Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
5
,
No
. 2, Oct
o
ber
2
0
1
4
,
pp
. 14
2~
15
2
I
S
SN
: 208
8-8
6
9
4
1
42
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
/
IJPEDS
Estimation of Harmonics in Th
ree-phase and Six-phase (Multi-
phase) Load Circuits
Deepak
Kum
a
r, Z
a
kir Hus
a
i
n
Departem
ent
of
Ele
c
tri
cal
Eng
i
n
eering
,
Na
tiona
l
Institute
of
Te
ch
nolog
y, Ham
i
rp
ur (HP), Indi
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 22, 2013
Rev
i
sed
Ju
l
10
,
20
14
Accepte
d Aug 2, 2014
The Harm
onics
are very
harm
ful within a
n
electrical s
y
s
t
em
and can have
s
e
rious
cons
e
que
nces
such as
re
ducing the life of
apparatus
,
s
t
re
ss
on cable and
equipm
ent etc. This
paper cite
s
extens
ive ana
l
y
tical s
t
udy of harmonic
characteristic
s of
multi
phase
(si
x
-
phase) a
nd three-
phase
sy
stem eq
uipped
with
two &
three le
vel inve
rters for non-lin
ear loads.
Multile
vel i
nverter
has
elevated voltage
capability
with voltage
li
m
i
t
e
d device
s; low harmonic
disto
r
tion; abri
d
g
ed switching l
o
sses. Multipha
se technolo
g
y
also pay
s
a
pro
m
i
s
ing r
o
le in har
m
onic red
u
ction.
Matlab
si
m
u
lation is ca
rried out to
compare the advantage of
multi-phase over three phas
e sy
stem
s
equipped with
two o
r
th
ree level inverter
s
fo
r non
-
linear l
o
a
d
harm
onic reduction.The
extens
i
v
e s
i
m
u
lat
i
on results
are
pres
ented ba
s
e
d on cas
e s
t
udie
s
.
Keyword:
Fast Four
ier
Tran
sfor
m
Harm
oni
cs
In
verte
r
s
Mu
lti p
h
a
se sy
ste
m
R
i
ppl
e
To
tal Harm
o
n
i
c Distortio
n
Copyright ©
201
4 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
:
Deepa
k
Kum
a
r,
Depa
rtem
ent of Elect
ri
cal
E
n
gi
nee
r
i
n
g,
Natio
n
a
l
In
stitu
te of Techn
o
l
o
g
y
,
H
a
m
i
r
p
u
r
, H
i
mach
al Pr
ad
esh
,
In
d
i
a-17
7005
.
Em
a
il: d
k
a
ro
raelectrical@g
mail.co
m
,
ti
m
o
th
yaro
ra@g
m
a
i
l
.co
m
1.
INTRODUCTION
Owi
n
g
t
o
th
e
b
udd
ing
b
e
n
e
fits resu
lting
from th
e u
s
e of a p
h
a
se ord
e
r
hig
h
e
r th
an
three in
m
u
lti-
pha
se t
r
ansm
i
s
si
on an
d di
st
ri
but
i
o
n, s
o
m
e
int
e
rest
has al
s
o
de
vel
o
ped i
n
t
h
e area o
f
m
u
lt
i
-
phase sy
st
em
an
alysis in
recen
t
p
a
st [1
]-[10
]
.
Also
, m
u
lti
-lev
el inv
e
rters
ha
ve em
erge
d as a
capa
b
le t
ool i
n
ac
hievi
n
g
high
p
o
wer ratin
gs with
vo
ltag
e
limited
d
e
v
i
ces. Th
is p
a
p
e
r presen
ts a fun
c
tio
n
a
l m
o
d
e
l o
f
two
and
th
ree lev
e
l
inve
rter
with
m
u
lti and t
h
re
e phase l
o
ad a
n
d sim
u
lati
on of
t
h
e
de
vel
o
p
e
d m
odel
i
s
d
one
wi
t
h
t
h
e
h
e
l
p
o
f
MATLAB/Simu
lin
k. Mu
lti-lev
e
l in
v
e
rter
fed
electric m
a
c
h
in
e
d
r
i
v
e syste
m
s h
a
v
e
em
e
r
g
e
d
as a
p
r
omisin
g
t
ool
i
n
ac
hi
evi
ng
hi
g
h
po
we
r
rat
i
ngs
wi
t
h
v
o
l
t
a
ge l
i
m
i
t
e
d devi
ces
[2
0]
.
The c
o
n
v
e
n
t
i
o
nal
i
nve
rt
ers
u
s
ed are
vol
t
a
ge s
o
urce
i
nvert
er
(VS
I
) and c
u
r
r
ent
sou
r
ce i
n
vert
e
r
(C
SI
) w
h
i
c
h
consi
s
t
s
o
f
a dc l
i
nk an
d I
n
vert
er
B
r
i
dge
. Ha
rm
oni
c red
u
ct
i
o
n i
s
achi
e
ve
d t
o
great
er e
x
t
e
nt
than conventi
onal inve
rt
er such as voltage s
o
urce
i
nve
rt
er, c
u
r
r
e
n
t
so
urce i
nve
r
t
er i
n
m
u
l
t
i
l
e
vel
i
nvert
e
r
an
d
m
u
l
t
i
phase l
o
ads.
Hi
g
h
phas
e
num
ber
dri
v
es o
w
n
several
a
d
vant
ages
ove
r c
o
n
v
ent
i
o
nal
t
h
ree
-
p
h
ase
dri
v
es s
u
ch
as:
re
duci
ng t
h
e am
pl
i
t
ude a
nd i
n
creas
i
ng t
h
e
fre
que
ncy
o
f
t
o
r
q
ue p
u
l
s
at
i
o
n,
red
u
ci
n
g
t
h
e
rot
o
r
harm
oni
c cur
r
ent
s
, re
d
u
ci
n
g
t
h
e c
u
r
r
e
nt
pe
r p
h
ase
wi
t
h
o
u
t
in
creasing
th
e v
o
ltag
e
p
e
r phase,
lo
wering
th
e
d
c
li
n
k
curren
t
h
a
rm
o
n
i
cs, h
i
gh
er
reliab
ility an
d
in
creased
po
we
r.
