TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 12, Decembe
r
2014, pp. 79
9
6
~ 800
0
DOI: 10.115
9
1
/telkomni
ka.
v
12i12.64
74
7996
Re
cei
v
ed
Jun
e
27, 2014; Revi
sed Septe
m
ber
21, 201
4; Acce
pted
Octob
e
r 16, 2
014
A High-accuracy Detection Method Research f
o
r
Electric Power Harmonic
Jingfan
g Wa
ng
Schoo
l of Information Sci
enc
e and En
gi
neer
ing, Hu
na
n Internatio
nal Ec
on
omics Univ
ersit
y
,
Chan
gsh
a
, Ch
ina, postco
de:4
102
05
email: matl
ab_
b
y
s
j
@1
26.com
A
b
st
r
a
ct
In this pa
per,
a time-freq
uen
cy filter is d
e
si
gne
d, w
h
ich ca
n detect th
e frequ
ency, a
m
pli
t
ude a
n
d
phas
e of any
order
har
mo
ni
cs and i
n
terh
a
r
mo
nics i
n
sig
nal by
mea
n
s of
time do
mai
n
conv
oluti
on. T
h
e
theory a
n
a
l
ysis
are carr
ie
d to
this
meth
od
a
nd the
calc
ul
ate for
m
ul
a ar
e
concl
ude
d, the
spectral
le
aka
g
e
and
the
b
a
rrier
do
mino
offect
are s
h
u
n
, the
non-
integ
e
r
or
der w
a
ve
ar
e
e
l
ud
ed, w
h
ic
h
a
r
e e
n
g
end
ere
d
i
n
F
ourier d
o
mai
n
. Experiment si
mu
lati
on resu
lts show
t
hat ti
me-fre
qu
ency filterin
g conv
olu
t
ion fluncti
on c
a
n
be des
ign
ed a
nd rea
l
i
z
e
d
ne
atly and co
nve
n
ie
ntly ; t
he influenc
es of fund
amenta
l
freque
ncy fluctuatio
n
o
n
har
mo
nic
an
al
ysis ar
e restra
i
ned
by
usi
n
g
the
ap
proac
h
p
r
esente
d
in t
h
i
s
pa
per
；
the
relative errors
of
calcul
atin
g fu
n
d
a
m
e
n
tal fr
eq
uenc
ies w
i
th
ma
ny
order
h
a
r
mo
nics an
d
i
n
terhar
monics
are no more
than
0.000
08
％
, th
e re
lative
er
or
s of c
a
lcu
l
atin
g
a
m
plitu
des
are no
more
than 0.00
01
3
％
, and
thos
e
of
calcul
atin
g initi
a
l ph
ases ar
e no more tha
n
0
.
078
％
.
Ke
y
w
ords
: har
mo
nic a
nalys
is
, time-freq
uenc
y filteri
ng, conv
oluti
on, freque
ncy fluctuatio
n
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
High
-p
re
cisio
n
analysi
s
of harm
onic power me
asu
r
em
ent, harm
oni
c po
wer fl
o
w
cal
c
ulatio
n, netwo
rk te
st
ing eq
uipme
n
t,
powe
r
system
h
a
rmonics com
pen
sation a
nd
sup
p
re
ssion
is of great
signifi
can
c
e
[1]. Becau
s
e n
on-syn
c
hron
ou
s sa
mpling a
nd
data
truncation, th
e use of fa
st Fouri
e
r tra
n
sf
orm (F
FT) al
gorithm to ge
nerate
harmo
nic an
alysi
s
a
nd
fence effe
ct of spect
r
um le
aka
ge, the
accuracy of ha
rmonic a
nalysi
s
[2-3].
