POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 18 |NUMBER: 4 |2020 |DECEMBER
DG Alloca ion in Dis ibu ion Ne wo ks wi h
Conside ing o Vol age S abili y Imp o emen
and Loss Reduc ion
Mohammad KAZEMINEJAD, Mahdi BANEJAD
Facul y o Elec ical and Robo ic Enginee ing, Shah ood Uni e si y o Technology, Shah ood, I an
[email protected], m.banejad@shah oodu .ac.i
DOI: 10.15598/aeee. 18i4.3873
Abs ac . The imp o emen o he line Load-abili y
(LL) o ol age s abili y es ablishes he main c i e ion
o dis ibu ion ne wo ks. The Dis ibu ed Gene a ion
(DG) esou ces play an impo an ole in he supply
o ac i e and eac i e powe loads, bus ol age p o iles,
and ol age s abili y in dis ibu ion sys ems. In his
pape , a new echnique has been p oposed o op imiza-
ion o he loca ion placemen and sizing o DGs, con-
side ing he Gene alized ol age S abili y Index (GSI)
o de e mine he maximum load-abili y. Also, an an-
aly ical me hod has been applied o in e he e ec s o
DGs on he dis ibu ion sys ems’ cha ac e is ics. The
s udy also conside s h ee ypes o DG modes, which a e
ol age con ol mode (PV mode), cons an powe mode
(PQ mode), and also ol age con ol mode wi h eac i e
powe cons ain (PV mode wi h VAR cons ain ). The
p oposed me hod is applied o 12-bus, modi ied 12-bus,
69-bus and 94-bus adial dis ibu ion sys ems.
Keywo ds
Dis ibu ed Gene a o , Gene alized ol age S a-
bili y Index, Loadabili y ma gin, Radial Dis i-
bu ion Ne wo ks.
1. In oduc ion
Vol age s abili y s udies p ac ically exp ess he max-
imum loadabili y o a powe sys em. In his espec ,
di e en ol age s abili y indices ha e been de eloped
wi h he aim o assessmen o he bounda y limi s
o he ol age s abili y [1], [2] and [3]. Fu he mo e,
speci ic op imiza ion app oaches ha e been sugges ed
o he loca ion o he ins alla ion o auxilia y equip-
men in acco dance wi h gi en indices and a e used
o imp o ing ol age s abili y in Radial Dis ibu ion
ne wo ks (RDS). Recen ly, se e al solu ions ha e been
discussed/p oposed ha ec i y he passi eness o RDS
by embedding elec ical sou ces wi h small capaci ies
o imp o e sys em eliabili y and ol age egula ion [4].
Such embedded gene a ion in he dis ibu ion sys ems
is called dispe sed gene a ion o Dis ibu ed Gene a-
ion (DG), which is expec ed o play an inc easing ole
in eme ging elec ical powe sys ems. I is unde s ood
ha op imum planning o DG uni s o employing in
exis ing dis ibu ion sys ems will ha e bo h economic
and echnical bene i s wi h he p e en ion o p oblems
on he eliabili y and ope a ion o he sys em [5].
Acco ding o a epo by Elec ic Powe Ins i u e,
a DG is de ined as a powe gene a ion uni p oducing
powe s spanned om “a ew kilowa s up o 50 MW”
[6]. Se e al adop ed echnologies o DG a e mic o-
u bines, small gas o hyd o u bines, uel cells, he
wind, and sola ene gy. S udies p edic ha DG will
cons i u e a signi ican pe cen age o he new gene a-
ions on he lines being ins alled [5], [6] and [7]. The
signi ican echnical bene i s o he ins alla ion DG a e
educed line losses, ol age p o ile imp o emen , in-
c eased o e all ene gy e iciency, imp o ed powe qual-
i y, enhanced sys em eliabili y, and secu i y. In o -
de o achie e he a o emen ioned bene i s, he DG’s
size and loca ion ha e been op imized using di e en
app oaches such as analy ical app oaches [8], [9] and
[10], heu is ic [11], [12] and [13], a i icial in elligence,
Gene ic Algo i hm (GA) and uzzy me hods [14], [15],
[16] and [17].
DG uni s a e mos ly connec ed a he dis ibu ion
le el due o hei locally a ailable esou ces and small
scale. The e o e, he pene a ion le el o dis ibu ed
gene a ion uni s in dis ibu ion sys ems is inc eased.
Acco dingly, connec ions o DGs o he powe sys em
a e no ably imp o ed on he powe sys ems’ s abili y
issues (i.e., angle, equency, and ol age s abili y) [18]
and [19].