Harm
oni
cs are
ve
ry
d
e
t
r
im
ent
a
l
wi
t
h
i
n
a
n
el
ect
ri
c
a
l
sy
st
em
and
can
have
seri
o
u
s c
o
nseq
ue
nc
es. F
o
r
exam
ple, the presence
of ha
rm
onics re
duce
s
t
h
e l
i
f
e o
f
ap
parat
u
s.
Harm
oni
cs ca
use t
h
i
ngs t
o
r
u
n h
o
t
,
whi
c
h
cause stress on the cables and equipm
ent.
In
th
e lo
ng
term
,
th
is d
e
g
r
ades
an electrical syste
m
. The presence
o
f
h
a
rm
o
n
i
cs
will also
m
ean
th
at alth
ou
gh
yo
u
will g
e
t b
i
lled
for th
e
power t
h
at yo
u
are supp
lied
,
a
larg
e
perce
n
t
a
ge
o
f
t
h
at
p
o
we
r m
a
y be n
o
t
vi
a
b
l
e
.
Harm
oni
c m
i
t
i
gat
i
on i
s
t
a
ki
n
g
act
i
on t
o
m
i
nim
i
ze t
h
e prese
n
ce o
f
harm
onics in y
o
ur electrical s
y
ste
m
and can
achi
e
ve
great
cost
savi
ng
s.
Harm
oni
c di
st
ort
i
o
n ca
n cau
se p
o
o
r
p
o
wer fact
o
r
, tran
sfo
r
m
e
r an
d d
i
stribu
tion
equ
i
p
m
en
t o
v
e
rheatin
g
,
rando
m b
r
eak
e
r tripp
i
n
g
, or ev
en
sensitiv
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Estima
tion
o
f
Ha
rmo
n
i
cs
in
Th
ree-pha
se an
d
S
i
x-pha
se (
M
u
lti-ph
ase)
Lo
ad
Circu
its (Deepa
k
K
u
ma
r)
14
3
eq
u
i
p
m
en
t fail
u
r
e. Sin
ce h
a
rm
o
n
i
cs affect t
h
e ov
erall po
wer d
i
stribu
tion
syste
m
, th
e p
o
w
er
u
tility
m
a
y ev
en
levy heavy fi
nes whe
n
a fac
ility is
affecting the utilities
’
ability to effi
ciently supply power to all of it
s
cu
sto
m
ers. Th
ese h
a
rm
o
n
i
cs can
b
e
sup
p
ressed
u
s
ing
m
u
ltil
ev
el inv
e
rter eq
u
i
p
p
e
d
with
m
u
l
ti-p
h
a
se load
s.
The m
u
lti-pha
se technology
receive
d a substantial worldwide atten
tion by the
vari
ous R&D’s a
nd
f
r
o
n
t
-
e
nd
industr
ies in
thr
e
e v
e
r
y
sp
ecif
i
c app
licatio
n
ar
eas,
n
a
m
e
ly
electr
i
c sh
ip
p
r
op
u
l
sion
, tractio
n
(including elec
tric and
hybrid elect
ri
c ve
hi
cl
es)
a
n
d
t
h
e conce
p
t
of
‘m
or
e
-
electric’
ai
rcra
ft. Irrespec
tive of
ab
und
an
t ad
van
t
ag
eo
us m
u
lti-p
h
a
se electric d
r
i
v
es are li
mited
to
eco
no
m
i
call
y
v
i
ab
le d
e
sign
,
p
o
wer
co
nv
er
ter
config
ur
atio
n
s
and clo
s
ed
c
o
ntrol aspects. Mul
ti-phase
powe
r system
s can
be used t
o
c
a
ncel
harm
oni
c
c
u
r
r
e
nt
s. Fo
r hi
g
h
e
r po
we
r
r
ect
i
f
i
e
r
ci
rc
ui
t
s
,
e
v
en
12
-p
hase
po
we
r
sy
st
em
s
ha
ve bee
n
us
ed fo
r
fu
rt
he
r ha
rm
oni
c cu
rre
nt
re
duct
i
o
n.
Si
x
p
h
ase t
r
a
n
sm
i
s
si
on l
i
n
es
are
po
p
u
l
a
r
due
t
o
i
t
s
i
n
crease
d
p
o
w
e
r
tran
sfer cap
a
b
ility b
y
3
ti
mes, main
tain
in
g
t
h
e sam
e
co
n
ducto
r con
f
iguratio
n
,
b
e
tter efficien
cy, b
e
tter
v
o
ltag
e
regu
latio
n
,
greater
stab
ility an
d
g
r
eat
er reliab
ility.
2.
MULTI-LEVEL INVE
RTE
R
The
po
wer el
e
c
t
r
o
n
i
c
s de
vi
ce
whi
c
h co
n
v
ert
s
DC
p
o
w
er t
o
AC
p
o
we
r at
r
e
qui
red
o
u
t
p
ut
vol
t
a
ge a
n
d
freq
u
e
n
c
y lev
e
l is kn
own
as i
n
v
e
rter. Inv
e
rt
ers can
b
e
b
r
o
a
d
l
y classified
i
n
to
t
w
o lev
e
l i
n
v
e
rter and
m
u
ltilev
e
l
in
v
e
rter. Mu
ltilev
e
l in
v
e
rter as co
m
p
ared
to
two
lev
e
l in
v
e
rters h
a
s adv
a
n
t
ag
es lik
e
min
i
m
u
m
h
a
rm
o
n
i
c
d
i
sto
r
tion
and
can
op
erate on sev
e
ral
vo
ltage lev
e
ls. A m
u
lti-stag
e in
v
e
rter is b
e
i
n
g
u
tilized
fo
r m
u
ltip
u
r
po
se
ap
p
lication
s
, su
ch
as activ
e
p
o
wer filters,
static v
a
r
co
mp
ensato
rs and
mach
in
e d
r
i
v
es for sinu
so
i
d
al an
d
trap
ezo
i
d
a
l curren
t ap
p
lication
s
. Th
e
dra
w
backs are t
h
e isolated power s
u
pplies re
qui
re
d for eac
h
one
of the
stag
es
o
f
th
e m
u
ltico
n
v
e
rter an
d it’s also
lo
t
h
a
rd
er to
bu
ild
, m
o
re exp
e
n
s
i
v
e, h
a
rd
er t
o
con
t
ro
l in
software.
