POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 3 |2023 |SEPTEMBER
Coo Bi d Beha io -Based Op imiza ion Algo i hm
Fo Op imal Placemen O Thy is o Con olled
Se ies Compensa o De ices In T ansmission Powe
Ne wo ks
Anh Tuan NGUYEN1, Chi Kien LE2, Minh Tan PHAN3T ung Thang NGUYEN3
1Ph.D. S uden , Facul y o Elec ical and Elec onics Enginee ing, Ho Chi Minh Ci y Uni e si y o Technology
and Educa ion, 01 Vo Van Ngan s ee , Thu Duc Dis ic , 700000, Ho Chi Minh ci y, Vie nam
2Facul y o Elec ical and Elec onics Enginee ing, Ho Chi Minh Ci y Uni e si y o Technology and
Educa ion, 01 Vo Van Ngan s ee , Thu Duc Dis ic , 700000, Ho Chi Minh ci y, Vie nam
3Powe 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, 19 Nguyen Huu Tho s ee , Tan Phong wa d, Dis ic 7, 700000 Ho Chi Minh Ci y, Vie nam
uanna.ncs@hcmu e.edu. n, kienlc@hcmu e.edu. n, phanminh[email p o ec ed],
nguyen[email p o ec ed]
DOI: 10.15598/aeee. 21i3.5244
A icle his o y: Recei ed May 25, 2023; Re ised Jul 25, 2023; Accep ed Aug 21, 2023; Published Sep 30, 2023.
This is an open access a icle unde he BY-CC license.
Abs ac . This s udy p esen s he new applica ion
o Coo bi d beha io -based op imiza ion algo i hm
(COOTBA) o op imal placemen o Thy is o Con-
olled Se ies Compensa o (TCSC) de ices in an
IEEE 30-node ansmission powe ne wo k wi h h ee
single objec i es, including uel cos , powe loss, and
ol age de ia ion. COOTBA is implemen ed o he
sys em wi h one case wi hou TCSC de ices and h ee
o he s wi h TCSC. COOTBA can each smalle cos
and loss han p e ious algo i hms by om 0.04% o
3.78%, and om 6.7% o 40.3% in he i s case wi h-
ou TCSC. In he second case wi h TCSC, COOTBA
can each smalle cos han o he s by om 0.008% o
0.66%. In addi ion, he compa isons o esul s om
COOTBA in he h ee cases wi h TCSC indica e ha
TCSC should be op imized o bo h loca ion and eac-
ance, and he limi a ion o TCSC de ices should be
high enough. Thus, COOTBA is an e ec i e algo i hm
o op imizing TCSC de ices on ansmission powe
sys ems.
Keywo ds
Coo bi ds, Thy is o con olled se ies compen-
sa o , ansmission powe ne wo k, uel cos ,
powe loss, ol age de ia ion.
1. In oduc ion. P oblem
De ini ion
A powe sys em’s mos basic elec ic pa s a e powe
plan s, ansmission g ids, dis ibu ion g ids, and loads
[1]. Typically, he wo p ima y componen s o powe
plan s a e gene a o s and ans o me s, whe eas ans-
mission g ids and dis ibu ion g ids a e mainly com-
p ised o lines, ans o me s, buses, and loads. T ans-
mission and dis ibu ion g ids ha e almos he same
elec ic componen s bu di e en sizes. G ea e com-
ponen size is o ansmission g ids, bu a smalle size
is o dis ibu ion g ids. Gene a o s and ans o me s
a powe plan s a e in cha ge o p oducing and ans-
mi ing elec ici y o ansmission lines [2]. Dis ibu-
ion lines ecei e elec ici y om ansmission lines and
p o ide elec ici y o loads. T ansmission lines play a
e y impo an ole in powe sys ems since hey ecei e
a e y high powe om powe plan s and supply he
powe o dis ibu ion powe ne wo ks. I he ans-
mission lines canno wo k s ably, powe gene a ed by
powe plan s canno be p o ided o dis ibu ion lines
and loads [3]. So, op imal powe low (OPF) o ans-
mission powe ne wo ks has become a signi ican p ob-
lem in powe sys ems.
