Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 1
,
Febr
u
a
r
y
201
6,
pp
. 21
~25
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
1.7
963
21
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
Three Dimension
a
l Space Vect
or
Modulation Theory: Practices
without Proofs
Bha
s
ka
r Bhatt
a
cha
r
ya
,
A
j
oy
Kuma
r
C
h
akra
bo
rt
y
Departm
e
nt o
f
E
l
ec
tric
al
Engin
e
e
r
ing, Na
tion
a
l In
stitute
of
Te
chno
log
y
, Agar
ta
la
,
Tripura
,
Ind
i
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Apr 30, 2015
Rev
i
sed
Sep 4, 20
15
Accepte
d Oct 2, 2015
In thre
e d
i
m
e
nsional (3D)
space
vect
or m
odulati
on (SVM) theory
with
α
-
β
-
γ
fram
e
there are
s
o
m
e
iss
u
es
whi
c
h are well kno
wn and are widel
y
pra
c
ti
ced
being quite obv
ious but withou
t an
y
proof
so far. In th
is paper
necessar
y
scientific found
ations
to those issues
have b
een
provided
.
The
foremost of
thes
e is
s
u
es
has
been with the
fram
e
of
reference to be considered in 3D
SVM applications for unbalanced
three ph
ase s
y
stems. Although for
balan
ced thr
ee p
h
as
e s
y
s
t
em
s
there has
bee
n
no controvers
y wit
h
α
-
β
frame
as the frame of r
e
feren
ce but
in 3D it
has not
y
e
t
been established
which one,
α
-
β
-
γ
fram
e
or
t
h
e a-b-
c fr
am
e,
i
s
m
a
them
atic
all
y
corre
ct
. Anothe
r
s
i
gnifi
cant
is
s
u
e addres
s
e
d
in this
work has
been to
as
cer
tai
n
the ex
act r
eas
on when a
three phase s
y
stem has to be r
e
pr
esented
in 2D or
3D space to
app
l
y
SVM. It
has
been pres
en
ted for the f
i
rs
t
tim
e in this
work that th
e ke
y factor th
at
determines whether 3D or 2D
SVM
has to be applied d
e
p
e
nds on th
e
presence of
time indep
e
ndent s
y
mmetr
ic
al com
ponents in a th
r
ee phase
ac
s
y
stem
. Also it h
a
s been proved
t
h
at th
e third
axis
, the
γ
–a
x
i
s,
re
pr
e
s
e
n
t
s
t
h
e
time indep
e
nden
t
quantity
and th
at it mu
s
t
be dir
e
cted p
e
rpend
i
cul
a
r to t
h
e
α
-
β
plane passing
through the orig
in.
Keyword:
α
-
β
-
γ
fram
e
Space Vector
Switching state
vector
Copyright ©
201
6 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
:
Bhaska
r B
h
attacharya,
Depa
rt
m
e
nt
of
El
ect
ri
cal
Engi
neeri
n
g
,
Natio
n
a
l
In
stitu
te of Techn
o
l
o
g
y
Ag
artala,
Barjala, Jira
nia,
Aga
r
ta
la, Tr
i
p
ur
a, In
d
i
a-
799
046
.
Em
a
il: b
h
a
sk
aro
h
m
m
@
g
m
a
il.
co
m
1.
INTRODUCTION
Space
Vector t
h
eory is
base
d upon t
h
e
d-q-0 a
n
d
-
-
t
r
ansf
o
r
m
a
ti
on t
h
eo
ri
es
prese
n
t
e
d
by
Pa
rk
(
192
9)
[1
] & Clar
k
e
et al. (
1
951
)
[2
] respectiv
ely. Orig
i
n
ally, it was
devel
ope
d f
o
r
st
udi
es o
f
el
ect
ri
cal
machines [3].
