TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 13, No. 3, March 2
015,
pp. 399 ~ 40
9
DOI: 10.115
9
1
/telkomni
ka.
v
13i3.709
3
399
Re
cei
v
ed
No
vem
ber 2
6
, 2014; Re
vi
sed
Jan
uar
y 6, 20
15; Accepted
Jan
uary 20, 2
015
Analysis of Unbalance Harmonic Propagation in a
Three-phase Po
wer System
Sy
ukri Yunus*
1
,
Khalid Mohamed Nor
2
1
Departme
n
t of Electrical En
gi
neer
ing, F
a
cult
y of Eng
i
ne
eri
n
g, Univers
i
t
y
of
Andal
as
2
Departme
n
t of Electrical Po
wer Engi
ne
erin
g, Un
iversiti T
e
knol
ogi Ma
la
ysi
a
, Johor, Mala
ysi
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: s
y
ukri
_
y
u
nus
@ft.unand.ac.i
d
1
, khalidmn@f
ke.utm.my
2
A
b
st
r
a
ct
Operatio
n is
n
on-li
ne
ar i
n
a
state of u
nba
l
ance
can
cau
s
e pro
b
l
e
ms h
a
rmonics
in
th
e p
o
w
e
r
system
. Ther
e are two parts over the
us
e
of com
put
ational tim
e
in
har
m
o
nic
load flow, the first in
the
constructio
n
of harmon
i
c ad
mittance matrix and the se
c
o
n
d
is the iteratio
n sche
m
e for s
o
lvin
g syste
m
s
of
line
a
r eq
uati
o
n
s
. Mechanic
a
l
compl
e
tion
of the har
mon
i
c a
d
mittance to th
e prob
le
m ca
n
be expr
essed
in
this pap
er, w
a
s devel
op
ed a
s
a har
mo
nic
ad
mittanc
e pa
ralle
l ap
plic
ati
ons, an
d a dir
e
ct algor
ith
m
t
o
calcul
ate th
e a
d
mittance
matr
ix el
e
m
e
n
ts ar
e pres
ent
e
d
. H
e
re, w
e
sh
ow
three
ph
ase
po
w
e
r flow
progr
a
m
is brok
en down into thre
e independent s
ub
problem
s, nam
e
ly: network seq
uenc
e of positive, negative, and
z
e
r
o
. Pos
i
tive
sequ
enc
e n
e
tw
ork w
ill b
e
s
o
lve
d
by
us
i
n
g
the
metho
d
of
Fast dec
ou
ple
w
i
thout
mo
dif
y
i
n
g
their for
m
u
l
atio
n. Neg
a
tive
an
d
z
e
ro s
e
q
uen
ce netw
o
rks s
o
lve
d
usi
ng
no
dal v
o
ltag
e e
q
uatio
n. All thr
e
e
netw
o
rks hav
e
bee
n
mo
de
le
d by
a se
que
nce of thr
ee
i
nde
pe
nde
nt cir
c
uits an
d so
lv
ed si
multa
neo
usly
usin
g multi-cor
e
process
o
rs in
paral
lel pr
ogr
a
m
mi
ng.
Ke
y
w
ords
:
ha
rmo
n
ics a
d
m
ittance, three-
ph
ase pow
er, pro
c
ess
Copy
right
©
2015 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Harmoni
cs ca
n occur b
e
ca
use the
comp
onent is
not li
near in the el
ectri
c
po
we
r netwo
rk
system
s in
cl
ude el
ect
r
ic
arc furn
aces, static
kon
p
ensator fo
r reactive p
o
wer
control a
n
d
electroni
c
eq
uipment
such
as
konvete
r
DC
and
mot
o
r
sp
eed
settings (Va
r
ia
ble spee
d
driv
es)
etc. The
s
e
compo
nent
s ca
use no
sinu
soid
al
current
s containin
g
ha
rmoni
c di
sto
r
tion
comp
one
nts.
Ha
rmo
n
ic
di
stortion
is q
u
ite influentia
l on the
po
wer lo
ss of i
n
ductio
n
moto
rs,
transfo
rme
r
s and chan
nel
s. So that the
harm
oni
c
ana
lysis ha
s be
come an imp
o
r
tant part of the
distrib
u
tion
system in li
ne
with the
ra
pi
d in
cre
a
se in
the u
s
e
of in
cre
a
sed l
oad
s a
r
e
no li
ner at
variou
s bu
s d
i
stributio
n system. No load
liner u
s
ag
e is incre
a
si
ng wi
th the growi
n
g techn
o
logy
in
electri
c
al e
ngi
neeri
ng with t
he use of ele
c
troni
c eq
uip
m
ent for co
ntrolling a
nd th
e gro
w
ing u
s
e of
comp
uters on
electri
c
ity co
nsum
ers.
And the u
s
e
of non-li
nea
r load
will b
e
sp
rea
d
in t
he greate
r
p
a
rt of the di
stribution
system
buses, while th
e non-linear load is
a g
enerat
o
r of
harmoni
c wave
s will cause
deviati
ons
in the volta
g
e
an
d
curre
n
t
wave
ele
c
trical
di
stri
buti
on system, so
the ha
rmo
n
ic pro
pag
ation
through the
system
will lead to t
he addition
unfortunate-
losses i
n
the di
st
ribution sy
stem
and
can
red
u
ce th
e equi
pment
and the
po
ssi
bility of
equip
m
ent will b
e
damag
ed d
u
e
to the overlo
ad
is gen
erate
d
due to the re
sonan
ce [1].
While
the l
o
a
d
flow is a
p
r
ocedu
re
that
is
i
n
u
s
e
ri
g
h
t to obtai
n
a voltage
in
a sta
b
le
con
d
ition of the power
system at the fundame
n
tal
freque
ncy. Ho
wever, th
e power
sup
p
ly
voltage sy
ste
m
whi
c
h d
o
e
s
not al
ways
provide th
e ri
ght pri
c
e b
e
cause of the i
n
fluen
ce of the
pre
s
en
ce of h
a
rmo
n
ic
curre
n
t injected by
the nonline
a
r load and p
o
w
er
swit
chin
g
device
s
on the
system e
nerg
y
incre
a
sed u
s
e in
the
syst
em due to its high effici
en
cy and ea
se
of control. Th
e
harm
oni
c currents will
cause pr
obl
em
s in the performance of the three-phase sy
stem.
