Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 3
,
Ju
n
e
201
6, p
p
. 1
233
~ 12
47
I
S
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: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
3.9
009
1
233
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
Field Oriented Control of PMSM Supplied
By Ph
ot
ovolt
a
ic Source
Mehimmede
t
s
i
Bouje
m
aa, Chenni
Rac
h
id
Electro
technical Departme
nt, M
e
ntouri Univ
ersity
, C
onstan
tine, Algeria,
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 12, 2015
Rev
i
sed
D
ec 14
, 20
15
Accepte
d Ja
n
2, 2016
The Permanent
magnet s
y
nchro
nous motor (PMSM) is
suitable for man
y
applications, such as
traction
,
aeronau
tics and generally
in industrial
autom
a
ted proc
e
sses. In our
work, we will stud
y
the appli
c
a
tion of PMSM in
renewabl
e energ
i
es
es
peci
all
y
in
s
o
lar pum
ping. Our objective i
s
to m
odel
the complete s
y
stem, includ
ing
the
photovoltaic inver
t
er
, PMSM and the
centr
ifugal pump under Matlab/Simulink envi
ronment. Solar panels generate
electrical en
erg
y
as dir
e
ct cu
rr
ent b
y
dir
ect conversion of so
lar r
a
diation
using sem
i
conductor m
a
ter
i
als
m
a
de of
m
onocr
y
stallin
e, pol
y
c
r
y
stallin
e or
am
orphous silicon. Th
e
ener
g
y
r
eceived d
e
pends
on rad
i
at
ion
and
on am
bien
t
tem
p
eratur
e.
Th
e perm
an
ent m
a
gnet
s
y
n
c
hron
ous motor (PMSM) is not
stable in op
en loop. To
control the
PMSM in terms of speed
, torque or
position, we ne
ed to im
plem
ent vector contro
l.
W
e
will establis
h the field
oriented con
t
rol
of a PMSM sup
p
lied b
y
a photo
voltaic source with a focu
s
on their
applications in
var
i
ab
le s
p
eed dom
ain
.
Keyword:
Fi
el
d
o
r
i
e
nt
e
d
cont
rol
Perm
anent
m
a
gnet
sy
nc
hr
on
o
u
s
machines
Pho
t
ov
o
ltaic
The i
nve
rter
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
:
M
e
hi
m
m
e
det
s
i
Boujem
aa,
Electrotechnic
a
l Depa
rtm
e
nt,
Uni
v
ersi
t
y
o
f
M
e
nt
o
u
ri
B
r
ot
hers
, C
onst
a
nt
i
n
e
1,
C
onst
a
nt
i
n
e, A
l
geri
a.
Em
a
il: m
o
n
i
r_
ifp@yaho
o.fr
1.
INTRODUCTION
The
perm
anent
m
a
gnet
sy
nch
r
o
n
ous m
o
t
o
r
(
P
M
S
M
)
has t
h
ree p
h
ases
wi
n
d
i
n
g
on
st
at
or
rep
r
ese
n
t
e
d
by the three a
x
es
(a,
b, c
)
phase-shifte
d
of 120° w
i
t
h
res
p
ect
t
o
eac
h
o
t
her
(Fi
g
ure
1
)
an
d ha
s pe
rm
anent
mag
n
e
ts in
th
e ro
tor en
suring its ex
citatio
n
.
Dep
e
nd
ing
on h
o
w th
e m
a
g
n
e
ts are p
l
aced, we can
d
i
sting
u
i
sh
two types of rotors; in the firs
t type,
m
a
gnets are
m
ounte
d
on the surface
of the
rotor
with a hom
ogene
ous air
g
a
p, th
e m
o
to
r is called
“sm
o
o
t
h
air
g
a
p
PM
SM” and
ind
u
cto
r
s are ind
e
pen
d
e
n
t
on
t
h
e ro
tor po
sition
.
