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This is an Accep ed Manusc ip o an con e ence pape published 2025 IEEE
In e na ional Con e ence on Indus ial Technology (ICIT) a ailable a :
10.1109/ICIT63637.2025.10965309
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FSC-MPC Swi ching Phase Con ol o In e lea ed
DC/DC Vehicle Cha ge
Ma ´
ıas Agui e
Membe , IEEE,
Se gio Vazquez
Fellow, IEEE,
Jose I. Leon
Fellow, IEEE,
Leopoldo G. F anquelo
Li e Fellow, IEEE
Abs ac —In e lea ed con e e con igu a ions a e a common
solu ion o he cha ging o elec ic ehicles. Ca ie phase shi
is a common and impo an design elemen o hese con e e s.
Recen esea ch shows ha a p ope egula ion o he phase
shi can imp o e he sys em pe o mance. This equi es mo e
complex con olle s and ac ua ion capabili ies.
Fini e Con ol Se Model P edic i e Con ol (FCS-MPC) has
he capabili y o manage mul iple con ol. Recen esea ch has
managed o achie e a sa is ac o y swi ching equency con ol
h ough a pe iod con ol app oach (PCA) o a single powe
con e e . Howe e , i does no con ol he swi ching phase
equi ed o an in e lea ed ope a ion wi h pa allel con e e s.
This pape p esen s he design and implemen a ion o a swi ch-
ing phase con ol o PCA-FCS-MPC, allowing he ope a ion o
an in e lea ed con igu a ion. The pe o mance is e alua ed o
di e en ope a ing poin h ough expe imen al alida ion.
Index e ms— Model P edic i e Con ol, Fini e Con ol Se ,
Fixed Swi ching F equency, In e lea ed Con e e , Vehicle
Cha ge
I. INTRODUCTION
The ansi ion om ossil uel ehicles o hyb id o ully
elec ical ones has inc eased in ecen yea s and many coun-
ies aim o a ull elec i ica ion in he nea u u e. A majo
aspec in he execu ion o his ansi ion is he in as uc u e
equi ed o accommoda e his echnologies. Mainly in his
ca ego y is he a ailabili y, capabili ies and obus ness o
elec ic cha ge s [1]. Technological ad ancemen in ma e ials,
so wa e and manu ac u ing ha e made i easie o e ime
o jump-s a he c ea ion o a unc ional ne wo k o suppo
he in eg a ion o elec ic ehicles. None heless, he e is s ill
much o do o achie e an ease o use compa able o ossil uel
ehicles in e ms o cha ging speed, eliabili y o a ailabili y.
In e ms o cha ging speed, one common s a egy o achie e
he equi ed powe wi hou incu ing in cos ly componen s, is
he use o in e lea ed con e e s [2]–[7]. These con igu a ions
allow mul iple modules o dis ibu e he powe ou pu while
imp o ing he o e all con ol pe o mance o he ele an
elec ical a iables. This also p o ides lexibili y and esilience
when dealing wi h mal unc ions o uncon en ional equi e-
men s.
The mos common scheme o con ol hese con e e s is
h ough PWM along linea con olle s. Ano he al e na i e
is h ough he use o Fini e Con ol Se Model P edic i e
Con ol (FCS-MPC), which o e s mo e lexibili y in e ms o
ac ua ion, while also p o iding a mo e lexible con ol scheme
capable o mul iple con ol objec i es and o di e en na u e.
None heless, due o he a iable swi ching equency achie ed
by he con en ional implemen a ion o FCS-MPC, i s use o
he con ol o in e lea ed con e e s has been limi ed.
