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Economic assessmen o ba e y ene gy s o age sys ems o equency
egula ion ese e p o ision: A case s udy o he Dominican Republic
Emely C uz-De-Jesús ∗, José Luis Ma ínez-Ramos , Alejand o Ma ano-Ma colini ,
An onio Gómez-Expósi o
Dep . o Elec ical Enginee ing, Uni e sidad de Se illa, Camino de los descub imien os, Se ille, 41092, Andalusia, Spain
A R T I C L E I N F O
Keywo ds:
Ba e y ene gy s o age sys em
Economic dispa ch
F equency egula ion
Uni Commi men
A B S T R A C T
This pape p esen s an economic assessmen o he in eg a ion o ba e y ene gy s o age sys ems o p o iding
equency egula ion ese es in island powe sys ems ha a e unde going a ansi ion o a deca bonized ene gy
mix. The Dominican Republic sys em is used as a pa adigma ic case s udy. The s udy employs ac ual da a
om 2022 and mul iple mixed-in ege linea p og amming op imiza ion models o e alua e he ope a ional
and equency egula ion p o ision cos s in di e en scena ios, bo h wi h and wi hou accoun ing o he
con ibu ion o he s o age sys ems o p ima y and seconda y equency egula ion. The indings indica e ha
he in eg a ion o ba e y ene gy s o age sys ems can lead o a educ ion in annual ope a ional cos s o 10%,
and enhance he pene a ion o enewable ene gy by 12% o 2030. Mo eo e , he economic analysis e eals
ha cu en ly, he payback pe iod o such in es men s is less han one yea o p ima y equency egula ion
and less han wo yea s o seconda y equency egula ion. The esul s highligh he dual bene i s o s o age
sys ems in enhancing g id s abili y and suppo ing he in eg a ion o enewable ene gy, hus con ibu ing o
a mo e sus ainable and esilien powe sys em.
Abb e ia ions
BESS Ba e y Ene gy S o age Sys em
ESS Ene gy S o age Sys em
FR F equency Regula ion
ICE In e nal Combus ion Engine
ISO Independen Sys em Ope a o
MILP Mixed In ege Linea P og amming
NIES Na ional In e connec ed Elec ical Sys em
PFR P ima y F equency Regula ion
RES Renewable Ene gy Sou ces
SFR Seconda y F equency Regula ion
UC Uni Commi men
∗Co esponding au ho .
E-mail add ess: [email p o ec ed] (E. C uz-De-Jesús).
In oduc ion
Con en ional powe plan s ha e adi ionally been used o p o ide
equency egula ion se ices in elec ic powe sys ems. By o e ing
his ancilla y se ice, hese plan s a e equi ed o ope a e below hei
maximum gene a ion capaci y in o de o main ain a egula ion ese e
band. As he p opo ion o Renewable Ene gy Sou ces (RES) in he
global elec ici y gene a ion mix con inues o g ow, Ba e y Ene gy
S o age Sys ems (BESS) a e eme ging as p omising candida es o p o-
ide equency egula ion se ices (Da a, Kalam, & Shi, 2021). These
sys ems enable op imal ope a ion o RES and con en ional plan s by
ully le e aging hei abili y o supply demand wi hou he need o
dedica ed equency egula ion ese es (Gomez & He mana, 2019).
BESS o equency egula ion (gene al case s udies)
The apid esponsi eness o BESS, cha ac e ized by ac i a ion imes
less han one second, along wi h hei abili y o manage signi ican
powe luc ua ions, a e a ibu es ha make hem a ac i e o e-
quency egula ion applica ions (P akash e al., 2022), as well as o
addi ional as esponse se ices (He, King, Luo, Doone , Li, & Wang,
h ps://doi.o g/10.1016/j.esd.2025.101749
Recei ed 27 Janua y 2025; Recei ed in e ised o m 7 May 2025; Accep ed 8 May 2025
Ene gy o Sus ainable De elopmen 88 (2025) 101749
A ailable online 4 June 2025
0973-0826/© 2025 The Au ho s. Published by Else ie Inc. on behal o In e na ional Ene gy Ini ia i e. This is an open access a icle unde he CC BY-NC-ND
license (
h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/ ).
E. C uz-De-Jesús e al.
2021). Fo example, in Shin e al. (2022), a BESS is in eg a ed wi h
a s eam u bine gene a o o imp o e he p ima y equency con ol,
leading o a be e esponse unde load changes. The s udy in A igo,
Bompa d, Me lo, and Milano (2020) assesses how BESS in luences he
p ima y equency con ol wi hin he elec ical sys em. The pe o -
mance o BESS, measu ed by an e ec i eness index elian on he
ine ia le el o he sys em and he ype o equency luc ua ion, was
de e mined o compa e a o ably o as u bine go e no s and su pass
ha o adi ional powe plan s.
Economic iabili y assessmen s o BESS
Nume ous esea ch pape s ha e explo ed he use o BESS o e-
quency egula ion, ene gy a bi age, and a ious ancilla y se ices.
In Rancilio, Filippo, and Me lo (2022) analyzed he echno-economic
e alua ion o a BESS pa icipa ing in he Fas Rese e, also a mul i-
se ice case, whe e he BESS pa icipa es in he balancing ma ke o
he p o ision o eplacemen ese e in he I alian ma ke wi h posi i e
bene i s o he g id ope a o , and he au ho sugges ed as p omising
u u e he pa icipa ion o BESS in he Au oma ic F equency Res o a-
ion Rese e. Also, in Yu, Zhu, Liang, Chen, and Xiong (2023), he BESS
is used o pa icipa e in an ancilla y eme gency backup se ice, which
has p o en o be mo e p o i able han pa icipa ing in he spo ma ke
o eal- ime balancing. In Maluenda, Có do a, Lo ca, and Neg e e-
Pince ic (2023), a chance-cons ained s ochas ic model is p esen ed
o he op imal ope a ion scheduling o a PV-BESS-Elec olyze sys em
con ibu ing o ene gy and ancilla y se ices ma ke s.
BESS in eg a ion wi hin island g id sys ems
Island powe sys ems p esen unique challenges and oppo uni-
ies o in eg a e enewable ene gy wi h he aid o BESS (Ami uddin,
Liebman, Da ga ille, & Gawle , 2024). In Pombo, Ma inez-Rico, and
Ma czinkowski (2022) e alua ed h ee scena ios o enewable ene gy
in eg a ion and gene a ion and s o age expansion planning, de ined as
business as usual, op imal, and 100% enewable scena io, using a di e -
si ied ene gy mix including BESS, using São Vicen e Island, Cape Ve de
in A ica as a case s udy. The objec i e was o minimize in es men
cos s, emissions, and ope a ion and main enance. Among he esul s,
i is men ioned ha he op imal scena io is be e compa ed o he
o he s in e ms o cos and emissions educ ion and a oids o e sizing.
Simila ly, he s udy in El-Bidai i, Nguyen, Mahmoud, Jayasinghe, and
Gue e o (2020) explo es he op imal size o a BESS on Flinde s Island,
demons a ing ha he ex en o RES pene a ion depends on he size
o he BESS.
Uni Commi men (UC) as a ool o op imal ope a ion
Se e al s udies ha e used UC as a key ool o analyze he p o i-
sion o equency egula ion ese es in powe sys ems. Fo example,
in Zhang e al. (2021), a equency esponse model is p oposed o
he pu pose o analyzing equency s abili y. The model inco po a es
con en ional uni s (hyd o and he mal plan s), wind gene a ion, and
BESSs. The UC is explici ly modeled o e lec he c i ical dependence
o sys em ine ia on he commi ed con en ional uni s du ing each
p og amming pe iod. The esul s demons a e he compu a ional e i-
ciency and u ili y o his model o he beha io al analysis o equency
esponse. Simila ly, in Hao e al. (2020), UC is employed o assess
he impac o inco po a ing a signi ican sha e o wind gene a ion in
he PFR. The esul s o he UC analysis we e used o iden i y high-
isk scena ios in ol ing demand, gene a ion, and dis u bances, which
we e hen e alua ed in e ms o equency s abili y unde speci ic
commi men s, aking in o accoun load shedding and wind gene a ion
cu ailmen as pa o he PFR s a egies. This in eg a ed UC model
gua an ees he sa e and cos -e ec i e ope a ion o he powe g id in
ligh o he indings p esen ed in he s udy.
Con ibu ions and o ganiza ion
This s udy in es iga es he economic impac o BESS in p o iding
PFR and SFR ese es wi hin a medium-sized islanded powe sys em,
ocusing speci ically on he Dominican Republic’s Na ional In e con-
nec ed Elec ical Sys em (NIES). The analysis conside s BESS pa icipa-
ion in equency ese e p o ision, explo ing wo scena ios: s andalone
pa icipa ion in PFR and SFR, and concu en pa icipa ion in bo h
se ices. The BESS analyzed a e s and-alone de ices, no associa ed
wi h gene a ion plan s. A UC model is u ilized o e alua e he economic
bene i s o powe sys em ope a ions om a ious BESS con igu a ions
p o iding egula ion ese es. The assessmen encompasses mul iple
weekly demand and RES gene a ion scena ios, conside ing he gen-
e a ion echnologies cu en ly employed in he NIES. The ne wo k is
ep esen ed using a single-bus model.
