Cos -E ec i e Ope a ion o Mic og ids: A MILP-Based Ene gy Managemen
Sys em o Ac i e and Reac i e Powe Con ol
Sebas i´
an Ga cía
a,*
, S e ano B acco
b
, An onio Pa ejo
a
, Ma eo F esia
b
,
Juan Ignacio Gue e o
a
, Ca los Le´
on
a
a
Depa men o Elec onic Technology, Escuela Poli ´
ecnica Supe io , Uni e si y o Se ille, Se ille 41011, Spain
b
Depa men o Elec ical, Elec onic, Telecommunica ions Enginee ing and Na al A chi ec u e, Uni e si y o Genoa, Geno a 16145, I aly
ARTICLE INFO
Keywo ds:
Dis ibu ed Ene gy Resou ces
Ene gy Managemen Sys ems
Mic og ids
ABSTRACT
Mic og ids (MGs) ha e eme ged as a po en ial solu ion o he in eg a ion o Dis ibu ed Ene gy Resou ces
(DERs) in o he dis ibu ion ne wo k. In his sense, o e ec i ely manage MGs, i is essen ial o implemen Ene gy
Managemen Sys ems (EMSs). This en ails no only pe o ming he uni commi men bu also conside ing he
ol age and eac i e powe echnical cons ain s and managing ancilla y se ices. This pape con ibu es wi h a
comp ehensi e EMS o he op imal managemen o ac i e and eac i e powe o a gene ic g id- ied MG
composed o Renewable Ene gy Sou ces (RESs), Ba e y Ene gy S o age Sys ems (BESSs), Diesel Gene a o (DGs)
uni s and loads, wi h he goal o educing he ope a ing cos s o he acili y. The EMS includes models o he
powe elec onics uni s o apply eac i e powe managemen and a gene ic o mula ion o he managemen o
he s a up and shu down cycles o dispa chable uni s. Fu he mo e, a de ailed modeling o BESS and DG uni s is
p esen ed, e lec ing he ac ual beha io o he de ices. The MG is modeled as a mul i-busba ne wo k, wi h he
applica ion o he powe low equa ions o es ablish he link be ween powe lows and nodal ol ages. All he
cons ain s a e linea ized o o mula e he EMS as a Mixed-In ege Linea P og amming (MILP) op imiza ion
p oblem. The EMS is alida ed in a eal acili y: he CATEPS Mic og id Li ing-Lab. The esul s demons a e he
ope a ional e ec i eness o he EMS in di e en seasons, exhibi ing a educ ion in cos s anging om 21.84 % in
summe o a 5.69 % in win e compa ed o a scena io wi h RES p oduc ion bu wi hou ene gy managemen . In
addi ion, a comp ehensi e examina ion o eac i e powe and ol age managemen is p esen ed. Fu he mo e,
an empi ical assessmen o he powe low equa ions linea iza ion demons a ed minimal disc epancy in he
esul s when compa ed wi h hose ob ained wi h he non-linea equa ions, exhibi ing a mean absolu e e o o
8.8e-5 p.u. and 3.2e-5 ad in ol age magni ude and phase angle, espec i ely, in he mos un a o able scena io.
A sensi i i y analysis o he s a up and shu down cycles managemen o he BESS e eals a negligible e ec on
ope a ional cos s, ye i p o ides a mechanism o managing he ba e y s ess by educing he numbe o s a ups
in a comple e week om 28 o 16 in summe and om 37 o 24 in win e . The dependence be ween he
maximum cha ging and discha ging powe on he s a e o cha ge o he BESS is also assessed in he use case.
1. In oduc ion
In ecen yea s, he Eu opean Union has assumed a commi men o
he ene gy ansi ion. In 2021, he Fi o 55 package was enac ed by he
Eu opean ins i u ions, wi hin he amewo k o he Eu opean G een Deal
[1]. The package p omo ed some challenging goals o he membe
s a es o he 2030 yea , in e ms o educ ion o g eenhouse gas emis-
sions, pene a ion o Renewable Ene gy Sou ces (RESs) wi hin he
gene a ion po olio [2] and p omo ion o ene gy de i ing om RESs
and ene gy e iciency in buildings, which ep esen one o he mos
ene gy-consuming sec o s a Eu opean le el [3].
Following hese legisla i e cons ain s, membe s a es a e p omo ing
incen i es o os e he ins alla ion o a la ge sha e o RESs wi hin na-
ional gene a ion po olios, in eplacemen o synch onous gene a o s
ypically ins alled in adi ional coal o gas- i ed powe s a ions. RES
powe plan s, mainly ep esen ed by Pho o ol aic (PV) and Wind Tu -
bine (WT) ins alla ions, canno p o ide he same pe o mance as syn-
ch onous gene a o s in e ms o equency and ol age suppo [4],
* Co esponding au ho .
E-mail add ess: [email p o ec ed] (S. Ga cía).
Con en s lis s a ailable a ScienceDi ec
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems
jou nal homepage: www.else ie .com/loca e/ijepes
h ps://doi.o g/10.1016/j.ijepes.2025.110458
Recei ed 24 July 2024; Recei ed in e ised o m 25 Sep embe 2024; Accep ed 3 Janua y 2025
Elec ical Powe and Ene gy Sys ems 165 (2025) 110458
A ailable online 10 Janua y 2025
0142-0615/© 2025 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY license ( h p://c ea i ecommons.o g/licenses/by/4.0/ ).
being connec ed o he dis ibu ion ne wo k h ough in e e s. Dedi-
ca ed con olle s mus be ins alled on in e e s o make hem pa icipa e
in equency and ol age suppo [5]. Mo eo e , PV and WT uni s a e
a ec ed by he inhe en unp edic abili y o he p ima y sou ce, he e-
o e being a ec ed by possible unexpec ed o e - o unde -p oduc ions.
Fo his eason, hese powe plan s a e usually coupled o s o age sys-
ems, ei he hyd oelec ic in la ge-scale applica ions [6] o Ba e y En-
e gy S o age Sys ems (BESSs) in small scale applica ions [7]. BESSs a e
able o abso b possible su plus RES p oduc ion du ing peak pe iods,
deli e ing i back o he ne wo k du ing low RES p oduc ion pe iods [8].
In eg a ed RES-BESS sys ems can pa icipa e in equency con ainmen
and es o a ion ese es [9]. In addi ion, BESSs mi iga e ol age luc-
ua ions ha may de i e om as a ia ions o RES powe ou pu [10].
A small scale, RESs and BESSs can be iden i ied as Dis ibu ed En-
e gy Resou ces (DERs): o example, in he esiden ial sec o , hese de-
ices a e ins alled in he nea by o buildings o on oo ops. Many DERs
a e connec ed o each o he , along wi h loads, Elec ic Vehicles (EVs)
cha ging s a ions and possible dispa chable gene a o s, such as mic o-
gas u bines o Diesel Gene a o s (DGs), in he so-called Mic og ids
(MGs) [11]. MGs may also be made up o plan s capable o p o iding
he mal and cooling ene gy, like boile s, Combined Hea and Powe
(CHP) uni s and Combined Cooling, Hea and Powe (CCHP) uni s
[12,13]. MGs a e usually ope a ed unde economic o en i onmen al
objec i es, aiming o minimize ope a ional cos s and/o CO
2
emissions.
Mo eo e , hey p o ide g ea e lexibili y o he dis ibu ion ne wo k, i
compa ed o he adi ional pa adigm [14]. Se e al di e en applica-
ions o he MG concep can be ound: emo e MGs ( o a -away a eas
and small islands), mobile MGs ( anspo able on aile ), MGs o mil-
i a y compounds, heal h ca e acili ies, and uni e si y campuses, MGs
o da a cen e s, MGs o po s and ai po s, e c. I is also impo an o
conside how many MG ins alla ions can now ake place in u ban a eas,
in all hose new neighbo hoods ha a e being c ea ed as consequence o
ede elopmen p ojec s on old indus ial si es. In hese new sus ainable
u ban dis ic s, local g een ene gy p oduc ion can help educe he ca -
bon oo p in o ci ies and imp o e he quali y o li e, as assessed in [15]
whe e he au ho s desc ibe he implemen a ion o a MG o eed a Posi-
i e Ene gy Dis ic (PED). In he c ea ion o hese new sus ainable
a eas, he placemen o dis ibu ed gene a ion mus be ca e ully e alu-
a ed o minimize he impac on he dis ibu ion ne wo k [16], e en
conside ing ex eme wea he e en s [17].
The op imal dispa ching o he uni s composing a MG is de ined by
an Ene gy Managemen Sys em (EMS), which is ypically he uppe le el
o a Supe iso y Con ol and Da a Acquisi ion Sys em (SCADA). EMSs
a e in cha ge, o example, o de ining he op imal scheduling o dis-
pa chable uni s and he op imal ac i e and eac i e powe p o ision by
DERs: o do his, capabili y cu es o in e e s mus be embedded wi hin
he EMS, as shown in [18], whe e hey a e modelled in acco dance wi h
I alian echnical s anda ds. Mo eo e , EMSs de ine he op imal p o ile o
powe exchange wi h he local dis ibu ion ne wo k, i he MG wo ks in
g id-connec ed mode; i needed, EMSs allow he MG o ope a e in
islanded mode, when equi ed by he dis ibu ion sys em ope a o .