The con en ional OPF p oblem has a ac ed a as
numbe o s udies o eaching di e en objec i e unc-
c
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Tab. 1: Nomencla u e
NT Gs Numbe o he mal gene a o s in exis ing powe sys em
α1n,α2n,α3nFuel coe icien s o he mal gene a o n
P Gn,QGnAc i e and eac i e powe gene a ed by he he mal gene a o n
CDab Conduc ance o he ansmission line a−b
Uaand UbVol age ampli udes a node aand node b
NND Numbe o nodes o he gi en ansmission ne wo k
P Gls
n,P Ghs
nThe lowes and highes ac i e powe gene a ion o he n h he mal gene a o
QGls
n,QGhs
nThe lowes and highes eac i e powe gene a ion o he n h he mal gene a o
SCls
a,SChs
aThe lowes and he highes eac i e powe gene a ion o he shun capaci o s a node a
Uls
load,Uhs
load The lowes and he highes ol age magni udes o load a he load node d
Uls
n,Uhs
nThe lowes and he highes ol age magni udes o he he mal gene a o n
NNLS Numbe o load nodes
T Sls ,T Shs The lowes and he highes ap se ing alue o all ans o me s
T SpTap se ing alue o he ans o me p
N ms T ans o me numbe
APkAppa en powe ansmi ed h ough he b anch k
AP hs
kThe highes appa en powe o he b anch k
NB s B anch numbe
Xls
T CSC ,Xhs
T CSC The lowes and highes eac ance alues o TCSC de ices
XT CSC,q The eac ance o he TCSC q
NT CSC The numbe o TCSC
B T CSC,q The b anch wi h he q h TCSC
dn0÷1A andom numbe wi hin one and ze o
ions such as elec ic gene a ion uel cos educ ion [4]
and pollu ed emission educ ion [5] o he mal powe
plan s (ThPPs), and ol age p o ile enhancemen [6].
When he end o using enewable ene gies becomes
popula , wind and sola pho o ol aic powe plan s a e
conside ed wi h ThPPs as majo powe sou ces in
ansmission powe ne wo ks [7]. Howe e , a big p ob-
lem o ansmission powe ne wo ks is he con ingency
o ansmission lines once powe plan s upg ade hei
powe o loads need mo e powe [8]. The addi ional in-
s alla ion o he mal gene a ing uni s, he ins alla ion
o new wind powe plan s and new sola pho o ol aic
powe plan s, he addi ional ins alla ion o wind u -
bines o sola pho o ol aic a ays in exis ing enewable
powe plan s, o changes in mode n echnologies a e
he eason ha ansmission lines cope wi h he s a us
o o e cu en [9].
The key mo i e o OPF is o ind he op imal ope a-
ion plan o gene a ing uni s and o he elec ic de ices
o cu ing he elec ic p oduc ion cos and ene gy loss
and enhancing powe quali y such as equency, ol -
age, and high eliabili y while sa is ying all cons ain s
om hese componen s [10]. In simula ing he OPF
p oblem, hanks o he aid o so wa e, pa ame e s o
elec ic componen s a e modeled as con ol a iables
and dependen a iables in which con ol a iables and
dependen a iables a e, espec i ely, ega ded as in-
pu da a and esul s o he New on-G aphson me hod
[11]. I he wo ypes o a iables a e wi hin allowable
limi s, he e is a alid solu ion o powe low. How-
e e , an op imal solu ion mus sa is y all cons ain s
and ha e a good objec i e unc ion [12]. Conside ing
he se ious issue o con ingency, inding solu ions o
he OPF p oblem ake mo e challenges, o e en he e
a e no alid solu ions ound by e y s ong me hods
o he cases. Combining powe low me hods such
as Gaussidel/New on-G aphson and he me aheu is ic
algo i hms is he mos e ec i e end [13]-[15]. Ma h-
powe was un o calcula ing powe lows; meanwhile,
an imp o ed gene ic algo i hm [13], imp o ed cuckoo
sea ch [14], and Jelly ish sea ch algo i hm (JSA) [15]
we e success ully applied o inding con ol a iables.
Howe e , i powe plan s mus p oduce high powe and
ansmi o loads, hese e y high-pe o mance me h-
ods also ail o ind easonable solu ions.
De i ed om he unexpec ed issues, Flexible Al e -
na ing Cu en T ansmission Sys em (FACTSs) com-
ponen s ha e been sugges ed o be used in powe sys-
ems. Se e al FACTS de ices ha e been applied o
minimize ac i e powe loss, educe ol age d op, and
a oid con ingency, such as S a ic Va Compensa o
(SVC) [16], s a ic synch onous compensa o (STAT-
COM) [17], Thy is o Con olled Se ies Compensa o
(TCSC) [1], [18]-[24], Uni ied Powe Flow Con olle
(UPFC) [25, 26], Thy is o Con olled Phase-Angle
Regula o (TCPAR) [25], he combina ion o TCPAR
and TCSC [27]-[30], and he combina ion o SVC and
TCSC [31]. Se e al s udies ha e conside ed he same
FACTs, bu di e en me aheu is ic algo i hms we e
used. The s udy [1] was a e y ea ly s udy abou
TCSC by p oposing a hyb id Simula ed annealing al-
go i hm and Tabu sea ch algo i hm (SAA/TSA) in
2002. The s udy has also implemen ed Gene ic algo-
i hm (GA), Tabu sea ch algo i hm (TSA), and Simu-
la ed annealing algo i hm (SAA) o in es iga ing he
solu ions ob ained by SAA/TSA. The s udy [16] has
