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
260
~ 12
73
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
3.8
193
1
260
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
Direct
I
n
stantan
e
ous
Power Con
t
rol f
o
r Three-L
e
vel
Grid-Connect
ed Invert
ers
Yo
ng
Y
a
n
g
School of Urb
a
n
Railway
Transp
orta
tion
,
Soocho
w University
, C
h
ina
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
May 12, 2015
Rev
i
sed
No
v 5, 201
5
Accepted Nov 25, 2015
Power electronic grid-connected inverters
are wid
e
ly
app
lied
as gr
id interface
in ren
e
wable en
erg
y
sources
. Th
is pape
r
presents
direct
instantan
e
ous power
control of
thr
e
e-phase
three-level
Neutral Point Clamped (
N
PC) grid-
connected inv
e
rters in photovoltaic gen
e
ration sy
stems. The
s
y
stem consists
of a PV array
,
D
C
/DC convert
er, three-
level NPC inverter, LC f
ilter
and th
e
grid. In order to achieve maximum po
wer p
o
int track
ing (MPPT), an
adaptive p
e
rturb
and observ
e
M
PPT is
used. Fo
r balancing
the
neutral poin
t
(NP) voltage, th
e control sch
e
me thr
ough propo
rtional integral (
P
I) contro
l
accord
ing to th
e dire
ction of t
h
e NP
current
bas
e
d on redun
dant ve
ctor
selec
tion
is use
d
. Dire
ct
instan
tane
ous power
control
is dev
e
loped in
a
rotating
s
y
n
c
hro
nous dq refer
e
n
ce fr
ame
with s
p
ace vector modulation
with
improved operation performance. In addi
tion, th
e paper gives a p
e
rformance
stud
y
of the positive sequen
ce d
e
tector (PSD) pl
us a sy
nchronou
s reference
frame phase-lo
c
ked loop
(PLL) as
th
e s
y
n
c
hronization
method. The
performance of
the proposed
method is
inves
tigated b
y
a g
r
id-connected
photovoltaic s
y
s
t
em
with a nom
inal pow
er of 1
2kW. The feasi
b
ilit
y
of
th
e
proposed method is verified th
rough
experimental resu
lts, showing good
stead
y
-
state and d
y
namic
per
f
or
mance.
Keyword:
Direct I
n
sta
n
taneo
u
s
Po
we
r
C
ont
r
o
l
Gri
d
-C
on
necte
d
In
verte
r
s
MPPT
PSD
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
:
Y
ong
Y
a
ng
,
Sch
ool
o
f
Ur
ba
n
R
a
i
l
w
ay
T
r
a
n
sp
o
r
t
a
t
i
on,
Soo
c
how
U
n
i
v
er
sity,
2A
3
2
1
,
Yan
g
c
h
en
g
h
u
C
a
m
pus, Ji
X
u
e R
d
.
N
o
.
8,
Xi
a
ngc
he
ng
Ar
ea,
SuZ
h
ou
,
C
h
i
n
a
.
Em
a
il: yan
g
y
1
9
81@sud
a
.edu.cn
1.
INTRODUCTION
No
wa
day
s
, t
h
e di
st
ri
but
e
d
gene
rat
i
o
n bas
e
d o
n
rene
wa
bl
e ener
gi
es,
suc
h
as ph
ot
o
vol
t
a
i
c
(P
V)
ener
gy
, wi
nd e
n
er
gy
an
d hy
d
r
o
p
o
we
r ene
r
g
y
have com
e
to assum
e
an ever-growi
ng [
1
]
-[2]
.
Th
e rene
wabl
e
en
erg
y
sou
r
ce
will red
u
ce carb
on
em
issio
n
.
Ph
o
t
ov
o
ltaic g
e
n
e
ration
can b
e
curren
tly reg
a
rd
ed
as on
e o
f
the
m
o
st
prom
i
s
i
n
g ene
r
gy
s
o
u
r
c
e
s i
n
t
h
e re
ne
wabl
e e
n
er
gy
sources
. Due to the
nonlin
ea
r cha
r
acteristics of
PV
array
,
t
h
e m
a
xi
m
u
m
powe
r
p
o
i
nt
(M
PP) t
r
ac
ki
n
g
(M
PP
T),
whi
c
h capt
u
res
t
h
e
m
a
xim
u
m
po
wer
fr
om
t
h
e P
V
array
,
bec
o
m
e
s an e
ssent
i
a
l
part
o
f
P
V
po
we
r ge
ne
rat
i
on sy
st
em
s. M
a
ny
M
PPT
al
go
ri
t
h
m
s
have
be
e
n
pr
o
pose
d
fo
r i
m
provi
n
g
t
h
e
effi
ci
ency
of
t
h
e P
V
ge
nera
t
i
on sy
st
em
s. The e
x
i
s
t
i
n
g
t
echni
que
s
var
y
i
n
sim
p
l
i
c
i
t
y
,
accuracy
, t
i
m
e respo
n
se
, cost
, a
nd
ot
he
r t
echn
i
cal
aspect
s. Am
ong t
h
em
,
pert
ur
b an
d o
b
ser
v
e
(P&
O
) m
e
t
h
o
d
i
s
t
h
e m
o
st
com
m
on fo
r si
m
p
l
i
c
i
t
y
, ease of
im
pl
em
ent
a
t
i
o
n.
Ho
we
ver
,
t
h
e m
e
t
hod i
t
s
el
f
i
s
no
t
q
u
ite accu
r
ate and
is
p
r
o
n
e
to
failing
in
qu
ick
l
y track
i
ng
th
e M
PP
[3]-[4
]. Th
e i
n
cre
m
en
tal co
nd
uctan
c
e
(INC) m
e
thod will achieve MPPT by co
m
p
aring the incre
m
ental and ins
t
an
taneous c
o
nducta
nce of P
V
array
[
5
]-[
6
]
.
I
t
is mu
ch m
o
r
e
sophisticated
an
d need
s co
m
p
licat
ed
im
p
l
e
m
en
ta
tio
n
o
f
h
a
r
d
w
a
r
e
an
d sof
t
w
a
re, bu
t it
seldom
reache
s
the MPP in pra
c
tical
situations. Fuzzy
logic c
ont
rolle
rs
,
ge
netic algorithm
s
and c
h
aotic
algorithm
s
are the m
o
st recent adva
nced M
P
PT m
e
t
hods,
whic
h own the
i
r im
porta
nt capability of ca
pturing
M
PP, e
v
en
u
n
d
er
pa
rt
i
a
l
l
y
shadi
n
g f
o
r P
V
s
y
st
em
s [7]
.
When
sel
ect
i
ng a
M
PPT m
e
t
hod am
ong m
a
ny
M
PPT
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Direct Instantaneous
Power
C
ontr
o
l for
Thre
e Level Grid C
o
nnected Inver
ters (Yong Yang)
1
261
m
e
t
hods
, a DC
-DC
co
n
v
ert
e
r
sho
u
l
d
be co
n
n
ect
ed bet
w
ee
n t
h
e PV a
rray
and t
h
e l
o
a
d
.
The B
o
ost
co
n
v
ert
e
r
has t
h
e
hi
g
h
ef
fi
ci
ency
am
ong
no
n
-
i
s
ol
at
ed
DC
-
D
C
co
n
v
er
t
e
rs [
8
]
.
In
t
h
e last d
ecad
e
s, m
u
ltilev
e
l in
v
e
rters
h
a
ve attracted
g
r
eat in
terest in
d
i
strib
u
t
ed
p
o
wer g
e
n
e
ratio
n
sy
st
em
s. They
are m
a
ny
ki
n
d
s
o
f
t
o
p
o
l
o
gi
es
, s
u
ch
as
di
o
d
e
-
cl
am
ped, cl
a
m
pli
ng-ca
paci
t
o
r
,
i
s
ol
at
e
d
H-
bri
dge
and
s
o
on
[
9
]
-
[
1
0
]
.