Fu he mo e, EMSs a e used o op imally schedule he ope a ion o
BESSs and o apply EV sma cha ging s a egies. The complexi y o
EMSs is mainly due o he mul iple inpu da a ha need o be p o ided o
op imally un i . This means economic pa ame e s (elec ici y pu chase
and selling p ices, main enance cos s, RES cu ailmen cos s, e c.),
echnical da a (pe o mance cu es desc ibing he ope a ion o DG
plan s a pa ial load, lowe and uppe bounds o powe p oduc ion,
maximum and minimum cha ging and discha ging powe o BESSs
usually dependen on s a e o cha ge, e c.) and en i onmen al pa ame-
e s (emission ac o s, e c.) [15]. Mo eo e , EMSs a e usually coupled
wi h o ecas ing ools used o es ima e bo h loads (elec ical, he mal
and cooling) and enewable ene gy p oduc ion. Fo ins ance, in [19] a
machine lea ning p obabilis ic o ecas ing app oach wi h obus op i-
miza ion is p oposed o de ine op imal dispa ching o MGs ha ing a
high pene a ion o RESs, while in [20] he analysis ocuses on models
used o es ima e he loads in a MG. A sepa a e issue conce ns he
managemen o elec ic mobili y wi hin a MG, as highligh ed in [21],
whe e a s udy o a emo e island ed by a MG wi h se e al EV cha ging
poin s is epo ed, and in [22], whe e a me hod o imp o e he o e-
cas ing accu acy o EV cha ging demand is p oposed. I is e y di icul
o es ima e anspo demand, and so he EV cha ging needs, as i de-
pends no only on en i onmen al and echnical ac o s, bu also on
beha io al aspec s o mobili y use s.
1.1. Li e a u e e iew
Se e al examples o EMSs o MGs can be ound in he li e a u e. A
comp ehensi e e iew o hem is p esen ed in [23], and also in [24]
whe e an analysis o he di e en op imiza ion echniques used o
add ess he ene gy managemen p oblems in MGs is p oposed. A com-
pa ison o se e al ene gy managemen s a egies in MGs is also epo ed
in [25], by highligh ing he c i icali ies in managing in e mi en RESs
and he impo ance o applying demand esponse.
A la ge po ion o he s udies p esen in he li e a u e models he MG
as a single busba sys em and neglec he impac o eac i e powe . The
applica ion o single busba model implies ha all he powe lows
among buses and all he ele an ol age phenomena a e neglec ed.
Among he s udies p esen in he li e a u e, [26] p oposes an EMS o
op imally ope a e a MG loca ed in Egyp wi h WT, PV and DG uni s, wi h
he aim o minimizing cos s and emissions. In [27] and [28] he au ho s
p esen a day-ahead EMS o he op imal managemen o a public pos al
acili y, equipped wi h mic o WTs and a PV sys em, owning a lee o EVs
o he deli e y o eigh . E en hough hese pape s in oduce an
app oxima ion o model he capabili y cu es o in e e s o conside
eac i e powe , he p oposed model has he po en ial o esul in
in e e o e load si ua ions, as e idenced by he esul s. The au ho s o
[29] p opose an op imal managemen s a egy o a mul i-ene gy MG
ope a ing in ene gy ma ke s. The p oposed scheme is hie a chical, wi h
a lowe laye made o single mul i-ene gy MGs and wi h an uppe laye
ha coo dina es he MGs, applying a dynamic p ice mechanism, and
ha is in e aced wi h he dis ibu ion ne wo k. Ne e heless, a single
busba model is employed o desc ibe he opology o he MGs and
eac i e powe is neglec ed. A me hodology o op imally ope a e a BESS,
p o iding lexibili y o manage PV and WT a iabili y, is p o ided in
[30], o a acili y equipped wi h a mic o u bine and a DG, oo. The
pu pose o he s udy is o y o employ he BESS as he unique lexible
sou ce, no elying on he DG. Howe e , as in he p e ious s udies, he
MG is modelled as a single busba sys em and eac i e powe is
neglec ed.
O he s udies apply a mul i-busba model o MGs, o adhe e o eali y
in a be e way. Fo example, in [31] an EMS o a MG eeding esi-
den ial, comme cial and indus ial use s wi h PV, WT and BESS uni s is
p esen ed, conside ing he powe lows among buses bu neglec ing he
analysis o ol age phenomena, eac i e powe exchanges and no ying
o limi he numbe o cha ging and discha ging cycles o he BESS, ha
could educe i s use ul li e. The au ho s o [32] also conside a mul i-
busba model o p esen an EMS o wind a ms combined wi h BESS
and dis ibu ed gene a o s. The s udy conside s a limi a ion on he
s a up and shu down cycles. Howe e , his las wo k neglec s he
impac o eac i e powe and jus conside he managemen o ac i e
powe . A wo-laye coo dina ed EMS o op imally manage dis ibu ion
ne wo ks wi h g id-connec ed MGs is p oposed in [33]. The i s laye
op imizes he MG ope a ion while he second op imizes he dis ibu ion
ne wo k ope a ion. A mul i-busba model is used o model he MG.
Howe e , he managemen o BESS does no conside he ela ionship
be ween he SoC and he exchanged powe , so possible disc epancies
could appea in eal implemen a ions. In addi ion, like o he pape s, i
does no a emp o limi s a ups o sho pe iods o ime. Ano he s udy
ha p esen s he in eg a ion o a mul i-busba model wi hin he EMS is
[34], whe e he s udy case is a MG wi h DERs and RESs. In his las
pape , Op imal Powe Flow (OPF) cons ain s a e also conside ed. The
S. Ga cía e al.
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 165 (2025) 110458
2
au ho s p opose a mul i-objec i e app oach, conside ing economic,
en i onmen al and powe quali y objec i es. Howe e , he p oblem is
non-linea (NLP) and non-con ex, equi ing me a-heu is ic op imiza ion
algo i hms o sol e i . In addi ion, BESSs a e no conside ed wi hin he
o mula ion, no assessing he p ominen ole ha hey will play in
scena ios wi h high RES pene a ion, due o hei lexibili y. Simila ly, in
[35] an EMS o he op imal dispa ching o mul i-mic og ids equi ing
me a-heu is ic op imiza ion algo i hms is p esen ed. The p oposal con-
side s PV, WT and BESS and models he mic og id as a mul i-busba
ne wo k. Howe e , he au ho s jus conside ac i e powe manage-
men , neglec ing he e ec o eac i e powe . In [36] he au ho s p o-
pose an EMS o manage i ual powe plan s connec ed o a dis ibu ion
ne wo k. The p oblem conside s RES and EV uni s’ managemen o
ac i e and eac i e powe managemen h ough he comple e OPF
equa ions. Howe e , he p oblem is non-linea and non-con ex,
equi ing high compu a ional imes and speci ic sol e s. A simila
app oach is p esen ed in [37] bu also conside ing hyd ogen s o age as a
po en ial solu ion o inc ease eliabili y and lexibili y o he ne wo k.
In [38] a mixed-in ege second-o de cone p og amming (MISOCP)
EMS o MGs inco po a ing RES, BESS and DG uni s is p oposed. The
o mula ion employs obus op imiza ion o asce ain he iabili y o he
p oposed solu ions. The EMS manages bo h ac i e and eac i e powe ,
employing a mul i-busba model wi h a con ex o mula ion o he OPF
equa ions. In [39], some o he same co-au ho s who con ibu ed o he
p e ious pape p esen ed a MINLP based EMS o islanded MGs ha was
la e linea ized as a MILP p oblem. This p oposal includes a mul i-
busba model, linea izing he OPF equa ions h ough he assump ion
o knowing es ima ed alues o ol ages and ac i e and eac i e powe
lows h ough lines. The p oposed app oach en ails a hie a chical so-
lu ion in which he MILP p oblem is ini ially sol ed and subsequen ly
he MINLP. While p oposals [38,39] a e comp ehensi e, hey lack any
s ipula ions p e en ing dispa chable uni s (BESS and DG) om mul iple
ac i a ions and deac i a ions in sho pe iods o ime, no ying o limi
he numbe o s a up and shu down cycles o hem, ha could educe i s
use ul li e. Addi ionally, he BESS model does no accoun o he ela-
ionship be ween maximum powe in cha ging/discha ging s a es and
he SoC, which could lead o inaccu a e solu ions ega ding he BESS
pe o mance.
To conclude his subsec ion and wi h he aim o p o ide a summa y
o he li e a u e e iew, Table 1 ou lines he p incipal a ibu es o each
o he pape s s udied in his subsec ion.
1.2. Con ibu ions
As a conclusion o he li e a u e e iew, ew pape s p opose a
comp ehensi e app oach o EMSs o MGs (see Table 1): some o hem
apply a single busba model o he MG, p e en ing he applica ion o
powe low equa ions and he assessmen o eac i e powe exchange by
RES in e e s and o he impac o RES p oduc ion luc ua ions on nodal
ol ages. O he pape s on he one hand apply a mul i-busba model o
he MG, including he OPF equa ions, bu on he o he hand do no
p o ide a de ailed insigh in o he ole ha BESSs and dispa chable DERs
play in MGs managemen , some o hem wi hou e en conside ing
eac i e powe con ol. I has been shown ha he in luence o s a up
and shu down cycles o dispa chable uni s (such as BESS o DGs) is o en
o e looked. Fu he mo e, he ela ionship be ween SoC and he powe
ha BESS can deli e is equen ly dis ega ded, which can esul in
inaccu a e assessmen s o BESS pe o mance. Many p oposals employ
non-con ex and non-linea o mula ions, equi ing heu is ic-based
sol e s o ob ain he solu ion o he p oblem. O he s u ilize con ex
quad a ic p og amming echniques, while ano he g oup employs hi-
e a chical app oaches. Fu he mo e, i has been obse ed ha he use-
cases p esen ed in he li e a u e a e ypically cons uc ed using syn-
he ic MGs. In addi ion, some o he pape s lack comp ehensi e in o -
ma ion ega ding he cha ac e is ics o he ne wo k o he asse s.