sol ed a mul iobjec i e unc ion, and i has used A
mul iobjec i e biogeog aphy-based op imiza ion algo-
c
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i hm (MOBBO). The s udy [17] also op imized he
ins alla ion o STATCOM and UPFC o educe cu -
en on ansmission lines. Pa icle swa m op imiza-
ion (PSO) [18], imp o ed an lion algo i hm (IALA)
[19], and Gene ic algo i hm (GA) [20, 21] we e e-
spec i ely applied o op imizing TCSC in ansmis-
sion powe ne wo ks. Two imp o ed e sions o pa -
icle swa m op imiza ion we e espec i ely applied in
he s udies [22, 23], including Cons ic ion ac o -based
pa icle swa m op imiza ion algo i hm (CF-PSO) [22],
and challenge s and aging leade algo i hm-based pa -
icle swa m op imiza ion (CALA-PSO) [23]. CF-PSO
was a popula imp o ed e sion o PSO ha has been
applied o many op imiza ion p oblems in enginee -
ing. Meanwhile, CALA-PSO was i s de eloped in
he s udy [23]. The s udy [24] has de eloped a hy-
b id ha mony sea ch algo i hm and di e en ial e olu-
ion algo i hm (HAS/DE) o he OPF p oblem wi h
TCSC; howe e , he s udy has no implemen ed single
algo i hms, such as ha mony sea ch algo i hm and Di -
e en ial e olu ion o he same p oblem in he s udy
[24]. The s udy [25] has sugges ed using an imp o ed
g asshoppe algo i hm (IGRA) o op imize he ins al-
la ion o ei he UPFC o TCPAR in he ansmission
powe ne wo k. Di e en algo i hms, such as hyb id
PSO [27], k ill he d algo i hm (KHA) [28], symbio ic
o ganisms sea ch algo i hm (SOSA) [29], and nondomi-
na ed so ing gene ic algo i hm-II (NSGA-II) [30], ha e
been applied o op imizing TCPAR and TCSC simul-
aneously. The s udies ha e indica ed ha he numbe
o FACTs de ices had a clea impac on he imp o e-
men o he ol age o loads, ene gy loss educ ion, and
educ ion o elec ic gene a ion cos s. GA, di e en ial
e olu ion (DE), and pa icle swa m op imiza ion ha e
been applied o op imizing bo h SVC and TCSC. SVC
could compensa e o eac i e powe a nodes ins alled
wi h SVC; meanwhile, TCSC could educe a pa o
a pa ame e o ansmission lines. So, he h ee al-
go i hms ha e imp o ed he echnical indica o s o
he applied sys ems, bu hei e ec i eness was di -
e en . In gene al, hese s udies ha e applied di e en
FACTs in ansmission powe sys ems o echnical and
economic ac o s. The esul s we e much be e han
hose o base ansmission powe sys ems wi hou he
FACTs de ice.
In his s udy, we apply an e ec i e me aheu is ic
algo i hm, Coo bi d beha iou -based op imiza ion al-
go i hm (COOTBA) o he OPF p oblem wi h he
placemen o TCSC de ices in a ansmission powe
ne wo k wi h 30 nodes. COOTBA has been p o en o
be e y e ec i e o placing sola gene a o s in dis ibu-
ion sys ems [31, 32]. The s udy [33] applied COOTBA
o an op imal powe low conside ing load nodes wi h
aluminum plan s o educing emission and powe loss.
COOTBA was p o ed o be success ul o he p oblem
and o be mo e e ec i e han glowwo m swa m algo-
i hm (GWSA) o all s udy cases. The pe o mance
o COOTBA was p o ed o be high o op imiza ion
p oblems in ansmission and dis ibu ion ne wo ks, al-
hough i has no been shown o be be e han all ex-
is ing me hods. So, COOTBA is applied in he s udy
o he OPF p oblem wi h he p esence o TCSC. The
no el y o he s udy is as ollows:
•Find he maximum limi o TCSC o he high-
es cos and loss educ ions, and he bes ol age
imp o emen .
•Compa e he pe o mance o COOTBA and p e i-
ous algo i hm in [34] in inding op imal loca ions
o TCSC.
The con ibu ion o he s udy a e as ollows:
•Reach smalle elec ici y gene a ion cos s, smalle
powe losses and be e ol age p o ile han p e i-
ous s udies.
•Find he mos op imal solu ions o TCSC in e-
ducing elec ici y gene a ion cos and powe loss,
and imp o ing ol age.
•Find a sui able algo i hm, COOTBA, o he
placemen o TCSC in ansmission powe ne -
wo ks.
2. P oblem desc ip ion
2.1. Objec i e unc ions
This s udy conside s h ee objec i e unc ions (OFs)
while e alua ing he con ibu ions o TCSC in ans-
mission powe ne wo ks, including o al uel cos min-
imiza ion (TFC) [35], ac i e powe loss minimiza ion
(APL) [36], and ol age de ia ion minimiza ion (VD)
[12]. Thei ma hema ical exp essions a e, espec i ely,
p esen ed as ollows:
TFC =
NT Gs
X
n=1
α1n+α2n.PGn+α3n.PG2
n(6S/h),(1)
APL =
NND
X
a=1
NND
X
b=1,b6=a
CDab.(U2
a+U2
b
−2.Ua.Ub.cos φab)(MW),(2)
V D =
NND
X
a
|Ua−UST R|(Pu).(3)
In Equa ion (2), ϕab is ob ained by using ϕab =ϕa−
ϕbwhe e ϕaand ϕba e ol age phase angels a node
aand node 4. In Equa ion (3), UST R is he s anda d
ol age alue, and i s alue is se o a a ed alue o
1.0 pu.
c
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Fig. 1: A simple illus a ion o he TCSC ins alled in he spe-
ci ic ansmission line.
