POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 20 |NUMBER: 4 |2022 |DECEMBER
Me a Heu is ic Algo i hm Based Mul i Objec i e
Op imal Planning o Rapid Cha ging S a ions
and Dis ibu ion Gene a o s in a Dis ibu ion
Sys em Coupled wi h T anspo a ion Ne wo k
Vijay VUTLA , Venkaiah CHINTHAM , Vinod Kuma Dulla MALLESHAM
Depa men o Elec ical Enginee ing, Na ional Ins i u e o Technology Wa angal,
NH 163, NITW Campus, 506004 Hanamkonda, Telangana, India
u la ijay[email p o ec ed], ch. enk[email p o ec ed], ino[email p o ec ed]
DOI: 10.15598/aeee. 20i4.4594
A icle his o y: Recei ed Jun 10, 2022; Re ised Sep 22, 2022; Accep ed Oc 13, 2022; Published Dec 31, 2022.
This is an open access a icle unde he BY-CC license.
Abs ac . The applica ion o Elec ic Vehicles (EVs)
is inc easing in many coun ies, causing many
esea che s o ocus on EV Rapid Cha ging S a ion
(RCS) ela ed issues. The op imal planning o RCS
conside ing only dis ibu ion ne wo ks is no a eli-
able app oach. Mo eo e , he RCS loca ion should
be con enien o he EV use in a gi en EV d i -
ing ange and he pe o mance o he dis ibu ion sys-
em. In his pape , a mul i-objec i e app oach o
op imal planning o RCS and Dis ibu ed Gene a o s
(DG) in a dis ibu ed sys em coupled wi h a ans-
po a ion ne wo k is analyzed. The p oposed op i-
mal planning me hod aims o achie e educed ac i e
powe loss, EV use cos s, and ol age de ia ion o
e ec i e RCS and DG planning. The app oach in-
cludes he analysis o he es sys em wi h he base case,
solo planning o RCS, planning o DGs wi h ixed RCS,
and simul aneous op imal planning o RCS and DGs.
Daily load a ia ion a buses and hou ly cha ging
p obabili y o EVs ha e been used in he analysis.
IEEE 33 bus dis ibu ion sys em supe imposed wi h
a 25-node anspo a ion ne wo k is conside ed he es
sys em. Rao 3 algo i hm is applied o op imiza ion,
and he esul s ha e been compa ed wi h PSO
and JAYA algo i hms.
Keywo ds
Dis ibu ed Gene a o , dis ibu ion sys em,
elec ic ehicle, Rao 3 algo i hm, Rapid Cha g-
ing S a ion.
1. In oduc ion
G eenhouse gas emission, deple ion o ossil uels,
and g owing oil p ices a e a ou ing he choice o EVs
o anspo a ion [1]. The deploymen o 20 million
Elec ic Vehicles (EVs) globally was a p omising
beginning o educe g eenhouse gas emissions by 2020.
Such a global deploymen o EVs will eplace 62 %
o lee ehicles by 2050 [2]. Al hough EVs ha e se e al
ad an ages, hey also ha e he d awback o low d i ing
ange. The cha ging ime and limi ed d i ing ange
o EVs a e he majo easons o he slow expansion
o EVs [3]. Ins alling p ope cha ging in as uc u e
can mi iga e he p oblem o low d i ing ange. The e
a e h ee cha ging me hodologies, among hem le el
1 and le el 2 ake a ew hou s o cha ging while DC
apid cha ging akes 15–20 minu es o cha ging [4].
So he deploymen o RCS can make he cus ome s
swi ch o EVs as RCS can quickly cha ge. Howe e ,
he g ow h o he EV popula ion c ea es a nega i e
e ec on powe sec o [5]. The placemen o RCS
a imp ope loca ions can u he enhance
he ha m ul impac on he dis ibu ion sys em ha
al e s he heal hy ope a ing condi ions o he powe
sys em [6].
The RCS hu s he dis ibu ion sys em. In he li -
e a u e, mos o he au ho s concen a ed on he mini-
miza ion o powe loss and ol age de ia ion as objec-
i es o suppo dis ibu ion sys ems in he p esence
o cha ging s a ions. In [7], minimiza ion o in es -
men cos , connec ion cos , o al cos o losses, and De-
mand Response (DR) cos we e used as objec i es o
©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 493
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placing RCS op imally. The concep o an incen i e-
based demand esponse p og am was used o achie e
he objec i e. Fo he bes posi ioning o cha ging s a-
ions and dis ibu ed gene a o s, he au ho in [8] used
hyb id g ey wol es and he pa icle swa m op imiza ion
me hod. The au ho s o [9] p oposed a me hodology o
scheduling EV in bo h V-G and G-V modes in he p es-
ence o DG o educe ne wo k powe loss and enhance
he ol age p o ile. In [10], he au ho s ha e p oposed
a wo s age app oach o op imal planning o Dis-
ibu ed Gene a o s (DGs), Shun Capaci o s (SCs)
and cha ging s a ions wi h g ass-hoppe op imiza ion
based uzzy mul i-objec i e echnique. The op imal
planning o DGs and SCs ha e been done in he i s
s age and he planning o CS is done in he second
s age.
The abo e li e a u e conside ed elec ical ne wo ks
only as a es sys em. Howe e , conside ing o only
elec ical ne wo ks o cha ging s a ion placemen is
no a c edible app oach. As he e is a equi e-
men o placing Rapid Cha ging S a ions (RCS)
along u ban oads o inc ease he u iliza ion o EVs,
he e is a necessi y o conside he oad ne wo k along
wi h elec ical ne wo k.