Gi en he s a e o he a , he aim o he p esen pape is o de ine a
comp ehensi e EMS o he op imal ope a ion o a g id- ied MG
composed o dis ibu ed RES uni s (PVs and WTs), dis ibu ed dis-
pa chable uni s (BESS and DGs) and loads, wi h he goal o educing he
ope a ing cos s o he acili y, and conside ing he limi a ions p e iously
iden i ied in he s a e-o - he-a . The EMS has been modelled as a Mixed-
In ege Linea P og amming (MILP) p oblem, o ensu e he exis ence o
an op imal solu ion and ha i ep esen s he global minimum. In
addi ion, linea o mula ions a e o en p e e ed o e con ex quad a ic
o mula ions due o hei simplici y and he ex ensi e suppo and
ma u i y o he sol e s ha a e a ailable. This app oach also educes he
compu a ional capaci y equi ed. Wi hin he EMS, dedica ed models o
powe elec onics uni s a e inse ed, aking in o accoun he capabili y
cu es o con e e s. This allows o conside he impac o eac i e
powe on he nodal ol age ampli udes, as well as managing po en ial
penal ies o eac i e powe exchange wi h he ex e nal g id. Powe low
equa ions a e linea ized and also included in he EMS o link powe
lows and nodal ol ages. Mo eo e , a de ailed model o BESS is
Table 1
Summa y o he li e a u e e iew. An emp y cell indica e ha he pape does no add ess he cha ac e is ic. The symbol ▴ deno es ha he pape discusses he use o
BESS bu does no conside he ela ion be ween exchanged powe and SoC. The symbol ◆ deno es ha he pape is using EVs as ene gy s o age. The symbol ■ deno es
ha he pape add esses he use o DGs bu does no conside he inhe en cons ain s o such sys ems.
Pape Op imiza ion
model
Reac i e
powe
con ol
OPF equa ions Implemen a ion o
in e e s’ capabili y
cu es
Limi s ON/OFF cycles
o dispa chable uni s
Use case DERs
PV WT BESS DG
[27,28] MILP ✔✔Syn he ic ✔ ✔ ◆
[29] Hie a chical
MILP
Syn he ic ✔ ✔ ▴ ■
[30] Quad a ic
P og aming
Syn he ic ✔ ✔ ▴ ■
[31] MILP Jus ac i e powe . Syn he ic ✔ ✔ ▴
[32] MILP DC powe low ✔Syn he ic ✔▴✔
[33] Hie a chical
MILP
✔B ach equa ions
linea ized
✔Syn he ic ✔ ✔ ▴ ■
[34] Non-con ex NLP ✔Non-con ex equa ions Syn he ic ✔ ✔
[35] Non-con ex NLP Non-con ex equa ion
jus o ac i e powe
Syn he ic ✔ ✔ ▴
[36,37] Non-con ex NLP ✔Non-con ex equa ions ✔Syn he ic ✔ ✔ ◆
[38] MISOCP ✔SOCP o mula ion ✔Syn he ic ✔ ✔ ▴✔
[39] Hie a chical
MILP-MINLP
✔Linea o mula ion
needing es ima ed g id
alues.
✔Syn he ic ✔▴✔
This
pape
MILP ✔✔ Nodal equa ions
linea ized
✔✔ ✔✔ Real
acili y
✔✔ ✔✔ ✔✔ ✔✔
S. Ga cía e al.
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 165 (2025) 110458
3
p o ided, aking in o accoun he dependence o he maximum cha ging
and discha ging powe on he S a e o Cha ge (SoC) and conside ing
cons ain s on he numbe o cha ging, discha ging and shu down cy-
cles, needed o ex end he use ul li e o he ba e y. Rega ding DG
gene a o s, amp-up and amp-down cons ain s ha e been included in
he EMS o mula ion, along wi h maximum and minimum ope a ing
egimes, o mimic he eal beha iou o he de ice. A g aphical ep e-
sen a ion o he EMS ope a ion is depic ed in Fig. 1.
In o de o s eng hen he p oposed EMS, i s alida ion is ca ied ou
in he Mic og id Li ing-Lab ins alled a he CATEPS building o he
Highe Poly echnic School o he Uni e si y o Se ille, equipped wi h all
he a o emen ioned echnologies. The echnical cha ac e is ics o he
acili y (MG ne wo k and he asse s deployed) a e ex ensi ely com-
men ed, wi h he objec i e o acili a e hei use by o he esea che s.
Resul s a e he e p esen ed and deeply commen ed, showing he ope a-
ions o he MG in di e en seasons. Addi ionally, a de ailed ocus is
p o ided on eac i e powe and ol age managemen . An empi ical
alida ion o he powe low equa ions linea iza ion is also conduc ed,
compa ing he esul s ob ained unde bo h he linea ized and non-
linea ized o mula ions. Finally, he e ec o he minimum numbe o
ON/OFF cha ging and discha ging cycles and he dependence o powe
wi h he SoC in he BESS model is also e alua ed.
The main con ibu ions o he p esen pape a e ep esen ed by:
•Inclusion o dedica ed models o powe elec onics, which conside
capabili y cu es and powe ac o limi a ions, allowing he assess-
men o eac i e powe managemen .
•Comp ehensi e app oach o manage dispa chable uni s, whe eby
minimum ON/OFF pe iods a e conside ed in o de o a oid he
occu ence o mul iple s a ups and shu downs in sho pe iods o
ime.
•Applica ion o mul i-busba model o he MG, oge he linea ized
powe low equa ions. Valida ion o he equa ions h ough compa -
ison o he esul s wi h he comple e non-linea powe low
equa ions.
•De ailed modelling o BESS, conside ing echnical cha ac e is ics as
he ela ion be ween maximum powe in cha ging/discha ging
phases and SoC. Including a sensi i i y analysis on he limi a ion on
he s a up/shu down cycles limi a ion.
•Comp ehensi e app oach o manage DG uni s, aking in o accoun
he echnical cons ain s inhe en o such sys ems, conside ing i s
ope a ing condi ions, including amp-up/ amp-down a es, mini-
mum ope a ing egime, and he numbe o ON/OFF cycles.
•Applica ion o he EMS o a eal es -case, conside ing he cha ac-
e is ics o ac ual acili ies and a oiding he use o syn he ic use-
cases.
The pape is o ganized as ollows: Sec ion 2 de ails he ma hema ical
o mula ion o he EMS, Sec ion 3 desc ibes he CATEPS Mic og id
Li ing-Lab, employed as es case, Sec ion 4 p esen s and discusses he
esul s, while Sec ion 5 is dedica ed o conclusions and also p o ides
some possible u he de elopmen s o he s udy.
2. EMS ma hema ical o mula ion
In his sec ion, he ma hema ical model o he EMS is desc ibed. The
model is buil as a MILP op imiza ion p oblem, aking ad an age o i s
simplici y and he ex ensi e suppo and ma u i y o he sol e s ha a e
a ailable compa ed wi h o he kinds o con ex o mula ions. The
objec i e o he EMS is o minimize he ope a ional cos o he MG while
conside ing he echnical cons ain s o i , main aining he MG be ween
easible ope a ional limi s. The inpu s o he model a e he o ecas ed
powe p oduc ion o all he RES uni s, he SoC o he BESS a he
beginning o he op imiza ion cycle, he o ecas ed consump ion o MG,
he echnical pe o mance pa ame e s o all he ene gy sou ces o he
MG (powe a ings, amp-up/down p o iles, ne wo k admi ance ma ix,
e c.) and, o cou se, he pa ame e s ela ed o cos s. The ou pu s o he
model a e he powe p o iles (bo h ac i e and eac i e) o all dis-
pa chable uni s and he ol age phaso s and powe s a all he nodes o
he MG. Unless o he wise speci ied, all elec ical uni s p esen ed in his
pape a e exp essed in he pe -uni (p.u.) sys em, wi h SB and VB ep-
esen ing he base powe and base ol age, espec i ely. A posi i e alue
in a powe a iable indica es he injec ion o powe in o he node, while
a nega i e powe alue indica es he abso p ion o powe . The o mu-
la ion is p esen ed in a gene ic o m and can be applied o any MG. The
Fig. 1. G aphical ep esen a ion o he EMS ope a ion.
S. Ga cía e al.
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 165 (2025) 110458
4
ime ho izon is ep esen ed by T, wi h ime being disc e ized in o N ime
s eps. The ime in e al be ween s eps is deno ed by Δ (Δ =T/N). In
gene al, a iables ha e wo supe sc ip s: he i s indica es he asse o
which i e e s (e.g., PV, BESS, DG, e c.) while he second desc ibes some
cha ac e is ic o he a iable. In he case o a gene al o mula ion
applicable o mul iple asse s, he supe sc ip symbol X is employed.
Subsc ip s se e o indica e he index o he gene a ing uni and he ime
index.
2.1. Powe elec onics uni model
In his subsec ion, he cons ain s ela ed o he asse s connec ed o
he MG by means o powe elec onics uni s (e.g. in e e s, ec i ie s,
and powe con e e s) a e p esen ed.
Fi s , hese asse s mus mee he powe a ing echnical limi s o he
powe elec onics (1) :
(SX,max
i)2≥ (PX
i, )2+ (QX
i, )2(1)
whe e PX
i, and QX
i, a e he ac i e and eac i e powe s o he i h asse
o echnology X a ime and SX,max
i he maximum appa en powe ha
can be deli e ed by he powe elec onics. Inequali y (1) is a quad a ic
exp ession, bu i can be linea ized conside ing ha he cons ain jus
de ines ha he hypo enuse (con o med by a igh iangle whose ca he i
a e P and Q) mus be equal o lowe han he appa en powe o he
in e e . This is he same as conside ing ha he appa en powe
deli e ed by he in e e mus be wi hin a ci cle o adius he maximum
a ing o i . The e o e, cons ain (1) can be linea ized by conside ing a
se o NPW linea cons ain s wi h he o m o (2). As NPW inc eases, he
se o cons ain s (2) becomes close o he non-linea capabili y cu e
(1). Thus, he highe NPW pa ame e he be e .
SX,max
i≥PX
i, cos(2
π
n/NPW)+QX
i, sin(2
π
n/NPW),∀n∈[1,NPW](2)
Second, powe elec onics uni s can ope a e only wi hin ce ain
powe ac o limi s. Conside ing ha ac i e powe could be posi i e o
nega i e, as could be he case o uni s ha include a ec i ie (e.g., he
ec i ie o a BESS), cons ain (3) mus hold o main ain he powe
ac o be ween easible limi s in he ou -quad an s:
− an(ϕX,PF
i)PX
i, ≤QX
i, ≤ an(ϕX,PF
i)PX
i, (3)
whe e ϕX,PF
i is ob ained as ϕX,PF
i=a ccos(PFX
i), being PFX
i he mini-
mum powe ac o a which he uni can ope a e. O cou se, he absolu e
alue unc ion is non-linea . Appendix A. shows he MILP implemen a-
ion o his unc ion. I he uni can only injec ene gy in o he g id, as is
he case o PV uni s, he absolu e alue unc ion i is no needed in
cons ain (3).
