Op imiza ion s a egy o elemen sizing in hyb id powe sys ems
Alejand o J. del Real, Alicia A ce and Ca los Bo dons
Abs ac — This pape p esen s a p ocedu e o e alua e he
op imal elemen sizing o hyb id powe sys ems. In o de o
gene alize he p oblem, his wo k is based on he “ene gy
hub” concep and o mula ion p e iously p esen ed in he
li e a u e. The esul ing op imiza ion minimizes an objec i e
unc ion based on cos s and e iciencies o he sys em elemen s,
while aking in o accoun he hub model, ene gy and powe
cons ain s and es ima ed ope a ional condi ions, such as ene gy
p ices, inpu powe low a ailabili y and ou pu ene gy demand.
The esul ing op imal a chi ec u e also cons i u es a amewo k
o u he eal– ime con ol designs.
Also, an example o a hyb id s o age sys em is conside ed.
In pa icula , he a chi ec u e o a hyb id plan inco po a ing
a wind gene a o , ba e ies and in e media e hyd ogen s o age
is op imized, based on eal wind da a and a e aged esiden ial
demands. The hyd ogen sys em in eg a es an elec olyze , a
uel cell s ack and hyd ogen anks. The esul ing op imal cos
o such hyb id powe plan is compa ed wi h he equi alen
hyd ogen–only and ba e y–only sys ems, showing imp o e-
men s in in es men cos s o almos 30% in he wo s case.
I. INTRODUCTION
The ene gy in as uc u es o oday a e abou o un-
de go a p o ound change: ossil uel p ices a e aising
e e y yea while, a he same ime, ene gy demand in-
c eases in e e y coun y. Mo eo e , he aim o educe
g eenhouse gas emissions is mo ing i s a en ion o mo e
en i onmen ally– iendly and sus ainable ene gy sou ces.
Wi h an inc eased u iliza ion o small dis ibu ed ene gy
esou ces o gene a ion o elec ici y and hea [1], enewable
ene gy gene a ion will cons i u e an impo an pa o he
o e all ene gy scena io in he coming yea s.
One o he main p oblems associa ed wi h hese kind o
sys ems is he eliabili y and quali y o he powe supply. As
a ma e o ac , since he enewable sou ce is in e mi en ,
unp edic able luc ua ions may appea in powe ou pu [2].
Also, elec ical gene a ion om enewable sou ces is no sub-
jec o demand, which c ea es imbalance in he sys em. One
way o o e come his p oblem is by including in e media e
s o age, such as ba e ies, wa e pumping, supe –capaci o s,
comp essed ai , ly wheels, supe conduc ing magne ic en-
e gy s o ages, e c [3]. Among he mos p omising s o age
echnologies a e hose based on hyd ogen p oduc ion and
u iliza ion, which is expec ed o be used o e y di e en
applica ions [4], [5] as hey cons i u e some in e es ing
This wo k was suppo ed by MEC-Spain (con ac DPI2008-04568) and
he Eu opean Commission (Hycon FPG-511368)
The au ho s a e wi h Escuela Supe io de Ingenie os, Depa amen o
de Ingenie ´
ıa de Sis emas y Au om´
a ica, Uni e si y o Se ille, 41092
Camino de los Descub imien os s/n, Se ille, Spain. e–mail:{adel eal,
aa ce}@ca uja.us.es, [email p o ec ed]
ad an ages in e ms o cos , au onomy, powe ange and
en i onmen al e ec s [6].
Howe e , hyb id ene gy s o age sys ems inc ease he com-
plexi y o he o e all powe plan , he con ol design ha ing
an impo an e ec on sys em pe o mance. Thus, he e a e
a numbe o con olle s a ailable in he li e a u e, such as
hose based on heu is ic ules and ial–and-e o echniques
[7], [8], [9], [10]. Fuzzy logic app oaches [11], [12] a e
equi alen o hose based on heu is ic ules in he sense
ha hey ely on sys em knowledge o ob ain he ‘bes ’
in ui i e powe managemen . None heless, o he app oaches
based on on–line op imiza ion can be ound, esul ing in
a mo e e–usable and igo ous design p ocess, so ha he
inal algo i hm achie es a gua an eed op imum le el [13].
Along hese lines, an on–line op imiza ion o minimize he
hyd ogen consump ion o esiden ial hyb id powe plan s
