TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.7, July 201
4, pp
. 4981 ~ 49
8
7
DOI: 10.115
9
1
/telkomni
ka.
v
12i7.458
4
4981
Re
cei
v
ed Se
ptem
ber 30, 2013; Revi
se
d F
ebruary 1
1
, 2014; Acce
pted March 7,
2014
An Approach for Assessing Harmonic Emission Level
Based on Robust Partial Least Squares Regression
Xiang Li
1
*, M
i
n
y
ou Chen
1
, Yong
w
e
i Zh
eng
2
, Shan Cheng
3
，
Fen
g
Li
1
1
State Ke
y
La
b
o
rator
y
of Po
w
e
r T
r
ansmission Equi
pme
n
t & S
y
stem Secur
i
t
y
an
d Ne
w
T
e
chno
log
y
,
Cho
ngq
in
g Uni
v
ersit
y
, Ch
on
g
q
in
g, Chin
a
2
Neiji
an
g Electr
ic Po
w
e
r Bur
e
a
u
of Sichua
n El
ectric
Po
w
e
r C
o
rpor
ation, Ne
ij
ian
g
, Sichu
an
Provinc
e
, Chin
a
3
Colle
ge of Ele
c
tric Engin
eeri
ng an
d Ne
w
E
nerg
y
, Ch
ina T
h
ree Gorg
es U
n
iversit
y
4
430
0
2
, Hube
i Provi
n
ce,
Chin
a
*
Corres
p
o
ndi
n
g
author, e-ma
i
l
: lian
dhe
qc@
1
63.com
A
b
st
r
a
ct
An appr
oac
h to eval
uate h
a
r
m
o
n
ic co
ntribu
tions at
the poi
nt of commo
n
coup
lin
g is pre
s
ented i
n
this pap
er. T
he prop
osed a
p
p
roac
h is base
d
on rob
u
st
pa
rtial least sq
ua
res regressi
on,
w
h
ich estimat
e
s
system
har
m
onic im
pedanc
e by ut
ili
z
ing the signals
of har
m
o
nic
voltage and
curr
ent m
eas
ured
synchro
nous
ly
at the
poi
nt
of co
mmon
co
upli
ng.
C
ons
e
que
ntly acc
o
rd
ing to
the IEC
T
e
chnic
a
l
Re
port
610
00-3-
6 the
har
mo
nic
emi
ssion
leve
l of
user is
c
a
lc
u
l
ated. T
h
e
pre
s
ented
metho
d
overc
o
mes t
h
e
disa
dvant
age
of variab
le d
e
pen
de
nce in e
s
tablis
hin
g
of the syste
m
mo
del a
nd re
duc
es or removes
the
effect of outlyi
ng d
a
ta po
ints. T
he metho
d
i
s
verifi
ed thr
o
u
gh a si
mulati
o
n
study a
nd w
i
th extensiv
e fi
el
d
me
asur
e
m
ents
.
Ke
y
w
ords
:
point of common c
oupling, harmonic
em
iss
i
on
lev
e
l,
syst
em harmonic im
pedance, r
o
bus
t
partia
l
least sq
uares re
gressi
on
Copy
right
©
2014 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
In the pa
st fe
w yea
r
s th
ere ha
s be
en
consi
derable i
n
crea
se i
n
th
e ha
rmoni
c d
i
stortion
level in the distrib
u
tion system due to extens
ive
use of po
we
r elect
r
oni
c
device
s
. The
s
e
harm
oni
cs of
ten has m
a
ny negative effects
such
as re
so
nan
ce p
r
oble
m
s,
overhe
ating
of
con
d
u
c
tors, stress in cap
a
c
itor ba
nks a
nd false
op
eration of prote
c
tion
device, whi
c
h eventu
a
lly
increa
se
s the
maintenan
ce
cost
s of
the
system [1]. Efforts are bei
n
g
made to re
duce the level of
harm
oni
cs through
the i
n
trodu
ction
of g
u
ideline
s
, re
commen
ded
p
r
acti
ce
s and
stand
ard
s
[2,
3].
Based
on the
philosophy o
f
powe
r
facto
r
penaltie
s
, in
centive-ba
se
d schem
es
were p
r
op
osed
[4
]
to enco
u
ra
ge
the utility and the custo
m
er side to
retain
harmo
nic di
stortion betwe
en the limits.