The p incipal con ibu ions o his wo k, in compa ison o he
exis ing s a e o he a , a e ou lined below.
•Economic E alua ion o BESS in F equency Regula ion wi h ull
Technical and Ope a ional Cons ain s: In con as o Lee and Kim
(2019), a UC model is employed ha includes all echnical and
ope a ional cons ain s o he mal uni s, ep esen ing demand and
enewable gene a ion a ia ions ac oss di e en ypical weeks o
he yea . Also his s udy analyzes he economic impac o BESS
pa icipa ion in equency egula ion se ices wi hin he speci ic
con ex o he NIES.
•Pe spec i e o he Sys em Ope a o : Unlike López-G ajales e al.
(2023) and B aeue , Rominge , McKenna, and Fich ne (2019),
which ocus on bene i s o indi idual agen s o ex e nal in-
es o s, his s udy conside s he independen sys em ope a o
esponsible o s o age in es men , e alua ing he economic im-
pac on weekly ope a ing cos s and he dispa ch o all sys em
uni s.
•Reduc ion o Sys em Ope a ing Cos s: Con a y o Pusceddu, Za-
ke i, and Cas agne o Gissey (2021), which do no add ess he
educ ion o ope a ing cos s om a sys em-wide pe spec i e, his
wo k e alua es how BESS pa icipa ion can dec ease o e all sys-
em ope a ing cos s. In Li, Xu, and Huang (2023), he combined
use o BESS o peak and alley egula ion and equency egula-
ion is in es iga ed. A echnical-economic e alua ion is pe o med
o selec he bes combina ion in echnical and economic e ms.
In his model, he en i onmen al bene i s o BESS pa icipa ion in
equency egula ion a e conside ed.
•Real-Wo ld Applica ion in an Island Sys em: The island elec ic-
i y sys em o he Dominican Republic is used as a case s udy,
analyzing he inclusion o s o age o equency egula ion and
i s con ibu ion o sys em s abili y and he ansi ion o a cleane
ene gy mix.
To summa ize, he aim is o assess he cos -e ec i eness, om he
Independen Sys em Ope a o (ISO) pe spec i e, o in eg a ing BESS
in o island sys ems o PFR and SFR pa icipa ion, wi h he Dominican
Republic se ing as a case s udy. The Dominican Republic is cu en ly
publishing egula ions on BESS, speci ically on i s pa icipa ion in he
a bi age se ice (Comisión Nacional de Ene gía, 2024a; Comisión Na-
cional de Ene gía, 2024b). In addi ion, a he end o 2024, i published
a egula ion on he pa icipa ion o BESS in he equency egula ion,
in which i se s a ixed annual incen i e o ewa d in es o s o pa ic-
ipa ing in his se ice (Supe in endencia de Elec icidad, 2024). While
i is oo ea ly o assess he eal eac ion o in es o s o his incen i e,
his a icle p esen s ano he al e na i e in which he ISO i sel ins alls
BESS o equency egula ion, he eby os e ing cos educ ions in he
ope a ion o he sys em. This app oach se es o encou age egula o s
and ene gy policymake s o explo e o he ways o di e si y he ene gy
ma ix and educe ope a ing cos s.
Ene gy o Sus ainable De elopmen 88 (2025) 101749
2
E. C uz-De-Jesús e al.
The es o he pape is o ganized as ollows: Sec ion ‘‘Business
model’’ desc ibes he business model o BESS pa icipa ing in e-
quency egula ion ese e p o ision, Sec ion ‘‘Me hodology’’ p esen s
he me hodology and ma hema ical o mula ion o he op imiza ion
p oblem; Sec ion ‘‘Resul s and Discussion’’ explains how he case s ud-
ies a e selec ed and de ined, and p o ides he esul s o he simula ions
and Sec ion ‘‘Conclusions’’ summa izes he main conclusions o his
wo k.
Business model
The ene gy and powe a ings o he di e en s o age echnologies
ange be ween 1 kWh and mo e han 1 GWh, wi h powe capaci ies
be ween 1 kW and 300 MW (Ene gy T ansi ion Expe ise Cen e (EN-
TEC), 2023). In pa icula , o ancilla y se ices and ansmission g id
suppo applica ions, he capaci ies a e be ween 1 MWh and 1 GWh.
The p o ision o ancilla y se ices, pa icula ly ese e con ainmen
se ice, is he second mos popula applica ion o BESS, he i s being
ene gy a bi age. Re enues om he pa icipa ion in he ancilla y se -
ice ma ke s in coun ies such as Aus ia (76,000 eu os/MW in 2020,
and 190,000 eu os/MW in 2021) make his applica ions a ac i e.
Also in Hameed, T æhol , and Hashemi (2023) e alua ed he p ices
o di e en equency egula ion se ice p oduc s in he No dic coun-
ies om 2015 o 2020, including he hou s and mon hs when i is
mos p o i able o pa icipa e in hese se ices. They also es ima e he
e enues ha would be ecei ed by BESS pa icipa ing in equency
egula ion se ices.
O de 755, as issued by he US Fede al Ene gy Regula o y Com-
mission (FERC), equi es ha Independen Sys em Ope a o s (ISOs)
and Regional T ansmission Ope a o s (RTOs) conside bo h speed and
accu acy when designing compensa ion a es o equency egula-
ion se ices. I in oduced he concep o ‘‘mileage’’, whe e se ice
p o ide s a e paid based on he cumula i e dis ance o upwa d and
downwa d adjus men s made du ing a se ice pe iod. Recognizing
he impo ance o speed and accu acy can signi ican ly enhance he
deploymen o s o age sys ems wi hin he powe g id (Taba i & Sha e ,
2020).
An illus a i e example can be ound in You e al. (2022),whe e he
p ima y equency egula ion e enues o he Ene gy S o age Sys ems
(ESS) a e calcula ed using he mileage concep . Seconda y egula ion
compensa ion is pe o med using equency con ol capaci y compen-
sa ion and equency con ol mileage compensa ion. The esul s show
ha he addi ion o ESS educes he in es men cos o equency
egula ion.
In Lee and Kim (2019), a me hod is p oposed o es ima e he
bene i s o in oducing ESSs o p o ide equency egula ion se ices in
he Ko ean elec ici y ma ke s. They also sugges ha he compensa ion
o ESSs o pa icipa ing in equency egula ion should be calcula ed
di e en ly om con en ional echnologies, since BESSs ha e supe io
pe o mance. The s udy examines h ee cases: day ime bene i s o a
one-yea pe iod, nigh ime bene i s, and all-day bene i s. As in he
p eceding case, he esul s demons a e ha he in ol emen o ESSs
in equency egula ion con e s bene i s o he sys em.
Ano he app oach is illus a ed in Me en, Olk, Schoenebe ge , and
Saue (2020). In his ins ance, a BESS linked o a i ual powe plan
(VPP) is employed o con ibu e o au oma ic equency es o a ion
ese e (aFRR) solely o p o ide upwa d ese e. The TSO ini ia es he
BESS ac i a ion eques acco ding o a me i o de lis , which is so ed
in acco dance wi h he powe bid p ice. The BESS also pe o ms ene gy
a bi age while no pa icipa ing in he aFRR. An es ima ion o he ime
se ies o aFRR eques s is pe o med using SARIMA p edic ion mod-
els. The esul s showed ha he s a egies used a e no economically
easible o he 2019 da a, since he sa ings do no compensa e o
he cos s o he BESS; o he 2025 p edic ions, he esul s seem o be
economically iable o BESS wo king in conjunc ion wi h he VPP, bu
no as an independen esou ce.
In Pusceddu e al. (2021), an economic e alua ion o a BESS pa ic-
ipa ing in Enhanced F equency Response (EFR) and ene gy a bi age is
conduc ed using his o ical da a om 2015 o 2018 o he powe sys em
in G ea B i ain. The indings indica e ha a BESS wi h a capaci y o
10 MW engaged in bo h ma ke s gene a es p o i s ha a e 25% highe
han hose gene a ed by pa icipa ion in EFR alone. Fu he mo e, he
esul s indica e ha one o he key de e minan s o he p o i abili y o
BESS in his con igu a ion is he ene gy- o-powe (E/P) a io, a he
han he discha ge e iciency. I was concluded ha he op imal E/P
a io is be ween 1.5 and 2 h.
Finally, in Ni sch, Deissen o h-Uh ig, Schimeczek, and Be sch
(2021), he p o i abili y o BESS pa icipa ion in he Day-Ahead (DA)
ma ke and aFRR is e alua ed using a case s udy in he Ge man ma ke
wi h da a o 2019 and es ima ed p ices o 2030. The esul s demon-
s a ed ha ba e y e iciency con ibu es only a minimal amoun o
annual e enue. Ne e heless, he capaci y o p o ide ene gy in he
sho e m ep esen s he mos luc a i e oppo uni y, wi h e enue
inc easing in p opo ion o he simul aneous pa icipa ion o BESS in
di e en ma ke s.
