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it
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ied
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By
a
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ly
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d
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:
C
u
r
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en
t
c
o
n
tr
o
ller
P
ar
allel
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n
v
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ter
T
o
tal
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ar
m
o
n
ic
d
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s
to
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tio
n
Co
p
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rig
h
t
©
201
7
In
s
t
it
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
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e
e
rin
g
a
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d
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c
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e
.
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rig
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re
se
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e
d
.
C
o
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s
p
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A
uth
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r
:
Su
r
ia
n
a
Sali
m
i
n
,
Dep
ar
t
m
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
FKEE
,
Un
i
v
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s
iti T
u
n
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s
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On
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la
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,
8
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it R
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a@
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.
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u
.
m
y
1.
I
NT
RO
D
UCT
I
O
N
Dis
tr
ib
u
ted
g
e
n
er
atio
n
u
s
es
r
en
e
w
ab
le
en
er
g
y
s
o
u
r
ce
s
t
h
at
in
clu
d
e
s
o
lar
,
w
i
n
d
,
w
a
v
e,
h
y
d
r
o
,
etc.
T
h
ese
tech
n
o
lo
g
ies
co
n
v
er
t
n
atu
r
al
r
eso
u
r
ce
s
to
m
o
r
e
u
s
ab
l
e
en
er
g
y
t
h
at
is
elec
tr
icit
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.
N
o
r
m
al
l
y
,
d
is
tr
ib
u
ted
g
en
er
atio
n
s
y
s
te
m
s
ar
e
o
f
s
m
all
s
ca
le,
s
ca
tter
ed
ar
o
u
n
d
a
n
d
clo
s
er
to
e
n
d
u
s
er
s
[
1
]
,
[
2
]
.
Mo
s
t
i
m
p
o
r
tan
tl
y
,
th
ese
s
y
s
te
m
s
u
s
e
in
v
er
ter
s
to
in
te
g
r
ate
th
e
g
e
n
er
atio
n
p
ar
t
i
n
to
th
e
g
r
id
an
d
m
u
s
t
en
s
u
r
e
t
h
at
th
e
y
s
u
p
p
l
y
th
e
s
tan
d
ar
d
q
u
alit
y
o
f
p
o
w
er
[
3
]
.
I
n
v
er
ter
s
h
a
v
e
to
f
u
lf
il
s
ev
er
al
i
m
p
o
r
tan
t
f
u
n
ctio
n
s
b
ef
o
r
e
th
e
o
u
tp
u
t
s
ca
n
b
e
f
ed
to
th
e
u
t
il
it
y
g
r
id
[
4
]
.
Ho
w
e
v
er
,
th
e
i
n
v
er
ter
s
y
s
te
m
s
d
o
h
av
e
th
eir
d
r
a
w
b
ac
k
s
w
h
ic
h
co
m
es
f
r
o
m
t
h
e
s
w
itc
h
in
g
p
r
o
ce
s
s
a
n
d
n
o
n
-
li
n
ea
r
it
y
i
n
th
e
co
m
p
o
n
en
ts
u
s
ed
.
T
h
e
lev
els
o
f
d
is
to
r
tio
n
d
u
r
i
n
g
co
n
v
er
s
io
n
a
n
d
co
n
tr
o
l
p
r
o
ce
s
s
ar
e
v
er
y
d
i
f
f
ic
u
lt
to
av
o
id
.
A
t
th
e
en
d
,
u
n
d
esire
ab
le
cu
r
r
en
t
an
d
v
o
ltag
e
h
ar
m
o
n
ics
ap
p
ea
r
at
th
e
in
v
er
ter
o
u
tp
u
t,
t
h
u
s
w
ill
p
o
ten
tiall
y
co
n
tr
ib
u
te
to
h
i
g
h
e
r
T
HD
v
alu
e
i
n
g
r
id
n
et
w
o
r
k
.
