Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
5, N
o
. 1
,
Febr
u
a
r
y
201
5,
pp
. 16
6
~
17
4
I
S
SN
: 208
8-8
7
0
8
1
66
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Impact
of Harm
onics on
P
o
we
r Quality and Losses in
Power Distribution Systems
M
.
Ja
wa
d Gho
r
ba
ni*, H.
Mo
kht
a
ri
**
* Dept. of CSEE, West Virg
inia
University
, Morgantown,
WV,
USA
** Dept. of
EE,
Sharif University
of Techno
log
y
, Tehran
, Ir
an
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 22, 2014
Rev
i
sed
D
ec 25
, 20
14
Accepte
d
Ja
n 10, 2015
This paper inv
e
stigat
es the h
a
rm
onic distortion and losses in power
distribution s
y
s
t
ems due to the dramatic
in
cre
a
se of nonline
a
r l
o
ads. This
paper
tries
to d
e
termine
the amount of
the harmonics gen
e
rated b
y
non
lin
ear
loads in resid
e
nt
ial
,
com
m
e
rcia
l
and offic
e
lo
ads in distribu
tion f
eeders an
d
es
tim
ates
the
e
n
erg
y
los
s
e
s
due to thes
e h
a
rm
onics
. Norton equival
e
nt
modeling techn
i
que has b
een
used
to m
odel
the non
line
a
r
loads.
The
presented h
a
rmonic Norton
equivalen
t
mode
ls
of
the
end us
er ap
plian
ces
ar
e
accur
a
t
e
l
y
obt
ai
ned bas
e
d
on th
e
exper
i
m
e
ntal
da
ta t
a
ken
from
th
e labo
rato
r
y
measurements. A 20 kV/400V
distribution
feed
er is simulated to analy
z
e th
e
impact of nonlin
ear loads on feeder harmonic distortion lev
e
l and
losses. The
model follows a “bottom-up” ap
proach
, star
ting
from end users
appliances
Norton equivalent model and then m
odeling residential,
com
m
e
rcial an
d
office lo
ads. Tw
o new indices ar
e intr
oduced b
y
the authors to q
u
antize th
e
effec
t
of each
nonline
a
r appli
a
nce on the power quali
t
y
of a
distributio
n
feeder
and loads are ranked
based
on these new defined indices.
Th
e
simulation r
e
sults show that h
a
r
m
onic di
stortion
in d
i
stribution s
y
stems can
increase power
losses up to 20%
.
Keyword:
Harm
oni
c Di
st
ort
i
o
n
Lo
ss Estim
a
tio
n
No
n-l
i
near Loa
d
s
No
rt
o
n
E
q
ui
va
l
e
nt
M
o
del
Power Qu
ality
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
M
.
Jawa
d G
h
o
r
ba
ni
,
Depa
rt
em
ent
of C
o
m
put
er
an
d El
ect
ri
cal
E
n
gi
nee
r
i
n
g,
West Virg
i
n
ia Un
i
v
ersity,
Mo
rg
an
to
wn
, W
V
,
2
650
5,
USA
Em
ail: m
ghorban@m
i
x.wvu.e
d
u
1.
INTRODUCTION
In
rece
nt years, the
use
of
n
onlinea
r electronic l
o
ads s
u
c
h
as c
o
m
p
act fluoresce
n
t la
m
p
s (CFLs),
com
puters, televisions, etc.
has inc
r
ease
d
significa
n
tly. Non
lin
ear load
s inj
ect ha
rm
onic curre
nts into
di
st
ri
b
u
t
i
on sy
st
em
s. When a
com
b
i
n
at
i
on o
f
l
i
n
ear an
d n
o
n
l
i
n
ear l
o
a
d
s i
s
fed f
r
om
a sinus
oi
dal
sup
p
l
y
, t
h
e
to
tal su
pp
ly cu
rren
t will con
t
ain
h
a
rm
o
n
i
cs. Th
e inj
ected
h
a
rm
o
n
i
c cu
rren
ts an
d
t
h
e resu
lted
h
a
rm
o
n
i
c
v
o
ltag
e
s can
cau
se po
wer quality
p
r
ob
lem
s
an
d
affect th
e p
e
rfo
r
m
a
n
ce o
f
th
e con
s
u
m
ers con
n
ected
to
th
e
el
ect
ri
c
po
we
r net
w
or
k [1]
.
Excessi
ve heat
i
n
equi
pm
ent
,
com
pone
nt
s agi
n
g an
d capa
c
i
t
y
decrease, m
a
l
f
unct
i
o
n o
f
pr
ot
ect
i
o
n
and m
easurem
ent
de
vi
ces, l
o
wer
po
we
r fact
or a
nd c
o
nse
q
u
e
n
tly r
e
du
cing
p
o
w
e
r
syste
m
efficiency
due
to
the
i
n
creasi
n
g l
o
ss
es are som
e
m
a
i
n
effect
s
of
harm
oni
cs i
n
po
we
r di
st
ri
b
u
t
i
on sy
st
em
s.
Harm
oni
c di
st
ort
i
o
ns
also increase t
h
e m
onetary costs in power s
y
ste
m
s by
increasing e
n
ergy losses,
pr
em
at
u
r
e ag
ing
or
de-
r
a
ti
ng
of el
ect
ri
cal
eq
ui
pm
ent
[2]
.
The ene
r
gy
l
o
ss
due t
o
ha
rm
oni
cs cause
d by
a l
a
rge num
ber of
no
nl
i
n
ea
r
l
o
ads
use
d
i
n
di
f
f
ere
n
t
p
o
w
er sy
st
e
m
sect
ors ca
n
be est
i
m
at
ed.
The diffe
re
nce betwee
n
the ge
nerate
d
power and
the
con
s
um
ed p
o
w
er
us c
o
nsi
d
ered a
s
t
h
e e
n
ergy
l
o
ss.
H
o
weve
r, e
n
e
r
gy
l
o
sses i
n
di
st
ri
b
u
t
i
on
net
w
o
r
ks
are
gene
rally estimated rather t
h
an m
easure
d
,
because of in
a
d
equate m
e
tering i
n
these
networks and also due
t
o
hi
g
h
cost
o
f
da
t
a
col
l
ect
i
on. M
o
re
ove
r,
po
wer sy
st
em
di
st
ri
but
i
o
n l
o
ss e
s
t
i
m
a
ti
on m
e
t
hods a
r
e rel
i
a
bl
e way
s
to dete
rm
ine the technical l
o
ss
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
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0
8
Imp
a
ct o
f
Ha
rmon
ics
on
Po
w
e
r Qu
a
lity
a
n
d
Lo
sses in
Po
w
e
r Distribu
tion S
y
stems
16
7
This work uses
an
accurate Nort
on
equivale
nt m
odel for
20
kV/
4
00V
fee
d
ers
to estim
a
t
e distri
bution
net
w
or
k l
o
sse
s. I
n
t
h
at
m
odel
,
resi
de
nt
i
a
l
,
com
m
erci
al an
d
of
fi
ce l
o
ad
t
y
pes a
r
e
m
odel
e
d u
s
i
n
g
t
h
ei
r
appl
i
a
nc
es m
odel
s
by
t
h
e
pr
ocess
of
sy
nt
h
e
si
s. T
h
en
a f
eeder
m
odel
i
s
o
b
t
a
i
n
e
d
by
agg
r
e
g
at
i
n
g
di
ffe
rent
resid
e
n
tial, commercial an
d
o
f
fice lo
ad
m
o
d
e
ls.