Las ly, i is necessa y o conside ha some uni s could deli e a
maximum ac i e powe alue (PX,max
i, )lowe han he nominal appa en
powe . Thus, i is necessa y o impose (4) o conside his possibili y. I
he uni canno abso b powe (e.g., a PV in e e ), he alue on he le -
hand side o (4) will be subs i u ed by ze o.
−PX,max
i≤PX
i, ≤PX,max
i(4)
In con as o o he models used in he li e a u e, he model p e-
sen ed in his subsec ion ensu es ha he powe elec onics ope a es
only wi hin i s capabili y cu e, he eby p e en ing bo h ou -o - ange
ope a ing zones and o e load condi ions.
2.2. Dispa chable uni s ON/OFF limi a ions
In his subsec ion, a se o cons ain s o s ablish minimum ON/OFF
pe iods o dispa chable uni s (e.g., BESS o DGs) a e p esen ed. This se
o cons ain s can be applied o all kinds o dispa chable uni s a ailable
in MGs. Howe e , hey only co e he case o dispa chable uni s wi h
PX
i, ≥0 (i.e., hey a e no bidi ec ional). Adap a ion in he case o bidi-
ec ional dispa chable uni s such as BESS is discussed in i s own sub-
sec ion.
In his sense, o a oid ha dispa chable uni s a e u ned ON/OFF
mul iple imes in sho pe iods o ime, cons ain (5) is in oduced o
main ain he i h uni o echnology X ON o a leas NX,on imes eps:
aX, on
i, ≤(1/NX,on)∑ +NX,on−1
k= aX,on
i,k(5)
whe e aX,on
i, is a bina y a iable indica ing ha he uni is ON a ime
s ep and aX, on
i, is a bina y a iable indica ing ha he uni has been
u ned ON a ime s ep . The alue o NX,on is ob ained as NX,on =
⌈TX,on/Δ ⌉, whe e ⌈x⌉ deno es he ceiling unc ion o x and TX,on is he
minimum ime ha he uni mus be ON.
Simila ly, i one wan s o impose ha he uni mus be main ained
OFF o a ce ain ime a e i has been u ned OFF, cons ain (6) could
also be included in he model o he dispa chable uni . In his case, aX, o
i,
is a bina y a iable deno ing ha he i h uni has been u ned OFF a
ime and NX,o ep esen s he numbe o ime s eps ha he uni mus
emain OFF.
aX, o
i, ≤1−(1/NX,o )∑ +NX,o −1
k= aX,on
i,k(6)
To ob ain he bina y a iable aX,on
i, indica ing whe he he uni is ON
o OFF, classical big-M cons ain s in (7) and (8) a e imposed:
PX
i, ≥∊−M(1−aX,on
i, )(7)
PX
i, ≤MaX,on
i, (8)
whe e M is a big posi i e numbe and ∊ a small posi i e ole ance o
simula e a >inequali y.
In addi ion, cons ain s (9) and (10) a e included in he uni model o
ob ain he bina y a iables ha indica e when he uni has been u ned
ON o OFF:
aX, on
i, −aX, o
i, =aX,on
i, −aX,on
i, −1(9)
aX, on
i, +aX, o
i, ≤1 (10)
2.3. Renewable ene gy sou ce uni s
The ac i e powe gene a ion p o iles o he RES uni s (e.g., PVs o
WTs) a e inpu s o he model (ob ained h ough o ecas ing ech-
niques). Howe e , in he case o eac i e powe , RES uni s can adap he
injec ion/abso p ion o he g id by means o he powe in e e s. Thus
QX
i, o RES uni s is a decision a iable. O cou se, his is possible i he
in e e a ing cons ain s a e me . The e o e, i is possible o use he
RES in e e as a eac i e ene gy dispa chable uni including a se o
cons ain s as (2) and (3) in he model.
2.4. Ba e y ene gy s o age sys em
In his subsec ion, he model o he BESS uni s is in oduced. Fi s ,
since he BESS is connec ed by means o an in e e / ec i ie o he
elec ic ne wo k, a se o cons ain s (2) o (4) a e included. In addi ion,
as a dispa chable asse , a se o cons ain s desc ibed in subsec ion 2.2
mus be included o con ol he ON/OFF cycles o he uni . Howe e , as
s a ed be o e, hese cons ain s only conside he case o dispa chable
uni s ha only injec ac i e powe in o he g id (e.g., DGs o CHPs).
Thus, i he uni is a ba e y ha can discha ge (injec ) o cha ge
(abso b), hese cons ain s only co e he discha ging case. The e o e, i
is necessa y o add ano he se o cons ain s (5)-(6) and (9)-(10) o
model he cha ging case. The supe sc ip on in he bina y a iables mus
be eplaced by ch and dis in each o he wo se s o cons ain s o
S. Ga cía e al.
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 165 (2025) 110458
5
dis inguish he cha ging and discha ging a iables. Mo eo e , di e en
numbe o minimum cha ging (NBESS,on,ch,NBESS,o ,ch) and discha ging
cycles (NBESS,on,dis,NBESS,o ,dis) could be de ined. In addi ion o hese,
cons ain s (11) and (12) mus be included o ob ain he aBESS,ch
i, bina y
a iable, which indica es whe he he uni is in a cha ging s a e. O
cou se, cons ain (13) mus hold be ween ch and dis a iables. I bo h
a iables a e ze o, he uni is OFF. Thus, he bina y a iable aBESS,on
i, ha
indica es i he uni is ON o OFF is ob ained wi h he equali y (14).
−PBESS
i, ≥∊−M(1−aBESS,ch
i, )(11)
−PBESS
i, ≤MaBESS,ch
i, (12)
aBESS,dis
i, +aBESS,ch
i, ≤1 (13)
aBESS,dis
i, +aBESS,ch
i, =aBESS,on
i, (14)
The ene gy model o he BESS is p esen ed in (15):
WBESS
i, +1=WBESS
i, −Δ (PBESS
i, (aBESS,ch
i,
η
ch
i+aBESS,dis
i, (1/
η
dis
i))+WBESS
i,
τ
BESS,sd
i)(15)
whe e WBESS
i, is he ene gy s o ed by he i h uni a ime ,
η
ch
i and
η
dis
i
a e he e iciency while cha ging and discha ging, espec i ely; and
τ
BESS,sd
i is he sel -discha ge loss exp essed as he pe uni loss o s o ed
ene gy pe hou .
As can be no iced, (15) is a non-linea unc ion due o he p oduc o
con inuous a iable PBESS
i, wi h bina y a iables aBESS,ch
i, and aBESS,dis
i, o
model he selec ion o cha ging/discha ging e iciencies. These non-
linea e ms can be linea ized by subs i u ing hem by wo auxilia y
con inuous a iables gBESS,dis
i, ≜aBESS,dis
i, PBESS
i, and gBESS,ch
i, ≜aBESS,ch
i, PBESS
i, ,
ob ained as desc ibed in Appendix B. Wi h his subs i u ion, (16) is he
linea equi alen o (15).
WBESS
i, +1=WBESS
i, −Δ (gBESS,ch
i,
η
ch
i+gBESS,dis
i, (1/
η
dis
i)+WBESS
i,
τ
BESS,sd
i)(16)
Cons ain s (17) and (18) a e included o limi he maximum and
minimum s a e o cha ge he ba e y can each:
WBESS
i, ≤WBESS,cap
iSoCBESS,max
i(17)
WBESS
i, ≥WBESS,cap
iSoCBESS,min
i(18)
whe e SoCBESS,max
i and SoCBESS,min
i a e he maximum and minimum SoC
he ba e y can each and WBESS,cap
i is he a ed capaci y o he ba e y.
The minimum powe a which he BESS mus ope a e, bo h in
cha ging and discha ging mode, can be de ined wi h cons ain s (19)
and (20). O cou se, i wan ed, di e en minimum alues could be
es ablished o he cha ging and discha ging cases.
PBESS
i, ≥ − PBESS,min
iaBESS,ch
i, (19)
PBESS
i, ≤PBESS,min
iaBESS,dis
i, (20)
In addi ion, he ela ionship be ween he SoC and he maximum
powe a which he ba e y can be cha ged/discha ged mus be
conside ed. Typically, when cha ging om a low SoC, he maximum
a ed powe can be deli e ed o he ba e y. Howe e , when a ce ain
SoC is eached while cha ging, he maximum powe accep ed by he
BESS s a s o dec ease un il i eaches i s ull capaci y. Simila ly, when
discha ging om a high SoC, he maximum a ed powe can be ex ac ed
om he ba e y. Howe e , when a ce ain SoC is eached while dis-
cha ging, he maximum powe ha can be ex ac ed om he BESS
s a s o dec ease un il i eaches i s minimum capaci y.
This beha io can be modeled by de ining wo addi ional linea
cons ain s linking he SoC wi h he powe exchanged by he BESS.
Speci ically, inequali y (21) models he cha ging scena io while (22)
models he discha ging one. In hese cons ain s, mBESS,ch
i and mBESS,dis
i
a e wo cons an s ob ained om equa ions (23) and (24), whe e Lch
i and
Ldis
i a e he SoC limi s a which injec ed/abso bed powe s a s o
dec ease. This o mula ion di e s om o he s in he li e a u e in ha i
a oids he use o piecewise unc ions, which conside s condi ional
o mula ion, in oducing mul iple bina y a iables. In his sense, his
o mula ion jus in oduces wo linea inequali ies in o he p oblem,
educing compu a ional e o .
PBESS
i, ≥mBESS,ch
i(SoCBESS
i, −1)(21)
PBESS
i, ≤mBESS,dis
iSoCBESS
i, (22)
mBESS,ch
i=PBESS,max
i/(1−Lch
i)(23)
mBESS,dis
i=PBESS,max
i/Ldis
i(24)
As a summa y o he BESS ope a ion, Fig. 2 shows g aphically he
easible ope a ional ange de ined by he cons ain s p esen ed in his
subsec ion.