2.2. The desc ip ion o TCSC
Thy is o con olled se ies compensa o (TCSC) is one
o he FACTs de ices ha can be ins alled in ansmis-
sion powe ne wo ks o economic and echnical a -
ge s such as powe gene a ion, ol age d op educ ion,
powe loss educ ion, e c. In a ansmission line wi h
he p esence o TCSC, he line model is plo ed in Fig-
u e 1 [37].
The eac ance model o he line a e ins alling
TCSC is ob ained by:
X0
ab =Xab −XT CSC .(4)
In addi ion, he ans e conduc ance and he suscep-
ance o he line a−ba e ins alling a TCSC de ice
a e ecalcula ed by [38]:
CDT CSC
ab =Rab
R2
ab + (Xab −XT CSC )2,(5)
STT CSC
ab =−(Xab −XT CSC )
R2
ab + (Xab −XT CSC )2,(6)
whe e CDT CSC
ab and STT CSC
ab a e, espec i ely, he
conduc ance and he suscep ance o he line a−ba e
he TCSC de ice is placed on he line; Raband Xaba e,
espec i ely, he esis ance and eac ance o he ans-
mission line a−bbe o e ins alling TCSC; XT CSC is
he eac ance o he TSCS de ice placed on he ans-
mission line a−b. No e ha CDT CSC
ab =CDT CSC
ba
and STT CSC
ab =STT CSC
ba a e used as conside ing he
ac o s in ansmission powe ne wo ks.
2.3. Cons ain s o OPF p oblem
wi h TCSC
1) Equali y cons ain
In OPF p oblem, he ac i e and eac i e powe balance
cons ain s a each node a(whe e a= 1, . . . , NND)
mus be sa is ied as shown in he ollowing exp essions
[39]:
PGa−PDa=Ua
NNo
X
b=1
Ub"CDT CSC
ab .cos(φab)
+STT CSC
ab .sin(φab)#,(7)
QGa+SCa−QDa=Ua
NNo
X
b=1
Ub"CDT CSC
ab .cos(φab)
−STT CSC
ab .sin(φab)#,
(8)
whe e PGaand QGba e, espec i ely, he ac i e and
eac i e powe injec ed a node aby he mal gene a-
o s; PDaand QDba e, espec i ely, he ac i e and
eac i e powe demands o loads a node a; and SCa
is he eac i e powe supplied by he eac i e powe
compensa o s connec ed a node a.
2) Inequali y cons ain s
These cons ain s a e conside ed o sa is y ope a ion
limi s o elec ic componen s in he ansmission powe
ne wo ks, such as he mal gene a o s, shun capaci o s,
loads, ans o me s, ansmission b anches, and addi-
ionally added TCSC de ices. The cons ain s a e ex-
p essed as ollows [1],[37],[40]:
PGls
n⩽PGn⩽PGhs
n,(9)
QGls
n⩽QGn⩽QGhs
n,(10)
SCls
a⩽SCa⩽SChs
a;a= 1, ..., NND,(11)
Uls
load ⩽Uload ⩽Uhs
load;load = 1, ..., NNLs,(12)
Uls
n⩽Un⩽Uhs
n;n= 1, ..., NT Gs,(13)
TSls
p⩽TSp⩽TShs
p;p= 1, ..., NT ms,(14)
APk⩽APhs
k;k= 1, ..., NB s,(15)
Xls
T CSC ⩽XT CSC,q ⩽Xhs
T CSC ;q= 1,2, .., NT CSC ,
(16)
1⩽B T CSC,q ⩽NB s;q= 1,2, ..., NT CSC .(17)
3. Coo bi d beha iou -based
op imiza ion algo i hm
(COOTBA)
COOTBA is also a me aheu is ic algo i hm based on
popula ion and andomiza ion. COOTBA is a ma he-
ma ical model exp essing he beha io s o an a e age-
size wa e bi d species, Coo s, while sea ching o ood.
Coo s end o ga he in a g oup wi h many indi idu-
als, and hey mo e o ind ood oge he . Based on
he amoun o ood ound, all coo s a e classi ied in o
a membe g oup and a leade g oup. COOTBA has
a di e en cons uc ion om o he me aheu is ic al-
go i hms due o he special cha ac e is ic o he coo
bi d species. COOTBA also needs a andomly ini ial
solu ion se , and hen he solu ion se can be imp o ed
based on wo echniques. The ini ial solu ion se and
i s upda e p ocess a e p oduced and implemen ed as
ollows:
The ini ial solu ion se has an uppe bound and a
lowe bound, Boundup and Boundlow, in which he
bounds con ain he maximum and minimum alues o
con ol a iables in a conside ed op imiza ion p ob-
lem, espec i ely. Each solu ion is ep esen ed o a
c
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coo in he swa m, and i is modeled by Coo c(whe e
c= 1, . . . , SP o, and SP o is he alue o popula ion).