The a
p
pl
i
a
nces
are m
odel
e
d
b
y
No
rt
o
n
e
qui
v
a
l
e
nt
t
echni
qu
e
.
To
o
b
t
a
i
n
t
h
e
N
o
rt
o
n
e
q
ui
va
l
e
nt
m
odel
o
f
an app
lian
c
e, m
easu
r
em
en
t resu
lts
un
d
e
r d
i
fferen
t o
p
e
ratio
n
con
d
ition
s
are requ
ired
. Thu
s
, v
o
ltag
e
an
d
cu
rren
t
wav
e
form
s fo
r m
o
re th
an
32
non
lin
ear app
lian
ces are m
easu
r
ed
usin
g
a
po
wer qu
ality an
alyzer set.
The Norton m
odel param
e
ters for each
applianc
e ar
e
calculated usi
ng t
h
e m
easure
m
ents results
under
d
i
fferen
t
op
eratin
g
co
nd
ition
s
. M
o
re
d
e
tails ab
ou
t Norto
n
equ
i
v
a
len
t
m
o
d
e
l o
f
app
lian
ces and
lo
ads i
s
prese
n
ted
in [3-5]. The
aut
h
ors have
also i
n
troduce
d
ne
w i
ndices
to
qu
antize each a
ppli
a
nce im
pact on the
p
o
wer
q
u
a
lity
in
power d
i
stri
b
u
tion system
s
.
Th
e
p
r
op
o
s
ed
ind
i
ces tak
e
th
e
h
a
rm
o
n
i
c
d
i
sto
r
tion cau
sed
b
y
each loa
d
, their rm
s curre
nt
va
lue an
d
daily operation tim
e into acc
ount.
Thi
s
pa
pe
r i
s
o
r
ga
ni
zed a
s
f
o
l
l
o
ws.
I
n
Sect
i
o
n 3
,
ha
rm
oni
c po
we
r f
o
rm
ul
at
i
on f
o
r
n
o
n
l
i
n
ear l
o
a
d
s i
s
in
trodu
ced. In Sectio
n 4,
characte
r
istics of s
o
m
e
nonlinear ap
pl
i
a
nces a
r
e
pres
ent
e
d a
n
d
ha
rm
oni
c
charact
e
r
i
s
t
i
c
s
of di
ffe
rent
ap
pl
i
a
nces are de
scri
be
d. I
n
Sec
t
i
on 5,
obt
ai
ni
ng a N
o
rt
on m
odel
f
o
r a n
onl
i
n
ea
r
l
o
ad ba
sed
on
t
h
e
m
easurem
ent
dat
a
i
s
di
scusse
d. I
n
sect
i
on 6
,
di
f
f
ere
n
t
appl
i
a
nces m
odel
s
are
pres
ent
e
d
.
Lo
ad
s effect on
po
wer qu
ality u
s
in
g
th
e
n
e
w in
tro
d
u
c
ed
in
d
e
x
e
s is d
i
scu
ssed
in
section
8
.
Th
e lo
sses d
u
e
to
n
o
n
lin
ear loads in a sam
p
le 20
kV/40
0
V feed
er are si
m
u
la
ted
and an
alyzed
i
n
sectio
n
9
.
Fin
a
lly
, th
e
concl
u
sions a
r
e sum
m
ar
ized
in
Section
10
.
2.
RELATED WORKS
Accu
rat
e
l
o
ss
est
i
m
a
t
i
on pl
ay
s an im
port
a
nt
ro
le in
determin
in
g
the sh
are
o
f
tech
n
i
cal and
co
mmercial lo
sses in
th
e to
tal lo
ss. Research
ers
h
a
v
e
tr
ied to
esti
mate
th
e lo
sses in
d
i
stribu
tio
n
system
s
b
y
d
i
fferen
t
m
e
th
o
d
s
. So
m
e
work
s
h
a
v
e
u
s
ed th
e sim
p
lifie
d
feed
er m
o
d
e
ls an
d curv
e fittin
g
app
r
o
a
ch
es to
est
i
m
a
t
e
t
h
e l
o
sses [6
-1
0]
. A
com
p
rehe
nsi
v
e
l
o
ss est
i
m
a
t
i
on m
e
t
hod
usi
n
g det
a
i
l
e
d fee
d
er and l
o
a
d
m
odel
s
i
n
a lo
ad-fl
o
w
p
r
o
g
ram
is p
r
esen
ted
i
n
[11
]
. A co
m
b
in
atio
n
of statistical an
d
lo
ad
-flow meth
od
s is
u
s
ed
to
find
vari
ous t
y
pes
of l
o
sse
s i
n
a sam
p
l
e
power
sy
st
em
i
n
[12]
. Sim
u
l
a
t
i
on o
f
di
st
ri
b
u
t
i
o
n f
eeders
wi
t
h
l
o
ad dat
a
est
i
m
a
t
e
d from
t
y
pi
cal
cust
om
er l
o
ads i
s
p
e
rf
orm
e
d i
n
[1
3]
. R
e
f. [
1
4]
appl
i
e
s som
e
appr
o
x
i
m
at
i
ons t
o
p
o
w
e
r
fl
o
w
eq
uat
i
o
ns
i
n
o
r
der t
o
est
i
m
a
t
e
t
h
e l
o
sses u
nde
r
vari
at
i
ons
i
n
p
o
we
r s
y
st
em
co
m
pon
ent
s
.
A f
u
zzy
-
b
ase
d
cl
ust
e
ri
n
g
m
e
tho
d
o
f
l
o
s
s
es
and
f
u
zzy
r
e
g
r
essi
on
t
ech
ni
q
u
e a
n
d
ne
u
r
al
net
w
or
k t
e
c
hni
que
f
o
r
m
odel
i
n
g
t
h
e
lo
sses are
ob
tain
ed in
[1
5,
1
6
]
. It is d
i
ffi
cu
lt to
gu
ar
an
t
ee th
e
reliab
ility o
f
th
e
sim
p
lified
,
statistical and
app
r
oxi
m
a
t
e
model
s
. The
dra
w
bac
k
o
f
t
h
e f
u
zzy
base
d m
e
t
h
o
d
s i
s
t
h
at
t
h
ey
don
’t
co
nsi
d
er t
h
e
po
we
r sy
st
em
dy
nam
i
cs.
3.
HA
RM
ON
IC POWER
FO
R
M
UL
ATIO
N
S
If a si
gnal
co
nt
ai
ns harm
oni
cs
, t
h
e In
di
vi
d
u
a
l
Harm
oni
c Di
st
ort
i
o
n (I
H
D
)
fo
r any
harm
oni
c or
der i
s
defi
ned
as:
1
100
(%)
U
U
U
h
h
1
100
(%)
I
I
I
h
h
Whe
r
e
I
/V
i
s
t
h
e
cu
rre
nt
/
v
ol
t
a
g
e
ha
rm
oni
c o
f
o
r
de
r
h,
an
d
I
/V
is t
h
e fun
d
a
m
en
tal cu
rren
t/v
o
ltage
com
pone
nt
.