In ecen publica ions, a solu ion o he swi ching equency
o FCS-MPC has been p oposed, named Pe iod Con ol Ap-
p oach (PCA-FCS-MPC), ha main ains he ime disc e e
na u e o he con olle [8], [9]. The achie ed swi ching pa e n
is close o a PWM, while pe o ming like FCS-MPC in mos
ele an me ics. An impo an d awback o his solu ion is he
lack o con ol o e he swi ching phase, hus being unable o
bene i a ull om he in e lea ed con igu a ion. This has been
sol ed in [10], whe e a swi ching phase con ol is implemen ed
in o PCA-FCS-MPC. Using his app oach, he phase swi ch
equi ed by he in e lea ed con igu a ion can be ealized and
u he op imized acco ding o di e en ope a ing poin s and
objec i es. The p oposed s a egy has been alida ed in s eady
s a e, bu a eal implemen a ion o a elec ic ehicle cha ge
would also equi e quick esponse imes o changes in he load,
o u he op imize he cha ging p ocess and quickly espond o
po en ial dis u bances. This pape aim o expand he analysis
p esen ed in [10], pa icula ly in ega ds o he ime esponse
o he o e all con ol s a egy, hus alida ing i s easibili y o
i s use in he applica ion o elec ic ehicle cha ging s a ions.
The s uc u e o his pape is as ollows. Sec ion II s a s
wi h a desc ip ion o he disc e e model o he selec ed
con e e o i s use in PCA-FCS-MPC Also, his sec ion
includes a b ie summa y o he classic con ol ope a ion wi h
equal phase shi be ween modules’ ca ie s, and he possibili y
o op imize his phase shi o di e en ope a ing condi ions.
A e his, in Sec ion III, he con ol s a egy o PCA-FCS-
MPC is desc ibed in de ail o acili a e i s implemen a ion.
In Sec ion IV, he p oposed s a egy o phase con ol is
desc ibed, bo h o phase measu emen and con ol. In Sec ion
V, expe imen al esul s a e p esen ed o illus a e and e alua e
he pe o mance o he p oposed s a egy. Sec ion VI inishes
his pape wi h conclusions and closing ema ks.
II. CONVERTER MODEL AND OPERATION
The selec ed sys em is an in e lea ed dc/dc buck powe con-
e e . I is composed o h ee modules in pa allel, as shown
in Fig. 1. The high ol age capaci o s eady s a e ol age, i,
is ixed by an ex e nal ol age sou ce. The bandwid h o his
ol age sou ce is limi ed, which means i is expec ed o each
a s able ol age, i, and cu en , ii, in s eady s a e, bu he
capaci o is s ill suscep ible o high equency dynamics o
dis o ions due o he con e e ’s ope a ion. The low ol age
capaci o ol age, o, and induc o s’ cu en s i1,i2and i3,
Fig. 1. Ci cui scheme o he dc/dc in e lea ed powe con e e .
a e he dc/dc buck con olle objec i e a iables. The load
ba e y is ep esen ed in simula ion by a esis o , wi hou loss
o gene ali y.
In o de o implemen an FCS-MPC me hod, a disc e e
model o he sys em is equi ed. A o wa d Eule app oxima-
ion wi h sampling pe iod τsis selec ed [11]. The e o e, he
equa ions ha desc ibe he beha io o he p oposed sys em
a e
I= [i1i2i3]T,S= [S1S2S3]T
Ik+1 =Ik+ ( i,kSk9 o,k)τs/L (1a)
i,k+1 = i,k +ii9ST
kIkτs/Ci(1b)
o,k+1 = o,k +1T
3Ik9io,kτs/Co(1c)
whe e 1n= [1 · · · 1]To leng h ‘n’.
A. In e lea ed Ope a ion
A common ope a ion s a egy o an in e lea ed powe
con e e is o dis ibu e he powe be ween modules, h ough
he use o PWM [12]–[14] and a phase shi θx o he ca ie
o each module.
θx, =x2π/M , (2)
whe e Mis he numbe o modules in pa allel [15]–[20] and
x∈ {1,2,· · · , M}.
One ad an age o his app oach is he educ ion o low
equency ha monic con en o he cu en a he high ol age
side o he con e e . This ex ends he expec ed li e ime o he
capaci o s, as shown in [21]. Ano he ad an age is he e ec i e
mul iplica ion o he swi ching equency obse ed a he o al
ou pu cu en , eaching a ac o o Mo e he swi ching
equency implemen ed a each module, hus achie ing a be e
pe o mance wi hou o e exe ing he semiconduc o s.
