s he esul s o ac i e and eac i e powe o wo diffe en s uc-
u es: (a) 2L−3PVSI and (b) 3L−3PNPC.
(a) 2L-3PVSI s uc u e
Senso s 2023, 23, x FOR PEER REVIEW 18 o 23
(b) 3L−3PNPC s uc u e
Figu e 20. Ac i e and eac i e powe .
Figu e 21 displays he o al ha monic dis o ion (THD) o he g id cu en o wo
diffe en s uc u es: (a) 2L−3PVSI and (b) 3L−3PNPC.
(a) 2L-3PVSI s uc u e
(b) 3L-3PNPC s uc u e
Figu e 21. G id cu en THD and i s zoom a i adiance = 400 W/m
2
.
Table 3 shows he compa a i e analysis o he wo s uc u es in e ms o powe ip-
ples, dynamic esponse, and o al ha monic dis o ion.
Table 3. Compa a i e analysis o he wo s uc u es.
I adiance (W/m
2
) = 200
S uc u e Powe ipples (kW) Dynamic esponse (s) THD
i
(%)
2L−3PVSI 0.09 N/A 6.83
3L−3PNPC 0.08 N/A 3.32
Figu e 20. Ac i e and eac i e powe .

Senso s 2023,23, 7901 17 o 22
Figu e 21 displays he o al ha monic dis o ion (THD) o he g id cu en o wo
di e en s uc u es: (a) 2L−3PVSI and (b) 3L−3PNPC.
Senso s 2023, 23, x FOR PEER REVIEW 18 o 23
(b) 3L−3PNPC s uc u e
Figu e 20. Ac i e and eac i e powe .
Figu e 21 displays he o al ha monic dis o ion (THD) o he g id cu en o wo
diffe en s uc u es: (a) 2L−3PVSI and (b) 3L−3PNPC.
(a) 2L-3PVSI s uc u e
(b) 3L-3PNPC s uc u e
Figu e 21. G id cu en THD and i s zoom a i adiance = 400 W/m
2
.
Table 3 shows he compa a i e analysis o he wo s uc u es in e ms o powe ip-
ples, dynamic esponse, and o al ha monic dis o ion.
Table 3. Compa a i e analysis o he wo s uc u es.
I adiance (W/m
2
) = 200
S uc u e Powe ipples (kW) Dynamic esponse (s) THD
i
(%)
2L−3PVSI 0.09 N/A 6.83
3L−3PNPC 0.08 N/A 3.32
Figu e 21. G id cu en THD and i s zoom a i adiance = 400 W/m2.
Table 3shows he compa a i e analysis o he wo s uc u es in e ms o powe ipples,
dynamic esponse, and o al ha monic dis o ion.
Table 3. Compa a i e analysis o he wo s uc u es.
I adiance (W/m2) = 200
S uc u e Powe ipples (kW) Dynamic esponse (s) THDi(%)
2L−3PVSI 0.09 N/A 6.83
3L−3PNPC 0.08 N/A 3.32
I adiance (W/m2) = 400
S uc u e Powe ipples (kW) Dynamic esponse (s) THDi(%)
2L−3PVSI 0.088 0.04 3.45
3L−3PNPC 0.075 0.025 1.75
I adiance (W/m2) = 800
S uc u e Powe ipples (kW) Dynamic esponse (s) THDi(%)
2L−3PVSI 0.087 0.07 1.66
3L−3PNPC 0.073 0.015 0.98
I adiance (W/m2) = 1000
S uc u e Powe ipples (kW) Dynamic esponse (s) THDi(%)
2L−3PVSI 0.086 N/A 1.31
3L−3PNPC 0.069 N/A 0.9
Senso s 2023,23, 7901 18 o 22
5. Discussion
As shown in Figu e 15, a di ec co ela ion is obse ed be ween he sola i adiance
p o ile and he powe deli e ed by he PV panels. When sola i adiance is high, he
gene a ed powe eaches i s maximum, while du ing pe iods o low i adiance, he gen-
e a ed powe dec eases. This close co ela ion be ween he sola i adiance p o ile and
he gene a ed powe con i ms ha he pho o ol aic sys em pe ec ly ollows he chosen
i adiance p o ile, demons a ing he e iciency o con e ing sola ene gy in o elec ici y
by he PV panels.