Ve y ew au ho s ha e conside ed bo h elec ical
and oad ne wo ks o op imal planning o cha g-
ing s a ions. The au ho o [11] p oposed a me hod
o posi ioning and sizing he Fas Cha ging S a ion
(FCS). In addi ion, o educing powe loss and wai -
ing imes, FCS posi ioning is done as e icien ly as
possible o compensa e o eac i e powe . In [12],
he bes si e o Cha ging S a ions (CS) was de e -
mined by minimizing powe loss and EV ene gy loss
incu ed du ing he ip o CS. The queuing heo y
was employed by he au ho o cap u e he dynamic be-
ha io o CS se iceabili y. In [13], [14], [15], and [16],
au ho s o mula ed he mul i objec i e p oblem o op-
imal planning o cha ging s a ions. In [13], op imal
planning was done wi h he goals o educing ol -
age a ia ion and powe loss, maximiza ion o EV low
supplied by he as -cha ging s a ion wi h con i ming
he impac o se ice adius and wai ing ime on plan-
ning. In [14], he au ho s applied me a-heu is ic
algo i hms o sol e he p oblem o educe ene gy loss,
ol age de ia ion and o minimize he land cos o sup-
po maximum EVs wi h low es ablishmen cos . Min-
imiza ion o he VRP (Vol age de ia ion, Reliabili y,
and Powe loss) index, ins alla ion and ope a ion cos ,
and imp o ing accessibili y index was conside ed o
op imal planning o cha ging s a ions in [15]. In [16],
he au ho s used he NSGA algo i hm o he simul a-
neous placing and sizing o FCS. Minimiza ion o in-
es men cos , ene gy losses, wai ing ime o cha ging,
and maximiza ion o cap u ed a ic low a e
conside ed o op imal planning.
In [17], he au ho used a heu is ic echnique o
op imal planning o DGs and D-s a com. Vol age
S abili y Index (VSI) was conside ed o op imal plan-
ning o D-s a com and Loss sensi i i y ac o is used
o op imal planning o DGs. In [18], he au ho
used mul i-objec i e ba algo i hm o op imal plan-
ning o DGs, he e maximiza ion o ol age sensi i -
i y index is used o op imal placemen and he mini-
miza ion o o al ac i e powe loss is used o op imal
sizing o DGs. In [17] and [18], he au ho s placed
DGs in he Dis ibu ion Sys em (DS) o imp o ing he
pe o mance o DS.
In he li e a u e, au ho s in [7] conside ed only DS
o RCS planning and au ho s in [8], [9] and [10]
planned RCS and DGs on DS only. Au ho s in [11],
[12], [13], [14], [15], and [16] conside ed coupled ne -
wo k o planning, and ye only RCS is op imally
planned. Howe e , op imal planning o RCS and DGs
has o be done on supe imposed ne wo k o elec i-
cal ne wo k and oad ne wo k. Because EV use s
always choose he closes RCS o cha ge hei ehi-
cles, conside ing he oad ne wo k is c ucial o e ec i e
planning. E en when RCS is posi ioned a he op i-
mal loca ions, hei p esence would inc ease powe loss
and ol age de ia ion. In his ega d, DG in eg a ion
is a easible solu ion o add ess he a o emen ioned is-
sues. Hence, in his pape , bo h he elec ical ne wo k
and he oad ne wo k we e aken in o conside a ion
while de e mining he bes loca ion o RCS and DGs.
In addi ion o he o he wo goals o minimizing ac-
i e powe loss and ol age de ia ion, he placemen
also conside ed cus ome con enience h ough he min-
imiza ion o EV use cos s. Mos ly in li e a u e, au-
ho s used he g ey wol op imiza ion algo i hm, g ass
hoppe op imiza ion algo i hm, chicken swa m op i-
miza ion, and hei hyb id o ms o inding op imal
solu ions. Howe e , mos algo i hms a e pa ame e de-
penden and equi e be e uning o pa ame e s o
inding op imal and accu a e solu ions. In his pape ,
he au ho s used pa ame e less no el Rao 3 algo i hm
o ob aining he op imal solu ions.
The main con ibu ions o his pape a e lis ed
below.
•The op imal placemen and sizing o RCS and DGs
ha e been done on he supe imposed elec ical
and oad ne wo k. In eg a ion o DGs in a dis i-
bu ion sys em coun e s he nega i e e ec s caused
by he p esence o RCS.
•Minimiza ion o Elec ic ehicle ene gy loss o
a elling om he cu en posi ion o he cha g-
ing s a ion loca ion is adequa ely deal wi h.
•The analysis akes in o accoun di e en
load ypes, hei a ia ion o e 24 hou s,
and he p obabili y o daily hou ly EV cha ging.
©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 494
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•Fo ge ing he bes RCS and DG loca ions
and sizes in a supe imposed ne wo k, h ee cases
a e aken in o conside a ion: case 1 is op imal
RCS planning alone; case 2 is op imal DG plan-
ning wi h case 1’s ixed RCS loca ions and sizes;
and case 3 is concu en op imal RCS and DG
planning.
•Fo he goal o ackling an op imiza ion
issue, he no el Rao 3 algo i hm is chosen,
and he solu ions a e compa ed wi h hose
ob ained using he PSO and JAYA algo i hms.