Since then
the
r
e have been
many applications
of
Space Vector Modul
a
tion (SVM) in powe
r
conve
r
ters and ac drives
[3
]-[7]. Electrical machines bei
n
g bala
nced
t
h
r
ee phase l
o
ad
s wi
t
h
o
u
t
zer
o s
e
que
nce
com
pone
nt
s su
ch st
u
d
i
e
s ha
v
e
rem
a
i
n
ed co
nfi
n
ed t
o
-
t
r
ans
f
orm
a
t
i
on onl
y
an
d t
h
e S
V
M
ap
pl
i
e
d w
a
s 2D
SVM. Th
e abilit
y o
f
rep
r
esen
tin
g a t
h
ree ph
ase
b
a
lanced
system
b
y
a sing
le
v
e
cto
r
app
l
yin
g
α
-
β
t
r
ans
f
o
r
m
a
ti
on
an
d t
h
e
succe
s
s
ful
a
p
pl
i
cat
i
ons
of
2
D
S
V
M
i
n
di
ffe
re
nt
ar
eas o
f
po
wer
c
o
n
v
e
r
t
e
r a
ppl
i
c
at
i
ons
e.g. dc dri
v
es, ac
dri
v
es,
i
n
ve
rt
ers, rect
i
f
i
e
rs,
and di
fferen
t flex
ib
le AC tran
sm
issio
n
syste
m
(FACTS) dev
i
ces
fo
r
po
we
r
qual
i
t
y
appl
i
cat
i
ons
[
3
]
-
[
15]
l
e
d re
searche
r
s t
o
a
p
pl
y
SVM
f
o
r t
h
ree
phase
u
n
b
a
l
anced
sy
st
em
s.
In a
n
unbalanced system the
-
c
o
m
pone
nt
i
s
not
zer
o so
t
h
e num
ber o
f
di
m
e
nsi
ons
of t
h
e act
i
v
e
space increa
se
s from
2 to 3, making th
e 3D SVM as the applicable SVM
.
The first 3D SVM was re
ported by
Zha
n
g
et
al
. [
16]
i
n
19
9
7
. I
n
[1
6]
,
-
-
fram
e
h
a
s b
e
en
u
s
ed
with
the
ax
is for
-
c
o
m
ponent
s
h
ow
n as
a
p
e
rp
en
d
i
cu
lar to
th
e
-
pl
a
n
e and
passi
ng t
h
r
o
ug
h t
h
e
ori
g
i
n
.
It
has
bee
n
st
at
ed t
h
e
r
ei
n
,
“
W
i
t
h
t
h
e a
d
di
t
i
onal
neut
ral leg, the space
vector
m
odulation c
ont
rol is m
u
ch
m
o
re com
p
lex and there is
no
precede
n
t literature
ad
dressi
n
g
th
is issu
e”. Using
3
D
SVM in
-
-
fram
e has
rem
a
ined an a
r
ea co
m
p
aratively less worke
d
a
nd
less reported
[1
7
]-[2
1
]
. To
ov
erco
m
e
th
e co
m
p
lex
ities an
d
d
i
fficu
lties of 3D
SVM i
n
-
-
fram
e
,
Perales et
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
2
1
– 25
22
al
. [2
2]
p
r
o
p
o
s
e
d t
o
use a
-
b
-
c
coo
r
di
nat
e
s f
o
r
3D
SVM
.
Si
n
ce t
h
en a
n
u
m
b
er o
f
w
o
rks
usi
ng a
-
b-c
fram
e
have
been
re
po
rt
ed
[2
3]
-[
2
6
]
.
B
u
t
n
one
o
f
t
h
ese
pape
rs
hav
e
ju
stified
a-b-c
fr
am
e a
s
a valid fra
m
e to
mathe
m
atica
l
l
y
represe
n
t a 3D space
or a
n
y vector in a
3D space. A c
o
mparison
of shunt active powe
r filter
wi
t
h
l
o
ad
cu
rre
nt
det
ect
i
on
an
d
wi
t
h
s
o
urce
c
u
r
r
ent
det
ect
i
o
n
but
wi
t
h
o
u
t
r
e
fere
nce t
o
s
p
a
ce vect
or
t
h
e
o
r
y
ha
s
been prese
n
ted in
[27].
The
pape
r
has
been
o
r
ga
ni
z
e
d i
n
di
f
f
ere
n
t
sect
i
ons
. I
n
S
ect
i
on-
2 t
h
e
m
a
t
h
em
ati
cal
ly
app
r
op
ri
at
e
fram
e
of
refe
r
e
nce
fo
r
3D
S
V
M
anal
y
s
i
s
has
bee
n
est
a
b
l
i
s
hed.
I
n
Sect
i
o
n
-
3
,
t
h
e
nec
e
ssary
an
d e
s
s
e
nt
i
a
l
condition
for a three phase syste
m
to be represented as
a 2D vector in ac
corda
n
ce
to space vector the
o
ry has
been
prese
n
t
e
d
and i
n
Sect
i
o
n
-
4 t
h
e l
o
gi
c fo
r
m
a
ppi
ng t
h
e o
n
e-
di
m
e
nsi
ona
l
vect
or re
pres
ent
i
ng ze
ro se
q
u
enc
e
com
pone
nt
o
f
sym
m
et
ri
cal
com
pone
nt
s
o
f
a t
h
ree
pha
se sy
st
em
al
ong
t
h
e
-a
xi
s
has bee
n
pre
s
ent
e
d
.