Mu
ltilev
e
l in
verters are
n
a
med
after th
e lev
e
l o
f
v
o
ltag
e
s th
at can
b
e
o
b
t
ain
e
d
fro
m th
em
. Fo
r
exam
pl
e a 2-l
e
vel
i
nve
rt
er ca
n t
a
ke
val
u
es +
V
an
d
–V a
n
d
3-l
e
vel
i
nve
rt
e
r
can
pr
o
duce
vol
t
a
ge l
e
vel
s
of +
V
,
0
an
d –V
wh
ere V
is th
e
vo
ltag
e
o
f
d
c
supp
ly.
Fo
r
2
lev
e
l inverter, th
ere are
two
lev
e
ls for p
h
a
se
vo
ltag
e
an
d
t
h
ree lev
e
l
s
for lin
e vo
ltag
e
as shown
in
fo
llowing
fi
g
u
re
o
f
m
a
t
l
ab
.
Fi
gu
re
1.
Va
n:
i
nve
rt
er
pha
se
out
put
v
o
l
t
a
ge;
Va
b:
I
n
vert
er
l
i
n
e o
u
t
p
ut
vol
t
a
ge;
Va
b
_
l
o
a
d
:
i
nve
rt
er
l
o
a
d
lin
e vo
ltag
e
after lin
ear tran
sfo
r
m
e
r shown in
th
e abov
e
fi
gures
res
p
ective
l
y
(y ax
is:
Vo
ltage; x
ax
is: Tim
e
)
Th
e system co
n
s
ists o
f
two
ind
e
p
e
nd
en
t circu
its
illu
stratin
g two
th
ree-ph
as
e two
-
lev
e
l PWM v
o
ltag
e
source inverte
r
s. Each invert
er fee
d
s an AC load through a three
-
phas
e transform
e
r. Both conve
rt
ers are
cont
rol
l
e
d i
n
o
p
en l
o
o
p
wi
t
h
t
h
e Di
scret
e
P
W
M
Ge
nerat
o
r
bl
oc
k. T
h
e t
w
o ci
rc
ui
t
s
use t
h
e sam
e
DC
vol
t
a
ge
,
carrier
fre
quency, m
odulation inde
x a
nd
ge
nerated
fre
que
ncy (f =
50 Hz
). Ha
rm
onic filtering is pe
rform
e
d by
the tra
n
sform
e
r leakage
indu
ctance a
n
d loa
d
capacitance.
Fo
r 3 lev
e
l i
n
verter, t
h
ere are th
ree lev
e
ls
o
f
ph
as
e
v
o
ltag
e
an
d 5 lev
e
ls
for lin
e
vo
ltag
e
as shown i
n
f
o
llow
i
ng
f
i
gu
re of
m
a
tlab
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
2
,
O
c
t
o
b
e
r 201
4 :
1
42 –
15
2
14
4
Fi
gu
re
2.
Va
n:
i
nve
rt
er
pha
se
out
put
v
o
l
t
a
ge;
Va
b:
I
n
vert
er
l
i
n
e o
u
t
p
ut
vol
t
a
ge;
Va
b
_
l
o
a
d
:
i
nve
rt
er l
o
a
d
l
i
n
e
v
o
ltag
e
after lin
ear transfo
r
m
e
r sh
own
in th
e abo
v
e
fi
g
u
res
resp
ectiv
ely. (y ax
is: Vo
ltag
e
; x
ax
is: Tim
e
)
Th
e syste
m
co
n
s
ists
o
f
two th
ree-p
h
a
se th
ree-lev
e
l
PW
M
volta
ge
source c
o
nve
rt
ers c
o
nnected in twi
n
co
nfigu
r
ation. Th
e in
verter feed
s an
AC lo
ad
thr
oug
h
a th
ree-p
h
a
se tran
sfo
r
m
e
r. Harm
o
n
i
c filteri
n
g
i
s
p
e
rf
or
m
e
d
b
y
th
e tr
an
sf
or
m
e
r
leak
ag
e inductan
ce and
lo
ad
cap
acitan
c
e. Each
of
th
e two
in
v
e
r
t
er
s
u
s
es th
e
Three
-
Le
vel
B
r
i
d
ge bl
oc
k
w
h
ere t
h
e
s
p
eci
fied power ele
c
tronic device
s
are IGBT/
D
i
ode
pairs
.
Eac
h
ar
m
con
s
i
s
t
s
o
f
4 I
G
B
Ts,
4 a
n
t
i
-
p
a
ral
l
e
l
di
o
d
es,
and
2
ne
ut
ral
c
l
am
pi
ng
di
o
d
e
s
. T
h
e i
n
ve
rt
er
i
s
co
nt
r
o
l
l
e
d i
n
ope
n
loop. Pulses are gene
rated
by the discrete 3-Phase
Di
scret
e
P
W
M
Ge
nera
t
o
r bl
ock
.