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A dynamic p og amming algo i hm in [8] is p oposed
o loca e he op imal si es wi h he maximum p o -
i s a ained in he objec i e unc ion. The au ho s in
[9] p esen he analy ical app oach o he op imal lo-
ca ion o he bes ype o DG ha can enhance he
ol age s abili y o dis ibu ion sys ems. They demon-
s a ed ha using he ol age sensi i i y index and bus
pa icipa ion ac o s de i ed om con inua ion powe
low and Modal Analysis could op imize DG uni s. He-
daya i e al. [10] based hei app oach ia an objec i e
unc ion ins alled on he DG uni s, wi h a ce ain ca-
paci y in hese buses. They explained ha he impac
o DG echnologies on s a ic ol age s abili y and anal-
ysis ools o s udying ol age s abili y is necessa y.
Tabu sea ch echnique o disco e ing he op imal
si e and size o he DG uni wi h loss minimiza ion
as i s objec i e unc ion is p oposed in [11]. A me a-
heu is ic app oach using Back acking Sea ch Algo-
i hm (BSA) is p oposed o op imal si ing and sizing o
DG uni in o de o educe powe loss and imp o e he
ol age p o ile in [12]. The au ho selec ed a numbe o
nomina ed c isis buses based on he powe loss index
o educe ime consump ion. In [13], a me a-heu is ic
me hod based on Symbio ic O ganism Sea ch (SOS) is
p esen ed o de e mine he op imal numbe , loca ion
and size o DG uni s in dis ibu ion sys ems. Using
a loss sensi i i y ac o me hod o de e mine he op i-
mal loca ion o DGs, hey ha e used he SOS me hod o
calcula e he op imum size. A me hodology o combi-
na ion u ilizing he GA me hod wi h o he echniques
o op imal DG planning is desc ibed in [14]. They also
u ilize elec ical ne wo k losses and he accep able e-
liabili y le el in he objec i e unc ion. In gene al, [15]
explained he linea p og amming me hod on he GA-
based op imiza ion p ocedu es in o de o be able o
alloca e and dimension DGs, aking in o accoun he
di e en objec i e unc ions. Also, he combina ion o
GA and PSO is p esen ed o op imal loca ion and ca-
paci y o DG by aking in o accoun mul i-objec i e
cons ain s, such as ol age s abili y and powe losses
[16]. In [17], a mul i-objec i e op imiza ion me hod
is used o maximize ol age s abili y, imp o e ol -
age p o ile, and educe losses in he adial dis ibu-
ion sys em. The au ho s pe o med he op imiza ion
p og am o achie e op imal esul s, using he ba al-
go i hm based on he weigh sum me hod and a uzzy
algo i hm echnique.
Howe e , mos analyses ha e been pe o med based
on cons an powe mode (PQ mode), and he o he
modes o DG ha e been neglec ed. The au ho in [20]
was conside ing hese h ee modes o DG o analyz-
ing DG sizing by econ igu a ion echnique o imp o e
he ol age p o ile and educe powe losses using a sim-
pli ied a i icial bee colony. Also, by using BSA op i-
miza ion and a mul i-objec i e alloca ion, he op imal
placemen o mul i- ype DG uni s is es ablished in a-
dial dis ibu ion ne wo ks [21] and [22]. In o de o
iden i y he ini ial DG’s loca ions, a se o uzzy ex-
pe ules by conside ing loss sensi i i y ac o s and
bus ol ages is aken in o accoun . I is shown by sug-
ges ion o DG ype ha capabili y o supply eac i e
powe in he ne wo k, he powe ac o , ol age p o ile
and s a ic ol age s abili y a e ce ainly imp o ed.
The main con ibu ion o his pape is he in oduc-
ion o a Gene alized ol age S abili y Index (GSI) as
a new index o op imize he loca ion and sizing o DG
in o de o achie e loss educ ion and maximum load-
abili y in p ac ical ne wo ks. The me hod in his pa-
pe is based on he analysis o sweep backwa d/ o wa d
powe - low in dis ibu ion sys ems and he de e mina-
ion o he mos sensi i e buses o he ol age collapse.
By ins alling DG uni s in c i ical buses ia an i e a i e
algo i hm and an objec i e unc ion, he capaci y o
he DG is calcula ed o ind i s op imum loca ion. The
p oposed me hod is applied on a 12-bus modi ied sys-
em, 69-bus and a eal 94-bus dis ibu ion sys em, such
ha o op imize he sizing o DGs in o de o educe
he o al sys em powe loss and inc ease load-abili y o
he co esponding bus.
This pape is o ganized as ollows: in Sec. 2. , he
DG placemen me hod based on in oducing a gene -
alized ol age s abili y index is p esen ed o iden i y
he c i ical buses in he dis ibu ion; he impac o dis-
ibu ed gene a o placemen on ol age p o ile, educ-
ion o sys em losses, and ol age s abili y imp o e-
men is desc ibed in Sec. 3. , he p oposed algo i hm
o op imal sizing and si ing o DG is elabo a ed upon
in Sec. 4. In Sec. 5. , he esul s and discussions a e
compa ed wi h p e ious wo k. Finally, he conclusion
is gi en in Sec. 6. .