Examples o he e ec s achie ed wi h a dis ibu ed phase
shi ope a ion is shown in Fig. 2 and he balanced esul s
o Fig. 3. Fig. 2 shows he cu en con ibu ion o each
module and he capaci o cu en , ici, in s eady s a e. Fig. 2(b)
illus a es he educed ipple in he ou pu cu en , compa ed
o he induc o ’s cu en ipple. Fig. 3, illus a es he e ec on
he cu en spec a o he high ol age capaci o . The esul s
clea ly illus a es he absence o low equency ha monics o
he balanced sys em. These equencies componen s a e o
majo impo ance, since hey a e among he main ac o s in
he educ ion o he capaci o li e ime expec ancy [21].
4
5
6
0 0.5 1 1.5 2 2.5 3
-2
0
2
4
(a)
(b)
Fig. 2. Induc o s and capaci o s cu en s o a (le ) balanced, (cen e )
unbalanced and ( igh ) op imized ope a ion in ime, a 2kHz swi ching
equency.
0 2 4 6 8 10 12 14 16
0
0.5
1
1.5
2
Fig. 3. Compa ison be ween he cu en spec um o Ci o a balanced,
unbalanced and op imized ope a ion, a 2kHz swi ching equency.
B. Op imal Phase Shi
A phase shi o 360◦
Mbe ween consecu i e modules achie es
a good pe o mance when he modules a e balanced, i.e.
all modules ope a e unde he same condi ions o ol age
and cu en . None heless, his is no longe he case when
he powe managed by each module di e s. This can be
he case o mul iple cha ging s a ions connec ed o ehicles
wi h di e en cha ging equi emen s, o a equi ed imbalance
o manage he emaining li e ime o he componen s. I
can also be he case ha one o he modules is de ec i e,
which may equi e an une en dis ibu ion o he cu en , o
disconnec ion o a module, hus being un i o he same phase
shi . This is illus a ed in Fig. 2(cen e ) and Fig. 3, whe e
an unbalanced con igu a ion leads o an inc ease in he low
equency ha monics o he cu en a he high ol age side o
he con e e .
The op imal phase shi o minimize low equency ha -
monics can be compu ed as a unc ion o he ope a ing poin
and he di e en pa ame e s o he sys em [21]. The e ec o
using he op imized phase shi is illus a ed a Fig. 2( igh ),
and u he emphasized by he spec a in Fig. 3.
III. PREDICTIVE CONTROL
The use o Pe iod Con ol App oach (PCA) has shown
o be e ec i e o ix he swi ching equency and shape he
spec um o he FCS-MPC [8], [9]. The e o e, i is possible
o implemen his algo i hm in he p esen sys em, achie ing
simila pe o mances as wi h PWM.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
0
10
20
Fig. 4. Example o pe iod compu a ion.
A. Pe iod Con ol App oach
Pe iod measu emen is achie ed by coun ing he ime in
be ween simila commu a ions o each module o he con-
e e . E e y ime a commu a ion akes places, he espec i e
coun e , Quo Qd, is ese o 1. Fig. 4 illus a es how his
p ocess un old. The pe iod alues Tuand Tda e only upda ed
when he espec i e commu a ion akes place, as
Q△= [Q1uQ2uQ3u]T,T△= [T1uT2uT3u]T,
Q▽= [Q1dQ2dQ3d]T,T▽= [T1dT2dT3d]T,
E△
kE▽
k=E△▽
k= [(Sk>Sk91) (Sk<Sk91)] (3a)
Q△
kQ▽
k=Q△▽
k=Q△▽
k91◦E△▽
k+ 1 (3b)
T△
kT▽
k=T△▽
k=T△▽
k91◦E△▽
k+τsQ△▽
k91◦E△▽
k(3c)
whe e ‘◦’ co esponds o he elemen wise p oduc .