In
t
h
e
secon
d
typ
e
,
mag
n
e
ts are mo
un
ted in
si
d
e
t
h
e
ro
t
o
r m
a
ss an
d th
e air
g
a
p
will v
a
ry
b
e
cau
se
of th
e salien
c
e
effect
. I
n
t
h
i
s
case, i
n
d
u
ct
o
r
s are hi
ghl
y
depe
n
d
ent
o
n
t
h
e rot
o
r p
o
si
t
i
on. Sy
nch
r
on
ous m
o
t
o
rs
ha
ve a
rem
a
rk
ab
le featu
r
e; th
e sp
eed
is con
s
tan
t
regard
less of th
e lo
ad.
The fi
el
d
o
r
i
e
nt
ed c
ont
rol
(
f
o
c) i
s
used
f
o
r
m
a
ny
y
ears. I
t
im
pl
em
ent
s
Par
k
t
r
ans
f
orm
a
t
i
on w
h
i
c
h
sho
w
s
,
l
i
k
e a
separat
e
l
y
exc
i
t
e
d dc m
achi
n
e, t
h
e e
x
pres
si
on
of t
h
e i
n
st
ant
a
ne
ous t
o
rq
ue as a
pr
o
duct
of
mag
n
e
tic flux
an
d
curren
t
. In ad
d
ition
,
t
h
ere is th
e po
ssib
i
l
ity to
red
u
ce t
h
e oscillatio
n
s
for a d
e
sired
t
o
rqu
e
,
to sa
ve e
n
ergy delive
r
ed, to
reduce t
h
e c
u
rrent
harm
oni
cs
an
d t
o
i
m
pro
v
e
po
we
r fact
or
.
Whe
n
t
h
e
m
o
t
o
r
m
o
d
e
l u
s
ed is
co
rr
ect,
the fo
c wo
rk
s
w
e
ll.
[
1
],
[
2
].
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. 3,
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47
1
234
2.
DY
N
A
MI
C M
O
DEL
O
F
A SY
NC
HR
ON
OUS
M
O
TO
R
2.
1.
Mathem
atical
Model
of the
Permane
nt
Magnet Synchr
onous
Motor
(PMSM)
The
dy
nam
i
c
m
odel
of a
per
m
anent
m
a
gnet
sy
nch
r
o
n
ous
m
o
t
o
r wi
t
h
rot
o
r
refe
re
nce f
r
a
m
e
can b
e
d
e
scri
b
e
d b
y
t
h
e equ
a
tio
ns b
e
l
o
w, co
n
s
i
d
eri
n
g
th
e cond
itio
ns of non
-sat
u
r
atio
n
o
f
t
h
e m
a
g
n
e
tic circu
it and
th
e
mag
n
e
to
m
o
tiv
e fo
rce MMF is a sinu
so
id
al
distrib
u
tion
created
b
y
t
h
e stator wi
nd
ing
s
.
ab
c
ab
c
a
b
c
d
VR
i
dt
(1)
;
a
ab
c
b
c
00
00
;
00
R
RR
R
;
a
ab
c
b
c
i
ii
i
;
a
ab
c
b
c
V
VV
V
(2)
Wi
t
h
V
abc
,
i
abc
and
Ф
abc
, rep
r
esen
ting
resp
ectiv
ely th
e
v
o
ltag
e
s, t
h
e
cu
rren
ts and
t
h
e t
o
tal flux
of stator
pha
ses.
R
indic
a
tes the re
sistance
of a stator
pha
se.
Total fluxes
are expres
sed by
:
ab
c
a
b
c
ab
c
Li
;
s
ss
s
s
ss
s
s
ss
s
LM
M
LM
L
M
MM
L
(3
)
L
ss
and
M
s
represen
ting
th
e self-ind
u
c
tan
ce an
d th
e m
u
tual inductance bet
w
een
st
at
or
wi
ndi
ng
s.
Ф
’
abc
is
th
e
rot
o
r
flux seen
by the stator winding
s. It rep
r
esen
ts th
e am
p
litu
d
e
s of th
e
vo
ltag
e
s indu
ced
in
th
e stato
r
p
h
a
ses
with
ou
t lo
ad
.
Fi
gu
re
1.