2. Vol age S abili y Re iew
Vol age s abili y has been de ined by he Sys em Dy-
namic Pe o mance Subcommi ee o he IEEE Powe
Sys em Enginee ing Commi ee as [23]:
“Vol age s abili y is he abili y o a sys em o main-
ain ol age so ha when load admi ance is inc eased
load powe will inc ease and so ha bo h powe and
ol age a e con ollable”.
To s udy he ol age s abili y, he e a e heo e ical
explo a ions o a simple sys em combined o wo buses,
as shown in Fig. 1. The sys em unde in es iga ion has
been modeled simply by a The enin impedance and an
elec ic sou ce, ep esen ed by Zsand Vs, espec i ely;
[24]. This equi alen ci cui can p o ide clea e ol age
s abili y analysis o de ec ion o c i ical buses in a eal
dis ibu ion sys em and is help ul o compu a ional
ime [25]. The ol age o each ecei ing dis ibu ion
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bus can be w i en as:
~
V ,i =~
Vs,i −~
Zs,i ·~
I ,i, i = 2, . . . , n, (1)
whe e Zsis he The enin impedance o he e mina ed
line o each bus om he main subs a ion, and i can
be calcula ed by he ollowing equa ions:
~
Ss−~
S =~
Zs·
~
Is
2
,(2)
~
Is=Ps+jQs
Vs∠δs∗
,(3)
whe e Ssand S a e he ans e ing appa en powe
om he main subs a ion and deli e y appa en powe
o each bus, espec i ely. nis numbe o buses. F om
Eq. (2) and Eq. (3), he equi alen impedance can be
ob ained.
~
Zs=(Ss−S )·|Vs|2
(P2
s+Q2
s).(4)
In his model, wi h inc easing load demands, he
load impedance (Z ) dec eases and I inc eases; his, in
u n, leads o a u he d op o ol age on he ecei ing
side o elec ic powe . By calcula ing I as:
~
I =Vs∠δs
Zs∠θ+Z ∠φ=
Vs
Zs
∠(δs−θ)
1 + Z
Zs
∠(φ−θ)
,(5)
whe e,

~
I =
Vs
Zs
s1 + 
Z
Zs
2
+ 2 
Z
Zs
cos (0 −(φ−θ))
.(6)
Vol age V and appa en powe S can be desc ibed
as:
|V |=|Z |·|I |,(7)
|S |=|V |·|I
∗|,(8)
Then by eplacing Eq. (6) in o Eq. (7) and Eq. (8), we
de i ed:
V =Z
Zs
Vs
"1 + Z
Zs2
+ 2 Z
Zs2
cos (β)#0.5,
(9)
S =Z
Zs
(Vs)2
Zs
"1 + Z
Zs2
+ 2 Z
Zs2
cos (β)#,(10)
whe e β=θ−φ. And θand φa e phase angles o
impedance and Zs,Z espec i ely.
Figu e 2 and Fig. 3 show hese equa ions in a g aphi-
cal o m o he esis i e and capaci i e loads. Fo gen-
e al ep esen a ion, Vsand Zs, bo h a e assumed o be
one pe uni . By his assump ion, esul s ha e implied
ha he maximum ansmi ed appea ance powe s o
loads will be achie ed when he a io Z
Zsequals one,
as shown in Fig. 3. The e o e, his a io has been con-
side ed mos ly as a c i ical poin o he de e mina ion
o he ol age collapses. In conclusion, he Z
Zs a io
mus be g ea e han one. This means ha any a bi-
a y inc ease in Zso dec ease in Z mus no lead o
ol age ins abili y o he sys em. Because, in o de o
a oid he ailu e o he mo o loads, alues o V mus
be always la ge han one; hus, any a ios o Z
Zsless
han one would be undesi able [24].
Vs
δsV
δ
Zs
θ
Rs+ jXs
P + jQ -PDG
Z
ϕ
IsI
Fig. 1: Single-line diag am o a educed sys em.
0.2 0.3 0.4 0.5 0.6
Powe (p.u.)
0.2
0.4
0.6
0.8
1
Vol age P o ile V (p.u.)
=75°
=90°
=100°
P 0
P 0-PDG
A
B
VDG
V 0
Fig. 2: Vol age-powe ela ion in he equi alen ci cui .
0 1 2 3 4 5
Load Impedance pe Sou ce Impedance a io (ZL ZS
-1)
0
0.5
1
Vol age (V ) & Appa en Powe (S )
Wi hou DG Wi h DG
Op imum
size o DG
A
E
G
CB
F
V
S
Fig. 3: Vol age and appa en powe e sus he load o he
sou ce impedance a io.
F om Fig. 2, i will be p o ed wi h injec ion PDG
he ol age p o ile is imp o ed om poin A o B, bu
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GSI =
2 [Rs(P −PDG) + XsQ ]+2 (Rs2+Xs2)h(P −PDG)2+Q 2i
|Vs|2.(11)
one ques ion a ises; wha would be he app op ia e size
o ins alling DG?
