Dao T.T e al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH
Resea ch A icle
THE IMPACTS OF ELECTRIC CHARGING
STATIONS ON DISTRIBUTION POWER GRIDS
UNDER DIFFERENT SIMULATIONS USING
JELLYFISH SWARM ALGORITHM
Dao T ong TRAN1,∗, Minh Phuc DUONG 2
1Di ision o MERLIN, Facul y o Elec ical and Elec onics Enginee ing, Ton Duc Thang Uni e si y,
Ho Chi Minh ci y, Vie nam
2Powe Sys em Op imiza ion Resea ch G oup, Facul y o Elec ical and Elec onics Enginee ing,
Ton Duc Thang Uni e si y, Ho Chi Minh Ci y, Vie nam
an[email p o ec ed], duongph[email p o ec ed]
∗Co esponding au ho : Dao T ong T an; [email p o ec ed]
DOI: 10.15598/aeee. 23i1.250101
A icle his o y: Recei ed Jan 1, 2025; Re ised Feb 14, 2025; Accep ed Ma 06, 2025; Published Ma 31, 2025.
This is an open access a icle unde he BY-CC license.
Abs ac . This esea ch p esen s di e en implemen-
a ions o placing elec ic cha ging s a ions (ECSs) in
dis ibu ion powe ne wo ks (DPNs) o achie e he bes
o al ac i e powe loss (TAPL). Sola gene a o s (SGs)
a e also used o alle ia e he ad e se e ec s esul ing
om he p esence o ECSs in he ne wo ks in e ms o
powe loss and ol age p o ile. A i icial hummingbi d
algo i hm (AHA), Jelly ish swa m algo i hms (JS), and
No he n goshawk op imiza ion (NGO) a e execu ed o
de e mine he bes placemen o ECSs and SGs in an
IEEE 33-node ne wo k o eaching a minimum loss
and sa is ying all he ela ed cons ain s. The e a e
ou cases conduc ed in he whole esea ch. In he i s
case, JS ou pe o ms bo h AHA and NGO by p o iding
he highes s abili y h oughou all he ial uns and
as es con e gence speed o he op imal solu ion in he
bes uns. Besides, he quan i a i e compa ison also
consolida es he obus ness and eliabili y o JS com-
pa ed o o he s. Based on he su p ising pe o mance,
JS is con inuously eapplied o sol e ano he h ee cases
o he conside ed p oblem. Th ough hose h ee cases
wi h he applica ion o JS, he TAPL alues o ou sce-
na ios wi h di e en numbe s o ECSs a e e alua ed.
Speci ically, he esul s achie ed by JS indica e ha he
highe numbe o ECSs leads o a highe alue o TAPL
and a highe ol age d op. On he o he hand, he si-
mul aneous placemen o SGs and ECSs can esul in
smalle luc ua ions o he ol age p o ile and smalle
TAPL. Thus, he op imiza ion placemen o ECSs and
SGs is c ucial o DPNs o economic and echnical pu -
poses.
Keywo ds
Elec ic cha ging s a ions, dis ibu ion powe
ne wo ks, sola gene a o s, o al ac i e powe
loss, ol age p o ile.
1. In oduc ion
Nowadays, global wa ming is one o he mos conce n-
ing p oblems due o i s nega i e e ec s, which can ap-
pa en ly be expe ienced all a ound he globe [1]. The
main con ibu ion o hese nega i e e ec s is he signi -
ican inc ease in CO2 concen a ion p oduced by di e -
en mode n ac i i ies, including diesel-based ehicles
[2]. Mo eo e , due o he apid g ow h o he wo ld
economy, he lee o gasoline and diesel ca s in la ge
ci ies and coun ies has imp essi ely g own, damaging
he en i onmen he e [3]. In his ci cums ance, he
shi o elec ic ehicles is acknowledged o be he a -
o dable solu ion o educing CO2 emissions and im-
p o ing ai quali y in such hus ling ci ies and places
[4, 5]. The g ow h o he use o elec ic ehicles leads
o a demand o elec ic cha ging s a ions (ECSs) con-
©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 72
Dao T.T e al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH
nec ed o he dis ibu ion powe ne wo k (DPN) [6].
Howe e , he placemen o ECS in he DPNs also has
some nega i e e ec s, such as powe loss enla gemen
o ol age de egula ion. Renewable powe sou ces a e
hen p oposed o educe ol age d op and powe loss
[7].