Each Coo cis p oduced wi hin he ange [Boundlow,
Boundup]. Each solu ion is exp essed by MCoo ain a
low-quali y se and LCoo bin a high-quali y se . The e
a e Nlow and Nhigh solu ions in he wo se s, espec-
i ely. COOTBA upda es new solu ions o he wo
se s as ollows:
3.1. Upda ing solu ions o he
low-quali y se
In he low-quali y solu ion se , COOTBA conside s
h ee condi ions o upda e cu en solu ions acco d-
ingly. The cu en and new solu ions a e se o
MCoo aand MCoo new
a, espec i ely. One ou o he
ollowing equa ions is applied o p oduce he new so-
lu ions.
MCoo new
a=MCoo a+SF1.(Coo d −MCoo a),
(18)
MCoo new
a=SF2.(MCoo a+MCoo a0,)(19)
MCoo new
a=LCoo d +SF3.(LCoo d −MCoo a),
(20)
Whe e SF1,SF2, and SF3a e scaling ac o s gi en
in Appendix A; MCoo a0is he closes solu ion o
MCoo a;MCoo d is a newly gene a ed solu ion
wi hin he ange [Boundlow,Boundup]; and LCoo d
is a andom solu ion in he high-quali y se .
3.2. Upda ing solu ions o he
high-quali y solu ion se
COOTBA uses wo o mulas o sea ch new solu ions
in he solu ion space, ei he Equa ion (21) o Equa ion
(22). In he equa ions, LCoo band LCoo new
ba e he
b h cu en and new solu ions in he popula ion. To
selec one ou o he wo equa ions, a andom numbe
wi hin ze o and one is p oduced and compa ed o 0.5.
I he numbe is smalle han 0.5, Equa ion (21) is
applied. O he wise, Equa ion (22) is selec ed. The
wo equa ions a e as ollows:
LCoo new
b=Coo bes +SF4(Coo bes −LCoo b)
(21)
LCoo new
b=−Coo bes +SF4(Coo bes −LCoo b)
(22)
whe e Coo bes is he bes solu ion in he high-quali y
se ; and SF4is a scaling ac o gi en in Appendix A.
3.3. Applica ion o COOTBA o
OPF p oblem wi h TCSC
In his s udy, COOTBA is esponsible o inding con-
ol pa ame e s o he con en ional OPF p oblem and
TCSCs’ pa ame e s. Sec ion 2 has men ioned hese
pa ame e s. The con en ional OPF p oblem’s pa am-
e e s mus sa is y cons ain s (9), (11), (13) and (14)
meanwhile TCSCs’ pa ame e s mus sa is y cons ain s
(16) and (17). A e ha ing hese pa ame e s, Ma h-
powe p og am is un o eaching dependen pa ame-
e s o he OPF p oblem, which can sa is y cons ain s
(10), (12) and (15). I hese dependen pa ame e s a e
no allen in o he limi s, hey mus be ined o ind-
ing penal y e ms. Finally, objec i e unc ions in Eqs.
(1)-(3) can be ob ained.
The lowcha o applying COOTBA o he p oblem
is p esen ed in Figu e 2.
4. Nume ical esul s
In he sec ion, COOTBA is implemen ed o he IEEE
30-node ansmission powe sys em o op imizing he
placemen o TCSC de ices wi h h ee di e en single
objec i e unc ions, including cos , ac i e powe loss,
and ol age de ia ion. In addi ion, COOTBA is also
implemen ed o he base sys em wi hou TCSC o
he same objec i es. The sys em is plo ed in Figu e
2, and i s da a can be aken om [41]. The limi a-
ions o eac ance o TCSC a e om 0.0 o 0.02 pu
[1]. Fo he case o using a sui able loca ion o TCSC
wi hou using he sea ch om COOTBA, he sole lo-
ca ion ob ained by implemen ing he loss sensi i i y
index me hod [34] is inhe i ed o be b anch 3-4. The
h ee s udy cases a e exp essed in de ail as ollows:
•Case 1: COOTBA is implemen ed o he sys em
wi hou TCSC de ices. Fo his case, SP o and
MI e a e, espec i ely, se o 20 and 200 by ex-
pe imen
•Case 2: Line 3-4 is employed o placing TCSC.
COOTBA is implemen ed o inding pa ame e s
in he powe sys em and eac ance o TCSC. Fo
his case, SP o and MI e a e, espec i ely, se o
40 and 200 by expe imen .
•Case 3: COOTBA is implemen ed o inding pa-
ame e s in he powe sys em, and loca ion and
eac ance o TCSC. Fo his case, SP o and MI e
a e, espec i ely, se o 40 and 500 by expe imen .