Thi
s
P
W
M
ge
nerat
o
r
o
r
m
odul
at
or
ca
n be used
t
o
ge
n
e
rat
e
p
u
l
s
es fo
r
3
-
phase
, 2-
l
e
vel
,
or 3
-
l
e
vel
con
v
e
r
t
e
rs usi
n
g one
b
r
i
d
ge o
r
t
w
o
bri
dges
T
h
e P
W
M
m
odul
at
o
r
gene
rat
e
s t
w
o set
s
o
f
12
pu
l
s
es (
1
set
pe
r
i
nve
rt
er)
.
T
h
e
gene
rat
o
r ca
n
ope
ra
t
e
ei
t
h
er i
n
sy
nc
hr
o
n
i
zed o
r
u
n
-sy
n
ch
r
oni
ze
d m
ode.
W
h
e
n
o
p
erat
i
n
g i
n
sy
nch
r
oni
ze
d m
ode, t
h
e carri
e
r
t
r
i
a
ng
ul
ar si
g
n
a
l
i
s
sy
nch
r
o
n
i
zed
on a
PLL
r
e
fere
nce a
ngl
e
connected to i
n
put '
w
t'
.
I
n
synch
r
on
ized
m
o
de, th
e
carrier chop
p
i
ng
freq
u
e
n
c
y is
sp
ecified b
y
t
h
e switch
i
n
g
rat
i
o
as a m
u
ltip
le
of th
e ou
tpu
t
frequ
e
n
c
y.
3.
HA
RM
ON
IC
S & F
O
U
R
IE
R
AN
ALY
S
IS
In three-pha
se
powe
r system
s
,
e
v
en
ha
rm
onics cancel
out,
s
o
only th
e o
d
d
harm
oni
cs
a
r
e of
co
nce
r
n
.
On three-phase
syste
m
s each
pha
se voltage is 120 de
grees
out of phase
,
causing th
e pha
s
e curren
t to
be 120
deg
r
ees
out
of
pha
se as wel
l
.
W
i
t
h
a si
nus
oi
dal
v
o
l
t
a
ge
,
cur
r
ent
harm
oni
cs d
o
not
l
e
ad t
o
a
v
era
g
e
po
we
r.
Howe
ver, current harm
onics
do increase the rm
s curre
nt
, and
hence they decreas
e the power fact
or. The
avera
g
e powe
r is:
Pav
∗
cos
Φ1
Φ
2
(
1
)
Whe
r
e
V1 a
n
d I1 are t
h
e peak val
u
es a
n
d, a
nd
Φ
1
and
Φ
2are t
h
e phase angles of
fundam
enta
l
vol
t
a
ge
an
d
cu
rre
nt
res
p
ect
i
v
el
y
.
The
rm
s cur
r
ent
c
o
nsi
d
e
r
i
ng t
h
e
harm
on
i
c
s i
s
gi
ve
n
by
(2
) as:
Rms C
u
rr
ent
∑
(
2
)
Whe
r
e I
n
i
s
t
h
e
peak c
u
r
r
e
n
t
at
any
harm
oni
c
num
ber.
W
i
t
h
no
n-l
i
n
ear l
o
a
d
s, t
h
e t
h
i
r
d ha
rm
oni
c on al
l
t
h
re
e
pha
ses i
s
exac
t
l
y
i
n
phase a
nd a
d
ds,
rat
h
e
r
t
h
an ca
n
cels
,
thus c
r
eating current
a
nd
heat
o
n
t
h
e
n
e
ut
ral
co
ndu
ctor. Left u
n
-treated, h
a
rm
o
n
i
c lo
ad
s can
redu
ce th
e
distrib
u
tion
capacity an
d
d
e
g
r
ad
e th
e
qu
ality
o
f
t
h
e
p
o
wer o
f
pu
b
l
i
c
u
tility
p
o
w
er syste
m
s, in
crease p
o
wer
and AC co
sts, an
d resu
lt in
equ
i
p
m
en
t
m
a
lfu
n
c
tio
n
s
suc
h
as c
o
m
m
uni
cat
i
o
n e
r
r
o
r
s
an
d
dat
a
l
o
s
s
.
A nonlinear l
o
ad in a
powe
r
syste
m
is characterized by t
h
e introdu
ct
i
o
n
of
a swi
t
c
hi
ng
act
i
on
a
n
d
con
s
eq
ue
nt
l
y
cur
r
ent
i
n
t
e
rr
u
p
t
i
o
n
s
. T
h
i
s
b
e
havi
or
pr
o
v
i
d
es cu
rre
nt
w
i
t
h
di
ffe
re
nt
com
pone
nt
s t
h
at
are
m
u
lt
i
p
l
e
s of
t
h
e f
u
n
d
am
ent
a
l
fre
que
ncy
of
t
h
e sy
st
em
. Thes
e com
pone
nt
s
are cal
l
e
d
ha
r
m
oni
cs.
THD
(Tot
al
h
a
rm
oni
c di
st
or
t
i
on) i
s
use
d
as harm
oni
c i
ndex f
o
r harm
oni
c
m
easurem
ent
whi
c
h i
s
gi
ve
n by
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Estima
tion
o
f
Ha
rmo
n
i
cs
in
Th
ree-pha
se an
d
S
i
x-pha
se (
M
u
lti-ph
ase)
Lo
ad
Circu
its (Deepa
k
K
u
ma
r)
14
5
∑
(
3
)
THD
i
s
u
s
ed
a
s
t
h
e
harm
oni
c
i
nde
x a
n
d ha
r
m
oni
c spect
ru
m
i
s
prese
n
t
e
d
fo
r eac
h l
o
ad
usi
n
g
FFT
(Fast F
o
u
r
ier
Tran
sf
orm
)
[1
7]
, [
18]
.
Fo
u
r
ier analy
s
is
of
a p
e
ri
o
d
i
c
functio
n
refers to th
e ex
tractio
n o
f
t
h
e
series o
f
si
n
e
s an
d
co
sin
e
s
wh
ich
wh
en
su
p
e
rim
p
o
s
ed
will rep
r
od
u
c
e th
e fun
c
tion
.