By ho oughly unde s anding he ad an ages and
disad an ages o placing ECS in he DPN, many e-
sea che s ha e conduc ed hei esea ch o enhance he
ad an ages o placing ECS while simul aneously y-
ing o mi iga e he nega i e impac s. Fi s ly, a gen-
e al look a he impac s caused by ha ing he ECSs
in DPN is gi en in [6]. Nex , he p esence o ECSs in
he DPN is e alua ed ega ding powe demand, ha -
monics, ol age sag, and ans o me powe loss [8].
Then, [9] ocuses on iden i ying and analysing he im-
pac o ECSs on he eliabili y o he IEEE-33 bus es
sys em. A e ha , he impac o ECSs on he DPN
planning p oblems is assessed and e alua ed in [10].
A e ha , he e ec s o ha ing ECSs in a eal DPN
in a La in Ame ican in e media e ci y a e in es iga ed
[11]. Fu he mo e, he in luences o ECSs on a esiden-
ial dis ibu ion ne wo k in Bangladesh a e also s ud-
ied in [12]. Since all he p oblems and nega i e impac s
caused by ECSs in DPN ha e been ully iden i ied, a
lo o pape s ha e been p oposed o pa ly mi iga e
all hese downsides o ECSs, conside ing di e en as-
pec s and o ien a ions. Fo example, he au ho s in
[13, 14] o e ed a me hod o sol e he p oblem o in-
c easing peak hou s caused by he cha ging p ocess o
elec ic ca s, which did no happen in he pas when
gasoline ca s we e in high demand. Mo eo e , he au-
ho s also a gue ha he inc ease in peak hou s leads
o o e load s a us, which badly a ec s all elec ical de-
ices in he ne wo k, such as ans o me s and dis ibu-
ion lines. Besides he nega i e e ec s on he elec ical
de ices, he luc ua ion o ol age and cu en a e o-
cused on in [15, 16]. In [17], an op imiza ion model is
sugges ed o minimize he ol age s abili y index and
e alua e he cha ging demand and he economy aspec
while building ECSs in he IEEE-33 node. In [18], a
mul i-objec i e unc ion has been o mula ed o mini-
mize ol age de ia ion and powe loss simul aneously.
The au ho s in [19] add essed he inadequacy o build-
ing an uncon olled numbe o ECSs on he g id, and
hen a cos model o ECS ope a ion was buil o di -
e en ci cums ances. A e ha , an op imiza ion ool
is applied o de e mine he op imal loca ion o ECSs.
In [20], he au ho s ocused on sho ening he capi al
o ECS while conside ing he ol age bounda ies and
eac i e powe loss o he whole sys em.
In p ac ice, enewable ene gy gene a o s (REGs),
mos ly sola gene a o s (SGs) and capaci o banks
(CBs), ha e been deployed independen ly o com-
pounded o alle ia e he nega i e impac s caused by
ECS in he g id and also educe he p essu e on he
ansmission ne wo k. Fo example, CBs a e combined
wi h dis ibu ed gene a o s (DGs) in [21] o op imize
he econ igu a ion o DPN based on he employmen
o a mul i-objec i e unc ion o each di e en indices
such as powe loss, in eg a ing le el, and ol age s a-
bili y in di e en scena ios. Nex , he au ho s in [22]
ocused on maximizing he powe supplied by sola gen-
e a o s by combining bo h he placemen o ECSs and
enewable ene gy gene a o s in DPN o educe he e-
liance on ansmission powe ne wo ks. Besides, CBs
a e also in eg a ed in o he IEEE-33 bus and 34-bus
DPN oge he wi h ECS o lessen he powe loss and
main ain he eliabili y o DPN [23]. On op o ha ,
he au ho s in [24] sugges ed ha using he CB is one
o he mos e icien me hods o handle he nega i e e -
ec s caused by he imp ope posi ion o placing ECSs
in he DPN. The au ho also added ha geog aphi-
cal con enience is he op p io i y while es ablishing
an ECS, no powe low op imiza ion o DPN; he e-
o e, using auxilia y enginee ing solu ions is highly ec-
ommended o main ain he designed capabili y o he
DPN. Howe e , he combina ion o CBs, SGs, and DGs
a e simul aneously in eg a ed wi h he DPN along he
ECSs o maximize he e iciency, as conduc ed in [25].
Besides, he ela ed modelling, simula ion, and con ol
me hods in e ms o ope a ions and cha ging me h-
ods o EVs unde di e en condi ions, bo h in heo y
and p ac ice, a e highly essen ial o p o iding e e -
ences and da a analysis in he de eloping and es -
ing phases [26, 27]. Addi ionally, he au ho in [28]
p esen s he app oach o sol ing he o ans e ing
powe he wi eless cha ging echnology and by enhanc-
ing he e iciency o he ba e y managemen sys em
(BMS) on EVs [29]. On op o ha , he ba e y is a
c ucial elemen in an EV, among o he s. The e o e,
manu ac u e s and esea che s also need an o e iew
o he ma ke o elec ic ehicle ba e ies [30].