The m
a
in id
e
a
be
hind th
e
incentive-b
a
s
ed
sch
e
me
s is to
identify harmoni
c-produ
cing
facilities for their contributions to the harmonic
di
stortion. Therefore,
a method for
quantifying
cu
stome
r
an
d utility sha
r
e of ha
rmo
n
i
c
s at t
he
poi
nt of co
mmo
n couplin
g (PCC) is ne
e
ded.
Variou
s te
ch
nique
s
have
alrea
d
y be
en
presented.
The
power-di
r
ectio
n
m
e
th
od [5] h
a
s b
een
widely u
s
ed
but acco
rdin
g to [6] may
lead to wr
on
g re
sults. No
w the existin
g
approa
che
s
to
estimate the
harm
oni
c em
issi
on l
e
vel are m
o
stly
based on estim
a
tion of the
utility harmonic
impeda
nce includi
ng invasi
ve methods a
nd non
-i
nva
s
ive methods. Con
s
id
erin
g the backg
ro
un
d
harm
oni
c, the two m
e
tho
d
s a
r
e
cal
c
ul
ating ha
rm
o
n
i
c imp
edan
ce
with ha
rmo
n
i
c di
sturban
ce at
PCC, n
o
t h
a
rmo
n
ic it
sel
f
[7]. The invasive meth
ods [8] a
ccurately e
s
tim
a
te utilities
and
customers
param
e
ters by injecting t
he harmonic
(or interharmonic)
cu
rrent to utilities or
swit
ching on
(or off)
any l
oad
s. These
methods m
a
y
be harmful t
o
power
syst
em. As utilizi
n
g
natural
distu
r
ban
ce of th
e
cu
stome
r
o
r
utility,
the non-inva
sive m
e
thod
s have t
he adva
n
tage
of
simple and safe operation. The non-i
n
vasive
m
e
thods compute
the
ut
ility harm
onic i
m
pedance
by measu
r
in
g harm
onic
voltage and
curre
n
t at
PCC, which
mainly inclu
d
e
the refere
nce
impeda
nce m
e
thod [9], the utility harmo
nic imp
edan
ce
linea
r reg
r
e
ssi
on meth
od
[10-13] an
d the
fluctuation m
e
thod [14, 1
5
]. The refe
rence im
pe
da
nce m
e
thod
cal
c
ulate
s
th
e use
r
ha
rm
onic
emission lev
e
l by means of gi
ven parameters
of utilit
ies and customer
side. The method is
effective, but
it needs to re
duce errors caused
by the cha
nges
of utilities and custom
ers
para
m
eters.
The flu
c
tuatio
n meth
od
est
i
mates
the
utility harmo
nic
impeda
nce b
y
the h
a
rm
on
ic
Evaluation Warning : The document was created with Spire.PDF for Python.
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046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 4981 – 49
87
4982
fluctuation
rat
i
on of volta
g
e
to
current.
Howeve
r,
it ma
y indu
ce
big
errors fo
r eva
l
uation
re
sult
s
becau
se of t
he ha
rmo
n
ic
para
m
eters v
a
riatio
n
of th
e utility side
and m
e
a
s
ure
m
ent noi
se.
The
linear
reg
r
e
s
sion meth
od
asse
sses the
harmo
nic e
m
issi
on level
base
d
on vo
ltage and
current
equatio
ns at
PCC.
Ro
bu
st re
gre
s
sion
i
s
a
meth
od
for th
e a
nalysis of
data
co
ntaining
outli
ers.
Ho
wever, this method is la
ck of an
alysi
s
of the
correl
ation variabl
e
s
. Partial lea
s
t squares
(PL
S
)
reg
r
e
ssi
on m
e
thod
ca
n e
s
timate p
a
ra
metric rel
a
tio
n
shi
p
s betwe
en the
s
e va
riable
s
, but t
h
e
pre
s
en
ce
of outliers can
have a sig
n
ificant
an
d un
desi
r
ed influ
e
n
ce u
pon th
e bilinea
r mo
del
obtaine
d.