In Figu e 16, when he 2L-3PVSI s uc u e is used, i can be obse ed ha he luc ua-
ions o he DC bus ol age a e no pe ec ly educed compa ed o he 3L-3PNPC s uc u e.
This indica es ha he 3L
−
3PNPC s uc u e is be e a egula ing he DC bus ol age, e-
ducing undesi able ol age a ia ions o a g ea e ex en . On he o he hand, he 2L-3PVSI
s uc u e shows a endency o exhibi la ge ipples in he DC bus ol age, which can ha e
an impac on he s abili y and quali y o he powe supply sys em.
In Figu e 17, when he 3L
−
3PNPC s uc u e is employed, i can be no iced ha he
cu en s a e pe ec ly sinusoidal compa ed o he 2L
−
3PVSI s uc u e. This indica es ha
he 3L-3PNPC s uc u e gene a es mo e egula and cu en s wi h highe quali y, esul ing
in he injec ion o ene gy o excellen quali y in o he elec ical g id. On he o he hand,
he 2L-3PVSI s uc u e exhibi s cu en s ha may ha e dis o ions and ha monics, which
can ad e sely a ec he quali y o he ene gy injec ed in o he g id. Consequen ly, he
u ilisa ion o he 3L
−
3PNPC s uc u e signi ican ly enhances he quali y o he ene gy
supplied o he ne wo k.
When using he 2L
−
3PVSI s uc u e, he 3L
−
3PNPC s uc u e gene a es a mo e s able
g id ol age ha is close o he e e ence alue, as illus a ed in Figu e 18. The s abili y
o he g id ol age is essen ial o ensu ing eliable and op imal ope a ion o elec ical
de ices linked o he g id. The e o e, he use o he 3L
−
3PNPC s uc u e can con ibu e o
enhancing he quali y o he elec ical ene gy supplied o he ne wo k.
In Figu e 19, bo h s uc u es ope a e wi h a uni y powe ac o , meaning ha hey
injec ac i e powe equal o he appa en powe in o he g id. Howe e , he 3L-3PNPC
s uc u e exhibi s be e s abili y in e ms o g id ol age and phase cu en han he 2L-
3PVSI s uc u e. S able g id ol age and phase cu en a e c ucial o main aining he
balance o he elec ical g id and ensu ing he p ope ope a ion o connec ed de ices. Thus,
he use o he 3L
−
3PNPC s uc u e can p o ide imp o ed s abili y and eliabili y when
supplying elec ical ene gy o he g id.
In Figu e 20, Fo bo h s uc u es, he ac i e and eac i e powe s ollow hei espec i e
e e ences, indica ing a balance be ween ene gy p oduc ion and consump ion. Howe e ,
he 3L
−
3PNPC s uc u e exhibi s supe io s abili y in e ms o bo h ac i e and eac i e
powe , wi h no luc ua ions, when compa ed o he 2L
−
3PVSI s uc u e. A s able and
ipple- ee beha iou o ac i e and eac i e powe is c ucial o ensu ing e icien and
eliable sys em ope a ion, as well as be e ene gy managemen . The e o e, he use o he
3L-3PNPC s uc u e ensu es inc eased s abili y in ac i e and eac i e powe s, ul ima ely
enhancing he quali y o he ene gy supplied o he g id.