By deeply unde s anding he posi i e e ec s b ough
by placing ECS combined wi h REGs o he dis ibu-
ion gi ds, his esea ch applied h ee me a-heu is ic
algo i hms including A i icial hummingbi d algo i hm
(AHA) [31], jelly ish algo i hm (JS) [32], and No h-
e n goshawk op imiza ion (NGO) [33] o op imize he
placemen o ECS in he gi en DPN o achie e he
minimum alue o he main objec i e unc ion which is
minimizing he o al ac i e powe loss (TAPL). The
h ee algo i hms a e p oposed based on he simula-
ion o li ing beha iou s o di e en species in na-
u e such as, hummingbi d, jelly ish, and no he n
goshawk. Besides, hose algo i hms a e also e alu-
a ed wi h a ious es s bo h in heo ical and eal-
wo ld p oblems and hey ha e p o en hei capabili-
ies while compa ed o o he published p e iously. Fo
AHA, speci ically, when es ed on he Mul iple Disc
Clu ch B ake design p oblem, he algo i hm demon-
s a ed i s supe io i y o e se e al o he s, including
A i icial Bee Colony (ABC), Teaching-Lea ning-Based
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Dao T.T e al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH
Op imiza ion (TLBO), and Passing Vehicle Sea ch
(PVS). JS, on he o he hand, exhibi ed high pe o -
mance compa ed o a ious algo i hms, such as Pa i-
cle Swa m Op imiza ion (PSO), i s imp o ed e sion
(IPSO), and Enhanced Colliding Bodies Op imiza ion
(ECBO), when add essing he 582-ba owe op imal
design p oblem. Las ly, NGO was also es ed on di -
e en p ac ical op imiza ion p oblems, such as P es-
su e Vessel Design, Welded Beam Design, and Speed
Reduce Design, du ing i s de elopmen phase. The
esul s ob ained ac oss hese p oblems indica ed ha
NGO ou pe o ms he Whale Op imiza ion Algo i hm
(WOA), Ma ine P eda o s Algo i hm (MPA), Tunica e
Swa m Algo i hm (TSA), and o he s.
Compa ed o p e ious s udies, he s udy has main
no el ies as ollows:
•Apply h ee me a-heu is ic algo i hms, including
AHA, JS, and NGO, o sol e he gi en p oblem
o op imizing he placemen o ECSs and REGs in
he gi en DPN.
•P opose di e en cases o op imizing REGs and
ECSs: 1) The placemen o ECSs is op imized in
he i s s ep, and hen he placemen o REGs is
op imized in he second s ep, and 2) The place-
men o EGSs is op imized in he i s s ep and
hen he placemen o ECSs is op imized in he
second s ep.
•Di e en pene a ion le els o ECSs a e es ed,
and hen he co esponding capaci y o REGs is
op imized.
A e unning he h ee algo i hms o simula ion
cases in an IEEE 33-node sys em, he con ibu ions
o he s udy can be summa ized as ollows:
•JS is he mos sui able algo i hm among he h ee
applied algo i hms o he p oblem o op imally
ins alling ECSs and REGs in dis ibu ion powe
g ids.
•The use o high pene a ion le els o ECSs in dis-
ibu ion powe g ids leads o a high ol age d op
and a high powe loss. Howe e , he use o REGs
can imp o e he ol age and o al powe loss in
he dis ibu ion sys em.
•The op imal placemen o REGs in he i s s age
and he op imal placemen o ECS in he nex
s age ha e a be e ol age p o ile and a smalle
powe loss.
In addi ion o he In oduc ion, o he sec ions o he
esea ch a e s uc u ed as ollows: Sec ion 2 p esen s
he ma hema ical model o he gi en p oblem in e ms
o he main objec i e unc ion and he ela ed con-
s ain s; Sec ion 3 b ie ly in oduces he applied algo-
i hms; Sec ion 4 p o ides he discussion on he esul s
achie ed by he applied algo i hms on di e en cases;
inally, Sec ion 5 e eals he impo an conclusions o
he whole esea ch.