In pra
c
tical p
r
oje
c
t, the m
odelin
g data
may co
ntain
outlying ob
se
rvations ma
d
e
by the
power sy
ste
m
fluctuation
or mea
s
u
r
em
ent error. To
solve this p
r
o
b
lem, this pa
per p
r
op
oses an
advan
ced
ap
proa
ch to
asse
ss th
e ha
rmonic
emi
ssi
on level ba
sed on
rob
u
st
PLS reg
r
e
s
sion.
This
metho
d
focu
se
s
on
incorp
oratin
g ro
bu
st
reg
r
essio
n
m
e
th
od into
PLS, overcom
e
s
th
e
deficie
nci
e
s o
f
existing wo
rk. Section
2 g
i
ves a b
r
ief in
trodu
ction of
robu
st PLS al
gorithm
and it
s
pro
c
ed
ure. Section
3 p
r
e
s
ents h
a
rm
oni
c sou
r
ce
mo
d
e
l, describe
s
its ba
sic pri
n
ciple
and
ma
ke
s
simulatio
n
studie
s
.
Sectio
n
4 pre
s
e
n
ts the
fiel
d m
e
a
s
ureme
n
t re
sults, an
d Se
ction 5
co
nclu
de
s
this pap
er.
2. Robus
t PLS Algorithm
The cla
s
sical
PLS proce
d
u
re
s are
kno
w
n to be sev
e
rely affecte
d
by the presen
ce of
outliers in the
data or d
e
viations from n
o
rmalit
y [16]. It’s beca
u
se
both stag
es
of the algorit
hm
are not re
si
stant towards
outlying obse
r
vations. Th
e
main strateg
i
es for ro
bu
st PLS regre
s
sion
is ro
bust e
s
ti
mation of the
covaria
n
ce
matrix. The PLS method a
r
e ro
bu
stified
by repla
c
ing
th
e
s
a
mple cr
oss-
c
o
var
i
ance
matr
ix S
xy
by a rob
u
st e
s
ti
mate of
xy
and
the empi
rical covari
an
ce
matrix S
x
by
a robu
st esti
mate of
x
and by performi
n
g a robu
st re
gre
ssi
on met
hod in
stead o
f
multiple linea
r reg
r
e
ssi
on (MLR) [17].
Thro
ugh
out this sectio
n column ve
ct
ors are pri
n
ted
in bold. A ma
trix
V
stand
s for the
transpo
se of
V and X
n,p
is an
(n
p
)
-d
imensi
onal matrix.
1n
n
,
p
(,
,
)
X
xx
and
1n
n
,
p
(,
,
)
Y
yy
are the re
gre
s
sors and the
resp
on
se variable
s
, respe
c
tively.
The linea
r re
gre
ssi
on mo
d
e
l we con
s
ide
r
is:
'
i0
q
,
p
i
i
B
y
β
xe
(
1
)
Whe
r
e the
error term
s
i
e
sat
i
sf
y
E
(
i
e
)=0 and
cov
(
i
e
)=
e
of
size
q.
The unknown
00
1
0
q
(,
,
)
'
and B
p,q
are
the
q
–dim
e
nsio
nal inte
rcept and the
unkno
wn sl
o
pe matrix,
r
e
spec
tively.
Assu
ming tha
t
the x and y
variable
s
a
r
e
related th
rou
gh a bilinea
r
model.
ip
,
k
i
i
P
xx
t
g
(2)
'
iq
,
k
i
i
A
yy
tf
(3)
In this
model,
x
and
y
are t
he mea
n
s
of the x- and
y- varia
b
le
s. The
i
t
are k-di
mensi
onal,
whi
c
h a
r
e the
score
s
of
m
ean-ce
ntered
data.
p
,k
P
and A
k,q
are the mat
r
ix of
x
-lo
adin
g
s an
d the
slop
e matrix in the reg
r
e
s
sion of
i
y
on
i
t
,resp
e
ctively.
i
g
and
i
f
are the resid
ual
s of each
equatio
n.
The bilin
ear
stru
cture (2
)
and (3) im
pli
e
s a t
w
o-ste
p
algo
rithm. In the first
st
age, we
sho
u
ld
obtai
n the
ro
bu
st sco
r
e
s
i
t
.