Th
is an
alysis can
be
expresse
d as a Fourier seri
es. The fast Fourier tra
n
sform is
a
mathematical
m
e
t
h
o
d
fo
r t
r
an
sf
or
m
i
ng a
fu
nct
i
o
n of t
i
m
e i
n
t
o
a fun
c
t
i
on o
f
fre
qu
ency
. Som
e
t
i
m
e
s i
t
i
s
descri
be
d as t
r
ansf
orm
i
ng fr
om
the t
i
m
e
dom
ai
n t
o
t
h
e f
r
eq
ue
ncy
d
o
m
a
i
n
.
It
i
s
ve
ry
us
eful
fo
r a
n
al
y
s
i
s
o
f
t
i
m
e-depe
nde
nt
phe
n
o
m
e
na.
On
e essen
tial ap
p
lication
o
f
FFT is fo
r th
e ex
amin
atio
n
o
f
so
und
. It is i
m
p
e
rativ
e to
assess th
e
fre
que
ncy distribution of the powe
r in
a sound
because the
hum
an ear exer
cises that capacity
in the hearing
pr
ocess
.
Fo
r a si
ne wa
ve wi
t
h
a si
ngl
e f
r
eq
uency
,
t
h
e F
F
T
consi
s
t
s
o
f
a
si
ngl
e pea
k
.
C
o
m
b
i
n
i
ng t
w
o so
u
n
d
wav
e
s
p
r
o
d
u
c
es a co
m
p
lex
pattern
in th
e time d
o
m
ain
,
bu
t th
e FFT clearly sho
w
s it
as con
s
isting
al
m
o
st
en
tirely o
f
two
frequ
en
cies. Fo
r a fu
ll-wave rectifie
d
sine wav
e
, m
ean
in
g
th
at th
e
wav
e
b
e
co
m
e
s p
o
s
itiv
e
whe
r
e
v
er
i
t
w
oul
d be negat
i
ve. Thi
s
c
r
eat
e
s
a
ne
w wa
ve
with
d
oub
le
the
frequ
en
cy
. You can see t
h
a
t
after
rectificatio
n
,
the fu
nd
am
en
tal freq
u
e
n
c
y is el
i
m
in
ated, and a
ll the eve
n
harm
onics are pre
s
ent.
Single
-
phase
non-linear l
o
ads
,
like electronic ballast
s, PC
(
P
ers
onal
C
o
m
put
e
r) a
nd
ot
h
e
r el
ect
ro
ni
c
appa
rat
u
s
,
cre
a
t
e
od
d ha
rm
oni
cs (i
.e.
3r
d,
5t
h,
7t
h
,
9t
h
,
et
c.). Tri
p
l
e
n
harm
oni
cs (
3
r
d
o
r
de
r an
d i
t
s
od
d
m
u
l
tip
les) are
b
o
t
h
e
rso
m
e for sing
le
ph
ase lo
ad
s
b
eca
use
the
A-phase t
r
iplen ha
rm
onics, B-phase tri
p
len
h
a
rm
o
n
i
cs and C-p
h
a
se trip
l
e
n
h
a
rm
o
n
i
cs are all in
th
e
p
h
a
se with
each
o
t
h
e
r. Th
ey
will ad
d
rather th
an
cancel on the
neut
ral conduc
tor
of a
3-phas
e, 4-wire
sy
stem
. Th
is can
burd
e
n
th
e
n
e
u
t
ral if it is n
o
t
sized
t
o
h
a
nd
le th
is type o
f
lo
ad
.
In
ad
d
ition
,
trip
len h
a
rm
o
n
i
cs cau
se circu
l
atin
g cu
rren
ts
o
n
the d
e
lta win
d
i
ng
of a
del
t
a
-wy
e
t
r
an
sfo
r
m
e
r desi
gn
. The res
u
l
t
i
s
trans
f
orm
e
r heat
i
ng si
m
i
l
a
r t
o
t
h
at
creat
ed by
un
bal
a
nce
d
3-
pha
se
cur
r
ent
.
O
n
t
h
e ot
he
r
ha
nd
,
3-
p
h
ase
n
o
n
-
l
i
n
ear l
o
a
d
s l
i
ke
3-
ph
ase
A
S
Ds,
3
-
phase
DC
d
r
i
v
es
,
3-
pha
se
rect
i
f
i
e
rs, et
c.,
do
not
p
r
o
d
u
ce
curre
nt
t
r
i
p
l
e
n
harm
oni
cs so m
u
ch. These t
y
pes of l
o
a
d
s c
a
use m
a
i
n
l
y
5th an
d
7t
h c
u
r
r
ent
ha
rm
oni
cs and a
m
i
nor am
oun
t
of 1
1
t
h
, 1
3
t
h
, a
nd
hi
g
h
er
or
der
base
d o
n
t
h
e de
si
g
n
of t
h
e
c
o
nv
er
te
r
u
s
ed
.
4.
THREE PHASE TO SI
X
PHASE T
R
AN
S
F
OR
MA
TIO
N
U
S
IN
G
TR
AN
S
F
O
R
MER
Three
phase
voltage
s obtai
n
ed from
the inve
rter
is
fed to t
h
ree
single
phase tra
n
sform
e
r for
con
v
e
r
t
i
ng t
o
si
x p
h
ase sy
st
em
. The ci
rc
ui
t
di
agram
fo
r
obt
ai
ni
ng
6
s
u
p
p
l
y
f
r
o
m
3
su
ppl
y
u
s
i
n
g
l
i
n
ear
tran
sform
e
r is sh
own
in Fi
g
u
re 3
.
Fi
gu
re
3.