Wi h a sola i adiance o 400 W/m
2
i can be obse ed ha he THD o he g id cu en
is lowe when he 3L
−
3PNPC s uc u e is used, wi h a alue o 1.75%, compa ed o he 2L-
3PVSI s uc u e, which exhibi s a THD o 3.45%, as shown in Figu e 21. This indica es ha
he 3L
−
3PNPC s uc u e gene a es g id cu en wi h less ha monic dis o ion, esul ing
in imp o ed quali y o he injec ed elec ical ene gy in o he g id. Howe e , wi h a sola
i adiance o 1000 W/m
2
, he 3L
−
3PNPC s uc u e once again demons a es a signi ican
imp o emen in e ms o ha monic dis o ion o he cu en , as shown in Figu e 22. I s THD
is 0.90%, while he 2L
−
3PVSI s uc u e has a THD o 1.31%. This di e ence highligh s he
supe io abili y o he 3L
−
3PNPC s uc u e o gene a e cleane g id cu en ha closely
app oxima es an ideal sinusoidal wa e o m, as de ailed in Table 3. Table 3also assesses bo h
dynamic esponse and powe luc ua ions. The 3L
−
3PNPC con igu a ion demons a es
supe io dynamic pe o mance when compa ed o he 2L-3PVSI se up. Speci ically, o
Senso s 2023,23, 7901 19 o 22
an i adiance ange o 0 o 400 W/m
2
, he esponse ime is educed om 0.04 s (in he
2L
−
3PVSI s uc u e) o 0.025 s (in he 3L
−
3PNPC s uc u e). Simila ly, o i adiance le els
be ween 400 and 800 W/m
2
, he 3L
−
3PNPC se up achie es a esponse ime o 0.015 s,
whe eas he 2L-3PVSI s uc u e lags behind, wi h a esponse ime o 0.07s. The 2L
−
3PVSI
exhibi s highe powe luc ua ions, whe eas hey a e educed when he i adiance is a
1000 W/m
2
. Speci ically, a an i adiance o 1000 W/m
2
, he 3L
−
3PNPC exhibi s a powe
luc ua ion o 0.069 kW, whe eas he 2L
−
3PVSI shows a sligh ly highe powe luc ua ion,
a app oxima ely 0.086 kW.
Senso s 2023, 23, x FOR PEER REVIEW 20 o 23
eliable sys em ope a ion, as well as be e ene gy managemen . The e o e, he use o he
3L-3PNPC s uc u e ensu es inc eased s abili y in ac i e and eac i e powe s, ul ima ely
enhancing he quali y o he ene gy supplied o he g id.
Wi h a sola i adiance o 400 W/m2 i can be obse ed ha he THD o he g id cu -
en is lowe when he 3L−3PNPC s uc u e is used, wi h a alue o 1.75%, compa ed o
he 2L-3PVSI s uc u e, which exhibi s a THD o 3.45%, as shown in Figu e 21. This indi-
ca es ha he 3L−3PNPC s uc u e gene a es g id cu en wi h less ha monic dis o ion,
esul ing in imp o ed quali y o he injec ed elec ical ene gy in o he g id. Howe e , wi h
a sola i adiance o 1000 W/m2, he 3L−3PNPC s uc u e once again demons a es a sig-
ni ican imp o emen in e ms o ha monic dis o ion o he cu en , as shown in Figu e
22. I s THD is 0.90%, while he 2L−3PVSI s uc u e has a THD o 1.31%. This diffe ence
highligh s he supe io abili y o he 3L−3PNPC s uc u e o gene a e cleane g id cu en
ha closely app oxima es an ideal sinusoidal wa e o m, as de ailed in Table 3. Table 3 also
assesses bo h dynamic esponse and powe luc ua ions. The 3L−3PNPC con igu a ion
demons a es supe io dynamic pe o mance when compa ed o he 2L-3PVSI se up. Spe-
ci ically, o an i adiance ange o 0 o 400 W/m2, he esponse ime is educed om 0.04
s (in he 2L−3PVSI s uc u e) o 0.025 s (in he 3L−3PNPC s uc u e). Simila ly, o i adi-
ance le els be ween 400 and 800 W/m2, he 3L−3PNPC se up achie es a esponse ime o
0.015s, whe eas he 2L-3PVSI s uc u e lags behind, wi h a esponse ime o 0.07s. The
2L−3PVSI exhibi s highe powe luc ua ions, whe eas hey a e educed when he i adi-
ance is a 1000 W/m2. Speci ically, a an i adiance o 1000 W/m2, he 3L−3PNPC exhibi s
a powe luc ua ion o 0.069 kW, whe eas he 2L−3PVSI shows a sligh ly highe powe
luc ua ion, a app oxima ely 0.086 kW.
(a) 2L−3PVSI s uc u e
(b) 3L−3PNPC s uc u e
Figu e 22. G id cu en THD and i s zoom a i adiance = 1000W/m2.