N
onet
h
el
ess,
fo
r
det
e
rm
i
n
i
ng t
h
e l
e
vel
of
ha
rm
oni
c cont
e
n
t
i
n
an al
t
e
r
n
a
t
i
ng si
g
n
al
, t
h
e t
e
r
m
“Tot
al
Ha
rm
oni
c Di
st
ort
i
o
n”
(T
HD
)
o
f
t
h
e
cu
rre
nt
a
n
d
v
o
l
t
a
ge si
gnal
s
are
wi
del
y
use
d
.
The
c
u
r
r
ent
an
d
vol
t
a
ge
T
H
D
o
f
a
harm
oni
c
p
o
l
l
u
t
e
d
wa
vef
o
rm
can be e
x
pr
essed a
s
:
100
1
2
2
I
I
THD
h
h
I
100
1
2
2
V
V
THD
h
h
U
)
1
(
2
2
1
2
I
THD
I
I
)
1
(
2
2
1
2
V
THD
V
V
Wh
ere I and
V are th
e curren
t and vo
ltage rm
s v
a
lu
es.
Th
e sep
a
ratio
n of th
e rm
s curren
t
and vo
ltag
e
int
o
fu
n
d
am
ent
a
l
and
ha
rm
oni
c t
e
rm
s resol
v
es
t
h
e ap
pare
nt
po
w
e
r i
n
t
h
e
fol
l
ow
i
ng m
a
nne
r [
1
6
]
.
2
2
1
2
2
1
2
2
1
2
2
)
).(
(
)
(
N
H
H
S
S
I
I
V
V
VI
S
2
1
2
S
S
S
N
Whe
r
e S1 is the fundam
ental
appa
re
nt
powe
r. T
h
e prese
n
c
e
of
harm
onics
causes the pre
s
ence
of a
ne
w type
of
n
o
n
-
f
u
n
d
am
ent
a
l
ap
pare
nt
po
we
r (
N
S
)
wh
ich is reso
lv
ed
i
n
t
h
e
fo
llowing
t
h
ree
d
i
stin
ctiv
e
term
s [1
7
]
:
(2
)
(1
)
(4
)
(3
)
(6
)
(5
)
(8
)
(7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l.
5
,
N
o
.
1
,
Feb
r
u
a
ry 2
015
:
16
6 – 17
4
16
8
2
2
2
2
H
V
I
N
S
D
D
S
I
H
I
THD
S
I
V
D
1
1
V
I
H
H
H
THD
THD
S
I
V
S
1
V
H
V
THD
S
I
V
D
1
1
In practical power system
s,
V
I
THD
THD
, and
N
S
can
be c
o
m
put
ed usi
n
g
t
h
e
fol
l
o
wi
n
g
e
x
p
r
essi
on:
I
N
V
I
N
THD
S
S
THD
THD
S
S
1
2
2
1
Power fact
or is
not only affect
ed by the phas
e
displacem
ent betwee
n voltage and curre
nt wave
form
s.
The exi
s
t
e
nce of
no
n-
f
u
n
d
am
ent
a
l
appa
re
nt
po
wer
(
N
S
) also affects the power f
actor. Power factor
will
decrease
in
pre
s
ence
of ha
rm
onics a
n
d conse
que
ntly
d
i
stor
tio
n pow
er (n
on-
fu
nd
am
en
tal ap
p
a
r
e
n
t
pow
er
, S
N
).
In the case of
prese
n
ce of ha
rm
onics, powe
r factor is
com
pos
ed
of t
w
o f
act
ors,
Di
spl
a
c
e
m
e
nt
Powe
r Fact
or
(p
fdi
s
p)
an
d
Di
st
ort
i
o
n P
o
wer
Fact
or
(
p
f
d
i
s
t
)
.
dist
disp
V
I
pf
pf
THD
THD
S
P
S
P
pf
2
2
1
1
1
1
1
S
P
pf
disp
S
S
THD
THD
pf
V
I
dist
1
2
2
1
1
1
Whe
r
e p is the
real power.
Nonlinea
r loa
d
s can be
consi
d
e
r
ed as ha
rm
onic real power s
o
urces that
i
n
ject
ha
rm
oni
c real
po
wer i
n
t
o
t
h
e
di
st
ri
b
u
t
i
on sy
st
em
whi
c
h i
s
t
h
e p
r
o
d
u
ct
of t
h
e
harm
oni
c v
o
l
t
a
ge an
d
cu
rren
t
o
f
t
h
e sam
e
o
r
d
e
rs. Alth
oug
h th
is p
o
wer is
m
u
ch
sm
aller th
an
th
e
f
undam
e
n
tal real powe
r
, the
p
r
esen
ce
of the d
i
stortion
p
o
wer cau
sed b
y
h
a
rm
o
n
i
cs wi
ll resu
lt in in
creased lo
sses i
n
th
e
u
tility s
u
pp
ly
syste
m
.
In t
h
e
pres
ence
of ha
rm
oni
cs,
t
h
e l
o
ss w
o
ul
d
be as sh
o
w
n
in Eq
.1
7. Th
erefo
r
e, it can
be s
een that a signi
ficant
in
crease in
loss o
f
th
e
u
tility will o
ccu
r in
th
e pres
en
ce o
f
h
a
rm
o
n
i
c d
i
sto
r
tion
s
. Fo
r ex
am
p
l
e, with
a
THDI=4
0%, t
h
e lo
ss wou
l
d
b
e
in
creased
by 1
6
%
. Fo
r a
th
ree-ph
ase t
h
ree-wire u
tility, th
e to
tal lo
sses are
sho
w
n i
n
E
q
.
1
8.
2
2
2
1
2
2
1
2
)
1
(
)
(
n
I
n
THD
RI
I
I
R
RI
Loss
2
2
3
N
N
p
p
I
R
I
R
P
Whe
r
e
Ip
i
s
t
h
e p
h
ase c
u
r
r
e
n
t
o
f
t
h
e
bal
a
nce
d
net
w
or
k a
n
d
In
i
s
t
h
e
ne
ut
ra
l
l
i
n
e cu
rre
nt
.
The
harm
oni
c
l
o
sse
s
are:
11
2
2
2
2
2
2
)
(
3
3
hh
Nh
N
ch
bh
ah
P
N
N
P
P
I
R
I
I
I
R
I
R
I
R
Loss
Whe
r
e
Ia
h,
Ib
h, a
n
d
Ich
are
the
harm
onic
h c
u
rre
nts in
p
h
ase
A,
B a
n
d
C re
spectiv
ely
,
I
Nh
is t
h
e
ht
h
harm
oni
c
of t
h
e ne
ut
ral
c
u
r
r
e
n
t
,
a
n
d
R
p
an
d
R
n
are
t
h
e
p
h
a
s
e an
d
ne
ut
ral
r
e
si
st
ances.