Li
nea
r
t
r
a
n
sf
o
r
m
e
r for
t
h
ree
p
h
ase
t
o
si
x
phase
t
r
a
n
sf
orm
a
t
i
o
n
Th
e t
r
an
sfo
r
mer is called linear if th
e co
ils are
wo
und
on m
a
g
n
e
tically l
i
n
ear m
a
terial (air,
p
l
astic,
Bak
e
lite, wo
od, etc.). Fl
u
x
is
p
r
op
ortio
n
a
l t
o
curren
t
in
t
h
e
wind
ing
s
.
5
.
MATLAB MODELS
Four
differe
n
t cases are c
o
nsidere
d
for t
h
e
harm
oni
c st
u
d
y
as sh
o
w
n
f
r
om
Fi
gure
4
t
o
Fi
g
u
re
7
com
p
ri
si
ng
o
f
2 a
n
d
3
l
e
vel
i
nve
rt
er
wi
t
h
t
h
ree
phase
o
r
si
x
pha
se rect
i
f
i
e
r ci
rc
ui
t
.
C
A
SE I:
Two l
e
vel
i
nvert
er- M
easur
em
en
t sys
t
e
m
- Three Phase Transformer- Three
Phase Re
ctifier.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
2
,
O
c
t
o
b
e
r 201
4 :
1
42 –
15
2
14
6
Fig
u
re 4
.
Two
lev
e
l
in
verter with
three ph
ase
rectifier
C
A
SE II:
Two Level
I
nvert
er- M
e
asurem
ent
Sy
stem
- Three Phase
t
o
si
x phase
transfor
m
e
r-
Six Phase Re
ctifier.
Fig
u
re 5
.
Two
lev
e
l
in
verter with
si
x
p
h
a
se rectifier
C
A
S
E
I
I
I
:
Three level
inverter- Measu
r
e
m
en
t s
y
s
t
e
m
- Three Ph
ase Transformer- Thre
e
Phase Re
ctifier.
Fig
u
re
6
.
Three lev
e
l inv
e
rter with
t
h
ree ph
ase rectifier
C
A
S
E
I
V
:
Three leve
l inver
t
er- Me
asure
m
en
t
sys
t
e
m
-
Three to six Phase Transformer- Six
Phase Re
ctifier.
Fig
u
re
7
.
Three lev
e
l inv
e
rter with
six
ph
ase rectifier
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Estima
tion
o
f
Ha
rmo
n
i
cs
in
Th
ree-pha
se an
d
S
i
x-pha
se (
M
u
lti-ph
ase)
Lo
ad
Circu
its (Deepa
k
K
u
ma
r)
14
7
M
a
t
l
a
b sim
u
l
i
nk m
odel
s
of
t
w
o an
d t
h
re
e l
e
vel
i
nvert
e
r
s are sh
ow
n
i
n
Fi
gu
re 8 a
nd Fi
gu
re 9
respect
i
v
el
y
.
T
h
ree l
e
vel
i
n
v
e
rt
er has a
dva
nt
age o
v
e
r
t
w
o l
e
vel
i
nve
rt
er t
h
at
whe
n
m
a
gni
t
u
de o
f
su
ppl
y
i
s
v
e
ry h
i
g
h
, u
s
e o
f
filter is sup
e
rfluo
u
s, constrain
t
on
th
e switch
e
s are l
o
w
for th
e reaso
n
t
h
at th
e switch
i
ng
fre
que
ncy
m
a
y be l
o
w, a
nd
r
eact
i
v
e po
we
r
fl
o
w
can
be co
nt
r
o
l
l
e
d. T
w
o
ful
l
-
bri
dges
V
S
I i
s
em
pl
oy
ed wi
c
h
cont
ai
n
s
t
w
el
v
e
IGB
T
whi
c
h
swi
t
c
h
on
dc s
o
u
r
ce [
1
2]
. Tw
el
ve p
u
l
s
es are
gene
rat
e
d
fo
r
a do
u
b
l
e
b
r
i
d
g
e
t
h
ree
p
h
a
se in
verter. Th
e first six
pu
lses (1
to
6
)
fire th
e six
d
e
v
i
ces o
f
t
h
e first
th
ree arm
b
r
idg
e
wh
ile th
e last six
pul
ses
(
7
t
o
12
) fi
re t
h
e
si
x
de
vi
ces
of t
h
e sec
o
n
d
t
h
ree
arm
bri
dges
.
Fi
gu
re
8.
M
a
t
l
a
b m
odel
o
f
t
w
o l
e
vel
i
n
v
e
rt
er
Fi
gu
re
9.
M
a
t
l
a
b M
odel
of
t
h
ree l
e
vel
i
nve
rt
er
A
non-linear load on a
powe
r system
is us
ually a
rect
i
f
i
e
r a
n
d
s
o
m
e
ki
nd
o
f
a
r
c
di
sc
har
g
e
de
vi
ce
suc
h
as a
fluorescent lam
p
, electric weldi
ng
machine,
or
a
r
c furnace in
which c
u
rre
n
t is not linea
rly rel
a
ted to
t
h
e vol
t
a
ge
. C
u
r
r
ent
i
n
t
h
ese
sy
st
em
s i
s
i
n
t
e
rr
upt
e
d
by
a swi
t
c
hi
n
g
act
i
on;
t
h
e cu
rre
nt
cont
ai
ns f
r
eq
uency
com
pone
nts that are m
u
ltiples of the
power
system
frequen
cy and leads
to distortion
of t
h
e c
u
rrent
wa
veform
whic
h in turn distorts the
vol
t
age wave
form. For a
n
alysis of three ph
ase non-linear loa
d
, RL
load is replaced
w
ith
th
r
ee ph
ase r
ectif
ier
cir
c
u
it. Fo
llow
i
ng
is th
e cir
c
u
it o
f
th
r
ee ph
ase r
ectif
ier
.