This p
r
oble
m
is increa
sin
g
ly becomi
n
g
more
attention in re
cent years i
s
due
to the
increa
se in
h
a
rmo
n
ics that
prop
agate t
h
rou
gh the
system ca
n re
sult in lo
sse
s
with in
cre
a
si
ng
interferen
ce i
n
the com
m
unication net
work a
nd th
e possibility of redu
cin
g
the age of t
h
e
equipm
ent. T
he procedu
re for an
alyzi
ng the h
a
rm
onic
pro
b
lem
s
can b
e
cla
ssifie
d
into t
w
o
method
s: the
metho
d
a
nd
time dom
ain f
r
equ
en
cy do
main. Th
erefore,
an i
n
tere
st in th
e
stud
y of
harm
oni
c loa
d
flow h
a
s
evolved ori
g
i
nally dev
elo
ped by n
e
twork an
alysis in stea
dy-state
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 3, March 2
015 : 399 – 4
0
9
400
con
d
ition
s
a
r
e expe
cting
a balan
ce
d
three
-
ph
ase
voltage at
the load t
e
rmin
als to
be
symmetri
c
al. Ho
wever, ha
rmonic a
nalysis req
u
ire
s
to
ols that are
more a
c
curate and se
nsiti
v
e
for the effects of harmoni
cs on the powe
r
system. A three-p
h
a
s
e po
wer flo
w
pro
g
ram a
s
soci
ated
with unbalanced
electri
c
al
system i
s
cl
early a
sol
u
tion to thi
s
problem, with
respect to its
ability
to con
s
id
er
the asymm
e
try that is u
s
ually
ig
nore
d
by co
nven
tional proced
ure
s
bal
an
ce
d
harm
oni
c loa
d
flow.
Therefore,
a
n
inte
re
st in
the stu
d
y of
harm
oni
c p
o
w
er flo
w
h
a
s evolved
whi
c
h
wa
s
origin
ally de
veloped
by
netwo
rk an
al
ysis i
s
stabl
e un
der con
d
itions
that are expe
ctin
g
a
balan
ce
d three p
h
a
s
e vo
ltage at the
load te
rmi
nal
s to
be
sym
m
etrical. Ho
wever,
ha
rm
onic
analysi
s
req
u
i
res mo
re to
ols to
obtain
accu
rate
an
d sen
s
itive h
a
rmo
n
ic imp
a
ct o
n
the
p
o
we
r
system. A three-p
h
a
s
e p
o
w
er flo
w
p
r
og
ram related t
o
an u
nbala
n
c
ed
po
wer
sy
stem
s is
clea
rly a
solution to this problem,
on it
s ability
to consi
d
er t
he asymmet
r
y that is usually ignored
by
conve
n
tional
pro
c
ed
ures l
oad
bala
n
ced
ha
rmoni
ou
s
flow. Harm
on
ic p
enetration
is th
e e
a
rlie
st
and m
o
st
si
mple m
e
thod
whi
c
h
a
ssu
mes
no i
n
fl
u
ence b
e
twe
e
n
the volta
g
e
and
the
non
-linea
r
netwo
rk [2].
So this met
hod i
s
modif
i
ed p
r
io
r to
penetration
iterative
harm
onic ha
rmo
n
i
c
s
influen
ce on t
he beh
avior o
f
non-line
a
r d
e
vice
s ca
n be
con
s
ide
r
ed [
3
].
It is nece
s
sa
ry to analyzin
g the propa
g
a
tion of
ha
rm
onics do
not
balan
ce in th
ree pha
se
power
syste
m
to be able
to overcome
the probl
em
of 3-pha
se
power flo
w
system, and a
l
so
provide
the basi
s
of
voltage and cu
rrent
a
s
we
ll
as th
e p
a
ra
meters of A
C
-DC conve
r
ters.
Beside
s, it also can be t
o
overcome
the pr
obl
em of penetratio
n
of
harmo
nics that provide
voltage harm
onics in thre
e
-
pha
se
syste
m
s.
Analyzing i
s
also po
ssible
to calculate loss
e
s
in the electri
c
ity tra
n
smi
ssi
on net
work an
d
developin
g
h
a
rmo
n
ic l
oad
cu
rrents
are
unbal
an
c
ed.
The
benefit
s to be
obtain
ed in thi
s
stu
d
y
were able to study the developme
n
t of unbal
an
ced p
o
we
r flow taking into acco
unt the effect of
non-li
nea
r lo
a
d
s that
gen
erate ha
rmoni
c cu
rre
nts i
n
je
cted into
the
electri
c
al
di
stribution
sy
ste
m
that will gen
e
r
ate a voltag
e and
curre
n
t
deviati
ons t
hat have an
impact o
n
po
wer
distri
buti
o
n
system
ele
c
tricity. By usi
ng the
devel
opment
of the p
r
op
os
ed
model
s
and
algo
rithms
are
expecte
d to
influen
ce th
e
ha
rmoni
cs
gene
rated
by
non
-line
a
r l
oad
s a
r
e
un
predi
ctabl
e a
nd
unkno
wn ma
gnitude,
so it
can
be me
asure
s
to elim
i
n
ate it. Harm
o
n
ic g
ene
ratio
n
in the o
pera
t
ion
of the po
wer system
can
be an
alyzed
accura
tely a
nd de
sign
of optimal tech
nique
s
can b
e
determi
ned.