T
h
e
p
r
o
b
lem
s
w
i
ll
en
h
a
n
ce
w
h
e
n
s
e
v
er
al
i
n
v
er
te
r
s
y
s
te
m
s
ar
e
co
n
n
ec
ted
to
g
e
t
h
er
in
p
ar
allel
an
d
f
ee
d
th
e
u
tili
t
y
g
r
id
.
T
h
is
i
s
b
ec
au
s
e,
ea
ch
in
v
er
ter
o
u
tp
u
t
v
o
ltag
e
a
n
d
cu
r
r
e
n
t
m
u
s
t
b
e
s
y
n
c
h
r
o
n
ized
to
t
h
e
g
r
id
v
o
ltag
e
an
d
cu
r
r
en
t.
Yet,
w
h
e
n
ap
p
ly
in
g
t
h
is
s
y
n
ch
r
o
n
i
za
tio
n
m
et
h
o
d
an
d
w
it
h
in
ter
a
ctio
n
o
f
a
clo
s
el
y
co
u
p
led
in
v
er
ter
s
y
s
te
m
s
m
a
y
p
o
ten
tiall
y
i
n
cr
ea
s
e
t
h
e
g
r
id
c
u
r
r
en
t a
n
d
v
o
ltag
e
T
HD
v
al
u
e
s
[
5
]
.
Stu
d
ies
h
av
e
b
ee
n
d
o
n
e
b
y
m
an
y
r
esear
ch
er
s
in
o
r
d
er
to
im
p
r
o
v
e
g
r
id
p
o
w
er
q
u
alit
y
t
h
u
s
r
ed
u
ce
th
e
g
r
id
T
HD
v
al
u
e
to
n
o
t
e
x
c
ee
d
th
e
li
m
i
tatio
n
b
y
I
E
E
E
s
tan
d
ar
d
[
6
]
.
I
n
[
7
]
,
s
p
ac
e
v
ec
to
r
p
u
ls
e
w
id
t
h
m
o
d
u
latio
n
(
SVP
W
M)
is
p
r
o
p
o
s
ed
as
a
co
n
tr
o
l
m
et
h
o
d
in
a
g
r
id
co
n
n
ec
ted
t
h
r
ee
p
h
a
s
e
s
o
lar
P
V
s
y
s
te
m
.
R
es
u
lts
s
h
o
w
t
h
at
th
e
f
ee
d
f
o
r
w
ar
d
g
r
id
v
o
lta
g
e
co
m
p
en
s
ati
o
n
i
m
p
r
o
v
e
th
e
g
r
id
h
ar
m
o
n
ic
s
p
ec
tr
u
m
a
n
d
th
u
s
ac
h
iev
e
t
h
e
r
eq
u
ir
ed
T
HD.
Ho
w
e
v
er
,
an
y
i
m
p
er
f
ec
t
co
m
p
en
s
atio
n
m
a
y
ca
u
s
e
h
ar
m
o
n
ics
in
g
r
id
cu
r
r
en
t
.
Oth
er
r
esear
ch
er
s
i
n
tr
o
d
u
ce
d
p
r
o
p
o
r
tio
n
al
in
teg
r
al
(
P
I
)
co
n
tr
o
ller
an
d
p
r
o
p
o
r
tio
n
al
r
eso
n
an
t
(
P
R
)
co
n
tr
o
ller
to
b
e
u
s
ed
to
g
et
h
er
i
n
o
r
d
er
to
c
o
n
tr
o
l
th
e
i
m
p
ac
ts
o
f
g
r
id
v
o
lt
ag
e
d
is
to
r
tio
n
.
I
n
t
h
e
p
ap
er
,
P
I
co
n
tr
o
ller
co
n
tr
o
ls
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
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8
8
-
8
694
R
ed
u
ctio
n
in
C
u
r
r
en
t THD
o
f G
r
id
P
a
r
a
llel I
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ve
r
ters
U
s
in
g
R
a
n
d
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miz
ed
P
R
C
o
n
tr
o
l (
S
.