was p esen ed in [14] and [15]. As o enewable sou ces, he
in e mi ency o he a ailable powe also has a g ea impac
on sys em pe o mance. Al hough no being sui able o
eal– ime con ol as he designs ci ed, he e a e some con ol
algo i hms based on p io knowledge o u u e condi ions
(such as wind speed da a) which a e use ul as a basis o
compa ison o he e alua ion o eal– ime con ol s a egy
quali y [16].
As well as he con ol design, i is e y impo an ha
componen sizing be aken in o accoun in o de o educe
ins alla ion in es men cos s and o achie e good o e all
pe o mance. Howe e , e y ew pape s ha e add essed his
issue. To his end, [17] discusses he bes coupling me hods
o con en ional s o age ba e ies wi h hyd ogen ene gy s o -
age which includes an elec olyze , hyd ogen s o age ank,
and a uel cell. The esul ing s udy shows ha i mul iple
ene gy s o age de ices wi h complemen a y pe o mance
cha ac e is ics a e used oge he , he esul ing hyb id sys em
can d ama ically educe he cos o ene gy s o age o e
single s o age sys ems. Also, [18] p oposes a e y gene al
ma hema ical o mula ion o hese hyb id powe plan s, he
so–called “ene gy hubs”, which is u ilized o de e mine he
op imal coupling o ene gy in as uc u es.
This pape , ollowing he concep and ma hema ical o -
mula ion o he ene gy hubs p esen ed in [18] and o he
ela ed pape s by he same au ho s such as [16], [19], [20],
[21], p oposes a no el op imiza ion, which is no aimed o
es ablishing he op imal hub layou as done in [18] bu a
de e mining he op imal hub size o a de e mined layou .
In he ollowing sec ion, ene gy hub concep and ma h-
ema ical o mula ion a e b ie ly ou lined, as he e is an
ex ensi e li e a u e by he co esponding au ho s desc ib-
ing hem. Sec ion III p oposes an inno a i e gene al cos
1
P
2
P
i
P
1
L
2
L
j
L
inpu s ou pu s
ene gy hub
Fig. 1. Gene al ene gy hub diag am
i
Pj
L
con e e
in e ace
s o age
k
E
k
Q
k
Q
Fig. 2. Ene gy hub basic elemen s: con e e (le ) and s o age ( igh )
unc ion o minimize componen sizing based on cos s and
e iciencies. Sec ion IV applies he gene al op imiza ion
scena io o a wind gene a o /hyd ogen/ba e ies powe plan ,
also discussing he esul s ob ained. Las ly sec ion V is
dedica ed o he concluding ema ks.
II. ENERGY HUB CONCEPT AND FORMULATION
As an inc eased u iliza ion o dis ibu ed gene a ion ech-
nologies will cha ac e ize u u e ene gy sys ems, e ms like
“mul iple ene gy ca ie sys ems” [22] and “hyb id ene gy
sys ems” [23] ha e become he no m when e e ing o
sys ems including a ious o ms o ene gy. In his way,
as no ed in [21], he e a e a numbe o app oaches o
o mula e hese kind o sys ems, such as “ene gy–se ices
supply sys ems” [24], “basic uni s” [25], “mic og ids” [26]
and he so–called “hyb id ene gy hubs” [27].
The la e o mula ion is adop ed he ein, which is ex en-
si ely desc ibed in he PhD hesis [21] and ela ed pub-
lica ions. Acco ding o his o mula ion, ene gy hubs a e
de ined as in e aces among ene gy p oduce s, consume s,
and he anspo a ion in as uc u e (see ig. 1, whe e Pi
a e powe inpu s and Ljpowe ou pu s), and con ain h ee
basic elemen s: di ec connec ions, con e e s and s o age
(see ig. 2, wi h Qkbeing he powe exchange, ˜
Qk he in e nal
powe and Ek he s o ed ene gy).
Con e e s link inpu s and ou pu s h ough coupling ac-
o s ci,j, which can be conside ed o be he con e e ’s
s eady–s a e ene gy e iciency, exp essed as:
Lj=ci,jPi(1)
Conside ing all he ene gy hub inpu s Pand ou pu s L, he
ollowing con e e coupling ma ix C esul s:
i
P
n
1
2
i,1
P
i,2
P
i,n
P
Fig. 3. Inpu powe Pidispa ch
i
Pj
L
con e e
in e ace
i
Q
i
Q
s o age
in e ace
j
M
j
M
s o age
i
Pj
L
Fig. 4. Con e e wi h s o age a he inpu and he ou pu sides