The o ganiza ion o he emaining pape is as ol-
lows: DG modelling and objec i e unc ion o mula ion
a e explained in Sec. 2. Sec ion 3. explains Rao 3,
Jaya algo i hms, and low cha o implemen a ion
o Rao 3 algo i hm o sol ing he p oblem. Resul s
a e discussed in Sec. 4. , ollowed by conclusions in
Sec. 5.
2. P oblem Fo mula ion
2.1. DGs Modeling
PV o PQ modelling can be used o model dis-
ibu ed gene a o s. In his pape , PQ (nega i e load
model) mode has been aken o modelling DGs. He e
he quan i ies ha a e emphasized eal powe ou pu
(Pdg) and powe ac o (p. ). Reac i e powe ou -
pu (Qdg) can be calcula ed om he ela ion go e n-
ing eal powe , eac i e powe , and powe ac o as
shown in Eq. (1). Eq. (2) and Eq. (3) show he cal-
cula ion o eal e ec i e load (Pe ec i eload) and eac-
i e e ec i e load (Qe ec i eload) a dis ibu ion buses,
espec i ely.
Qdg =Pdg an(cos−1(p )),(1)
Pe ec i eload =Pload −Pdg,(2)
Qe ec i eload =Qload −Qdg.(3)
2.2. Mul i Objec i e Func ion
(MOF)
In his pape , he minimiza ion o ac i e powe loss,
EV use cos and ol age de ia ion we e conside ed o
op imal planning o cha ging s a ions and DGs. He e
he weigh ed mul i-objec i e o mula ion was done
wi h equal weigh s.
MOF = min(w1AP LRI +w2MV DRI +w3EV UCI).
(4)
In Eq. (4) w1,w2, and w3a e weigh s be ween [0,1]
and he sum o hese weigh s needs o be 1. In his
pape , equal weigh s a e conside ed o all indi idual
objec i es.
1) Ac i e Powe Loss Reduc ion Index
(APLRI)
Powe low in a dis ibu ion sys em causes ac i e Powe
loss (Ploss). The addi ion o Rapid Cha ging S a-
ions (RCS) o he dis ibu ion sys em pu s mo e
s ain on he ne wo k, esul ing in highe powe losses
and ol age magni ude deg ada ion o buses. Fu he ,
he placemen o RCS a imp ope places inc eases
losses abno mally and al e s he heal hy ol age p o-
ile. Usually, RCS is conside ed as he load a he powe
dis ibu ion subs a ion. Ma hema ically, he load due
o EVs a i h RCS (CSi
load) is calcula ed as pe Eq. (5).
The connec o s a i h RCS (CSi
connec o s) and he ca-
paci y o i h RCS (CSi
capaci y) a e calcula ed using
Eq. (6) and Eq. (7), espec i ely. Powe losses can be
educed by minimizing he Ac i e Powe Loss Reduc-
ion Index (APLRI). He e APLRI (Eq. (8)) is he a io
o daily Ploss a e he placemen o CS o DG o bo h,
o he daily Ploss be o e he placemen o bo h.
CSi
load =NiCS
e ,(5)
CSi
connec o s = max(Pe c)NiCS
e ,(6)
CSi
capaci y =CSi
connec o sRc,(7)
AP LRI =P24
=1 P cs/dg
loss
P24
=1 Ploss
.(8)
2) EV Use Cos Index (EVUCI)
Elec ic ehicle use has a choice o selec he nea es
RCS o cha ge hei EV. This decision no only helps
he use bu also educes he ene gy loss om a el-
ling o he RCS. Conside mpossible cha ging s a ion
loca ions and qcha ging demand nodes which belong
o oad ne wo k nodes. The selec ion o RCS in op i-
mal planning is done by he calcula ion o he dis ance
be ween q h demand node o all a ailable RCS and is
s o ed in Dma ix wi h he o de o [q, z]z∈m. A -
e compa ing he dis ances o q h demand node o all
RCS, EVs p esen a he demand node a e assigned
o he nea es RCS and he co esponding dis ance is
s o ed in DD ma ix. He e DD ma ix has he o de
o [q, 1].
D=





d1c1d1c2. . . d1cz
d2c1d2c2. . . d2cz
.
.
..
.
..
.
..
.
.
dqc1dqc2. . . dqcz





,DD =





min()
min()
.
.
.
min()





,
(9)
©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 495
POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 20 |NUMBER: 4 |2022 |DECEMBER
d=[d1, d2, . . . , dq] is he se o demand poin s,
c=[c1, c2, . . . , cm] is he se o cha ging nodes belonging
o oad ne wo k nodes. EV use cos can be calcula ed
om Eq. (10). He e Ne (i)is o al numbe o EVs
a i h RCS, EC is he ene gy consump ion o EVs
and Peis he elec ici y p ice.
EV use cos =
q
X
n=1
DD(i)Ne (i)ECPe.(10)
Calcula ing he dis ance om q h demand node
o all mcha ging nodes and choosing he longes dis-
ance among hem o e s he maximum dis ance ha
an EV cus ome mus a el om he q h demand node.
DDmax is he esul o o ming a DD ma ix o max-
imum dis ances. The alues o maximum EV use loss
cos and EV use cos index a e gi en by he Eq. (11)
and Eq. (12).