Re u ning o Fig. 3, we can obse e he load-abili y
and ol age s abili y ( a ios o Z
Zs) in he sys em de-
c ease om poin G o F by pu ing he inapp op ia e
size o DG. As shown in Fig. 3, he op imal sizing o
DG, when no educ ion is has occu ed in he ansmis-
sion powe , is a ound he poin o G o e he ansmis-
sion appea ance powe cu e. I is obse ed ha he
load-abili y o he sys em is imp o ed, and he ol age
p o ile also e o med a he han poin A. This, con-
sequen ly, is an equi alen poin o C o he sys em
ol age. Hence, i shows he bes size o DG exac ly
ela ed o bo h he ol age s abili y index and powe
losses in he sys ems.
2.1. Gene alized Vol age S abili y
Index (GSI)
Re e ing o Fig. 1, Vs∠δsand V ∠δ a e, espec i ely
sending and ecei ing end ol ages and Zs∠δ=Rs+
jXs, he line impedance be ween he wo buses.
The Zs∠φis he co esponding load impedance, wi h
φ an−1Q
P . By Subs i u ing ~
I =P +jQ
V ∠δ in
Eq. (1) and he sepa a e his in o wo eal and imagi-
na y pa s [26], he e o e:
VsV cos(δ) = |V |2+ [Rs(P −PDG) + XsQ ],
(12)
VsV sin(δ)=[Xs(P −PDG)−RsQ ],(13)
whe e (δ=δs−δ )is he di e ence in he angle be-
ween he ol ages o he sending bus (Vs)and he
ecei ing bus (V ). The alues o P ,Q a e he o-
al ac i e and eac i e powe demands by he ecei ing
bus in he dis ibu ion sys em, and de e mined om
con en ional powe low calcula ions.
Taken oge he wi h he wo sides o he squa e
Eq. (12) and Eq. (13) and elimina e δ, can each o:
|V |4+n2 [Rs(P −PDG) + XsQ ]−|Vs|2o|V |2+
+nRs2+Xs2h(P −PDG)2+Q 2io= 0,
(14)
The e o e,
|V |2=n|Vs|2−2 [Rs(P −PDG) + XsQ ]o±√∆
2,
(15)
∆ = n2 [Rs(P −PDG) + XsQ ]−|Vs|2o2
+
−4nRs2+Xs2h(P −PDG)2+Q 2io ,(16)
As a esul , o ha e a eal answe , i mus be ∆≥0.
In [26], Chak o e y and Das a e de i ed om he ol -
age s abili y index as SI om he Eq. (14), Eq. (15) and
Eq. (16). Based on his index, he buses wi h lowe
ol age ampli ude always a e close o ol age ins abil-
i y han o he buses.
Acco ding o Eq. (15), ou answe s can be ob ained
o he alues o V which only one o hem is accep able.
2 [Rs(P −PDG) + XsQ ]−|Vs|2≤
≤ −2 (Rs2+Xs2)h(P −PDG)2+Q 2i.(17)
So, by ea anging he inequali y o Eq. (17), we ob-
ain a gene alized ol age s abili y index wi h he p es-
ence o DG as ollows in he Eq. (11).
In Eq. (11), all cha ac e is ics o he ac i e and e-
ac i e powe consump ion a ec he limi s o ol age
s abili y. The s udied dis ibu ion sys em will be s a-
ble when he alue o a de ined index o each bus is
less han one (0≤GSI<1). This ol age s abili y indi-
ca o is dimensionless, and as a esul , bo h ac ual and
pe -uni alues can be used.
3. Impac o Dis ibu ed
Gene a ion (DG)
Mos o he equipmen in dis ibu ion sys ems is a -
anged based on he assump ion ha he elec ic powe
lows om he main subs a ion o he loads. Thus,
due o ou pu luc ua ions o a e e se low om dis-
ibu ed gene a ion uni s, some issues a ec dis ibu-
ion sys ems like powe losses, ol age p o ile, and e-
liabili y [5] and [27].
3.1. Vol age P o ile and Vol age
S abili y
To egula e he ol age and educe he ol age d op
in dis ibu ion sys ems, he capaci o s on he eede s
can be used. Mo eo e , he use o ap changing a
subs a ion ans o me s o ol age egula o s is also
use ul. This o m o ol age con ol assumes ha he
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powe lows om he subs a ion o he loads, bu DG
inse s e e sed powe lows, which may c ea e in e e -
ence wi h hese adi ional egula ion me hods [15] and
[17]. The e o e, unsui able DG alloca ion can cause
o e - ol ages in he sys em. On he o he hand, inap-
p op ia e DG planning can in luence ol age s abili y
and load-abili y ma gin as well. Equa ion (1) indica es
ha he educ ion o Zs·I componen is an impo -
an ac o o imp o e he ol age a he ecei ing end
by p o iding ac i e powe suppo locally using dis-
ibu ed esou ces Fig. 1.