Th
e lo
ss in
th
e n
e
u
t
ral wire can
b
e
con
s
id
erab
le and
m
a
y resu
lt in
ov
erload
ing
du
e t
o
1) th
e unb
alan
ced
lo
ad
s
and 2) t
h
e zero-seque
n
ce c
u
rrents [11].
4.
NO
NLINE
A
R
LOA
D
S
CH
AR
A
C
TERIS
TICS
This section
prese
n
ts t
h
e
measurem
ent results
for
some comm
on reside
ntial and c
o
mm
ercial
applianc
es.
The m
easurem
en
ts consist of c
u
rrent a
n
d
vo
ltag
e
THD’s, lo
ad rm
s cu
rren
t,
p
o
wer
facto
r
,
and
activ
e and
reactiv
e po
wers. Al
l th
e m
easu
r
emen
ts ar
e
don
e usin
g
a HIOKI 9
624
p
o
wer q
u
ality
an
alyzer.
The ac curre
nt waveform
of a 4W
CFL a
s
a nonlinear
lo
ad
is shown in
th
e Fig
u
re 1
.
In
Figu
re
2
,
th
e
harm
onic spec
tra are shown
for three
di
ff
er
ent
bra
n
ds o
f
C
F
Ls. Tabl
e
1
sh
ows the ele
c
trical param
e
ters for
so
m
e
lin
ear and
non
lin
ear app
lia
nces
whi
c
h
are us
ual
l
y
us
ed i
n
resi
de
n
tial, comm
ercia
l
and
office loa
d
types.
Active, reacti
v
e powers a
n
d
also
non-funda
m
ental apparent powe
r (
N
S
),
whi
c
h has a
n
onze
r
o val
u
e
f
o
r
nonlinea
r loa
d
s
,
are
calcula
ted for eac
h a
p
pliance.
Fort
unately, for m
a
ny appliances the harm
onic real
power i
s
m
u
ch sm
aller that the funda
mental real
powe
r. But, t
h
e harm
onic current inc
r
eases t
h
e appa
rent
po
wer
(S
), inc
r
ea
sing t
h
e p
o
w
er
losses.
In
this
wo
rk
,
the powe
r factor for all appli
a
nces is also measured
a
nd
the effect of di
splacem
ent and distortion fa
ctors on
th
e to
tal power fact
o
r
is inv
e
stig
ated.
Wh
at fo
llows
is
a summ
ary of t
h
e m
easure
m
ents of the
some
appl
i
a
nc
es.
(1
2)
(1
3)
(1
5)
(1
9)
(1
1)
(1
0)
(9
)
(1
6)
(
14
)
(1
8)
(1
7)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Imp
a
ct o
f
Ha
rmon
ics
on
Po
w
e
r Qu
a
lity
a
n
d
Lo
sses in
Po
w
e
r Distribu
tion S
y
stems
16
9
5.
NORTON EQUIVALENT
MODEL
To
ob
tain
a Norton
m
o
d
e
l for a n
o
n
lin
ear lo
ad
, th
e circu
it sh
own
in
Figu
re 3
can
b
e
u
s
ed
[12
,
13
].
In
th
is circu
it, th
e su
pp
ly sid
e
is rep
r
esen
ted b
y
th
e Th
ev
en
in
equ
i
v
a
len
t
wh
ile th
e n
o
n
lin
ear lo
ad
sid
e
is
rep
r
ese
n
t
e
d
by
i
t
s
Nort
on e
q
u
i
val
e
nt
. T
o
cal
cul
a
t
e
t
h
e N
o
rt
on m
odel
pa
ra
m
e
t
e
rs, t
h
e m
e
asurem
ent
of
v
o
l
t
a
ge
(
V
)
and cu
rr
en
t
(
I
) spect
ra
at
t
w
o
di
ffe
rent
ope
rat
i
n
g
c
o
n
d
i
t
i
ons
of
t
h
e
sup
p
l
y
sy
st
em
are
neede
d
.
The
chan
ge
i
n
t
h
e s
u
p
p
l
y
sy
st
em
operat
i
n
g c
o
ndi
t
i
on
can
f
o
r
e
x
a
m
pl
e be o
b
t
a
i
n
ed
by
s
w
i
t
c
hi
n
g
a
s
h
u
n
t
ca
pa
ci
t
o
r,
a paral
l
e
l
t
r
an
sfo
r
m
e
r, sh
unt
im
pedance
or
som
e
ot
her c
h
an
ges t
h
at
cause a c
h
an
ge i
n
t
h
e s
u
ppl
y
s
y
st
em
harm
oni
c i
m
pedance
[
1
2,
1
3
]
.
Fi
gu
re 1.
M
easure
d
C
u
r
r
e
nt
an
d
V
o
l
t
a
g
e
Wave
f
o
rm
for
a 4
W
CFL
Fi
gu
re 2.
Norm
alized Magnitude
[%] Spectra
C
o
m
p
ari
s
on
f
o
r 3 di
ffe
rent
C
F
Ls
Table
1. Meas
urem
ent res
u
lts for s
o
m
e
appli
a
nces
Load
%
CFL
155.
00
8.
06
4.
00
-7
.0
0
12.
50
0.
48
0.
89
0.
54
Fan
5.
39
49.
59
49.
50
-2
.9
6
2.
67
0.
99
0.
99
1.
00
Ref
r
igerator
15.
53
130.
59
106.
95
74.
93
20.
28
0.
80
0.
81
0.
99
Co
m
puter
114.
05
152.
20
95.
91
-
118.
18
173.
59
0.
63
0.
95
0.
66
L
a
ptop
159.
60
51.
82
26.
00
-
44.
83
82.
71
0.
50
0.
94
0.
53
T
e
levision
142.
73
93.
47
49.
60
-
79.
23
133.
42
0.
53
0.
92
0.
57
W
a
shing m
achine
2.
42
2072.
2
8
2072.
2
-
12.
31
50.
15
0.
48
0.
48
1.
00
Vacuu
m
21.
97
1024.
9
4
987.
36
275.
00
225.
18
0.
96
0.
99
0.
98
Iro
n
2.
96
1119.
6
0
1119.
4
-
21.
00
33.
17
1.
00
1.
00
1.
00
Blow dr
y
e
r
(
S
low
Rate)
8.
43
526.
76
525.
00
43.
00
44.
42
1.
00
1.
00
1.
00
Blow dr
y
e
r
(
F
ast Rate)
3.
15
980.
17
980.
00
18.
00
30.
88
1.
00
1.
00
1.
00
f
r
eezer
9.
69
313.
37
217.
79
225.
32
30.
36
0.
69
0.
70
1.
00
Fluorescent la
m
p
8.
23
74.
78
28.
95
68.
95
6.
16
0.
38
0.
39
1.
00
Incandescent la
m
p
2.
83
96.
17
96.
10
-3
.7
0
2.
72
1.
00
1.
00
1.
00
Split air conditioner
22.
54
2692.
1
5
1834.
4
1970.
4
0
606.
81
0.
87
0.
89
0.
98
Air
conditioner
23.
96
1417.
9
1
1032.
3
972.
00
339.
73
0.
94
0.
97
0.