C
oncl
u
si
o
n
has
bee
n
prese
n
t
e
d i
n
Sect
i
o
n-
5.
2.
THE CORRE
C
T
MATHE
M
ATICAL
FR
AM
E FOR
3
D
ANA
LY
SIS:
-
-
OR
A-
B-
C?
Space
vector t
h
eory is a
n
effective
analytical tool to analy
ze three
ph
ase
syste
m
s. In t
h
is m
e
thod any
tim
e
-varying t
h
ree
phase sys
t
em
is conve
rted from
tim
e
dom
ain to a se
t of t
w
o
vectors in s
p
ace
dom
a
in. If
v
a
(t)
,
v
b
(t),
an
d
v
c
(t)
b
e
three ph
ase
q
u
a
n
tities in
a-b-c
p
l
an
e th
en
t
h
e syste
m
can
b
e
represen
ted
b
y
a sp
ace
vector
V
wh
ich
i
s
th
e
resu
ltan
t
o
f
two
v
ecto
r
qu
an
tities
V
and
V
as:
V
V
V
(
1
)
whe
r
e,
V
s
= (
V+
j
V
αβ
) , a
2D s
p
ace vect
or i
n
t
h
e
-
c
o
m
p
l
e
x
pl
ane,
s
h
o
w
n i
n
Fi
g
u
r
e
1,
wi
t
h
real axis
unit vector
V
α
d
i
rected
alo
n
g
p
h
a
se q
u
an
tity
v
a
(t) i
n
t
h
e a
-
b-c
plane
and j=
-1
=
01
2
2
(
a
v
(
t)
+
a
v
(
t)
+
a
v
(
t)
)
ab
c
3
,
whe
r
e: a =
j2
π
/3
e
= (-
1
2
- j
3
2
)
(
2
)
and,
V
z
=
1
(
v
(
t
)
+
v
(
t)
+
v
(
t)
)
ab
c
3
(
3
)
V
α
V
β
Fi
gu
re
1.
Tra
n
s
f
o
r
m
a
ti
on
fr
om
a-
b-c t
o
-
If t
h
e su
m
o
f
t
h
ree ph
ase
qu
an
tities b
e
zero th
en
V
z
is zero and
(1)
becom
e
s:
V
V
(
4
)
A
p
p
licatio
n of Clar
k
e
tr
ansfor
m
a
t
i
o
n
co
nv
e
r
ts the
sam
e
three
phase
syst
e
m
of
v
a
(t
), v
b
(t) a
n
d
v
c
(t)
fr
om
a-b-c t
o
-
-
f
r
a
me
.
T
h
e
t
r
an
s
f
o
r
ma
t
i
o
n
,
w
h
en
v
a
(t
) +
v
b
(t
) +
v
c
(t
)
≠
0
,
is as fo
llows:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Three
Di
m
e
nsi
o
n
a
l
Sp
ace
Ve
ct
or M
o
d
u
l
a
t
i
o
n T
h
e
o
ry:
Pr
ac
t
i
ces w
i
t
hout
P
r
oof
s
(
B
ha
skar
Bh
at
t
a
ch
ary
a
)
23
1
-
1/2
-
1/2
vv
α
a
2
v
=
0
3
/2
-
3
/2
v
β
b
3
1/2
1
/2
1/2
v
c
v
γ
(
5
)
Bu
t fo
r th
e syste
m
w
h
er
e
v
a
(t)
+ v
b
(t) +
v
c
(t
)
= 0,
t
h
e C
l
ar
ke
t
r
ans
f
orm
a
t
i
on i
s
gi
ven
i
n
(6
).
v
a
v
-1
/
2
-1
/
2
1
2
α
=v
b
v
3
0
3/
2
3
/2
β
v
c
(
6
)
C
l
arke t
r
a
n
s
f
o
r
m
a
ti
on e
quat
i
ons
(
5
)
an
d
(6
) ha
ve
bee
n
d
e
vel
o
ped
wi
t
h
pha
se-a
vect
o
r
v
a
al
i
gne
d
al
on
g
-axi
s a
nd t
h
e
-a
xis located at right angles to the
-ax
i
s.