Am
ong
t
h
ese t
o
p
o
l
o
gi
e
s
, t
h
e
t
h
ree-l
e
vel
neut
ral
p
o
i
n
t
cl
am
ped (
N
PC
)
vol
t
a
ge s
o
u
r
ce
i
nve
rt
er (V
SI
) has bec
o
m
e
t
h
e
m
o
st
wi
del
y
use
d
i
n
i
n
du
st
r
y
[1
1]
. It
does
not
re
qui
re
cl
a
m
pi
ng
capaci
t
o
rs
an
d
i
s
ol
at
i
on t
r
ans
f
orm
e
rs an
d t
h
u
s
i
t
s
ha
rd
ware
i
s
sim
p
l
e
an
d t
h
e t
o
t
a
l
harm
oni
c di
st
ort
i
o
n i
n
i
t
s
out
put
v
o
l
t
a
ges
an
d
cu
rren
ts is s
m
aller
th
an
th
at in
th
e co
nv
en
tion
a
l two-lev
e
l VSI, for
wh
ich
th
e th
ree lev
e
l NPC VSI h
a
s
com
e
t
o
wi
des
p
rea
d
use i
n
di
st
ri
but
e
d
p
o
w
e
r
ge
nerat
i
on sy
st
em
s, especi
al
l
y
i
n
PV ge
ne
r
a
t
i
on sy
st
em
s.
Yet
i
t
rai
s
es a wi
del
y
reco
g
n
i
zed
q
u
e
st
i
on
ho
w t
o
achi
e
ve t
h
e n
e
ut
ral
-
poi
nt
(
N
P
)
v
o
l
t
a
ge
bal
a
n
c
i
ng.
S
o
fa
r,
v
a
ri
o
u
s
st
rat
e
gi
es
have
bee
n
prese
n
t
e
d a
n
d
succe
ssf
ul
bal
a
nc
i
n
g o
p
erat
i
o
ns ha
ve
bee
n
dem
onst
r
at
ed.
O
n
e
c
o
m
m
on
strateg
y
is to em
p
l
o
y
two
separate
dc
so
u
r
ce
s, w
h
i
c
h are
u
s
ual
l
y
su
ppl
i
e
d
b
y
a tran
sformer
with
two
sep
a
rate
wind
ing
s
v
i
a dio
d
e
fu
ll-bridge rectifiers. Howev
e
r, th
e
dc s
o
urces are large, expe
nsi
v
e and
of low effic
i
ency.
An
ot
he
r st
rat
e
gy
, as
pr
esent
e
d i
n
[
12]
, i
s
i
n
ject
i
n
g
a curren
t i
n
to
the
NP t
h
ro
ugh
an add
itio
n
a
l con
v
e
rter,
whic
h a
d
ds to the system
cost and control c
o
m
p
lexity.
Th
e grid
sy
n
c
h
r
on
izatio
n
tech
n
i
q
u
e
s can
b
e
sp
lit in
to
two
m
a
in
categ
o
r
i
e
s. Th
e m
e
th
od
s b
a
sed
on
zero
-
cr
ossi
ng
det
ect
i
on (
Z
C
D
)
whi
c
h d
o
es
not
co
nt
ai
n a
pha
se co
nt
r
o
l
l
e
r an
d t
h
e m
e
tho
d
s
based
o
n
phase
locke
d
l
o
op
(PLL) t
h
at invol
ves a
phase
controller. Si
n
ce
the ZCD m
e
thod can
be
detected only at e
v
ery hal
f
cycle of t
h
e
grid freque
ncy, s
o
a
fast
dynamic perfor
m
a
nce
cannot be obtained.
R
ecentl
y, there
has
be
en
a
n
in
creasing
in
terest in
PLL tech
n
i
q
u
e
s for grid
-con
n
ected
i
nve
rt
er sy
st
em
s [13]
-
[
1
4
]
.
The m
a
i
n
t
a
sk of t
h
e
PLL algo
rith
m is to
p
r
ov
id
e
th
e p
h
ase ang
l
e o
f
th
e
g
r
id
vo
ltag
e
s wh
ich
is
m
o
stly u
s
ed
to
syn
c
hron
ize th
e
out
put
c
u
rre
nt
s
of
t
h
e t
h
ree
-
p
h
a
se i
n
vert
er
wi
t
h
t
h
e
gri
d
vol
t
a
ges at
t
h
e p
o
i
n
t
o
f
c
o
m
m
on cou
p
l
i
n
g
(PC
C
). T
h
e
dq
-PL
L
m
e
t
hod
, al
so k
n
o
w
n as sy
nc
h
r
o
n
ous re
fer
e
nce fram
e
phase loc
k
ed
loop is the classical
syn
c
hron
ization
algo
rith
m
,
th
at is easy
to
im
p
l
e
m
en
t, b
u
t
it is a
l
so
v
e
ry
sen
s
itiv
e to
the u
tility
g
r
id
vo
ltag
e
u
n
b
a
lan
c
es, wh
ich
will p
r
odu
ces second
o
r
d
e
r harm
o
n
i
cs in
d
q
syn
c
hrono
u
s
referen
ce
fram
e (ro
tatin
g
at th
e
angular s
p
eed
) due t
o
t
h
e ef
fect
of t
h
e ne
g
a
t
i
v
e seque
nc
e
voltage (rotating at the angular speed
) o
f
the
unbalance
d
utility grid voltages. F
o
r this
reas
on, a
large am
ount
of studies
ha
ve
bee
n
ca
rrie
d
out i
n
thi
s
area in
o
r
d
e
r to
find
a so
l
u
tio
n. Th
e
po
sitiv
e sequ
en
ce
detecto
r
p
l
u
s
a d
q
-PLL
(PSD+d
q-PLL)
m
e
t
h
od
was
pr
o
pose
d
i
n
[
1
4]
, w
h
i
c
h
ha
ve
anal
y
zed a
nd
t
e
st
ed usi
n
g a
m
odel
of a g
r
i
d
-c
o
nnect
e
d
sy
st
em
and i
n
t
r
o
duci
n
g
so
m
e
d
i
stu
r
b
a
n
ces to th
e t
h
ree-p
h
a
se u
tility g
r
id
su
ch
as vo
ltag
e
u
n
b
a
lan
ces, frequ
e
n
c
y
v
a
riation
s
and
harm
oni
c di
st
o
r
t
i
ons
.
Vari
ous
control
m
e
thods
for
P
W
M i
nve
rter ha
ve als
o
bee
n
propose
d
i
n
recent works.
But
m
o
st
of
th
e work
s fo
cus o
n
th
e two
-
lev
e
l to
po
log
y
an
d
few dwell on
th
e th
ree-level PW
M inv
e
rt
er. Mo
reov
er, o
w
i
ng
to
th
e
sp
ecial
req
u
i
rem
e
n
t
s o
f
th
e th
ree-lev
e
l PW
M
inv
e
rter, su
ch
as NP vo
ltag
e
b
a
lan
ce, th
e co
n
t
ro
l
st
rat
e
gi
es fo
r t
h
e t
w
o
-
l
e
vel
P
W
M
i
nve
rt
er c
a
nn
ot
be di
rect
l
y
appl
i
e
d. A
n
d t
h
e wel
l
-
kn
o
w
n m
e
t
hod o
f
vol
t
a
ge
-
orie
nted control (VOC) that are suita
bl
e fo
r t
h
e t
h
ree-l
e
v
e
l
PW
M
i
n
vert
er em
pl
oy
s an out
e
r
dc l
i
nk v
o
l
t
a
ge
cont
rol
l
o
op a
nd a
n
i
n
ner c
u
r
r
ent
c
ont
r
o
l
l
o
o
p
t
o
g
u
ara
n
t
ee an excel
l
e
nt
dy
nam
i
c perf
orm
a
nce [1
5
]
-[1
8]
.