To re
du
ce
su
ch e
r
rors, scholars at h
o
m
e
and abro
ad
ba
sed on recta
ngul
ar windo
w
[4],
Han
n
ing
wind
ow [5], Ham
m
ing win
d
o
w
[6], Blackma
n
wind
ow [7], Blackm
an
-Harri
s wi
ndo
w
[8],
Kaise
r
wind
o
w
[9]
and
ot
her wi
ndo
we
d inte
rpolatio
n FFT
signal
analy
s
is alg
o
rithm
s
, FFT
ca
n
redu
ce
the e
n
co
unter alo
ne an
d fen
c
e
effect
of
sp
ectru
m
lea
k
a
ge p
r
obl
ems
and im
prove
the
detectio
n
accura
cy of harmonic p
a
ra
m
e
ters, but
ca
n not detect integer h
a
rm
onics ha
rmo
n
ics
near the
aski
ng; u
s
e
com
b
ination
of hig
h
-en
d
wind
o
w
-b
ased
dou
ble-co
sine
sp
ectru
m
[5,7,1
0] or
line [11-12] interpol
ation
FFT algo
rith
m to es
timat
e
fundam
ent
al and the h
a
r
moni
c pa
ra
meters,
need to solve high-order
equatio
n [13-15], comput
i
ng com
p
lex; contin
uou
s wavelet transf
o
rm
[16-17] ca
n be
reali
z
ed betwe
en/ha
rmonic
dete
c
t
i
on,
but the
wavelet fun
c
t
i
ons of different
scale
s
exist
in the freque
ncy do
main i
n
terferen
ce,
whe
n
the te
st si
gnal
co
n
t
ains h
a
rm
on
ic
freque
nci
e
s
close to, the d
e
tection meth
od failure
; Prony method [
18-1
9
] is ha
rmonic, ha
rmo
n
ic
analysi
s
and
modelin
g of
i
n
ter-effective
way to
a
c
curately estim
a
te the
si
nu
soi
dal
com
pone
nt of
freque
ncy, a
m
plitude a
n
d
phase an
gle
,
but the nee
d to solve eq
uation
s
and t
w
o sets of o
dd a
polynomial, computation
a
l compl
e
xity and high se
ns
iti
v
ity
to noise; there a
r
e oth
e
r metho
d
s [20-
22], or limite
d
freq
uen
cy
resolution,
or com
put
ing
cap
a
city, bot
h in the
spe
c
ific
appli
c
ati
on
limitations.
This p
ape
r
pre
s
ent
s a t
i
me-fre
que
ncy filter
s, time domai
n convolution
with high
accuracy by
detecting t
he sig
nal a
m
ong all
th
e harm
oni
cs and the ha
rmoni
c fre
q
u
ency,
amplitude
an
d pha
se. In th
is pa
per,
a th
eoreti
c
al a
nal
ysis a
nd
cal
c
ulation formul
a is d
e
rived, t
h
e
method
to av
oid the
Fo
uri
e
r
(FFT
)
do
main
spe
c
tral
lea
k
ag
e, the
entire
sub
-
b
a
rri
er effect
and
non-wave
ph
enome
non. The simul
a
tion
results show
that: time-fre
que
ncy
co
nvolution
filter
desi
gn flexibl
e
, easy to u
s
e, this algo
rit
h
m ca
n elimi
nate the h
a
rmonic i
n
terfe
r
ence an
d imp
r
ove
sign
al analysi
s
pre
c
i
s
ion, hi
gh accu
ra
cy for ha
rmoni
c a
nalysi
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A High-accu
racy Dete
ction
Method Re
search
for Ele
c
tri
c
Powe
r Harm
onic (Jin
g
f
ang Wa
ng)
7997
2. The Time-Freque
nc
y
F
ilter Design
Time-frequ
en
cy filter:
t
j
at
e
at
at
at
t
g
0
)
90
)
(
30
)
(
12
)
(
(
)
,
(
6
5
4
0
(
1
)
Whe
r
e
B
a
3
2
Cent
er fo
r the filte
r
pa
ram
e
ters,
the
c
oefficie
n
t B to adj
ust
the filter
ban
dwidth
(su
c
h a
s
ta
king B = 0.04),
ω
0 cente
r
fre
quen
cy. The frequ
en
cy do
main expression is:
7
0
6
6
0
5
5
0
4
0
0
))
(
(
8
))
(
(
4
))
(
(
2
)
(
)
,
(
j
a
a
j
a
a
j
a
a
H
G
(
2)
Figure 1
sho
w
s the trend
of time-frequ
ency filter
ch
ara
c
teri
stics,
(a) tren
ds in
the time
domain
g
r
ap
h, (b
) trend
s
in the f
r
eq
ue
ncy d
o
ma
in;
they chan
ge
with the
cent
er frequ
en
cy
ω
0.