This
study is also very u
s
eful to incre
a
se
the d
e
si
re of research in the dep
artment,
becau
se it uses the fa
cilities and la
bo
rat
o
ry tool
s a
nd
Distri
bution E
l
ectr
i
c
Power
System (STDE
laboratory). T
he re
sults of t
h
is stu
d
y may be publ
i
s
hed
in accredite
d
journal
s an
d can b
e
used to
sup
p
leme
nt / com
p
leme
nt power
syste
m
analysi
s
to
ols that exi
s
t today. Model
system
s
will
be
develop
ed p
r
ogra
m
is al
so very useful in the ele
c
tri
c
al
system in
the regio
n
o
f
West Suma
tra
PLN when in
serte
d
data
e
x
ist for the fo
reign te
rrito
ry
of We
st Sumatra, so tha
t
the relation
ship
betwe
en the Dep
a
rtme
nt of Electrical
Enginee
ring
and the Faculty of Engin
eerin
g Un
an
d in
gene
ral with
stakehol
ders
can b
e
nurtu
red.
2.
Three
-Phas
e
Po
w
e
r Flo
w
Calcula
t
ion Metho
d
Thre
e ph
ase
harm
oni
c current inje
ction
and volt
ag
e i
n
variou
s
parts of the
syst
em an
d
their
settlem
ent on
sym
m
etrical
com
pone
nt
s th
at dep
end
on
the ma
gnit
ude
and
ph
ase
seq
uen
ce of
the harm
oni
c inje
ction
were m
e
t by the ha
rmoni
c sou
r
ce, and
wheth
e
r the
i
r
relation
shi
p
a
nd their three
-
pha
se lin
ear
load is lo
ad b
a
lan
c
ed o
r
no
t balanced.
Thre
e-p
h
a
s
e harm
oni
c
pe
netration req
u
ire
s
a cle
a
r understan
di
ng of the rel
a
tionship
betwe
en the i
n
jectio
n sym
m
etric
co
mpo
nent of ha
rm
onics a
nd h
a
rmonic volta
g
e
so
urce a
n
d
the
curre
n
t flowin
g from the
ha
rmoni
c
sou
r
ce appli
c
at
io
n
for the lin
er
system. Source harmoni
cs
are
con
s
id
ere
d
a sou
r
ce of inje
ction or treat
e
d
as a si
mple
harmo
nic
current so
urce
s.
The app
roa
c
h use
s
a du
mmy node (node fa
ke
) a
nd a line of multi-pha
se
system
conve
r
ts i
n
to
a complete
th
ree
pha
se
sy
stem. U
nde
r t
h
is
app
roa
c
h,
the three-ph
ase
po
we
r flo
w
is n
o
t bal
an
ced in
the
form of a
net
wo
rk of
con
c
e
p
tual o
r
de
r
ca
n
be
co
mplete
d. The
solutio
n
of
the thre
e-ph
ase
po
we
r fl
ow
usin
g
se
quen
ce
co
m
pone
nts
req
u
ire
con
s
tructi
on of a
mo
d
e
l o
f
three
-
ph
ase electri
c
po
we
r system
s in t
he form of co
mpone
nts of their o
r
de
r.
Powe
r flow calcul
ation me
thod ba
se
d t
h
ree
-
p
h
a
s
e
symmetrical
compon
ents h
a
ve bee
n
develop
ed to solve the lateral multiph
a
se u
s
i
ng virtual node ap
proa
ch a
nd virtual cha
n
n
e
ls.
Thus thi
s
me
thod ha
s bee
n able to re
p
r
esent almo
st
all of the circum
stan
ce
s that exist in the
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Analysis of Unbala
n
ce Ha
rm
onic Propa
gation in
a Th
ree
-
ph
ase Power S
ystem
(Syukri Yunu
s)
401
distrib
u
tion
n
e
twork
su
ch
as th
e un
bala
n
ce
d loa
d
, lat
e
ral
multi-p
h
a
s
e
and t
he p
r
ese
n
ce of pl
a
n
ts
with rene
wa
ble en
ergy
source
s. The
r
efore, a
met
h
od b
a
sed
on symm
etri
cal
com
pone
n
ts
sele
ct
ed in t
h
i
s
st
udy
.
3.
Load
and Ca
pacitor Ban
k
s
The L
oad
s
can be
a
spo
t
load o
r
loa
d
dist
ribute
d
along
the
chann
el. They
can
be
con
n
e
c
ted a
s
a delta or st
ar and
ca
n b
e
modele
d
as the con
s
tant
power (P
Q), con
s
tant current
(
I
)
,
or
a
c
ons
ta
n
t
impe
d
a
n
c
e (
Z
)
or
a c
o
mb
i
natio
n
of the
s
e typ
e
s
Loa
d mo
deled
by
current
injectio
n at p
hase compo
n
ents. Th
en, the inje
ct
ion
current in p
h
a
s
e
coo
r
din
a
te
s chan
ged m
en
so he
r pa
rtne
r in seq
uen
ce
compo
nent
s.
Distri
buted
lo
ad i
s
mo
del
ed by
usin
g
a mo
del
of co
ncentrate
d Di
strib
u
ted
load
is
modele
d
by usin
g a mod
e
l of concen
trated load
s.
This model
divides the load dist
ribut
e
d
betwe
en the
chan
nel en
ds u
s
ing a
certai
n ratio
η
. This ratio
is cal
c
ulate
d
based on
the
magnitud
e
of the voltage at node term
inal line te
rm
inal. It is possible to co
nsi
der the ratio
η
become
s
0.5
.
In this pa
p
e
r,
η
ratio i
s
cal
c
ul
ated
p
e
r ite
r
ation
for th
e p
o
wer flow sol
u
tio
n
.
Cap
a
cito
r b
a
n
k
con
n
e
c
ted
to a pa
rticul
ar n
ode to
compen
sate
reactive p
o
we
r to imp
r
ove
the
voltage profil
e in the power gri
d
or to redu
ce net
work losse
s
cap
a
citor
ban
k can be conn
e
c
ted
as a star
o
r
delta.
T
he cap
a
cito
r
i
s
usu
a
lly
det
e
r
mined
by th
e st
ren
g
th of
their reactiv
e
at
nominal o
perating voltage.
Therefo
r
e, th
ey ar
e mod
e
l
e
d simila
r to the co
nsta
nt PQ load.