Howev
e
r, th
e
fin
a
l con
f
iguratio
n
and
p
e
rforman
ce o
f
th
e syste
m
larg
ely
d
e
p
e
nd
o
n
t
h
e
q
u
a
lity o
f
th
e ap
p
lied
cur
r
ent
c
ont
rol
st
rat
e
gy
. I
n
[
18]
, t
h
e t
h
ree
-
pha
se t
h
ree
-
l
e
vel
NPC
i
n
ver
t
er usi
n
g V
O
C
i
s
al
so appl
i
e
d i
n
ph
ot
o
v
o
l
t
a
i
c
g
e
nerat
i
o
n sy
st
e
m
s, but
N
P
vol
t
a
ge bal
a
nce i
s
not
c
o
nsi
d
e
r
ed
.
In t
h
is pa
per, direct insta
n
taneous
powe
r
control wit
h
s
p
ace vect
or m
o
dulation (SVM) is
i
m
p
l
e
m
en
ted
in
a
ro
tating
syn
c
hrono
u
s
dq referen
ce fr
ame, wh
ich
p
o
ssesses th
e capab
ility o
f
elimin
atin
g
steady-state error a
n
d fast
transient
res
p
onse by
dec
o
u
p
l
i
n
g
co
nt
r
o
l
.
Th
e pa
per
u
s
es t
h
ree
-
l
e
vel
NP
C
gri
d
-
connected inverters
base
d
on Boost c
o
nve
rter,
which is
ab
le to
sim
p
lif
y th
e pro
cess
o
f
M
PPT con
t
ro
l and
br
oa
den t
h
e ra
nge
of
PV a
r
r
a
y
i
nput
vol
t
a
ge. T
h
e N
P
v
o
l
t
a
ge bal
a
nce
i
s
achi
e
ved t
h
r
o
ug
h p
r
op
or
t
i
onal
integral (PI) c
ont
rol accordi
ng to the
direc
tion of the
NP curre
nt base
d
on re
dundant
vector selection. The
p
o
s
itiv
e sequ
en
ce d
e
tecto
r
(PSD) p
l
u
s
a syn
c
hrono
us
referen
ce frame p
h
ase-l
o
ck
ed
loo
p
(PLL) as the
sy
nch
r
o
n
i
zat
i
o
n m
e
t
hod i
s
ad
opt
e
d
. T
h
e P
V
sy
st
em
usi
ng a
32
bi
t
di
gi
t
a
l
si
gnal
p
r
oc
esso
r
(TM
S
3
2
0
F
2
8
0
8
)
i
s
im
pl
em
ent
e
d. Ex
peri
m
e
nt
al
resul
t
s
o
b
t
a
i
n
e
d
on a
1
2
k
W
pr
ot
ot
y
p
e s
h
ow
hi
g
h
pe
rf
o
r
m
a
nce, s
u
c
h
as a
near
-
uni
t
y
po
we
r f
act
or (
9
9
.
9
%
),
hi
gh M
P
PT effi
ci
ency
(
9
9.95
%), h
i
gh
pow
er
co
nv
ersion
ef
f
i
cien
cy an
d
l
o
w
cu
rren
t t
o
tal h
a
rm
o
n
i
c d
i
stortio
n (THD) less
th
an
3
%
.
2.
SY
STEM
M
O
D
EL
AND
CON
T
ROL
STR
A
TEGY
Fi
gu
re 1 s
h
ow
s t
h
e ove
ral
l
con
f
i
g
urat
i
o
n
o
f
a t
r
ans
f
o
r
m
e
rless three
-
p
h
a
s
e th
ree-lev
e
l NPC grid-
connected inve
rter system
.
Th
e sy
st
em
i
s
co
m
posed
of a
P
V
ar
ray
,
DC
/
D
C
B
oost
co
n
v
e
r
t
e
r, t
h
ree
-
l
e
ve
l
NPC
g
r
i
d
-co
n
n
ected in
v
e
rter, LC
filter an
d
t
h
e g
r
i
d
. Th
e Boost co
nv
erter
perfo
r
m
s
MPPT co
n
t
ro
l. Th
e Bo
o
s
t
con
v
e
r
t
e
r al
l
o
ws f
o
r a
wi
de
r
a
nge
of
PV
v
o
l
t
a
ges. T
h
e o
u
t
put
vol
t
a
ge
of
t
h
e PV a
rray
i
s
wi
del
y
vary
i
n
g f
r
om
30
0 V t
o
90
0
V. T
h
e dc b
u
s
cont
ai
ns t
w
o
nom
i
n
al
l
y
i
d
ent
i
cal
capaci
t
o
rs. T
h
e cl
am
ped p
o
i
n
t
o
f
t
h
e NPC
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
6
0
– 12
73
1
262
i
nve
rt
er i
s
co
n
n
ect
ed t
o
t
h
e c
a
paci
t
o
rs at
t
h
e
m
i
dpoi
nt
N
wh
ich
is assu
m
e
d
to
be th
e circu
it v
o
ltag
e
referen
c
e.
Th
e
NPC inv
e
rter regu
lates dc lin
k
v
o
ltag
e
an
d
con
t
ro
ls the activ
e and
reactiv
e po
wers. For th
e
u
tility
g
r
i
d
,
th
e ou
tpu
t
of
t
h
e inv
e
r
t
er
syste
m
is d
e
f
i
n
e
d
as 12
kW
, 400
V
,
5
0
H
z
. To
ob
tain
h
i
gh
syste
m
ef
f
i
cien
cy,
a lo
w
P
W
M
s
w
i
t
c
hi
n
g
f
r
eq
ue
ncy
i
s
cho
s
en
, w
h
i
c
h
i
s
set
t
o
be 1
0
kHz
fo
r
bot
h t
h
e DC
/
D
C
B
o
ost
co
nv
ert
e
r a
nd t
h
e
NPC in
ve
rter.
PV
I
PV
V
1
C
a
e
b
e
c
e
N
N
i
a
i
b
i
c
i
1
L
dc
U
L
C
1
a
S
1
b
S
1
c
S
2
a
S
3
a
S
4
a
S
4
b
S
4
c
S
2
b
S
2
c
S
3
b
S
3
c
S
p
V
n
V
a
b
c
2
C
2
C
Fi
gu
re
1.
Di
a
g
r
a
m
of t
h
e t
h
ree
-
p
h
ase t
h
ree
-
l
e
vel
N
P
C
gri
d
-c
on
nect
ed
i
n
ver
t
er sy
st
em
2.
1.
MPPT c
o
n
t
rol
A PV array is
co
nsisted
b
y
nu
m
b
ers
o
f
so
lar cell in
series
o
r
p
a
rallel, an
d th
e t
o
tal power
o
f
th
e PV
array
i
s
t
h
e su
m
powe
r
o
f
al
l
of t
h
e i
ndi
vi
d
u
al
sol
a
r cel
l
s
.
M
a
ny
m
e
t
hods
have
pr
o
pos
ed
fo
r m
odel
i
ng t
h
e
P
V
cel
l
.
The
P
V
array
pr
o
duce
s
di
f
f
ere
n
t
l
e
ve
l
s
of
po
wer
u
nde
r
di
f
f
ere
n
t
sol
a
r i
rra
di
at
i
o
n a
n
d
t
e
m
p
erat
ure.
Figure
1 dis
p
lays the P-V curve of a PV array. As s
h
own
in
Figur
e 2, th
er
e is on
e op
eratin
g
po
in
t
where th
e
PV a
rray
ge
ner
a
t
e
s m
a
xim
u
m
po
we
r.
Fi
gu
re
2.
C
h
a
r
act
eri
s
t
i
c
of a
PV a
rray
P&O m
e
t
hod
i
s
t
h
e m
o
st
wi
d
e
l
y
used i
n
co
m
m
e
rci
a
l
PV con
v
e
r
t
e
rs,
w
h
e
r
e t
h
e m
e
t
hod i
s
co
nsi
d
e
r
ed
as “trial and error”. T
h
e m
a
in
adv
a
n
t
ag
e of t
h
e MPPT algorith
m
is i
t
s si
mp
le con
t
ro
l and stru
ct
u
r
e, bu
t
it h
a
s
som
e
draw
bac
k
s s
u
ch a
s
osci
l
l
a
t
i
ons i
n
st
ea
dy
-st
a
t
e
ar
ou
n
d
M
PP a
n
d fai
l
i
ng t
o
t
r
ac
k t
h
e M
PP u
n
d
er s
u
d
d
e
n
irrad
i
ation
ch
an
g
e
[1
8
]
.