EV max
use cos =
q
X
n=1
DDmax(i)Ne (i)ECPe,(11)
EV UCI =EV use cos
EV max
use cos
.(12)
3) Maximum Vol age De ia ion Reduc ion
Index (MVDRI)
Loading he dis ibu ion sys em wi h RCS can cause
a de ia ion o ol age beyond i s limi s. The AC
load low gi es he alue o he ol age a each bus.
The maximum ol age de ia ion (V Dmax) can be
calcula ed using Eq. (13).
Maximum ol age de ia ion:
V Dmax = max(1 − (i)), i = 1,2,3, . . . , Ndis nodes.
(13)
MVDRI e e s o he a io o maximum ol age de i-
a ion o e he day wi h he in eg a ion o RCS/DG o
bo h o he maximum ol age de ia ion o e he day
wi hou he in eg a ion o bo h RCS and DG. I is
calcula ed as ollows:
MV DRI =P24
=1 V DRCS/DG
max ,
P24
=1 V Dmax, .(14)
2.3. Sys em Cons ain s
Each RCS mus ha e a leas one cha ging connec o
o supply he EVs, and Eq. (15) suppo his con-
s ain . Eq. (16) and Eq. (17) a e he eal eac-
i e powe balance cons ain s, espec i ely in he sys-
em. In eg a ion o RCS al e s he ol age p o ile,
so he e is a need o check ol age limi s in op i-
mal planning. Eq. (18) adds he ol age limi s as
a cons ain . Each DG has maximum and minimum
capaci y limi s (Eq. (19)), and he maximum o al ca-
paci y supplied by all DGs(PT,max
DG ) is a use -de ined
quan i y and should be less han he minimum o al
eal powe consump ion h oughou a day (Eq. (20)).
CSi
connec o ≥1i= 1,2, . . . , z(numbe o RCS),
(15)
Psub +XPdg =PD+XPRCS +Ploss,(16)
Qsub +XQDG =QD+Qloss,(17)
|Vmin|≤|Vn|≤|Vmax|n= 1,2, . . . , Nbus,(18)
Pmin
dg ≤Pa,dg ≤Pmax
dg , a = 1,2, . . . , NDG,(19)
NDG
X
a=1
Pa,DG ≤PT,max
DG <min(Pn,D).(20)
He e Psub and Qsub a e he subs a ion eal powe
and eac i e powe espec i ely. PD,QD,Ploss
and Qloss a e eal powe demand, eac i e powe de-
mand, eal powe loss and eac i e powe loss in a aken
es sys em. He e RCS a e conside ed as only eal
powe loads, i is (PRCS) equal o CSi
load.Vmin,
Vmax,Pmin
dg and Pmax
dg a e he ol age minimum limi ,
ol age maximum limi , DGs minimum eal powe
limi and DGs maximum eal powe limi espec i ely.
PT,max
DG is he maximum limi o o al ac i e powe sup-
plied by all DGs. Pn,D eal powe demand a n h node
o he dis ibu ion sys em.
3. Algo i hm
3.1. Raos 3 Algo i hm
Rao 3 algo i hm was p oposed by Rao in 2020 [19].
The algo i hm is easy o unde s and and has he ad-
an age o me apho -less and ew algo i hm-speci ic
pa ame e s. The p inciple behind his algo i hm is
andom in e ac ion be ween he candida e solu ions,
and he candida e solu ions mo e owa ds he bes so-
lu ions and away om he wo s solu ions in he op i-
miza ion p ocess. This algo i hm is a popula ion-based
echnique and upda es equa ions in each i e a ion as
shown below.
X′
i,j,k =Xi,j,k + 1j,k(Xj,bes ,k − |(Xj,wo s ,k)|)+
+ 2j,k((|Xi,j,ko X ,j,k|)−(X ,j,ko Xi,j,k)).
(21)
He e X′
i,j,k is he upda ed solu ion
o i h candida e, j h a iable in k h
i e a ion. Xi,j,k is he solu ion o i h candida e,
©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 496
POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 20 |NUMBER: 4 |2022 |DECEMBER
j h a iable in k h i e a ion, 1, 2a e andom
alues be ween [0,1]. Xj,bes ,k is he bes alue
o j h a iable o Xin he k h i e a ion. Xj,wo s ,k
is he wo s alue o j h a iable o Xin he k h
i e a ion. X ,j,k andomly selec ed h candida e,
j h a iable in k h i e a ion. The lowcha o he Rao 3
algo i hm o op imal planning is shown in Fig. 1.
Read he sys em da a, ini ialize he algo i hm pa ame e s and sys em
cons an s.
s a
Ini ialize easible popula ion acco ding o cases, e alu e he i ness
alues.
Ob ain he bes and wo s alues based on he i ness alue.
Se gen=1
s op
Conside upda ed solu ion
and disca d old solu ion
= new
X=Xnew
Conside old solu ion and
disca d upda ed solu ion
= old
X=Xold
gen=gen+1
Yes No
Upda e he popula ion acco ding o
RAO 3 upda e equa ion and e alua e
he i ness unc ion.
I ( new < old)
I (gen>MaxGen)
Yes No
Fig. 1: Flowcha o implemen a ion o Rao 3 algo i hm.
Lcspop =





X1,1X1,2. . . X1,z
X2,1X2,2. . . X2,z
.
.
..
.
..
.
..
.
.