L1
.
.
.
Li



| {z }
L
=


c1,1... ci,1
.
.
.....
.
.
c1,j... ci,j



| {z }
C



P1
.
.
.
Pj



| {z }
P
(2)
As he inpu low Pican be dis ibu ed among a ious
con e e de ices (see ig. 3), dispa ch ac o s
ν
i,nspeci y
how much o he inpu powe Pi lows in o he con e e n:
Pi,n=
ν
i,nPi(3)
Conse a ion o powe also in oduces he cons ain s
0⩽
ν
i,n⩽1∀i,∀n(4a)
∑
n
ν
i,n=1∀i(4b)
Wi h espec o s o age, powe exchange Qkand s o ed
ene gy Eka e linked h ough he equa ion:
e
Qk=ekQk=dEk/d ≈ 4Ek/4 ,˙
Ek(5)
ekbeing he e iciency o he cha ge/discha ge s o age in e -
aces, exp essed as
ek=½e+
ki Qk≥0(cha ging/s andby)
1/e−
kelse (discha ging)(6)
When s o age elemen s exis , powe conse a ion leads o
he ollowing, depending on which side o he con e e he
s o age is loca ed (see ig. 4):
e
Pi=Pi−Qi(7a)
e
Lj=Lj+Mj(7b)
Adding he s o age o he hub equa ion (2) leads o:
[L+M] = C[P−Q](8)
Hub layou
design
Hub size
design
Hub con ol
design
Op imal powe
dispa ch
Es ima ed
ope a ional condi ions
OPTIMAL ENERGY HUB DESIGN
Fig. 5. Op imal ene gy hub design s eps
Assuming a cons an con e e coupling ma ix Cand ap-
plying supe posi ion, he equi alen s o age lows a e:
Meq =C Q +M(9)
Rew i ing (8) in a mo e condensed o m,
L=C P −Meq (10)
De ining he s o age coupling ma ix S o desc ibe how
changes o he s o age ene gy de i a i es a ec he hub
ou pu lows, he equi alen s o age powe lows Meq can
be s a ed as