First, we appl
y
rob
u
st pri
n
cip
a
l comp
onent analy
s
is
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An Approa
ch
for Assessin
g
Harm
oni
c Em
ission Le
vel
Based on
Ro
bust Partial
…
(Xiang Li)
4983
(ROBPCA) on Z
n,m
=(X
n,p
, Y
n,q
). Then
a robu
st e
s
timate of the center of Z,
''
'
Zx
y
(,
)
, and
an estimate o
f
its shape
z
are yielded.
z
ca
n be split into
:
xx
y
z
yx
y
(4)
W
e
es
timate
the cr
os
s-
covar
i
anc
e
matr
ix
xy
instea
d of
Sxy and co
m
pute the
wei
ght
vectors ra in
robu
st PLS algorithm . In eac
h
step the robu
st score
s
are calculate
d
as:
'
ia
i
x
a
t(
)
xr
(5)
I
n
t
he se
con
d
st
age
，
the r
e
sp
o
n
s
e
ar
e
r
e
gresse
d
onto these
k
c
o
mp
on
en
ts
. T
h
e
reg
r
e
ssi
on m
odel is thu
s
:
'
i0
q
,
k
i
i
A
y
tf
(6)
Whe
r
e E(
i
f
)=0 and cov(
i
f
)=
f
. Multiple linea
r regre
s
sion p
r
o
v
ides e
s
timates:
1'
1
'
k,
q
t
t
y
k,
p
x
p
,
k
k
,
p
x
y
A(
)
(
R
R
)
R
(7)
'
0q
,
k
A
y
t
(8)
Whe
r
e
y
and
t
are the ro
bu
st covarian
ce
matrices of the y
-
and
t
-
v
a
riable
s
. By
insertin
g
'
ik
,
p
i
R(
)
tx
x
in (3), we o
b
tain estimate
s for the para
m
eters in the origin
al mode
l (1), i.e.:
p
,q
p
,
k
k
,q
BR
A
(9)
'
0q
,
p
B
y
x
(10)
3. Verificatio
n b
y
Simulation Stud
y
A simulatio
n
study of the
method
of a
s
se
ssi
ng h
a
rm
onic
emi
ssi
on
ba
sed
on
ro
bust PLS
reg
r
e
ssi
on
was p
e
rfo
r
me
d
with the
M
A
TLAB software. T
he
sim
u
lation
study
inclu
d
e
s
three
ca
se
s. In case 1, the
simu
lation re
sult
s
are
obt
aine
d
based o
n
PL
S without o
u
tliers. In
ca
se
2,
the results are base
d
on PLS with outliers, and in
case 3, based o
n
robu
st PLS with outliers. All
the re
sult
s a
r
e compa
r
e
d
with e
a
ch oth
e
r. Th
e b
a
si
c
equivalent
ci
rcuit for ha
rmo
n
ic
analy
s
is a
nd
the prin
ciple
of assessin
g emission leve
l
are intro
d
u
c
ed before the
simulation
study.
3.1. The Basi
c Principle
The equival
e
nt circuit is prese
n
ted in Figure 1.
In Fig
u
re 1, the disturban
ce
sou
r
ce
s a
r
e
the custo
m
er harmoni
c
source
I
ch
and the
utility harm
oni
c
source
U
sh
;
Z
ch
and
Z
sh
ar
e th
e
harm
oni
c imp
edan
ce
s of the respe
c
ti
ve system
s. The
current ph
asor
I
ph
and voltage ph
asor
U
ph
are me
asure
d
at the PCC.
h
is a parti
cu
lar ha
rmoni
c
orde
r.
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 4981 – 49
87
4984
Figure 1. Basic Equivalent
Circuit for Ha
rmoni
c Analy
s
is
Assu
ming th
a
t
the circuit i
m
peda
nces
a
r
e
kno
w
n, the
harm
oni
c so
urce on
the u
t
ility side
can b
e
cal
c
ul
ated dire
ctly from the mea
s
ured q
uantitie
s:
••
•
sh
p
h
p
h
s
h
=+
UU
I
Z
(11)
Split phaso
r
Equation (5) i
n
to the real p
a
rt and ima
g
i
nary pa
rt:
s
h
x
phx
phx
s
h
x
phy
s
h
y
=+
-
UU
I
Z
I
Z
(12)
s
h
y
phy
phx
s
h
y
p
h
y
s
h
x
=+
+
UU
I
Z
I
Z
(13)
Reg
r
e
ssi
on coefficient
s
U
sh
x
,
U
sh
y
,
Z
sh
x
,
Z
sh
y
are worked o
u
t throu
gh linea
r re
gression.