•Case 4: Simila o Case 3, bu he maximum limi
o TCSC is one pu ins ead o 0.02 pu as in Case
3. The se ings o SP o and MI e a e simila o
hose o Case 3.
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POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 3 |2023 |SEPTEMBER
Fig. 2: Applica ion o COOTBA o OPF p oblem wi h TCSC
de ices.
Fig. 3: The IEEE 30-node sys em.
To each objec i es in he ou cases abo e,
COOTBA is implemen ed o 50 ial uns. Ma lab
so wa e wi h e sion 2018b is used o code he p o-
g am, and a pe sonal compu e wi h he p ocesso o
2.4 GHz and 8 GB o RAM is p o ided o ins alling
he Ma lab so wa e.
4.1. Resul compa ison o 3 cases
Table 2 p esen s he bes uel cos , he bes powe loss,
and he bes ol age de ia ion o he h ee cases abo e
om 50 success ul uns o each case. In gene al, Case
3, wi h op imal loca ion and pa ame e o TCSC, is
he bes o op imizing he conside ed objec i es, cos ,
loss, and ol age. The base sys em wi hou TCSC in
Case 1 is he wo s case o educing uel cos and im-
p o ing ol age, bu Case 2 is he wo s o educing
powe loss. In de ail, he h ee alues a e espec i ely
$799.378, 2.946 MW and 0.142 Pu in Case 1, $799.314,
2.954 MW and 0.140 pu in Case 2, and $799.207, 2.929
MW, and 0.138 pu in Case 3. A s ange issue is ha
Case 2 wi h TCSC a he p ede e mined line 3-4 su -
e s a highe powe loss han he base sys em o Case
1 by (2.954-2.946=0.008 MW). This unexpec ed esul
indica es ha he placemen o TCSC on ansmission
line 3-4 is ine ec i e in educing powe loss. Case 3
inds he ansmission line 2-5 o TCSC, and his so-
lu ion is mo e e ec i e han Case 2 by eaching a loss
educ ion o (2.954-2.929=0.025 MW).
Taking a look a he eac ance o TCSC can see ha
Case 2 needs a 0.0176-pu, 1.52e-06-pu, and 0.0067-pu
TCSC bu Case 3 needs he maximum eac ance o 0.02
pu o all h ee s udy cases. Case 2 wi h powe loss ob-
jec i e needs app oxima ely ze o eac ance o TCSC
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Tab. 2: Summa y o he bes esul s om h ee s udy cases by
unning COOTBA
S udy Resul Objeci e unc ion
Case Fuel cos
($)
Powe
loss
(MW)
Vol age
de ia ion
(pu)
Case 1 Objec i e
alue
799.378 2.946 0.142
Case 2 Objec i e
alue
799.314 2.954 0.140
XT CSC
(Pu)
0.0176 1.52e-06 0.0067
Case 3
Objec i e
alue
799.207 2.929 0.138
XT CSC
(Pu)
0.02 0.02 0.02
Loca ion
o TCSC
Line 2-5 Line 2-5 Line 1-18
wi h he alue o 1.52e-06 pu. The op imal ansmis-
sion line o placing a TCSC de ice is line 2-5 o cos
and loss objec i es and line 18-1 o he ol age ob-
jec i e. I is no ed ha i he TCSC de ice wi h a
highe maximum limi o 0.02 Pu, he e ec i eness o
he TCSC de ice is g ea e han Case 3. In ac , Case
4 is implemen ed, and i s esul s a e p esen ed in Table
3. I can be seen clea ly ha he cos , loss, and ol age
de ia ion o Case 4 a e be e han hose o Case 3 in
Table 2 by $0.08, 0.033 MW, and 0.026 pu. Case 4
uses he same line 2-5 as Case 3 o cos op imiza ion
bu di e en lines o loss and ol age de ia ion objec-
i es. Line 27-28 and line 10-20 a e employed by Case
4 ins ead o line 2-5 and line 1-18 o loss and ol -
age de ia ion. The eac ance o TCSC is also di e en
be ween Case 3 and Case 4. The eac ance alues o
Case 4 a e, espec i ely, 0.0497, 0.2620, and 0.3998 pu,
while hose o Case 3 a e 0.02.
Tab. 3: Summa y o he bes esul s om Case 4 by unning
COOTBA
Resul Objeci e unc ion
Cos ($) Loss (MW) Vol. De .
(pu)
Objec i e
alue
799.127 2.896 0.116
XTCSC
(Pu)
0.0497 0.2620 0.3998
Loca ion o
TCSC
Line 2-5 Line 27-28 Line 10-20
The uel cos o gene a o s is plo ed in Figu e 4 and
Figu e 5 o compa e Case 2 and Case 1, and Case 3
and Case 1. The wo igu es show ha he same gen-
e a o s ha e a e y small cos di e ence. In addi ion,
he sa ing cos o each gene a o in Case 2 and Case
3 is also calcula ed as compa ed o Case 1 and plo ed
by using blue a eas in he wo igu es. Gene a o s 1
and 5 o Case 2 and Case 3 use smalle cos han hose
o Case 1 by $0.65 and $2.03, and $0.68 and $0.95 bu
o he gene a o s 2, 3 and 4 o Case 2 and Case 3 use
highe cos han hose o Case 1. Gene a o 6 o Case
Fig. 4: Compa ison o gene a o uel cos be ween Case 2 and
Case 1.