All th
e v
ecto
r
s
v
a
,
v
b
,
v
c
,
v
α
&
v
β
are
on the sam
e
plane, a
2D s
p
ac
e as show
n in
Fig
u
re
1
.
Th
is
2
D
sp
ace is th
e
-
plane
as
well as the a
-
b-c pla
n
e
with origi
n
s
of bot
h fram
es located at the
s
a
m
e
point.
He
nce a-b-c frame has its a
ll three axes
on the sam
e
plane
but for a
fram
e
to repres
ent a 3D s
p
ace
all its ax
es cannot lie on one
plane as
pe
r mathem
atics. So a-b-c
fram
e
is not the correct fram
e
for analyzing
any 3D sp
ace
vector. It ca
n
be seen from
(2) that a 2D
vec
t
or
V
lies on the a
-
b-c plane i.e. t
h
e
-
plane. T
o
m
a
the
m
atica
l
ly repre
s
ent a
3D vect
or
V
as in
(1
), a
not
her
1
D
vector
V
has t
o
be
out
si
de
t
h
e
α
-
β
plane
where t
h
e 2D vect
or
V
li
es. In
-
-
fr
am
e
V
i
s
m
a
ppe
d al
o
n
g
a
th
ird d
i
recti
o
n
called
-a
xis a
n
d he
nce it is t
h
e c
o
rrect m
a
them
at
ical frame for
3D s
p
ace
vector a
n
alysis.
3.
CONDITION FOR
REPRE
S
ENTING A THREE
PHASE
SYSTEM WITH A 2
D
VECTOR
As pe
r sym
m
e
trical com
pone
nt theo
ry [28],
any single
pha
se
qua
ntity of
a three phase s
y
stem
can be
expresse
d as a function of three vectors
represe
n
tin
g cor
r
es
po
n
d
i
n
g
phase o
f
t
h
r
ee di
ffer
e
nt
b
a
l
a
nced
syste
m
s: p
o
s
itiv
e seq
u
e
n
ce,
n
e
g
a
tiv
e sequ
en
ce an
d
ze
ro
sequ
en
ce.
Wh
i
l
e p
o
s
itiv
e and
n
e
g
a
tiv
e sequ
en
ce
com
pone
nt
s a
r
e f
unct
i
o
ns
o
f
t
i
m
e
t
h
e zero
s
e
que
nce
com
pone
nt
i
s
t
i
m
e inde
pe
nde
nt
.
E
quat
i
o
ns
(
2
)
a
n
d
(
6
)
reveal
t
h
at
t
h
e
zero
seq
u
e
n
ce
com
pone
nt
s
o
n
l
y
ha
ve
been
l
e
ft
out
o
f
t
h
e
-
co
m
p
lex
plan
e. Ex
pr
essi
o
n
of
V
com
put
ed
fr
o
m
(5) an
d t
h
e
r
i
ght
han
d
si
de
(r.
h.s
)
of
(
3
)
ar
e eq
ual
i
.
e.
V
V
(
7
)
Hence t
h
e t
i
m
e i
nde
pe
nde
nt
zero se
q
u
e
n
ce
com
pone
nt
V
d
o
es no
t lie o
n
t
h
e
-
plane
.
This fact
lead
s to th
e con
c
lu
si
o
n
th
at t
h
e
c
o
ndition for representing a thr
ee phase sys
t
em with a 2D vec
t
or
is th
at
t
h
e sy
st
em
wil
l
not
have
a
n
y
t
i
m
e
-i
nvari
ant
sy
m
m
e
t
r
i
c
al
com
pone
nt
.
It
d
o
es
n
o
t
excl
u
d
e t
h
e
n
e
gat
i
v
e
seq
u
ence sy
m
m
et
ri
cal
co
m
pone
nt
s i
.
e. a
t
h
ree
p
h
ase sy
st
em
havi
n
g
n
e
gat
i
v
e se
que
nce c
o
m
pone
n
t
s but
wi
t
h
o
u
t
any
ze
ro se
q
u
ence c
o
m
pone
nt
can
be re
pre
s
ent
e
d
by
a 2
D
vect
or
on
α
-
β
p
l
an
e.
Th
is is d
i
fferen
t
from
the pre
v
a
iling conce
p
t of s
p
ace
vector
in 2D
or in
3D
base
d upon
the
balance
d
or unbalance
d
state
of
t
h
e t
h
ree
phas
e
sy
st
em
un
der
con
v
e
r
si
o
n
.