Table 4 illus a es ha he THD esul s exhibi signi ican a ia ions compa ed o
hose epo ed in e e ences [18,19], wi h highe THD alues in mos cases o he wo-
Figu e 22. G id cu en THD and i s zoom a i adiance = 1000W/m2.
Table 4illus a es ha he THD esul s exhibi signi ican a ia ions compa ed o hose
epo ed in e e ences [
18
,
19
], wi h highe THD alues in mos cases o he wo-le el
s uc u e p esen ed in his s udy. This may indica e a mo e subs an ial ha monic dis o ion
in he g id cu en o he 2L
−
3PVSI con igu a ion used. Howe e , i is wo h no ing ha
hese alues emain wi hin accep able limi s acco ding o IEEE 512 s anda ds.
Table 4. G id cu en THD o he 2L-3PVSI s uc u e in p e ious wo ks.
2L-3PVSI
Re e ence [18]
I adiance (W/m2)1000 800 400 200
THD (%) 2.25 N/A N/A N/A
Re e ence [19]
I adiance (W/m2)1000 800 400 200
THD (%) 1.40 1.60 2.6 6.1
Senso s 2023,23, 7901 20 o 22
Table 5 e eals ha he THD esul s exhibi signi ican a ia ion compa ed o hose
epo ed in e e ences [
15
–
17
], wi h highe THD alues in mos cases o he h ee-le el s uc-
u e (3L
−
3PNPC) p esen ed in his s udy. This may indica e a mo e subs an ial ha monic
dis o ion in he g id cu en o he 3L
−
3PNPC con igu a ion used. Ne e heless, hese
alues emain wi hin accep able limi s acco ding o he IEEE 512 s anda ds. The disc epan-
cies be ween his s udy and he e e ences o bo h s uc u es (3L
−
3PNPC and 2L
−
3PVSI)
can be a ibu ed o di e ences in simula ion pa ame e s and componen models.
Table 5. G id cu en THD o 3L−3PNPC s uc u e in p e ious wo ks.
3L−3PNPC
Re e ence [15]
I adiance (W/m2)1000 800 400 200
THD (%) 0.97 1.51 3.2 N/A
Re e ence [16]
I adiance (W/m2)1000 800 400 200
THD (%) N/A N/A 3.45 N/A
Re e ence [17]
I adiance (W/m2)1000 800 400 200
THD (%) 1.57 N/A N/A N/A
6. Conclusions
This s udy aimed o assess he pe o mance o wo con igu a ions o in eg a ing
sola ene gy in o he elec ical g id, namely, he wo-le el in e e sys em (2L
−
3PVSI)
and he h ee-le el NPC in e e sys em (3L
−
3PNPC), using a Fini e Se Model P edic i e
Con ol (FS-MPC) app oach. The esul s ob ained clea ly demons a e ha he 3L-3PNPC
in e e has signi ican ad an ages in e ms o he quali y o he ene gy injec ed in o
he g id and dynamic pe o mance compa ed o he 2L
−
3PVSI in e e . Howe e , he
2L
−
3PVSI in e e s ill main ains i s appeal in e ms o cos and ease o modelling and
con ol, especially o sola i adiance le els exceeding 400 W/m2.
Ne e heless, i is c ucial o no e ha his s udy has limi a ions. The simpli ied models
used o bo h he 2L
−
3PVSI and 3L
−
3PNPC in e e s may no ully ep esen pe o mance
in eal-wo ld en i onmen s, and he lack o in eg a ion o g id dis u bances is also a
poin o conside . The e o e, u he esea ch is needed o explo e hese sys ems mo e
comp ehensi ely, inco po a ing mo e de ailed models and g id dis u bance scena ios.
Fu u e esea ch equi ed in his ield includes he op imisa ion o con ol s a egies
o bo h con igu a ions, aking in o accoun dynamic a ia ions in sola i adiance and
g id dis u bances. Addi ionally, expe imen al s udies a e necessa y o alida e simula ion
esul s and assess he ac ual pe o mance o hese sys ems. Finally, analysing he cos
e ec i eness and en i onmen al impac o hese con igu a ions in eal-wo ld condi ions is
a p omising esea ch a ea o guiding he p ac ical implemen a ion o he in eg a ion o
sola ene gy in o elec ical g ids.