When a e y high o e y low ou pu is equi ed, he con ol
signal would no swi ch, bu he in e nal coun is s ill upda ed
as i a ze o wid h commu a ion we e implemen ed. This i ual
commu a ion is achie ed as
E
k=Q△
k>Q ∧Q▽
k<Q 1T
2(4a)
T△▽
k=T△▽
k◦E
k+τsQ E
k,(4b)
Q△▽
k=Q△▽
k9Q E
k.(4c)
The ha monic mean is used o compu e he e ec i e pe iod
pe module, T, and he sys em’s a e age pe iod, T, as
Tk= 2 T△▽
k
911291
,(5a)
Tk= 3 1T
3T91
k91.(5b)
whe e he ‘91’ exponen ope a es elemen wise.
The p edic ion s age, signaled by he subindex ‘p′ ollows
a di e en algo i hm based on he p edic ed ac ua ion, as
E△
p= (Sp>Sk),E▽
p= (Sp<Sk)(6a)
Q△▽
p=Q△▽
k+E△▽
p.(6b)
B. Cos Func ion
The coun and cu en p edic ed alues, Q△▽
pand Ip, a e
included in he cos unc ion, J, h ough quad a ic e o as
Q = [Q1 Q2 Q3 ]T,I = [I1 I2 I3 ]T
Jq=
Q△
p9Q
2+
Q▽
p9Q
2(7a)
Ji=∥Ip9I ∥2(7b)
J=λiJi+λQJQ(7c)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
10
20
Fig. 5. Phase measu emen example.
whe e λiand λQa e he weigh ac o s o cu en and pe iod
espec i ely, and ∥X∥2=XTX, o single column ec o s.
C. F equency Re e ence Co ec ion
As i is, PCA-FCS-MPC achie es a s eady swi ching e-
quency wi h a s eady s a e e o [8]–[10]. This p oblem is
add essed in [9], whe e an o se , Fo, is included o he
swi ching equency e e ence, F , o compensa e o he e o ,
as
Fo,k =Fo,k91+F 9T91λo,(8)
whe e λois equi alen o an in eg a o gain in a PI con olle .
Due o he in eg a ing na u e o his o se , a sa u a ion limi
o ±F 1
2is applied. Thus, he base e e ence used in he cos
unc ion is
Q ,k =τs(F +Fo,k)91.(9)
This e e ence is he same o all modules o he con e e .
IV. PREDICTIVE PHASE MEASUREMENT AND CONTROL
PCA-FCS-MPC achie es con ol o he swi ching equency
wi h a sligh de ia ion om he e e ence. This de ia ion is
no c i ical in mos applica ions, hus being ee o d i as
equi ed by he con olle . This na u al d i ing can be used o
add ess he swi ching phase con ol.
A. Swi ching Phase Measu emen
The c i ical a iable o pe o mance imp o emen is he
phase di e ence, o ela i e phase, be ween modules, Φxy,
which, as illus a ed in Fig. 5, is compu ed based on he coun
measu emen s, Q, used o pe iod con ol as
Φ△= [Φ12uΦ23uΦ31u],⇃X= [XnX1· · · Xn91]T,
Φ▽= [Φ12dΦ23dΦ31d],↿X= [X2· · · XnX1]T,
Φ△
kΦ▽
k=Φ△▽
k=2π
Q Q△▽
k9 ↿Q△▽
k(10)
whe e ⇃Xand ↿Xindica es a e ical shi o he elemen s o
he espec i e ec o o ma ix.