Meq
1
.
.
.
Meq
k



| {z }
Meq
=


s1,1... s1,k
.
.
.....
.
.
s1,k... sk,k



| {z }
S



˙
E1
.
.
.
˙
Ek



| {z }
P
(11)
Summa izing all he p e ious equa ions, he comple e hub
ene gy model would be:
L=C P −S˙
E(12)
III. OPTIMAL HUB SIZE
Op imal hub design can be di ided in o wo di e en s eps:
op imal hub a chi ec u e design and hub con ol design (see
ig. 5). Mos o he pape s in he li e a u e, as men ioned
in sec ion I, a e dedica ed solely o he con olle design,
no add essing a chi ec u e design. Acco dingly, di e en
ypes o con olle s a e p oposed: heu is ic ules, uzzy logic,
on–line op imiza ion, e c. The be e he con olle design,
he be e he pe o mance o a gi en sys em. Howe e ,
hub a chi ec u e and con ol designs a e no independen
om one ano he . As a ma e o ac , he pe o mance o
he o e all sys em no only depends on he quali y o he
con olle bu also on he hub a chi ec u e.
Op imal hub sizing o any gi en hub layou en ails
op imiza ion o con e e and s o age elemen sizes. To ha
end, cos and e iciencies associa ed wi h each componen , as
well as he es ima ed wo king condi ions o he hub (such as
ene gy p ices, inpu ene gy lows a ailabili y, ou pu powe
demand, e c.) ha e o be aken in o accoun . The o e all
op imal a chi ec u al design esul s in an i e a i e p ocess,
e alua ing he op imal cos o each hub layou in o de
o selec he one ha minimizes he in es men cos while
assu ing a de e mined pe o mance le el based on he agen s
a ec ing he sys em.
Gi en he op imal hub a chi ec u e, and supposing knowl-
edge o he sys em ope a ional condi ions, a sui able op i-
miza ion p oblem minimizing a de e mined objec i e unc-
ion would hen ep esen he basis o compa ison o he
e alua ion o eal– ime con ol s a egy quali y. This ype
o op imiza ion p oblem is e e ed o as “op imal powe
dispa ch” [16].
The p oblem p esen ed by op imal hub sizing, which is
he objec i e o his wo k, can be basically exp essed wi h
h ee ela ions: an objec i e unc ion which accoun s o he
minimiza ion o he sys em in es men cos ; physical laws
ep esen ing he hub; and echnical limi a ions. By making
he op imiza ion ho izon as la ge as possible o co e he
highes numbe o possible ope a ional condi ions and si ua-
ions, he op imiza ion is s a ed as a mul i–pe iod nonlinea
cons ained p oblem including an objec i e unc ion, equali y
and inequali y cons ain s.
The ene gy hub is desc ibed by he equali y cons ain s
p esen ed in sec ion II. Ex ending ha o mula ion o con-
side mul iple ime pe iods, he model would be:
L( )=C( )P( )−S( )˙
E( )∀ (13)
whe e
˙
E( )
k=e( )
kQ( )
k−e( −1)
kQ( −1)
k(14)
also aking in o accoun he dispa ch ac o p ope ies gi en
by (4).
Inequali y cons ain s co espond o he echnical limi a-
ions o he con e e and s o age elemen s. Equa ion (15a)
exp esses powe limi s o he con e e s. Equa ions (15b) and
(15c) co espond o change in s o age ene gy limi s, which
a e a esul o he echnical cha ac e is ics o he s o age
in e aces, while (15d) conside s he ene gy capaci y limi s
o he s o age elemen s. The las inequali y (15e) is also
included so ha s o ed ene gy a he end o he op imiza ion
pe iod N is equal o o g ea e han he ini ial amoun , in
o de o ensu e sus ainable s o age u iliza ion.
Pi,n≤
ν
( )
i,nP( )
i≤Pi,n∀ ,∀i,∀n(15a)
Qi≤Q( )
i≤Qi∀ ,∀i(15b)
Mj≤M( )
j≤Mj∀ ,∀j(15c)
Ek≤E( )
k≤Ek∀ ,∀k(15d)
E(0)
k≤E(N )
k∀k(15e)
The objec i e unc ion Fdepends on he con e e and
s o age elemen limi s, which a e ela ed o i s size. No e
ha , as he cha ging s o age in e ace may be di e en o he
discha ging in e ace, Qiand Mjco espond o he cha ging
limi s, while Qiand Mja e ela ed o he discha ging
Fig. 6. Hyb id ene gy s o age sys em
limi s. The solu ion o he op imiza ion p oblem p o ides
he op imal alues o he limi s o he cons ains (15). This
way, he o al objec i e can be exp essed as:
F=F¡Pi,Ek,Qi,Mj,Qi,Mj¢(16)
Conside ing a quad a ic unc ion, he objec i e emains:
F=∑
i
cPiP2
i+∑
k
cEkE2
k+∑
i¡cQiQ2
i+cQiQ2
i¢
+∑
j¡cMjM2
j+cMjM2
j¢(17)
cPibeing he cos pe W ins alled o he con e e i,cEk he
cos pe J ins alled o he s o age elemen k, and cQi,cMj,cQi
and cMj he cos pe W ins alled o he cha ging/discha ging
in e aces iand j.
The hub size op imiza ion p oblem can inally be s a ed
as:
Minimize objec i e unc ion (17)
subjec o ene gy hub model (4),(13),(14)
ene gy and powe cons ain s (15)
When he objec i e unc ion is con ex and he cons ain s
a e exp essed as linea equa ions, he global op imum can
be ound u ilizing nume ical me hods, as he solu ion space
is con ex.
IV. APPLICATION
Conside ing he sys em shown in ig. 6, he p ima y ene gy
sou ce is a wind gene a o , which is connec ed o a esiden ial
load (L ). The elec ici y p oduced ia wind (w) can be
deli e ed o he load and/o be di e ed o an elec olyze (E)