2. P oblem o mula
2.1. The main objec i e unc ion
This s udy minimizes he alue o ac i e powe loss
in he dis ibu ed powe ne wo k (DPN). The ma he-
ma ical exp ession o he objec ion unc ion is gi en as
ollows [14]:
Minimize T AP L =
NDL
X
n=1
Rn×I2
n(1)
whe e T AP L is he o al ac i e powe loss in he con-
side ed DPN; nis he dis ibu ion line n;NDL is he
numbe o dis ibu ion lines o he conside ed DPN;
Rnand Ina e espec i ely he esis ance and cu en
alues o he dis ibu ion line n.
2.2. The ela ed cons ain s
1) The powe balance cons ain s
These cons ain s mean ha he o al ac i e and e-
ac i e powe supplied by all he gene a ing sou ces in
he g id mus equal he ac i e and eac i e powe de-
manded by he end use and powe loss. The ma h-
ema ical exp ession o he cons ain s is gi en below
[34]:
PSL +
NSGs
X
m=1
PSG,m =PLD +
NCS1
X
i=1
P L1,i +
NCS2
X
j=1
P L2,j
+
NCS3
X
k=1
P L3,k +Ploss
(2)
and
QSL +
NCBs
X
c=1
QCB,c =QLD +Qloss (3)
In Equa ions (2) and (3), PSL and QSL a e ac i e
and eac i e powe ecei ed om he ansmission ne -
wo k a slack node; P L1,i is he powe supplied by
he i h ECS le el 1 wi h i= 1. . . NCS1and NCS1is
he numbe o ECS le el 1 in g id; P L2,j is he powe
supplied by he j h ECS le el 2 wi h j= 1. . . NCS2
and NCS2is he numbe o ECS le el 2 in g id; P L3,k
is he powe supplied by he k h ECS le el 3 wi h
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Dao T.T e al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH
k= 1. . . NCS3and NCS3is he numbe o ECS le el
3 in g id; PSG,m is he powe supplied by he SGs m,
wi h m= 1. . . NSGs and NSGs is he numbe o he
SGs in g id; QCB,c is he eac i e powe supplied by
c h CB wi h c= 1. . . NCBs and NCBs is he numbe o
capaci o banks; PLD and QLD a e ac i e and eac i e
powe demanded by load; inally, PLoss and QLoss a e
espec i ely ac i e and eac i e powe loss caused by
he ansmission p ocess.
2) The ope a ing cons ain s o capaci o
banks (CBs) and sola gene a o s (SGs)
Simila o o he elec ical de ices, bo h CBs and SGs
will wo k sa ely and e ec i ely i hei ou pu s a e a -
ied in he allowed anges as desc ibed in [35]:
Plow
SG,m ≤PSG,m ≤Phigh
SG,m (4)
Qlow
CB,c ≤QCB,c ≤Qhigh
CB,c (5)
whe e Plow
SG,m and Phigh
SG,m a e he lowes and highes
alue o ac i e powe gene a ed by he m h SG; Qlow
CB,c
and Qhigh
CB,c a e he lowes and highes alues o eac i e
powe supplied by he c h CB.
3) The cons ain s o ol age and cu en
ampli ude
The p esence o CBs and SGs in he conside ed DPN
leads o a a ia ion o bo h ol age and cu en ampli-
ude in he whole ne wo k. Howe e , hese alues can
only change wi hin pa icula bounda ies o ensu e he
s abili y and eliabili y o he ne wo k [36].
Ulow
nd ≤Und ≤Uhigh
nd (6)
In≤Ihigh
n(7)
whe e Ulow
nd and Uhigh
nd a e he lowes and highes alue
o ol age a he nd h node; Ihigh
nd is he highes alue o
cu en allowed o sen h ough he dis ibu ion line n;
Und is he ol age alue a he nd h node wi h nd h =
1. . . Nnd and Nnd is he numbe o node in g id.
4) The cons ain s o elec ical cha ging
s a ions (ECSs)
This cons ain means ha only all he ECSs can be
placed om node wo onwa d on he sys em. Mo e-
o e , each node is allowed o place only one ECS. The
o mula ion o he cons ain is gi en as ollows [35]:
2≤P oECS−L1, P oECS−L2, P oECS−L3≤Nnd (8)
P oECS−L1=P oECS−L2=P oECS−L2(9)
whe e P oECS−L1,P oECS−L2,P oECS−L3a e he posi-
ion o he ECS le el 1, 2, and 3 in he g id.
5) Cons ain o posi ion o placing CBs
and SGs
Simila o EVSs, bo h CBs and SGs can be placed om
node wo onwa ds in he ne wo k, as desc ibed below
[37]:
2≤P oSG,m, P oCB,c ≤Nnd (10)
whe e P oSG,m and P oCB,c a e he posi ion o he SGs
and CBs in he g id.