For P&O algo
rithm
,
a larg
er
pertu
r
b
a
tion
size will lead
to faster
d
y
n
a
m
i
cs for
cap
turing
power fro
m
th
e PV array bu
t will cau
ses os
cillatio
n
s
in
PV curren
t
and PV
v
o
ltag
e
,
a sm
a
l
l
p
e
rt
u
r
b
a
tio
n
si
ze will red
u
ces in
PV curren
t
an
d
PV
v
o
ltage b
u
t
will p
r
odu
ce a slower
dyn
amics o
f
ex
t
r
actin
g
po
we
r f
r
om
t
h
e P
V
ar
ray
[
18]
.
As a c
o
m
p
rom
i
se, a v
a
ri
abl
e
st
ep
P
&
O m
e
t
hod i
s
em
pl
oy
ed t
o
ext
r
act
m
a
xim
u
m
po
w
e
r f
r
o
m
the PV
array
an
d t
o
d
e
liver it to
the
inve
rter.
The
r
e
fere
nce
v
o
ltage
fo
r t
h
e P
V
array
s
is calcu
lated
as fo
llo
ws [18
]
:
ref,
+
1
r
e
f,
k
kk
k
P
VV
M
V
(1)
whe
r
e
k
and
1
k
are th
e sa
m
p
lin
g in
stan
ts,
M
is the step size and
/
kk
PV
is th
e in
stan
tan
e
ou
s
p
o
wer
slope
at the
PV array
output.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Direct Instantaneous
Power
C
ontr
o
l for
Thre
e Level Grid C
o
nnected Inver
ters (Yong Yang)
1
263
The m
a
i
n
job
i
s
t
o
cho
o
se and
desi
g
n
a hi
ghl
y
efficient conve
r
ter
whe
n
the va
riable
step P&O
m
e
t
hod i
s
use
d
,
whi
c
h i
s
co
nsi
d
e
r
ed a
s
t
h
e
m
a
i
n
part
o
f
t
h
e M
PPT
. The
B
oost
c
o
n
v
e
r
t
e
r has l
o
w s
w
i
t
chi
n
g
l
o
sses a
n
d
hi
g
h
e
ffi
ci
ency
a
m
ong n
o
n
i
s
ol
a
t
ed DC
-DC
co
nve
rt
ers
.
T
h
u
s
,
t
h
e B
oost
co
n
v
ert
e
r
i
s
em
pl
oy
ed i
n
desi
g
n
i
n
g t
h
e
M
PPT. C
o
nt
ro
l
of
B
o
ost
c
o
n
v
ert
e
r
i
s
base
d
o
n
t
w
o
co
nt
r
o
l
l
o
o
p
s a
n
d t
w
o se
ri
al
-co
n
n
e
c
t
e
d P
I
cont
rol
l
e
rs
, w
h
i
c
h i
s
sh
ow
n
i
n
Fi
gur
e 3.
The re
fere
nce PV ar
ray
vol
t
a
ge
*
P
V
V
in
o
u
t
er lo
op
is set b
y
an
adapt
i
v
e
P
&
O
M
PPT m
e
t
hod
. T
h
e
refe
rence
PV
ar
ray
vol
t
a
ge
*
P
V
V
is c
o
m
p
ared
with t
h
e m
e
asure
d
PV arra
y
vol
t
a
ge
P
V
V
an
d
the error is sen
t
to
propo
rtion
a
l in
teg
r
al (P
I)
con
t
ro
ller
.
Th
e
ou
tpu
t
sig
n
a
l fro
m
th
e PV
array
vol
t
a
ge
*
P
V
I
is th
e referen
ce cu
rren
t o
f
th
e PV
array. Th
en
th
e ou
tpu
t
o
f
cu
rrent co
n
t
ro
l lo
op
is u
s
ed
b
y
si
m
p
le
m
odul
at
i
on t
o
gene
rat
e
s
w
i
t
c
hi
n
g
pul
se
o
f
B
oost
co
n
v
ert
e
r
.
*
PV
V
PV
V
*
PV
I
PV
I
PV
I
PV
I
P
V
V
1
C
1
L
PV
V
Fi
gu
re
3.
C
o
nt
rol
sc
hem
e
of
M
PPT
base
d
o
n
B
oost
c
o
nve
r
t
er
2.
2.
Grid sy
nchroniza
t
io
n
PLL
w
ill d
e
tect th
e ph
ase angle an
d th
e m
a
g
n
itu
d
e
of the three-p
h
a
se
u
tilit
y g
r
id vo
ltag
e
s w
ith
good
steady-state and
dynam
i
c response
. T
h
ere
a
r
e m
a
ny
st
udi
e
s
w
h
i
c
h
sh
o
w
di
ffe
re
nt
st
r
u
ct
ures
an
d al
go
ri
t
h
m
s
fo
r PL
L m
e
t
hods
. T
h
e sy
nc
hr
o
n
o
u
s
refe
re
nce f
r
am
e PLL m
e
t
hod,
wh
i
c
h has
u
s
ed
i
n
m
a
ny
rene
wabl
e
gene
rat
i
o
n sy
st
em
s, i
s
di
spl
a
y
e
d i
n
Fi
g
u
re
4
.
The
st
ruct
ure
i
s
con
s
i
s
t
e
d b
y
C
l
arke t
r
an
s
f
o
r
m
a
ti
on a
nd
Pa
r
k
trans
f
orm
a
tion as phase dete
ction (P
D), the
PI regulato
r a
s
the loop filter, and the
integrat
or as the voltage-
co
n
t
ro
lled oscillato
r (VCO).
As sho
w
n
i
n
t
h
e Fi
g
u
re
4
,
th
e inpu
t
v
a
riab
les
o
f
t
h
e
PLL are th
e t
h
ree-ph
ase
u
tility g
r
id
vo
l
t
ag
es, an
d
t
h
e
o
u
t
p
u
t
v
a
riab
les o
f
t
h
e PL
L are th
e
p
h
a
se an
g
l
e
o
f
t
h
e three-ph
ase
u
tilit
y g
r
id
vol
t
a
ge
s.
1
s
'
αβ
dq
e
e
d
e
v
q
e
a
e
b
e
c
e
ab
c
αβ
sin
co
s
Fi
gu
re
4.
B
l
oc
k
di
ag
ram
of t
h
e d
q
-
P
LL m
e
t
hod
Th
e m
easu
r
ed sig
n
a
ls of the th
ree-ph
ase
u
tility
g
r
id
v
o
ltag
e
s are conta
m
in
ated
with
h
a
rm
o
n
i
cs,
vol
t
a
ge
u
nbal
a
nces, a
nd
fre
q
u
ency
vari
at
i
o
ns.
A sol
u
t
i
o
n fo
r t
h
ese
pr
o
b
l
e
m
s
caused
by
t
h
e u
nbal
a
nce
d
t
h
re
e-
p
h
a
se u
tility
g
r
i
d
vo
ltag
e
s
is to
add
a po
sitiv
e sequ
ence d
e
tecto
r
(PSD)
b
l
ock, wh
ich
is
b
a
sed o
n
t
h
e
sym
m
etrical com
pone
nt m
e
thod
.