97
Howev
e
r, su
ch ch
ang
e
s in
th
e su
pp
ly syste
m
will n
o
t
yield
u
n
i
q
u
e
p
a
ram
e
ters for th
e Norton
m
o
d
e
l,
and the M
odel
param
e
ters are depe
nde
nt on the am
ount
of c
h
ange. T
h
i
s
m
a
kes the accuracy of the
m
odel
debat
a
bl
e.
In
[
13]
, i
t
i
s
s
h
ow
n t
h
at
t
h
e
No
rt
on
m
odel
pa
ra
m
e
t
e
rs whi
c
h
are
obt
ai
ne
d
b
y
chan
gi
n
g
t
h
e
su
ppl
y
vol
t
a
ge
are m
o
re ac
cu
rat
e
a
n
d
val
i
d
f
o
r
a
wi
de
r
ran
g
e
of
v
o
l
t
a
ge
var
i
at
i
ons.
Al
so
,
chan
gi
n
g
t
h
e
sup
p
l
y
v
o
ltag
e
,
b
e
sid
e
its sim
p
lic
ity,
do
es
no
t require switch
i
ng l
a
rge
capacitors or im
pedanc
es w
h
i
c
h
m
a
y
cause
som
e
pro
b
l
e
m
s
f
o
r
net
w
o
r
k
co
m
ponent
s.
As Fi
gu
re
3 s
h
ows
,
whe
n
t
h
e
su
ppl
y
vol
t
a
g
e
va
ri
es,
harm
oni
c
v
o
l
t
a
ge
h
V
and ha
rm
onic c
u
rrent
h
I
will ch
ang
e
, an
d
h
N
I
,
fi
nds a
pat
h
whi
c
h c
onsi
s
t
s
of a
pa
ral
l
e
l
com
b
i
n
at
i
on
of
h
N
Z
,
and t
h
e s
u
pply system
i
m
p
e
d
a
n
c
e.
W
i
th
th
e assu
m
p
tio
n of
n
o
ch
ange in
th
e op
erati
n
g cond
itio
n
s
o
f
t
h
e
n
o
n
lin
ear lo
ad
, it can
be seen
fr
om
Fi
gure
3
t
h
at
1
,
h
I
and
2
,
h
I
can
be expres
sed as:
1
,
,
,
1
,
h
ZN
h
N
h
I
I
I
2
,
,
,
2
,
h
ZN
h
N
h
I
I
I
The harm
oni
c No
rt
o
n
i
m
peda
nce
c
u
r
r
ent
h
ZN
I
,
,
bef
o
r
e
an
d a
f
te
r th
e
ch
a
n
g
e
ca
n
b
e
ex
pr
e
s
s
e
d
as
:
0
20
40
60
80
100
1
3
5
7
9
1
11
31
5
1
71
92
1
2
32
5
Taban
4W
CFL
Harmonic
Order
Am
p
(100%)
(2
)
(1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l.
5
,
N
o
.
1
,
Feb
r
u
a
ry 2
015
:
16
6 – 17
4
17
0
h
N
h
h
ZN
Z
V
I
,
1
,
1
,
,
h
N
h
h
ZN
Z
V
I
,
2
,
2
,
,
Fi
gu
re
3.
N
o
rt
on
M
o
del
of
L
o
ad
-Si
d
e a
n
d
T
h
eve
n
i
n
E
qui
v
a
l
e
nt
o
f
S
u
ppl
y
Sy
st
em
[11]
By su
bstitu
tin
g Eq
s.
(3) and
(4
) in
to Eq
s. (1) an
d (2
) an
d so
lv
ing fo
r
h
N
Z
,
and
h
N
I
,
,
t
h
e follo
win
g
fo
rm
ulas
are ac
hieve
d
[13]:
)
(
)
(
1
,
2
,
2
,
1
,
,
h
h
h
h
h
N
I
I
V
V
Z
h
N
h
h
h
N
h
h
h
N
Z
V
I
Z
V
I
I
,
2
,
2
,
,
1
,
1
,
,
W
h
er
e
V
,
and
I
,
are t
h
e
ha
rm
onic voltage
a
n
d
current
m
easure
m
ents be
fore
the c
h
a
nge
in t
h
e
operating
co
nd
itio
n, and
V
,
and
I
,
are t
h
e measurem
ents after the c
h
a
nge
.
These e
q
uations are c
o
m
p
lex and the
pha
se
angles
should
be
m
easured precisely.
In
th
e fo
llowing
sect
io
n
,
a
No
rt
o
n
m
odel
i
s
de
vel
o
pe
d f
o
r s
o
m
e
co
m
m
o
n
l
y
use
d
a
p
pl
i
a
nces.
6.
RESI
DENTI
A
L, CO
M
M
ERCI
AL A
N
D
OFFI
CE LO
AD
S
NO
RTO
N
EQ
UI
VAL
ENT M
O
DEL
In
th
is section
,
a
m
o
d
e
l fo
r resid
e
n
tial, commerc
i
a
l and of
fi
ce l
o
ads i
s
devel
o
pe
d by
aggr
egat
i
n
g
t
h
ei
r co
rres
p
o
ndi
ng a
p
pl
i
a
n
ces
m
odel
s
. T
o
de
vel
o
p t
h
e
No
rt
o
n
m
odel
for eac
h a
p
pl
i
a
nce at
l
east
t
w
o
measu
r
em
en
ts at d
i
fferen
t
operatin
g
cond
itio
n of th
e
s
upply syste
m
are n
eed
ed
. More
d
e
tails abo
u
t
ho
w to
achi
e
ve t
h
e
No
rt
o
n
eq
ui
val
e
nt
m
odel
param
e
t
e
rs usi
n
g
m
e
a
s
u
r
em
en
t resu
lts is d
e
scri
b
e
d
in
prev
i
o
us sectio
n
s
and
[
1
6-
20]
.
No
rt
o
n
e
qui
va
l
e
nt
m
odel
pa
r
a
m
e
t
e
rs consi
s
t
of
and
for each harm
onic order. T
h
e
Norton
equi
val
e
nt
m
odel
i
s
d
e
vel
o
p
e
d f
o
r eac
h
h
a
rm
oni
c or
de
r
sepa
rat
e
l
y
, and
t
h
e c
o
m
p
l
e
t
e
No
rt
o
n
e
q
u
i
val
e
nt
m
odel
i
s
obt
ai
ned
by
com
b
i
n
i
ng t
h
e
s
e m
odel
s
. The
No
rt
o
n
m
odel
para
m
e
t
e
rs for
di
f
f
e
rent
re
si
de
nt
i
a
l
l
o
ad
s
are
gi
ve
n i
n
Ta
bl
e 3
.
In
t
h
is work,
m
o
re th
an
two d
i
fferen
t op
eratin
g
co
nd
itio
ns are co
nsid
ered
to
ob
tain
b
e
tter m
o
d
e
lin
g
resu
lts.