2.5. Diesel gene a o s
As a dispa chable uni , he model o he DG mus complain wi h he
es ic ions imposed in subsec ion 2.2 o limi he ON/OFF cycles. Thus,
a se o cons ain s like he ones om (5) o (10) a e included o each
DG uni .
In addi ion o he minimum ON/OFF ime limi a ions, due o he
na u e o DGs, cons ain s (25) and (26) a e included o limi he amp-
up (PDG,RU
i) and amp-down (PDG,RD
i) a es espec i ely. The wo a o e-
men ioned pa ame e s a e gi en in W/h in he da ashee s (subsequen ly
ans o med in o he pe -uni sys em as all he a iables in he EMS
o mula ion).
PDG
i, −PDG
i, −1≤Δ PDG,RU
i(25)
PDG
i, −1−PDG
i, ≤Δ PDG,RD
i(26)
Mo eo e , DGs usually ha e a minimum powe ope a ing egime. To
each his ope a ing egime, hey need a ce ain pe iod o ime in he
s a up. In a simila way, hey may need a ce ain ime o shu down.
Thus, o conside his possibili y, cons ain (27) is used o es ablish a
minimum powe in he s a iona y ope a ing egime.
⎛
⎝aDG
i, −∑
k= −NDG, on −1
aDG, on
i,k−∑
+NDG, o −1
k=
aDG, o
i,k⎞
⎠PDG,min
i≤PDG
i, ≤PDG,max
(27)
The le -hand side o he inequali y es ablishes a minimum powe
injec ion in he s a iona y egime. The minimum powe injec ion is
deac i a ed when he uni is OFF o when he uni is in he s a up/
shu down pe iods. Speci ically, he minimum powe injec ion is deac-
i a ed o NDG, on and NDG, o imes eps o he s a up and shu down
espec i ely. These a iables a e ob ained as (28) and (29) espec i ely:
NDG, on =⌈PDG,min
i/(Δ PDG,RU
i)⌉ (28)
NDG, o =⌈PDG,min
i/(Δ PDG,RD
i)⌉ (29)
whe e ⌈x⌉ deno es he ceiling unc ion o x. I is wo h men ioning
ha (27) implici ly imposes ha NDG,on ≥NDG, on +NDG, o mus be
sa is ied o he uni o ope a e. Fig. 3 shows g aphically he in e p e-
a ion o he a iables desc ibed in his subsec ion.
S. Ga cía e al.
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 165 (2025) 110458
6
Finally, he p oduc ion cos o he i h DG uni a ime (CDG
i, ) is
p esen ed in (30):
CDG
i, =c uelSBΔ (aDG
i,
ρ
iPDG,n
i+
σ
iPDG
i, )(30)
whe e c uel is he uel cos (in
€
/L),
ρ
i and
σ
i a e he uel in e cep and
he uel slope ob ained om he da ashee o he DG (bo h uni s in
L/kWh) [40,41], PDG,n
i is he nominal powe o he uni and SB is he base
powe used in he pe -uni ope a ions.
2.6. Elec ic ne wo k model
The simples way o model he elec ic ne wo k o a MG is o use a
single bus ep esen a ion, in which all asse s a e connec ed o he same
elec ical poin . As e idenced in he in oduc ion, his is he mos
common app oach obse ed in he li e a u e. Despi e he simplici y o
his modeling app oach, which me ely in oduces wo cons ain s o
ensu e he balance o ac i e and eac i e powe s, i ails o conside he
link be ween powe lows (ac i e and eac i e) and nodal ol ages.
Addi ionally, i dis ega ds he echnical cons ain s associa ed wi h
elec ical a iables, such as ol age limi s. To add ess his limi a ion, he
p oposed EMS inco po a es he powe low equa ions in o he o mu-
la ion. Howe e , powe low equa ions a e non-linea . Thus, in his
subsec ion, a linea ized e sion o he powe low equa ions is
p esen ed.
Conside ing a MG wi h Nn nodes (o buses), he complex powe
phaso Si, a node i and ime is gi en by (31):
Si, =Vi, Ii,
*=Vi, ∑Nn−1
k=0Yik
*Vk,
*(31)
whe e Vi, and Ii, a e he ol age and injec ed cu en phaso s a node
i, while Yik deno es he i,k elemen o he ne wo k admi ance ma ix. I
should be no ed ha * ep esen he complex-conjuga e. As usual in
powe low no a ion, he powe a nodes i=0,⋯,(Nn−1)is composed
by he sum o he ne injec ed powe s o he elemen s connec ed o ha
node. Node 0 is designa ed as he slack o he ne wo k ( e e ence bus),
wi h V0, =1∠0 (p.u.). In his sense, he Poin o Common Coupling
(PCC) o he MG wi h he dis ibu ion ne wo k will be conside ed he
slack node.
As s a ed, (31) is non-linea . A possible linea iza ion o i is o ob ain
he i s o de Taylo expansion cen e ed a ope a ional poin V=
1∠0p.u.. The esul o his linea iza ion is shown in (32).
Si, ≈∑Nn−1
k=0Yik
*+(∑Nn−1
k=0Yik
*)(Vi, −1∠0)+∑Nn−1
k=0(Yik
*(Vk, −1∠0))
(32)
In low- ol age ne wo ks, shun admi ances a e insigni ican and can
be neglec ed. Thus, he sum o elemen s a columns (and ows) in he
admi ance ma ix is ze o, simpli ying (32) o (33).
Si, =∑Nn−1
k=0Yik
*(Vk,
*−1∠0)(33)
Equa ion (33) can be ew i en in ec angula o m as (34) consid-
e ing ha i he pe uni sys em is adop ed and ope a e in adians,
Vi, =Vi, ∠δi, can be app oxima ed as Vi, ≈Vi, +jδi, , being Vi, and δi,
he ol age magni ude and phase angle a node i and ime . In his
con ex , j is he imagina y uni . This is a alid app oxima ion when
ol age magni ude alues a e no oo a om he base alue and phase
angle di e ences ac oss lines a e no la ge, as is he case o small size
elec ical ne wo ks as MGs (Re(Vi, )=Vi, cos(δi, )≈Vi, and Im(Vi, )=
Vi, sin(δi, )≈δi, ).
Spli ing he eal and imagina y pa s in (34) and se ing ΔVk, =
Vk, −1, equa ions (35) and (36) a e he linea ized powe low equa ions
o he ac i e and eac i e powe s a node i and ime . Whe e Gik and Bik
a e he conduc ance and suscep ance o he b anch be ween nodes i and
k, espec i ely. Consequen ly, a se o Nn cons ain s o each ime in-
e al in he o m o (35) and (36) a e included in he model o conside
he elec ical ne wo k o he MG. A alida ion o he linea iza ion o he
powe low equa ions will be p esen ed in he esul s sec ion.
Fig. 2. Feasible ope a ional egions o he BESS.
Fig. 3. DG s a up and shu down a iables.
S. Ga cía e al.
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 165 (2025) 110458
7
Pi, +jQi, =∑Nn−1
k=0(Gik −jBik)(Vk, −1)−∑Nn−1
k=0(Gik −jBik)jδk, (34)
Pi, =∑Nn−1
k=0(GikΔVk, −Bikδk, )(35)
Qi, = − ∑Nn−1
k=0(Gikδk, +BikΔVk, )(36)
In oducing he ne wo k model in o he op imiza ion p ocess allows
o include sui able ol age and phase angle bounds o ensu e he p ope
ope a ion o he MG (37)-(38).
Vmin ≤Vi, ≤Vmax (37)
δmin ≤δi, ≤δmax (38)
Finally, he cos o bo h ac i e and eac i e powe abso bed/deli -
e ed om/ o he dis ibu ion ne wo k (i.e., a node 0) a ime is p e-
sen ed in equa ion (39):
Cg id
=SBΔ (P0, (cP,buy
(1−aP
0, )+cP,sell
aP
0, )+Q0, (cQ,buy
(1−aQ
0, )
−cQ,sell
aQ
0, )) (39)
whe e cP,buy
and cP,sell
a e he cos and e enue o ac i e powe ene gy
a ime espec i ely while cQ,buy
and cQ,sell
a e he penal ies o eac i e
powe abso p ion and injec ion espec i ely. The bina y a iables aX
0,
a e employed o indica e whe he ac i e powe (supe sc ip P) o eac-
i e powe (supe sc ip Q) is lowing in o (aX
0, =1) o om (aX
0, =0)
he dis ibu ion ne wo k. These a iables a e ob ained using cons ain s
as (7) and (8). As always, SB is he base powe used in he pe -uni
ope a ions.
As can be no iced, (39) is non-linea due o he mul iplica ion o he
bina y a iables aX
0, wi h he ac i e and eac i e powe con inuous de-
cision a iables o model he selec ion o buying o selling cos s. As
happened in he ba e y model, he p oduc o bina y wi h a con inuous
a iable can be linea ized by de ining an auxilia y a iable ob ained as
explained in Appendix B. Thus, ob aining wo auxilia y a iables gP
0, ≜
aP
0, P0, and gQ
0, ≜aQ
0, Q0, , equa ion (39) can be ew i en in a linea o m
as (40):
Cg id
=SBΔ (cP,buy
(P0, −gP
0, )+cP,sell
gP
0, +cQ,buy
(Q0, −gQ
0, )−cQ,sell
gQ
0, )(40)
2.7. Objec i e unc ion
The objec i e o he model is o minimize he ope a ional cos s o he
MG. In o he wo ds, he objec i e is o ind he solu ion ha educes he
o al p ice paid o ene gy subjec o he cons ain s o he de ice models
desc ibed in his sec ion. In his sense, wo p ima y sou ces o economic
expenses a e p esen in he MG model: he cos o he ene gy exchanged
wi h ex e nal g id and he cos o he uel o he DGs. Thus, he objec i e
unc ion can be desc ibed as ollows:
min∑N−1
=0(Cg id
+∑NDG−1
i=0CDG
i, )(41)
whe e Cg id
and CDG
i, a e he cos o he elec ical ene gy exchanged
wi h he dis ibu ion ne wo k (eq. (40)) and he cos o he uel o he i
h DG (eq. (30)), espec i ely. N and NDG deno e he numbe o imes eps
o he op imiza ion ho izon (N=T/Δ ) and he numbe o DG uni s in
he MG, espec i ely.