Me hodology
This sec ion is dedica ed o he p esen a ion o he models employed
o quan i y he cos associa ed wi h FR ese es and he sa ings ha can
be achie ed h ough he u iliza ion o dis inc BESS con igu a ions.
Th ee dispa ching models a e employed. The i s model seeks o
mee demand while accoun ing o he echnical limi a ions o gen-
e a o s, excluding he FR equi emen ( esul ing in CM1 cos s). The
second model inco po a es he PFR and SFR cons ain s, esul ing in
CM2 cos s. Finally, he hi d model compu es he o al cos , conside ing
he con ibu ion o BESS o FR ( esul ing in CM3 cos s). A weekly s udy
ho izon wi h hou ly esolu ion is conside ed, wi h he objec i e o mini-
mizing ope a ing cos s. Th ee op imiza ion p oblems a e cons uc ed o
desc ibe he dispa ching models. Each o hese leads o a Mixed In ege
Linea P og amming (MILP) p oblem, which is implemen ed in GAMS
using he CPLEX sol e .
The choice o MILP as an op imiza ion me hodology is mainly
jus i ied by i s abili y o handle complex p oblems in ol ing bo h
con inuous and disc e e decisions, which a e common in ene gy, de-
sign and ope a ion p oblems. Unlike o he app oaches such as Linea
P og amming (LP), which only deals wi h con inuous a iables, MILP
allows he modeling o bina y o in ege a iables, which is c ucial in
UC p oblems. In con as , Non-Linea P og amming (NLP) can s uggle
o ind globally op imal solu ions due o he p esence o mul iple local
op ima. MILP sol e s, such as CPLEX and Gu obi, ha e been shown o
be highly e icien a sol ing la ge p oblems in e ms o a iables and
cons ain s, e en in ela i ely sho ime. Mo e de ails can be ound
in Pu z, Schwabenede , Aue , and Fina (2021) Alex e al. (2024), Oli os
and Valenzuela (2025).
Fig. 1 depic s he p oposed me hodology. The cos o implemen ing
FR ese e cons ain s is calcula ed as he di e ence be ween he CM2
and CM1. Sys em sa ings om implemen ing FR wi h he suppo om
BESS a e calcula ed as he di e ence be ween CM3 and CM2.
Model assump ions and limi a ions
The ollowing assump ions and limi a ions ha e been conside ed o
his s udy:
•A single-bus model has been conside ed, which does no include
he ne wo k cons ain s ha can a ec he daily ope a ion o he
sys em and inc ease ope a ing cos s. Addi ionally, powe plan s
o he same echnology ha e been g ouped, which may imply a
pe cen age o e o wi h he ac ual scheduling ha con ains all
he de ails o he ne wo k and indi idual gene a ing uni s.
Ene gy o Sus ainable De elopmen 88 (2025) 101749
3
E. C uz-De-Jesús e al.
Fig. 1. Me hodology o e alua ing sa ings in FR cos s using BESS.
•De e minis ic demand and enewable gene a ion p o iles ha e
been conside ed, so he impac o unce ain y on he model is no
e alua ed.
•This s udy does no include he cha ging and discha ging model
o he BESS, as he objec i e is o e alua e he impac o BESS
on he ese e o equency egula ion. Acco ding o Sa gen
(2024), a Li-ion ba e y ypically deg ades by 1.5% pe yea ,
assuming a ull daily cha ge–discha ge cycle. Howe e , when
egula ing equency, a BESS may no comple e a ull daily cycle,
and he dep h o discha ge o his se ice is usually small, bo h
o which posi i ely a ec he de ice’s deg ada ion. Addi ionally,
conside ing he p ojec ed educ ion in ba e y ene gy cos s p e-
sen ed in Sachs (2024), he impac o deg ada ion cos s will also
g adually dec ease o e ime.
Ma hema ical o mula ion
The h ee models a e subjec o a di e en block o cons ain s,
con ingen on he FR equi emen s o each case. Ou lined below a e
he speci ic a ibu es o each model:
•Model 1: Fig. 1 shows he cons ain s o CM1 and he choice o
hese cons ain s is due o he ac ha his model aims o quan i y
only he cos o mee ing he demand o he sys em, since his is
an ideal case in which no powe ese e is needed o he possible
equency a ia ion. The decision a iables o his model a e he
gene a o s a us o he con en ional gene a o (𝑢𝑝𝑔
𝑡) whe he i
is on o o , he a iable (𝑦𝑝𝑔
𝑡) ha indica es he s a -up o he
adi ional gene a o , a iable (𝑧𝑝𝑔
𝑡) ha indica es shu -down, he
powe ou pu o each con en ional gene a o (𝐺𝑝𝑔
𝑡) ha includes
he ese oi hyd opowe plan .
•Model 2: The objec i e o he cons ain s o CM2 is o e alua e
he cos o he sys em including he ese e cons ain s o he PFR
and SFR, which a e included in he sys em ope a ion schedules o
egula o y and sys em secu i y easons. The decision a iables o
his model a e he gene a o s a us o he con en ional gene a o
(𝑢𝑝𝑔
𝑡), he a iable (𝑦𝑝𝑔
𝑡) ha indica es he s a -up o he adi-
ional gene a o , he a iable o he 𝑧𝑝𝑔
𝑡 ha indica es shu -down,
he gene a ion o each con en ional gene a o 𝐺𝑝𝑔
𝑡 including he
ese oi hyd opowe plan , he egula ion ese e o con en-
ional gene a o s and ese oi hyd opowe plan pa icipa ing in
PFR (𝑅𝑟𝑝𝑓𝑔𝑝𝑔
𝑡) and he egula ion ese e o he un-o - i e hy-
d opowe plan (𝑅𝑟𝑝𝑓ℎ𝑟𝑛
𝑡) pa icipa ing in PFR, and he egula ion
ese e o con en ional gene a o s pa icipa ing in SFR (𝑅𝑟𝑠𝑓𝑔𝑝𝑔
𝑡)
and he egula ion ese e o he un-o - i e hyd opowe plan
(𝑅𝑟𝑠𝑓ℎ𝑟𝑛
𝑡) pa icipa ing in SFR bu in his case he e a e no plan s
o his ype wi h a ailable powe o he SFR.
•Model 3: The objec i e o he cons ain s o CM3 is o e alua e
he impac o he BESS on he sys em ese e cons ain s, and
how he ope a ing cos is educed by including he BESS. The
objec i e is o e alua e he easibili y o he BESS in his se ice
and whe he i is o in e es o he sys em. The decision a i-
ables o his model a e he gene a o s a us o he con en ional
gene a o (𝑢𝑝𝑔
𝑡), he a iable (𝑦𝑝𝑔
𝑡) ha indica es he s a -up o
he adi ional gene a o , he a iable o he 𝑧𝑝𝑔
𝑡 ha indica es
shu -down, he powe ou pu o each con en ional gene a o 𝐺𝑝𝑔
𝑡
ha includes he ese oi hyd opowe plan , he egula ion e-
se e o con en ional gene a o s and ese oi hyd opowe plan
pa icipa ing in PFR (𝑅𝑟𝑝𝑓𝑔𝑝𝑔
𝑡) and he egula ion ese e o he
un-o - i e hyd opowe plan (𝑅𝑟𝑝𝑓ℎ𝑟𝑛
𝑡) pa icipa ing in PFR,
and he egula ion ese e o con en ional gene a o s pa icipa -
ing in SFR (𝑅𝑟𝑠𝑓𝑔𝑝𝑔
𝑡) and he egula ion ese e o he un-o - i e
hyd opowe plan (𝑅𝑟𝑠𝑓ℎ𝑟𝑛
𝑡) pa icipa ing in SFR bu in his case
he e a e no plan s o his ype wi h a ailable powe o he SFR.
As i can be seen, he decision a iable ha di ec ly a ec s in
he objec i e unc ion is he powe ou pu o he con en ional powe
plan (𝐺𝑝𝑔
𝑡), as a he same ime is a ec ed o he a iable o he
powe ese e ha each powe plan has o he equency egula ion
(𝑅𝑟𝑝𝑓𝑔𝑝𝑔
𝑡), pa icipa ing in PFR, and he egula ion ese e o con en-
ional gene a o s pa icipa ing in SFR (𝑅𝑟𝑠𝑓 𝑔𝑝𝑔
𝑡) in Model 2 and Model
3. Also, 𝐺𝑝𝑔
𝑡 is a ec ed by he gene a ion o enewable plan s (𝐺𝑤𝑟𝑛
𝑡) in
he h ee models. Due o he way equency egula ion compensa ion is
handled in he Dominican Republic, hese a iables we e no included
in he objec i e unc ion wi h an assigned p ice. A de ailed o mula ion
o he equa ions and desc ip ion o each model is explained in he
ollowing pa ag aphs.