Xpop,1Xpop,2. . . Xpop,z





,(22)
Ldgpop =





Y1,1Y1,2. . . Y1,n
Y2,1Y2,2. . . Y2,n
.
.
..
.
..
.
..
.
.
Ypop,1Ypop,2. . . Ypop,n





,(23)
Sdgpop =





S1,1S1,2. . . S1,n
S2,1S2,2. . . S2,n
.
.
..
.
..
.
..
.
.
Spop,1Spop,2. . . Spop,n





.(24)
Ini cspop = [Lcspop]is he ma ix used o op i-
mal planning o only RCS (Case 1). This ma ix
consis o easible loca ions o RCS in a dis ibu-
ion sys em. Ini dgpop = [Ldgpop,Sdgpop]is he ma-
ix consis ing o andomly ini ialized easible loca-
ions and he co esponding size o DGs used in o -
de o plan DGs in he dis ibu ion sys em op imally
(Case 2). Ini csdgpop = [Lcspop,Ldgpop,Sdgpop]is
he ma ix ha consis s o RCS loca ion, DG loca-
ion and he co esponding DG size. I is u ilised
o plan RCS and DGs a he same ime o ge
he bes esul s (Case 3). He e Xindica es he
loca ion o RCS, Yindica es he loca ion o DG and S
indica es he size o he DG.
3.2. Jaya Algo i hm
Rao p oposed he Jaya algo i hm [20], which
is a popula ion-based me a-heu is ic algo i hm.
The p emise o his algo i hm is ha he solu ion
o an op imiza ion p oblem goes owa ds he global
bes solu ion while a oiding he wo s solu ion.
I has he ad an age ha i equi es only he com-
mon con ol pa ame e s which a e: popula ion size
and maximum i e a ions, and i does no equi e any
algo i hm-speci ic pa ame e se ing.
The modi ied alue o k h candida e i h a iable
in j h i e a ion is ob ained using he Eq. (25) gi en
below:
x′
k,i,j =xk,i,j + 1i,j (xbes ,i,j −xk,i,j)+
− 2i,j(xwo s ,i,j −xk,i,j).(25)
He e x′
k,i,j is he modi ied k h candida e, i h a iable
in j h i e a ion, xk,i,j is he p esen k h candida e, i h
a iable in j h i e a ion. 1, 2a e he andom alues
be ween 0 and 1 i.e. [0 1]. xbes ,i,j is he bes solu ion
o i h a iable among all candida es in j h i e a ion.
xwo s ,i,j is he wo s solu ion o i h a iable among
all candida es in j h i e a ion. I he objec i e alue
yield by he modi ied x′
k,i is be e han xk,i, hen
he modi ied candida e solu ion is accep ed in each
i e a ion. Accep able solu ions a e kep in each
i e a ion, and subsequen sea ches a e based
on he solu ions in he ollowing i e a ion. When
he e mina ion c i e ia a e me , he inal op imal
solu ions a e achie ed.
4. Simula ion Resul s
and Analysis
Supe imposed IEEE 33 bus elec ical sys em and 25
node oad ne wo k we e ea ed as es sys em [15], as
shown in Fig. 2. All he buses in IEEE 33 bus es
sys em we e seg ega ed as 17 esiden ial load buses,
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9 indus ial load buses and 5 comme cial load buses
shown in Tab. 1. Bus da a and line da a we e aken
om [21]. The hou ly load a a ious buses a y
acco ding o he load pa e ns (in p.u.) as shown
in Fig. 3. The da a ega ding oad ne wo k was aken
om [22], and 1 km pe uni was conside ed. Supe -
imposed nodes o he dis ibu ion ne wo k and oad
ne wo k we e aken om [15], which a e ep esen ed
in Tab. 3.
1 2 3 4 5 6 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22 26 27 28 29 30 31 32 33
23 24 25
1
7
5
15
16
12
11
17
19
18
2021
252423
22
14
10
8
4
9
3
2
6
13
7
Fig. 2: Supe imposed IEEE 33 bus dis ibu ion sys em wi h
25 node oad ne wo k.
Time (hou s)
2 4 6 8 10 12 14 16 18 20 22 24
0.2
0.4
0.6
0.8
1
1.2
Comme cial load
Indus ial load
Residen ial load
Demand in (p.u.)
Fig. 3: Plo o di e en ypes o load pa e ns.
Tab. 1: Iden i ica ion o ypes o load buses.
Residen ial Comme cial Indus ial
loads loads loads
2, 3, 5, 6 4, 11, 12, 18 22, 26, 27, 28
7, 8, 9, 10 19 29, 30, 31, 32
13, 14, 15, 16 – 33
17, 20, 21, 23, 24 – –
Tab. 2: Elec ic ehicle echnical pa ame e s.
Pa ame e Value
To al numbe o EVs (NT EV ) 238
Connec o a ing (Rc) (kW) 96
EV ba e y capaci y (Pb) (kWh) 50
Ene gy Consump ion (EC) (kWh·km−1) 0.219
Elec ici y P ice (Pe) ($·MWh−1) 87.7
The o al assumed EV popula ion a oad ne wo k
nodes was 238, and we e allowed o cha ge a selec ed
cha ging s a ions acco ding o he p obabili y o EV
cha ging shown in Fig. 4. Table 4 gi es he assumed
numbe o EVs p esen a he nodes o he oad ne -
wo k. In his wo k, all 25 oad ne wo k nodes we e
conside ed demand nodes. Fo all op imiza ion algo-
i hms, 100 maximum gene a ions and 30 popula ion
size a e conside ed. Fo he PSO algo i hm ine ia con-
s an s C1=C2= 2 a e conside ed. Simula ions we e
ca ied ou on PC wi h windows 10 ope a ing sys em,
4 Gb am, and MATLAB 2014b so wa e.
Tab. 3: Coupling o he oad ne wo k nodes (Rn) wi h
he dis ibu ion ne wo k nodes (Dn).