3. Use case: CATEPS Mic og id Li ing-Lab
The expe imen al alida ion o he p oposed EMS has been ca ied
ou in he Mic og id Li ing-Lab deployed a he CATEPS building o he
Highe Poly echnic School o he Uni e si y o Se ille. This ecen ly
cons uc ed building houses he labo a o ies, adminis a i e a eas and
o ices o he Poly echnic School.
The CATEPS building is shown in Fig. 4. The building is composed o
h ee dis inc sec ions: an open-plan labo a o y a ea, an adminis a i e
zone, and he o ices and esea ch labo a o ies. The open-plan labo a-
o y is loca ed on he wes side, whe eas he adminis a i e a ea is
loca ed on he eas side. Bo h a eas a e wo independen h ee- loo sub-
buildings, sepa a ed by a pa io. On op o hese wo s uc u es, ou
h ee- loo sub-buildings a e si ua ed ans e sally, housing o ices and
esea ch labo a o ies (see Fig. 4).
The Mic og id Li ing-Lab is a Sma G id es bed in eg a ed in o he
building’s h ee-phase low- ol age ne wo k, which is connec ed o he
medium ol age dis ibu ion ne wo k h ough i s own seconda y dis-
ibu ion subs a ion. The mic og id was ully ope a ional a he begin-
ning o 2023. The Mic og id Li ing-Lab ne wo k can be modeled as a
adial g id wi h wel e busba s. Fig. 5 shows he single-line model o he
MG. In his ci cui model, he o al ene gy consump ion o he six p e-
iously desc ibed a eas o he building is ep esen ed as six single
agg ega ed loads connec ed each one o i s co esponding node. In his
sense, he load a N1 comp ises he consump ion o he open-plan lab-
o a o y, he load a N2 he consump ion o he adminis a i e a ea and
he loads a N4 o N7 he consump ion o each o he ou ans e sal
sub-buildings espec i ely. The consump ion a hese nodes comp ises a
conside able numbe o indi idual loads, some o hem h ee-phase and
o he s single phase. The la e a e dis ibu ed equally in all phases in
acco dance wi h Spanish egula ions [42]. Consequen ly, he agg ega e
load a he a o emen ioned nodes is p edominan ly balanced when all
hese loads a e combined.
The asse s deployed in he CATEPS Mic og id Li ing-Lab a e depic-
ed in Fig. 6. The lis o he elemen s and he echnical speci ica ions o
hem a e p o ided below:
•A o al o ou PV ields, each comp ising 28 PV panels a anged in
wo s ings. The panels a e monoc ys alline o Passi a ed Emi e
and Rea Cell (PERC) echnology, each one wi h a a ed powe o
650Wp. Each PV ield has a h ee-phase in e e wi h a a ed powe
o 15kVA. The ou PV ields a e o equal speci ica ions and a e
ins alled in he same moun ing posi ion and wi h he same azimu h
angle.
•A BESS composed o six 48Vdc Li hium I on Phospha e (LiFePO4)
ba e y packs connec ed in pa allel. Each ba e y pack has a nominal
capaci y o 280Ah. The BESS is equipped wi h six single-phase in-
e e s/ ec i ie s, which a e connec ed in wo g oups o h ee and
synch onized o o m a h ee-phase sys em. Each in e e / ec i ie
has a a ed powe o 10kVA.
Fig. 4. CATEPS building. The Mic og id Li ing-Lab is deployed in his building.
S. Ga cía e al.
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 165 (2025) 110458
8
•Two H-Type Da eus e ical WTs, each wi h a a ed powe o 3kWp.
Bo h WTs a e managed by he same in e e wi h a a ed powe o
5kVA.
•One DG wi h bo h on-g id and backup capabili ies. The DG is con-
s uc ed wi h a ou -s oke V16 diesel engine and an 800kVA h ee-
phase gene a o .
•A con ol oom equipped wi h a SCADA sys em o moni o ing plan
ope a ions and da a collec ion.
3.1. Inpu pa ame e s and es scena ios
In his subsec ion, he inpu pa ame e s o he EMS a e desc ibed.
The EMS ope a es wi h a ime ho izon o T=24 h wi h aΔ =15 min
imes ep, esul ing in 96 imes eps pe op imiza ion ho izon. The ac i e
powe p oduc ion o he RESs and he load consump ion (bo h ac i e
and eac i e) a e p o ided by de e minis ic machine lea ning
o ecas ing echniques [43]. I should be no ed ha , al hough a ixed
op imiza ion ho izon wi hou o e lapping has been selec ed o ob ain
he esul s, he e is no inhe en limi a ion in he o mula ion o be
implemen ed in a olling-ho izon app oach, he eby educing possible
impac s o s ochas ici y in enewable ene gy sou ces (RES).
As men ioned abo e, he g id is modeled as a wel e-bus ba ne wo k
as shown in Fig. 5. The cha ac e is ics o each b anch a e epo ed in
Table 2. The bus ba N0 is conside ed he slack o he ne wo k (V0 =1p.
u., δ0=0 ad). The ol age and powe bases o he pe uni ope a ions
a e 400 V and 30kVA espec i ely (nominal line ol age o he g id and
maximum powe o he BESS espec i ely). The ol age limi s (Vmin,
Vmax) ha e been se o be be ween 0.95 and 1.05p.u. while he ol age
phase limi s (δmin,δmax) ha e been se o be be ween −0.1 and 0.1 ad.
PV ields a nodes N8 o N11 ha e a maximum powe a ing o
SPV,max
i =15kVA and PPV,max
i =15 kW. The minimum powe ac o a
which PV in e e s can ope a e is PFPV
i =0.85 (bo h induc i e and
capaci i e). The WT in e e has a maximum powe a ing o SWT,max
1 =
5kVA and PWT,max
1 =5 kW. The WT in e e can ope a e a a minimum
powe ac o o PFPV
i =0.8 (bo h induc i e and capaci i e). In bo h RES
uni s, eac i e powe QX
i, is a decision a iable subjec o cons ain s (2)-
(3).
The BESS a node N3 has a a ed capaci y o WBESS,cap =80.64kWh.
Fig. 5. CATEPS Mic og id Li ing-Lab ne wo k model.
Fig. 6. Asse s deployed a he CATEPS Mic og id Li ing-Lab.
Table 2
Cha ac e is ics o each o he b anches o he mic og id.
B anch Cable Type Leng h (m)
N0-N1 RZ1-K(AS) 4x(3x150mm) 36
N1-N2 RZ1-K(AS) 4x(3x150mm) 5
N2-N3 RZ1-K(AS) 4x50mm 21
N2-N4 RZ1-K(AS) 4x70mm 34
N2-N5 RZ1-K(AS) 4x(2x95mm) 31
N2-N6 RZ1-K(AS) 4x70mm 57
N2-N7 RZ1-K(AS) 4x150mm 60
N4-N8 RZ1-K(AS) 4x10mm 54
N5-N9 RZ1-K(AS) 4x10mm 77
N6-N10 RZ1-K(AS) 4x6mm 57
N7-N11 RZ1-K(AS) 4x6mm 57
S. Ga cía e al.
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 165 (2025) 110458
9
in he ba e y is close o he minimum le el (SoCBESS,min
i), he maximum
powe ha could p o ide he BESS would be limi ed by he emaining
ene gy s o ed, he ime in e al Δ and he e iciency o he powe
elec onics. Fo he discha ging case, his implici cons ain can be
exp essed by he inequali y (43). The unc ion o he g ay do ed line in
Fig. 15 can now be elucida ed: i co esponds o his implici cons ain .
In a simila way, inequali y (44) ep esen s he implici cons ain o
he cha ging case. In con as o he discha ge case, his cons ain has a
minimal e ec in he case shown in Fig. 15 (g ay do ed line in he
discha ge a ea). This is because he maximum allowed SoC is close o
100 % han he minimum allowed SoC is om 0 %.
PBESS
i, ≤
η
dis
i(SoCBESS
i, −SoCBESS,min
i)WBESS,cap
i
Δ (43)
PBESS
i, ≥(SoCBESS
i, −SoCBESS,max
i)WBESS,cap
i
η
ch
iΔ (44)
As a conclusion o his subsec ion, he co ec ope a ion o he
cons ain s ha ha e been included in o he EMS o link he s a e o
cha ge (SoC) o he maximum powe ha can be exchanged by he BESS
has been alida ed. Howe e , depending on he SoC limi s, cons ain s
(43)-(44) may be mo e es ic i e.
5. Conclusions
The inc easing p esence o DERs equi es he implemen a ion o an
e ec i e managemen s a egy. MGs o e an e ec i e solu ion o he
in eg a ion o RESs, BESS uni s, CCHP uni s, DG uni s, e c. in he dis-
ibu ion ne wo k.
This pape con ibu es wi h a comp ehensi e EMS o he op imal
ope a ion o gene ic g id- ied MGs, wi h he objec i e o educing he
ope a ional cos s. The p oposed EMS conside s se e al key aspec s,
including ac i e and eac i e powe managemen , he applica ion o
powe low equa ions, he use o speci ic models o powe elec onics
uni s and dispa chable uni s, and he in eg a ion o de ailed de ice
models o BESSs and DGs. In o de o educe he compu a ional
equi emen s while ensu ing he exis ence o an op imal solu ion ha
ep esen s he global minimum, he EMS is o mula ed as a MILP op i-
miza ion p oblem. Consequen ly, all he cons ain s ha e been
linea ized.
The main unc ionali ies o he p oposed EMS ha e been assessed in a
use case ha in ol es a ep esen a i e acili y: he CATEPS Mic og id
Li ing-Lab. The EMS ope a ion o he MG was e alua ed in di e en
seasons which showed a signi ican cos educ ion in he MG ope a ion
when using he p oposed EMS, especially in he summe (21.84 %) and
sp ing (14.84 %) scena ios. Fu he mo e, he ope a ion o he DG in he
p oposed scena ios was examined. The indings indica ed ha , gi en he
size o he DG and he cu en load o he building in ques ion, i s
ope a ion becomes economically iable only when elec ici y p ices
each ele a ed le els.