3.2. Powe Losses
One o he impo an bene i s o DG u iliza ion is hei
imp o emen s on he ac i e powe low as well as e-
ac i e powe low. DG has a posi i e impac on line
losses due o i s p oximi y o load cen e s and should
be posi ioned in loca ions whe e hey esul in maxi-
mum educ ion o losses.
Thus, i is impo an o selec he loca ion o he DG
ha will esul in a minimum loss as well as imp o ing
he ol age p o ile. Once ha size and loca ions o
DG a e de e mined, he e is a need o check he en i e
sys em again o make su e hose s abili y cons ain s
a e no iola ed.
4. Op imal DG Placemen
Me hodology
In o de o achie e he maximum bene i s o DG, such
as imp o ing eliabili y and ol age s abili y, he op i-
mal loca ions and op imum sizes o DG uni s a e nec-
essa y o he dis ibu ion ne wo ks. Fig. 4 shows he
p oposed algo i hm as a lowcha wi h p og amming
in MATLAB en i onmen .
4.1. Placemen Algo i hm o DG
Acco ding o Fig. 4, he loca ion o he DG uni s in
he Radial Dis ibu ion Sys em (RDS) is implemen ed
based on he execu ion o an i e a ion algo i hm. Fo
inding he mos sui able loca ion o he placemen
o DG, he GSI index is used o de e mine he mos
c i ical buses in he sys em. Then, he op imum size
o DG is de e mined based on he p oposed me hod
o he nex sec ion and placed a c i ical buses one
a a ime. In each case, GSI is calcula ed again o
de e mine he lowes alue o GSI on espec i e buses.
The bus connec ed wi h DG and he lowe alue o GSI
indica es he op imum loca ion o he DG.
Read he Sys em Da a
Choose he i s c i ical bus as = 1 and SZ = 0
Ge I = 1 as i e a ion numbe
S a
Run dis ibu ion powe low; Calcula e TPL;
Calcula e GSI alues o all buses
Ranke 5 o 15 c i ical buses as K
Run dis ibu ion powe low and I = I + 1;
Calcula e GSI alues o all buses
Calcula e he Objec i e unc ion; Calcula e TPL;
Se PDG = SZ a bus k
= + 1
I = 0
Is he
las bus?
Se PDG as op imum size o bus k
S o e alues o GSI and TPL
Check he
Objec i e unc ion
( )new < ( )old
PDG = PDG + SZ
SZ(s ep size)
F om s o ed da a,
se PDG as ob imum size
in op imal loca ion o k
S op
,
1
0i
n
DG load
i
PP



No
Yes
Yes Yes
No
No
Fig. 4: Flowcha o he p oposed me hod.
4.2. P oposed Algo i hm
The main objec i e in his wo k is o op imize he size
o he DG by minimizing he To al Powe Losses (TPL)
pe pe -uni , enhancing he ol age s abili y and im-
p o ing he ol age p o iling in he gi en RDS. The
simple objec i e unc ion is o mula ed as:
= min 

Pb
i=1 |Ii|2Ri
TPLNo mal−Load
+ GSI


.(18)
Subjec ed o maximize gene a ion and ol age con-
s ain s:
0≤PDG ≤
n
X
i=1
Pload,i ,(19)
Vi,min ≤Vi≤Vi,max, i = 1,2, . . . , n. (20)
In each i e a ion, TPL =Pb
i=1 |Ii|2Riand max-
imum alue o GSI calcula e by conside ing DG selec-
ion. Also, nis he numbe o nodes; b he numbe o
b anches; Pload,iis he connec ed load in each node i;
PDG he dis ibu ed gene a ion powe ; and he accep -
able ange o ol age a each node o he RDS should
no exceed wi hin 0.9 p.u. o 1.05 p.u.
Gene ally, he ollowing s eps a e pe o med o de-
e mine he op imal size o DG:
•By pu ing DG wi h he minimum alue a he
i s node, he o al losses and GSI index is calcu-
la ed.
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Tab. 1: Pe o mance o he p oposed algo i hm on adial dis ibu ion sys ems a e DG ins alla ion in PQ mode.
Bus
sys em
Main
subs a ion
bus
P oposed algo i hm Golden sec ion
sea ch algo i hm [29]
Bus
no.
Op imum
size (MW)
Max. GSI
alue
Bus
no.
Op imum size
(MW)
12 1.00 9 h 0.2388 0.9954 9 h 0.2354
Modi ied 12 1.00 8 h 1.3942 0.9953 9 h 1.1912
69 1.00 61s 1.8259 0.9906 61s 1.8727
•By assump ion o he cons an powe ac o , he
DG size is a ied om a minimum alue o an
amoun equal o he o al powe load demands in
cons an S ep Sizes (SZ) o each bus in he i e -
a ion loop. Fo each i e a ion, he sys em losses
wi h he alue o GSI a e calcula ed o ound hei
minimum alues.
•The esul s in minimum losses and minimum ol -
age s abili y index a e aken as DG size op imum
o each bus.