4.
MA
PPI
NG ZERO SEQ
U
ENCE S
Y
M
M
ETRIC
AL C
O
MP
ONE
N
T
ALON
G
-AX
I
S IN
-
-
FRAME
That
and
ax
e
s
of
-
pl
ane wi
t
h
m
u
t
u
al
l
y
perpe
ndi
c
u
l
a
r di
rect
i
o
ns h
a
ve bee
n
cl
earl
y
defi
ne
d i
n
C
l
arke t
r
a
n
sf
or
m
a
t
i
on but
t
h
e
di
rect
i
o
n o
f
γ
-axis o
f
α
-
β
-
γ
fram
e
h
a
s n
o
t
b
een
so d
e
fi
n
e
d. In
the literatu
re so
far the
γ
-axi
s of
t
h
e
α
-
β
-
γ
fram
e
has
been s
h
o
w
n t
o
be di
rect
e
d
i
n
a di
rect
i
on m
u
t
u
al
l
y
perpe
n
di
cul
a
r t
o
b
o
t
h
and
β
ax
es bu
t
wh
y it sh
all
b
e
so
d
i
rected h
a
s
n
o
t
b
e
en
foun
d in
literature.
It has
been
noted that the s
p
a
ce vect
o
r
re
pre
s
ent
a
t
i
on
of a t
h
ree
p
h
ase sy
s
t
em
havi
ng
zer
o se
que
nc
e
com
pone
nt
s i
s
a t
h
ree di
m
e
nsi
onal
vect
or
. C
o
m
b
i
n
i
ng e
qua
t
i
ons (
1
) a
n
d (
7
) t
h
e
ge
neral
fo
rm
of t
h
e 3
D
spac
e
vector for s
u
ch a three
phase
syste
m
is,
V
=
V
+
V
i.e. t
h
e re
sul
t
ant of a
2D ve
ctor
V
on
α
-
β
plane and
a 1D
vector
V
al
ong
a
n
axi
s
-
wh
ich
is no
t on
the
-
plane. The
direction
of
-ax
i
s of
‐
‐
fram
e has not
been
clearly defi
ned as
an
d
ax
es ha
ve
bee
n
.
To sat
i
s
fy
t
h
e
dem
a
nd
of sy
mme
trical compon
e
n
t facts
that eac
h
i
ndi
vi
dual
pha
se
m
a
pped
o
n
α
-
β
pl
ane
m
u
st
ha
ve
eq
ual
sha
r
e
o
f
zer
o
se
que
nce
com
p
o
n
en
t
s
i
m
pl
i
e
s t
h
at
V
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
2
1
– 25
24
has t
o
be s
o
l
o
cated a
n
d di
rec
t
ed that it
rem
a
ins c
o
mm
on to each individual phase in ide
n
tical m
a
nner.
Henc
e
t
h
e onl
y
l
ogi
ca
l
di
rect
i
on f
o
r
-a
xi
s i
s
al
ong
t
h
e l
i
n
e perpe
n
di
cul
a
r t
o
and
axes and passing through their
poi
nt
of i
n
t
e
rs
ect
i
on. T
h
i
s
m
a
kes
-
-
fra
m
e exactly analogous to Cart
esian fram
e
. Access to Cartesian
fram
e
ope
ns
up
possibility of appl
ying m
a
the
m
atical tools in space
vector theory
applications.
5.
CO
NCL
USI
O
N
Th
is
work
h
a
s
p
r
ov
id
ed
th
e mu
ch n
e
ed
ed
sci
e
n
tific
pro
o
f
s
fo
r so
m
e
h
ypo
t
h
eses
of
3
D
SV
M th
eo
r
y
.
Th
ese
h
ypo
th
eses h
a
v
e
b
e
en
t
a
k
e
n fo
r gr
an
ted
w
ith
ou
t an
y
p
r
oo
f
on
th
e gro
und
th
at t
h
ey
ar
e obv
iou
s
and
w
e
ll
kn
o
w
n
.