Applying
the theorem
,
the unbalance
d
t
h
ree
-
phase
utility grid voltages can
b
e
d
eco
m
p
o
s
ed
in
t
o
its positiv
e, n
e
g
a
tive and
zero
seq
u
e
n
ces. Th
e in
stan
tan
e
ou
s po
sitiv
e sequ
en
ce
com
pone
nt
s (
a
e
,
b
e
,
c
e
) o
f
an
un
b
a
lanced
u
tility
g
r
id
v
o
ltag
e
s
(
a
e
,
b
e
,
c
e
)
i
s
gi
ve
n by
:
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
6
0
– 12
73
1
264
2
2
2
1
1
1
3
1
aa
bb
cc
ee
ee
ee
(2)
whe
r
e:
2/
3
/
2
24
/
3
/
2
1/
2
3
(
)
/
2
1/
2
3
(
)
/
2
jj
jj
ee
ee
(3
)
Usin
g
(3
) a
n
d (
4
)
,
the
instanta
neo
u
s
p
o
sitive
seq
u
ence
com
pone
nts
(
a
e
,
b
e
,
c
e
)
ca
n be obtaine
d as:
90
90
90
11
1
()
(
)
36
23
11
1
()
(
)
(
)
36
23
11
1
()
(
)
36
23
aa
b
c
b
c
bb
c
a
c
a
a
c
cc
a
b
a
b
ee
e
e
S
e
e
ee
e
e
S
e
e
e
e
ee
e
e
S
e
e
(4)
whe
r
e S
90
is a 9
0
d
e
g
r
ee
p
h
ase sh
ift op
erato
r
,
wh
ich
can b
e
realized
by a si
m
p
le first-o
r
d
e
r filter an
d
its
fol
l
o
wi
n
g
t
r
a
n
s
f
er f
unct
i
o
n
ca
n be obt
ai
ne
d
a
s
:
90
S
(s) =
0
0
1(
/
)
1(
/
)
s
s
(5)
whe
r
e
0
is th
e an
gu
lar frequ
e
ncy o
f
th
e
u
tility
grid
vo
ltag
e
s.
90
()
Ss
1/
2
1/
(
2
3
)
1/
3
1/
2
1/
(
2
3
)
1/
3
a
e
a
e
b
e
c
e
b
e
c
e
90
()
Ss
90
()
Ss
Fi
gu
re
5.
B
l
oc
k
di
ag
ram
of t
h
e PS
D
bl
oc
k
Acco
r
d
i
n
g t
o
(
5
)
,
t
h
e PS
D bl
ock ca
n be ac
hi
eve
d
, w
h
i
c
h
i
s
sho
w
n i
n
Fi
gu
re 5
.
The P
S
D d
q
-
P
LL
syn
c
hron
ization
al
g
o
rith
m
will b
e
ach
iev
e
d
b
y
ad
d
i
n
g
th
e
PSD b
l
o
c
k
to
th
e classical d
q
-PLL stru
cture sh
own
in
Fig
u
re 4
,
wh
ich
can
ach
i
ev
e a reliab
l
e d
e
tectio
n
of th
e p
o
s
itiv
e sequ
en
ce vo
lt
ag
e o
f
th
e
p
h
ase an
d
freq
u
e
n
c
y
o
f
t
h
e
u
n
b
a
lan
c
ed th
ree-ph
ase
u
t
ilit
y g
r
id vo
ltag
e
s. Th
e
ov
erall
stru
cture o
f
th
e
PSD dq
-PLL
i
s
di
spl
a
y
e
d
i
n
Fi
gu
re 6.
1
s
'
αβ
dq
e
e
d
e
v
q
e
a
e
b
e
c
e
abc
αβ
si
n
co
s
a
e
b
e
c
e
Fi
gu
re
6.
B
l
oc
k
di
ag
ram
of t
h
e PS
D
dq
-PL
L
m
e
t
hod
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Direct Instantaneous
Power
C
ontr
o
l for
Thre
e Level Grid C
o
nnected
Inver
ters (Yong Yang)
1
265
2.
3.
PWM modulation
The t
h
r
ee-l
e
ve
l
NPC
gene
rat
e
s 27
vect
o
r
s as sho
w
n i
n
Fi
g
u
re
7 (a):
3 ze
r
o
v
o
l
t
a
ge vect
ors
(ZV
V
s
)
(
N
N
N
,
OOO
,
P
PP)
,
1
2
sm
all
v
o
ltag
e
v
ector
s (
S
VV
s) (ON
N
,
P
OO
, OON
, PPO
,
NON
, O
P
O
,
O
P
P, NO
O, OO
P,
NN
O, PO
P, O
N
O
)
, 6
m
e
di
um
vol
t
a
ge vect
ors (M
V
V
s
)
(
P
ON
,
O
P
N
,
N
P
O, NO
P, ON
P
)
,
a
nd 6
l
a
r
g
e vol
t
a
ge
vectors (LVVs
)
(PNN,
PPN, NPN, NP
P,
NNP, PNP). L
V
Vs
divi
de the
pl
ane i
n
to six
sectors
,
whe
r
e
each
sector cove
rs the space c
o
rre
s
ponding
to 60 degree. For the sake of
bre
v
i
t
y,
m
a
the
m
a
tic
al form
ulations are
prese
n
ted only for the
first se
ctor.
Figure
7
(b) s
h
ows
t
h
e
space
vector represe
n
tation
of t
h
e fi
rst sec
t
or a
nd
consists of four triangles num
bered from
1 to 4.
Base
d on the s
p
ace vector m
odulation (SVM
) the
o
ry, the
expect
e
d
vol
t
a
ge
vect
o
r
of a
n
NPC
c
o
n
v
ert
e
r i
s
sy
nt
hesi
ze
d
by
t
h
ree a
d
ja
cent
v
o
l
t
a
ge
ve
ct
ors.
In the
NPC
conve
rter, Z
VVs
or L
V
Vs
do
not
aff
ect the
neut
ral point
(NP)
balance
because t
h
ey
co
nn
ect t
h
e
p
h
ase curren
t
s
no
t to th
e NP,
b
u
t
t
o
t
h
e
po
sitiv
e or
n
e
g
a
tive d
c
rail. M
V
Vs con
n
ect
one of the
p
h
a
se curren
t
s to
th
e NP thu
s
m
a
k
i
n
g
th
e NP
v
o
ltag
e
dep
e
nd
en
t p
a
rtly o
n
th
e l
o
ad
i
n
g
con
d
ition
s
, wh
ich
becom
e
the
main factor res
u
lting in
NP voltage unbalance. SVVs c
o
m
e
in
pairs a
n
d each pair e
x
ports a pai
r
of
v
o
l
t
a
ges
of
t
h
e sam
e
val
u
e b
u
t
i
n
op
p
o
si
t
e
di
rect
i
o
ns.
H
e
nce,
SV
Vs ca
n
be f
u
rt
her
di
vi
de
d i
n
t
o
posi
t
i
v
e
SVVs and
n
e
gativ
e SVVs. C
o
n
s
equ
e
n
tly, in ord
e
r t
o
m
a
in
t
a
in
balan
c
ed
vo
ltag
e
s i
n
the
dc-lin
k cap
acit
o
rs, t
h
e
prese
n
t
vol
t
a
g
e
im
bal
a
nce a
n
d t
h
e
di
r
ection of th
e in
stan
tan
e
ou
s ou
tpu
t
sh
ou
ld b
e
k
nown
.
If th
e NP cu
rren
t
N
i
is po
sitiv
e/n
e
gativ
e, it will d
i
sch
a
rg
e/ch
arg
e
th
e lowe
r capacito
r. Tak
e
Fig
u
re
1
for ex
am
p
l
e, if th
e outp
u
t
current
a
i
is p
o
s
itiv
e, ONN wi
ll d
i
sch
a
rg
e the lo
wer cap
aci
to
r (
Na
ii
), an
d
POO will ch
arg
e
th
e lo
wer
capacitor (
0
Nb
c
a
ii
i
i
). A p
o
s
itiv
e SVV an
d
a
n
e
g
a
tive SVV
form
a
p
a
ir, an
d
th
ey
ex
ert ex
actly
op
p
o
si
t
e
effect
s on t
h
e N
P
v
o
l
t
a
ge. C
o
nseq
u
e
nt
l
y
, cont
ro
l
of th
e NP vo
ltage is ach
iev
e
d
th
rou
g
h
selectin
g
t
h
e
switch
i
ng
p
a
tt
ern
o
f
th
e
v
ecto
r
s. Mod
u
l
ation
fo
r th
e
NPC
co
nv
erter u
tilizes sy
mm
e
t
ric
a
l p
l
ace
m
e
n
t
v
ecto
r
s,
o
f
wh
ich
th
e fi
rst effectiv
e
v
e
cto
r
is a n
e
g
a
tiv
e SVV.