Due to the
eq
uivalent mod
e
l, the cu
sto
m
harm
oni
c source i
s
equ
a
l
to a con
s
tan
t
current
sou
r
ce with a
very sm
all internal
resi
st
ance wh
ile
the
system
h
a
rmo
n
ic source i
s
equ
al t
o
a
con
s
tant volt
age
so
urce
with a
large i
n
ternal
resi
st
ance. The
r
ef
ore
owi
ng to
ch
sh
Z
Z
, the
cu
stome
r
harmonic e
m
issi
on level ca
n be ca
l
c
ul
ated
approxim
atel
y as Equation
(14).
ph
ch
s
h
ch
p
h
s
h
p
h
ch
ch
sh
U
ZZ
UI
Z
I
ZZ
Z
(14)
3.2. Simulation Res
u
lts a
nd Discu
ssi
on
The com
pute
r
simulatio
n
b
a
se
d
o
n
the
harm
oni
c sou
r
ce
dete
c
tion
model evalua
tes
the
hth harmoni
c voltage emi
s
sion l
e
vel usi
ng the
softwa
r
e Matla
b
/Simulink,
whe
r
e
ph
50
5
1
U
V,
ph
6.
3
6
45
I
A, the mean value of
Z
sh
and
Z
ch
are
15+j
3
0
and 2
5
+j3
0
0
r
e
s
pec
tive
ly
.
The sim
u
latio
n
cre
a
te suffi
cient waveform chan
ge
s for utility impedance determi
nation.
The harmoni
c voltage and
current data
measured
at PCC are sh
o
w
n in Figu
re
2, which
has 5
00 sam
p
le point
s.
Figure 2. Magnitude
Wave
forms of
h
-th
Voltage and
Curre
n
t at PCC
Figure 3.
h
-th
Harm
oni
c Impeda
nce of
Har
m
oni
c Po
wer Sy
ste
m
0
10
0
20
0
30
0
40
0
50
0
20
0
25
0
s
a
m
p
le
p
o
in
t
s
n
u
m
b
e
r
(a
) v
o
l
t
a
g
e
wa
v
e
f
o
rm
Up
h
/
V
0
10
0
20
0
30
0
40
0
50
0
5
5.
5
6
s
a
m
p
le
p
o
in
t
s
n
u
m
b
e
r
(b
) c
u
rr
e
n
t
w
a
v
e
f
o
r
m
Ip
h
/
A
0
5
10
15
20
10
12
14
16
18
(a
)
R
e
(Z
s
h
)/
Ω
0
5
10
15
20
24
26
28
30
32
(b
)
I
m
(Z
s
h
)/
Ω
ca
se
2
ca
s
e
2
ca
se
1
ca
se
1
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An Approa
ch
for Assessin
g
Harm
oni
c Em
ission Le
vel
Based on
Ro
bust Partial
…
(Xiang Li)
4985
The
re
sults o
f
the Z
sh
ar
e e
s
tima
ted
in th
r
e
e d
i
ffe
ren
t
c
a
s
e
s
(
5
0 s
a
mp
le
p
o
i
nts
as
a
subi
nterval
)
. In ca
se
1, the
estimatio
n
result
s a
r
e
co
mputed
ba
se
d on PLS
reg
r
essio
n
. In ca
se
2, five outliers are a
dded i
n
every 50 sample volt
ag
e and cu
rrent
points artifici
ally. As shown in
Figure 4, it’s difficult to re
move the
out
liers
dire
ctly. The re
sult
s o
f
the Z
sh
are estimated
wit
h
these
data b
a
s
ed
on PLS a
gain. In case
3, the re
sult
s
are
estimate
d
based o
n
ro
bust PLS
with
outliers. The result
s in thre
e ca
se
s are
shown in Figu
re 3 and Figu
re 5.