Au ho Con ibu ions:
Concep ualisa ion, A.F., S.V., M.M. and S.G.; Me hodology, S.G., A.F., A.B.,
A.M. and M.M.; So wa e, S.G., A.F., A.B., A.M. and S.V.; Valida ion, S.G., A.F., A.B., A.M. and M.M.;
Fo mal analysis, S.V., S.G. and A.B.; In es iga ion, S.G., A.F., A.B. and A.M.; Resou ces, S.G., A.F. and
M.M.; Da a cu a ion, S.G., A.F., M.M., A.M. and A.B.; W i ing—o iginal d a , e iew and edi ing,
S.G., A.F., A.B., A.M., S.V. and M.M.; Simula ions and isualisa ion, S.G., A.B., A.M., S.V. and M.M.
All au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Funding:
This wo k was suppo ed by he Eu opean Regional De elopmen Fund in he Resea ch
Cen e o Ad anced Mecha onic Sys ems p ojec , CZ.02.1.01/0.0/0.0/16_019/0000867 wi hin he
Ope a ional P og amme Resea ch, De elopmen , and Educa ion and he p ojec SP2023/074 Applica-
Senso s 2023,23, 7901 21 o 22
ion o Machine and P ocess Con ol Ad anced Me hods suppo ed by he Minis y o Educa ion,
You h and Spo s, Czech Republic.
Da a A ailabili y S a emen :
The da a used in his pape can be ob ained om he au ho s upon
eques .
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Abb e ia ions
2L-3PVSI Two-Le el, Th ee-Phase Vol age Sou ce In e e
3L-3PNPC Th ee-Le el, Th ee-Phase Neu al Poin Clamped
DC Di ec Cu en
ESS Ene gy S o age Sys em
FS-MPC Fini e Se Model P edic i e Con ol
IC Inc emen al Conduc ance
MPPT Maximum Powe Poin T acking
PI P opo ional In eg a o
PLL Phase Looked Loop
PV Pho o ol aic
PVA Pho o ol aic A ay
RES Renewable Ene gy Sou ce
SPVS Sola Pho o ol aic Sys em
SSGC-SPVS Single S age G id Connec ed Sola Pho o ol aic Sys em
THD To al Ha monic Dis o ion
N/A No e Applica ed
Re e ences
1.
Saini, G.; Kannan, R.; Benini, E.; Kuma , K. Enabling Me hodologies o Renewable and Sus ainable Ene gy, 1s ed.; CRC P ess: Boca
Ra on, FL, USA, 2023.
2.
Ca e a, B.; Sim, M.K.; Jung, J.Y. PVHybNe : A hyb id amewo k o p edic ing pho o ol aic powe gene a ion using bo h
wea he o ecas and obse a ion da a. IET Renew. Powe Gene . 2020,14, 2192–2201. [C ossRe ]
3.
Fekik, A.; Benam ouche, N. Modeling and Con ol o S a ic Con e e s o Hyb id S o age Sys ems, 1s ed.; IGI Global: He shey, PH,
USA, 2022.
4.
Meng, J.; Zhang, Z.; Zhang, G.; Ye, T.; Zhao, P.; Wang, Y.; Yang, J.; Yu, J. Adap i e model p edic i e con ol o g id- o ming
con e e s o achie e smoo h ansi ion om islanded o g id-connec ed mode. IET Gene . T ansm. Dis ib.
2023
,17, 2833–2845.
[C ossRe ]
5.
Ba a seh, I.; Alluhaybi, K. Eme ging oppo uni ies in dis ibu ed powe elec onics and ba e y in eg a ion: Se ing he s age o
an ene gy s o age e olu ion. IEEE Powe Elec on. Mag. 2020,7, 22–32. [C ossRe ]
6.
Fekik, A.; Hamida, M.L.; Denoun, H.; Aza , A.T.; Kamal, N.A.; Vaidyana han, S.; Bousbaine, A.; Benam ouche, N. Mul ile el
in e e o hyb id uel cell/PV ene gy con e sion sys em. In Modeling and Con ol o S a ic Con e e s o Hyb id S o age Sys ems,
1s ed.; Fekik, A., Benam ouche, N., Eds.; IGI Global: He shey, PH, USA, 2022; pp. 233–270.