For six
p
h
a
se non-
lin
ear
lo
ad
, six RL load
is
rep
l
aced
with
two
su
ch
circu
its.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
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-86
94
I
J
PED
S
Vo
l.
5
,
No
.
2
,
O
c
t
o
b
e
r 201
4 :
1
42 –
15
2
14
8
Fi
gu
re
1
0
. M
a
t
l
ab m
odel
o
f
T
h
ree
t
o
si
x-
p
h
a
s
e t
r
an
sf
orm
e
r
Figure 11.
T
h
ree-phase rectifi
e
r
circ
uit
Fi
gu
re
1
2
. M
a
t
l
ab m
odel
o
f
Si
x-P
h
ase
R
ect
i
f
i
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Estima
tion
o
f
Ha
rmo
n
i
cs
in
Th
ree-pha
se an
d
S
i
x-pha
se (
M
u
lti-ph
ase)
Lo
ad
Circu
its (Deepa
k
K
u
ma
r)
14
9
6.
SIMULATION RESULTS
A nonli
n
ear load in a power syste
m
is character
i
zed
by
t
h
e be
gi
n
n
i
n
g
of a s
w
i
t
c
hi
n
g
act
i
on an
d
con
s
eq
ue
nt
l
y
cur
r
ent
i
n
t
e
rr
u
p
t
i
o
n
s
. T
h
i
s
b
e
havi
or
pr
o
v
i
d
es cu
rre
nt
w
i
t
h
di
ffe
re
nt
com
pone
nt
s t
h
at
are
m
u
lt
i
p
l
e
s of t
h
e fu
n
d
am
ent
a
l
fre
que
ncy
of t
h
e sy
st
em
. These com
pone
nt
s are cal
l
e
d
ha
rm
oni
cs w
h
i
c
h
i
f
n
o
t
su
ppressed
will cau
se sev
e
re
p
r
ob
lem
s
in
p
o
wer
d
i
stribu
tion
syste
m
. So
, to
an
alyze th
e effects of no
n-lin
ear
l
o
ad,
FF
T a
n
al
y
s
i
s
i
s
d
one
f
o
r
t
h
e
fo
ur
di
ffe
r
e
nt
cases a
s
m
e
nt
i
one
d a
b
ov
e.
On
ce th
e sim
u
latio
n
is co
m
p
leted
,
op
en th
e Powerg
u
i
an
d select ‘FFT An
alysis' to
d
i
sp
lay the
freq
u
e
n
c
y sp
ectru
m
o
f
sign
als sav
e
d
in
t
h
e stru
ct
u
r
es. Th
e FFT
will be p
e
rfo
rm
ed
on
a
2
-
cycle
win
d
o
w
st
art
i
ng at
t
=
0.
1 -
2/
50
(l
ast
2 cy
cl
es
of
re
cor
d
i
n
g)
. M
eas
urem
ent
of
p
h
a
s
e v
o
l
t
a
ge F
F
T
of
l
o
a
d
w.r
.
t
g
r
o
u
n
d
fo
r a
n
onl
i
n
ea
r
Loa
d
i
s
s
h
ow
n
fr
om
Fi
gure
1
3
t
o
Fi
gu
re
1
6
:
Fig
u
re
13
.
FFT an
alysis at two
lev
e
l i
n
verter
ou
tpu
t
with three
p
h
a
se rectifier lo
ad
(Case I)
Fig
u
re
14
.
FFT an
alysis at three lev
e
l inv
e
rter
out
put
with t
h
ree
phase
rect
ifier loa
d
(Cas
e III)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
2
,
O
c
t
o
b
e
r 201
4 :
1
42 –
15
2
15
0
Fig
u
re
15
.
FFT an
alysis at two
lev
e
l i
n
verter
ou
tpu
t
with si
x
p
h
a
se rectifier lo
ad
(Case
II)
Fig
u
re
16
.
FFT an
alysis at three lev
e
l inv
e
rter
out
put
wi
t
h
si
x pha
se
rect
i
f
i
e
r
l
o
a
d
(C
ase-
I
V
)
Tot
a
l
harm
oni
c di
st
ort
i
o
n (
T
HD
) f
o
r t
w
o l
e
vel
an
d t
h
ree
l
e
vel
i
nvert
e
r
wi
t
h
t
h
ree
p
h
a
se and si
x
pha
se rectifie
r
loads
are
shown in Ta
ble 1.
Type of inverte
r
Curren
t THD
for
3-phase recti
f
ier
load
Curren
t THD
for
Multi-phase (6-
phase) R
ecti
f
ier
load
T
w
o L
e
vel I
nver
t
er
38.
69%
4.
24%
T
h
r
ee level inver
t
er
37.
37%
3.
69%
For nonlinea
r current
T.H.D (Total
Harm
o
n
ic Distortio
n) i
n
t
h
e lo
ad curren
t is
foun
d to b
e
m
o
re i
n
three phase
.
Powe
r fact
or c
o
m
p
ensation re
qui
rem
e
nt is
mo
re in t
h
ree
phase load as c
o
m
p
ared to thre
e phase
i
s
al
so
f
o
u
n
d
by
si
m
u
l
a
t
i
on. R
ect
i
f
i
e
d
out
put
v
o
l
t
a
ge
u
n
d
er
t
h
ese
f
o
ur
di
ffe
re
nt
cases
i
s
al
so
s
h
o
w
n
w
h
i
c
h
shows
that the
r
e are
fewe
r
ripples
in six
ph
ase rectifier ci
rcuit.