Th
e m
easu
r
em
en
ts are p
e
rform
e
d
at
m
o
re th
an
two
hu
ndred
d
i
fferen
t
o
p
e
ratin
g
con
d
ition
s
o
f
t
h
e
sup
p
l
y
vol
t
a
ge
. T
h
e
o
b
t
a
i
n
ed
No
rt
o
n
eq
ui
val
e
nt
cu
rre
nt
a
n
d
i
m
pedances
val
u
e
s
at
di
f
f
ere
n
t
o
p
erat
i
n
g
co
nd
itio
ns co
nv
erg
e
t
o
sp
ecific v
a
lu
e
wh
ich
mak
e
s th
e
results
m
o
re reliab
l
e.
After m
odeling eac
h appliance,
reside
ntial, comm
erci
al and
o
ffi
ce l
o
ad
s N
o
rt
on
equi
val
e
nt
m
odel
are
achi
e
ve
d
by
agg
r
e
g
at
i
n
g
t
h
ei
r co
rre
sp
o
n
d
i
ng a
p
pl
i
a
nces
N
o
rt
on
eq
ui
val
e
nt
m
odel
s
. A
fee
d
e
r
N
o
rt
on
eq
u
i
v
a
len
t
m
o
d
e
l will th
en
be o
b
t
ain
e
d
b
y
ag
greg
atin
g
correspo
n
d
i
ng
resid
e
n
tial, co
mmercial an
d
o
f
fice lo
ad
No
rt
o
n
e
q
ui
val
e
nt
m
odel
s
.
7.
S
I
MU
LA
TION
OF
A
2
0
KV
DIST
RIBUTION FEEDE
R
Thi
s
sect
i
on a
n
al
y
s
es t
h
e char
act
eri
s
t
i
c
s of a sam
p
l
e
di
st
ri
but
i
on
net
w
or
k
feede
r
m
odel
e
d by
N
o
rt
on
equi
val
e
nt
t
e
c
hni
que
. T
h
i
s
f
eeder m
odel
i
s
obt
ai
ne
d
by
a
g
g
r
e
g
at
i
ng t
h
e
No
rt
o
n
e
qui
v
a
l
e
nt
m
odel
of
al
l
end
u
s
er app
lian
ces fo
r all typ
e
ty
p
e
s
o
f
lo
ad
s i.e. resi
d
e
n
tial, commercial an
d
o
f
fice lo
ad
s.
A si
m
p
l
e
schem
a
t
i
c
for a 3-
p
h
ase bal
a
nced
di
st
ri
b
u
t
i
on
net
w
o
r
k i
s
s
h
o
w
n i
n
Fi
gu
re 4
.
As
Fi
gu
re 4 s
h
o
w
s, t
h
e
sam
p
le feeder
feeds
3
diffe
re
nt loa
d
s
(re
sid
e
ntial, com
m
ercial, office). T
h
e total
fee
d
er lo
ad is equ
a
l
to
th
e
su
m
o
f
all 3
lo
ad
s. In
th
is
sectio
n
,
a samp
le offi
ce loa
d
m
odel and
its characterist
i
cs are specifically
in
v
e
stig
ated
, an
d th
en
sim
u
latio
n
resu
lts
for a feed
er co
n
s
i
s
tin
g
o
f
resi
d
e
n
tial, co
mm
erc
i
al an
d office l
o
ads
are prese
n
ted.
Using the m
o
dels for each a
ppliance
,
a
n
e
s
ti
m
a
t
i
on
of the powe
r quality of a
n
office
load ca
n
be
obt
ai
ne
d.
It
i
s
assum
e
d t
h
at
t
h
e o
ffi
ce l
o
ad
con
s
i
s
t
s
of
2 P
C
s, 2 C
F
Ls
an
d 2
fa
ns wi
t
h
s
l
ow a
nd
fast
ra
t
e
s. Th
e
l
o
ads t
u
rn
on
one
by
one
. Fi
gs. 5 a
nd
6 sh
ow t
h
e rm
s curre
nt
and t
h
e T
HD
of t
h
e o
ffi
ce l
o
ad. T
h
e p
o
i
n
t
s
o
f
(6
)
(5
)
(4
)
(3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Imp
a
ct o
f
Ha
rmon
ics
on
Po
w
e
r Qu
a
lity
a
n
d
Lo
sses in
Po
w
e
r Distribu
tion S
y
stems
17
1
turning on or
off for each
a
p
pliance are s
p
e
c
ified in Figure 5. Th
e T
o
tal Harm
onic Distortion (T
HD)
of the
of
fi
ce l
o
ad
de
pen
d
s
on i
t
s
a
ppl
i
a
nce
s
TH
D an
d t
h
ei
r
r
m
s curre
nt
val
u
e.
As Fi
gs
. 5
and
6 sh
o
w
, t
h
e TH
D
decrease
s
as the accum
u
lative load cu
rrents i
n
crease
s
. To model a distribu
t
i
on fee
d
er, it is
assum
e
d that
a 20
kV fee
d
er feeds
reside
ntial,
commercia
l and office loads. E
ach loa
d
type a
ppl
i
a
nce
s
are
d
e
scri
be
d i
n
Ta
bl
e 2
.
The appliance
s
turn on one
by one, and finally, all of
the appliance
s
are in se
rvice
.
The effect of each
applianc
e
on the fee
d
er
THD i
s
de
pe
nde
nt
on each a
p
plianc
e THD a
n
d its
current
rm
s value.
Table
2.
Sim
u
lated resi
dential
,
comm
ercial a
n
d office l
o
ad
applianc
es
Load Ty
pe
Applianc
e
s
Residential
2 CFLs, Ref
r
iger
ator, TV,
W
a
shing Machin
e, Vacuum
, Iron, Fan
Office
2 PCs, 2CFLs,
Laptop,
TV
,
Refr
i
g
erator
, P
r
in
ter
,
F
a
n
Com
m
e
rcial
2 CF
Ls
, TV
, F
a
n
,
P
C
Fi
gu
re
4.
Sc
he
m
a
t
i
c
of a sam
p
l
e
2
0
kv/
40
0
v
feede
r
Table 3. N
o
rto
n
M
o
del Para
m
e
ters
fo
r
Resi
dential
appl
i
a
nc
es(
A
,
Ω
)
Har
m
onic Or
der
3
h
5
h
7
h
9
h
11
h
13
h
CFL
h
N
I
,
0.03
0.028 0.023
0.018 0.014 0.011
h
N
Z
,
800 600 500
250 200 180
Ref
r
igerator
h
N
I
,
0.45 0.175 0.15 0.13 0.007
0.007
h
N
Z
,
15 20 25
30
100
120
Fan (Slow
rate)
h
N
I
,
0.023 0.0225 0.013 0.007 0.0016 0.015
h
N
Z
,
500 300 400
500 550 550
Fan (Fast
rate)
h
N
I
,
0.026 0.011 0.008
0.009 0.001 0.001
h
N
Z
,
500 400 440
200 300 330
PC
h
N
I
,
0.75 2
2.5
0.4
0.3
0.175
h
N
Z
,
30 2
1.5
6
3 12
L
a
ptop
h
N
I
,
0.22 0.2
0.2 0.2 0.15
0.125
h
N
Z
,
100
30 20
10 10 10
TV
h
N
I
,
200
175 80 10
5
3
h
N
Z
,
0.3
0.3
0.22 0.5 0.125 0.1
Vacuu
m
Cleaner
h
N
I
,
1.5
0.4
0.25
0.12 0.03 0.02
h
N
Z
,
30 25 25
25 30 13
PC Monitor
h
N
I
,
0.15 0.11 0.09
0.08 0.02 0.16
h
N
Z
,
110
150 90 50
40
3
W
a
shing
Machine
h
N
I
,
0.5 0.5 0.1
0.2
0.02
0.01
h
N
Z
,
12.5
20 30
20 20 20
Fi
gu
re
5.