7.
Kou o, S.; Leon, J.I.; Vinniko , D.; F anquelo, L.G. G id-connec ed pho o ol aic sys ems: An o e iew o ecen esea ch and
eme ging PV con e e echnology. IEEE Ind. Elec on. Mag. 2015,9, 47–61. [C ossRe ]
8.
Wu, Y.K.; Lin, J.H.; Lin, H.J. S anda ds and guidelines o g id-connec ed pho o ol aic gene a ion sys ems: A e iew and
compa ison. IEEE T ans. Ind. Appl. 2017,53, 3205–3216. [C ossRe ]
9.
Monopoli, V.G.; Alcaide, A.M.; B uno, L.; Rendine, G.; Leon, J.I.; Lise e, M.; F anquelo, L.G. A hyb id modula ion echnique
o ope a ing medium- ol age high-powe CHB con e e s unde g id ol age dis u bances. IEEE T ans. Ind. Elec on.
2023
,71,
462–472. [C ossRe ]
10.
Feng, W.; Xuebing, C.; Shuyu, C.; Beng, S.C.; Zhiqiang, C.; Je , T.K.; Vila hgamuwa, D.M. MPC based dynamic ol age egula ion
using g id-side BESPS wi h he conside a ion o communica ion delay. IEEE T ans. Ene gy Con e s.
2023
,38, 838–848. [C ossRe ]
11.
Jupin, S.; Vechiu, I.; Tapia-O agui, G. Uni e sal swi ched s a e-space ep esen a ion o model p edic i e con ol o powe
con e e s. Elec . Powe Sys . Res. 2020,180, 106120. [C ossRe ]
12.
Munee , V.; Biju, G.M.; Bha acha ya, A. Op imal machine-lea ning-based con olle o shun ac i e powe il e by au o machine
lea ning. IEEE J. Eme g. Sel. Top. Powe Elec on. 2023,11, 3435–3444. [C ossRe ]
13.
Yao, W.; Dongliang, K.; Qi, H.; Wang, F.; Rod iguez, J. Mul is ep p edic i e cu en con ol o elec ical d i es wi h adap i e
ho izons. IEEE T ans. Ind. Elec on. 2023,71, 250–260.
14.
Jamal, I.; Elmo shedy, M.F.; Dabou , S.M.; Rashad, E.M.; Xu, W.; Almakhles, D.J. A comp ehensi e e iew o g id-connec ed PV
Sys ems Based on Impedance Sou ce In e e . IEEE Access 2022,10, 89101–89123. [C ossRe ]

Senso s 2023,23, 7901 22 o 22
15.
A ik, N.; Badoud, A.E.; Me ahi, F.; Laib, A.; Lazha , R. An imp o ed DC-link con ol o dual-s age g id connec ed Pho o ol aic
sys em using h ee-le el Neu al Poin Climped in e e . In P oceedings o he 19 h In e na ional Mul i-Con e ence on Sys ems,
Signals & De ices, Se i , Alge ia, 6–10 May 2022. [C ossRe ]
16.
Bonala, A.K.; Sandepudi, S.R.; Muddineni, V.P. Selec i e ini e-s a es model p edic i e con ol o g id in e aced h ee-le el
neu al poin clamped pho o ol aic in e e o inhe en capaci o ol age balancing. IET Powe Elec on.
2018
,13, 2042–2080.
[C ossRe ]
17.
Dennai, M.Y.; Tedjini, H.; Nas i, A.; Taibi, D. MPC con olle o PV sys em based Th ee-Le el NPC In e e unde di e en
clima ic condi ions connec ed o he g id. P zegl ˛ad Elek o echniczny 2021,97, 130–137. [C ossRe ]
18.
Zhao, Y.; An, A.; Xu, Y.; Wang, Q.; Wang, M. Model p edic i e con ol o g id-connec ed PV powe gene a ion sys em conside ing
op imal MPPT con ol o PV modules. P o . Con ol Mod. Powe Sys . 2021,6, 32. [C ossRe ]
19.