A de ailed ocus was gi en o eac i e powe and ol age manage-
men , showing he capaci y o RES o compensa e o eac i e powe ,
ensu ing he ope a ional limi s o he in e e s. Fu he mo e, o alida e
he linea iza ion o he powe low equa ions, a compa ison was con-
duc ed be ween he p oposed powe low equa ions and he comple e
non-linea ones. In his sense, he ol age esul s (magni ude and angle)
ob ained by he p oposed EMS we e hen con as ed wi h hose yielded
by a powe low sol e employing he comple e non-linea equa ions.
The MAE me ic demons a ed minimal disc epancies be ween he
linea and non-linea equa ions: 8.8e-5 p.u. and 3.2e-5 ad o ol age
magni ude and phase angle espec i ely; he eby p o ing he e ec-
i eness o he p oposed app oach.
The dispa chable uni s ON/OFF model cons ain s we e assessed
using he BESS as a case s udy, which demons a ed he abili y o he
p oposed model o modula e he s a up and shu down pe iods o he
de ice. The esul s indica ed ha he ON/OFF pa ame e s had an
impe cep ible impac on he ope a ing cos s and on he o al ene gy
exchanged by he BESS. This inding sugges s ha he echnical limi a-
ions o he de ice can be add essed while main aining a minimal impac
on he ope a ional cos . Fo ins ance, he o al numbe o s a ups in a
ypical win e week was educed om 37 o 24 while he di e ence in
ope a ional cos s jus inc eased by 0.22
€
, wi h he o al ene gy
exchanged by he BESS emaining almos cons an in bo h scena ios
( om 1657.17kWh o 1656.57kWh). Fu he mo e, he dependence
Fig. 15. Ac i e powe exchanged by he BESS as unc ion o he SoC. The g ay lines ep esen he ope a ional limi s de ined in he BESS model.
S. Ga cía e al.
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 165 (2025) 110458
16
be ween he maximum cha ging and discha ging powe on he SoC was
also e alua ed. The esul s alida ed he linea model in oduced o
implemen his ela ionship. Mo eo e , he esul s showed ha he
inhe en ela ionship be ween he a ailable ene gy in he BESS and he
maximum powe may be mo e es ic i e, depending on he maximum
and minimum SoC and on he del a ime adop ed in he op imiza ion
p ocess.
Fu u e esea ch will add ess he impac o he o ecas accu acy due
o he inhe en s ochas ici y o RESs. This will in ol e explo ing po-
en ial solu ions o mi iga e his aspec using p obabilis ic o ecas ing
echniques and a olling ho izon op imiza ion app oach, wi h he aim o
dynamically upda ing he EMS execu ion. The p oposed EMS is in ended
o a e ia y con ol o g id-connec ed MGs, u u e esea ch will also
add ess he inclusion o seconda y and p ima y con ol (p- and -q
con ol) o suppo he ope a ion o he CATEPS MG in islanded mode as
well as he in eg a ion o he p oposed EMS in o he SCADA sys em.
CRediT au ho ship con ibu ion s a emen
Sebas i´
an Ga cía: W i ing – o iginal d a , So wa e, Me hodology,
In es iga ion, Fo mal analysis, Da a cu a ion, Concep ualiza ion. S e-
ano B acco: W i ing – o iginal d a , Valida ion, In es iga ion. An o-
nio Pa ejo: W i ing – e iew & edi ing, Visualiza ion, Valida ion.
Ma eo F esia: W i ing – o iginal d a , Valida ion, In es iga ion. Juan
Ignacio Gue e o: W i ing – e iew & edi ing, Resou ces, P ojec
adminis a ion, Da a cu a ion. Ca los Le´
on: W i ing – e iew & edi ing,
Supe ision, P ojec adminis a ion, Funding acquisi ion.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing inancial
in e es s o pe sonal ela ionships ha could ha e appea ed o in luence
he wo k epo ed in his pape .
Acknowledgemen s
The publica ion is pa o he p ojec TED2021-129702B-I00, unded
by MICIU/AEI/10.13039/501100011033 and he Eu opean Union
“Nex Gene a ionEU”/PRTR.
Appendix A. . MILP o mula ion o ob aining absolu e alues
Le be x a con inuous a iable in he ange [ − C,C]wi h C being a cons an alue. The absolu e alue o x can be ob ained imposing he ollowing se
o cons ain s:
x≤aM (45)
x≥ (a−1)M(46)
x−y≤ (1−a)M(47)
x−y≥ (a−1)M(48)
x+y≤aM (49)
x+y≤aM (50)
whe e a is a bina y a iable, M a big posi i e numbe (M≥2C) and y a posi i e con inuous a iable. Cons ain s (45) and (46) a e used o se a=1
i x is posi i e and a=0 i nega i e. Cons ain s (47) and (48) a e used o impose y=x when x is posi i e while cons ain s (49) and (50) a e used o
impose y= − x when x is nega i e. The e o e, imposing cons ain s (45)-(50) is he same ha y= |x|.
Appendix B. . MILP o mula ion o linea ize he p oduc o a bina y and a con inuous a iable
Le x be a con inuous a iable x∈ [ − C,C]wi h C being a cons an alue. Le be a a bina y a iable. The non-linea p oduc o x and a can be
linea ized eplacing i by a con inuous auxilia y a iable g≜ax i he ollowing se o cons ain s a e imposed:
g≥ − Ma (51)
g≤Ma (52)
g≤x+M(1−a)(53)
g≥x−M(1−a)(54)
whe e M is a big posi i e numbe (M≥C). Cons ain s (51) and (52) se s g=0 i a=0 while (53) and (54) imposes g=x i a=1.
Da a a ailabili y
The da a ha has been used is con iden ial.
Re e ences
[1] Filipo i´
c S, Lio N, Rado ano i´
c M. The g een deal – jus ansi ion and sus ainable
de elopmen goals Nexus. Renew Sus ain Ene gy Re 2022;168:112759. h ps://
doi.o g/10.1016/j. se .2022.112759.
[2] Kougias I, Taylo N, Kakoulaki G, J¨
age -Waldau A. The ole o pho o ol aics o he
Eu opean G een Deal and he eco e y plan. Renew Sus ain Ene gy Re 2021;144:
111017. h ps://doi.o g/10.1016/j. se .2021.111017.
[3] Gonz´
alez-To es M, P´
e ez-Lomba d L, Co onel JF, Maes e IR, Yan D. A e iew on
buildings ene gy in o ma ion: T ends, end-uses, uels and d i e s. Ene gy Rep
2022;8:626–37. h ps://doi.o g/10.1016/j.egy .2021.11.280.
[4] Chen J, Liu M, O’Donnell T. Replacemen o Synch onous Gene a o by Vi ual
Synch onous Gene a o in he Con en ional Powe Sys em. IEEE Powe & Ene gy
Socie y Gene al Mee ing (PESGM) 2019;2019:1–5. h ps://doi.o g/10.1109/
PESGM40551.2019.8973650.
[5] Ojo Y, Benmiloud M, Les as I. F equency and Vol age Con ol Schemes o Th ee-
Phase G id-Fo ming In e e s. IFAC-Pape sOnLine 2020;53:13471–6. h ps://doi.
o g/10.1016/j.i acol.2020.12.713.
S. Ga cía e al.
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 165 (2025) 110458
17
[6] Ju asz J, Mikulik J, K zywda M, Ciapała B, Janowski M. In eg a ing a wind- and
sola -powe ed hyb id o he powe sys em by coupling i wi h a hyd oelec ic
powe s a ion wi h pumping ins alla ion. Ene gy 2018;144:549–63. h ps://doi.
o g/10.1016/j.ene gy.2017.12.011.
[7] Al Essa MJM. Powe managemen o g id-in eg a ed ene gy s o age ba e ies wi h
in e mi en enewables. J S o age Ma e 2020;31:101762. h ps://doi.o g/
10.1016/j.es .2020.101762.
[8] B i io C, Mandelli S, Me lo M. Ba e y ene gy s o age sys em o p ima y con ol
ese e and ene gy a bi age. Sus ainable Ene gy G ids Ne wo ks 2016;6:152–65.
h ps://doi.o g/10.1016/j.segan.2016.03.004.
[9] Azizipanah-Aba ghooee R, Malekpou M, Ka imi M, Te zija V. In eg a ion o wind
and sola ene gies wi h ba e y ene gy s o age sys ems in o 36-zone G ea B i ain
powe sys em o equency egula ion s udies. In J Elec Powe Ene gy Sys
2024;156:109737. h ps://doi.o g/10.1016/j.ijepes.2023.109737.
[10] Alam MJE, Mu aqi KM, Su an o D. Ba e y Ene gy S o age o Mi iga e Rapid
Vol age/Powe Fluc ua ions in Powe G ids Due o Fas Va ia ions o Sola /Wind
Ou pu s. IEEE Access 2021;9:12191–202. h ps://doi.o g/10.1109/
ACCESS.2021.3051283.
[11] Muh adi A, Pandi D, Nguyen N, Mi a J. Dis ibu ed Ene gy Resou ces Based
Mic og id: Re iew o A chi ec u e, Con ol, and Reliabili y. IEEE T ans Ind Appl
2021;57:2223–35. h ps://doi.o g/10.1109/TIA.2021.3065329.
[12] Cao W, Xiao J-W, Cui S-C, Liu X-K. An e icien and economical s o age and ene gy
sha ing model o mul iple mul i-ene gy mic og ids. Ene gy 2022;244:123124.
h ps://doi.o g/10.1016/j.ene gy.2022.123124.
[13] Khala ian F, Iliaee N, Diakina E, Pa sa P, Alhaide MM, Masali MH, e al.
Capabili ies o comp essed ai ene gy s o age in he economic design o enewable
o -g id sys em o supply elec ici y and hea cos ume s and sma cha ging-based
elec ic ehicles. J S o age Ma e 2024;78:109888. h ps://doi.o g/10.1016/j.
es .2023.109888.