Swi
t
c
hi
n
g
pat
t
e
r
n
s f
o
r
di
ffe
re
nt
vo
l
t
a
ge vect
o
r
s i
n
t
h
e
first sector a
r
e
prese
n
ted in
T
a
ble 1.
Su
pp
osi
ng t
h
e
t
o
t
a
l
on
du
rat
i
o
n t
i
m
e
of SV
V
s
i
s
SV
V
T
, and t
h
e
o
n
d
u
r
at
i
on t
i
m
e of a ne
gat
i
v
e
SV
V i
s
s
nS
V
V
Tm
T
(
01
m
), th
at of th
e co
rresp
ond
ing
p
o
s
itiv
e
SVV
s
p
T
can hence
be det
e
rm
i
n
ed vi
a
t
h
e
fol
l
o
wi
n
g
e
x
pr
essi
on:
(1
)
s
pS
V
V
Tm
T
(6)
The NP
voltage can be balanced
through a linear PI controller accord
ing to the direction of the
NP
cur
r
ent
,
t
h
e re
l
a
t
i
onshi
p bet
w
een s
w
i
t
c
hi
n
g
st
at
es of SV
Vs an
d o
u
t
p
ut
phase cu
rre
nt
s whi
c
h i
s
sh
o
w
n i
n
Tabl
e 2. C
o
nt
r
o
l
schem
e
for bal
a
nci
n
g N
P
vol
t
a
ge i
s
di
s
p
l
a
y
e
d i
n
Fi
gu
re 8 an
d t
h
e sym
bol
d
u
i
s
defi
ned
as
t
h
e di
ffe
rence
bet
w
ee
n
P
V
and
n
V
.
α
β
α
β
re
f
U
(a)
(
b
)
Fi
gu
re
7.
S
p
ac
e v
o
l
t
a
ge
vect
o
r
f
o
r t
h
ree-l
e
ve
l
NPC
i
nve
rt
er
Tabl
e 1.
Vector se
que
nce i
n
t
h
e
first sector
Region
Vector
sequence
1 ONN-
OON
-OOO
-
P
OO-P
OO-
OOO-
OON-
ONN
2 ONN-P
NN-
PON-
POO-P
OO-P
ON-
P
NN-O
N
N
3 ONN-
OON
-PON
-
P
OO-P
OO-P
ON-
OON-
ONN
4 OON-P
ON-
PPN-
P
PO-PPO
-PPN
-PO
N
-OO
N
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
2088-
8
708
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
12
6
0
– 12
73
1
266
Tabl
e 2.
R
e
l
a
t
i
ons
hi
p
bet
w
ee
n s
w
i
t
c
hi
n
g
st
a
t
es of
S
V
V
an
d
o
u
t
p
ut
p
h
ase
c
u
r
r
ent
s
Negative SVV
NP current
Positive SVV
NP current
ONN
Na
ii
POO
Na
ii
OON
Nc
ii
PPO
Nc
ii
NON
Nb
ii
OPO
Nb
ii
NOO
Na
ii
OPP
Na
ii
NNO
Nc
ii
OOP
Nc
ii
ONO
Nb
ii
POP
Nb
ii
d
u
p
V
n
V
d
u
p
V
n
V
(
a
)
(b)
Fi
gu
re
8.
C
o
nt
rol
sc
hem
e
for
bal
a
nci
n
g
NP
vol
t
a
ge
(a
)
wh
en
0
N
i
(b
)
wh
en
0
N
i
2.
4.
NPC inverter
control
In t
h
e stationa
ry
refere
nce
fra
m
e
for a
bala
n
ced th
ree-
p
h
as
e syste
m
, the inve
rter
output currents
in
Figur
e
1
can b
e
exp
r
essed as fo
llo
w
s
:
d
d
d
d
a
i
Lu
e
R
i
t
i
Lu
e
R
i
t
(7)
whe
r
e
u
and
u
are
the
and
com
pone
nt
s
of
NPC
i
nve
rt
er
o
u
t
p
u
t
vol
t
a
ges
resp
ect
i
v
el
y
.
e
and
e
are
th
e
and
com
pone
nt
s of gri
d
vol
t
a
ge
s, respe
c
t
i
v
el
y
.
i
and
i
are the
and
com
ponent
s of
i
n
vert
e
r
out
put
c
u
rre
nt
s
,
res
p
ect
i
v
el
y
.
L
is th
e filter i
n
du
ctan
ce.
R
is th
e to
tal resistan
ce of th
e NPC in
v
e
rter.
Tran
sf
orm
a
t
i
on (
7
)
fr
om
st
ati
ona
ry
refe
ren
ce fram
e
to rot
a
ting
dq
co
or
d
i
n
a
tes, th
e syn
c
hr
on
ou
s
dq
refe
rence
f
r
am
e g
r
i
d
c
u
r
r
e
n
t
s
can
be
obt
ai
ne
d as
d
d
d
d
d
dd
d
q
q
qq
q
d
i
Lu
e
R
i
i
t
i
Lu
e
R
i
i
t
(8)
whe
r
e
d
u
and
q
u
are
d
-a
xi
s a
n
d
q
-a
xi
s
o
u
t
p
ut
vol
t
a
ges of
t
h
e NP
C
i
nve
rt
er res
p
ect
i
v
el
y
.
d
e
and
q
e
are
d
-a
xis
and
q
-a
xi
s gri
d
v
o
l
t
a
ges, res
p
ect
i
v
el
y
.
d
i
and
q
i
are
d
-a
xis and
q
-axis grid
c
u
rre
nts,
res
p
ectively
.
is g
r
i
d
vol
t
a
ge
an
g
u
l
a
r f
r
eq
ue
ncy
.
d
i
and
q
i
are indu
ced v
o
ltages du
e t
o
th
e tr
an
sformatio
n
o
f
filter ind
u
c
tan
ce
fr
om
fram
e
to
dq
.