Figure 4. 50 Sample Point
s
of Voltage a
nd
Curre
n
t at PCC and Five O
u
tliers
Figure 5.
h
-th
Harm
oni
c Impeda
nce of Powe
r
Sys
t
em
The relative
errors of Z
s
h
x
and Zshy e
s
timated in
case
1, ca
se
2
and
ca
se 3
a
r
e sho
w
n
in Table
1. The erro
r of ev
ery estim
a
tio
n
is me
an val
v
e of results
by Equation (12) a
nd Equ
a
t
ion
(13
)
.
Table 1. Co
m
pari
s
on of Errors of
Z
sh
of Ca
se 1,Case 2 and Case 3
Error
%
Z
sh
x
1 2 3 4
5 6 7 8 9 10
Mean
Value
Case
1
0.49 0.27 0.89 0.56
1.32 0.39 1.91 0.51 0.68 0.62 0.764
Case
2
20.98
22.39
23.61
17.76
19.10
17.30
15.59
29.01
19.37
20.65
20.576
Case
3
1.60 2.02 0.75 0.36
0.98 0.73 0.81 0.76 1.57 1.37 1.095
Z
sh
y
Case1
0.51 0.64 0.24 0.10
0.66 0.37 0.64 0.75 0.55 0.12 0.458
Case2
9.55 11.77
10.23
8.54
9.39 8.46 8.87 15.65
8.48 9.76 10.07
Case3
0.42 0.80 0.40 0.71
0.98 1.03 0.80 1.51 0.56 0.82 0.803
As is
sho
w
n i
n
Figu
re 3
an
d Figu
re 5, th
e estimatio
n
result
s of Z
sh
are n
e
a
r
ly the sam
e
by Equation
(13)
and Eq
ua
tion (1
4) in
ca
se 1
an
d ca
se 3. However, the re
sults a
r
e very
differe
nt
in case 2. A
n
d from
Ta
ble
1, we
can
se
e the
es
tim
a
tion e
r
rors i
n
case
2
are a
b
out ten tim
e
s in
ca
se 1 an
d case 3. Estima
tion errors in ca
se 1 an
d case 3 a
r
e bot
h small. The
simulatio
n
re
sults
show the sensibility to outliers of PLS and
effectiveness and
robustness of robust PLS.
Acco
rdi
ng to
Equation
(1
4), the
custo
m
er
harmoni
c e
m
ission
le
vel is
193.0
4
V
, about
86.91% of th
e harmoni
c
voltage at
PCC. Th
e a
s
sessment
re
sult
agre
ed in
the theoretical
cal
c
ulatio
n re
sult indi
cate
s that the prop
ose
d
method
is valid.
4. Result
fro
m
Field Study
In this se
ctio
n, we use ro
bust PLS reg
r
es
sio
n
menti
oned a
bove to cal
c
ulate th
e utility
harm
oni
c imp
edan
ce
s an
d the harm
oni
c voltage emissi
on levels of the cu
stome
r
i
n
real
-world.
-5
-4
-3
-2
-5
-4.
8
-4.
6
-4.
4
-4.
2
-4
-3.
8
-3.
6
R
e
(I
ph)/
Ω
Im
(
Ip
h
)/
Ω
-60
-4
0
-20
20
0
21
0
22
0
23
0
24
0
R
e
(U
ph)/
Ω
I
m
(U
p
h
)/
Ω
o
u
t
lie
r
s
o
u
t
lie
r
s
0
5
10
15
20
10
12
14
16
18
(a
)
R
e
(Z
s
h
)/
Ω
0
5
10
15
20
24
26
28
30
32
(b
)
I
m
(Z
s
h
)/
Ω
ca
s
e
1
ca
se
3
ca
se
1
ca
se
3
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 4981 – 49
87
4986
Measurement
s have
be
en t
a
ke
n at a
35
KV bus
of Qi
ngga
ng Sub
s
tation co
nne
cted to a
disturbing
loa
d
: a
steel
mill
. The
minimu
m shor
t
-
ci
rcui
t cap
a
city i
s
120.8MVA
an
d the
maximu
m
s
h
ort-c
i
rc
uit capac
i
ty is
250MVA.