[14] Majzoobi A, Khodaei A. Applica ion o Mic og ids in Suppo ing Dis ibu ion G id
Flexibili y. IEEE T ans Powe Sys 2017;32:3660–9. h ps://doi.o g/10.1109/
TPWRS.2016.2635024.
[15] Sawhney A, Del ino F, Bon ini B, B acco S. EMS o Ac i e and Reac i e Powe
Managemen in a Polygene a ion Mic og id Feeding a PED. Ene gies 2024;17:610.
h ps://doi.o g/10.3390/en17030610.
[16] Pi ouzi S, Zadehbaghe i M, Behzadpoo S. Op imal placemen o dis ibu ed
gene a ion and dis ibu ed au oma ion in he dis ibu ion g id based on ope a ion,
eliabili y, and economic objec i e o dis ibu ion sys em ope a o . Elec Eng
2024. h ps://doi.o g/10.1007/s00202-024-02458-w.
[17] Zadehbaghe i M, Dehghan M, Kiani M, Pi ouzi S. Resiliency-cons ained placemen
and sizing o i ual powe plan s in he dis ibu ion ne wo k conside ing ex eme
wea he e en s. Elec Eng 2024. h ps://doi.o g/10.1007/s00202-024-02583-6.
[18] F esia M, Bo do L, Del ino F, B acco S. Op imal day-ahead ac i e and eac i e
powe managemen o mic og ids wi h high pene a ion o enewables. Ene gy
Con e s Manage: X 2024;23:100598. h ps://doi.o g/10.1016/j.
ecmx.2024.100598.
[19] Aguila D, Quinones JJ, Pineda LR, Os anek J, Cas illo L. Op imal scheduling o
enewable ene gy mic og ids: A obus mul i-objec i e app oach wi h machine
lea ning-based p obabilis ic o ecas ing. Appl Ene gy 2024;369:123548. h ps://
doi.o g/10.1016/j.apene gy.2024.123548.
[20] Tziolis G, Lopez-Lo en e J, Baka M-I, Koumis A, Li e a A, Theocha ides S, e al.
Di ec sho - e m ne load o ecas ing in enewable in eg a ed mic og ids using
machine lea ning: A compa a i e assessmen . Sus ainable Ene gy G ids Ne wo ks
2024;37:101256. h ps://doi.o g/10.1016/j.segan.2023.101256.
[21] He H, Huang Y, Senjyu T. Mic og id load o ecas ing and op imiza ion o u u e
emo e island elec ic ehicle mass pene a ion: The case o Okinawa Island.
Ene gy Rep 2024;11:5532–41. h ps://doi.o g/10.1016/j.egy .2024.05.024.
[22] Wu C, Jiang S, Gao S, Liu Y, Han H. Cha ging demand o ecas ing o elec ic
ehicles conside ing unce ain ies in a mic og id. Ene gy 2022;247:123475.
h ps://doi.o g/10.1016/j.ene gy.2022.123475.
[23] Abbasi AR, Baleanu D. Recen de elopmen s o ene gy managemen s a egies in
mic og ids: An upda ed and comp ehensi e e iew and classi ica ion. Ene g
Con e Manage 2023;297:117723. h ps://doi.o g/10.1016/j.
enconman.2023.117723.
[24] Thi una ukka asu GS, Seyedmahmoudian M, Jamei E, Ho an B, Mekhile S,
S ojce ski A. Role o op imiza ion echniques in mic og id ene gy managemen
sys ems—A e iew. Ene g S a Re 2022;43:100899. h ps://doi.o g/10.1016/j.
es .2022.100899.
[25] Sha ma P, Du Ma hu H, Mish a P, Bansal RC. A c i ical and compa a i e e iew
o ene gy managemen s a egies o mic og ids. Appl Ene gy 2022;327:120028.
h ps://doi.o g/10.1016/j.apene gy.2022.120028.
[26] Abdelsa a M, Ismeil MA, Aly MM, Abu-Elw a SS. Ene gy Managemen o
Mic og id Wi h Renewable Ene gy Sou ces: A Case S udy in Hu ghada Egyp . IEEE
Access 2024;12:19500–9. h ps://doi.o g/10.1109/ACCESS.2024.3356556.
[27] B acco S, F esia M. Ene gy Managemen Sys em o he Op imal Ope a ion o a
G id-Connec ed Building wi h Renewables and an Elec ic Deli e y Vehicle. In:
IEEE EUROCON 2023–20 h In e na ional Con e ence on Sma Technologies;
2023. p. 472–7. h ps://doi.o g/10.1109/EUROCON56442.2023.10198884.
[28] F esia M, B acco S. Elec ic Vehicle Flee Managemen o a P osume Building
wi h Renewable Gene a ion. Ene gies 2023;16:7213. h ps://doi.o g/10.3390/
en16207213.
[29] Zhao J, Wang W, Guo C. Hie a chical op imal con igu a ion o mul i-ene gy
mic og ids sys em conside ing ene gy managemen in elec ici y ma ke
en i onmen . In J Elec Powe Ene gy Sys 2023;144:108572. h ps://doi.o g/
10.1016/j.ijepes.2022.108572.
[30] ´
Al a ez-A oyo C, Ve gine S, de la Nie a AS, Al a ado-Ba ios L, D’Amico G.
Op imising mic og id ene gy managemen : Le e aging lexible s o age sys ems and
ull in eg a ion o enewable ene gy sou ces. Renew Ene gy 2024;229:120701.
h ps://doi.o g/10.1016/j. enene.2024.120701.
[31] E eno˘
glu AK, S
¸eng¨
o ˙
I, E dinç O, Tas
¸cıka ao˘
glu A, Ca al˜
ao JPS. Op imal ene gy
managemen sys em o mic og ids conside ing ene gy s o age, demand esponse
and enewable powe gene a ion. In J Elec Powe Ene gy Sys 2022;136:107714.
h ps://doi.o g/10.1016/j.ijepes.2021.107714.
[32] Pi ouzi S. Ne wo k-cons ained uni commi men -based i ual powe plan model
in he day-ahead ma ke acco ding o ene gy managemen s a egy. IET Gene
T ansm Dis ib 2023;17:4958–74. h ps://doi.o g/10.1049/g d2.13008.
[33] Sabzalian MH, Pi ouzi S, A edes M, Wande ley F anca B, Ca olina CA. Two-Laye
Coo dina ed Ene gy Managemen Me hod in he Sma Dis ibu ion Ne wo k
including Mul i-Mic og id Based on he Hyb id Flexible and Secu able Ope a ion
S a egy. In T ans Elec Ene gy Sys 2022;2022:3378538. h ps://doi.o g/
10.1155/2022/3378538.
[34] Nusai K, Alasali F. Op imal Powe Flow Managemen Sys em o a Powe Ne wo k
wi h S ochas ic Renewable Ene gy Resou ces Using Golden Ra io Op imiza ion
Me hod. Ene gies 2020;13:3671. h ps://doi.o g/10.3390/en13143671.
[35] Wu N, Xu J, Linghu J, Huang J. Real- ime op imal con ol and dispa ching s a egy
o mul i-mic og id ene gy based on s o age collabo a i e. In J Elec Powe
Ene gy Sys 2024;160:110063. h ps://doi.o g/10.1016/j.ijepes.2024.110063.
[36] Akba i E, Fa aji Naghibi A, Veisi M, Shahpa nia A, Pi ouzi S. Mul i-objec i e
economic ope a ion o sma dis ibu ion ne wo k wi h enewable- lexible i ual
powe plan s conside ing ol age secu i y index. Sci Rep 2024;14:19136. h ps://
doi.o g/10.1038/s41598-024-70095-1.
[37] Liang H, Pi ouzi S. Ene gy managemen sys em based on economic Flexi- eliable
ope a ion o he sma dis ibu ion ne wo k including in eg a ed ene gy sys em o
hyd ogen s o age and enewable sou ces. Ene gy 2024;293:130745. h ps://doi.
o g/10.1016/j.ene gy.2024.130745.
[38] Gi aldo JS, Cas illon JA, L´
opez JC, Ride MJ, Cas o CA. Mic og ids Ene gy
Managemen Using Robus Con ex P og amming. IEEE T ans Sma G id 2019;10:
4520–30. h ps://doi.o g/10.1109/TSG.2018.2863049.
[39] Ve ga a PP, L´
opez JC, Ride MJ, da Sil a LCP. Op imal Ope a ion o Unbalanced
Th ee-Phase Islanded D oop-Based Mic og ids. IEEE T ans Sma G id 2019;10:
928–40. h ps://doi.o g/10.1109/TSG.2017.2756021.
[40] Aska zadeh A. Dis ibu ion gene a ion by pho o ol aic and diesel gene a o
sys ems: Ene gy managemen and size op imiza ion by a new app oach o a s and-
alone applica ion. Ene gy 2017;122:542–51. h ps://doi.o g/10.1016/j.
ene gy.2017.01.105.
[41] Kip oo MK, Lo y ME, Adewuyi OB, Con eh A, Howlade AM, Senjyu T. In eg a ed
app oach o op imal echno-economic planning o high enewable ene gy-based
isola ed mic og id conside ing cos o ene gy s o age and demand esponse
s a egies. Ene g Con e Manage 2020;215:112917. h ps://doi.o g/10.1016/j.
enconman.2020.112917.
[42] Real Dec e o 842/2002, de 2 de agos o, BOE-A-2002-18099, po el que se ap ueba
el Reglamen o elec o ´
ecnico pa a baja ensi´
on. n.d.
[43] Pa ejo A, B acco S, Pe sonal E, La ios DF, Del ino F, Le´
on C. Sho -Te m Powe
Fo ecas ing F amewo k o Mic og ids Using Combined Baseline and Reg ession
Models. Appl Sci 2021;11:6420. h ps://doi.o g/10.3390/app11146420.
[44] Pe˜
na e Ve a S. G idCal 2024. h ps://gi hub.com/SanPen/G idCal (accessed July
4, 2024).
[45] G ainge J, S e enson WD. Powe Sys em Analysis. McG aw-Hill. Educa ion 1994.
S. Ga cía e al.
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 165 (2025) 110458
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