S
a
limin
)
291
th
e
i
n
n
er
i
n
v
er
ter
o
u
tp
u
t
cu
r
r
e
n
t
co
n
tr
o
l
lo
o
p
w
h
il
s
t
a
co
m
b
in
atio
n
o
f
b
o
th
P
I
an
d
P
R
co
n
tr
o
ller
r
eg
u
late
t
h
e
o
u
ter
g
r
id
cu
r
r
en
t
co
n
tr
o
l
lo
o
p
[
8
]
.
Un
f
o
r
tu
n
ate
l
y
,
t
h
is
s
tr
ate
g
y
m
a
y
in
cr
ea
s
e
th
e
co
m
p
le
x
it
y
o
f
co
m
p
u
tatio
n
a
l
alg
o
r
ith
m
.
O
th
er
r
e
s
ea
r
ch
a
s
i
n
[
9
]
p
r
o
p
o
s
ed
a
P
R
co
n
tr
o
ller
an
d
ad
d
ed
s
ev
er
al
h
ar
m
o
n
ic
co
m
p
e
n
s
ato
r
s
(
HC
)
to
r
ed
u
ce
T
HD
v
alu
es.
T
h
i
s
m
et
h
o
d
is
also
b
elie
v
ed
to
in
cr
ea
s
e
th
e
s
a
m
e
co
m
p
le
x
it
y
o
f
t
h
e
co
m
p
u
tatio
n
a
l
alg
o
r
ith
m
.
E
l
s
e,
i
n
[
1
0
]
-
[
1
2
]
,
r
ep
etitiv
e
co
n
tr
o
ller
-
b
ased
h
ar
m
o
n
ic
eli
m
i
n
atio
n
is
u
s
ed
.
Ye
t,
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
i
s
tech
n
iq
u
e
is
s
e
n
s
i
tiv
e
t
o
f
r
eq
u
en
c
y
v
ar
iatio
n
an
d
m
a
y
af
f
ec
t
t
h
e
s
tab
ili
t
y
as
m
e
n
ti
o
n
ed
in
[
1
3
]
.
I
n
th
is
p
ap
er
,
th
e
ad
v
a
n
tag
e
o
f
P
R
co
n
tr
o
ller
is
ta
k
en
an
d
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Evaluation Warning : The document was created with Spire.PDF for Python.
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22
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
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8
,
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296
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,
2
0
1
1
.
[2
]
B.
W
il
li
a
m
s,
e
t
a
l
.,
“
Us
in
g
M
icr
o
g
rid
s
t
o
I
n
teg
ra
te
Distri
b
u
te
d
Re
n
e
wa
b
les
i
n
to
th
e
Gr
i
d
,
”
In
n
o
v
a
ti
v
e
S
m
a
rt
G
rid
T
e
c
h
n
o
lo
g
ies
Co
n
f
e
re
n
c
e
Eu
r
o
p
e
,
p
p
.
1
-
5
,
2
0
1
0
.
[3
]
K.
S.
K,
e
t
a
l
,
“
Po
we
r
Qu
a
li
ty
in
Gr
id
Co
n
n
e
c
ted
Ren
e
wa
b
le
En
e
rg
y
S
y
ste
ms
:
Ro
le
o
f
Cu
sto
m
Po
we
r
De
v
ice
s
,
”
In
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
Re
n
e
w
a
b
le E
n
e
rg
ies
a
n
d
P
o
w
e
r
Qu
a
li
ty
,
2010.
[4
]
M.
Ca
lais,
e
t
a
l
,
“
In
v
e
rte
rs
fo
r
S
i
n
g
le
P
h
a
se
Gr
id
Co
n
n
e
c
ted
P
h
o
t
o
v
o
lt
a
ic
S
y
ste
m
-
a
n
Ov
e
rv
iew
,
”
P
o
w
e
r
El
e
c
tro
n
ics
S
p
e
c
ialists Co
n
f
e
re
n
c
e
,
p
p
.
1
9
9
5
-
2
0
0
0
,
2
0
0
2
.
[5
]
M.