6) The cons ain s o SGs’ powe ac o
SGs a e supposed o ha e powe ac o s in he ange o
0.85 o 1.0. so, he op imal powe ac o is cons ained
wi hin he ange below:
P F low
SG,m ≤P FSG,m ≤P F high
SG,m (11)
whe e Plow
SG,m and P F high
SG,m a e he lowe and uppe lim-
i s o he m h SG’s powe ac o .
3. Applied me hods
This sec ion will b ie ly in oduce he upda e mecha-
nisms o he h ee applied algo i hms o new solu ions.
No e ha he upda e mechanism is c i ical in di e en i-
a ing a pa icula me a-heu is ic algo i hm om many
o he s.
3.1. The A i icial hummingbi d
algo i hm (AHA)
The upda e me hod o new solu ions o AHA is in-
spi ed by he a ia ion on posi ion o he hummingbi d
in i s o aging p ocess in na u e. The upda e p ocess
is subsequen ly execu ed using h ee phases and hei
speci ic exp essions will be gi en as ollows [31]:
Xnew,P 1
n=Xsl +ε1×NV ×(Xn−Xsl)(12)
Xnew,P 2
n=Xn+ε2×NV ×Xn(13)
Xnew,P 3
n=HBn+Rnd ×(HBn−LBn)(14)
In he h ee equa ions abo e, Xnew,P 1
n,Xnew,P 2
n,
and Xnew,P 3
na e espec i ely he new posi ion o he
hummingbi d n a each phase, espec i ely wi h n=
1,...NP s and NP s is ini ial popula ion size; Xsl is he
andom selec ed posi ion in he sea ch space; ε1and ε2
a e he amplying ac o s; NV is he na iga ing ac o ;
HBnand LBn he highes and lowes bounda ies o
he sea ch space; Rnd is he andom numbe be ween
0 and 1.
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3.2. The Jelly ish algo i hm (JS)
As men ioned ea lie , he de elopmen o JS is based on
he li ing p ac ices o jelly ish in na u e, pa icula ly
hei mo emen p ac ices in he ocean. These mo e-
men s a e also he main idea o he upda e me hod
o p oducing new solu ions in he sea ch p ocess o
he op imal solu ion. The pa icula exp ession o he
upda e me hod o JS is gi en below [32]:
Xnew
n=(Xn+m ×Rnd ×(HBn−LBn)
Xn+ST
wi h n= 1 . . . NP S
(15)
Wi h
ST =Rnd ×DT (16)
DT =(XR−Xni FR> FXn
Xn−XRi FXn< FR
(17)
In Equa ions (15) – (17), Xnew
nand Xna e he new
upda ed posi ion and he conside ed posi ion belonged
o he jelly ish no he popula ion; m is he mo ing
ansi ion ac o and acco ding o he au ho s m is
se by 0.1 o op imize he sea ching abili y o he al-
go i hm; ST is he leng h o he jump s ep; DT is he
di ec ion e m; XRand FRa e espec i ely he an-
dom jelly ish selec ed om he ini ial popula ion and
i s i ness alue.
3.3. The No he n goshawk
op imiza ion (NGO)
Simila o AHA and JS, he upda e me hod o new
NGO solu ions is also de eloped by simula ing he li -
ing p ac ices o he no he n goshawk, pa icula ly he
hun ing beha io , which is sepa a ed in o wo phases.
The ma hema ical exp essions o each phase will be
gi en as ollows [33]:
Xnew,P 1
n
=(Xn+AF1(XR−AF2×Xn), FXR< Xn
Xn+AF1(Xn−XR), FXR≥Xn
(18)
whe e Xnew,P 1
nis he new posi ion o he he no he n
no he popula ion wi h n= 1,2, . . . NP s and NP s
is he ini ial popula ion size; Xn he cu en posi ion
o he no he n n; AF1and AF2a e, espec i ely, he
ampli ying ac o s a e hei alues is andom gene a ed
be ween 0 and 1; XRis he andom selec ed posi ion
in he sea ch space.
A e he upda e p ocess o new solu ions in he
i s phase is comple ed, he upda e o new solu ion
in he second phase is execu ed using he exp ession
below [33]
Xnew,P 1
n=Xn+SP HA ×(2 ×AF1−1) ×Xn(19)
Wi h
SP HA = 0.02 1−IT
IT max (20)
In Equa ions (19) and (20), Xnew,P 1
nis he new posi-
ion o he no he n nin phase 2; SP HA is he ac eage
o he posible hun ing a ea; IT and IT max a e, espec-
i ely, he cu en index o i e a ion and he maximum
index o i e a ion.