Ap
pl
y
i
ng
a sa
m
p
li
ng
peri
od
s
T
, th
e eq
u
a
ti
o
n
(8
) can b
e
d
i
scretized
as fo
llows:
(
1
)
(
1
)
()
(
(
)
(
)
)
()
(
1
)
(
1
)
()
(
(
)
(
)
)
()
ss
dd
d
d
s
q
ss
qq
q
q
s
d
TR
T
ik
ik
u
k
ek
T
i
k
LL
TR
T
ik
i
k
u
k
e
k
T
i
k
LL
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Direct Instantaneous
Power
C
ontr
o
l for
Thre
e Level Grid C
o
nnected
Inver
ters (Yong Yang)
1
267
The i
n
stanta
ne
ous
power can
be c
o
m
put
ed i
n
st
at
i
o
nary
coo
r
di
nat
e
s as
fol
l
ows:
Pe
i
e
i
Qe
i
e
i
(10)
After th
is t
r
ansform
a
tio
n
,
the th
ree-p
h
a
se
activ
e power
a
n
d reactive
power can be
obtained i
n
dq
ro
tating
fram
e as fo
llo
ws:
dd
q
q
qd
d
q
Pe
i
e
i
Qe
i
e
i
(11)
The active
and
reactive
powe
rs in t
h
e rotating
refe
rence
fr
a
m
e at
(k+
1
)
sa
m
p
li
ng i
n
st
ant
can
be
gi
ve
n as
(1
)
(
1
)
(1
)
(
1
)
(1
)
(1
)
(
1
)
(1
)
(
1
)
(1
)
dd
q
q
qd
d
q
Pk
e
k
i
k
e
k
i
k
Qk
e
k
i
k
e
k
i
k
(12)
Fo
r a sm
all en
o
ugh
sam
p
lin
g ti
m
e
, it can
b
e
ob
tain
ed as
(1
)
(
)
(1
)
(
)
dd
qq
ek
ek
ek
ek
(13)
By su
b
s
titu
ting (9
) and
(13
)
in (1
2),
we
ob
tain
:
(
1
)
[
(
1
)
(
)
(
()
(
)
)
(
)
]
()
[(
1
)
(
)
(
(
)
(
))
(
)
]
(
)
(
1
)
[
(
1
)
(
)
(
()
()
)
(
)
]
()
[
(
1
)
()
(
(
)
(
)
)
()
]
(
)
ss
dd
d
s
q
d
ss
qq
q
s
d
q
ss
dd
d
s
q
q
ss
qq
q
s
d
d
TR
T
Pk
i
k
u
k
e
k
T
i
k
e
k
LL
TR
T
ik
u
k
ek
T
i
k
e
k
LL
TR
T
Qk
i
k
u
k
e
k
T
i
k
e
k
LL
TR
T
ik
u
k
ek
T
i
k
e
k
LL
(
1
4)
B
y
usi
ng PS
D
dq
-PLL sy
nc
hr
o
n
i
zat
i
on al
g
o
ri
t
h
m
,
t
h
e q-a
x
i
s
gri
d
v
o
l
t
a
g
e
q
e
will b
e
zero
,
an
d
the
ab
ov
e equ
a
tion (1
4)
for th
e instan
ta
ne
ous
powers
can be
si
m
p
lified as:
2
(
1
)
[
(
1
)
(
)
(
()
()
()
)
(
)
(
)
(
1
)
(
1
)
(
)
()
()
()
()
ss
dd
d
s
d
q
ss
qd
s
d
d
TR
T
Pk
Pk
u
k
e
k
e
k
T
e
k
i
k
LL
TR
T
Qk
Qk
u
k
e
k
T
e
k
i
k
LL
(
1
5)
In
order
to m
a
ke the NPC inverter
out
put a
c
tive
and react
ive powers at the (k+
1
) sam
p
ling instant
eq
u
a
l t
o
the
g
i
v
e
n activ
e and
reactiv
e
p
o
wers at th
e
(k) sam
p
lin
g in
stan
t, it can
b
e
ob
tain
ed
as:
(1
)
(
)
(1
)
(
)
ref
re
f
Pk
P
k
Qk
Q
k
(
1
6)
Sub
s
titu
tin
g (16
)
in
(15) an
d rearran
g
i
n
g
th
e
resu
lts,
()
d
uk
and
()
q
uk
be calculated
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
2088-
8
708
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
12
6
0
– 12
73
1
268
1
()
[
(
()
)
(
)
]
(
)
1
(
)
[
(
()
)
(
)
)
]
()
dr
e
f
d
dd
qr
e
f
dd
LL
uk
P
P
k
R
P
k
e
Q
k
eT
s
e
LL
u
k
Qk
Q
R
Qk
Pk
eT
s
e
(
1
7)
The eq
uat
i
o
n (
1
7
)
co
nt
ai
ns t
h
e d-axi
s
an
d q
-
axi
s
com
pone
n
t
s of t
h
e NPC
i
nve
rt
er o
u
t
p
ut
vol
t
a
ge
s i
n
th
e ro
tating
referen
ce fram
e.
After tran
sformatio
n
fro
m
rotatin
g
dq
co
ord
i
nates to
static
refere
nce fram
e
,
th
e g
a
ting
si
gn
als will th
en
p
r
od
u
c
ed
accord
i
n
g
t
o
abov
e
m
e
n
tio
n
e
d
PWM techn
i
qu
e for three-lev
e
l NPC
i
nve
rt
ers.
The direct inst
antane
ous power cont
rol wit
h
sp
ace vect
or
m
odulation c
ont
rol algorithm
shown in
Fi
gu
re 9 co
nt
ai
ns t
h
e fol
l
o
wi
n
g
bl
oc
ks:
t
h
ree
-
l
e
ve
l thre
e-phase SVM, the th
ree-pha
se active power and
reactiv
e power calcu
latio
n
,
on
e ou
ter
d
c
-link
vo
ltag
e
c
o
n
t
ro
l loo
p
, grid
syn
c
hron
ization
(PSD
dq
-PLL) and
req
u
i
r
e
d
NPC
i
nve
rt
er v
o
l
t
a
ge
cal
cul
a
t
i
on.
T
h
e dc-l
i
n
k vol
t
a
ge di
ffe
re
nce (er
r
o
r) o
f
t
h
e g
i
ven dc-l
i
nk v
o
l
t
a
ge
*
dc
U
an
d t
h
e m
easure
d
dc-l
i
n
k
v
o
l
t
a
ge
dc
U
is d
e
liv
ered
to th
e l
i
n
ear PI
co
n
t
ro
ller, wh
ich
will
ach
iev
e
stabilizing the
dc-link
voltage
of the
three-le
vel three-phase
in
verter. The
reactive power
refe
rence
can
be set
depe
n
d
i
n
g o
n
t
h
e nee
d
s o
f
t
h
e po
wer sy
st
e
m
and t
h
e t
h
re
e-phase inverte
r
can send
or a
b
sorb reactive
powe
r,
while the refe
rence val
u
e of the activ
e p
o
w
e
r
i
s
cal
cul
a
t
e
d
base
d o
n
m
easure
d
dc
-l
i
n
k v
o
l
t
a
ge o
f
t
h
e i
n
vert
er
an
d th
e
ou
tpu
t
v
a
lu
e
of th
e
outer d
c
-lin
k vo
ltag
e
co
n
t
ro
l. Th
e requ
ired
NPC in
v
e
rter
vo
ltag
e
in syn
c
h
r
on
ou
s
rotating fram
e
in each
sam
p
ling pe
riod ca
n
be
direc
tly calculated acc
ording t
o
the
give
n active a
n
d re
active
powe
rs, the measure
d
active
and reactive
powe
rs, the m
easu
r
ed
grid
vo
ltag
e
s, th
e
measure
d
grid c
u
rrents
,
filter ind
u
c
tance and
t
h
e total resistan
ce, th
rou
g
h
si
mp
le m
a
th
e
m
at
i
cal calcu
latio
n
s
. After coord
i
n
a
te
tran
sform
a
t
i
o
n
(
dq
/
) fr
om
sy
nchr
o
n
o
u
s rot
a
t
i
ng
f
r
am
e
dq
in
t
o
station
a
ry co
ord
i
n
a
tes
u
s
i
n
g gr
id
sy
nch
r
o
n
i
zat
i
o
n (P
SD
d
q
-P
L
L
), t
h
e t
r
a
n
s
f
o
r
m
a
ti
on si
g
n
al
s are gi
v
e
n t
o
SVM
bl
ock i
n
put
.
A
nd i
n
o
r
der t
o
b
a
lan
c
e NP
v
o
l
tag
e
throug
h the red
i
stribu
tio
n of th
e po
sitiv
e and
n
e
g
a
tiv
e small v
ecto
r
s
u
s
ag
e, a PI co
n
t
ro
ller
has
been included. T
h
e
out
put SVM si
gna
l
s determ
inate
curre
n
t states of
th
e
po
wer switch
e
s. Th
ere is a
possibility to c
ont
rol
both acti
v
e
powe
r a
n
d reactive power i
nde
pe
nde
ntly.
abc
αβ
a
e
b
e
c
e
e
e
e
e
C
abc
αβ
a
i
b
i
c
i
dq
αβ
i
i
d
i
q
i
αβ
dq
d
e
q
e
p
V
n
V
dc
U
N
i
N
dq
αβ
d
u
q
u
u
u
p
V
n
V
d
u
d
i
q
i
d
e
q
e
dd
q
q
qd
d
q
P
ei
e
i
Qe
i
e
i
()
P
k
()
Qk
*
dc
U
dc
U
ref
P
re
f
Q
L
s
L
s
R
()
P
k
()
Qk
q
e
d
e
d
i
q
i
Fi
gu
re
9.