DnRnDnRn
03 09 20 04
06 08 23 22
14 11 26 05
16 12 28 07
17 16 30 06
Time (hou s)
0 5 10 15 20 25
0
0.02
0.04
0.06
0.08
0.1
Pe c
Fig. 4: Va ia ion o Elec ic Vehicle cha ging p obabili y.
In his pape , he analysis was done by conside ing
he base case, case 1, case 2, and case 3.
•Base case: In his case, he load low was done
on he dis ibu ion sys em wi hou he in eg a ion
o RCS and DG o ind daily ac i e powe loss
and maximum ol age de ia ion.
•Case 1: In his case, op imal placemen and siz-
ing o RCS is done on he supe imposed ne wo k
o minimize he EV use cos , ac i e powe loss
and ol age de ia ion.
•Case 2: The load due o he cha ging s a ions
om case 1 is added o he cu en load a he co -
esponding dis ibu ion bus in case 2. In his
sys em, op imal placemen and sizing o DGs a e
done o minimize he EV use cos , ac i e powe
loss and ol age de ia ion.
•Case 3: In his case, concu en placemen
and sizing o RCS and DGs a e done o minimize
he ac i e powe loss, EV use cos and ol age
de ia ion.
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Tab. 4: Assumed EVs p esen a oad ne wo k nodes.
RnEVs RnEVs RnEVs RnEVs RnEVs
1 5 6 8 11 3 16 15 21 9
2 9 7 15 12 3 17 8 22 12
3 13 8 6 13 10 18 6 23 15
4 8 9 4 14 12 19 7 24 5
5 5 10 15 15 15 20 15 25 15
4.1. Base Case
The es sys em consis s o IEEE 33 bus dis ibu ion
sys em. As i is adial and has a high R/X a io,
he eed o wa d and backwa d sweep load low algo-
i hm was used o load low s udy. In he base case,
he dis ibu ed load low s udy was simula ed wi hou
he in eg a ion o RCS and DGs in o he es sys em
by conside ing hou ly load pa e ns o di e en load
ypes o e 24 hou s.
I was obse ed ha he load low led o daily ac i e
powe loss o 2811 kW and daily maximum ol age de-
ia ion o 1.5816 (p.u.). The lowes ol age o 0.8968
(p.u.) was obse ed a 18 h node in 17 h hou . Vol age
p o ile o e 24 hou s is as shown in Fig. 5
Vol age (p.u.)
0.8
0.85
0.9
0.95
1
1 hou
2 hou
3 hou
4 hou
5 hou
6 hou
7 hou
8 hou
9 hou
10 hou
11 hou
12 hou
13 hou
14 hou
15 hou
16 hou
17 hou
18 hou
19 hou
20 hou
21 hou
22 hou
23 hou
24 hou
Bus numbe
0 5 10 15 20 25 30
Fig. 5: Dis ibu ion sys em ol age p o ile in base case.
4.2. Case 1: Op imal Planning
o RCS
Case 1 deals wi h he op imal placemen and sizing
o RCSs. The placemen was done based on he ollow-
ing assump ions:
•The supe imposed nodes a e conside ed o RCS
placemen .
•RCS can be placed a 3 buses and i is ob-
se ed ha placemen a mo e han 3 buses makes
he sys em uns able.
In case 1, RCS was op imally planned. In op imal
planning, p ima ily all EVs we e dis ibu ed among
he ini ialized RCS loca ions o minimize EV use cos s
by selec ing he nea es RCS. A e adding he RCS
load, he dis ibu ion load low algo i hm is applied
o he es sys em o ind Ploss and MVD. To min-
imize he conside ed mul i-objec i e unc ion a ious
algo i hms a e applied. I is obse ed om Tab. 5 ha ,
dis ibu ion sys em pe o mance is a ec ed by RCS in-
s alla ion. Daily ac i e powe loss inc eased by 19.5 %,
12.1 %, and 9.73 % compa ed wi h he base case Ploss,
ob ained using PSO, JAYA, and Rao 3 algo i hms,
espec i ely. The p esence o RCS is also wi nessed
wi h he inc eased alue o MVD (1.6120 (p.u.))
in compa ison wi h base case MVD (1.5816 (p.u.)).
He e Rao 3 algo i hm ga e he leas MVD compa ed
o he o he wo algo i hms. The sys em’s minimum
ol age was 0.8949 (p.u.), which appea ed a he 18 h
bus in he 17 h hou using he Rao 3 algo i hm, as
shown in Fig. 6.
Tab. 5: Compa ison o a ious algo i hms o op imal
alloca ion o RCS in case 1.