Fro
m
Fig
u
re
1
7
to
2
0
, it is no
ted
that ri
p
p
l
e i
n
case
of six
ph
ase
rectifier is less
wh
ich
is an
un
desi
ra
bl
e fa
ct
or i
n
m
a
ny
el
ect
roni
c ap
pl
i
cat
i
on as
larg
e rip
p
l
es sh
orten
th
e life o
f
el
ectro
lytic cap
acito
r,
reduce t
h
e resolution
of electronic test
a
n
d measurem
ent ins
t
rum
e
nts etc.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Estima
tion
o
f
Ha
rmo
n
i
cs
in
Th
ree-pha
se an
d
S
i
x-pha
se (
M
u
lti-ph
ase)
Lo
ad
Circu
its (Deepa
k
K
u
ma
r)
15
1
Figure
17. T
h
ree-phase l
o
ad
rectifier
lo
ad
o
u
tp
u
t
(2
lev
e
l in
verter): Y ax
is: Rectified
o
u
t
p
u
t
d
c
vo
ltag
e
,
rect
i
f
i
e
d
o
u
t
p
ut
dc c
u
rre
nt
, C
u
rre
nt
t
h
ro
u
g
h
d
i
ode,
v
o
ltag
e
acro
s
s
d
i
od
e ;
X ax
is:
ti
m
e
. (Case I)
Fi
gu
re
1
8
Si
x-
pha
se l
o
a
d
rect
i
f
i
e
r l
o
a
d
out
p
u
t
(
2
lev
e
l in
verter): Y ax
is: Rectified
o
u
t
p
u
t
d
c
vo
ltag
e
,
rect
i
f
i
e
d
o
u
t
p
ut
dc c
u
rre
nt
, C
u
rre
nt
t
h
ro
u
g
h
d
i
ode,
voltage
across
diode; X axis: t
i
m
e
(Case II)
Figure
19 T
h
re
e-phase l
o
ad re
ctifier loa
d
out
put
(3
lev
e
l in
verter): Y ax
is: Rectified
o
u
t
p
u
t
d
c
vo
ltag
e
,
rect
i
f
i
e
d
o
u
t
p
ut
dc c
u
rre
nt
, C
u
rre
nt
t
h
ro
u
g
h
d
i
ode,
vol
t
a
ge
acr
oss
di
o
d
e;
Xa
xi
s:
t
i
m
e
. (C
ase I
I
I
)
Fi
gu
re
2
0
Si
x-
pha
se l
o
a
d
rect
i
f
i
e
r l
o
a
d
out
p
u
t
(
3
lev
e
l in
verter): Y ax
is: Rectified
o
u
t
p
u
t
d
c
vo
ltag
e
,
rect
i
f
i
e
d
o
u
t
p
ut
dc c
u
rre
nt
, C
u
rre
nt
t
h
ro
u
g
h
d
i
ode,
voltage
across
diode; X axis: t
i
m
e
. (Case IV)
7.
CO
NCL
USI
O
N
Th
is
p
a
p
e
r
p
r
esen
ts a
q
u
a
ntitativ
e stu
d
y
o
n
re
d
u
c
tion
o
f
h
a
rm
o
n
i
c an
alysis for si
x
p
h
a
ses as
com
p
ared to t
h
ree
phases
by si
m
u
lin
k
(MATLAB) for two
lev
e
ls and
th
ree lev
e
ls i
n
v
e
rter
for non
lin
ear
lo
ad
s. Declin
e in
h
a
rm
o
n
i
cs in
lo
ad
is ob
serv
ed
fo
r si
x
phase as com
p
ared to thr
ee phas
e load. In addition t
o
h
a
r
m
o
n
i
c study au
th
or
s
f
ound
th
at r
i
p
p
l
es
o
f
r
ectif
ied
o
u
tp
u
t
in
case
of six
ph
ase l
o
ad
cir
c
u
its is less as
com
p
ared t
o
its three
phas
e co
un
terp
art. As
th
e rating
s
of v
a
riou
s
power electronic s
w
itches a
r
e li
mited,
m
u
l
tilev
e
l v
o
ltag
e
sou
r
ce t
o
po
log
i
es are usefu
l
for
h
i
gh
voltag
e
and
h
i
gh
p
o
wer ap
p
licatio
n
s
alon
g wit
h
low
do
w
n
ha
rm
oni
cs.
W
i
t
h
t
h
e a
ugm
ent
of l
e
v
e
l
s
of i
n
ve
rt
er,
dr
op i
n
cu
rre
nt
TH
D i
s
o
b
s
e
rve
d
w
h
i
c
h f
u
rt
her
redu
ces with
t
h
e in
crease
o
f
th
ree p
h
a
ses to
six
p
h
a
ses. Th
is i
m
p
lies
th
at th
ere is
less req
u
i
rem
e
n
t
of
h
a
rm
o
n
i
c co
m
p
ensatio
n
i
n
case o
f
m
u
ltip
h
a
se lo
ad
circu
it. So
, m
u
ltilev
e
l
in
v
e
rter with
m
u
l
tip
h
a
se tech
no
logy
pay
s
a
pr
om
i
s
ing
t
o
ol
f
o
r
co
st
-ef
f
ect
i
v
e sy
ste
m
with effectively reduced ha
rm
onics.
REFERE
NC
ES
[1]
Shantanu Chatt
e
rje
e
. A Multi
leve
l
Inverter Based on SVPWM Technique
for Photovoltaic Application
,
International Jo
urnal of
Power
Elec
tronics and
Drive
System (
I
JPEDS)
. 2013; 3(
1): 62~73.
[2]
Risnidar C, I
.
Daut, S
y
afruddin H,
N. Hasim, Influence of Harmonics in
Laborator
y
due
to
Nonlinear
Loads,
International Jo
urnal of
Power
Elec
tronics and
Drive
System (
I
JPEDS)
. 2012; 2(
2): 219~224.
[3]
L Srinivas Goud, T Srivani.
A Sim
u
lation of Three
Phase to Multi Phase Transform
a
tion
using a Special
Transformer.
In
ternational Jour
nal of Sc
ience a
nd Research
(
I
JSR)
, India Onlin
e ISSN: 2319-70
64
.
2013; 2(7).
Evaluation Warning : The document was created with Spire.PDF for Python.