4. Resul s
AHA, JS and NGO a e implemen ed o he simula-
ion and e alua ion. Each algo i hm is un i y ials
o collec he op imal solu ions, he bes and wo s
solu ions wi h he smalles and highes powe losses,
he bes un con e gence cha ac e is ic and he mean
con e gence cha ac e is ic o all uns. The p og am o
sol ing s udy case is coded in MATLAB on a compu e
wi h 2.6 GHz o CPU and 8GB o RAM. Fo each case,
he popula ion and i e a ion numbe a e se o 30 and
100. The selec ion o he popula ion and he maxi-
mum i e a ion numbe mus be selec ed sui ably o
ge ing he mos op imal solu ion and he simula ion
ime is no long [38]. Besides, he h ee applied algo-
i hms a e execu ed o 50 ial uns o he bes solu-
ion be o e all he compa isons ake place. This sec ion
employs he o iginal IEEE 33-node dis ibu ion powe
g id o in es iga e he ins alla ion o SGs and ECSs.
The single-line diag am o he g id is plo ed in Figu e
1 [25]. Inpu da a o he g id consis ing o load demand
a each node, esis ance, and eac ance o each line a e
aken om [25]. The o al load demand is 213.41 kW
[25]. In he s udy, we simula e h ee scena ios and ou
s udy cases o each scena io, including:
•Case 1: Op imize he placemen o h ee SGs in
he o iginal g id.
•Case 2: Use esul s om Case 1 and con inue op-
imize he placemen o ECSs.
•Case 3: Op imize he placemen o ESCs in he
o iginal g id.
•Case 4: Use esul s om Case 3 and con inue o
op imize hee SGs.
In Scena io 1, 1 Le el-1 EVS, 1 Le el-2 EVS and 1
Le el-3 EVS a e conside ed. In he scena ios 2 and 3,
each EVS ype has wo and h ee s a ions, espec i ely.
I is assumed ha he Le el-1 EVS can cha ge 1000
ca s simula aneously and he s a ion needs he supply
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Fig. 1: The con igu a ion o he IEEE 33-node sys em.
o 206.kW. Simila ly, he ca numbe and he capaci y
o Le el-2 and Le el-3 s a ions a e 1000 ca s and 435
kW, and 10 ca s and 1,087 kW, espec i ely. The a ed
powe o each cha ge is 1.9 kW in he Le el-1 s a ion,
4.0 kW in he Le el-2 s a ion and 100 kW in he Le el-
3 s a ion [16]. The e iciency o each cha ge is selec ed
o be 0.92.
4.1. Op imal placemen o h ee SGs
The h ee cu es in Figu e 2a p esen he powe loss
o he ial uns and he summa y o all ial uns, in-
cluding he bes , mean and wo se loss, and s anda d
de ia ion a e gi en in Figu e 2b. JS’s powe losses in
ed cu e a e less han hose o NGO in black cu e
and AHA in g een cu e. The sho es ba s o JS,
NGO and AHA ha e he same loss o 14.52; howe e ,
JS eaches sho e maximum and mean loss ba s han
o he s. Fu he mo e, JS ge s he smalles s anda d de-
ia ion (STD). In addi ion, he bes un and mean un
o i y ials a e gi en in Figu e 3a and 3b. In Figu e
3a, JS is as e han AHA and NGO om he ou y h
i e a ion o he eigh y h i e a ion, hen he h ee al-
go i hms each he same loss a he inal i e a ion. In
Figu e 3b, he mean loss o NGO is always g ea e han
ha o AHA and JS. AHA can each be e mean loss
alues han JS o he i s ou y i e a ion bu hen JS
eaches be e mean alues han AHA o o he i e a-
ions. Clea ly, JS is as e and mo e s able han AHA
and NGO.
In summa y, he h ee algo i hms could each he
same bes solu ion bu he mean solu ion and wo s
solu ions om JS a e less. JS each as e and mo e
s able con e gence. Thus, JS is he mos sui able algo-
i hm o Case 1, and JS is selec ed o unning o he
emaining cases.
Table 1 p esen s he op imal solu ions achie ed by
JS in Case 1.
(a) Fi y op imal solu ions
(b) Summa y o esul s om i y op imal solu ions
Fig. 2: Resul s ob ained by execu ed algo i hms o Case 1.