Di
a
g
r
a
m
repre
s
ent
i
n
g st
at
o
r
wi
n
d
i
n
g i
n
abc
an
d
d
q
fram
e
s
Sub
s
titu
tin
g (3) in (1
):
ab
c
ab
c
a
b
c
ab
c
di
VR
i
L
dt
(4
)
The el
ect
r
o
m
a
gnet
i
c
t
o
r
que
i
s
ex
pre
ssed
by
:
1
t
ea
b
c
a
b
c
t
r
Te
i
(5
)
Whe
r
e
ab
c
ab
c
d
e
dt
re
prese
n
ts the
electrom
o
tive forces
gene
rat
e
d
by
t
h
e st
at
o
r
pha
se
s.
ω
r
Is ro
tation
sp
eed
o
f
th
e
ro
t
o
r in
[
rad / s
].
No
te th
at th
e eq
u
a
tion
(4) lead
s to
jo
in
ed
and
h
i
gh
ly no
n-lin
ear eq
u
a
tion
s
. To
sim
p
lify
th
is p
r
ob
lem
,
th
e m
a
j
o
rity of research in literatu
re
p
r
efer to
u
s
e t
h
e Park
tran
sform
a
t
i
o
n
wh
ich,
b
y
a tran
sform
a
t
i
o
n
ap
p
lied
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8-8
7
0
8
Fi
el
d Ori
e
nt
ed
C
o
nt
rol
of
PM
SM
S
u
p
p
l
i
e
d B
y
Ph
ot
ov
ol
t
a
i
c
So
urce
(
Mehi
m
medet
s
i
B
o
uj
e
m
a
a
)
1
235
to real
variabl
e
s (voltages
,
c
u
rrents a
n
d
fl
ux
), prov
ides fi
ctiv
e v
a
riab
les called
d
q
com
p
o
n
en
t
s
or
Park's
equations
. Physically,
th
is tran
sform
a
t
i
o
n
is in
terp
reted
as
a su
b
s
titu
tion
for statio
n
a
ry win
d
i
ng
s (a,b
,c) b
y
ro
tating
wi
n
d
i
n
g
s
(d
,q
) wh
ich
ro
tate with th
e ro
tor.
Th
is t
r
an
sfo
r
m
a
tio
n
mak
e
s th
e
d
yna
m
i
c eq
u
a
tio
ns o
f
AC
mo
t
o
r
s
s
i
mp
l
e
r
.
The
Par
k
t
r
a
n
s
f
o
r
m
a
ti
on i
s
de
fi
ne
d as
f
o
l
l
o
w
s
:
dqo
abc
XK
X
(6
)
Whe
r
e
X
m
a
y be a
c
u
r
r
ent
,
a v
o
l
t
a
ge
or
a
fl
u
x
a
n
d
θ
is th
e
ro
t
o
r po
si
tio
n
.
X
dq
rep
r
esen
t long
itu
d
i
nal an
d
t
r
ans
v
ersal
c
o
m
ponent
s
of
t
h
e st
at
or
va
ri
abl
e
s (
vol
t
a
ge
s, c
u
r
r
ent
s
, fl
uxe
s
and
i
n
duct
a
nce
s
).
Th
e tran
sform
a
tio
n
m
a
trix
K
θ
i
s
gi
ve
n
by
[
3
]
:
1
co
s
s
i
n
2
21
2
2
co
s
s
i
n
33
3
2
14
4
co
s
s
i
n
33
2
K
(7)
The i
nve
rse m
a
trix
1
11
1
22
2
22
4
co
s
c
o
s
c
o
s
33
3
24
si
n
s
i
n
si
n
33
t
t
KK
(8
)
Ap
pl
y
i
ng
t
h
e t
r
ansf
o
r
m
a
ti
on (
6
)
t
o
t
h
e sy
st
e
m
(1) we
ha
ve
the electrical e
quations
in t
h
e
dq
re
fere
nce:
sd
ds
s
d
r
s
q
d
VR
i
dt
(9
)
sq
qs
s
q
r
s
d
d
VR
i
dt
(1
0
)
The fl
u
x
e
quat
i
on:
s
ds
d
s
d
f
Li
(1
1
)
s
qs
q
s
q
Li
(1
2
)
Φ
f
is t
h
e fl
ux
created
by the
magnets in the
rot
o
r.