A
rm
stro
n
g
,
e
t
a
l
,
“
L
o
w
Ord
e
r
Ha
r
m
o
n
ic
Ca
n
c
e
ll
a
ti
o
n
i
n
a
G
rid
Co
n
n
e
c
ted
M
u
lt
i
p
le
In
v
e
rter
S
y
ste
m
v
ia
Cu
rre
n
t
Co
n
tr
o
l
P
a
ra
m
e
ter Ran
d
o
m
iza
ti
o
n
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r
El
e
c
tro
n
ics
,
v
o
l.
2
0
,
p
p
.
8
8
5
-
8
9
2
,
2
0
0
5
.
[6
]
“
IEE
E
Re
c
o
m
m
e
n
d
e
d
P
ra
c
ti
c
e
f
o
r
Util
it
y
In
terf
a
c
e
o
f
P
h
o
to
v
o
lt
a
ic
(P
V
)
S
y
ste
m
s
,
”
IEE
E
S
t
d
9
2
9
-
2
0
0
0
,
2
0
0
0
.
[7
]
S.
A.
L
a
k
sh
m
a
n
a
n
,
e
t
a
l
,
“
A
No
v
e
l
Cu
rr
e
n
t
C
o
n
tr
o
ll
e
d
S
VP
W
M
T
e
c
h
n
iq
u
e
fo
r
Gr
id
C
o
n
n
e
c
ted
S
o
l
a
r
PV
S
y
ste
m
,
”
IEE
E
P
E
S
G
e
n
e
ra
l
M
e
e
ti
n
g
,
Co
n
f
e
re
n
c
e
a
n
d
Ex
p
o
sit
io
n
,
p
p
.
1
-
5
,
2
0
1
4
.
[8
]
T
.
L
iu
,
e
t
a
l
,
“
A
No
v
e
l
Cu
rr
e
n
t
Du
a
l
-
L
o
o
p
Co
n
tro
l
S
tra
te
g
y
fo
r
T
h
re
e
Ph
a
se
Gr
id
-
c
o
n
n
e
c
ted
VS
I
wi
th
L
CL
Fi
l
ter
,
”
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
M
o
t
io
n
Co
n
tro
l
Co
n
f
e
re
n
c
e
,
v
o
l.
1
,
p
p
.
6
2
6
-
6
3
0
,
2
0
1
2
.
[9
]
R.
T
e
o
d
o
re
sc
u
,
e
t
a
l
,
“
A
Ne
w
Co
n
tro
l
S
tr
u
c
tu
re
fo
r Gr
id
Co
n
n
e
c
ted
L
CL
PV
In
v
e
rte
rs
wit
h
Z
e
ro
S
tea
d
y
-
sta
te E
rr
o
r
a
n
d
S
e
lec
ti
v
e
Ha
rm
o
n
ic
C
o
mp
e
n
sa
ti
o
n
,
”
A
p
p
li
e
d
P
o
w
e
r
El
e
c
tro
n
ics
Co
n
f
e
re
n
c
e
a
n
d
Ex
p
o
siti
o
n
,
v
o
l.
1
,
p
p
.
5
8
0
-
5
8
6
,
2
0
0
4
.
[1
0
]
P.
M
a
tt
a
v
e
ll
i
a
n
d
F
.
P.
M
a
ra
f
a
o
,
“
Re
p
e
ti
ti
v
e
-
b
a
se
d
Co
n
tr
o
l
f
o
r
S
e
l
e
c
ti
v
e
Ha
r
m
o
n
ic
Co
m
p
e
n
sa
ti
o
n
i
n
A
c
ti
v
e
P
o
w
e
r
F
il
ters
,
”
IEE
E
T
ra
n
s.
In
d
.
E
lec
tro
n
,
v
o
l
/i
ss
u
e
:
51
(
5
)
,
p
p
.
1
0
1
8
-
1
0
2
4
,
2
0
0
4
.
[1
1
]
R.
C
.