It
has
been s
h
ow
n t
h
at
bet
w
een
α
-
β
-
γ
and a-b-c
fra
m
es, the
-
-
fram
e
is the
correct fram
e
that fits
th
e m
a
th
e
m
at
i
cal co
nd
ition
s
essen
tial to
represen
t
3D sp
ace v
ectors. Th
is wo
rk
h
a
s
d
e
term
in
ed
th
e crit
erion
that is necessary for a three phase unbala
nce
d
syste
m
to
determ
i
n
e whet
he
r t
h
at
has t
o
be
represe
n
t
e
d i
n
a 3D
space or in a
2D space
. It ha
s
been justified here why
the
γ
-axis in
-
-
fram
e
m
u
st
be per
p
e
ndi
c
u
l
a
r t
o
t
h
e
α
-
β
pl
a
n
e an
d
why
i
t
m
u
st
pass t
h
r
o
ug
h t
h
e poi
nt
o
f
i
n
t
e
rsect
i
on
o
f
α
&
β
axe
s
.
W
i
t
h
these c
o
nfirmations
,
coo
r
di
nat
e
ge
o
m
et
ry
or vect
o
r
anal
y
s
es ca
n
no
w
be ap
pl
i
e
d f
o
r
3
D
S
V
M
appl
i
cat
i
o
ns u
s
i
ng
-
-
fr
ame
as it
exactly
m
a
tches Cartesian fra
m
e. Th
e p
r
ese
n
t
w
o
r
k
has
pr
ovi
ded t
h
e m
a
th
em
atical and
logi
cal explanations
whi
c
h
had
bee
n
s
o
far
m
i
ssi
n
g
i
n
t
h
e t
h
e
o
ry
.
REFERE
NC
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r
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u
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ft, e
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antan
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e
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e
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l l
e
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ith
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7
0
8
Three
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e
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o
n
a
l
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o
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l
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o
n T
h
e
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ac
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i
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r
oof
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B
ha
skar
Bh
at
t
a
ch
ary
a
)
25
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ector
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C
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t
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t
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”
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.
G
a
rc
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a,
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A
gen
e
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i
z
e
d
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a
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i
v
e fi
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a
sed
on m
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BIOGRAP
HI
ES OF
AUTH
ORS
Bhaskar Bhattachar
y
a
gradu
a
ted
in Electrical
En
gineer
ing from REC Durgapur,
India in 1971.
From 1972 to 1
979 he worked as a Design En
gin
eer
in Development Consultants Pvt. Ltd
.,
Kolkata, India. He worked as a
self entrepr
e
neu
r
in electrical co
nstructions from 1980 to 1986
and major work
s were
construc
tion of mini H
y
d
e
l Power Sta
tion
,
33KV Substation and 132K
V
Transmission Line Survey
. From 1986
to 200
8 he
worked as Foreman Instru
ctor at Tripu
r
a
Institute of T
e
chnolog
y
,
Tripur
a, India. He jo
i
n
ed National Institute of T
echn
o
log
y
Agar
tal
a
,
Tripura, India
in 2009 as a Teaching Assistant in
Electrical
Engineer
i
ng Department and is a
Res
earch
F
e
ll
ow
ther
e.
H
i
s
curr
e
n
t ar
ea
of r
e
s
ear
ch is
pow
e
r
qua
l
i
t
y
is
s
u
es
.
Ajo
y
Kumar C
h
akraborty
obtai
ned his
L.E.E from state
co
unc
il of
Engg
. and technical
education, West Bengal
in 197
9, B.E.E from
Jadavpur Universi
ty
in
1987, M.Tech
(Power
S
y
stem) from IIT, Kharagpur
in 1990 and Ph.D
(Engg) in 2007 from Jadavpur University
res
p
ect
ivel
y.
H
e
is
cu
rrent
l
y
w
o
rking as
an A
s
s
o
cia
t
e P
r
ofes
s
o
r
in the
D
e
par
t
m
e
nt of E
l
e
c
tri
cal
Engineering, NI
T Agartala, India. Befor
e
he
joined the NIT A
g
artala in 2010
, he was with
coll
ege of
Engi
neering
& M
a
n
a
gem
e
nt,
K
o
lag
h
at,
India as a
Professor.
He
has 16
y
e
ars of
teaching and 14
y
e
ars of industrial
exp
e
rien
ces.
His areas of intere
st includ
e Application of soft
computing tech
niques to diff
er
ent power s
y
s
t
em probl
e
m
s,
Po
we
r Qua
l
i
t
y
,
F
A
CTS & HVD
C
and Deregu
lated
Power S
y
stem. He has published sever
a
l p
a
pe
r
s
in national an
d intern
ation
a
l
conferen
ce and
journals. He is a
Fellow of Instit
u
tion of
Engineer
s (India) and Lif
e
member of
IS
TE.
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