Pa ame e PSO JAYA Rao 3
CS loca ions 23,20,30 23,20,26 20,23,3
EVs 129,50,59 144,76,18 105,114,19
Connec o s 13,5,6 14,8,2 11,11,2
Size (kW) 1248,480,576 1344,768,192 1056,1056,192
Ploss (kW) 3359.8 3151.8 3084.6
EVUC ($) 34.0335 36.1270 36.3383
MVD (p.u.) 1.6608 1.6271 1.612
APLRI 1.1952 1.1212 1.0973
EVUCI 0.3643 0.3867 0.3890
MVDRI 1.0501 1.0288 1.0193
MOF 0.8690 0.8447 0.8343
Time (sec) 250.4 169.3 155.6
Vol age (p.u.)
1 hou
2 hou
3 hou
4 hou
5 hou
6 hou
7 hou
8 hou
9 hou
10 hou
11 hou
12 hou
13 hou
14 hou
15 hou
16 hou
17 hou
18 hou
19 hou
20 hou
21 hou
22 hou
23 hou
24 hou
Bus numbe
0.8
0.85
0.9
0.95
1
0 5 10 15 20 25 30
Fig. 6: Dis ibu ion sys em ol age p o ile in case 1.
RCS placemen caused, he down all o sys em min-
imum ol age om 0.8968 (p.u., base case) o 0.8949
(p.u.). EVUC is 36.3383 $ wi h Rao 3 algo i hm which
is high among EVUC o PSO and JAYA algo i hms.
Howe e , he o e all objec i e unc ion alue o 0.8343
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by he Rao 3 algo i hm is he lowes in compa ison
wi h he JAYA algo i hm (0.8447) and PSO algo i hm
(0.8690). Rao 3 algo i hm ook less ime o e olu ion
compa ed o PSO and JAYA algo i hms. To coun e
he e ec s caused by RCS ins alla ion in he dis ibu-
ion sys em DGs a e ins alled.
4.3. Case 2: Op imal Planning
o DGs
Ins alling DGs in he dis ibu ion sys em educes
powe loss and imp o es ol age p o ile. Renewable
ype DGs o size 5 kW–1 MW a e conside ed o in e-
g a ion. I has been obse ed ha in eg a ion o h ee
DGs in a dis ibu ion sys em ou pe o ms in eg a ion
o single DG o wo DGs. I ’s also been obse ed ha
adding mo e han h ee DGs o a dis ibu ion sys em
doesn’ signi ican ly inc ease pe o mance. As a esul ,
h ee DGs we e conside ed in his s udy. The hou ly
o al eal load demand on he sys em, which includes
RCS load and he hou ly cha ging p obabili y o EVs,
is depic ed in Fig. 7. Acco ding o his plo , he min-
imum eal powe load demand o 1420.8 kW appea ed
a he 4 h hou . As a esul , he o al eal powe
injec ion by all DGs is limi ed o less han o equal
o 1400 kW (<1420.8) acco ding o he cons ain
Eq. (20).
Time (hou s)
0 5 10 15 20
0
1000
2000
3000
4000
5000
6000
Wi h ou RCS load
Wi h RCS load
Real Powe Demand (kW)
Fig. 7: Plo o hou ly a ying load demand wi h and wi h ou
RCS load.
Tab. 6 shows he op imal placemen s, DG sizes,
and nume ous echnical obse a ions. When com-
pa ed o he base case, ac i e powe loss was e-
duced o 38.42 % in case 2. This educ ion was aided
by he inse ion o DGs in he dis ibu ion sys em.
The PSO and JAYA algo i hms educed ac i e powe
loss by 40.06 % and 39.45 %, espec i ely, bu he op i-
mal placemen s and sizes o DGs ob ained by he Rao 3
algo i hm educed ac i e powe loss o he maxi-
mum in compa ison wi h he o he wo algo i hms.
The maximum ol age de ia ion wi h he Rao 3 algo-
i hm was 0.5215 (p.u.), which is highe han he 0.5151
(p.u.), 0.5162 (p.u.) o he PSO, and JAYA algo i hms,
espec i ely.
Fu he mo e, as compa ed o 0.3718 o PSO
and 0.3699 o JAYA, he Mul i-Objec i e Func ion
(MOF ) wi h he Rao 3 algo i hm was 0.3675, which
was he lowes alue. The ol age p o ile a all buses
h oughou he day is depic ed in Fig. 8, wi h he DGs
placed a op imal loca ions and sizes using he Rao 3
algo i hm. A minimum ol age o 0.9626 (p.u.)
appea ed a he 30 h bus in he 19 h hou , acco ding
o Fig. 8. The lowes ol age a he 18 h bus imp o ed
om 0.8968 (p.u. base case) o 0.9627 in he 17 h hou
(p.u.). The placemen o DGs in he p ope loca ions
is esponsible o his imp o emen . When compa ed
o he PSO and JAYA algo i hms, Rao 3 p oduced
e icien ou comes in he sho es ime.
Tab. 6: Compa ison o a ious algo i hms o op imal
alloca ion o DGs in case 2.
Pa ame e PSO JAYA Rao 3
DGs loca ions 15,33,5 33,15,8 33,15,12
Size (kW) 609,784,5 793,554,52 773,429,196
Ploss (kW) 1126.3 1108.9 1080
EVUC ($) 36.3383 36.3383 36.3383
MVD (p.u.) 0.5151 0.5162 0.5215
APLRI 0.4007 0.3945 0.3841
EVUCI 0.3890 0.3890 0.3890
MVDRI 0.3257 0.3264 0.3297
MOF 0.3718 0.3699 0.3675
Time (sec) 274.2 136.1 130.5
4.4. Case 3: Concu en Op imal
Planning o RCS and DGs
In his case, he Rao 3 algo i hm was used o plan
RCS and DGs a he same ime. RCS loca ion, DG
loca ion, and DG size make up he ini ializa ion ma-
ix. The sys em was examined o imp o ed o e all
objec i e unc ion once hese wo we e added. Tab. 7
shows he op imal esul s by he a ious algo i hms.