Si
m
u
l
a
t
e
d o
ffi
ce l
o
a
d
rm
s curre
nt
Fi
gu
re
6.
TH
D
t
r
en
d
fo
r a
si
m
u
l
a
t
e
d
of
fi
ce l
o
ad
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
1.
8
2
x 1
0
4
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
Ti
m
e
(
s
)
I r
m
s
Fa
n
2
(
F
a
s
t
R
a
t
e
)
(
O
N
)
F
a
n
1
(
S
l
o
w Rat
e
)
(
O
N
)
CF
L
2
(
O
N
)
CF
L1(O
N
)
PC
2
(
O
N
)
PC
1
(
O
N
)
Fa
n
2
(
F
a
s
t
R
a
t
e
)
(
O
FF)
Fa
n
1
(
S
l
o
w
R
a
t
e
)
(
O
FF)
CF
L
2
(
O
F
F
)
C
F
L
1
(
O
FF)
P
C
2
(
O
FF)
PC
1
(
O
F
F
)
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
1.
8
2
x 1
0
4
0
20
40
60
80
100
120
140
160
180
200
Ti
m
e
(
s
)
TH
D
(%
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l.
5
,
N
o
.
1
,
Feb
r
u
a
ry 2
015
:
16
6 – 17
4
17
2
8.
NO
NLINE
A
R
LOA
D
S
R
A
N
K
IN
G BA
SED O
N
T
W
O
N
E
W POWE
R
QU
ALITY
IN
DICE
S
In
t
h
is sectio
n,
two
n
e
w i
n
d
i
ces are in
trod
u
c
ed
to
determ
ine the im
pact of e
ach appliance
on a
fee
d
e
r
powe
r quality. The
first inde
x
indicates the
c
ont
ribution of
each loa
d
i
n
the fee
d
er THD.
This inde
x is
define
d
in
E
q
.
(1
).
Wh
ere
K
THD
is to
tal
h
a
rm
o
n
i
c d
i
stortion
of l
o
ad
k and
is its cu
rren
t
rm
s v
a
lu
e.
As
d
e
scri
b
e
d
in
(1
),
C
THD
indicat
es the c
ont
ribution
of eac
h l
o
ad in the
feede
r
T
HD i
n
prese
n
ce
of
ot
he
r l
o
ads.
Ass
u
m
i
ng
that all loads i
n
Ta
ble 2 a
r
e i
n
se
rvice, t
h
e
THD
inde
x for each
applianc
e can
be calculated.
The
results a
r
e
sh
own
in
Table 4
.
As shown
in
Tab
l
e 4
,
th
e Sp
lit air co
nd
ition
e
r
h
a
s th
e m
o
st
d
e
stru
ctiv
e effect in
co
m
p
ariso
n
wi
th
th
e o
t
h
e
r load
s.
Alth
oug
h, th
e THD
o
f
t
h
e Sp
lit air co
nd
itio
n
e
r is n
o
t
m
o
re th
an
th
at o
f
th
e
o
t
h
e
r lo
ad
s, it
h
a
s a wo
rse effect o
n
power qu
ality th
an
o
t
hers.
THDc is a u
s
efu
l
in
d
e
x
to
classify lo
ad
s b
a
sed
on
th
eir effects o
n
power
q
u
ality, b
u
t
it
is e
v
id
en
t th
at
ap
p
lian
c
es
o
p
eratin
g ti
m
e
d
u
ring
th
e
d
a
y is also
a
v
e
ry i
m
p
o
r
tan
t
fact
or an
d sh
ou
ld
b
e
con
s
id
ered
in
th
e
calculations.
T
h
ere
f
ore, a
ne
w index
(E
q.2) which ta
kes
into acc
ount
the daily operation tim
e for each
appl
i
a
nc
e i
s
de
fi
ne
d,
1
*
*1
00
*
k
k
kr
m
s
C
k
rm
s
k
TH
D
I
TH
D
IT
H
D
1
**
24
*
100
**
24
k
k
k
kr
m
s
St
k
k
rm
s
k
t
TH
D
I
TH
D
t
IT
H
D
Whe
r
e
k
t
is the a
ppliance
operating ti
m
e
per day. In Table
5,
loads are
ran
k
e
d
base
d o
n
the
new in
de
x val
u
e.
As sho
w
n
in
Tab
l
e
5
,
th
e
new lo
ad
s r
a
nk
in
g b
a
sed on
ST
THD
inde
x is
di
ffe
re
nt wit
h
that
w
h
en
the
loa
d
s
ran
k
in
g ba
sed
on
C
THD
inde
x.
Acc
o
r
d
in
g to the
n
e
w ra
nki
ng
, ap
pliances wit
h
lon
g
e
r
o
p
eratin
g tim
e
per day
have
hig
h
e
r
ra
nks
. F
o
r e
x
am
ple, lo
ng
o
p
er
ation tim
e of a com
puter ca
uses a
higher
rank
based
on
ST
THD
inde
x as com
p
ared to t
h
e ranking
by
C
THD
index
.
9.
POWER LOSS SIMUL
A
TIONS IN
A DISTRIBUTION FEEDE
R
In this section, losses in a
distri
butio
n
fee
d
e
r
ar
e sim
u
lated usi
n
g
the
eq
ua
tions i
n
tr
od
uce
d
i
n
sectio
n
3. T
h
e sc
hem
a
tic diagram
of t
h
e sim
u
lated fee
d
e
r
s
h
o
w
n i
n
Fi
gu
re
4 co
ntains t
w
o im
pedances
fo
r the
transm
ission lines
(Z
1 a
n
d
Z
2
)
.
Fi
gu
re
7 s
h
ows
the
losse
s
due
to
Z1
im
pedance
f
o
r a
n
of
fice loa
d
a
n
d
Fig
u
re
8 sh
ows lo
sses
due to Z2 im
pedance
whe
n
f
eedin
g reside
nt
ial, co
m
m
ercia
l
and office loads. T
h
e pea
k
value
of the
feede
r
l
o
ss is whe
n
all t
h
e a
ppliances a
r
e
on. Z
1
an
d
Z
2
ar
e
co
ns
id
er
e
d
r
e
s
i
s
tiv
e
w
i
th
v
a
lu
e
s
o
f
1
o
h
m
.
Total loss in Z
1
an
d Z
2
im
pedance
s
f
o
r t
h
e
sim
u
lated feed
er is sh
ow
n in
Figu
re 9
.
A
s
Figu
re
9 sh
o
w
s, the
loss tren
d co
p
e
s with the ag
gre
g
ated loa
d
s
rm
s curre
nt
. The total am
ount o
f
losses i
n
this sam
p
le
feede
r
reaches
m
a
xim
u
m
1100
W. T
h
e am
ount
of l
o
sses
ve
rsus th
e total fee
d
er load is
plotted i
n
Fi
gure
10.