Each phase e e ence, θx, , can be ob ained h ough an op-
imiza ion algo i hm, and he di e ence be ween consecu i e
modules is used as he e e ence o he ela i e phase
Θ = [θ1, θ2, θ3, ]T
Φ =Θ 9 ↿Θ (11)
The ela i e phase compu a ion o (10) gi es pai s o
measu emen s, Φ△
kand Φ▽
k, ha should each he same alue
0
10
20
30
0 0.5 1 1.5 2 2.5 3 3.5 4
0
10
20
30
(a)
(b)
Fig. 6. Phase adjus men example, wi h e e ence Φxy, =20
25 π ad, when
he ela i e phase s a s (a) u he apa and (b) close han he e e ence.
in he s eady s a e ope a ion. The e o e, each pai is gi en he
same e e ence. Thus, he phase e o is compu ed as
Φ△▽
e=Φ△▽
k9Φ 1T
2(12)
When a commu a ion akes place, he alue o he espec i e
coun is ese o 1and he espec i e phase measu emen would
expe ience a la ge s ep. This would cause a la ge s ep in he
phase e o , which could des abilize he phase con ol. Since
he phase e o is an angle, measu ed in adians, he s ep
p oblem is sol ed by changing he e o such ha i emains
in he ange [9π π], by adding o sub ac ing mul iples o 2π
as equi ed.
B. Phase Con ol
I he ela i e phase e o s, Φxyu,e and Φxyd,e, a e posi i e,
i means ha he phase o module xis u he han needed om
he phase o module y. The e o e, o ix he ela i e phase,
module xshould d i o wa d in ime o module yshould
d i backwa ds, as illus a ed in Fig. 6(a). I he ela i e phase
e o s a e nega i e, he opposi e co ec ion is due, as illus a ed
in Fig. 6(b).
To achie e his co ec ion, he coun e e ence gi en o
module xis o se om he base e e ence, Q , as unc ion o
he e o s ela ed o i . Fo he 3 module con e e , he o se
e e ences o each module a e
Q =Q +Φ△▽
e9 ⇃Φ△▽
e12λΦQ(13)
whe e λΦQis a con e sion ac o , o change uni s om adians
o s ep coun s.
A inal conside a ion o ake in o accoun , is he imple-
men a ion o a limi in he o se . A high o se in he coun
e e ence migh lead o uns able o unp edic able beha io
since i would o ce la ge de ia ions om he ac ual e e ence.
This limi is e alua ed in simula ions, o e i y s abili y. Thus,
he alues in pa en hesis in equa ion (13), a e limi ed o be
be ween ±π/6.
V. EXPERIMENTAL RESULTS
The p oposed s a egy o phase shi con ol is implemen ed
in a 1007 dSPACE con ol pla o m, and an in e lea ed con-
e e p o o ype was cons uc ed, as shown in Fig. 7. The
Fig. 7. Labo a o y p o o ype o he in e lea ed powe con e e wi h 3 pa allel
modules.
TABLE I
EXPERIMENTAL PARAMETERS.
Symbol Name Value
RLoad Resis o 7.5 Ω
CoOu pu Capaci o 470 µF
CiInpu Capaci o 940 µF
LxLine Induc o 15 mH
F Swi ching F equency Re e ence 1.5kHz
FsSampling F equency 50 kHz
τsSampling Pe iod 20 µs
iInpu Vol age 140 V
oOu pu Vol age 70 V
pa ame e s used o he expe imen al es a e p esen ed in
able I
An ini ial es is done o compa e he pe o mance achie ed
by PCA-FCS-MPC, wi hou special conside a ion o he
phase be ween modules, and wi hou and wi h he p oposed
algo i hm o phase con ol. Fo his es , all modules ha e
he same cu en e e ence, hus being a balanced con e e .
Fig. 8 shows he esul ing cu en h ough each module, in
yellow, g een and magen a, and he cu en a he high ol age
side o he con e e in cyan. Two di e en expe imen s a e
plo ed. The igh side shows he pe o mance when he e is
no con ol o e he swi ching phase o each module, and he
le , when he swi ching phase con ol is ac i e. As illus a ed,
he swi ching equency is p ope ly con olled, and a s able
s eady s a e is achie ed. This base es shows in ough e ms
he co ec ope a ion o he phase con ol in he in e lea ed
con e e .