B
y
repl
aci
n
g
(
1
1
)
a
n
d (
1
2)
an
d i
n
V
q
, V
d
we
o
b
t
ain th
e
fo
llowing
eq
u
a
tion
s
[9
]:
sd
d
s
sd
sd
r
s
q
s
q
di
VR
i
L
L
i
dt
(1
3
)
sq
qs
s
q
s
q
r
s
d
s
d
f
di
VR
i
L
L
i
dt
(1
4
)
Eq
uat
i
ons
(
1
3)
an
d (
1
4
)
fo
rm
a
sec
o
nd
o
r
de
r di
ffe
re
nt
i
a
l
equat
i
o
n sy
st
em
t
h
at
m
odel
s
t
h
e el
ect
ri
cal behavi
or
of
t
h
e sy
nch
r
o
n
o
u
s
pe
rm
anent
m
a
gnet
[
3
]
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1
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q
r
d
L
d
V
d
I
s
R
d
r
s
R
q
L
Vq
I
q
f
r
Fi
gu
re
2.
Eq
ui
val
e
nt
ci
rc
ui
t
o
f
a
perm
anent
m
a
gnet
sy
nc
hr
on
o
u
s m
o
t
o
r i
n
t
h
e
dq
f
r
am
e
The electrom
a
gnetic t
o
rque
(
T
e
)
i
s
pr
od
uc
ed
by
t
h
e
i
n
t
e
ract
i
o
n
bet
w
ee
n t
h
e
pol
es
f
o
rm
ed by
t
h
e
ro
t
o
r m
a
g
n
e
ts
an
d th
e
po
les
gen
e
rated
b
y
th
e MMF (stator cu
rren
ts) in th
e
g
a
p.
es
d
s
q
s
q
s
d
Tp
i
i
(1
5
)
Or
ef
q
d
q
d
q
Tp
i
L
L
i
i
(1
6
)
The equation of the m
e
ch
anical torque is
m
el
m
d
TJ
T
B
dt
(1
7
)
m
el
m
d
JT
T
B
dt
and
r
m
p
(1
8
)
ω
m
and
ω
r
re
prese
n
t the mechanical s
p
ee
d and th
e ele
c
trical speed
resp
ectiv
ely; with
:
B
,
J
,
P
, and
T
l
respect
i
v
el
y
de
fi
ne t
h
e
dam
p
i
n
g
coe
ffi
ci
e
n
t
,
m
o
m
e
nt
of i
n
ert
i
a
o
f
t
h
e
r
o
t
o
r
an
d t
h
e
n
u
m
ber of
pai
r
s
of
p
o
l
e
s
and the l
o
ad torque.
Fi
gu
re 3.
Im
pl
em
ent
a
t
i
on of PM
SM
i
n
Si
m
u
l
i
n
k
i
n
d
q
fra
m
e
W
e
can de
duce
t
h
e fi
nal
form
of PM
SM
eq
uat
i
ons i
n
the dq
fram
e
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:
208
8-8
7
0
8
Fi
el
d Ori
e
nt
ed
C
o
nt
rol
of
PM
SM
S
u
p
p
l
i
e
d B
y
Ph
ot
ov
ol
t
a
i
c
So
urce
(
Mehi
m
medet
s
i
B
o
uj
e
m
a
a
)
1
237
1
q
ds
s
d
ds
r
q
s
dd
d
qs
q
sd
f
qs
r
d
s
r
qq
q
q
r
f
qs
d
q
ds
q
s
L
r
L
di
R
V
ip
i
dt
L
L
L
di
V
RL
ip
i
p
dt
L
L
L
L
d
pB
iL
L
i
i
T
dt
J
J
J
(1
9
)
3.
FIELD ORIE
NTED
CO
NT
ROL P
R
I
N
C
I
PAL
We can
determine the reference torque to im
pose
on the
m
o
tor and the spee
d re
ference from
the
el
ect
rom
a
gnet
i
c
t
o
r
que
eq
uat
i
o
n
ex
pre
ssed
i
n
t
e
rm
s of
Par
k
’s
com
p
o
n
ent
s
sh
ow
n i
n
(
1
6)
, i
f
we i
m
pose t
h
e
current
i
sd.ref
=0
, th
e torqu
e
’s fo
rm
u
l
a will b
e
:
e
f
sq
sq
Tp
i
k
i
the current
.
er
e
f
sq
r
e
f
f
T
i
p
(2
0
)
To preserve the torque
T
e
prop
ortion
a
l to
th
e cu
rren
t
i
sq
, w
e
m
u
st
cont
r
o
l
t
h
e angl
e
α
=
π
/ 2
, and the
angl
e
α
is
d
e
termin
ed
b
y
th
e
fo
llo
w
i
n
g
fo
r
m
u
l
a [3
].
s
q
s
d
i
arc
t
g
i
(2
1
)
3.
1.
I
n
v
e
rt
e
r
mo
d
e
lin
g
Th
e i
n
v
e
rter t
r
an
sfo
r
m
s
a DC vo
ltag
e
in
t
o
an
altern
ating vo
ltag
e
with
a v
a
ryin
g am
p
litu
d
e
an
d
fre
que
ncy
.
It
s
bri
dge st
r
u
ct
u
r
e i
s
co
m
pose
d
m
o
st
ly
of el
ectro
ni
c swi
t
c
hes
suc
h
as IGB
T
s
,
po
we
r t
r
ansi
s
t
ors
o
r
th
yristo
rs. Its
op
erating
p
r
i
n
cip
l
e is b
a
sed
o
n
co
n
t
ro
lled swi
t
ch
in
g in
a su
itab
l
e m
a
n
n
e
r (usu
ally a p
u
l
se
widt
h
m
odul
at
i
on)
, t
h
e s
o
u
r
ce i
s
m
o
d
u
l
a
t
e
d t
o
o
b
t
ai
n a want
e
d
AC
si
g
n
al
fre
q
u
ency
.
Tw
o t
y
pes
of i
n
ve
rt
er
s are
u
s
ed
; th
e
vo
ltag
e
inv
e
rter and th
e cu
rren
t i
nverter.
The v
o
l
t
a
ge i
nve
rt
er
wi
t
h
s
i
x swi
t
c
hes
,
sup
p
l
i
e
d
by
t
h
e ph
ot
o
v
o
l
t
a
i
c
gene
rat
o
r an
d
ope
rat
i
n
g i
n
p
u
l
se-wi
d
th
m
o
du
latio
n (PWM) is co
mm
o
n
l
y u
s
ed fo
r th
is app
licatio
n
[3
]
.
Fi
gu
re
4.
The
vol
t
a
ge
i
n
vert
e
r
wi
t
h
si
x
s
w
i
t
c
hes
We
have
i
m
m
e
di
at
el
y
t
h
e f
o
l
l
o
wi
ng
rel
a
tions at the l
o
ad (balanced
system)
0;
0
ab
c
a
b
c
ii
i
v
v
v
(2
2
)
Co
m
p
lex
vo
ltag
e
fun
c
tion
s
:
Dc
2
Dc
1
Db
2
Db
1
Da
2
Ta
1
Ta
2T
b
2
T
c
2
Tb
1
T
c
1
Da
1
Ia
Ib
ic
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
. 3,
J
u
ne 2
0
1
6
:
12
3
3
– 12
47
1
238
ab
a
o
b
o
bc
bo
c
o
ca
co
a
o
uv
v
uv
v
uv
v
(2
3)
by
m
a
ki
ng t
h
e
di
ffe
re
nce m
e
m
b
er t
o
m
e
m
b
er
we
obt
ai
n
23
ab
ca
ao
bo
co
a
uu
v
v
v
v
T
h
e
r
efo
r
e
1
2
3
aa
o
b
o
c
o
vv
v
v
1
2
3
bb
o
a
o
c
o
vv
v
v
(2
4
)
1
2
3
cc
o
b
o
a
o
vv
v
v
Th
e con
t
ro
l
variab
les act
upo
n th
e con
t
ro
llab
l
e switch
e
s, we can
d
e
fine th
e
fo
llowing
switch
i
ng
fun
c
tion
to set
th
e state of t
h
e
switch
e
s.
Th
e
vo
ltag
e
o
f
th
e inv
e
rter
b
r
an
ch relativ
e t
o
th
e n
e
g
a
tiv
e pole o
f
th
e
DC
bu
s is:
21
1
12
1
3
11
2
aa
DC
bb
cc
vd
V
vd
vd
(2
5)
3.
2.
The hysteresis
current c
o
ntr
o
l tec
hnique
It is a sim
p
le techni
que
di
rec
tly
interested in curren
t control; it li
mits the m
a
xi
m
u
m
current and is
less sensitive t
o
loa
d
va
riations. t
h
is m
e
thod is
use
d
to
c
ont
rol t
h
e c
u
rrent of a
voltage inve
rter i
n
s
u
ch to
force the
phase curre
n
ts of
the m
o
tor to
fo
llow a sin
u
s
o
i
d
al re
fere
nce c
u
rrent calc
u
lated
from
the current
s
(isdref, isqref) and from
the
rotor position
φ
. if the error, which is the
difference between the re
ferenc
e
current
of a
phase a
nd t
h
e sa
m
e
phase
c
u
rrent,
reac
hed t
h
e upper lim
it (
i
ref
+
Δ
I
) the switch arm
of the
inve
rter co
rres
p
o
n
d
in
g to the
sam
e
phase is started a
nd
connected to t
h
e (-) pole
of
the power source to
reduce t
h
e c
u
rrent while, if the error
reache
d
the l
o
we
r lim
it (
i
ref
-
Δ
I
) th
e sw
itc
h
co
nn
e
c
t
ed
to the (+
) terminal
of
the
p
o
we
r s
o
u
r
ce s
h
oul
d
b
e
started t
o
i
n
c
r
ease the
fl
ow
of
the c
o
r
r
es
po
ndi
ng
p
h
ase
.
The lower and upper limits
of the hysteresis band
Δ
I are set by the
m
o
tor ab
sorbe
d
current and the
m
a
xim
u
m
switchin
g
fre
que
nc
y
of
switche
s r
e
spectively
.
A n
a
r
r
o
w
ban
d
of
hy
steresis
im
plies a cur
r
e
nt m
o
re sim
i
lar to t
h
e sine
wave
with a
lo
w
harm
onic
conte
n
t, a
n
d
a
switchin
g
fre
q
u
ency
hig
h
e
r
a
n
d
hi
ghe
r,
an
d
vice ve
rsa.
Th
e cu
rr
en
t r
e
fer
e
n
ces ar
e g
i
ven
b
y
[4
]
.
.
.
.
co
s
2
2
co
s
23
4
co
s
23
ar
e
f
er
e
f
br
e
f
f
cr
e
f
i
T
Ii
p
i
(2
6)
These currents are
sinusoidal functions of ro
t
o
r
position. They creat
e in the
gap
a field
with
magnetic axis in quadrat
ure
with the
axis of the m
a
gnets’ field. They a
r
e in pha
se with the electrom
o
tive
fo
rces i
n
d
u
ce
d
in these
wi
ndi
n
g
s
by
the
m
a
gnets.
Whe
n
the re
ference curre
nt in a phase de
viates fr
om
its reference
,
each controller require
s
switchi
ng
the switches
of each i
nve
rter a
r
m
and
keeps it within the
hysteresis ba
nd
Δ
I
[3
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
Field Orie
nted
C
o
ntrol
of PM
SM
S
u
p
p
lied B
y
Ph
otov
oltaic
So
urce
(
M
ehim
medetsi B
o
uje
m
a
a
)
1
239
Fig
u
r
e
5
.
Represen
tatio
n of
hyster
e
sis cur
r
e
n
t
con
t
ro
l
4.
MODELING OF
THE
PHOTOVOLTAIC CELL
Th
e pho
tovo
ltaic g
e
n
e
r
a
to
r
wh
ich
pr
odu
ces a co
n
tinuou
s electr
i
cal cu
rr
en
t is r
e
p
r
esen
ted
b
y
a
standa
rd m
ode
l with a single diode
, establishe
d by
Sh
ockley for a single PV cell
and gene
ralized to a PV
m
odule by
c
o
n
s
iderin
g it as
a
set of
ide
n
tical cells con
n
ected
in se
ries-
p
aral
lel [5]
,
[
6
]
.
Figu
re
6.
O
n
e
dio
d
e e
qui
vale
nt circ
uit m
odel of
PV
cell
0
exp
1
CS
C
C
S
C
Cp
h
CS
h
qV
R
I
V
R
I
II
I
nk
T
R
(2
7
)
p
h
I
Ph
otoc
u
rre
nt [
A
]
0
I
Sat
u
ratio
n c
u
rre
nt [
A
]
q
Electro
n ch
arg
e
: 1.
602
.1
0
-19
co
ulom
b
k
B
o
ltzm
a
nn’s c
onsta
nt :1
.3
81
.1
0
-23
J/K.
n
Ideality factor
,
varies
fr
o
m
1 to 2
The cu
rre
nt so
urce
depe
n
d
s m
a
inly
on radi
ation an
d
operating cell te
m
p
erature, which
is described
as follows:
,,
PH
s
c
I
S
C
c
c
r
ef
re
f
G
II
T
T
G
(2
8
)
While
I
sc
represents cell shor
t circuit current
at
25
°C
a
n
d
1
0
0
0
W/m
2
,
IS
C
Short circ
uit c
e
ll te
m
p
erature
coe
fficient
T
c ref
is the cell refere
nce tem
p
erature
a
n
d
G
is the
solar radiation in W
/
m
2
, on t
h
e othe
r
han
d
t
h
e saturatio
n c
u
rre
nt va
ries wi
th cell tem
p
erature, it is
descr
i
bed
as follows:
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
. 3,
J
u
ne 2
0
1
6
:
12
3
3
– 12
47
1
240
3
00
,
,,
11
exp
ga
p
c
ref
cr
e
f
c
r
e
f
c
qe
T
II
Tn
k
T
T
(2
9
)
0,
re
f
I
reve
rse sat
u
rat
i
on c
u
r
r
e
n
t at the re
fere
nce te
m
p
erature. the
width
o
f
the
ba
nd
ga
p
g
ap
e
fo
r the
semiconductor
material, for silicon equal to
1.11
eV
.
The tem
p
erature of the
cell is
calculated
by:
20
80
0
ca
G
T
T
NO
CT
(3
0
)
a
T
Am
bient tem
p
erature
°C.
N
OCT
Nom
i
nal operation cell tem
p
erature in
°C
Whe
r
e,
P
Hr
e
f
IG
is known under the standard conditions of
2
10
00
/
re
f
GW
m
(1 sun) at spec
tral
d
i
str
i
bu
tio
n of AM 1.
5
and cell te
m
p
er
atu
r
e
o
f
25
°C
or as ot
herwise specifi
ed
(on
curv
es)
From th
e
manufact
ures
catalogues of
a typical silic
on m
o
nocr
ystalline PV cell SOLAREX
MSX-83, t
h
e value
of
Short-ci
rcuit current
5.
2
7
A
PH
r
e
f
S
C
IG
I
and Open-circuit
voltage
21
.2
OC
VV
MSX83 S
o
lare
x m
odule
,
typi
cal of 83
W,
polycryst
alline
was
chose
n
t
o
m
odel the
phot
ovoltaic
gene
rato
r , t
h
e
m
odule co
ntains
36 cells c
o
n
n
ected i
n
serie
s
. M
o
deling
o
f
the P
V
m
odul
e is
m
a
de by
M
a
tlab
soft
ware
.
Figu
re
7.
Im
plem
entation
of
PV i
n
M
a
tlab /
Sim
u
link
5.
SIZ
I
NG OF
P
HOTO
V
OLT
A
IC MODUL
E
S
The following equation determines
the
m
a
xim
u
m
nu
m
b
er
o
f
P
V
m
o
d
u
les in se
ries
max
1.1
5
s
co
U
N
U
(3
1)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
Field Orie
nted
C
o
ntrol
of PM
SM
S
u
p
p
lied B
y
Ph
otov
oltaic
So
urce
(
M
ehim
medetsi B
o
uje
m
a
a
)
1
241
N
S
:
m
a
xim
u
m
num
ber
of
P
V
m
odules in se
ri
es
U
ma
x
: Maxim
u
m
acceptable input
voltage
U
co
:
ope
n ci
rc
uit v
o
ltage
of
a
m
odule
1.
15:
safety
fac
t
or
req
u
ire
d
by
the sta
nda
rd
U
TE C
1
5-
7
1
2
Th
e m
a
x
i
m
u
m
n
u
m
b
e
r
o
f
photo
v
o
ltaic str
i
ngs in
p
a
r
a
llel is
calcu
lated
b
y
th
e
f
o
llowing
fo
r
m
u
l
a:
ma
x
1.25
p
cc
I
N
I
(3
2)
I
cc
: short-circuit current
of photovoltaic m
o
dules
I
ma
x
:
m
a
xim
u
m
power acceptabl
e by the inverter
Figu
re
8.
C
o
nfi
g
u
r
atio
ns
of
P
V
a
rray
The c
o
nnectio
n
betwee
n
dc li
nk
p
o
w
er
an
d i
n
to
p
o
we
r
rotat
i
ng
dq
fram
e
can
be e
x
presse
d as
dc
dc
dc
sd
sd
sq
s
q
PV
I
V
I
V
I
(3
3)
The m
odules i
n
a PV system
are us
ually connected in
a
rray
s
. Figure
8 illustrates the case
of a
n
array
with
M
P
parallel branches each
with
M
S
m
o
dules in series.
The e
q
uation
fo
r a
PV
m
odu
le can be e
x
p
r
essed
usin
g th
e one
-
d
io
de P
V
cell
m
odel as follo
ws
Ns
num
ber
of
cells in se
ries a
n
d
N
p
num
b
er
of
cells parallel. [5]
PV
M
S
P
V
C
VN
V
(3
4)
PV
M
P
PV
C
IN
I
(3
5)
Whe
r
e
M
designates
a
PV
m
odule an
d
C
desi
gnate
a
PV
cell.
PV
m
odules ar
e co
uple
d
to
get
h
er
f
o
rm
a
PV
array
.
Th
e equ
a
tio
n fo
r a
PV
ar
ray
c
a
n
be e
x
p
r
esse
d
by
ada
p
tin
g t
h
e
PV
m
odule’
s eq
uatio
n as
f
o
llow
s
:
PV
A
S
S
P
V
C
VM
N
V
(3
6)
PV
A
P
P
P
V
C
IM
N
I
(3
7)
The num
b
er
of
PV
array
c
onta
i
ns
36
m
odules
with a
total
pe
ak
po
we
r.
P
V
m
odules are c
o
llected in sizes
usin
g
1
8
m
odu
les in se
ries an
d
2 m
odules
in
pa
rallel.
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I
S
SN:
2
088
-87
08
IJEC
E
V
o
l. 6,
No
. 3,
J
u
ne 2
0
1
6
:
12
3
3
– 12
47
1
242
Figu
re
9.
Im
plem
entation the
PVa
rray
Fig
u
r
e
10
.
C
h
ar
acter
istic Power
(I
) and
U
(
I) fo
r
Ns=3
6,
Np=1
,
Ms=18
,
M
p
=2
6.
BOOST CONVERTER
Figu
re
11
p
r
es
ents a sc
hem
a
tic of a
DC
/DC
b
oost c
o
nve
rt
er it is b
u
ild
b
y
po
wer
com
pone
nts a
n
d
passive
c
o
m
ponents
,
R, L
and
C.
The m
a
in task of the boost conver
ter is regulating the voltage of the
ph
oto
v
o
ltaic generat
o
r, to
get
m
a
xim
u
m
po
wer; thr
o
ug
h c
ont
rol o
f
the d
u
ty
cy
cle
D
. it
is used as an i
n
terface
betwee
n the PV ge
nerat
o
r
and the in
vert
er. A B
o
os
t converter increases the
voltage provided by the
ph
oto
v
o
ltaic cell, there
b
y
re
d
u
c
ing t
h
e
num
b
e
r
of ce
lls
required t
o
reach the desired
voltage level.
Fig
u
r
e
11
.
C
o
nv
er
ter boo
st
d
c
/ d
c
The electrical
equations of
boost
converter
in
Continuous Conduction
M
ode can be written:
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