Losses
d
u
e t
o
transm
ission lines im
pedance
fo
r t
h
e
sim
u
lated
power
n
e
twor
k can b
e
up
to 18
%
of
the total fee
d
e
r
po
wer
an
d
th
is am
ount o
f
l
o
ss m
eans a c
onsi
d
era
b
le c
o
st fo
r
distrib
u
tion
net
w
o
r
ks th
at ca
n
not be neglect
ed. Sha
r
e of n
onlinea
r
lo
ads
an
d
thei
r
ha
r
m
onics in cau
sing l
o
ss
of
p
o
we
r in
distri
butio
n
netw
or
ks c
o
uld
be o
b
taine
d
by
the E
q
1
6
.
B
a
sed
on the si
m
u
lation results,
the
a
v
e
r
age Total Ha
rm
onic
Distortio
n
(TH
D
)
of t
h
e sim
u
lated p
o
w
er distribution feeder with
the lo
ads m
e
ntioned in Ta
ble 2, can be
co
nsid
er
ed
to
be 50
%, th
is m
e
ans
20%
of tot
a
l loss is caused
by
ha
rm
onics in t
h
e sim
u
lated
feede
r
.
10
.
CO
NCL
USI
O
NS
In t
h
is
pape
r,
a com
p
rehe
nsi
v
e in
vestigatio
n
has
been
d
o
n
e to
dete
rm
in
e the im
pacts of
ha
rm
onic
distortio
ns on po
we
r
sy
stem
distrib
u
tion
ne
two
r
ks
. The st
udy
u
s
es the N
o
rt
on e
qui
valent
m
odel of
di
ffe
rent
applianc
es to
m
odel a dis
t
ributio
n
feed
er. T
h
e i
ndi
v
i
dual m
odels
are
obtai
ned
by
a
n
aly
z
ing loa
d
s
m
easurem
ent results.
Diffe
re
nt load
ty
pe m
odels are fo
u
nd
by
a
g
g
r
egatin
g the
N
o
rt
on e
q
uivale
nt m
odel of t
h
e
i
r indi
vid
u
al
applianc
es. T
w
o
new indice
s are introduce
d to quanti
ze the im
pact of each app
liance
in causing ha
rm
onic
distortio
ns
in
a
distri
butio
n
fe
eder
. T
h
ese
in
dices c
o
n
s
id
er
not
only the THD into acc
ou
nt,
b
u
t also
the
cu
rre
nt
rm
s value an
d t
h
e loa
d
s
o
p
erat
ion
d
u
ratio
n
pe
r
day
.
A distribution
feeder is si
m
u
lated using resi
dentia
l, commercial and
office Norton load
m
odels. The
losses in a transm
ission line are estim
a
ted, and the e
ffect o
f
harm
onics o
n
causing extra
losses is discussed.
The results are
reasona
b
ly accurate, si
nce the Norton equivalent
m
odels ar
e
precise
a
nd obtained base
d on
t
h
e
real world m
easurem
ent resul
t
s. The re
sults
show that the l
o
sses can be
up
to 18%
of t
h
e feede
r
power usage
while the
s
h
are
o
f
harm
onics i
n
ca
usin
g t
h
ese
losses
is
de
pe
nde
nt to
the
T
H
D
o
f
the fee
d
er c
u
rrent.
(2
)
(1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
Impact of
Harmonics
on Pow
e
r Quality
and
Losses in
Pow
e
r Distribution Systems
17
3
Table
4. L
o
a
d
s
R
a
n
k
in
g B
a
se
d
On
THD
In
dex
Table
5. L
o
a
d
s
R
a
n
k
in
g B
a
se
d
On
ST
THD
THD
In
de
x
Load Type
C
TH
D
Split a
i
r
condit
i
o
n
er
22.6
M
i
crow
ave
22.5
Vacuum
17.5
Air conditioner
11.65
Television
10
Com
puter
9.5
P
r
inter
8.1
Laptop
6.2
W
a
shing m
achin
e
4.1
M
onitor
3.3
H
eater
2.9
Blow dr
y
e
r(Fast
Rate)
2.37
freez
er
2.32
Blow dr
y
e
r(Slo
w Rate)
2.21
Iron
2.20
Vi
de
o
1.61
Refriger
a
tor
1.57
Fan (Fast rate)
1.19
F
l
uores
cent
lam
p
0.58
CD Play
er
0.44
Fan (Slow rate)
0.2
CFL
0.2
Incandes
c
ent
la
m
p
0.15
Sound recorder
0.15
Load Type
Operation ti
m
e
p
er
day (
h
our)
St
THD
Split air conditioner
5
31
Co
m
puter
10
17
Air
conditioner
5
15
T
e
levision
6
11
L
a
ptop
6
6.
7
Monitor
10
6
f
r
eezer
5
2
Microwave
0.
5
2
Vacuu
m
0.
5
1.
5
Ref
r
igerator
5
1.
4
Video
3
0.
87
W
a
shing m
achine
1
0.
75
Printer
0.
5
0.
73
Heater
1
0.
52
Fluorescent la
m
p
6
0.
5
CFL
6
0.
47
Fan
(Fast
rate
)
2
0.
4
Incandescent la
m
p
6
0.
2
Sound r
ecor
d
er
2
0.
2
CD Pla
y
er
3
0.
1
Iro
n
0.
2
0.
07
Fan
(Slo
w
rate)
2
0.
07
Blow dr
y
e
r
(
F
ast Rate)
0.
1
0.
04
Blow dr
y
e
r
(
S
low
Rate)
0.
1
0.
03
Figu
re
7.
Lo
ss
es d
u
e t
o
Z
1
i
m
pedance for
an
office
load
Figure
8. Losses due t
o
Z
2
i
m
pedance whe
n
feedi
n
g
three l
o
ads
Figu
re
9.
Total
losses i
n
Z
1
a
n
d
Z
2
im
pedan
ces
Figu
re
1
0
. R
e
a
l
po
we
r los
s
ve
rsus
total fee
d
e
r’s
real
po
we
r
0
10
00
20
00
30
00
4
000
5
000
60
00
70
00
80
00
90
00
100
00
11
000
0
5
10
15
20
25
30
t(
s)
Lo
s
s
(
W
)
0
10
00
20
00
300
0
40
00
500
0
60
0
0
700
0
80
0
0
900
0
10
0
0
0
110
0
0
0
10
0
20
0
30
0
40
0
50
0
60
0
70
0
t(
s)
Los
s
(
W
)
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
1.
8
2
x 1
0
4
0
200
400
600
800
1000
1200
t(
s
)
Los
s
(
W
)
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
1.
8
2
x 1
0
4
0
0.
0
2
0.
0
4
0.
0
6
0.
0
8
0.
1
0.
1
2
0.
1
4
0.
1
6
0.
1
8
t(
s)
Los
s
p
e
r
t
o
t
a
l
pow
er
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-87
08
I
J
ECE
Vo
l.
5
,
No.
1
,
Feb
r
u
a
ry 2
015
:
16
6 – 17
4
17
4
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