By (2) a
nd
Figure 1
(b) sho
w
s G
(
ω
,
ω
0) only
in a n
a
rro
w
band
ce
ntered
ω
0 signifi
cant
amplitude, th
e other is al
m
o
st ze
ro. Fa
rther a
w
ay fro
m
the
ω
0, | G
(
ω
,
ω
0) | is smaller.
Figure 1. Time-fre
que
ncy filter of time/frequen
cy
3, Theore
t
ic
al Analy
s
is a
nd Calcula
t
ion Formulas
b
y
3.1. Analy
s
is
of Con
t
inuo
us
If
ω
0 centere
d
within the range of na
rro
w
-b
and frequ
ency
ω
1 of the harm
oni
c si
gnal:
)
cos(
)
(
1
t
A
t
f
(
3
)
Its freque
ncy
domain exp
r
e
ssi
on:
]
)
(
)
(
[
)
(
1
1
j
j
e
e
A
F
(
4
)
)]
(
)
(
)
(
)
(
[
)
(
)
(
)
(
)
,
(
)
(
1
0
1
1
0
1
0
0
j
j
e
H
e
H
A
F
H
F
G
Y
(5)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 7996 – 80
00
7998
]
)
(
)
(
[
2
)
,
(
)
(
)
(
1
1
0
1
0
1
0
t
j
j
t
j
j
e
e
H
e
e
H
A
t
g
t
f
t
y
(6)
Whe
r
e
for the convol
ution o
peratio
n,
0
|
)
(
|
0
1
H
:
Arg
d
t
t
y
Arg
d
)))
(
(
(
1
is Angular
(7)
|
)
(
|
|
)
(
|
2
0
1
H
t
y
A
(8)
mod[]
)
(
(
]
2
,
mod[
))
(
(
0
1
1
H
Arg
t
t
y
Arg
The rem
a
ind
e
r is divisi
ble
(9)
3.2. Calculati
on of Disc
rete
Set of di
scret
e
samplin
g freque
ncy f
s
, t
he
sam
p
ling
perio
d
DT
=
fs
1
, Numb
er of
sa
mples
is
N; tak
e
N
1
=[0.5N], N
2
=[0.
94N], Com
p
u
t
ing discrete
convol
ution:
N
k
i
k
f
i
g
DT
k
y
N
k
N
k
i
,
,
2
,
1
)
(
)
(
)
(
}
,
1
min{
}
,
1
max{
(10)
)
11
(
function
Sign
;
,
,
))}
1
(
(
))
(
(
(
,
0
max{
2
))
1
(
(
))
(
(
)
(
2
1
N
N
k
k
y
Arg
k
y
Arg
Sign
k
y
Arg
k
y
Arg
k
(11
)
The ha
rmoni
c frequen
cy f (Hz), amplitud
e A, the initial phase
φ
(
℃
) as
, res
p
ec
tively:
2
1
)
(
)
1
(
2
1
2
N
N
k
k
N
N
fs
f
(12)
fs
f
2
1
(13)
2
1
|
)
(
|
)
1
(
|
)
(
|
2
1
2
0
1
N
N
k
k
y
N
N
H
A
(14)
)
15
(
))
(
(
})
]
2
,
)
1
(
2
mod[
))}
(
(
(
,
0
max{
2
))
(
(
{
(
)
1
(
1
0
1
1
2
2
1
H
Arg
fs
f
k
k
y
Arg
Sign
k
y
Arg
N
N
N
N
k
(15
)
)})
(
,
0
max{
2
(
180
Sign
(
1
6
)
4. Experimental Ev
aluation
Signal
co
ntains fu
nda
men
t
al, DC,
bet
wee
n
2
an
d
3
harmoni
c ha
rmoni
c,
a
nd thei
r
para
m
eters in
Table 1, the expre
ssi
on:
6
0
)
cos(
)
(
i
i
i
i
t
A
t
f
(
1
6
)
Its sampli
ng f
r
equ
en
cy fs = 2000
Hz, n
u
m
ber of
sam
p
les
N =
500
0. This meth
o
d
re
sults
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A High-accu
racy Dete
ction
Method Re
search
for Ele
c
tri
c
Powe
r Harm
onic (Jin
g
f
ang Wa
ng)
7999
are i
n
Ta
ble
1 the
rig
h
t
depa
rtment.