Applicatio
n of
sequ
en
ce
co
mpone
nts eff
e
ctiv
ely red
u
ce the magnitu
de of the pro
b
lem of
three
-
ph
ase
power-flow. I
n
additio
n
, the ord
e
r
of
de
caying ti
ssue
, positive seq
u
en
ce, ne
gati
v
e
seq
uen
ce, a
nd ze
ro seq
uen
ce ca
n a
l
so be solve
d
by using p
a
rallel p
r
o
c
e
ssi
ng. Seque
nce
balan
ce
d po
wer flo
w
formulation utili
zing a
n
e
s
ta
blish
ed three
-
pha
s
e
po
we
r-flo
w metho
d
to
solve th
e po
sitive seq
uen
ce net
work.
Decom
p
o
s
ition
ba
sed
on
sy
mmetrical
co
mpone
nts
all
o
ws
the integratio
n of many syst
ems of po
wer
studie
s
su
ch a
s
bala
n
ce
d and un
balan
ce
d three-
pha
se ele
c
tri
c
cu
rrent and
-erro
r
cal
c
ul
a
t
ions in a si
n
g
le tool. Thre
e pha
s
e po
wer flow p
r
og
ram
based on sy
mmetrical co
mpone
nts in
d
epen
dently develope
d in consi
s
ts of three su
b-p
r
obl
e
m
s
asso
ciated
wi
th the network
of positive, negative, and
ze
ro
-seq
uen
c
e, as Fi
gure 1.
Figure 1. Three-p
h
a
s
e flo
w
algo
rith
m b
a
se
d on sym
m
etrical com
pone
n
ts
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 3, March 2
015 : 399 – 4
0
9
402
As we menti
oned
earli
er
that the po
si
ti
ve sequ
en
ce network
solved u
s
ing
Ne
wton-
Rap
h
son sta
ndards
witho
u
t any modification in thei
r formulation
since the e
nd
of the set value of
the ord
e
r net
work i
s
still e
x
perien
c
in
g the sa
me form of negative and zero seque
nce net
works
solved
usi
ng
nodal volta
g
e
equatio
n. Ce
rtain valu
es
o
f
the neg
ative and
ze
ro
se
q
uen
ce n
e
two
r
k
is expresse
d
as a
n
inje
ctio
n cu
rrent. Th
erefo
r
e, the
solution of
b
o
th neg
ative an
d ze
ro
-sequ
e
n
ce
netwo
rks
ca
n
be exp
r
e
s
sed with
the
usu
a
l no
dal
voltage eq
ua
tion as follo
ws,
usin
g m
a
trix
notation:
d
2_Specifie
2
2
I
V
Y
(1)
d
0_Specifie
0
0
I
V
Y
(
2
)
After solvin
g the
sequ
en
ce
netwo
rks, p
h
a
se
voltage t
o
the b
a
se
ca
n be
cal
c
ul
ated. Thi
s
pro
c
e
s
s is re
peated
until t
he
conve
r
ge
n
c
e
criterio
n
i
s
re
ach
ed. At t
h
is
stag
e of
p
r
og
ram
voltage
mismat
ch, the mismat
ch seque
nce of positive vo
ltag
e and po
sitive seq
uen
ce
power mi
sma
t
ch
can b
e
used
as a converg
ence crite
r
io
n
.
The algo
rith
m has b
een i
n
clu
ded in th
e distri
bution
netwo
rk fe
atu
r
es m
u
ch like
mesh
ed
netwo
rk o
r
ra
dial, single
-
p
hase, two-p
h
a
se, thre
e-ph
ase line, tra
n
s
form
er with l
oad conne
cti
on,
spot an
d distributed to all types an
d co
n
nectio
n
s.
The total cu
rrent harm
oni
c cha
nge
s can
be obtain
ed b
y
the followin
g
equatio
n:
2
22
2
2
2
23
4
11
..
...
....
.
10
0
%
10
0%
h
h
n
th
d
I
II
I
I
Ix
x
II
(
3
)
The total of rms
current:
22
r
m
s
f
un
d
h
ar
m
I
II
(
4
)
Or,
2
1
100
th
d
rm
s
f
u
n
d
I
II
(
5
)
The funda
me
ntal curre
n
t (in fundame
n
ta
l frequen
cy):
2
1
rm
s
f
und
th
d
I
I
I
(
6
)
Total cha
nge
in fundame
n
tal curre
n
t:
2
()
1
rm
s
th
d
f
u
n
d
fu
n
d
I
I
I
(
7
)
T
o
ta
l d
e
m
an
d D
i
s
t
o
r
tion
(
T
D
D
)
:
2
222
2
2
23
4
......
h
h
n
TD
D
l
o
ad
l
oad
I
I
II
I
I
II
(
8
)
Where : I
load
= maximum demand lo
ad
current (
f
undame
n
tal)
pada the PCC
TDD = ‘Total demand di
storti
on’ of curre
n
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Analysis of Unbala
n
ce Ha
rm
onic Propa
gation in
a Th
ree
-
ph
ase Power S
ystem
(Syukri Yunu
s)
403
4.
Admittance Matrix
Base on
Harmonic
Thre
e-p
h
a
s
e
harm
oni
c cu
rrent inje
ction
and vo
ltage i
n
variou
s pa
rts of the syst
em and
their settleme
n
t
on symme
trical co
mpo
n
ents
th
at
de
p
end on
th
e magnitud
e
a
nd
p
h
a
s
e of the
injectio
n seq
uen
ce h
a
rm
o
n
ics a
r
e m
e
t by the ha
rmo
n
ic
sou
r
ce, a
nd whethe
r t
heir
relatio
n
ship
and their th
re
e-ph
ase linea
r load is a the
load bala
n
ce
d or not bala
n
ced.
Thre
e-p
h
a
s
e harm
oni
c
pe
netration req
u
ire
s
a cle
a
r understan
di
ng of the rel
a
tionship
betwe
en the i
n
jectio
n of symmetrical co
mpone
nt
s an
d harm
oni
cs
sou
r
ce ha
rm
onic voltag
e and
curre
n
t flowi
ng from the
sou
r
ce
appli
c
ation to
ha
rmonic line
r
system. Sou
r
ces
of ha
rmo
n
ics
con
s
id
ere
d
or treated a
s
a sou
r
ce of inje
ction sim
p
le h
a
rmo
n
ic
curre
n
t source
s [4]
.