The Rao 3 algo i hm was shown o gene a e a be -
e MOF o 0.3441. The daily ac i e powe loss
was 1079.2 kW, o 38.39 % o he base ac i e powe
loss. In compa ison o he PSO and JAYA algo i hms,
he Maximum Vol age De ia ion (MVD) was 0.5960
(p.u.), which was he lowes o he alues. Wi h
he Rao 3 algo i hm, EV use cos o an elec ic ehicles
was 25.3715 $, which is cos - e ec i e when compa ed
o he 42.3306 $ and 31.1142 $ o PSO and JAYA,
espec i ely.
The sys em’s ol age p o ile is shown in Fig. 9,
wi h he RCS and DGs placed simul aneously using
he Rao 3 algo i hm. A 16 h bus in 20 h hou , he sys-
em’s minimum ol age is 0.9518 (p.u.). The ol age
imp o ed om 0.8968 (p.u., base case) o 0.9629 (p.u.)
a he 18 h bus in he 17 h hou . When compa ed
o he o he wo algo i hms, he Rao 3 algo i hm akes
less ime o simula e and p oduce op imal esul s.
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We know om Tab. 8 ha , daily ac i e powe loss
is g adually educed om case 1 o case 3. Though
he maximum ol age de ia ion is sligh ly highe
in case 3 compa ed o case 2, EVUC and o e all ob-
jec i e unc ion a e he smalles o all cases (case 1
and case 2) in case 3. Based on hese indings, i can
be in e ed ha using he Rao 3 algo i hm o plan RCS
and DGs concu en ly (case 3) gene a ed he bes ou -
comes.
Tab. 7: Compa ison o a ious algo i hms o concu en
op imal alloca ion RCS and DGs in case 3.
Pa ame e PSO JAYA Rao 3
CS loca ions 20,28,16 23,20,6 16,20,23
EVs 44,112,82 104,40,94 67,73,98
Connec o s 4,11,8 10,4,9 7,7,10
Size (kW) 384,1056,768 960,384,864 672,672,960
DGs loca ions 13,11,30 14,31,30 31,11,17
Size(kW) 514,69,791 569,461,151 615,389,395
Ploss (kW) 1271.9 1219.2 1079.2
EVUC ($) 42.3306 31.1142 25.3715
MVD (p.u.) 0.8192 0.6714 0.5960
APLRI 0.4525 0.4337 0.3839
EVUCI 0.4531 0.3331 0.2716
MVDRI 0.5179 0.4245 0.3768
MOF 0.4745 0.3971 0.3441
Time (sec) 298.8 160.1 148.06
1 hou
2 hou
3 hou
4 hou
5 hou
6 hou
7 hou
8 hou
9 hou
10 hou
11 hou
12 hou
13 hou
14 hou
15 hou
16 hou
17 hou
18 hou
19 hou
20 hou
21 hou
22 hou
23 hou
24 hou
Bus numbe
0.9
0.92
0.94
0.96
0.98
1
1.02
0 5 10 15 20 25 30
Vol age (p.u.)
Fig. 8: Dis ibu ion sys em ol age p o ile in case 2.
Bus numbe
0 5 10 15 20 25 30
1 hou
2 hou
3 hou
4 hou
5 hou
6 hou
7 hou
8 hou
9 hou
10 hou
11 hou
12 hou
13 hou
14 hou
15 hou
16 hou
17 hou
18 hou
19 hou
20 hou
21 hou
22 hou
23 hou
24 hou
0.9
0.92
0.94
0.96
0.98
1
1.02
Vol age (p.u.)
Fig. 9: Dis ibu ion sys em ol age p o ile in case 3.
I e a ions
0 10 20 30 40 50 60 70 80 90 100
0.84
0.86
0.88
0.9
0.92 PSO
JAYA
RAO3
MOF
Fig. 10: Con e gence cha ac e is ics by a ious algo i hms
in case 1.
Tab. 8: Compa ison o Ploss, MVD, and EVUC in a ious cases
by Rao 3 algo i hm.
Pa ame e Base case Case 1 Case 2 Case 3
Ploss (kW) 2811 3084.2 1080 1079.3
MVD (p.u.) 1.5816 1.6120 0.5215 0.5960
EVUC ($) – 36.3383 36.3383 25.3715
MOF – 0.8343 0.3675 0.3441
I e a ions
0 10 20 30 40 50 60 70 80 90 100
0.4
0.45
0.5
PSO
JAYA
RAO3
MOF
Fig. 11: Con e gence cha ac e is ics by a ious algo i hms
in case 2.
100
I e a ions
0 10 20 30 40 50 60 70 80 90
0.35
0.4
0.45
0.5 JAYA
RAO3
PSO
MOF
Fig. 12: Con e gence cha ac e is ics by a ious algo i hms
in case 3.
5. Conclusion
Adop ing elec ic ehicles o oad anspo is a easi-
ble way o educe g eenhouse gas emissions. Al hough,
RCS p omo es EV sales, i can ha m he dis ibu ion
©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 501