To the
ha
rm
onic freq
uen
cy, amplitud
e
,
initial pha
se of
testing the va
lue of the real
value and are plotted in
the same pl
ot, the re
sult is very accu
rate.
Figure 2. The
harmo
nic
ch
ara
c
teri
stics
of the
true value of para
m
e
t
ers
comp
are
d
with the
measured val
ues
Table
1 h
a
rmonic of the
frequ
en
cy f =
350.
7
H
z
spe
c
ific icon
nea
r the
d
e
tection
algorith
m
s 3,
Figure (a
), (b), (c
) of the
absci
ssa as t
he sample
p
o
ints. Figu
re
(a) th
e type (10)
the magnitud
e
, Figure (c) signal after
filtering
in fre
quen
cy dom
ain inverse F
ourie
r tran
sfo
r
m
(IFFT) of th
e amplitu
de,
both i
n
the
sa
me
500
points;
Figu
re (b) th
e type
(11
)
tran
sient
freque
ncy.
Figure 3. The
result
s of har
monic frequ
e
n
cy f = 350.7
H
z
5. Conclusio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 7996 – 80
00
8000
This pa
per p
r
esents a
tim
e
-fre
que
ncy f
ilter
, thro
ugh
the time
-d
o
m
ain
co
nvolu
t
ion can
accurately de
tect the signa
l between all
the
harmo
nics and the ha
rmonic freque
ncy, amplitud
e
and
pha
se. In
this pa
per,
a
theoreti
c
al
an
alysis an
d
cal
c
ulatio
n fo
rm
ula i
s
d
e
rive
d
,
the meth
od
to
avoid the Fo
urie
r (FF
T
) d
o
main
spe
c
tral leak
age, t
he entire su
b
-
ba
rrie
r
effect
and no
n-wa
ve
phen
omen
on.
The
simulati
on re
sult
s sh
ow that: time
-freque
ncy
co
nvolution filte
r
de
sign flexi
b
le,
proje
c
t imple
m
entation an
d the algorith
m
is si
mple
convenie
n
t, quick respon
se.
This algo
rith
m
can elimi
nate
the harmo
nic interfere
n
ce and imp
r
ov
e sign
al analysi
s
pre
c
i
s
ion, hi
gh accu
ra
cy for
harm
oni
c ana
lysis.
Referen
ces
[1]
Ortme
y
er T
H
,
Chakr
a
varthi K
R
, Mahmou
d
A A.
T
he effects of po
w
e
r s
y
stem h
a
rmon
i
cs on po
w
e
r
s
y
stem e
qui
p
m
ent an
d lo
ad
s.
IEEE Trans. on Pow
e
r Ap
paratus
and S
ystems
. 19
85;
104(
9): 255
5-
256
3.
[2]
Gregori
o
A, Mario S, Am
erig
o T
.
W
i
ndo
w
s
a
nd
i
n
ter
pol
ation
al
gori
t
hms to impr
ove e
l
ectrica
l
measur
ement accurac
y
. IEEE Trans. on Instrum
e
ntation and Meas
urem
ent.
1989; 38(
4): 856-8
63.
[3]
X
U
E H, YANG RG.
Pre
c
ise
alg
o
r
it
h
m
s fo
r
ha
rmo
n
i
cs an
a
l
ysis b
a
s
e
d
on
FFT a
l
g
o
r
it
h
m
.
Procee
din
g
s
of the CSEE. 2002; 22(
12): 10
6-11
0.
[4]
Jain VK, Co
lli
ns WL, Davis DC. Hig
h-accu
ra
c
y
ana
lo
g measur
ements v
i
a inter
pol
ated
F
F
T
.
IEEE
T
r
ans. Instrum.
Meas.
1979; 2
8
(2): 113-
12
2.
[5]
PAN W
,
QIAN
YSH, Z
H
OU E. Po
w
e
r h
a
r
m
onics me
asu
r
ement b
a
se
d
on
w
i
nd
o
w
s
a
nd i
n
terpo
l
ate
d
FFF
(
Ⅱ
) dual interpo
l
ate
d
F
F
T
algorithms.
T
r
ansacti
ons of Chin
a Electrot
echn
ical Soc
i
et
y
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