The ap
pro
a
ch use
s
a du
mmy node a
nd many sy
stem
s co
nve
r
t line pha
se
into a
compl
e
te th
re
e-ph
ase
syst
em. Based o
n
this app
ro
a
c
h, three
-
ph
a
s
e
po
wer flo
w
i
s
not
bala
n
ce
d
in the form of
a con
c
e
p
tual
netwo
rk
ord
e
r
ca
n
be
com
p
leted. Soluti
on of the thre
e-ph
ase po
wer
flow se
que
nces u
s
e the
s
e
comp
onent
s requi
re the b
u
ilder of a m
odel of a thre
e-ph
ase ele
c
tri
c
power sy
ste
m
s in the form of their ord
e
r co
mpo
nent
s.
Powe
r flow calcul
ation me
thod ba
se
d t
h
ree
-
p
h
a
s
e
symmetrical
compon
ents h
a
ve bee
n
develop
ed fo
r re
solvin
g la
teral multi
-
ph
ase
app
ro
ach usi
ng virtu
a
l nod
es and
virtual chan
nels.
Thus thi
s
method wa
s a
b
le to represent almost
a
ll of the circumstan
ce
s that exist in the
distrib
u
tion
n
e
twork a
s
th
e loa
d
i
s
n
o
t
balan
ce
d,
and th
e late
ral m
u
lti-ph
a
s
e
plant
s
wi
th
rene
wa
ble en
ergy sou
r
ce
s.
The
r
efore symmetrical co
mpone
nt-b
ased
meth
od i
s
sel
e
cte
d
in t
h
is
s
t
udy [5-7].
4.1. Decou
p
led Model Se
quenc
e As
y
mmetrical Lines
Serie
s
re
si
sta
n
ce
and in
du
ctan
ce of three
pha
se t
r
a
n
smi
ssi
on lin
es b
e
twee
n n
ode
s are
lumped
in th
e middl
e. Sh
unt ca
pa
citan
c
e of th
e tra
n
smi
ssi
on li
n
e
is
divided i
n
to two
se
cti
ons
and lum
ped a
t
the node
s conne
cted to t
he line. Line
seri
es
and
sh
unt imped
an
ce matrix entry
is
given by:
cc
ij
z
cb
ij
z
ca
ij
z
bc
ij
z
bb
ij
z
ba
ij
z
ac
ac
z
ab
ij
z
aa
ij
z
abc
ij
Z
cc
ij
y
cb
ij
y
ca
ij
y
bc
ij
y
bb
ij
y
ba
ij
y
ac
ij
y
ab
ij
y
aa
ij
y
abc
ij
Y
(9)
Cha
nnel seri
es impe
dan
ce and sh
unt impeda
nce matrix of the three-p
h
a
s
e line
given by
(1) b
e
cha
n
g
ed in pairs them in se
qu
ence com
p
o
nent. The re
sulting
seri
es impedan
ce
and
shu
n
t impeda
nce mat
r
ix in the orde
r of the com
pon
en
ts is given by:
22
21
20
12
11
10
02
01
00
012
22
21
20
12
11
10
02
01
00
012
Y
Z
ij
ij
ij
ij
ij
ij
ij
ij
ij
ij
ij
ij
ij
ij
ij
ij
ij
ij
ij
ij
y
y
y
y
y
y
y
y
y
z
z
z
z
z
z
z
z
z
(
1
0
)
If the three-p
hase line is fully transp
o
se,
then the impeda
nce a
nd admittan
c
e matrices
in equation
(1
) will be sym
m
etrical. Co
mpone
nt of it
s ord
e
r will b
e
diagon
al m
a
trice
s
. Ho
we
ver, if
the chan
nel
is untran
s
p
o
se
d three
-
p
hase,
three-comp
one
nt pha
se co
mp
onent admitt
ance
matrix in
(1)
will be full
and sy
mm
etri
cal, but not
phas
e-wi
se that
is
balanced.
Therefore, t
h
e
matrix entry seque
nce will be full and no
t symmetrical
.
Orde
r
co
uple
d
line
mod
e
l
can
be
de
co
mposed i
n
to
a sequ
en
ce
of thre
e in
de
pend
ent
circuits
[6-7]. This ca
n
be achi
eved
by repla
c
ing
th
e clutch,
ie
the element
s
off-diago
nal
in (2),
by the equiva
lent curre
n
t compen
satio
n
as follo
ws.
m
j
nm
ij
l
i
nl
ij
m
j
m
i
nm
ij
l
j
l
i
nl
ij
n
i
V
y
V
y
V
V
z
V
V
z
I
)
(
1
)
(
1
(
1
1
)
On
Fig
u
re
1
sho
w
s
the ch
annel model
descri
bed
in
the order of
cou
p
ling
bet
wee
n
the
comp
one
nts
of the orde
r e
n
tered by the
comp
en
sa
tio
n
netwo
rk flo
w
is compute
d
usin
g (3
).
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 3, March 2
015 : 399 – 4
0
9
404
ij
mm
z
i
m
V
j
m
V
ij
mm
y
ij
mm
y
i
m
I
j
m
I
Figure 1. Ord
e
r of line de
couple
d
model
s
In the ea
rly stage
s m
ade
the bu
s nu
mberi
ng syst
em
to
be an
alyzed.
T
he buses are
con
n
e
c
ted to
pre
-
num
be
re
d gen
erato
r
a
fter the bu
s n
u
mbe
r
ing
co
n
t
inued in th
e l
oad b
u
ses, th
e
bus that h
a
s the la
rge
s
t g
e
neratin
g
cap
a
c
ity ch
osen
a
s
the
sl
ack
b
u
s
and
was g
i
ven the
num
ber
1 (o
ne), to
anothe
r b
u
s
that is
con
n
e
cted
to
the
gene
rato
r g
i
ven num
ber 2 (t
wo) a
s
the
gene
rato
r bu
s and the lo
a
d
bus i
s
num
bere
d
0 (zero
)
.