Fig. 5: Compa ison o gene a o uel cos be ween Case 3 and
Case 1.
2 and Case 3 ha e he same cos as Case 1. The esul s
indica e ha he placemen o TCSC on ansmission
line 3-4 in Case 2 and ansmission line 2-5 in Case 3
changed he powe gene a ed by gene a o s and led o
cos educ ion.
The con e gence p ocesses o each he bes cos o
Cases 1 and 2, and Cases 3 and 4 a e gi en in Figu e 6
and Figu e 7. The igu es show ha COOTBA always
each be e cos in Case 2 han Case 1, and in Case
4 han Case 3 a he same i e a ion. A he inal i e -
a ion, he cos s o Case 2 and Case 4 a e espec i ely
be e han hose o Case 1 and Case 3.
The ol age o 30 nodes o he ol age de ia ion
objec i e is plo ed in Figu e 8 o compa ing Case 2
and Case 1, and in Figu e 9 o compa ing Case 3 and
Case 1. The wo igu es indica e ha he powe sys em
in he h ee s udy cases can sa is y ol age cons ain s.
Nodes ha e a ange o ol age om highe han 0.97
pu and smalle han 1.04 pu, in which he limi s o
ol age a e om 0.95 o 1.05 pu. The ol age di e ence
a nodes is no clea be ween Case 2 and Case 1, and
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Fig. 6: Con e gence p ocesses o each he bes cos o Cases
1 and 2.
Fig. 7: Con e gence p ocesses o each he bes cos o Cases
1 and 2.
Case 3 and Case 1. Clea ly, COOTBA is e y use ul in
op imizing he con ol pa ame e s o he base sys em
in Case 1. So, he use o TCSC in Case 3 canno each
much be e esul s han in Case 1. To cla i y he
e ec i eness o COOTBA, he ollowing sec ion will
compa e he pe o mance o COOTBA wi h p e ious
me hods o s udy cases.
4.2. Compa ison o pe o mance
be ween COOTBA and o he s
COOTBA is compa ed o o he me hods o Case 1
wi hou TCSC o cos and loss objec i es in Table
4. COOTBA is compa ed o adap i e PSO (APSO)
[42], cons ic ion ac o -based PSO (CF-PSO) [43],
imp o ed CF-PSO (ICF-PSO) [43], imp o ed g oup
sea ch op imiza ion algo i hm (IGSOA) [44], con en-
ional Honey Bee Ma ing algo i hm (CHBMA) and
imp o ed o CHBMA (IHBMA) [45], mul i-objec i e
ma hema ical p og amming algo i hm (MOMPA) [46],
Fig. 8: Vol age o nodes in Case 1 and Case 2.
Gaussian ba e bone impe ialis compe i i e op imiza-
ion algo i hm (GBBICOA), modi ied social spide al-
go i hm (MSSA) [48], imp o ed e olu ion p og am-
ming algo i hm (IEPA) [49], eaching and lea ning
based algo i hm (TLBA) [50] and hyb id TLBA, and
impe ialis compe i i e algo i hm (HTLBA-ICA) [50].
The cos compa ison shows ha COOTBA is supe io
o many algo i hms o cos objec i e and loss objec-
i es, excluding ICF-PSO [43] and MSSA [48]. Fo he
cos compa ison, COOTBA has ound a smalle cos
han o he s, om $0.292 (compa ed o CF-PSO[43])
o $31.472 (compa ed o GBBICOA [47]), co espond-
ing o 0.04% o 3.78%. Fo loss compa ison, COOTBA
has ound a smalle loss han o he s, om 0.21 MW o
1.991 MW, co esponding o om 6.7% o 40.3%. How-
e e , COOTBA is wo se han MSSA and ICF-PSO due
o a highe cos o $0.038. So, COOTBA is also a highly
e ec i e algo i hm, and i s esul s om TCSC de ice
placemen a e highly eliable.
Tab. 4: Compa ison o cos and powe loss om Case 1
Me hod SAA/TSA [1] APSO [42]
Cos ($) 804.7837 801.97
Me hod GBBICOA [47] MSSA [48]
Cos ($) 830.85 799.34
Me hod IGSOA [44] CHBMA [45]
Cos ($) 801.75 802.21
Me hod HTLBA-ICA [50] CF-PSO [22]
Cos ($) 801.0488 799.9512
Me hod CF-PSO [43] ICF-PSO [43]
Cos ($) 799.67 799.34
Me hod IEPA [49] TLBA [50]
Cos ($) 802.465 801.6524
Me hod IHBMA [45] MOMPA [46]
Cos ($) 801.99 801.76
Me hod HAS/DE [24] COOTBA
Cos ($) 799.5762 799.378
Me hod MOMPA [46] GBBICOA [47]
Powe loss (MW) 3.156 4.937
Me hod MSSA [48] COOTBA
Powe loss (MW) 2.945 2.946
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Fig. 9: Vol age o nodes in Case 1 and Case 3.