•Compa ing he esul s, he lowes ou come om
all op imum DG sizing in each bus is selec ed as
he op imal loca ion.
5. Resul s and Discussion
The p oposed me hod o op imal placemen and he
sizing o DG is implemen ed in MATLAB p og amming
and es ed o se e al adial dis ibu ion ne wo ks. In
his case, i is assumed ha one DG is app op ia e o
ins all a selec i e case s udy. The a ing ac i e powe
o he dis ibu ed gene a ion uni is limi ed o he o al
ac i e powe load, and he powe ac o is uni y. The
sweep backwa d/ o wa d powe low me hod is applied
o accomplish an e icien load low and a small numbe
o i e a ion o sol ing he dis ibu ion sys em s a es.
The es sys em o 12-bus, 69-bus and 94-bus adial
dis ibu ion es sys ems a e shown in Fig. 5, Fig. 9
and Fig. 12, espec i ely.
Main
Subs a ion
1 2 3 4 5 6 7 8 9 10 11 12
Fig. 5: Schema ic diag am o 12-bus adial dis ibu ion ne -
wo k.
5.1. Modi ied 12-bus and 12-bus
Tes Sys em
To be e exp ess he e ec i eness o he p oposed al-
go i hm, a modi ied 12-bus sys em is used. In his
case, he all ac i e powe loads o 12-bus es sys em
mul iply o i e. So, he modi ied 12-bus sys em is
a adial 11 kV, he sys em wi h a o al load o
2.175 MW, 0.405 MVa , and 11 b anches, as shown
in Fig. 5. The o al eal powe loss in he sys em
is 434.112 kW, while he o al eac i e powe loss is
a 166.836 kVa when calcula ed using he load low
me hod [28]. Figu e 6 illus a es he o al powe losses
o he modi ied 12 bus es sys em when he co e-
sponding op imum DG size o each bus calcula e.
I shows ha he minimum ac i e and eac i e losses
occu by he ins alla ion o DG on bus 8.
Wi hou DG
3 4 5 6 7 8 9 10 11 12
Ac i e Powe Suppo in Bus Numbe s (-)
0
100
200
300
400
500
To al Powe Losses (-)
To al Ac i e Powe Losses (MW)
To al Reac i e Powe Losses (M a )
3
2
Fig. 6: Sys em losses p o ile o he modi ied 12-bus wi h co e-
sponding op imum DG size a each bus.
The esul s o he bes loca ion and op imum sizing
p oblems o DG, based on he lowcha and p oposed
objec i e unc ion, a e desc ibed in Tab. 1. The p o-
posed algo i hm is also compa ed wi h he Golden Sec-
ion Sea ch (GSS) me hod [29], implemen ed using he
VS&OP powe ool. The esul s clea ly show he ad-
an ages o he p oposed echnique o op imal loca ion
and sizing o DG in all h ee es sys ems wi h he loss
educ ion and imp o emen in ol age s abili y ma gin,
which will be discussed u he . Table 1 demons a es
he bes size and loca ion o DG a e 0.2388 MW, a
bus 9, which imp o es GSI alues in he en i e sys em.
I ob ains ha he esul s o he p oposed algo i hm
a e e y close o he GSS me hod.
The ole o DG in educing he losses and imp o -
ing he ol age p o ile o a modi ied 12-bus sys em is
shown in Fig. 7 and Fig. 8, espec i ely. In his case,
he o al ac i e and eac i e losses a e illus a ed by
sepa a ely pu ing he op imal size on each bus. I can
be obse ed ha he sui able loca ion o DG, in e ms
o objec i e unc ion minimizing, is a bus 8. Figu e 8
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1 2 3 4 5 6 7 8 9 10 11 12
Bus Numbe (-)
0.7
0.75
0.8
0.85
0.9
0.95
1
Vol age P o ile (pe uni )
Wi hou DG
GSS Algo i hm
P oposed Algo i hm
Fig. 7: E ec o DG on Vol age p o ile o he modi ied 12-bus
sys em.
123456789101112
Bus Numbe (-)
0
0.2
0.4
0.6
0.8
1
GSI (-)
P oposed Algo i hm
GSS Algo i hm
Wi hou DG
Fig. 8: Schema ic GSI alue o each node in a modi ied 12-bus
sys em in h ee cases.
p o es his ou come by ins alling he amoun o DG
equal o 1.1912 MW a bus 9 [29], i can be seen ha
he o he buses will go o he collapse poin (bus num-
be 4 is closed o collapse poin ); bu by pu ing he
alue equal 1.3942 MW a bus 8, i will no only de-
c ease he powe losses bu also imp o e he ol age
s abili y ma gin in he sys em. The eason o chang-
ing he loca ion o he c i ical node is non-op imal
DG ins alling and a ia ion o Z
Zs a io, desc ibed
in Sec. 2. .