Compil
e data
on the
syste
m
to be a
nal
yzed
wh
i
c
h i
n
clu
d
e
s
data
from the
re
sistan
ce,
rea
c
tan
c
e
an
d capa
citan
c
e bet
ween
li
nes, tran
sformer ta
pping
the data, th
e
load th
e d
a
ta
sched
uled, t
he d
a
ta g
e
n
e
ration,
assu
ming initial
voltage m
agni
tude a
nd
ph
ase
an
gle
b
u
s
voltage. Cal
c
ulation be
gin
s
by forming
netwo
rk im
pe
dan
ce
ij
Z
with the formula:
ij
Z
=
ij
R
+
ij
jX
(12)
Whe
r
e
ij
Z
: Network im
peda
nce bet
wee
n
bu
s i and bu
s j
ij
R
: Network resistan
ce bet
we
en bu
s i and
bus j
ij
X
: Network rea
c
tan
c
e bet
we
en bu
s i and
bus j
Then conve
r
ted Net
w
ork i
m
peda
nc
e to Network admi
ttance:
ij
Y
=
ij
Yr
+
ij
jY
x
(13)
Whe
r
e,
22
ij
ij
r
ij
i
j
R
Y
R
X
(14)
The next bu
s admittance
matrix Y is forme
d
by th
e com
pon
ent
s comp
risi
ng
Network
admittance, capa
citan
c
e a
nd line
tran
sf
orme
r ta
p
p
in
g ch
ang
e. Th
en the
bu
s a
d
mittance
ma
trix
Y is fo
rme
d
in
a recta
n
gular
shap
e
conve
r
ted
int
o
pol
ar form
. Whe
r
e
p
r
e
v
iously the
b
u
s
admittance m
a
trix Y is sep
a
rated i
n
to co
mpone
nt
s of t
he matrix G
a
nd the mat
r
ix B. Schedul
ed
power availa
ble on ea
ch b
u
s is
cal
c
ulat
ed by the formula:
Pi
jd
=
P
G
i
–
P
l
i
(
1
5
)
In the pro
c
ess of iteration,
the ca
l
c
ulate
d
power soug
ht by Formula
:
1
co
s
(
)
N
ii
n
i
n
i
n
n
i
n
PY
V
V
(17)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Analysis of Unbala
n
ce Ha
rm
onic Propa
gation in
a Th
ree
-
ph
ase Power S
ystem
(Syukri Yunu
s)
405
1
si
n(
)
N
ii
n
i
n
i
n
n
i
n
QY
V
V
(18)
Whe
r
e
P
i
: The calcula
t
ed active po
wer o
n
bu
s i
Q
i
: The calcul
ated rea
c
tive power on b
u
s i
V
i
,
θ
i
: Voltage magnitude a
nd p
hase angl
e o
n
bus i
V
j
,
θ
j
: Voltage magnitude a
nd p
hase angl
e o
n
bus j
in
Y
,
in
: Magnitud
e
and ph
ase angle of admi
ttance matrx
element
s Y
The cal
c
ul
ate
d
power Mi
smatch obtai
n
ed with the e
quation o
n
this belo
w
:
j
dh
i
t
ii
i
P
PP
(19)
j
dh
i
t
ii
i
QQ
Q
(20)
Whe
r
e
i
P
: Active power Mism
atch
on bus i
i
Q
:
Reac
tive power Mis
m
atc
h
on bus
i
A
f
t
e
r P
o
we
r
Mismat
ch i
s
cal
c
ulat
e
d
s
o
is
fo
rmed
Jaco
bian
matrix. Jacobian
matrix
formation in F
a
stDecoupl
e method ha
s some differe
nces compa
r
e
d
with other m
e
thods.
This differen
c
e arises b
e
ca
use:
a)
Comp
ari
s
o
n
X/R line
of hi
gh e
nou
gh
so
that the
valu
e
si
n
i
j
ij
ij
GB
. Differenc
e of
each pha
se v
o
ltage bu
s fai
r
ly small so that:
si
n
s
i
n
ij
i
j
i
j
(21)
c
o
s
c
os
1.
00
ij
i
j
(22)
b)
The value of each bu
s rea
c
tive power Q
i
is
alway
s
smaller tha
n
the value of BiiVi 2
so obtai
ned t
he followi
ng e
quation:
[
∆
P]=
[V
'
B
V][
∆δ
]
(23)
"
V
QV
B
V
V
(24)
Whe
r
e mat
r
ix elements B'
and B'' are m
a
trix element
s B with the formul
a as foll
ow:
'
1
ij
ij
B
X
i
≠
j
(25)
'
1
1
n
ij
j
ij
B
X
i =
j
(26)
'
ij
i
j
B
B
(27)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 3, March 2
015 : 399 – 4
0
9
406
And then the
Equation (15) and (16
)
be
come:
'
P
B
V
(20)
"
Q
BV
V
(21)
So in the next calculation o
b
tained:
1
'
P
B
V
(22)
1
"
Q
VB
V
(23)
The Equ
a
tio
n
(2
2)
or
(2
3) i
s
kno
w
n
as
Fa
st De
cou
p
le L
oad
Flow
. Difference
in
magnitud
e
a
nd ph
ase a
n
g
le value
s
o
f
each
bu
s
voltage bet
ween the
old
and
ne
w th
en
comp
ared
wi
th a pre
dete
r
mine
d value
accuracy
. If the value
of accuracy
has
not be
e
n
achi
eved, the iteration is repeate
d
from
the begi
nning to the
accu
ra
cy and conve
r
g
e
n
ce
achi
eved fulfilled.