•Se s
𝑡∈𝑇Hou s o he s udy ho izon whe e 𝑇= {𝑡𝑖∣𝑖∈Z,0≤𝑖≤168}
ℎ𝑡∈𝑇Subse o hou s o he s udy ho izon whe e 𝑇= {𝑡𝑖∣𝑖∈Z,1≤
𝑖≤168}
𝑑∈ℎ𝑡Whe e d is an alias o ℎ𝑡
𝑝𝑔 ∈𝑃 𝑔 Con en ional gene a o whe e 𝑃 𝑔 = {𝑝𝑔𝑖∣𝑖∈Z,1≤𝑖≤19}
𝑟𝑛 ∈𝑅𝑛 Renewable gene a ion echnology whe e 𝑅𝑛 = {𝑟𝑛𝑖∣𝑖∈
Z,1≤𝑖≤4}
•Pa ame e s
𝐿𝑡Demand load a hou [MW]
𝐶𝑟𝑟𝑛
𝑡A ailabili y o enewable esou ces a hou [MW]
𝑉 𝑃 𝐶𝑝𝑔 Va iable p oduc ion cos s o gene a ion plan s [$/MWh]
𝑃 𝑚𝑖𝑛𝑝𝑔 Minimum powe o gene a ion plan s [MW]
𝑃 𝑚𝑎𝑥𝑝𝑔 Maximum powe o gene a ion plan s [MW]
𝑅𝑢𝑝𝑝𝑔 Ramp up a e [MW/h]
𝑅𝑑𝑤𝑝𝑔 Ramp down a e [MW/h]
𝑆𝑢𝑝𝑔 S a -up amp [MW/h]
𝑆𝑑𝑝𝑔 Shu -down amp [MW/h]
𝑂𝑛𝑝𝑔 Minimum up ime [h]
𝑂𝑓 𝑓 𝑝𝑔 Minimum down ime [h]
𝑈𝑎𝑝𝑔 Numbe o ope a ing hou s o he powe plan 𝑝𝑔 a he begin-
ning o he s udy [h]
𝑈𝑓𝑝𝑔 Numbe hou s he powe plan 𝑝𝑔 is ou o ope a ion a he
beginning o he s udy [h]
𝑈𝑖𝑛𝑖𝑝𝑔 Ini ial condi ion o gene a o s
𝑊𝑝𝑔 Numbe o hou s ha he plan mus emain online du ing he
i s hou s o he s udy ho izon [h]
Ene gy o Sus ainable De elopmen 88 (2025) 101749
4
E. C uz-De-Jesús e al.
𝑁𝑝𝑔 Numbe o hou s o be o line du ing he i s hou s o he s udy
ho izon [h]
𝐽To al hou s o s udy ho izon [h]
𝑀𝑟𝑝𝑓𝑝𝑔 Maximum gene a o PFR ese e [MW]
𝑀𝑟𝑠𝑓𝑝𝑔 Maximum gene a o SFR ese e [MW]
𝑀ℎ𝑝𝑓𝑟𝑛 Maximum un-o - i e hyd opowe PFR ese e [MW]
𝑀ℎ𝑠𝑓𝑟𝑛 Maximum un-o - i e hyd opowe SFR ese e [MW]
𝑃 𝑔𝑟𝑝𝑝𝑔 Gene a o s’ pa icipa ion in he PFR
𝑃 𝑔𝑟𝑠𝑝𝑔 Gene a o s’ pa icipa ion in he SFR
𝑃 ℎ𝑟𝑝𝑟𝑛 Pa icipa ion o un-o - i e hyd opowe in he PFR
𝑃 ℎ𝑟𝑠𝑟𝑛 Pa icipa ion o un-o - i e hyd opowe in he SFR
𝑃 𝑟𝑝𝑓 To al pe cen age o ese e o PFR [%]
𝑃 𝑟𝑠𝑓 To al pe cen age o ese e o SFR [%]
𝑃 𝑑𝑠𝑝 Ba e y powe o PFR [MW]
𝑃 𝑑𝑠𝑠 Ba e y powe o SFR [MW]
𝐶𝑚𝑔𝑐𝑡Sho - e m ma ginal cos a hou [$]
•Va iables
𝑂𝐶 To al ope a ing cos [$]
𝑢𝑝𝑔
𝑡Va iable equal o one i he gene a o is in ope a ion o ze o
i i is idle a hou
𝑦𝑝𝑔
𝑡Va iable equal o one i he gene a o is s a ed up a hou
𝑧𝑝𝑔
𝑡Va iable equal o one i he gene a o is shu -down a hou
𝐺𝑝𝑔
𝑡Powe ou pu o powe plan s a hou [MW]
𝐺𝑤𝑟𝑛
𝑡Powe ou pu o enewable gene a o a hou [MW]
𝑃 𝑚𝑎𝑥𝑝𝑔
𝑡Maximum ope a ing powe o gene a o s a hou [MW]
𝑅𝑟𝑝𝑓𝑔𝑝𝑔
𝑡Regula ion ese e o gene a o s pa icipa ing in PFR a hou
[MW]
𝑅𝑟𝑠𝑓𝑔𝑝𝑔
𝑡Regula ion ese e o gene a o s pa icipa ing in SFR a hou
[MW]
𝑅𝑟𝑝𝑓ℎ𝑟𝑛
𝑡PFR egula ing ese e o un-o - i e hyd opowe plan a
hou [MW]
𝑅𝑟𝑠𝑓ℎ𝑟𝑛
𝑡SFR egula ing ese e o un-o - i e hyd opowe plan a
hou [MW]
Cons ain s
The objec i e unc ion o he h ee models is speci ied in (1), while
he cons ain s a e elabo a ed upon subsequen ly.
The objec i e unc ion o he h ee models is as ollows,
𝑂𝐶 =∑
𝑡∈𝑇⧵{𝑡0}∑
𝑝𝑔∈𝑃 𝑔
𝑉 𝑃 𝐶𝑝𝑔 ⋅𝐺𝑝𝑔
𝑡,(1)
whe e 𝐺𝑝𝑔
𝑡 is he gene a ion o each con en ional plan 𝑝𝑔 a hou
𝑡, and 𝑉 𝑃 𝐶𝑝𝑔 is he a iable p oduc ion cos associa ed wi h each
con en ional plan . In models 2 and 3, he cos s associa ed wi h he
FR a e implici ly included in Eq. (1) as he p oduc ion o con en ional
plan s is signi ican ly cons ained by FR equi emen s.
•Gene a ion-demand balance
The balance be ween demand and gene a ion o models 1 and 2 is
es ablished as ollows:
∑
𝑝𝑔∈𝑃 𝑔
𝐺𝑝𝑔
𝑡+∑
𝑟𝑛∈𝑅𝑛
𝐺𝑤𝑟𝑛
𝑡=𝐿𝑡,∀𝑡∈𝑇⧵{𝑡0},(2)
Whe e 𝐺𝑤𝑟𝑛
𝑡 is he enewable gene a ion a hou , his gene a ion be-
longs o he pho o ol aic, wind, biomass and un-o - i e hyd opowe
plan , and 𝐿𝑡 is he hou ly demand load.
•Ope a ing s a us o gene a ion uni s
The on o o s a us o each con en ional powe plan is de e mined
by he a iable 𝑢𝑝𝑔
𝑡, and 𝑦𝑝𝑔
𝑡 o he s a -up, and 𝑧𝑝𝑔
𝑡 o he shu -down:
𝑦𝑝𝑔
𝑡−𝑧𝑝𝑔
𝑡=𝑢𝑝𝑔
𝑡−𝑢𝑝𝑔
𝑡−1,∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (3)
𝑦𝑝𝑔
𝑡+𝑧𝑝𝑔
𝑡≤1,∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔. (4)
•Minimum up ime cons ain s
Likewise, Eq. (5) allows calcula ing he ime ha he plan mus emain
online i i has been in ope a ion consecu i ely be o e he beginning
o he s udy ho izon. I he plan is s a ed, i mus emain online
consecu i ely o 𝑂𝑛𝑝𝑔 hou s; his dynamic is modeled in (6). In case i
ecei es a s a up du ing he las 𝑂𝑓 𝑓 −1 h, i mus emain in ope a ion
un il he inal hou (7) (A oyo & Conejo, 2000; Xie, Pinson, Xu, &
Chen, 2024). He e, 𝑊𝑝𝑔 is he numbe o hou s ha he plan mus
emain online du ing he i s hou s o he s udy ho izon, i ollows ha
𝑊𝑝𝑔 =𝑀𝑖𝑛 [𝐽, (𝑂𝑛𝑝𝑔 −𝑈𝑎𝑝𝑔)⋅𝑈𝑖𝑛𝑖𝑝𝑔]. 𝑂𝑛𝑝𝑔 is he minimum up ime, 𝐽
is he o al hou s o he s udy ho izon, 𝑈𝑎𝑝𝑔 is he numbe o hou s
ha he con en ional plan s ha e been on ope a ion a he beginning
o he s udy, and 𝑈𝑖𝑛𝑖𝑝𝑔 is he ini ial condi ion o gene a o s a 𝑢𝑝𝑔
𝑡0, o
example, he plan can be in ope a ion o o line a he beginning o
he s udy. Also in he model, he ou pu powe o he gene a o a he
beginning o he s udy 𝐺𝑝𝑔
𝑡0 can be speci ied, bu his is no manda o y,
i depends on he assump ions o he ini ial condi ions.