5.2. The 69-bus Radial Dis ibu ion
Sys em
The second es case is a 69-bus adial dis ibu ion sys-
em on 12.66 kV, wi h se en la e al lines and a o al
load o 3.804 MW and 2.693 MVa , which is p esen ed
in Fig. 9 The p oposed algo i hm is es ed on he sec-
ond case s udy o compa ison wi h p e ious wo ks.
The ol age p o ile and e ec o op imiza ion me hods
on he GSI index a e illus a ed in Fig. 10 and Fig. 11.
Figu e 10 demons a es ha he ol age magni ude o
bus-65 has a lowe ol age le el wi hou DG ins alla-
ion, which a e op imum DG signi ican ly imp o es.
Resul s show ha s abili y indices o he whole sys-
em imp o ed a e ins alling he op imally planned
DG; while he buses c i ical o ol age ins abili y a e
mo e han nine buses a om subs a ion wi hou any
Main
Subs a ion
1 2 3 4 5 6 7 8 9 10 11 12
29
30
28
32
33
31
33
34
51
52
66
67
68
69
13 14 15 16 17 18 19
21
22
23
24
25
20
26
27
35
41
39
38
40
37
36
42 43 44 45 46
47 48 49 50 53 54 55 56 57 58 59
65
64
63
62
61
60
Fig. 9: Schema ic diag am o 69-bus adial dis ibu ion.
1 6 11 16 21 26 31 36 41 46 51 56 61 6669
Bus Numbe (-)
0.9
0.92
0.94
0.96
0.98
1
Vol age P o ile (Pe Uni )
Wi hou DG
GSS Algo i hm
P oposed Algo i hm
Fig. 10: E ec o DG on ol age p o ile o 69-bus es sys em.
0 10 20 30 40 50 60 70
Bus numbe (-)
0
0.2
0.4
0.6
0.8
1
GSI (-)
(a) P oposed algo i hm: DG size = 1.8259 MW a Bus 61.
0 10 20 30 40 50 60 70
Bus numbe (-)
0
0.2
0.4
0.6
0.8
1
GSI (-)
(b) P oposed algo i hm: wi hou DG.
Fig. 11: GSI alue o each node in he 69-bus sys em.
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Tab. 2: E ec o DG ins alla ion on powe losses in he 69-bus sys em.
Main subs a ion
ol age DG size (MW) To al losses
P(kW) Q(kVa ) Max. GSI
1.00 Wi hou DG – 225.072 102.240 0.9933
Bus 61 1.8259 83.289 40.644 0.9906
1.05 Bus 61 1.8221 83.302 40.656 0.9815
Tab. 3: E ec o main subs a ion ol age on GSI.
Bus
sys em
Main subs a ion
ol age (p.u.)
P oposed algo i hm
Bus no. Op imum size (MW) Max. GSI alue
12
1.00 -Wi hou DG 0.9987
9 h 0.2388 0.9954
1.05 -Wi hou DG 0.9985
9 h 0.2384 0.9946
Modi ied 12 1.00 8 h 1.3942 0.9953
1.05 8 h 1.3898 0.9935
69 1.00 61s 1.8259 0.9906
1.05 61s 1.8221 0.9815
Tab. 4: Op imal loca ion and size o DG in di e en modes.
Case
s udy
12 Buses Modi ied 12 Buses 69 Buses
DG
loca-
ion
P
(MW) PF
Powe
losses
(kW)
DG
loca-
ion
P
(MW) PF
Powe
losses
(kW)
DG
loca-
ion
P
(MW) PF
Powe
losses
(kW)
PQ mode
PV mode wi h
Va Cons ain
PV mode
9 0.2388 1.0 10.776 8 1.3942 1.0 59.091 61 1.8259 1.0 83.289
9 0.2793 0.95 5.937 8 1.2615 0.95 55.078 61 2.0617 0.95 38.397
8 0.2832 0.8 3.505 9 0.9374 0.8 98.922 61 1.8068 0.8 23.282
DG ins alla ion ha is demons a ed in Fig. 11(b).
I is shown ha he c i ical nodes shi ed o some p i-
ma y buses ha can be suppo ed by inc easing he
ol age magni ude o he main subs a ion.
In Tab. 2, he e ec s o DG ins alla ion on powe
losses in 69-bus es sys em illus a e ha he op imal
size alue is 1.8259 MW a bus 61. I shows ha he
o al ac i e and eac i e losses each 83.289 kW and
40.644 kVA , espec i ely. Also, by inc easing he main
subs a ion ol age o 1.05 p.u., he ol age s abili y
index imp o es in he whole sys em. Table 3 shows
he e ec o DG ins alla ion on GSI as he a ia ion
in he main subs a ion ol age. Table 3 p o es ha
he subs a ion ol age helps imp o e ol age s abili y.
The esul s show ha an inc ease o main subs a ion
ol age leads o inding he minimum size o DG by
enhancing GSI alues.