Slack Bu
s po
wer at the ne
xt calculate
d
afte
r conve
r
g
ence is re
ach
ed. The form
ula used
is:
1
co
s
N
ii
n
i
n
i
n
n
i
n
PY
V
V
(24)
1
si
n
N
ii
n
i
n
i
n
n
i
n
QY
V
V
(
2
5
)
Whe
r
e
P
i
: Active power on Slack b
u
s
Q
i
: Reactive po
wer o
n
Slack
bus
Beside
s that
rea
c
tive po
wer
at PV bus
(Bus St
ation)
wa
s also
cal
c
ulat
ed after
conve
r
ge
nce is achieved,
while the
formula used is
the formula (25).
Powe
r flow b
e
twee
n bu
se
s is calculate
d
usin
g the formula:
**
**
ij
i
i
j
i
j
i
ij
SV
V
Y
V
Y
c
(26)
**
ij
ij
i
i
j
i
j
i
i
i
j
Pj
Q
V
V
V
Y
V
V
Y
c
(27)
Whe
r
e:
S
ij
: Complex power flow from bus
i to bus
j
P
ij
: Ac
tive power flow from bus
i to bus
j
Q
ij
: Reac
tive power flow from bus
i to bus
j
V
i
: Voltage vector bus i
V
j
: Voltege vector bus j
V
ij
: Voltage Vector betwe
en bus i an
d bu
s j
Y
ij
: Admittance betwe
en bu
s i and bus j
Yc
ij
: Charging li
n
e
admittan
c
e
betwe
en bu
s
i and
bus
j
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Analysis of Unbala
n
ce Ha
rm
onic Propa
gation in
a Th
ree
-
ph
ase Power S
ystem
(Syukri Yunu
s)
407
Powe
r loss b
e
twee
n bu
se
s is calculate
d
usin
g the formula:
ij
ij
j
i
S
l
osse
s
S
S
(
2
8
)
W
h
er
e
ij
S
l
osses
: Complex power loss
es
from bus
i to bus
j
ij
S
: Complex power from bus
i to bus
j
ji
S
: Complex power from bus
j to bus
i
5. Res
earc
h
method
This research
was
con
d
u
c
ted with the fo
llowing m
e
tho
dology:
5.1. Rese
arc
h
Design an
d Procedur
e
s
This
study wil
l
perform the
followin
g
step
s:
1.
Review library and conferenc
e surveys taken from j
ournal
IIIE / IEE. This phase i
s
to review the
literature to deter
min
e
the state of the art right.
2.
The dat
a set i
s
taken from
the
dat
a
net
work Sumatra, IEEE t
e
st system
s. Modeling
of the tran
smissi
on
syst
em it wo
uld
use
mathe
m
atical m
o
d
e
ls to
rep
r
e
s
ent accu
ratel
y
the
sy
st
em p
r
a
c
t
i
cally
.
3. Con
c
ept
ual p
o
wer flow
pro
g
ram
in the
co
nve
n
tional
pro
g
rams that h
a
v
e bee
n
modified by
clicki
ng chan
g
e
the value o
f
t
he transmi
ssi
on line
on
the harm
oni
c orde
r and t
h
e
use
of no
n-lin
ear l
oad
s, the
n
to elimi
nate
tung
n
onlin
e
a
r h
a
rm
oni
c
current of the
bus and
all
b
u
s
voltages. And
make
s the al
gorithm.
4. T
h
is algorithm
will
be validated by
t
he
system
test and
com
pare
the results with
previou
s
resu
lts.
5.
Overall testing and p
e
rfecte
r of t
he system mo
del and an a
l
gorithm that will be
done.
5.2. Opera
t
ional Frame
w
o
r
k
Harmoni
c loa
d
flow pro
g
ra
m will use the
unbala
n
ce
d load of pap
ers ever pu
blished. Are
being
a
c
tively ca
rri
ed o
u
t b
y
usin
g a
sm
all scale
an
d
the re
sult
s o
b
t
ained
will b
e
com
p
a
r
ed
wi
th
previou
s
resu
lts related.
5.3. Subjects
or Data Sources
The main data that will be used in
the analysi
s
will be collected from:
a) IEEE
Data
b)
Data from tut
o
rial
s / pape
rs publi
s
h
e
d
c
)
Data from
Network
PLN
region III
5.4. Instrum
e
nt &
Analy
s
is
Instrum
entati
on and d
a
ta a
nalysi
s
used i
n
this study.
a)
Microsoft Visual Studio 20
10
b)
Usi
ng Flu
k
e
RPM for the
measurement
of harmoni
cs
6.
Resul
t
s And Discus
s
ion
The p
u
rp
ose
of this
stud
y is more
c
oncern
ed a
b
out the deve
l
opment of
solution-
harm
oni
c
el
e
c
tri
c
current. The re
sults
p
r
esented
he
re
will
di
scuss the i
s
sue
of
reu
s
e
(reu
se
). In
addition,
a n
u
meri
cal
exa
m
ple of th
e
completion
of
the 32
-bu
s
system is not
balan
ce
d [11]
is
given wh
en the nonli
nea
r device i
s
on the network.
6.1. Benchm
ark of
Reus
e
(Reu
se)
Reu
s
e i
s
imp
l
emented by
the cla
ss
size
by calcul
ating that have been ma
de b
a
se
d on
inherite
d
, co
mpositio
n, or developed
from scra
t
c
h
.
The size
of the class and re
-u
se
of
comp
one
nts
are summa
ri
zed in Table 1.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 3, March 2
015 : 399 – 4
0
9
408
Table 1. Measure for re-usability in
the development of harmoni
c penetration
Reuse Composition
Inher
itance
Scratch
%
Reuse
Power s
y
stem M
odel (classes)
2
6
-
Composition25%
%5%
Inherited75
%
Solution Algoritm (component
)
4
-
1
Composition80%
Inherited 20
%
First, the
mo
del of th
e el
ectri
c
al
sy
ste
m
that rep
r
e
s
ent
s the
a
c
tual d
e
vice
from the
power gri
d
, there are 6 cla
s
se
s whi
c
h is
a derivat
ive form of basi
c
power sy
ste
m
librari
es where
there a
r
e t
w
o
cla
s
ses
reu
s
ed by compo
s
ition. In con
nectio
n
with t
he solution a
l
gorithm, the
r
e
are fou
r
com
pone
nts are reused. They are two
co
m
p
onent
s to the flow of power is not balan
ced,
one compo
n
e
n
t of the admittance matrix
, and a linea
r comp
onent t
o
the settlem
ent. In addition
to high reu
s
a
b
ility, compo
nents m
u
st b
e
reu
s
e
d
wi
th
out kn
owi
ng t
he alg
o
rithm
s
that are p
a
cked
in it. This is
becau
se the
comp
one
nts
are d
e
si
gne
d
with a cl
ea
r interface ba
sed
on the d
a
ta
netwo
rk i
s
already kn
own to elec
t
r
ical e
ngine
ers. On
the other h
a
n
d
the formula
t
ion of compl
e
x
algorith
m
s hi
dden in
side
compon
ents of
privac
y or p
r
otected from comp
one
nt parts.