4.2. Resul s ob ained o all s udy
cases
The esul s ob ained o ou cases o h ee scena ios
by unning JS a e shown in Figu e 4. Case 1 is he
same o all scena ios, bu Case 2, Case 3 and Case
4 a e di e en in all scena ios. In gene al, he powe
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(a) The bes un
(b) The mean o all uns
Fig. 3: Compa ison o con e gence cha ac e is ics ob ained by
algo i hms o Case 1.
loss is inc eased om Scena io 1 o Scena io 3. The
losses a e 17.858, 35.040, and 74.701 kW o Case 2 in
Scena ios 1, 2 and 3, espec i ely. Simila ly, he losses
a e 224.496, 270.355, and 357.126 kW o Case 3, and
20.832, 42.609, and 74.295 kW o Case 4, espec i ely.
The esul s a e ob ious because he numbe o ECSs is
inc eased om 3 o 6 and 9 in Scena ios 1, 2 and 3.
Among ou s udy cases, Case 1 each he smalles
powe loss because no ECSs bu h ee SGs a e placed
in he g id. Case 3 su e s om he highes loss because
load demand is g ea e due o he adding mo e ECSs
and no SGs a e placed. Case 2 and Case 4 had bo h
Tab. 1: The op imal solu ion achie ed by he JS in Case 1.
Va iables Case 1
P oSG,1;PSG,1(kW) 30; 1199.92
P oSG,2;PSG,2(kW) 24; 1032.44
P oSG,3;PSG,3(kW) 13; 753.55
P FSG,10.85
P FSG,20.87
P FSG,30.86
Powe loss (kW) 14.51576
Fig. 4: Compa ison o powe loss o scena ios o Cases.
ECSs and SGs in he g id. Howe e , Case 2 placed SGs
i s and ECS hen bu Case 4 placed ECSs i s and
SGs hen. In Scena io 1, he loss is 17.858 kW o Case
2, and 20.832 kW o Case 4. In Scena io 2, he loss is
35.040 kW o Case 2, and 42.609 kW o Case 4. In
Scena io 3, he loss is 74.701 kW o Case 2, and 74.295
kW o Case 4. Case 4 su e s a highe loss han Case
2 by abou 3 kW in Scena io 1, 5.6 kW in Scena io 2.
Bu Case 2 su e s a li le highe loss han Case 4 by
abou 0.5 kW in Scena io 3.
The ol age p o ile o h ee scena ios o placing ECSs
o he g id in Case 2 is p esen ed in Figu e 5. The igu e
clea ly shows ha he inc ease in he numbe o ECSs
placed on he g id will lead o a highe ol age d op.
Mainly, Scena io 3 esul ed in he highes ol age d op,
while Scena io 1 showed he smalles one among he
h ee conside ed scena ios. No e ha he ol age d op,
in his case, is de e mined by op imizing he placemen
o SGs i s a Case 1, and hen ECSs a e subsequen ly
op imized.
Figu e 6 shows he ol age p o ile in Case 3 wi h
di e en scena ios o placing ECSs in he conside ed
DPN. The deg ee o ol age d op a buses a e com-
ple ely huge compa ed o Case 2. Addi ionally, he
placemen o ECSs in Scena io 3 has iola ed he ol -
age limi desc ibed by he wo ed lines in he igu e.
No e ha he placemen o ECSs in h ee scena ios in
his case is no suppo ed by SG as seen in Case 2.
The e o e, he p esence o mo e ECSs will inc ease he
load demand compa ed o he o iginal con igu a ion o
he gi d and also lead o ano he ex ensi ely ol age
d op.
Case 4 is conduc ed wi h he addi ional placemen o
SGs o imp o e he ol age p o ile a all buses in Case
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Fig. 5: Vol age p o ile o sys ems o di e en scena ios o Case
2 ob ained by JS.
Fig. 6: Vol age p o ile o sys ems o di e en scena ios o Case
3 ob ained by JS.
3, and he esul s a e displayed in Figu e 7. Mo eo e ,
o cou se, he placemen o SGs in he g id is also op i-
mized, besides he op imal posi ion o ECSs execu ed
in Case 3. The p esence o SGs, in his case, has sub-
s an ially imp o ed ol age d op a all buses compa ed
o Case 3. Howe e , compa ed o Case 2, whe e he
placemen o SGs is i s op imized, he luc ua ion o
ol age alue in Case 4 is s ill mo e signi ican , espe-
cially a buses 19 o 25.
Tables 2, 3, and 4 p esen he op imal solu ions
achie ed by JS in he h ee scena ios o he las h ee
cases.