Table 4 shows he op imal DG esul s o h ee di -
e en modes on all es sys ems. I can be seen when
DG ope a es in PV mode; he lowes powe loss alue is
ob ained. I is because o he eac i e powe injec ion
in o he ne wo k by he DG uni when ope a ing in PV
mode. Mo eo e , he ol age p o ile imp o es, and he
impac |I|2·Ro educes bu he ol age s abili y index
in he sys em has become o s ess s a us. Con e sely,
by ope a ing o DG in PQ mode, he DG is modeled
as a nega i e load and supplied he eal powe o some
o he loads in he sys em. The e o e, due o he lack
o eac i e powe injec ion, he powe loss in PQ mode
is highe han PV mode in all es sys ems.
The second case ela es o he PV mode o DG wi h
lead powe ac o equal o 0.95 (i.e. injec ion eac i e
powe by DG). I can be obse ed ha he powe losses
dec ease in all sys ems. Also, in he case o PV mode
wi h 0.8 leading Powe Fac o (PF = 0.8), he DG siz-
ing educes o 0.9374 MW, speci ically in he modi ied
12-bus es sys em.
5.3. The 94-bus Radial Dis ibu ion
Sys em
The hi d es case is an ac ual Po uguese adial dis i-
bu ion sys em on 15.00 kV, wi h 94-bus and 22 la e al
lines and a o al load o 4.797 MW and 2.324 MVa ,
which is p esen ed in Fig. 12. All da a o he sys em
a e add essed in [21]. The ol age p o ile and e ec
o op imiza ion me hods on he powe losses educ ion
a e illus a ed in Fig. 13 and Tab. 5.
Figu e 13 illus a es he ol age magni ude o he
sys em wi hou and wi h conside ing o DG op imal in
wo cases. The DG ype in PV mode (PF = 0.853)
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Main
Subs a ion
1 2 3 4 5 6 7 8 9 10 11 12
34 39
40
41
42
43
44
45
46 47
48
49
50
51
67
68
69
13 14 15 16 17 18 19 20 21 22 23
74 75 76 83
84
85
86
24 25 26 27 28
88 89 94
35
36
37
38 52
53
54
55
56
57
58
59
70
71
72
73
77
78
79
80
81
82
87 90
91
92
93
60 61 62 63 64 65 66
Fig. 12: Schema ic diag am o 94-bus adial dis ibu ion sys em.
Tab. 5: Op imal loca ion and size o DG in di e en modes in 94-bus es sys em.
Case s udy
P oposed algo i hm BSAO me hod [21]
DG
loca ion
PDG
(MW) PF Powe losses DG
loca ion
PDG
(MW) PF Powe losses
P(kW) Q(kVA ) P(kW) Q(kVA )
PQ mode PV mode
wi h Va Cons ain
19 (104s.) 2.6863 1 132.47 163.87 21 (118s.) 2.3985 1 153.86 177.46
19 (130s.) 2.4944 0.853 82.97 92.70 18 (234s.) 2.3985 0.853 85.13 97.18
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 9194
Bus Numbe (-)
0.8
0.85
0.9
0.95
1
Vol age P o ile (P.U.)
Wi hou DG
DG wi h PF=1
DG wi h PF=0.853
Fig. 13: E ec o DG on ol age p o ile o 94-bus es sys em.
compa es wi h DG by PF = 1, and i shows ha he
DG in PV mode can signi ican ly imp o e he magni-
ude o bus ol ages. Table 4 desc ibes he compa ison
be ween he p oposed algo i hm and me a-heu is ic
B ain S o m Op imiza ion Algo i hm (BSOA) ech-
nique. The esul s show ha he alues ob ained om
he p oposed algo i hm o he loca ion and size o DG
a e e y close o he esul s o he BSOA. By selec -
ing c i ical buses nomina ed o ol age ins abili y om
GSI o DG loca ion algo i hm, he op imal size o DG
could be apidly calcula ed. In addi ion, 15 nomina ed
buses in 94-bus dis ibu ion sys em a e 11, 12, 13, 14,
15, 16, 17, 18, 19, 52, 10, 53, 9, 55, and 8.
6. Conclusion
This pape p oposes a eliable echnique o he de e -
mina ion o loca ion and sizing o DGs. This new ana-
ly ical app oach is sui able o ol age s abili y analysis
and can be applied o eal sys ems. The pe o mance
o he gene al ol age s abili y indica o o inding he
op imal placemen and op imum sizing o DG is ap-
plied o achie e adequa e esul s in all adial dis ibu-
ion sys ems. The c i ical buses o DG placemen a e
selec ed by gene alized ol age s abili y index. Th ee
modes o DG (PQ mode, PV mode and PV mode wi h
VAR cons ain ) a e applied o he s udy o he e ec s
o eac i e powe injec ion in o he sys em, especially
o he educ ion o powe losses and imp o emen o
he ol age p o ile. The obse ed ou comes well jus i y
usage o he algo i hm o he pu pose o imp o emen
in ol age p o ile, ol age s abili y ma gin, and educ-
ion o powe losses.
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