Co
ste
ll
o
,
e
t
a
l
,
“
Od
d
Ha
rm
o
n
ics
Dig
it
a
l
Re
p
e
ti
ti
v
e
Co
n
tro
l
o
f
a
S
in
g
le
-
p
h
a
se
Cu
rre
n
t
A
c
ti
v
e
F
il
ter
,
”
IEE
E
T
ra
n
s.
Po
we
r E
lec
tro
n
,
v
o
l
/
issu
e
:
19
(
4
)
,
p
p
.
1
0
6
0
-
1
0
6
8
,
2
0
0
4
.
[1
2
]
S.
Jia
n
g
,
e
t
a
l
,
“
L
o
w
T
HD
,
F
a
st
T
ra
n
sie
n
t
a
n
d
Co
st
Ef
fe
c
ti
v
e
S
y
n
c
h
ro
n
o
u
s
-
f
ra
m
e
Re
p
e
ti
ti
v
e
Co
n
tro
ll
e
r
f
o
r
T
h
re
e
P
h
a
se
UPS
i
n
v
e
rters
,
”
IEE
E
T
ra
n
s.
Po
we
r E
lec
tro
n
,
v
o
l
/i
ss
u
e
:
27
(
6
)
,
p
p
.
2
9
9
4
-
3
0
0
5
,
2
0
1
2
.
[1
3
]
J.
M.
Olm
,
e
t
a
l
,
“
S
tab
il
it
y
A
n
a
l
y
sis
o
f
Di
g
it
a
l
Re
p
e
ti
tri
v
e
Co
n
tro
l
S
y
st
e
m
s
u
n
d
e
r
T
i
m
e
V
a
r
y
in
g
S
a
m
p
li
n
g
P
e
rio
d
,
”
IET
Co
n
tro
l
T
h
e
o
ry
Ap
p
li
c
a
ti
o
n
,
v
o
l
/i
su
e
:
5
(
1
)
,
p
p
.
2
9
-
3
7
,
2
0
1
1
.
[1
4
]
R.
T
e
o
d
e
re
sc
u
,
e
t
a
l
.
“
Pr
o
p
o
rtio
n
a
l
-
re
so
n
a
n
t
Co
n
tro
ll
e
rs
a
n
d
Fi
lt
e
rs
fo
r
Gr
id
Vo
lt
a
g
e
-
so
u
rc
e
Co
n
v
e
rte
rs
,
”
El
e
c
tri
c
P
o
w
e
r
A
p
p
li
c
a
ti
o
n
s
,
IEE
P
ro
c
e
e
d
in
g
s,
v
o
l.
1
5
3
,
p
p
.
7
5
0
-
7
6
2
,
2
0
0
6
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
S
u
rian
a
S
a
li
m
in
is
a
lec
tu
re
r
in
F
a
c
u
lt
y
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
(F
KEE)
,
UT
HM.
Af
ter
g
ra
d
u
a
ted
f
ro
m
h
e
r
f
irst
d
e
g
r
e
e
i
n
El
e
tri
c
a
l
En
g
in
e
e
rin
g
(UT
M
-
2
0
0
6
),
sh
e
w
o
rk
e
d
a
s
a
tu
to
r
in
UT
HM
f
o
r
6
m
o
n
th
s
a
n
d
c
o
n
ti
n
u
e
d
f
o
r
M
S
c
i
n
P
o
w
e
r
Distrib
u
ti
o
n
En
g
in
e
e
rin
g
i
n
Ne
w
c
a
stle
Un
iv
e
rsit
y
(2
0
0
7
).
S
h
e
c
o
m
p
lete
d
h
e
r
P
h
D
i
n
El
e
c
tri
c
a
l
E
n
g
in
e
e
rin
g
in
2
0
1
4
a
lso
f
ro
m
Ne
w
c
a
stle Un
iv
e
rsit
y
,
UK
.
S
h
e
h
a
s p
u
b
li
s
h
e
d
a
f
e
w
p
a
p
e
rs i
n
Ju
rn
a
ls
a
n
d
p
ro
c
e
e
d
i
n
g
sin
c
e
2
0
1
3
.