and ba e ies (B). The ene gy consumed by he elec olyze
(QE) is used o p oduce hyd ogen, which is s o ed in he
anks placed in he hyd ogen line (EH2). The uel cell s ack
(FC), ed by hose anks, can p oduce elec ici y (QFC).
Simila ly, he ba e ies can be cha ged (QB,ch), s o ing he
ene gy (EB), and discha ged (QB,dis), hus complemen ing
he o al powe supplied o he load.
De i ing his speci ic case om he gene al p oblem, and
assuming a ce ain se o ope a ional condi ions, he op imal
hub sizing o he p oposed sys em is calcula ed. To ha end,
he op imiza ion p oblem is o mula ed as in he p e ious
sec ion III
η
η
η
η
Fig. 7. Co esponding ene gy hub o a hyb id ene gy s o age sys em
TABLE I
HYBRID ENERGY STORAGE SYSTEM EFFICIENCIES
Hub elemen E iciency
Elec olyze
η
E=0.74
Fuel cell
η
FC =0.47
Ba e y cha ging
η
B,ch =0.7
Ba e y discha ging
η
B,dis =0.9
A. Ene gy hub model
Model equa ions a e based on he no a ion p esen ed in
sec ion II. This way, he speci ic ene gy hub is illus a ed in
ig. 7. Inpu , ou pu and s o age ene gy de i a i e ec o s o
mul iple ime pe iods, can be de ined as
P( )=hP( )
wi(18a)
L( )=hL( )
i(18b)
˙
E( )=h˙
E( )
H2˙
E( )
BiT(18c)
Also, ollowing he a o emen ioned no a ion, con e e
coupling ma ix C( )and s o age coupling ma ix S( )a e
s a ed as:
C( )=£1¤(19)
S( )=h1/e( )
H21/e( )
Bi(20)
whe e e( )
H2and e( )
Ba e he s o age in e ace e iciencies (see
able I), he elec olyze being he ‘cha ging’ in e ace and
he uel cell he ‘discha ging’ in e ace o he hyd ogen line.
Also, no ice ha di e en ba e y cha ging and discha ging
e iciencies a e conside ed, esul ing in he ollowing ela-
ions:
e( )
H2=(
η
Ei Q( )
H2≥0(elec olyze )
1/
η
FC else ( uel cell)(21a)
e( )
B=½
η
B,ch i Q( )
B≥0(ba e y cha ging)
1/
η
B,dis else (ba e y discha ging)
(21b)
wi h he powe exchanges Q( )
H2,Q( )
Band s o age ene gy
de i a i es ˙
E( )
H2,˙
E( )
Bexp essed as:
˙
E( )
H2=e( )
H2Q( )
H2−e( −1)
H2Q( −1)
k(22a)
˙
E( )
B=e( )
BQ( )
B−e( −1)
BQ( −1)
B(22b)
B. Ene gy and powe cons ain s
Technical limi a ions a e modeled as hey we e in (15).
Inpu powe limi s, s o age in e aces powe exchange ca-
paci ies and s o ed ene gy limi a ions a e e alua ed nex .
Wi h espec o he inpu , wind powe P( )
wdepends on he
a ailable wind powe , as well as on he size o he wind
gene a o . De ining b
P( )
was he no malized powe p oduced
by a 1W wind gene a o gi en a ce ain wind speed a ime
, powe inpu limi s would be:
£0¤≤hP( )
wi≤hb
P( )
wPwi(23)
wi h Pwbeing he size o he wind gene a o o he p oposed
hyb id s o age plan .
Powe s o age exchange is also limi ed by he maximum
powe ha can be p o ided by he s o age in e aces:
·−QFC
−QB,dis ¸≤"Q( )
H2
Q( )
B#≤·QE
QB,ch ¸(24)
whe eas o he hyd ogen line, QEand QFC ep esen he
maximum capaci ies o elec olyze and uel cell espec-
i ely. Conce ning he ba e ies, QB,ch and QB,dis a e he
limi cha ging/discha ging a es. No ice ha hese a es a e
usually a unc ion o o al ba e y size E, assuming he e ha
QB,ch =0.2Eand QB,dis =2E.
Maximum s o ed ene gy depends on he size o he
hyd ogen anks EH2and he ba e ies EB. Due o echnical
cons ain s, he ba e ies should ne e be o ally d ained no
ully cha ged; hey should always be in a pa ially cha ged
s a e. Taking hese conside a ions in o accoun and assuming
a sa e cha ge le el, he cons ain can be exp essed as:
·0
0.2EB¸≤"E( )
H2
E( )
B#≤·EH2
0.9EB¸(25)
Finally, a cons ain o e i y sus ainable ene gy s o age is
also in oduced, so ha
"E(0)
H2
E(0)
B#≤"E(N )
H2
E(N )
B#(26)
C. Objec i e unc ion
Mo ing om he gene al (17) o he speci ic, he objec i e
unc ion, whose cos e ms a e shown in able II [17], would
be:
F=cPwP2
w+cEH2E2
H2+cEBP2
B+cQFC Q2
FC +cQEQ2
E(27)
TABLE II
HYBRID ENERGY STORAGE ELEMENT COSTS
Hub elemen Cos
Wind powe cPw=$2/W
Elec olyze cQE=$1.9/W
Fuel cell cQFC =$2.5/W
Hyd ogen ank cEH2=$0.03/Wh
Ba e y cEB=$0.2/Wh
0 500 1000 1500
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ime (h)
no malized wind powe
Fig. 8. No malized wind powe da a se ( eco ded o e a wo-mon h pe iod)
D. Ope a ional condi ions
As he op imal hub a chi ec u e design is based on es i-
ma ed ope a ional condi ions, he mo e p ecise he u ilized
da a a e, he mo e accu a e a e he a chi ec u al esul s. As
o he powe inpu , a wo–mon h wind powe no malized
da a se b
P( )
wwas conside ed (see ig 8). Conce ning he load
L , he da a used is shown in ig. 9, which ep esen s he
a e age daily load o he esiden ial sec o in Spain [28].
The sampling ime o all he da a se s is 1h.
E. Op imiza ion esul s
The op imiza ion was done o h ee hub layou s: hyb id,
hyd ogen–only and ba e y–only s o age, and was imple-
men ed in Ma lab using he sol e ”CPLEX”, esul ing in a
0 5 10 15 20
0
100
200
300
400
500
600
ime (h)
esiden ial load (W)
Fig. 9. Residen ial sec o a e age daily loads