𝑊𝑝𝑔
∑
ℎ≥1[1 − 𝑢𝑝𝑔
ℎ]= 0,∀𝑝𝑔 ∈𝑃 𝑔, 𝑊 𝑝𝑔 ≥1,(5)
ℎ+𝑂𝑛𝑝𝑔 −1
∑
𝑑≥ℎ[𝑢𝑝𝑔
𝑑]≥𝑂𝑛𝑝𝑔 ⋅𝑦𝑝𝑔
ℎ,
∀ℎ=𝑊𝑝𝑔 + 1...𝐽 −𝑂𝑛𝑝𝑔 + 1, 𝑊 𝑝𝑔 + 1 ≤𝐽−𝑂𝑛𝑝𝑔 + 1,∀𝑝𝑔 ∈𝑃 𝑔,
(6)
𝐽
∑
𝑑≥ℎ[𝑢𝑝𝑔
𝑑−𝑦𝑝𝑔
ℎ]≥0,∀ℎ=𝐽−𝑂𝑛𝑝𝑔 + 2...𝐽 , 𝑂𝑛𝑝𝑔 ≥2,∀𝑝𝑔 ∈𝑃 𝑔. (7)
•Minimum down ime cons ain s
Simila ly, Eqs. (8)–(10) ha e he same objec i e as Eqs. (5)–(7), bu in
his case, i is he minimum ime ha he plan mus be down when i
goes o line (A oyo & Conejo, 2000; Xie e al., 2024). He e, 𝑁𝑝𝑔 is he
numbe o hou s o be o line du ing he i s hou s o he s udy ho i-
zon, i ollows ha 𝑁𝑝𝑔 =𝑀𝑖𝑛 [𝐽 , (𝑂𝑓 𝑓 𝑝𝑔 −𝑈𝑓𝑝𝑔 )⋅(1 − 𝑈𝑖𝑛𝑖𝑝𝑔 )] whe e
𝑂𝑓 𝑓 𝑝𝑔 is he minimum down ime, and 𝑈𝑓𝑝𝑔 is he numbe o hou s
he plan has been ou o ope a ion a he beginning o he s udy.
𝑁𝑝𝑔
∑
ℎ≥1[𝑢𝑝𝑔
ℎ]= 0,∀𝑝𝑔 ∈𝑃 𝑔, 𝑁𝑝𝑔 ≥1,(8)
ℎ+𝑂𝑓 𝑓𝑝𝑔 −1
∑
𝑑≥ℎ[1 − 𝑢𝑝𝑔
𝑑]≥𝑂𝑓 𝑓 𝑝𝑔 ⋅𝑧𝑝𝑔
ℎ,
∀ℎ=𝑁𝑝𝑔 + 1...𝐽 −𝑂𝑓 𝑓 𝑝𝑔 + 1, 𝑁𝑝𝑔 + 1 ≤𝐽−𝑂𝑓𝑓 𝑝𝑔 + 1,∀𝑝𝑔 ∈𝑃 𝑔
(9)
𝐽
∑
𝑑≥ℎ[1 − 𝑢𝑝𝑔
𝑑−𝑧𝑝𝑔
ℎ]≥0,
∀ℎ=𝐽−𝑂𝑓 𝑓 𝑝𝑔 + 2...𝐽, 𝑂𝑓 𝑓 𝑝𝑔 ≥2,∀𝑝𝑔 ∈𝑃 𝑔. (10)
•The mal powe plan ope a ional limi s
The maximum powe o he gene a o s depends on hei p e ious and
ollowing s a us. Fo enewable plan s, he minimum powe is ze o,
and he maximum powe depends on he hou ly powe a ailabili y
o he esou ce. He e, he 𝑃 𝑚𝑎𝑥𝑝𝑔
𝑡 is he a iable ha indica es he
maximum ope a ing powe o gene a o s, and 𝑃 𝑚𝑎𝑥𝑝𝑔 is a pa ame e
ha indica es he maximum echnical powe o gene a ion plan s, 𝑆𝑑𝑝𝑔
Ene gy o Sus ainable De elopmen 88 (2025) 101749
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E. C uz-De-Jesús e al.
is he shu -down amp o each gene a o , 𝑅𝑢𝑝𝑝𝑔 is he amp up a e o
each gene a o and 𝑅𝑑𝑤𝑝𝑔 is he amp down a e, 𝑆𝑢𝑝𝑔 is he s a -
up amp, 𝑃 𝑚𝑖𝑛𝑝𝑔 is he minimum powe o gene a ion plan s. The
powe ou pu o he enewable gene a o is indica ed by 𝐺𝑤𝑟𝑛
𝑡, and he
a ailabili y o he esou ces each hou is indica ed by 𝐶𝑟𝑟𝑛
𝑡.
These cons ain s a e es ablished by
𝑃 𝑚𝑎𝑥𝑝𝑔
𝑡≤𝑃 𝑚𝑎𝑥𝑝𝑔 [𝑢𝑝𝑔
𝑡−𝑧𝑝𝑔
𝑡+1]+𝑆𝑑𝑝𝑔 ⋅𝑧𝑝𝑔
𝑡+1,
∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (11)
𝑃 𝑚𝑎𝑥𝑝𝑔
𝑡≤𝐺𝑝𝑔
𝑡−1 +𝑅𝑢𝑝𝑝𝑔 ⋅𝑢𝑝𝑔
𝑡−1 +𝑆𝑢𝑝𝑔 ⋅𝑦𝑝𝑔
𝑡,
∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (12)
𝐺𝑝𝑔
𝑡−1 −𝐺𝑝𝑔
𝑡≤𝑅𝑑𝑤𝑝𝑔 ⋅𝑢𝑝𝑔
𝑡+𝑆𝑑𝑝𝑔 ⋅𝑧𝑝𝑔
𝑡,
∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (13)
𝐺𝑝𝑔
𝑡≤𝑃 𝑚𝑎𝑥𝑝𝑔
𝑡,∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (14)
𝐺𝑝𝑔
𝑡≥𝑃 𝑚𝑖𝑛𝑝𝑔 ⋅𝑢𝑝𝑔
𝑡,∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (15)
𝐺𝑤𝑟𝑛
𝑡≤𝐶𝑟𝑟𝑛
𝑡,∀𝑡∈𝑇⧵{𝑡0},∀𝑟𝑛 ∈𝑅𝑛, (16)
When he ese e cons ain s o PFR and SFR a e in oduced,
he minimum and maximum dispa ch powe o he ope a ing plan s
change, espec ing he echnical limi s o each plan , so ha in models
2 and 3 (14)–(16) a e changed o (17)–(20) espec i ely (Lagos &
Ha zia gy iou, 2021). He e 𝑅𝑟𝑝𝑓𝑔𝑝𝑔
𝑡 and 𝑅𝑟𝑝𝑓ℎ𝑝𝑔
𝑡 a e he egula ion
ese e o gene a o s pa icipa ing in PFR, and 𝑅𝑟𝑠𝑓𝑔𝑝𝑔
𝑡 and 𝑅𝑟𝑠𝑓ℎ𝑟𝑛
𝑡
a e he egula ion ese e o gene a o s pa icipa ing in SFR.
𝐺𝑝𝑔
𝑡≤𝑃 𝑚𝑎𝑥𝑝𝑔
𝑡−𝑅𝑟𝑝𝑓𝑔𝑝𝑔
𝑡−𝑅𝑟𝑠𝑓𝑔𝑝𝑔
𝑡,
∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (17)
𝐺𝑝𝑔
𝑡≥𝑃 𝑚𝑖𝑛𝑝𝑔 ⋅𝑢𝑝𝑔
𝑡+𝑅𝑟𝑝𝑓𝑔𝑝𝑔
𝑡+𝑅𝑟𝑠𝑓𝑔𝑝𝑔
𝑡,
∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (18)
𝐺𝑤𝑟𝑛
𝑡≤𝐶𝑟𝑟𝑛
𝑡−𝑅𝑟𝑝𝑓ℎ𝑟𝑛
𝑡−𝑅𝑟𝑠𝑓ℎ𝑟𝑛
𝑡,
∀𝑡∈𝑇⧵{𝑡0},∀𝑟𝑛 ∈𝑅𝑛, (19)
𝐺𝑤𝑝𝑔
𝑡≥0 + 𝑅𝑟𝑝𝑓ℎ𝑟𝑛
𝑡+𝑅𝑟𝑠𝑓ℎ𝑟𝑛
𝑡,∀𝑡∈𝑇⧵{𝑡0},∀𝑟𝑛 ∈𝑅𝑛. (20)
•Gene a ion ese e o equency egula ion
The ese e o PFR and SFR ha each gene a o can con ibu e is
limi ed by i s maximum ese e ma gin. The maximum gene a o PFR
ese e is indica ed by 𝑀𝑟𝑝𝑓𝑝𝑔 , and he maximum gene a o SFR
ese e is indica ed by 𝑀𝑟𝑠𝑓𝑝𝑔 , he same is o he enewable gene a o
speci ically un-o - i e plan s ha a e he one ha pa icipa e in
he equency egula ion wi h 𝑀ℎ𝑝𝑓𝑟𝑛 and 𝑀ℎ𝑠𝑓𝑟𝑛. This beha io is
ep esen ed by,
𝑅𝑟𝑝𝑓𝑔𝑝𝑔
𝑡≤𝑀𝑟𝑝𝑓𝑝𝑔 ⋅𝑢𝑝𝑔
𝑡, 𝑡 ∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, 𝑃 𝑔𝑟𝑝𝑝𝑔 ≥1,(21)
𝑅𝑟𝑠𝑓𝑔𝑝𝑔
𝑡≤𝑀𝑟𝑠𝑓𝑝𝑔 ⋅𝑢𝑝𝑔
𝑡, 𝑡 ∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, 𝑃 𝑔𝑟𝑠𝑝𝑔 ≥1,(22)
𝑅𝑟𝑝𝑓ℎ𝑟𝑛
𝑡≤𝑀ℎ𝑝𝑓𝑟𝑛, 𝑡 ∈𝑇⧵{𝑡0},∀𝑟𝑛 ∈𝑅𝑛, 𝑃 ℎ𝑟𝑝𝑟𝑛 ≥1,(23)
𝑅𝑟𝑠𝑓ℎ𝑟𝑛
𝑡≤𝑀ℎ𝑠𝑓𝑟𝑛, 𝑡 ∈𝑇⧵{𝑡0},∀𝑟𝑛 ∈𝑅𝑛, 𝑃 ℎ𝑟𝑠𝑟𝑛 ≥1.(24)
The sum o he ese es o all gene a o s mus sa is y he minimum
o al ma gin equi ed by he sys em o he PFR and he SFR whe e
𝑃 𝑟𝑝𝑓 and 𝑃 𝑟𝑠𝑓 a e pe cen ages imposed o main ain he ese e o
he PFR and SFR a a ce ain le el, ha is,
∑
𝑝𝑔∈𝑃 𝑔,𝑃 𝑔𝑟𝑝𝑝𝑔 ≥1
𝑅𝑟𝑝𝑓𝑔𝑝𝑔
𝑡+∑
𝑟𝑛∈𝑅𝑛,𝑃 ℎ𝑟𝑝𝑟𝑛≥1
𝑅𝑟𝑝𝑓ℎ𝑟𝑛
𝑡≥
𝑃 𝑟𝑝𝑓 ⋅(∑
𝑝𝑔∈𝑃 𝑔
𝐺𝑝𝑔
𝑡+∑
𝑟𝑛∈𝑅𝑛
𝐺𝑤𝑟𝑛
𝑡),∀𝑡∈𝑇⧵{𝑡0},
(25)
∑
𝑝𝑔∈𝑃 𝑔,𝑃 𝑔𝑟𝑠𝑝𝑔 ≥1
𝑅𝑟𝑠𝑓𝑔𝑝𝑔
𝑡+∑
𝑟𝑛∈𝑅𝑛,𝑃 ℎ𝑟𝑠𝑟𝑛≥1
𝑅𝑟𝑠𝑓ℎ𝑟𝑛
𝑡≥
𝑃 𝑟𝑠𝑓 ⋅(∑
𝑝𝑔∈𝑃 𝑔
𝐺𝑝𝑔
𝑡+∑
𝑟𝑛∈𝑅𝑛
𝐺𝑤𝑟𝑛
𝑡),∀𝑡∈𝑇⧵{𝑡0}.
(26)
The con ibu ion o he ba e ies o he p ima y and seconda y
egula ion is desc ibed by (27)–(28), whe e he BESS is modeled wi h
cons an powe , i s con ibu ion o he ese e o equency egula ion
is added on he le -hand side o hese equa ions. He e, he 𝑃 𝑑𝑠𝑝 is he
con ibu ion o he BESS o he PFR, and he 𝑃 𝑑𝑠𝑠 is he con ibu ion
o he BESS o he SFR.
𝑃 𝑑𝑠𝑝 +∑
𝑝𝑔∈𝑃 𝑔,𝑃 𝑔𝑟𝑝𝑝𝑔 ≥1
𝑅𝑟𝑝𝑓𝑔𝑝𝑔
𝑡+∑
𝑟𝑛∈𝑅𝑛,𝑃 ℎ𝑟𝑝𝑟𝑛≥1
𝑅𝑟𝑝𝑓ℎ𝑟𝑛
𝑡≥
𝑃 𝑟𝑝𝑓 ⋅(∑
𝑝𝑔∈𝑃 𝑔
𝐺𝑝𝑔
𝑡+∑
𝑟𝑛∈𝑅𝑛
𝐺𝑤𝑟𝑛
𝑡), 𝑡 ∈𝑇⧵{𝑡0},(27)
𝑃 𝑑𝑠𝑠 +∑
𝑝𝑔∈𝑃 𝑔,𝑃 𝑔𝑟𝑠𝑝𝑔 ≥1
𝑅𝑟𝑠𝑓𝑔𝑝𝑔
𝑡+∑
𝑟𝑛∈𝑅𝑛,𝑃 ℎ𝑟𝑠𝑟𝑛≥1
𝑅𝑟𝑠𝑓ℎ𝑟𝑛
𝑡≥
𝑃 𝑟𝑠𝑓 ⋅(∑
𝑝𝑔∈𝑃 𝑔
𝐺𝑝𝑔
𝑡+∑
𝑟𝑛∈𝑅𝑛
𝐺𝑤𝑟𝑛
𝑡),∀𝑡∈𝑇⧵{𝑡0}.(28)
•Sho - e m ma ginal cos
This is no exac ly a cons ain , i is a calcula ion a e he model has
been un. Fo each hou o he scheduling ho izon, he ma ginal cos is
calcula ed as he VPC o he mos expensi e plan dispa ched. The VPC
o he mos expensi e he mal uni dispa ched in each hou is gi en by
Eq. (29),
𝐶𝑚𝑔𝑐𝑡=𝑀𝑎𝑥 [𝑃 𝑔, (𝐺𝑝𝑔
𝑡>0), 𝑉 𝑃 𝐶𝑝𝑔 ],∀𝑡∈𝑇⧵{𝑡0}.(29)
To summa ize, Model 1 is made up o he Eq. (1)–(2), (3)–(16) and
(29). Model 2 is made up o he Eq. (1)–(2), (3)–(13), (17)–(26) and
(29). Finally, Model 3 is made up o he Eq. (1), (2)–(13), (17)–(24)
and (27)–(29).
•Va iable Domains
𝑂𝐶 ∈R
𝑢𝑝𝑔
𝑡∈ {0,1} ∀𝑝𝑔 ∈𝑃 𝑔, ∀𝑡∈𝑇
𝑦𝑝𝑔
𝑡∈ {0,1} ∀𝑝𝑔 ∈𝑃 𝑔, ∀𝑡∈𝑇
𝑧𝑝𝑔
𝑡∈ {0,1} ∀𝑝𝑔 ∈𝑃 𝑔, ∀𝑡∈𝑇
𝐺𝑝𝑔
𝑡∈R+∀𝑝𝑔 ∈𝑃 𝑔, ∀𝑡∈𝑇
𝑃 𝑚𝑎𝑥𝑝𝑔
𝑡∈R+∀𝑝𝑔 ∈𝑃 𝑔, ∀𝑡∈𝑇
𝑅𝑟𝑝𝑓𝑔𝑝𝑔
𝑡∈R+∀𝑝𝑔 ∈𝑃 𝑔, ∀𝑡∈𝑇
𝑅𝑟𝑠𝑓𝑔𝑝𝑔
𝑡∈R+∀𝑝𝑔 ∈𝑃 𝑔, ∀𝑡∈𝑇
𝐺𝑤𝑟𝑛
𝑡∈R+∀𝑟𝑛 ∈𝑅𝑛, ∀𝑡∈𝑇
𝑅𝑟𝑝𝑓ℎ𝑟𝑛
𝑡∈R+∀𝑟𝑛 ∈𝑅𝑛, ∀𝑡∈𝑇
𝑅𝑟𝑠𝑓ℎ𝑟𝑛
𝑡∈R+∀𝑟𝑛 ∈𝑅𝑛, ∀𝑡∈𝑇
Ene gy o Sus ainable De elopmen 88 (2025) 101749
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Table 1
Key S a is ics o he Dominican Republic in 2022.
Popula ion Load (GWh) Capaci y (GW) GDP (M$)
10,760,028 22,143.59 5.08 114
Resul s and discussion
This sec ion p esen s he main cha ac e is ics o he da a om he
NIES sys em in he Dominican Republic used in his s udy. Fi s , he
NIES and i s main igu es a e desc ibed. Then, he main esul s ob ained
o each case s udy a e p esen ed.
Se e al case s udies a e p oposed o in es iga e he impac o BESS
on he cos o p o iding egula o y ese es. The case s udies a e
e alua ed using a combina ion o median demand and median a ail-
abili y p o iles o sola , wind, and un-o - i e hyd o gene a ion. These
p o iles a e calcula ed o pe iods ha include di e en mon hs o he
yea (i.e., Janua y–Feb ua y, Ma ch–Ap il, May–June, July–Oc obe ,
No embe –Decembe ).
The Dominican Republic powe sys em
The Na ional In e connec ed Elec ici y Sys em (NIES) o he Do-
minican Republic, an island in he Ca ibbean, has expe ienced a sig-
ni ican inc ease in enewable ene gy gene a ion in ecen yea s due
o he commissioning o new p ojec s. In 2021, wind and sola ech-
nologies accoun ed o 7.40% and 6.10% o he o al ins alled capaci y,
espec i ely. By 2022, hese igu es had inc eased o 8.22 % and 7.99%,
and by 2023 hese igu es changed o be 7.3% and 11.9% espec-
i ely (O ganismo Coo dinado , 2022a, 2023a, 2024). Table 1 p esen s
key da a o he sys em, including he o al elec ici y gene a ed in
2022 and he o al ins alled capaci y. The g oss domes ic p oduc
(GDP) g ew by 4.9% in 2022, indica ing a simila inc ease in ene gy
consump ion (Banco Cen al, 2023).
Demand
Fo his s udy, he ac ual deli e ed demand in 2022 was p o-
ided by he O ganismo Coo dinado del Sis ema Eléc ico Nacional
In e conec ado o he Dominican Republic (O ganismo Coo dinado ,
2023a). One week o demand was selec ed om each subse o mon hs
wi h simila demand p o iles o c ea e ealis ic scena ios. The mon hs
we e g ouped as ollows: Janua y–Feb ua y, Ma ch–Ap il, May–June,
July–Oc obe , and No embe –Decembe . In acco dance wi h Gene al
Elec ici y Law No. 125-01 and i s Applica ion Regula ion, 3% o he
o al gene a ion pe pe iod was modeled as a ese e o p ima y and
seconda y equency egula ion (PFR and SFR) (Supe in endencia de
Elec icidad, 2001, 2007).
Fig. 2 shows he mono onic load cu e o 2022, whe e he peak
powe is 3,161.48 MW. The p ominen nega i e peak co esponds o
Sep embe 19, hou 24. On his day, mul iple ansmission line ips
occu ed due o T opical S o m Fiona, a ec ing se e al 69 kV lines.
Fig. 3 illus a es he a e age hou ly demand o e he cou se o a
week, beginning on Monday and concluding on Sunday. I is e iden
ha he daily demand displays simila ends, wi h peak consump ion
occu ing oughly be ween 20:00 and 22:00, and educed demand
obse ed be ween 5:00 and 7:00. No ably, a dec ease in demand is
obse ed du ing he weekend.
Powe plan s
The maximum powe a ailabili y decla ed o each powe plan du -
ing 2019–2020 was used as he maximum powe o he simula ions.
PFR and SFR ma gins we e also conside ed. Fo plan s wi hou amp-up
and amp-down da a, hese alues we e calcula ed based on maximum
and minimum powe and amp-up and amp-down imes, exp essed
in MW/min. The amp-up and amp-down alues we e limi ed o he
maximum powe o he plan o a oid inconsis encies.
Fig. 2. Mono onic load cu e in MW. Annual demand 2022.
Fig. 3. Weekly p esen a ion o a e age hou ly demand (Monday o Sunday).
Table 2
Ins alled capaci y by echnology in 2022.
Technology Capaci y (MW)
Sola 405
Wind 417
Hyd oelec ic 623
Combined cycle 1,129
Gas Tu bine 134
In e nal combus ion engine 1,209
S eam u bine 1,158
The s a -up amp o each plan was calcula ed using he minimum
powe and ho s a -up ime in hou s, limi ed by he minimum and
maximum powe o ensu e ha all plan s each he echnical minimum
du ing he s a -up pe iod. Fo he shu down amp, he maximum
powe and he ime o each s andby condi ion we e conside ed, simi-
la ly limi ed by he minimum and maximum powe . In some cases, he
s a -up and shu down amp we e conside ed he same.
Plan s we e g ouped by echnology, wi h he minimum powe as-
sumed o be he lowes minimum powe in he g oup. Fo he a iable
p oduc ion cos s (VPCs), he a e age dispa ch cos s om O ganismo
Coo dinado (2023b) we e used. Table 2 shows he ins alled capaci y
by echnology o 2022 (O ganismo Coo dinado , 2023a).
Hyd opowe plan s we e ca ego ized in o ese oi and un-o - i e
ypes. All ese oi plan s we e g ouped in o a single en i y, modeled
as he mal, wi h 𝑃𝑚𝑎𝑥 calcula ed conside ing he median gene a ion
o 2020. PFR and SFR ma gins we e included. Fo un-o - i e plan s,
2020 da a we e used, inco po a ing hei PFR and SFR ma gins in o he
op imiza ion p oblem. In he case o he biomass plan , ac ual a e age
hou ly gene a ion in 2020 was used. Fo wind and sola plan s, 2022
hou ly ac ual gene a ion da a we e used.
Ene gy o Sus ainable De elopmen 88 (2025) 101749
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E. C uz-De-Jesús e al.
Table 3
Pa ame e s o he mal powe plan s and ese oi hyd opowe plan s.
Uni Fuel Technology VPC Pmin Pmax Rup Rdw M p M s Su Sd
$/MWh (MW) (MW) (MW/h) (MW/h) (MW) (MW) (MW/h) (MW/h)
P1 Wa e Hyd opowe 0 0 113 113 113 13 10 113 113
P2 Coal S eam u bine 42 150 375 160 174 10 0 155 150
P3 Coal S eam u bine 43 142 375 135 213 8 0 142 148
P4 Na u al Gas Combined cycle 50 66 218 169 218 14 16 66 218
P5 Coal S eam u bine 51 100 120 18 63 0 0 100 100
P6 Na u al Gas Combined cycle 53 66 90 16 90 3 7 66 86
P7 Coal S eam u bine 54 94 120 18 57 0 0 94 94
P8 Na u al Gas Combined cycle 54 66 90 17 90 3 7 66 81
P9 Na u al Gas Combined cycle 55 66 224 183 224 21 24 86 224
P10 Na u al Gas Combined cycle 57 66 90 14 90 3 9 66 90
P11 Coal S eam u bine 64 29 52 46 39 0 0 41 29
P12 Na u al Gas Combined cycle 82 150 300 267 300 14 45 150 242
P13 Na u al Gas Combined cycle 95 185 315 189 137 20 0 185 185
P14 Na u al Gas Combined cycle 103 49 110 110 110 4 5 110 110
P15 Fuel Oil No. 6 ICE 126 6 423 254 372 19 31 344 423
P16 Fuel Oil No. 6 ICE 128 14 34 34 34 2 9 34 34
P17 Na u al Gas ICE 129 14 25 25 25 2 6 25 25
P18 Fuel Oil No. 6 ICE 139 5 135 135 135 6 12 95 119
P19 Fuel Oil No. 2 Gas u bine 292 60 85 85 85 5 0 85 85
Table 4
Compa ison be ween he ope a ing cos s ob ained wi h model 2 (CM2) and he a e age
weekly ope a ing cos s epo ed by he Dominican sys em ope a o .
Mon hs CM2 (M$) Repo 2022 (M$) Repo 2023 (M$)
Jan– eb 18.32 23.94 25.18
Ma –Ap 18.46 25.28 20.59
May–jun 22.38 34.47 26.62
Jul–oc 23.29 32.77 30.49
No –dec 19.07 27.76 24.99
Table 3 p o ides he main pa ame e s o he mal powe plan s and
ese oi hyd opowe plan s, wi h VPCs e e ing o 2023 alues.
Resul s o case s udy 1. Calcula ion o he cos o p o ision o FR in he
NIES
The objec i e o his case s udy is o compu e he cos o p o ision o
FR acco ding o he ules o he NIES sys em. The me hodology in ol es
a compa ison o he cos s ob ained using Model 1 and Model 2.
As p e iously s a ed, Model 1 solely conside s he ene gy balance,
whe eas Model 2 inco po a es he PFR and SFR cons ain s o he mal
and hyd o plan s. Fig. 4 shows he inc emen in o al ope a ing cos
(OC) when ese e cons ain s a e included in Model 2. In he yea s
2022 and 2026, he equi ed ese e o PFR and SFR is 3% o he
sys em demand. In he yea 2030, he ese e equi emen s a e in-
c eased o 4% o PRF and 4.5% o SFR, as p oposed in O ganismo
Coo dinado (2020) o accommoda e he an icipa ed ise in enewable
ene gy in eg a ion. Consequen ly, a mo e p onounced inc ease is ob-
se ed o 2030, e lec ing a u u e scena io wi h educed pa icipa ion
o coal- i ed powe plan s.
Table 4 p esen s a compa ison o he weekly ope a ing cos s de i ed
om ou Model 2 (CM2), which inco po a es bo h he echnical con-
s ain s o he uni s and he FR cons ain s, agains he a e age weekly
ope a ing cos s epo ed by he Dominican sys em ope a o (O ganismo
Coo dinado , 2023c). As can be seen, he ope a ing cos s o he ac ual
schedule and hose ob ained om he simula ions a e o simila mag-
ni ude. The eal cos s a e highe , which may be due o se e al ac o s,
including he addi ional cons ain s ha he eal model conside s in he
ne wo k, such as gene a ion cons ain s due o low con ol, ne wo k
main enance, and una ailabili y o powe plan s.
Resul s o case s udy 2. E alua ion o he con ibu ion o BESS o PFR
This case s udy aims o compa e ope a ional cos sa ings wi h
and wi hou BESS o a ious gene a ion and demand scena ios. The
Fig. 4. Cos o p o iding FR in scena ios o di e en yea s.
me hodology employs wo models: Model 2 (wi hou BESS) and Model
3 (wi h BESS). The con ibu ion o BESS is e alua ed o capaci ies
anging om 14 MW o 47 MW, wi h a s o age capaci y o 0.5 h.
In o de o e alua e he in luence o inco po a ing BESS as a com-
ponen o he PFR se ice, a se ies o s o age powe pene a ion a es
we e de ised, wi h he peak demand obse ed in he NIES du ing 2022
(3,161.48 MW) o he da a p o ided se ing as a poin o e e ence.
The maximum ese e ma gin equi ed by he egula ion is 3% o
he a o emen ioned maximum demand, i.e., 94.84 MW. Then, he BESS
a ed powe was selec ed a ou alues co esponding app oxima ely
o inc easing pe cen ages (15%, 25%, 40% and 50%) o he equi ed
ese e ma gin. Fo his applica ion, he ba e ies we e modeled as a
cons an powe sou ce, since he cha ge and discha ge cycles occu in
less han one hou , which is he ime ame in which he esul s o hese
models we e ob ained.
Resul s o case s udy 3 (E alua ion o he con ibu ion o BESS o SFR)
and compa ison wi h case s udy 2
Simila o Case S udy 1, his s udy ocuses on SFR ins ead o PFR.
The me hodology ollows he same app oach as Case S udy 2, assessing
BESS con ibu ions o SFR ac oss di e en hou s. The e alua ion o
BESS in ol es capaci ies anging om 14 MW o 47 MW, wi h a s o age
capaci y o 0.5 h.
Ene gy o Sus ainable De elopmen 88 (2025) 101749
8
E. C uz-De-Jesús e al.
Fig. 5. Change in ope a ing cos s when using BESS o PFR o SFR.
In o de o e alua e he impac o BESS on ope a ing cos s when
i con ibu es o he SFR (case s udy 3), he same p ocedu e was
employed as ha used o he PFR. Despi e he iden ical equisi e
pe cen ages o PFR and SFR, no all plan s eligible o PFR a e simila ly
quali ied o SFR. Fu he mo e, some o he plan s in ques ion do no
possess he equisi e ma gins o pa icipa ion in bo h SFR and PFR.
Fig. 5 illus a es he pe cen age educ ion in o al ope a ing cos s
when BESS wi h a ying capaci ies pa icipa e in PFR (case s udy 2)
and SFR (case s udy 3) sepa a ely. I can be seen ha he g ea es
sa ings a e ob ained in he PFR.
Table 5 p esen s he cos s associa ed wi h BESSs o a ying di-
mensions, encompassing expendi u es o ba e ies, ans o me s, land,
enginee ing, and o he pe inen componen s. I was assumed ha he
cos s associa ed wi h he ba e ies, land, BESS ins alla ion, and BESS
balance o he plan a e dependen on he ene gy capaci y (MWh),
while he cos s ela ed o he main ans o me and elec ical in e -
connec ion a e con ingen on he powe a ing (MW). Fu he mo e, he
cos s associa ed wi h enginee ing, p ocu emen , and cons uc ion (EPC)
a e inco po a ed. I is expec ed ha he ba e ies will ha e a se ice li e
o 20 yea s, based on he du y cycle associa ed wi h FR se ice only.
The cos es ima es o li hium-ion ba e y s o age p ojec s we e de i ed
om Sa gen (2024) and Sachs (2024).
In his s udy, he Ene gy- o-Powe (E/P) a io has been kep con-
s an a 0.5 h o he equency egula ion applica ion, e lec ing he
sho du a ion cha ac e is ic o his ype o ancilla y se ice.
By sol ing he UC p oblems co esponding o Model 2 and Model
3, he weekly ope a ing cos sa ings we e de e mined o se e al BESS
con igu a ions. These weekly sa ings we e hen mul iplied by he num-
be o weeks in each g oup o mon hs o es ima e he annual sa ings, as
shown in Table 5. The esul s indica e ha as he BESS powe inc eases,
he annual sa ings also ise. I is no ewo hy ha he maximum pay-
back pe iod o he ini ial in es men in he PFR applica ion was less
han one yea . This highligh s he BESS as a p o i able in es men o
he sys em ope a o , whose objec i e is o ensu e eliable se ice a he
lowes possible cos . Fo he SFR applica ion, he maximum payback
pe iod was less han wo yea s, implying ha he BESS would gene a e
bene i s o he sys em o app oxima ely 18 yea s. In summa y, each
o hese se ices is p o i able o he sys em, e en when conside ed
sepa a ely. The Ne P esen Value (NPV) and In e nal Ra e o Re u n
(IRR) calcula ions p esen ed in Table 5 show ha he in es men in
hese s o age sys ems is p o i able. Fo he calcula ion o he discoun
a e, we used he a e o inancial e u n o elec ici y ansmission
and dis ibu ion o 2020 in Spain, equal o 6.003%, and conside ing
ha he in es men is in he Dominican Republic, we added he isk
Table 5
Ope a ional cos sa ings wi h he inclusion o BESSs in he PFR and SFR se ices o
2022.
Con 1 Con 2 Con 3 Con 4
Powe (MW) 14 23 37 47
Ene gy (MWh) 7 11.5 18.5 23.5
Powe cos ($/kW) 224
Ene gy cos ($/kWh) 448
Capi al cos (M$) 3.14 5.15 8.29 10.53
Annual sa . PFR (M$) 5.13 8.02 11.86 14.17
Pay-back (yea s) 0.61 0.64 0.70 0.74
NPV (M$) 32 50 74 87
IRR (%) 162 153 141 132
PFR eal cos 2022 (M$) 51.78
PFR eal cos 2023 (M$) 56.81
Annual sa . SFR (M$) 3.65 5.81 8.16 9.27
Pay-back (yea s) 0.86 0.89 1.02 1.14
NPV (M$) 22 35 48 53
IRR (%) 114 111 96 86
SFR eal cos 2022 (M$) 37.98
SFR eal cos 2023 (M$) 36.26
p emium o Mexico, equal o 7.85, due o he a ailabili y o da a and
he ac ha his coun y is close o he Dominican Republic in e ms o
isk p emium. The discoun a e used was 13% (expansion.com, 2024a,
2024b; S a e Agency O icial S a e Gaze e, 2019).
Table 5 p esen s he ac ual expenses associa ed wi h FR o he
yea s 2023 and 2022, ob ained om O ganismo Coo dinado (2023a)
and O ganismo Coo dinado (2024), along wi h he sa ings p ojec ed
by ou model. I is e iden ha he implemen a ion o BESS in o he
sys em could lead o subs an ial educ ions in FR cos s. Addi ionally, i
is impo an o accoun o he cos o o ced dispa ch, which amoun ed
o M$ 1.24 in 2022 and M$ 0.26 in 2023 due o FR.
Resul s o case s udy 4. E alua ion o he con ibu ion o BESS o bo h PFR
and SFR simul aneously
The objec i e o his case s udy is o assess he combined impac
o BESS on bo h PFR and SFR. The me hodology uses he same median
demand and gene a ion scena ios om Janua y o Decembe as in Case
S udies 2 and 3. The con ibu ion o a 47 MW BESS o PFR and ano he
47 MW BESS o SFR is e alua ed simul aneously.
The impac o inco po a ing BESS o PFR and SFR in he NIES is
e alua ed in he p esen con ex and o p ospec i e u u e scena ios,
aking in o accoun he long- e m p og am o he sys em ope a o , as
ou lined in O ganismo Coo dinado (2022b).
Resul s o 2022
This sec ion p esen s he esul s o inco po a ing wo 47 MW a ed-
powe BESS o PFR and SFR in pa allel. The a ed powe o he BESS is
app oxima ely 50% o he ese e equi ed o FR, which is conside ed
a sa is ac o y a io. The o al annual sa ings amoun o $23.6 million.
Based on he da a p esen ed in Table 5, he payback pe iod is calcula ed
o be 0.89 yea s.
BESS o PFR and SFR in u u e scena ios
A se ies o u u e scena ios we e e alua ed by inc easing he o al
load, as well as he capaci ies o he PV and wind pa ks, and by also
conside ing he po en ial addi ion o a 190 MW na u al gas plan (O -
ganismo Coo dinado , 2022b). I is again assumed ha 47 MW o BESS
is used o PFR and a u he 47 MW o SFR.
Table 6 illus a es he impac o BESS on enewable ene gy in eg a-
ion o he u u e scena io o he yea 2026. The inclusion o BESS
esul s in inc eased ene gy gene a ion ac oss all enewable sou ces.
Speci ically, he o al inc ease in RES in eg a ion is o 3%, wi h he
highes impac on Hyd o gene a ion in eg a ion. Table 6 includes bo h
ese oi and un-o - i e hyd opowe plan s. Addi ionally, Table 7
Ene gy o Sus ainable De elopmen 88 (2025) 101749
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