The
sam
p
le
freque
ncy
of
the in
strum
ent
is
12
8 sample
s per
50Hz-cycl
e; FFT (Fa
s
t
Fouri
e
r
Tra
n
s
form
) i
s
im
p
l
emented
to
get t
he harm
onic
voltage
and cu
rrent para
m
eters. The
500
t
r
an
sformation
d
a
ta a
r
e obtaine
d. The wavefo
rm of the
5th
harm
oni
c volt
age
and
current at
th
e
PC
C
ar
e
s
h
ow
n
in
F
i
gu
r
e
6
The e
s
timat
ed results o
f
the utility harm
oni
c im
peda
nce ba
sed
on
rob
u
st PLS
reg
r
e
ssi
on are sho
w
n in Fi
gure 7.
Figure 6. 5th Harmoni
c Vol
t
age and
Current
at PCC
Figure 7. 5th Harmoni
c Impeda
nce of Powe
r
Sys
t
em
The m
ean val
ue of Z
s5
cal
c
ulated b
a
sed
on the
estim
a
ted re
sult
s i
s
48.276
. Then
the
cu
stome
r
ha
rmonic
emi
ssi
on level i
s
calcul
at
ed by
the Equatio
n (15
)
. It’s
about 8
2
.827
V,
24.92% of th
e harmoni
c voltage at
PCC. Du
e to the low
ratio o
f
nonlinea
r lo
ad, the cu
sto
m
harm
oni
c emi
ssi
on level is
low. However, th
is steel has little impact
on the utility
grid.
Acco
rdi
ng to
the
sho
r
t-ci
rcuit
ca
pa
city
mentione
d
above, th
e
fundam
enta
l
wave
impeda
nce of
the
real
syst
em rang
es from 5.4
7
6
and
11.33
3
. The
es
timated fifth harmonic
rea
c
tan
c
e i
s
48.12
, then the funda
men
t
al wave rea
c
tan
c
e i
s
9.6
2
4
, which i
s
con
s
i
s
tent
with the
actu
al impe
dan
ce variatio
n range. T
he
e
s
timated
re
sults of t
he
re
al syste
m
further
verify the accura
cy and effectivene
ss of robu
st PLS re
gre
ssi
on.
5. Conclusio
n
This p
ape
r p
r
ese
n
ts a
new approa
ch to
t
he evaluatio
n of cu
stome
r
and
utility harmo
nic
contri
bution
s
at PCC. The
prop
osed a
ppro
a
ch
is b
a
se
d on
rob
u
st PLS re
gression. Esse
ntial
advantag
e of
PLS ap
pro
a
c
h
are
its
ab
ility to deal
with
colline
a
r variabl
es an
d optimi
z
e th
e
compl
e
xity of the mo
del.
Ho
wever, it’
s
seve
rely
aff
e
cted
by outl
i
ers. In
p
r
acti
cal
proj
ect, t
h
e
observation
s at PCC m
a
y contain
some outlie
rs
due to the
powe
r
sy
stem fluctuatio
n or
measurement
error.
The
robu
st PLS o
v
erco
me
s the
defe
c
t of PL
S and
retain
s its adva
n
ta
ge.
The
pro
p
o
s
e
d
meth
od
ha
s b
een
teste
d
u
s
ing
si
mu
lation
studie
s
and
field
m
easure
m
ent
s. Its
perfo
rman
ce
and
accu
racy h
a
ve b
een fo
und
very goo
d.
The m
e
thod
is
adeq
uat
e for
determi
ning t
he syste
m
ha
rmoni
c impe
d
ance and
system or cu
sto
m
er emi
ssi
on
level.
Referen
ces
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M F
a
rhoo
dn
ea
, A Moham
ed,
H Shar
eef.
N
o
vel Meth
od
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Deter
m
in
in
g th
e Co
ntrib
u
tion
of Utility
and
Custo
m
er Har
m
o
n
ic Distorti
o
n in Distrib
utio
n Systems.
T
h
e 4th Internalti
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l Po
w
e
r En
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eeri
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onfere
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rm
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u
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)
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5
y
/
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Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An Approa
ch
for Assessin
g
Harm
oni
c Em
ission Le
vel
Based on
Ro
bust Partial
…
(Xiang Li)
4987
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