He
r
re
s
e
a
rc
h
in
tere
sts
a
r
e
o
n
p
o
w
e
r
q
u
a
li
ty
i
m
p
ro
v
e
m
e
n
t,
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
sy
ste
m
s
a
n
d
h
a
rm
o
n
ics
m
it
ig
a
ti
o
n
.
S
h
a
m
su
l
A
iz
a
m
Zu
lk
if
li
,
M
IEE
E,
is
w
o
rk
in
g
a
s
a
se
n
io
r
lec
tu
r
e
r
in
F
a
c
u
lt
y
o
f
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ic
E
n
g
in
e
e
rin
g
(F
KEE)
,
UT
HM.
He
o
b
tain
e
d
h
is
P
h
D
d
e
g
re
e
in
Co
n
tro
l
S
y
ste
m
f
ro
m
L
o
u
g
h
b
o
r
o
u
g
h
Un
iv
e
rsity
,
Un
it
e
d
Kin
g
d
o
m
-
UK
in
2012
.
He
h
a
s
c
o
m
p
lete
d
h
is
Ba
c
h
e
lo
r
d
e
g
re
e
in
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ic
E
n
g
in
e
e
rin
g
a
n
d
M
a
ste
r
S
c
ien
c
e
in
El
e
c
ti
c
a
l
P
o
w
e
r
En
g
in
e
rin
g
in
2
0
0
3
a
n
d
2
0
0
6
re
sp
e
c
ti
v
e
ly
f
ro
m
Un
iv
e
rsity
P
u
tra
M
a
lay
sia
(UP
M
),
M
a
lay
sia
.
He
h
a
s
a
n
u
m
b
e
r
o
f
p
u
b
li
c
a
ti
o
n
s
in
re
n
o
w
n
e
d
jo
u
r
n
a
ls
in
tern
a
ti
o
n
a
ll
y
.
His
re
s
e
a
rc
h
i
n
tere
sts
in
Ro
b
u
st
c
o
n
tr
o
l,
H
-
in
f
in
it
y
c
o
n
tro
ll
e
r,
p
o
w
e
r
q
u
a
li
ty
m
it
ig
a
ti
o
n
,
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
.
M
a
tt
h
e
w
A
r
m
stro
n
g
(M
En
g
,
P
h
D)
is
a
se
n
io
r
lec
tu
re
r
in
Ne
w
c
a
s
tl
e
Un
iv
e
rsit
y
.
He
is
a
m
e
m
b
e
r
o
f
th
e
In
stit
u
ti
o
n
o
f
En
g
in
e
e
rin
g
a
n
d
T
e
c
h
n
o
l
o
g
y
(M
IET
).
He
h
a
s
a
n
u
m
e
ro
u
s
n
u
m
b
e
r
o
f
p
u
b
li
c
a
ti
o
n
s
to
d
a
te.
His
m
a
in
re
se
a
rc
h
in
tere
sts
li
e
in
p
o
w
e
r
e
lec
tro
n
ics
c
o
n
v
e
rters
,
p
o
w
e
r
e
lec
tro
n
ic
c
o
n
tro
l
lers
,
e
lec
tri
c
d
riv
e
s
,
a
n
d
d
ig
it
a
l
c
o
n
tro
l
s
y
ste
m
s.
He
h
a
v
e
a
p
a
rti
c
u
lar
in
tere
st
in
g
rid
c
o
n
n
e
c
ted
in
v
e
rter
s
y
ste
m
s
,
p
o
w
e
r
q
u
a
li
t
y
m
o
n
it
o
rin
g
a
n
d
i
m
p
ro
v
e
m
e
n
t,
h
a
rd
w
a
re
-
in
-
th
e
-
lo
o
p
(HIL
)
e
m
u
latio
n
sy
ste
m
s,
a
n
d
sy
ste
m
id
e
n
ti
f
ic
a
ti
o
n
(p
a
r
a
m
e
ter
e
sti
m
a
ti
o
n
)
o
f
p
o
w
e
r
e
lec
tro
n
ic sy
ste
m
s
.
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