TABLE III
HYBRID ENERGY STORAGE SYSTEM COSTS
Hyb id Hyd ogen–only Ba e y–only
Equipmen cos cos cos
(size) (size) (size)
Wind gene a o $7600 $8600 $12500
(3800 W) (4300 W) (6250 W)
Elec olyze $656 $665 —
(345 W) (350 W)
Fuel cell $450 $1375 —
(180 W) (550 W)
H2 ank $1642 $3681 —
(54.730 kWh) (122.695 kWh)
Ba e ies $2268 —$3651
(11.34 kWh) (18.255 kWh)
To al cos $12616 $14321 $16151
Inc emen Baseline 11.91% 28.02%
0 500 1000 1500
0
100
200
300
400
ime (h)
ba e y ou pu powe (W)
0 500 1000 1500
0
50
100
150
200
ime (h)
uel cell powe (W)
Fig. 10. Op imal u ilisa ion o ba e y (uppe g aph) and uel cell (lowe
g aph) o a hyb id s o age powe sys em
Mixed In ege Quad a ic P og amming (MIQP). Con i ming
he s udies p esen ed in [17], hyb id s o age p o ed o be
signi ican ly cheape han o he possible s o age sys ems. In
pa icula , hyd ogen–only s o age cos is 11.91% highe han
he hyb id plan , he ba e y–only choice being 28.02% mo e
expensi e han such hyb id sys em (see able III o de ailed
in o ma ion).
As can be seen in ig. 10, hyb id s o age layou combines
he bes cha ac e is ics o bo h ene gy s o age de ices. In
pa icula , he uel cell is used as a base powe supplie ,
while ba e ies a e u ilized o deli e he powe peaks. In a
hyd ogen—only choice, he uel cell size has o be inc eased
in o de o c ea e he powe peaks, which esul s in a cos
inc ease due o he high cos o he equipmen . On he
o he hand, ba e y–only s o age equi es a la ge o al ene gy
capaci y, which is cos ly oo.
V. CONCLUDING REMARKS
In his pape , an op imiza ion s a egy o sizing hyb id
powe sys ems is p esen ed. The ma hema ical o mula ion is
based on he “ene gy hub” concep desc ibed in p e ious li -
e a u e. The op imiza ion p ocedu e was applied o a hyb id
powe plan inco po a ing a wind gene a o , con en ional
ba e ies and a hyd ogen s o age sys em comp ised o a
uel cell, an elec olyze and hyd ogen anks. The op imal
a chi ec u e esul ed in a 30% imp o emen among he
possible sys em layou s in e ms o cos e ec i eness.
VI. ACKNOWLEDGMENTS
The au ho s g a e ully acknowledge he con ibu ion o
Ca los Pa do, who is wo king on his mas e hesis in ela ed
issues.
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