Güle , N.; I mak, E. MPPT Based Model P edic i e Con ol o G id Connec ed In e e o PV Sys ems. In P oceedings o he 8 h
In e na ional Con e ence on Renewable Ene gy Resea ch and Applica ions, B aso , Romania, 3–6 No embe 2019.
20.
Weng-Hooi, T.; Mohamad-Saleh, J. C i ical e iew on in e ela ionship o elec o-de ices in PV sola sys ems wi h hei e olu ion
and u u e p ospec s o MPPT applica ions. Ene gies 2023,16, 850.
21.
Dusa, A.; Li in i, P.; Badea, N.; Luca, L. Compa a i e analysis o he me hods used o ac i e powe il e ing in a g id-connec ed
pho o ol aic sys em. J. Ene gy Powe Eng. 2021,15, 135–149.
22.
He, J.; Zhang, X. A dual-objec i e modula ed model p edic i e con ol scheme o he poin -o -load in e e in dc mic og id wi h
dicho omy algo i hm. In P oceedings o he 2020 IEEE Ene gy Con e sion Cong ess and Exposi ion (ECCE), De oi , MI, USA,
11–15 Oc obe 2020; pp. 2276–2280.
23.
Mo a, A.; Ca denas, R.; Aguile a, R.P.; Angulo, A.; Lezana, P.; Lu, D.-C. P edic i e Op imal Swi ching Sequence Di ec Powe
Con ol o G id-Tied 3L-NPC Con e e s. IEEE T ans. Ind. Elec on. 2021,68, 8561–8571. [C ossRe ]
24.
Anand, M.; Sen hilkuma , R. Analysis o neu al poin clamped mul ile el in e e using space ec o modula ion echnique. In .
J. Eng. Tech. Res. 2015,3, 32–37.
25.
Abdullah, B.U.D.; La a, S.; Jaiswal, S.P.; Bhado ia, V.S.; Fo is, G.; San as, A.; Ekonomou, L. A Hyb id A i icial Ecosys em
Op imize and Inc emen al-Conduc ance Maximum-Powe -Poin -T acking-Con olled G id-Connec ed Pho o ol aic Sys em.
Ene gies 2023,16, 5384. [C ossRe ]
26.
Singh, S.; Saini, S.; Gup a, S.K.; Kuma , R. Sola -PV in e e o he o e all s abili y o powe sys ems wi h in elligen MPPT
con ol o DC-link capaci o ol age. P o . Con ol Mod. Powe Sys . 2023,8, 15. [C ossRe ]
27.
Xie, H.; Tian, W.; Gao, X.; Wang, F.; Rod iguez, J.; Kennel, R. An ensemble egula ion p inciple o mul iobjec i e ini e-con ol-se
model-p edic i e con ol o induc ion machine d i es. IEEE T ans. Powe Elec on. 2023,38, 3069–3083. [C ossRe ]
28.
Xie, H.; Du, J.; Ke, D.; He, Y.; Wang, F.; Hackl, C.; Rod iguez, J.; Kennel, R. Mul is ep model p edic i e con ol o elec ical
d i es-A as quad a ic p og amming solu ion. Symme y 2022,14, 626. [C ossRe ]
29.
Lakhda i, A.; Benlahbib, B.; Abdelk im, T. Model p edic i e con ol o h ee-phase h ee-le el NPC in e e based APF in e acing
single s age pho o ol aic sys em o he g id. J. Eu . Des Sys . Au om. 2022,55, 25–34. [C ossRe ]
30.
Shahid, M.B.; Jin, W.; Abbasi, M.A.; Husain, A.R.; Hassan, M. To que e o based au o- uning o weigh ing ac o in model
p edic i e o que con ol o induc ion mo o d i e. J. Elec . Eng. Technol. 2023,18, 1959–1973. [C ossRe ]
31.
Laib, A.; K ama, A.; Sahli, A.; Kihal, A.; Abu-Rub, H. Recon igu able model p edic i e con ol o g id connec ed PV sys ems
using hi een-le el packed e-cell in e e . IEEE Access 2022,10, 102210–102222. [C ossRe ]
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The s a emen s, opinions and da a con ained in all publica ions a e solely hose o he indi idual
au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o
people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .