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©
2
01
6
I
n
s
t
i
t
u
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e
o
f
A
d
v
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d
E
n
g
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e
.
A
l
l
r
i
g
h
t
s r
es
er
ved
.
1.
I
n
tr
o
d
u
c
ti
o
n
T
he
el
ec
t
r
i
c
i
t
y
dem
and
i
n
t
he
w
or
l
d’
s
de
v
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c
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t
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s
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nc
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ap
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s
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gr
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t
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w
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t
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t
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c
l
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at
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and
t
h
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en
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.
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m
ai
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g
y
s
our
c
e f
or
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pr
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t
i
o
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n t
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l
d t
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s
t
h
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t
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uel
s
.
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o
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,
w
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t
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l
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m
at
e c
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he us
e of
t
hes
e m
us
t
ar
guabl
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d
ec
r
eas
e.
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he pow
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gener
at
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on
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s
g
l
o
bal
l
y
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l
ar
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t
s
our
c
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of
gr
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n
-
ho
u
s
e
gas
es
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,
pr
ef
er
ab
l
y
,
t
he
gen
er
at
i
on
s
houl
d b
e s
h
i
f
t
ed t
o m
or
e r
ene
w
abl
e s
o
ur
c
es
.
S
ol
ar
p
o
w
er
i
s
of
t
en
r
egar
ded
as
o
ne
of
t
he m
os
t
pr
om
i
s
i
ng
ener
g
y
s
our
c
es
f
or
t
he
f
ut
ur
e,
b
ut
i
t
i
s
t
od
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y
one
of
t
he
m
os
t
ex
pens
i
v
e
s
our
c
es
,
due
t
o hi
gh i
nv
es
t
m
ent
c
os
t
s
.
H
o
w
e
v
er
,
t
h
e pr
i
c
e h
as
s
t
ead
i
l
y
dec
r
eas
e
d an
d i
n s
om
e c
ount
r
i
es
,
gr
i
d
c
onnec
t
e
d s
ol
ar
pan
el
s
i
s
t
oda
y
ec
on
om
i
c
al
l
y
f
eas
i
bl
e.
I
n pl
ac
es
w
i
t
h a
l
ot
of
s
ol
ar
r
adi
at
i
o
n an
d
a
w
eak
ex
i
s
t
i
ng
po
w
er
gr
i
d,
s
pec
i
f
i
c
al
l
y
f
or
of
f
-
gr
i
d
l
oc
a
t
i
ons
,
s
o
l
ar
po
w
er
i
s
r
egar
d
ed
as
a
c
os
t
-
ef
f
ec
t
i
v
e s
ol
u
t
i
o
n [
1
]
.
T
he der
egu
l
at
i
on
of
el
ec
t
r
i
c
i
t
y
m
ar
k
et
s
and r
equi
r
e
m
ent
t
o
r
educ
e gr
e
enh
ou
s
e gas
em
i
s
s
i
on
f
r
o
m
t
he
c
on
v
ent
i
ona
l
e
l
ec
t
r
i
c
po
w
er
ge
ner
at
i
on
m
a
k
e
t
he
d
i
s
t
r
i
b
ut
e
d
g
e
ner
at
i
on
(
D
G
)
r
ene
w
a
bl
e
e
ner
g
y
s
y
s
t
em
s
ga
i
n
a
gr
eat
op
por
t
u
ni
t
y
a
s
a
n
e
w
m
eans
of
po
w
er
g
ener
at
i
o
n
t
h
at
m
eet
t
he ac
c
el
er
a
t
e
d
dem
and f
or
el
ec
t
r
i
c
ener
g
y
[
2
,
3]
.
A
m
ong
al
l
t
he
v
ar
i
ous
D
G
t
ec
hno
l
og
i
es
,
s
o
l
ar
phot
o
v
ol
t
ai
c
s
y
s
t
em
s
ar
e
r
api
d
l
y
gr
o
w
i
n
g
i
n
el
ec
t
r
i
c
i
t
y
m
ar
k
et
s
due
t
o
t
he
dec
l
i
n
i
ng
c
os
t
of
P
V
m
odul
es
[
4,
5]
,
i
nc
r
eas
i
n
g
ef
f
i
c
i
e
nc
y
of
P
V
c
el
l
s
,
m
anuf
ac
t
ur
i
ng
-
t
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hn
ol
o
g
y
en
hanc
em
ent
s
and
ec
onom
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c
s
o
f
s
c
al
e.
H
o
w
e
v
er
,
t
he
i
nc
r
eas
i
ng
pe
net
r
at
i
o
n
l
e
v
e
l
s
of
P
V
s
y
s
t
em
s
i
nt
o
t
he
g
r
i
d
ha
v
e
g
i
v
en
r
i
s
e
t
o
pot
e
nt
i
a
l
pr
ob
l
em
s
r
el
at
i
ng
t
o p
o
w
er
qua
l
i
t
y
an
d P
V
p
er
f
or
m
anc
e [
6
-
8
].
O
ne
of
t
he
m
os
t
i
m
por
t
ant
app
l
i
c
at
i
o
ns
of
phot
ov
ol
t
ai
c
(
P
V
)
s
t
an
dal
one
s
y
s
t
em
s
i
s
f
or
r
ur
al
ar
eas
t
hat
h
av
e
a
c
o
ns
i
der
a
bl
e
am
ount
of
s
ol
ar
r
adi
at
i
o
n
an
d
no
ac
c
es
s
t
o
nat
i
on
al
gr
i
ds
[9
].
T
he per
f
or
m
anc
e of
P
V
s
y
s
t
em
i
s
a
f
f
ec
t
ed due
t
o t
he am
ount
of
s
un r
adi
at
i
o
n and t
he
env
i
r
onm
ent
al
am
bi
ent
t
em
per
at
ur
e
[
1
0]
.
Man
y
t
ec
hn
i
q
ues
w
er
e
us
ed
f
or
MP
P
T
w
i
t
h
P
V
s
y
s
t
em
[
11
-
15]
.
T
he F
O
P
I
D
c
ont
r
o
l
l
er
i
s
f
i
r
s
t
l
y
us
e
d
w
i
t
h P
V
s
y
s
t
em
as
i
n [
15]
but
n
one
o
f
t
he pr
ev
i
ous
r
es
ear
c
h us
ed t
he f
u
z
z
y
l
o
gi
c
f
or
adopt
i
ng t
h
e par
am
et
er
s
of
t
he
F
O
P
I
D
c
ont
r
o
l
l
er
.
T
he f
uz
z
y
l
og
i
c
t
ec
hni
que
i
s
f
r
equent
l
y
us
ed
w
i
t
h
P
V
s
y
s
t
em
as
i
n
[
16
-
2
0]
but
n
one
of
pr
ev
i
ous
r
es
ear
c
h
i
m
pl
em
ent
s
t
he
f
u
z
z
y
l
og
i
c
f
or
a
dapt
at
i
on
f
or
F
O
P
I
D
c
ont
r
ol
l
er
.
F
u
z
z
y
t
y
pe
2
w
a
s
i
m
pl
e
m
ent
ed
f
r
o
m
2013
i
n
t
h
e
r
es
ear
c
h
and
s
om
e
aut
hor
s
us
e
t
hi
s
t
ec
hn
i
qu
e
f
or
MP
P
T
of
P
V
s
y
s
t
em
as
i
n
[
21]
and
[
22]
but
no
ne
of
t
h
em
us
e t
hi
s
t
ec
hn
i
qu
e
w
i
t
h
F
O
P
I
D
c
ont
r
o
l
l
er
.
T
he s
y
s
t
em
us
ed i
n t
h
i
s
paper
i
s
r
el
at
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a r
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pum
pi
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t
at
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har
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t
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i
n
E
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pt
.
T
he pum
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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F
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B
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t
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f
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I
n t
h
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h
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MP
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i
s
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une
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or
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b
y
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i
ns
t
ead
of
t
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c
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e
nt
i
ona
l
P
I
D
c
ont
r
ol
l
er
.
T
he
F
O
P
I
D
c
ont
r
ol
l
er
i
s
t
un
ed
us
i
n
g t
he
c
o
nv
e
nt
i
ona
l
f
u
z
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y
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o
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c
and
f
u
z
z
y
l
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i
c
t
y
pe
2.
T
he s
i
m
ul
at
i
o
n i
s
i
m
pl
em
e
nt
ed o
n 50
0 K
W
s
t
andal
o
ne P
V
s
y
s
t
em
s
uppl
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i
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um
pi
n
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s
t
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i
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ons
i
s
t
of
f
our
80
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m
ps
.
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t
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i
s
t
es
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f
f
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o
ns
us
i
n
g M
A
T
LA
B
S
I
MU
LI
N
K
t
o
dem
ons
t
r
at
e t
he
v
al
i
d
at
i
on of
t
h
e pr
o
pos
ed t
ec
h
ni
que.
2.
T
h
e P
V
M
o
d
e
l
I
n
t
hi
s
p
aper
,
t
he
as
s
em
bl
y
of
P
V
m
odel
c
onnec
t
e
d
t
o
t
he
pum
pi
ng
s
t
at
i
o
n
i
n
di
c
a
t
ed
i
n
F
i
gur
e
1 a
nd
2.
T
he t
o
t
al
p
o
w
er
r
eq
ui
r
e
d f
or
t
he
pum
pi
ng s
t
at
i
on
i
s
abo
ut
3
20
K
W
.
T
he pum
pi
ng
s
t
at
i
o
n i
s
c
ons
i
s
t
i
ng of
f
our
pu
m
ps
dr
i
v
en b
y
A
C
m
ot
or
80 K
W
r
at
i
ng an
d 40 K
W
ot
her
l
oads
i
nc
l
u
di
ng
l
i
g
ht
i
ng
a
nd
a
i
r
c
ondi
t
i
o
ni
n
g.
F
i
gur
e
3
s
ho
w
t
h
e
b
l
oc
k
di
agr
am
of
MP
P
T
us
i
ng
c
onv
e
nt
i
ona
l
P
I
D
c
o
nt
r
ol
l
er
.
F
ig
ur
e
1
.
P
V
s
u
pp
l
y
i
ng
t
he
pum
pi
ng s
t
at
i
on
F
ig
ur
e
2
.
T
he P
V
ar
r
a
y
s
y
s
t
em
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
25
02
-
4
752
I
J
E
EC
S
V
o
l.
4
,
N
o.
1,
O
c
t
o
ber
20
16
:
10
–
19
12
F
ig
ur
e
3
.
T
he b
l
oc
k
di
agr
a
m
o
f
MP
P
T
3
.
C
e
n
tr
i
fu
g
a
l
P
u
m
p
M
o
d
e
l
I
n ge
ner
a
l
,
t
w
o t
y
p
es
of
pu
m
p
s
ar
e c
om
m
onl
y
us
ed
f
or
w
at
er
-
pum
pi
ng
ap
pl
i
c
at
i
o
ns
[
23]
.
O
ne i
s
pos
i
t
i
v
e di
s
p
l
ac
em
ent
pum
p and anot
her
i
s
c
e
nt
r
i
f
ugal
pum
p.
I
n di
s
pl
ac
e
m
ent
pu
m
ps
,
t
he
w
at
er
out
put
i
s
di
r
ec
t
l
y
pr
op
or
t
i
o
na
l
t
o t
he
s
p
eed
of
t
he
pum
p,
but
a
l
m
os
t
i
ndepe
nde
nt
of
head
.
C
en
t
r
i
f
uga
l
pum
ps
ar
e us
ed
f
or
l
o
w
-
h
ead
app
l
i
c
at
i
ons
.
C
ent
r
i
f
ugal
pum
ps
ar
e des
i
gne
d
f
or
f
i
x
ed
-
head
ap
pl
i
c
at
i
ons
,
and
t
he
pr
es
s
ur
e
d
i
f
f
er
enc
e
gen
er
at
e
d
i
nc
r
eas
es
i
n
r
el
at
i
on
t
o
t
he
s
peed
of
t
he p
um
p.
C
ent
r
i
f
uga
l
pum
ps
al
s
o
ha
v
e r
e
l
a
t
i
v
e
l
y
h
i
g
h
ef
f
i
c
i
enc
y
an
d a
r
e
c
apab
l
e
of
pum
pi
ng a hi
gh v
ol
um
e of
w
at
er
.
T
he c
ent
r
i
f
ugal
pu
m
p
i
s
us
ed i
n t
hi
s
ar
t
i
c
l
e.
A
n
y
p
um
p i
s
c
har
ac
t
er
i
z
ed
b
y
i
t
s
abs
or
pt
i
v
e
po
w
er
w
hi
c
h
i
s
o
bv
i
ous
l
y
a m
ec
hani
c
a
l
p
o
w
er
on t
he s
h
af
t
c
oupl
ed t
o t
h
e pum
p,
w
h
i
c
h
i
s
gi
v
e
n b
y
:
(
1)
U
s
ef
ul
po
w
er
:
po
w
er
c
ons
u
m
ed of
t
he abs
or
pt
i
v
e
po
w
er
i
s
gi
v
e
n b
y
:
(
2)
W
h
er
e
η,
t
he
t
ot
al
out
p
ut
;
ρ
,
dens
i
t
y
(
K
g/
m
3)
;
G
,
ac
c
el
er
at
i
o
n
of
gr
av
i
t
y
(
m
2/
S
)
;
H
,
hei
ght
of
r
i
s
e
(
m
)
; Q
, f
l
o
w
(
m
3
/
S
)
.
T
he pu
m
p
s
ar
e dr
i
v
en
us
i
n
g
A
C
i
n
duc
t
i
o
n m
ot
or
s
.
T
he
m
ot
or
s
us
ed t
o dr
i
v
e
t
he
pum
ps
i
n
t
hi
s
ar
t
i
c
l
e
t
a
k
i
ng
t
he
m
agnet
i
c
s
at
ur
at
i
o
n
i
n
c
ons
i
d
er
at
i
on
bas
e
d
o
n
t
he
π
-
m
odel
[2
4
].
4.
F
O
PI
D
B
a
s
e
d
C
o
n
tr
o
l
l
e
r
F
r
ac
t
i
ona
l
-
or
der
c
a
l
c
ul
us
i
s
an ar
ea of
m
at
hem
at
i
c
s
t
hat
de
al
s
w
i
t
h der
i
v
at
i
v
e
s
an
d
i
nt
e
gr
al
s
f
r
om
non
-
i
nt
eger
o
r
der
s
.
T
hi
s
c
onc
ept
w
as
pr
opos
ed
b
y
P
od
l
u
bn
y
i
n 1
99
7,
i
t
d
eal
s
w
i
t
h
der
i
v
at
i
v
es
and i
n
t
egr
a
l
s
f
r
om
non
-
i
nt
eger
or
der
s
I
n ot
her
w
or
ds
,
i
t
i
s
a ge
ner
a
l
i
z
at
i
on of
t
he
t
r
adi
t
i
on
al
c
al
c
u
l
us
t
hat
l
e
a
ds
t
o
s
i
m
i
l
ar
c
o
nc
ept
s
a
nd
t
ool
s
,
but
w
i
t
h
a
m
uc
h
w
i
de
r
app
l
i
c
a
bi
l
i
t
y
.
I
n
t
he
l
as
t
t
w
o
d
ec
ades
,
f
r
ac
t
i
on
al
c
a
l
c
ul
us
has
b
een
r
edi
s
c
ov
er
ed
b
y
s
c
i
e
nt
i
s
t
s
and
e
ng
i
ne
er
s
and a
ppl
i
e
d i
n
an i
nc
r
eas
i
n
g num
ber
of
f
i
el
ds
,
nam
el
y
i
n t
he ar
e
a of
c
ont
r
ol
t
heor
y
.
T
he s
uc
c
es
s
of
f
r
ac
t
i
onal
-
or
der
c
o
nt
r
o
l
l
er
s
i
s
unq
ues
t
i
on
abl
e
w
i
t
h a
l
ot
of
s
uc
c
es
s
due t
o em
er
gi
ng
of
ef
f
ec
t
i
v
e m
et
hods
i
n
di
f
f
er
ent
i
a
t
i
o
n a
nd
i
nt
e
gr
at
i
on
of
non
-
i
nt
eg
er
or
der
e
qu
at
i
ons
.
F
r
ac
t
i
ona
l
-
or
der
pr
op
or
t
i
on
al
-
i
n
t
egr
a
l
-
der
i
v
at
i
v
e
(
F
O
P
I
D
)
c
ont
r
ol
l
er
s
h
av
e r
ec
e
i
v
ed a
c
ons
i
der
a
bl
e
at
t
e
nt
i
on
i
n
t
h
e
l
as
t
y
e
ar
s
bot
h
f
r
om
ac
adem
i
c
and
i
ndus
t
r
i
a
l
po
i
nt
of
v
i
e
w
.
I
n
f
ac
t
,
i
n pr
i
nc
i
p
l
e,
t
he
y
pr
o
v
i
de
m
or
e
f
l
ex
i
bi
l
i
t
y
i
n t
he c
o
nt
r
ol
l
er
des
i
gn,
w
i
t
h r
es
p
ec
t
t
o t
he s
t
a
nd
ar
d
P
I
D
c
on
t
r
ol
l
er
s
,
b
ec
aus
e t
h
e
y
ha
v
e f
i
v
e p
ar
am
et
er
s
t
o s
el
ec
t
(
i
ns
t
ead
of
t
hr
ee)
.
H
o
w
e
v
er
,
t
h
i
s
al
s
o
i
m
pl
i
es
t
hat
t
h
e
t
u
ni
n
g
of
t
he
c
ont
r
ol
l
er
c
an
be
m
uc
h
m
or
e
c
om
pl
ex
.
I
n or
der
t
o
ad
dr
es
s
t
hi
s
pr
obl
em
,
di
f
f
er
ent
m
et
hods
f
or
t
he
des
i
gn
of
a
F
O
P
I
D
c
ont
r
o
l
l
er
ha
v
e
been
pr
o
pos
e
d.
F
ur
t
her
r
es
ear
c
h
ac
t
i
v
i
t
i
es
ar
e
r
unn
i
ng
i
n
or
der
t
o
de
v
e
l
op
n
e
w
t
u
ni
n
g
r
ul
es
f
or
f
r
ac
t
i
onal
C
o
nt
r
ol
l
er
s
,
s
t
u
d
y
i
n
g
pr
ev
i
o
us
l
y
t
he
ef
f
ec
t
s
of
t
he
non
-
i
nt
e
ger
or
der
of
t
he
der
i
v
at
i
v
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
EC
S
IS
S
N
:
2
502
-
4
752
F
O
P
I
D
C
o
nt
r
ol
l
er
B
as
e
d A
C
P
u
mp
S
up
pl
i
e
d f
r
om
P
V
…
(
M
oh
ame
d
Mah
mou
d I
s
mai
l
)
13
and
I
nt
e
gr
al
par
t
s
t
o
des
i
g
n
a
m
or
e
ef
f
ec
t
i
v
e
c
ont
r
ol
l
er
t
o
b
e
us
ed
i
n
r
e
al
-
l
i
f
e
m
ode
l
s
.
S
om
e
of
t
hes
e
t
ec
h
ni
ques
ar
e
bas
e
d
on
a
n
ex
t
ens
i
on
of
t
he
c
l
as
s
i
c
al
P
I
D
c
ont
r
o
l
t
he
or
y
.
T
he
ex
t
ens
i
on
of
di
f
f
er
ent
i
at
i
o
n and i
nt
e
g
r
at
i
on or
der
f
r
o
m
i
nt
eger
t
o non
-
i
nt
e
ger
num
ber
s
pr
ov
i
des
a m
or
e
f
l
ex
i
bl
e t
uni
ng s
t
r
at
e
g
y
a
nd
t
her
ef
or
e an eas
i
er
ac
hi
ev
i
ng of
c
ont
r
ol
r
equ
i
r
em
ent
s
w
i
t
h r
es
pec
t
t
o
c
l
as
s
i
c
al
c
on
t
r
ol
l
er
s
.
T
he f
r
ac
t
i
on
or
der
c
o
nt
r
ol
l
er
f
or
m
i
s
[
25]
an
d [
2
6]
:
s
s
d
i
p
c
k
k
k
s
G
µ
λ
+
+
=
)
(
(
3)
T
he i
nt
er
es
t
of
t
hi
s
k
i
nd of
c
ont
r
ol
l
er
i
s
j
us
t
i
f
i
ed b
y
a bet
t
er
f
l
ex
ib
il
it
y
,
s
in
c
e
it
e
x
h
ib
it
s
f
r
ac
t
i
onal
po
w
er
s
(
λ
an
d
μ
)
of
t
he
i
n
t
egr
a
l
a
nd
der
i
v
at
i
v
e
par
t
s
,
r
es
p
ec
t
i
v
el
y
.
T
hus
,
f
i
v
e
par
am
et
er
s
c
an
be
t
une
d
i
n
t
hi
s
s
t
r
uc
t
ur
e
(
λ
;
μ
;
k
p;
k
i
and
k
d)
,
t
hat
i
s
,
t
w
o
m
or
e
par
am
et
er
s
t
han
i
n t
he c
as
e
of
a c
o
nv
ent
i
on
al
P
I
D
c
o
nt
r
o
l
l
er
(
λ
=
1
a
nd
μ
=
1)
.
T
he
f
r
ac
t
i
on
al
or
der
s
λ
and
μ
c
an
be us
ed t
o f
ul
f
i
l
l
add
i
t
i
on
al
s
pec
i
f
i
c
at
i
ons
of
des
i
gn o
r
ot
her
i
nt
er
es
t
i
n
g r
equi
r
e
m
ent
s
f
or
t
he
c
ont
r
ol
l
ed
s
y
s
t
em
.
I
n
t
hi
s
p
aper
a
s
i
m
ul
at
i
on
f
or
a
f
r
ac
t
i
onal
-
or
der
s
y
s
t
e
m
i
s
done
b
y
us
i
n
g
t
he
f
r
e
quenc
y
dom
ai
n appr
ox
i
m
at
i
ons
,
t
h
e f
r
ac
t
i
onal
or
der
e
qua
t
i
o
n
s
of
t
he s
y
s
t
em
i
s
f
i
r
s
t
c
ons
i
der
ed
i
n t
he
f
r
equenc
y
d
om
ai
n and t
he
n Lap
l
ac
e f
or
m
o
f
t
he f
r
ac
t
i
on
al
i
nt
e
gr
al
oper
a
t
or
i
s
r
epl
ac
ed b
y
i
t
s
i
nt
e
ger
or
d
er
ap
pr
ox
i
m
at
i
on t
h
en t
h
e a
ppr
ox
i
m
at
ed equ
at
i
ons
i
n f
r
equenc
y
dom
ai
n ar
e
t
r
ans
f
or
m
ed bac
k
i
nt
o t
he t
i
m
e
do
m
ai
n.
T
he opt
i
m
i
z
a
t
i
on
w
or
k
i
s
done t
hr
ou
gh
us
i
ng G
A
a
nd
N
i
nt
eger
t
oo
l
b
ox
.
N
i
nt
e
ger
i
s
a t
ool
box
f
or
MA
T
LA
B
i
nt
ende
d t
o hel
p de
v
e
l
op
i
ng f
r
ac
t
i
on
al
-
or
d
er
c
ont
r
ol
l
er
s
and
as
s
es
s
t
h
ei
r
per
f
or
m
anc
e.
T
hi
s
t
ool
box
i
nc
l
ud
es
abo
ut
t
h
i
r
t
y
m
et
hods
f
or
i
m
pl
em
ent
i
ng
appr
ox
i
m
at
i
ons
of
f
r
ac
t
i
onal
-
or
der
an
d
t
hr
ee
i
d
ent
i
f
i
c
at
i
o
n
m
et
hods
.
T
he
N
i
nt
eger
t
ool
box
al
l
o
w
s
i
m
pl
em
ent
i
ng,
s
i
m
ul
at
i
ng
an
d a
na
l
y
z
i
n
g F
O
P
I
D
c
o
nt
r
ol
l
er
s
eas
i
l
y
v
i
a
i
t
s
f
unc
t
i
ons
.
T
he m
os
t
c
o
m
m
on f
or
m
of
a
f
r
ac
t
i
onal
or
der
P
I
D
c
ont
r
ol
l
er
i
s
t
he P
I
λ
D
μ
c
on
t
r
ol
l
er
.
I
nv
ol
v
i
ng
a
n
i
nt
e
gr
at
or
of
or
der
λ
and
a
d
i
f
f
er
ent
i
at
or
of
or
der
μ
w
h
er
e
λ
a
nd
μ
c
an
b
e
a
n
y
r
eal
num
ber
s
.
T
he t
r
ans
f
er
f
unc
t
i
on of
s
uc
h a c
on
t
r
ol
l
er
h
as
t
he f
or
m
:
=
(
)
(
)
=
+
1
+
,
(
,
>
0
)
(
4)
W
he
r
e
G
c
(
s
)
i
s
t
he t
r
ans
f
e
r
f
unc
t
i
on of
t
he c
ont
r
ol
l
er
,
E
(
s
)
i
s
an er
r
or
,
and U
(
s
)
i
s
c
ont
r
ol
l
er
’
s
out
p
ut
.
T
he
i
nt
egr
at
or
t
er
m
i
s
1/
s
λ
,
t
hat
i
s
t
o
s
a
y
,
on
a
s
em
i
-
l
ogar
i
t
hm
i
c
pl
an
e.
T
he c
ont
r
ol
s
ig
n
a
l
u(
t
)
c
an
t
he
n b
e ex
pr
es
s
ed i
n
t
he
t
i
m
e dom
ai
n a
s
:
(
5)
T
he
bl
oc
k
-
di
agr
am
c
onf
i
gur
at
i
o
n
of
F
O
P
I
D
i
s
pr
es
ent
e
d
i
n
F
i
g
ur
e
4.
C
l
e
ar
l
y
,
s
e
l
e
c
t
i
ng
λ
=
1
a
nd
μ
=
1
,
a
c
l
as
s
i
c
al
P
I
D
c
ont
r
ol
l
er
c
an
be
r
ec
o
v
er
e
d.
T
he
s
el
ec
t
i
ons
of
λ
=
1,
μ
=
0,
an
d
λ
=
0
,
μ
=
1
r
es
pec
t
i
v
el
y
c
or
r
es
pon
ds
c
onv
ent
i
on
al
P
I
&
P
D
c
ont
r
ol
l
er
s
.
A
l
l
t
hes
e c
l
as
s
i
c
a
l
t
y
pes
of
P
I
D
c
ont
r
ol
l
er
s
ar
e t
he s
p
ec
i
a
l
c
as
es
of
t
he f
r
ac
t
i
on
al
P
I
λ
D
μ
c
ont
r
ol
l
er
.
F
ig
ur
e
4
.
B
lo
c
k
-
di
agr
am
of
F
O
P
I
D
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
25
02
-
4
752
I
J
E
EC
S
V
o
l.
4
,
N
o.
1,
O
c
t
o
ber
20
16
:
10
–
19
14
T
he anal
y
t
i
c
m
et
hod,
w
h
i
c
h l
i
es
beh
i
nd
t
he
pr
op
os
ed t
u
ni
n
g r
ul
es
,
i
s
b
as
ed
on a
s
pec
i
f
i
ed
des
i
r
a
bl
e
be
ha
v
i
or
of
t
he c
o
nt
r
ol
l
e
d s
y
s
t
e
m
;
i
n t
hi
s
s
ec
t
i
on t
he
des
i
r
abl
e
d
y
nam
i
c
s
des
c
r
i
bed b
y
t
he f
ol
l
o
w
i
ng
c
r
i
t
er
i
a i
s
onl
y
opt
i
m
i
z
ed t
hr
oug
h
m
i
ni
m
i
z
at
i
on t
h
e o
v
e
r
a
l
l
s
quar
ed
er
r
or
,
ov
er
s
hoot
,
r
i
s
e
t
i
m
e and
s
et
t
l
i
n
g t
i
m
e,
w
h
i
c
h
m
eans
t
hat
t
h
e r
es
po
ns
e
be as
c
l
os
e
as
pos
s
i
bl
e
t
o
t
he
s
et
p
oi
nt
v
a
l
ue
al
ong
t
he
t
i
m
e
l
i
n
e
t
i
l
l
t
he
s
t
ea
d
y
s
t
at
e
and
l
eads
t
o
ha
v
e
a
Z
er
o
s
t
ead
y
-
s
t
a
t
e
er
r
or
.
T
he
f
i
t
n
es
s
f
unc
t
i
on
us
ed
f
or
t
h
e
G
A
w
i
l
l
b
e
s
qu
ar
e
of
er
r
or
pl
us
s
q
uar
e
of
er
r
or
di
f
f
er
ent
i
at
i
on
5.
F
u
z
z
y
L
o
g
i
c
B
a
s
e
d
P
I
D
C
o
n
tr
o
l
l
e
r
T
he f
uz
z
y
l
o
gi
c
pr
ogr
am
m
i
ng
has
b
een
bec
om
e
w
i
d
el
y
us
ed
i
n i
ndus
t
r
y
.
E
x
t
e
ns
i
v
e
num
ber
of
r
es
ear
c
hes
w
er
e dev
el
ope
d us
i
n
g f
u
z
z
y
l
ogi
c
t
ec
h
ni
q
ue.
T
hi
s
pap
er
pr
opos
ed t
w
o
i
np
ut
s
-
t
hr
ee
out
p
ut
s
s
el
f
-
t
u
ni
n
g of
a
P
I
D
c
on
t
r
ol
l
er
.
T
he c
ont
r
o
l
l
er
des
i
gn
us
ed
t
he er
r
or
a
nd
c
hange
of
er
r
or
as
i
nput
s
t
o
t
he s
el
f
-
t
un
i
ng,
and t
he g
ai
ns
(
K
P
1,
K
I
1
,
K
D
1)
as
out
p
ut
s
.
T
he F
LC
i
s
ad
di
n
g
t
o
t
h
e
c
o
nv
ent
i
o
nal
P
I
D
c
ont
r
o
l
l
er
t
o
adj
us
t
t
he
par
am
et
er
s
of
t
he
P
I
D
c
ont
r
ol
l
er
on
-
l
i
n
e ac
c
or
d
i
ng
t
o t
he c
h
a
nge
of
t
he s
i
gna
l
s
er
r
or
and c
h
an
g
e of
t
h
e er
r
or
.
T
he c
ont
r
ol
l
er
pr
opos
e
d
al
s
o
c
on
t
a
i
n
a
s
c
al
i
n
g
ga
i
ns
i
nput
s
(
K
e,
K
∆
e)
as
s
ho
w
n
i
n
F
i
gur
e
(
5)
,
t
o
s
at
i
s
f
y
t
he
oper
at
i
o
nal
r
ang
es
(
t
he
uni
v
er
s
e of
di
s
c
o
ur
s
e)
m
a
k
i
ng t
hem
m
or
e gener
al
.
N
o
w
t
h
e c
ont
r
ol
ac
t
i
o
n of
t
h
e P
I
D
c
ont
r
o
l
l
er
af
t
er
s
el
f
-
t
uni
n
g c
an
be d
es
c
r
i
bi
ng as
:
dt
t
de
K
ed
t
K
t
e
K
U
d
I
P
PI
D
)
(
)
(
*
2
2
2
+
∫
+
=
(
6)
W
h
er
e K
P
2,
K
I
2,
a
nd
K
D
2
ar
e t
he
ne
w
ga
i
ns
of
P
I
D
c
ont
r
ol
l
er
and
ar
e e
qua
l
s
t
o:
KP
2
=
KP
1
*
K
P,
KI
2
=
KI
1
*
KI
,
a
n
d
KD
2
=
KD
1
*
K
D
(
7)
W
h
er
e K
P
1,
K
I
1,
a
nd
K
D
1
ar
e t
he g
ai
ns
out
p
ut
s
of
f
uz
z
y
c
o
nt
r
ol
t
hat
ar
e v
ar
y
i
ng
onl
i
ne
w
i
t
h t
he
out
p
ut
of
t
he s
y
s
t
em
under
c
ont
r
ol
.
A
nd
K
P
,
K
I
,
a
nd
K
D
ar
e t
he i
ni
t
i
a
l
v
al
ues
of
t
he c
onv
ent
i
on
al
PI
D
.
F
ig
ur
e
5
.
P
r
opos
e
d F
u
z
z
y
S
el
f
T
uni
n
g
A
s
s
h
ow
n i
n F
i
gu
r
e
5
,
t
her
e
ar
e t
w
o i
npu
t
s
t
o t
he c
o
nt
r
ol
l
er
:
er
r
or
a
nd r
a
t
e c
h
ang
e
of
t
he
er
r
or
s
i
gna
l
s
.
T
he
er
r
or
i
s
def
i
ned
as
e(
t
)
=
r
(
t
)
-
y
(
t
)
,
R
at
e
of
er
r
or
i
s
def
i
n
ed
as
∆
e(
t
)
=
de(
t
)
/
dt
,
w
her
e
r
(
t
)
i
s
t
he
r
ef
er
enc
e
i
np
ut
,
y
(
t
)
i
s
t
h
e
out
put
,
e(
t
)
i
s
t
he
er
r
or
s
i
gna
l
,
an
d
∆
e
(
t
)
i
s
t
he
r
at
e
of
er
r
or
.
T
he
s
ev
ent
h
t
r
i
a
ng
ul
ar
i
n
put
a
nd
out
put
m
e
m
ber
s
hi
p
f
unc
t
i
ons
of
t
he
f
uz
z
y
s
el
f
-
t
uni
ng
ar
e s
ho
w
n i
n t
h
e F
i
g
ur
e
6
,
7
an
d 8.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
EC
S
IS
S
N
:
2
502
-
4
752
F
O
P
I
D
C
o
nt
r
ol
l
er
B
as
e
d A
C
P
u
mp
S
up
pl
i
e
d f
r
om
P
V
…
(
M
oh
ame
d
Mah
mou
d I
s
mai
l
)
15
F
ig
ur
e
6
.
M
em
ber
s
hi
ps
F
un
c
t
i
on
of
I
nput
s
(
e)
F
ig
ur
e
7
.
M
em
b
er
s
hi
ps
F
un
c
t
i
on
of
I
nput
s
(
∆
e)
F
ig
ur
e
8
.
M
em
ber
s
hi
ps
F
un
c
t
i
ons
of
O
ut
p
ut
s
T
he s
a
m
e c
ont
r
ol
l
er
i
s
a
l
s
o i
m
pl
em
ent
ed b
y
us
i
ng
t
he f
u
z
z
y
l
o
gi
c
t
y
p
e 2.
T
he
m
ai
n
di
f
f
er
enc
e
bet
w
e
en
t
he
t
y
pe
2
an
d
t
he
c
on
v
e
nt
i
on
al
f
u
z
z
y
c
ont
r
ol
l
er
i
s
t
he
s
hape
of
t
he
m
e
m
ber
s
hi
p
f
unc
t
i
o
n.
F
i
gur
e
9,
10
and
11
ar
e
t
he
i
n
p
ut
ou
t
put
m
e
m
ber
s
hi
p
f
unc
t
i
ons
us
ed
f
or
f
uz
z
y
t
y
p
e
2 P
I
D
c
ont
r
ol
l
er
.
F
ig
ur
e
9
.
M
em
ber
s
hi
ps
F
un
c
t
i
on
of
I
nput
s
(
e)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
25
02
-
4
752
I
J
E
EC
S
V
o
l.
4
,
N
o.
1,
O
c
t
o
ber
20
16
:
10
–
19
16
F
ig
ur
e
10
.
Mem
b
er
s
hi
ps
F
u
nc
t
i
on
of
I
npu
t
s
(
∆
e)
F
ig
ur
e
11
.
Mem
ber
s
hi
ps
F
u
nc
t
i
ons
of
O
ut
put
s
.
6.
F
u
z
z
y
L
o
g
i
c
F
O
P
I
D
C
o
n
tr
o
l
l
e
r
T
he c
ons
t
r
uc
t
i
on
of
f
uz
z
y
l
o
gi
c
F
O
P
I
D
i
s
s
ho
w
n i
n F
i
gu
r
e
12
.
FOI
FOD
FUZZY LIKE
PID
+
+
PLAN
T
Re
ference
+
output
K
p
Ki
K
d
F
ig
ur
e
12
.
F
u
z
zy
F
O
P
I
D
co
n
st
r
u
ct
i
o
n
F
or
t
he f
uz
z
y
F
O
P
I
D
,
w
e
ar
e us
i
ng t
h
e s
am
e
f
uz
z
y
l
o
gi
c
l
i
k
e P
I
D
c
ont
r
o
l
l
er
w
i
t
h
m
ul
t
i
pl
y
i
n
g
t
h
e
p
ar
am
et
er
of
F
O
I
w
i
t
h
t
he
t
er
m
of
K
i
f
u
z
z
y
out
put
an
d
F
O
D
w
i
t
h
t
he
t
er
m
o
f
K
d
f
uz
z
y
ou
t
put
.
T
he t
r
ans
f
er
f
unc
t
i
on of
F
O
I
w
i
l
l
be
s
i
c
k
s
G
λ
=
)
(
,
w
h
i
l
e t
he t
r
a
ns
f
er
f
unc
t
i
on of
F
O
D
w
il
l b
e
:
s
d
c
k
s
G
µ
=
)
(
T
he c
ons
t
r
uc
t
i
on
o
f
f
uz
z
y
F
O
P
I
D
c
ont
r
ol
l
er
us
i
ng
MA
T
LA
B
S
i
m
ul
i
nk
i
s
i
nd
i
c
at
ed
i
n
F
i
gur
e
13.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
EC
S
IS
S
N
:
2
502
-
4
752
F
O
P
I
D
C
o
nt
r
ol
l
er
B
as
e
d A
C
P
u
mp
S
up
pl
i
e
d f
r
om
P
V
…
(
M
oh
ame
d
Mah
mou
d I
s
mai
l
)
17
F
ig
ur
e
13
.
F
u
z
z
y
F
O
P
I
D
c
o
ns
t
r
uc
t
i
on i
n MA
T
LA
B
S
i
m
ul
i
nk
7
.
S
i
m
u
l
a
ti
o
n
R
e
s
u
l
ts
T
he s
i
m
ul
at
i
on
i
s
per
f
or
m
e
d us
i
n
g M
A
T
LA
B
S
i
m
ul
i
nk
b
y
s
upp
l
y
i
n
g a
pum
pi
ng s
t
at
i
on
l
oc
at
e
d i
n r
as
ghar
e
b c
i
t
y
i
n E
g
y
pt
w
hi
c
h c
o
ns
i
s
t
of
f
our
pum
ps
80 K
W
r
at
i
ng u
s
i
ng 5
00
K
W
t
hr
ee p
has
e s
t
an
dal
on
e p
hot
o
v
o
l
t
a
i
c
s
y
s
t
em
s
.
T
he
pum
ps
ar
e dr
i
v
en
b
y
a
n i
nduc
t
i
on m
ot
or
.
T
he
t
es
t
i
s
di
v
i
de
d
i
n
t
hr
ee
c
as
es
,
t
he
f
i
r
s
t
c
as
e
i
s
d
on
e
b
y
us
i
ng
t
he
P
V
s
y
s
t
em
w
i
t
h
out
MP
PT
t
ec
hni
que
,
i
n t
h
e s
ec
ond
c
as
e t
he s
y
s
t
em
i
s
t
es
t
ed us
i
ng M
P
P
T
t
ec
hni
q
ue
w
i
t
h a
i
de
d of
a
c
onv
e
nt
i
ona
l
P
I
D
t
u
ned
us
i
ng
f
u
z
z
y
l
og
i
c
an
d
i
n
t
he
t
h
i
r
d
c
as
e
t
he
F
O
P
I
D
i
s
i
m
pl
em
ent
ed.
T
he
F
O
P
I
D
i
n t
h
i
s
ar
t
i
c
l
e
i
s
t
un
ed us
i
n
g t
y
p
e 1 and t
y
pe
2 f
uz
z
y
l
og
i
c
.
T
he
s
i
m
ul
at
i
on i
s
don
e at
c
ons
t
ant
t
em
per
at
ur
e
and
r
adi
at
i
on.
T
he
s
i
m
ul
at
i
o
n
r
e
s
ul
t
s
ar
e
i
ndi
c
a
t
ed
i
n
f
i
g
ur
e
s
.
F
i
gur
e
1
4,
15 an
d 15 r
epr
es
ent
t
h
e
gr
eat
ef
f
ec
t
of
us
i
ng MP
P
T
t
ec
hni
que f
or
i
m
pr
ov
em
ent
of
pum
p
s
r
es
pons
e.
F
i
g
ur
e 17 i
n
di
c
at
e a c
om
pl
et
e c
o
m
par
i
s
on
f
or
t
he pu
m
ps
r
es
pons
e us
i
ng MP
P
T
w
hen
us
i
ng
d
i
f
f
er
ent
t
ec
hni
ques
f
or
t
uni
ng
t
h
e
MP
P
T
c
ont
r
ol
l
er
.
T
he
c
ont
r
ol
l
er
i
n
t
hi
s
ar
t
i
c
l
e
i
s
t
une
d us
i
ng
f
u
z
z
y
l
o
gi
c
t
ec
hni
que.
C
o
nv
ent
i
on
al
t
y
p
e
of
P
I
D
c
ont
r
ol
l
er
a
n
d F
O
P
I
D
ar
e
i
m
pl
em
ent
ed.
T
he
ol
d
t
y
p
e
of
f
uz
z
y
l
o
g
i
c
t
ec
hn
i
q
ue
a
nd
f
u
z
z
y
l
og
i
c
t
y
p
e
2
ar
e
u
s
ed.
F
i
gur
e
17
s
ho
w
t
hat
t
he
b
es
t
r
es
po
ns
e i
s
ac
hi
ev
ed
w
he
n
us
i
ng
MP
P
T
bas
ed
on
F
O
P
I
D
t
u
ned
us
i
n
g f
u
z
z
y
l
og
i
c
t
y
p
e 2.
A
l
s
o t
h
e f
i
gur
e s
ho
w
t
ha
t
t
he p
um
p
r
es
pons
e i
s
i
m
pr
ov
ed
b
y
us
i
ng F
O
P
I
D
c
ont
r
ol
l
er
f
or
MP
P
T
i
ns
t
ea
d
of
t
he c
onv
e
nt
i
ona
l
P
I
D
c
o
nt
r
ol
l
er
.
T
he s
i
m
ul
at
i
on r
es
ul
t
s
s
ho
w
t
h
at
t
he f
u
z
z
y
l
ogi
c
t
y
p
e 2
gi
v
e s
l
i
g
ht
i
m
pr
ov
em
ent
f
or
t
he p
um
p r
es
pons
e.
F
ig
ur
e
14
.
P
um
p s
peed r
es
pons
e
w
i
t
h
an
d
w
i
t
h
out
MP
P
T
F
ig
ur
e
15
.
P
um
p T
or
que r
e
s
pons
e
w
i
t
h
and
w
i
t
h
out
MP
P
T
0
2
4
6
8
10
12
14
16
-2
0
0
20
40
60
80
100
120
140
160
t
i
m
e (
s
ec
)
s
peed (
r
.
p.
m
)
pum
p s
peed w
i
t
h M
P
P
T
bas
ed P
I
D
pum
p s
peed w
i
t
hout
M
P
P
T
0
2
4
6
8
10
12
14
16
-2
0
2
4
6
8
10
12
14
t
i
m
e (
s
ec
)
T
or
que (
N
.
M
)
pum
p t
or
que w
i
t
h M
P
P
T
bas
ed P
I
D
pum
p t
or
que w
i
t
hout
M
P
P
T
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
25
02
-
4
752
I
J
E
EC
S
V
o
l.
4
,
N
o.
1,
O
c
t
o
ber
20
16
:
10
–
19
18
F
ig
ur
e
16
.
V
o
l
t
a
ge
app
l
i
ed
on t
h
e p
um
ps
w
i
t
h
and w
i
t
h
out
MP
P
T
F
ig
ur
e
17
.
C
om
par
i
s
on b
et
w
een
pum
p s
peed
r
es
pons
e w
i
t
h and
w
i
t
hou
t
MP
P
T
us
i
ng
di
f
f
er
ent
t
un
i
ng
t
ec
hn
i
q
ues
8
.
C
o
n
c
l
u
s
i
o
n
T
hi
s
paper
pr
es
en
t
s
500
M
W
t
hr
ee phas
e s
t
a
nda
l
o
ne ph
ot
o
v
o
l
t
a
i
c
s
y
s
t
em
s
s
upp
l
y
i
ng
pum
pi
ng
s
t
at
i
o
n
i
ns
t
ea
d
of
ut
i
l
i
t
y
gr
i
d.
T
he
MP
P
T
t
ec
hni
que
i
s
app
l
i
ed
f
or
t
he
P
V
s
y
s
t
em
.
T
he
P
I
D
a
nd
F
O
P
I
D
c
o
nt
r
ol
l
er
s
ar
e
us
e
d
f
or
MP
P
T
.
T
he
f
u
z
z
y
l
o
gi
c
t
y
p
e
1
and
t
y
p
e
2
ar
e
us
ed
f
or
t
uni
ng
t
he
p
ar
am
et
er
s
of
t
he
c
ont
r
ol
l
er
T
he
new
t
ec
h
ni
ques
ar
e
t
es
t
ed
us
i
ng
M
A
T
LA
B
S
i
m
ul
i
nk
T
he s
i
m
ul
at
i
on
r
es
ul
t
s
ho
w
t
hat
t
he
n
e
w
t
ec
hn
i
qu
es
ar
e s
uc
c
eed
ed
t
o
i
m
pr
ov
e t
h
e p
er
f
or
m
anc
e
of
t
he
pum
ps
.
T
he
s
i
m
ul
at
i
ons
i
n
di
c
at
e
t
ha
t
t
he
F
O
P
I
D
c
ont
r
ol
l
er
g
i
v
e
a
gr
e
at
ef
f
ec
t
f
or
s
y
s
t
em
r
es
pons
e
i
m
pr
ov
em
ent
w
h
i
l
e
t
h
e
f
u
z
z
y
l
o
gi
c
t
y
p
e
2
g
i
v
e
a
s
l
i
ght
ef
f
ec
t
r
at
her
t
ha
n
t
he
ef
f
ec
t
o
f
c
onv
e
nt
i
ona
l
f
u
z
z
y
l
og
i
c
t
ec
hni
que.
R
ef
er
en
ces
[1
]
H
ui
Z
han
g,
H
ongw
ei
Z
hou,
J
i
n
g
R
en,
W
e
i
z
en
g
Li
u,
S
h
aohu
a
R
uan,
Y
ongj
un
G
ao
.
T
hr
ee
-
P
has
e
G
r
i
d
-
C
onnec
t
ed
P
hot
o
v
o
l
t
ai
c
S
y
s
t
em
w
i
t
h
S
V
P
W
M
C
ur
r
ent
C
ont
r
ol
l
er
.
P
r
oc
e
edi
ngs
o
f
I
EEE
6
t
h
I
nt
er
na
t
i
o
nal
C
o
nf
er
e
nc
e on P
ow
er
E
l
ec
t
r
on
i
c
s
an
d M
ot
i
on C
ont
ro
l
(I
PEM
C
).
2009:
21
61
-
216
4
.
[2
]
S
at
y
ar
anj
a
n
J
ena
,
B
C
hi
t
t
i
B
abu,
S
R
S
am
a
nt
ar
ay
,
M
oham
ay
ee
M
oh
apa
t
r
a.
C
om
p
ar
at
i
v
e
S
t
u
d
y
b
et
w
een
A
da
pt
i
v
e
H
y
s
t
er
e
s
i
s
and
S
V
P
W
M
C
ur
r
ent
C
o
nt
r
ol
f
or
G
r
i
d
-
c
o
nn
ec
t
e
d I
nv
e
r
t
er
S
y
s
t
e
m
.
P
r
oc
ee
di
n
gs
o
f
I
EEE St
u
d
e
n
t
s
'
T
ec
hnol
ogy
S
y
m
po
s
i
u
m
(
T
ec
hS
y
m
)
.
201
1:
31
0
-
3
15.
[3
]
Y
uk
ai
Li
u
,
Z
hi
j
i
a
n H
u,
Z
i
y
on
g Z
ha
n
g,
J
i
an
gl
e
i
S
uo,
K
ai
b
i
n
Li
a
ng.
R
e
s
ear
c
h o
n t
he
T
hr
ee
-
ph
as
e
P
hot
ov
ol
t
ai
c
G
r
i
d
-
c
onn
ec
t
e
d C
ont
r
ol
S
t
r
at
e
gy
.
E
ner
g
y
a
nd P
ow
er
E
ngi
neer
i
ng
.
201
3;
5:
31
-
35
.
[4
]
MG
V
illa
lv
a
,
J
R
G
az
ol
i
,
E
R
F
ilh
o
.
C
o
m
pr
e
hen
s
i
v
e appr
oac
h
t
o m
o
del
i
ng and
s
i
m
ul
at
i
on of
phot
ov
ol
t
ai
c
ar
r
ay
s
.
I
EEE T
r
a
n
s
a
c
t
i
o
n
s
o
n P
ow
er
E
l
ec
t
r
oni
c
s
.
2009;
24
(
5
):
11
98
-
1
208.
[5
]
A
hm
ed
S
K
h
a
lif
a
,
Eh
a
b
F
El
-
S
aadany
.
C
ont
r
ol
of
t
hr
ee
ph
as
e
gr
i
d
c
onne
c
t
e
d
pho
t
ov
ol
t
ai
c
p
ow
er
sys
t
e
m
s
.
P
r
oc
e
ed
i
n
gs
o
f
I
E
E
E
14t
h I
nt
er
nat
i
ona
l
C
onf
er
en
c
e on H
ar
m
on
i
c
s
and Q
ua
l
i
t
y
of
P
ow
e
r
(I
C
H
Q
P).
2010:
1
-
7.
[6
]
H
Ha
e
ber
l
i
n,
L
B
or
gna,
M
K
aem
p
f
er
,
U
Z
w
ahl
en.
N
e
w
Te
s
t
a
t
G
r
i
d
-
C
onn
ec
t
ed
P
V
I
nv
er
t
er
s
:
O
v
er
v
i
ew
ov
er
T
es
t
R
e
s
u
l
t
s
a
nd
M
eas
ur
ed
V
al
ue
s
of
T
ot
al
E
f
f
i
c
i
enc
y
.
2
1t
h
E
ur
opea
n
P
hot
o
vo
l
t
a
i
c
S
ol
ar
E
n
er
gy
C
onf
er
en
c
e.
D
r
es
d
e
n,
G
er
m
a
ny
.
200
6.
[7
]
S
i
m
ee
n S
M
uj
aw
ar
,
G
M
K
ar
v
e.
C
ont
r
ol
of
gr
i
d c
onn
ec
t
e
d i
nv
er
t
e
r
s
y
s
t
em
f
or
s
i
nus
oi
dal
c
ur
r
e
n
t
in
je
c
t
i
on w
i
t
h i
m
pr
ov
ed p
er
f
or
m
an
c
e.
I
nt
er
nat
i
on
al
J
o
ur
na
l
o
f
I
nno
v
at
i
on
s
i
n E
ngi
neer
i
ng
R
es
ear
c
h
a
nd T
e
c
h
nol
o
gy
.
201
4;
1
(
2
).
[8
]
Z
Y
ao,
L
X
i
ao,
J
M
G
uer
r
er
o.
A
n i
m
pr
ov
ed c
ont
r
o
l
s
t
r
at
egy
f
or
t
he
t
hr
ee
-
ph
as
e gr
i
d
-
c
o
n
ne
c
t
ed
i
nv
er
t
er
.
I
E
T
R
enew
abl
e
P
ow
e
r
G
ener
at
i
on
.
201
5.
[9
]
M
A
E
l
gendy
,
B
Z
ah
aw
i
,
D
J
A
t
k
in
s
on
.
C
o
m
par
i
s
o
n
o
f
di
r
ec
t
l
y
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.
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1
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R
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).
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4
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[1
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V
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[1
6
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S
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[1
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20
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[1
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s
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10(
3)
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9
-
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.
[1
9
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B
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nanav
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12;
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).
[2
4
]
HA
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:
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-
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[2
6
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.
20
12:
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0
-
4
42.
Evaluation Warning : The document was created with Spire.PDF for Python.