As conside ing he OPF p oblem wi h TCSC, he
uel cos s a e compa ed in Table 5. Abou he uel
cos o Case 2, COOTBA has eached a smalle cos
han all compa ed algo i hms, including SAA/TSA [1],
CF-PSO [22], HAS/DE [24] by $5.335, $0.460, $0.060,
co esponding 0.66%, 0.058%, and 0.008%. Clea ly,
COOTBA is a high-pe o mance algo i hm o he
OPF p oblem wi h he placemen o TCSC de ices.
Howe e , when applying he no el y wi h he de e -
mina ion o op imal loca ions (Case 3) and inc ease o
TCSC limi , which is highe han 0.02 Pu (Case 4),
COOTBA could each much smalle cos s han hese
me hods. COOTBA s ill used he uppe limi wi h
0.02 Pu o TCSC in Case 3, bu i used a highe alue
o TCSC wi h 0.0497 Pu in Case 4. And he change
o assump ions (loca ion o placing TCSC and TCSC
limi ) has led o a clea e ec i eness in educing elec-
ici y gene a ion cos .
Tab. 5: Compa ison o cos and powe loss om Case 1
Me hod Fuel cos ($) XT CSC (pu)
SAA/TSA [1] (Case 2) 804.6497 0.02
CF-PSO [22] (Case 2) 799.7741 0.0107
HAS/DE [24] (Case 2) 799.3743 0.0200
COOTBA (Case 2) 799.314 0.0176
COOTBA (Case 3) 799.207 0.02
COOTBA (Case 4) 799.127 0.0497
5. Conclusion
This s udy applied Coo bi d beha io -based op imiza-
ion algo i hm o sol ing op imal powe lows o he
IEEE 30-node ansmission powe ne wo k. Fou s udy
cases ha e been implemen ed, in which Case 1 neglec s,
bu o he s conside TCSC de ices. Case 2 only op i-
mized he eac ance o TCSC, while Case 3 and Case 4
op imized bo h loca ion and eac ance o TCSC. Case
3 used he maximum eac ance o 0.02 pu; meanwhile,
Case 4 expanded he ange o 1.0 Pu. The esul s can
be summa ized as ollows:
•COOTBA was supe io o abou i y o he algo-
i hms in p e ious s udies o Case 1. As com-
pa ed o he wo s compa ed algo i hm, COOTBA
could each a smalle cos and loss by 3.78% and
40.3%, espec i ely.
•COOTBA could each less cos han h ee al-
go i hms, including a hyb id me aheu is ic algo-
i hm and imp o ed e sions o PSO o Case
2. The highes educ ion in cos could be up o
0.66%.
•Case 3 could each smalle cos , loss, and ol age
de ia ion han Case 1 and Case 2, bu i eached
wo se alues han Case 4.
The esul s indica ed ha COOTBA is e y e ec i e
o he con en ional OPF p oblem and expanded OPF
p oblem wi h TCSC de ices. COOTBA was e ec i e
in sea ching he loca ion and eac ance o TCSC de-
ices. Ano he algo i hm based on loss sensi i i y ac-
o s was applied o ind ansmission line 3-4 o TCSC
placemen , bu COOTBA could ind mo e sui able
ansmission lines. Wi h di e en limi s o TCSC’s e-
ac ance, COOTBA ound di e en lines, and he di e -
en lines could lead o be e esul s han o he s ud-
ies. So, he s udy has high con ibu ions o applying
COOTBA and sugges s op imizing bo h eac ance and
loca ion o TCSC. Howe e , he s udy has unexpec ed
sho comings in e ms o he pe o mance o COOTBA
and he conside a ion o mo e se ious cons ain s. In
he u u e, he s udy will be imp o ed by conside ing
mo e FACTs de ices such as SVC, UPFC, and TCPAR
o imp o ing he e ec i eness o ansmission powe
ne wo ks wi h la ge-scale up o 118 nodes. On he
o he hand, enewable ene gies will be employed, and
he FACTS de ices will be employed o a oid he o e -
load s a us o lines as well as imp o e uel cos , powe
loss, and ol age p o ile o ansmission powe sys ems.
Au ho Con ibu ions
Bo h N.A.T. and T.M.P. pe o med he analy ic cal-
cula ions and pe o med he nume ical simula ions.
L.C.K. and T.T.N w o e he whole pape . N.A.T.
and T.T.N con ibu ed o he inal e sion o he
manusc ip .
Re e ences
[1] ONGSAKUL, W. and P. BHASAPUTRA. Op i-
mal powe low wi h FACTS de ices by hyb id
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