5. Conclusions
This pape applied h ee me a-heu is ic algo i hms o
op imize he placemen o SGs and ECSs in di e en
cases o TAPL e alua ion. The h ee algo i hms a e
Tab. 2: The op imal esul s ob ained by JS in Scena io 1 o he
las h ee cases.
Va iable Case 2 Case 3 Case 4
P oECS−L130 20 20
P oECS−L219 19 19
P oECS−L32 2 2
P oSG,1;30; 1199.92 - 24; 1110.379
PSG,1(kW)
P oSG,2;24; 1032.44 - 30; 1214.597
PSG,2(kW)
P oSG,3;13; 753.55 - 13; 764.416
PSG,3(kW)
P FSG,10.85 - 0.887
P FSG,20.87 - 0.85
P FSG,30.86 - 0.868
Powe 17.858 224.496 20.832
loss (kW)
Tab. 3: The op imal esul s ob ained by JS in Scena io 2 o he
las h ee cases.
Va iable Case 2 Case 3 Case 4
P oECS−L120; 30 22; 3 22; 3
P oECS−L223; 3 20; 21 20; 21
P oECS−L319; 2 19; 2 19; 2
P oSG,1;30; 1199.92 - 12; 933.958
PSG,1(kW)
P oSG,2;24; 1032.44 - 30; 1295.216
PSG,2(kW)
P oSG,3;13; 753.55 - 21; 1450.431
PSG,3(kW)
P FSG,10.85 - 0.873
P FSG,20.8722 - 0.85
P FSG,30.8635 - 0.95
Powe 35.04 270.355 42.609
loss (kW)
Tab. 4: The op imal esul s ob ained by JS in Scena io 3 o he
las h ee cases.
Va iable Case 2 Case 3 Case 4
P oECS−L121; 24; 30 4; 23; 24 4; 23; 24
P oECS−L24; 20; 23 20; 21; 22 20; 21; 22
P oECS−L32; 3; 19 2; 3; 19 2; 3; 19
P oSG,1;30; 1199.92 - 30; 1279.705
PSG,1(kW)
P oSG,2;24; 1032.44 - 24; 1914.165
PSG,2(kW)
P oSG,3;13; 753.55 - 12; 948.250
PSG,3(kW)
P FSG,10.85 - 0.85
P FSG,20.8722 - 0.95
P FSG,30.8635 - 0.893
Powe 74.701 357.126 74.295
loss (kW)
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Fig. 7: Vol age p o ile o sys ems o di e en scena ios o Case
4 ob ained by JS.
including he a i icial hummingbi d algo i hm (AHA),
he jelly ish algo i hm (JS), and No he n goshawk op-
imiza ion (NGO). These algo i hms a e execu ed on
he IEEE 33-node o he i s case o ind ou he bes
one. In he i s case, JS ou pe o med wo o he s in
inding he op imal placemen o SGs and eaching he
bes powe loss alue. Then, JS is used o in es iga e
he TAPL alue o he whole g id in he h ee emain-
ing cases wi h he numbe o ECSs inc easing om one
o h ee o h ee scena io and he ixed numbe o
SGs. The esul s om hese scena ios indica e ha
he op imal placemen o SGs o he g id be o e ECSs
esul s in a be e powe loss alue, excep o Sce-
na io 3, whe e he numbe o ECSs a all le els is h ee
o each. Besides, he mo e ECSs in eg a ed in o he
g id, he g ea e he powe loss and he ol age d op.
Addi ionally, se e al limi a ions emain ha should be
add essed o enhance he p ac icali y and con ibu ion
o his wo k:
•The analysis is limi ed o he s anda d IEEE -node
DPN con igu a ion; a p ac ical DPN should also
be conside ed.
•O he objec i e unc ions, such as minimizing
he o al ol age de ia ion index, minimizing he
powe sou ce, minimizing he ene gy cos , e c.,
should be e alua ed.
•The s udy p ima ily ocuses on sol ing he gi en
p oblem om a planning pe spec i e. The ope a-
ional pe spec i e should be explo ed.
•Gi en ha sola gene a o s (SGs) p o ide powe
only du ing dayligh hou s, ene gy s o age sys-
ems (ESSs) should be in eg a ed o compensa e
o nigh ime sho ages when SGs a e inac i e.
•The easibili y o SG and ESS placemen si es
should be e alua ed, conside ing he geog aphic
cons ain s o p ac ical nodes.
Au ho Con ibu ions
D. T. T. de eloped he applied me hods, pe o med
he simula ion and esul s, and edi ed he inal e -
sion o he manusc ip . Bo h D. T. T. and M. P. D.
con ibu ed o he i s d a o he manusc ip and
supe ised he p ojec .
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