Figu e Fig. 9 shows he ansien when he phase con ol is
ac i a ed, a 5ms. I can be obse ed ha he bo h cu en
con ol and equency con ol a e main ained success ully
du ing he ansien , while eaching he desi ed phase.
To p ope ly e alua e he phase acking pe o mance, one
needs he phase alues as measu ed by he con olle , as
well as he spec al dis ibu ion o he cu en s. Wi h a phase
e e ence o 0 ad, 2
3π ad and 4
3π ad ( ela i e phase be ween
modules o 2
3π ad), he ollowing esul s a e ob ained. As
show in Fig. 10(a), wi hou phase con ol (le ), he cu en
h ough each module has he same mean alue, as expec ed
om p edic i e con ol, bu he esul ing capaci o cu en does
no ha e a consis en shape.
Fig. 8. Induc o s cu en (yellow, g een and magen a), and Cicu en (cyan),
wi hou phase con ol (le ) and wi h phase con ol ( igh ).
012345678910
2
2.5
3
3.5
4
Fig. 9. T ansien esul s o he ac i a ion o phase con ol.
I can be seen in Fig. 10(a), ha wi hou a phase con-
ol, hey can d i andomly, which explains why ici has a
di e en shapes a di e en imes, when compa ing Fig. 8
and Fig. 10(a). When he phase con ol is ac i a ed ( igh ),
he ela i e phase be ween all modules eaches 2
3π ad, and
d ama ically imp o es he pe o mances obse ed in ici. This
is mo e clea ly app ecia ed in Fig. 10(c), whe e he cu en
spec a o low equency ha monics is much highe wi hou
he phase con ol.
Wi h he balanced ope a ion e i ied, he nex s ep is o
check he pe o mance when an unbalanced cu en is equi ed
o he con e e . Fo his, a de ec i e module is simula ed
h ough a lowe cu en e e ence. Fig. 11 shows he esponse
ime o he p oposed s a egy o changes in he inpu ol age,
om 150[V] o 250[V] (le ) and ou pu load om 7.5 [Ω] o
3.75 [Ω] ( igh ). These esul s illus a e he e ec i eness o he
phase and equency con ol.
Rega dless o he cu en a each module, as long as a se o
phases is a ailable o op imize he powe con e e ope a ion,
hen i is possible o apply a phase con ol o PCA-FCS-MPC
and each a desi able pe o mance.
VI. CONCLUSION
The p esence o low equency ha monics is a majo
con ibu o in he decay o he capaci o li e ime, and is
in gene al an undesi ed elemen . In e lea ed con e e s can
add ess his issue when PWM con ol echniques a e used in
balanced sys ems, by shi ing he ca ie phase o each module.
Howe e , i is an unsol ed p oblem when FCS-MPC s a egy
is used o ope a e he con e e .
In his pape , PCA-FCS-MPC is success ully implemen ed
o achie e an accu a e phase con ol wi hou majo changes in
-4
-2
0
2
4
0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4
-120
-60
0
60
120
(a)
(b)
0123456789
0
0.1
0.2
0.3
0.4
(c)
Fig. 10. Expe imen al esul s o a balanced sys em.
2
4
6
8
10
12
50
100
150
200
-10 0 10 20 30
1.4
1.6
1.8
-10 0 10 20 30
(a)
(b)
(c)
(d)
(e)
( )
Fig. 11. Unbalanced sys em ansien esponse o (a-c) an inpu ol age s ep
and (d- ) a load s ep.
he co e algo i hm. This phase con ol achie es an imp o e-
men o e he cu en spec al dis ibu ion, as expec ed wi h
a p ope phase shi o an unbalanced sys em. The co e idea
o he s a egy is ha , once a a s eady swi ching equency is
achie ed, he pe iod e e ence o each module can be adjus ed
h ough an o se , o b ie ly nudge he equency, such ha a
phase adjus men is achie ed. The phase con ol is shown o
be e ec i e and unha m ul o o he con ol objec i es, hus
main aining a good con ol pe o mance o e ol ages and
cu en s, and a as ansien when ac i a ed.
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