4.2.
Examples of Numeric
a
l Resul
t
s
Harmoni
c po
wer flo
w
an
a
l
ysis u
s
ing
CBD appli
c
atio
n has
bee
n
tested by u
s
i
ng 32
buses, to obt
ain or calcula
t
e pervert
s an
harmo
nic vol
t
age at all bu
se
s are a
s
fol
l
ows:
Ca
se 1: Ha
rmonic voltag
e for co
nne
ction of a nonlin
ear devi
c
e.
Ca
se 2: Ha
rmonic voltag
e due to an u
nbala
n
ced lo
ad dema
nd.
In the first
case, th
ere
is a n
online
a
r
devic
e wh
ic
h is
c
o
n
n
e
c
t
ed
to
th
e 3
2
-b
u
s
te
s
t
system
s whe
r
e
Converte
rs Six
Pulse no.
ID
conn
ec
te
d
on th
e b
u
s:
32, 41
an
d 4
5
on
the
32
b
u
s,
with 50% of total bus
con
n
e
cted to the l
oad, the
re
su
lt there are i
r
regula
r
ities p
o
i
nted it towards
total harmo
ni
c voltage at a
ll buse
s
in the
system.
If only one device is
con
n
e
cted to a
system
of nonli
near
32 bu
s test syste
m
, harmo
ni
c
distortio
n
i
s
l
o
w. T
h
is is b
e
ca
use
whe
n
more
nonlin
ear devi
c
es
conne
cted
to t
he b
u
s net
wo
rk,
harm
oni
c volt
age
deviation
will in
crea
se
at all
bu
ses i
n
the
network. This i
s
due
to the fa
ct th
a
t
the total o
r
th
e amo
unt of
harm
oni
c current in
j
e
cte
d
i
n
to the n
e
twork have
in
creased a
nd th
us
will incre
a
se
the harm
oni
c voltage devi
a
tion in the b
u
s net
wo
rk.
Voltage THD (%) for the
32 -
bus sy
stem
when Pul
s
e
Storie
s a
r
e
con
necte
d o
n
the
bu
s n
o
.ID 3
2
,
41 a
nd
45
with 50 %
of th
e
total load (bal
anced).
In the
se
con
d
case, the
voltage
harmo
nics d
ue to
t
he d
e
man
d
l
oad i
s
not b
a
lan
c
ed,
nonlin
ear
dev
ice
s
conne
ct
ed to the bu
s are a
s
ked l
o
ads
adapte
d
to increa
se
20
% for pha
se
A,
an increa
se
of 10 % for pha
se B and
a decrea
s
e
of 5 % for phase C. For
example, de
mand
loadin
g
o
n
th
e bu
s with
th
e ID num
ber
41 fo
r the
32
- b
u
s test
sy
stem tailored t
o
the
individu
al
will incre
a
se
20 % for ph
a
s
e A, an in
crease of 10
% for pha
se
B and a d
e
crease of 5 %
for
pha
se
C. Adj
u
stment
of d
e
mand
loa
d
in
g is don
e
so
that the h
a
rm
onic voltage
deviation in
the
bus
network as the
de
mand i
s
n
o
t balan
ce
d i
n
the loa
d
in
g obtain
ed
and exami
n
ed.
7.
Conclu
sions
and Rec
o
mmendation
s
This
study h
a
s p
r
e
s
ente
d
the develop
ment of
obje
c
t com
pon
en
ts for the three-p
h
a
s
e
power flo
w
a
nalysi
s
of un
balan
ce
d ha
rmonic Algo
ri
thms u
s
e
d
h
a
rmo
n
ic
pen
e
t
ration a
nd n
odal
voltage meth
od for ha
rmo
n
ics ha
s bee
n develop
ed
as a compo
n
ent obje
c
t. Harmo
n
ic a
nal
ysis is
requi
re
d as a
n
extensio
n of the basi
c
l
i
bra
r
ie
s for th
e power
syst
em nonlin
ea
r device mo
d
e
ls.
Comp
one
nts
of the nodal
voltage meth
od ha
s be
en
integratin
g th
e com
pon
ent
s of thre
e-ph
ase
power flow
into the existing ne
w compon
ent
-ba
s
ed a
ppli
c
ati
ons. Reu
s
e
of pre-exi
s
ting
comp
one
nts
with a
very
high frequ
en
cy sugg
est
s
that the a
nal
ysis i
s
ve
ry
compl
e
x po
wer
system
s
can
be devel
oped
with g
r
eat fle
x
ibility that
can not be fo
un
d in alternative pro
g
rammi
ng
approa
che
s
.
Modelin
g co
mpone
nt for t
he propo
se
d
algorith
m
can
be extend
ed
to model
s of
th
e
method
s are more
comp
re
hen
sive as
th
e iterative harmonic
re
solut
i
on.
Ackn
o
w
l
e
dg
ements
We a
r
e very
grateful to my institution
,
Andalas u
n
i
versity engin
eerin
g facult
y, which
alrea
d
y provide supp
ort a
nd finan
cial
a
ssi
stan
ce,
so
that we
ca
n
do this
re
se
a
r
ch. An
d al
so
to
Evaluation Warning : The document was created with Spire.PDF for Python.