Di
re
ct
i
n
st
ant
a
ne
o
u
s
p
o
we
r c
o
nt
r
o
l
schem
e
for
t
h
ree-l
e
vel
NPC
i
nve
rt
ers
3.
E
X
SPERIME
N
TAL RESULTS
In o
r
der t
o
ve
r
i
fy
t
h
e perf
or
m
a
nce of t
h
e p
r
o
p
o
sed c
ont
ro
l
st
rat
e
gy
, an expe
ri
m
e
nt
al
t
e
st
benc
h ha
s
been
de
vel
o
pe
d as s
h
ow
n i
n
Fi
gu
re
10
. S
o
m
e
experi
m
e
nt
s ha
ve b
een ca
rri
ed
o
u
t
o
n
a
l
a
bo
rat
o
ry
set
u
p o
f
a
12
-
k
W t
h
ree-
p
h
ase t
h
ree
-
l
e
ve
l
NPC
i
nvert
e
r
whi
c
h c
o
n
s
i
s
t
s
of a m
i
cropr
ocess
o
r
based
on a co
nt
r
o
l
ci
rcui
t
an
d
a po
wer circu
it. For th
e co
n
t
ro
l circu
it, th
e con
t
ro
l strat
e
g
y
is i
m
p
l
e
m
en
ted
in
a so
ft
ware adop
tin
g
a 3
2
-
bi
t
fi
xe
d
-
p
o
i
n
t
DS
P TM
S
3
20
F2
80
8,
t
h
e
P
W
M
pul
ses
ar
e ge
nerat
e
d t
h
ro
u
g
h
t
h
e i
n
t
e
r
n
al
p
u
l
s
e
ge
ne
rat
o
r
o
f
t
h
e D
SP a
n
d
ext
e
n
d
ed
by
t
h
e c
o
m
p
l
e
x pr
og
ram
m
abl
e
logi
c
de
vi
ce (
C
PLD)
EPM
7
25
6,
an
d
vol
t
a
ge a
n
d
current signals
are
m
easured
via a 12-b
it reso
lu
tion
o
f
in
tern
al an
alog
-t
o
-
dig
ital (A/D) con
v
e
rter in
tegrated
in
t
h
e DSP TM
S
3
2
0
F
2
80
8. F
o
r t
h
e po
wer c
i
rcui
t
,
i
t
uses t
h
e Vi
nc
ot
ech
’s IGB
T
60
0
V
-
7
5
A
f
o
r t
h
e NPC
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Direct Instantaneous
Power
C
ontr
o
l for
Thre
e Level Grid C
o
nnected
Inver
ters (Yong Yang)
1
269
in
v
e
rter. Tab
l
e 3
presen
ts th
e ex
p
e
rim
e
n
t
al
p
a
ram
e
ters
. To facilitate th
e o
p
e
ration
a
l ev
al
u
a
tio
n
of th
e syste
m
per
f
o
r
m
a
nces, a PV ar
ray
em
ul
at
or i
s
of
par
t
i
c
ul
ar im
port
a
nce i
n
or
der t
o
avoi
d any
si
gn
i
f
i
cant
im
pact
on t
h
e
M
PPT an
d
di
r
ect
po
wer c
o
nt
rol
o
f
the t
h
re
e-phase three-l
e
vel NPC inve
rter.
In t
h
e experim
e
nt, the Topc
on
Qu
adro
3
2
K
p
r
o
g
ramm
ab
le DC p
o
wer sup
p
l
y is u
tilized
as
th
e PV array em
u
l
a
t
o
r
,
wh
ich fun
c
tion
s
as a
real-
ti
m
e
e
m
u
l
ato
r
o
f
th
e
PV array o
u
t
pu
t ch
aracteristics.
The
PV c
h
aracteris
tic curves a
n
d ope
rating points can
be
gra
p
hi
cal
l
y
m
oni
t
o
red t
h
r
o
ug
h c
o
m
m
uni
cat
i
on
bet
w
ee
n t
h
e set
u
p
an
d a
com
put
er.
In the e
x
periment, there are t
w
o PV a
rray c
u
rves.
T
h
e fi
rs
t PV array c
u
rve is set at the PV array
o
p
e
n-circu
it vo
ltag
e
oc
1
65
0
V
V
, the PV short
-
circuit
curre
nt
sc
1
27
A
I
and the PV a
rray
MPPT voltage
MP1
520
V
V
while the sec
o
nd
PV array
curve is s
e
t at
the PV array
open-circ
u
it vol
t
age
oc
2
65
0
V
V
, the
PV s
h
ort-ci
rcui
t current
sc
2
13
.5
A
I
an
d t
h
e P
V
a
rray
M
PPT
vol
t
a
ge
MP2
520
V
V
.
Fi
gu
re
1
0
.
P
h
ot
o
g
ra
p
h
of e
x
peri
m
e
nt
al
t
e
st be
nch
Tabl
e 3.
Exper
i
m
e
ntal
p
a
r
a
me
t
e
r
s
Sy
m
bol Descr
i
ption
Value
Sy
m
bol Descr
i
ption
Value
P
Rated output powe
r
12kW
g
e
No
m
i
nal gr
id phase voltage (
r
m
s
)
230V
s
f
Switching fr
equen
c
y
10kHz
g
f
No
m
i
nal gr
id fr
eq
uency
50Hz
PV
V
PV input voltage
300V-
900V
L
Grid filter inducta
nce
0.8
m
H
1
L
Boost inductance
1.
2
m
H
C
Grid filter c
a
pacitor
4.
7
μ
F
1
C
Boost capacitor
100
μ
F
R
Total resistance
0.1
2
C
Dc-
link bus voltag
e
capacitor
800
μ
F
M
MPPT step size
0.2
3.
1.
PSD dq-PLL method oper
ation
In t
h
i
s
sect
i
o
n, t
h
e
per
f
o
r
m
a
nce o
f
t
h
e
desi
gne
d P
S
D
dq
-PLL
m
e
t
h
o
d
i
s
e
v
al
uat
e
d t
h
r
o
ug
h
expe
rim
e
nts. In the fi
rst stu
d
y
,
th
e steady
-
state performance is investig
ated.
The c
o
s
i
ne value
of the gri
d
angl
e
cos
and
t
h
e
si
ne
val
u
e
of
t
h
e
g
r
i
d
a
n
gl
e
sin
as
well as t
h
e
phase a
gri
d
volta
ge
a
e
und
e
r the
nom
i
n
al
gri
d
are sh
ow
n i
n
F
i
gu
re 11 (
a
).
Fi
gu
re 1
1
(b
)
di
spl
a
y
s
t
h
e gr
i
d
angl
e
cos
and t
h
e gri
d
a
ngl
e
sin
as well as th
e p
h
a
se a
g
r
id
v
o
ltag
e
a
e
un
de
r
t
h
e di
st
ort
e
d gri
d
. I
n
t
h
e se
con
d
st
u
d
y
,
t
h
e dy
nam
i
c
per
f
o
r
m
a
nce i
s
i
nvest
i
g
at
ed.
Fi
gu
re
1
2
(a
) i
l
l
u
st
rat
e
s
th
e ex
p
e
rim
e
n
t
al resu
lts of th
e phase a grid vo
ltag
e
a
e
,
the gri
d
angle
cos
and
gri
d
v
o
l
t
a
g
e
fre
que
ncy
g
f
w
h
en t
h
e g
r
i
d
v
o
l
t
a
ge un
der
g
oe
s a fre
que
ncy
s
t
ep cha
n
g
e
fr
om
50 Hz t
o
56
Hz. Fi
gu
re
12
(b
) s
h
o
w
s t
h
e p
h
ase a
gri
d
vol
t
a
ge
a
e
, the grid angle
cos
and
gri
d
v
o
l
t
a
ge
fre
que
ncy
g
f
wh
en t
h
e
g
r
i
d
vol
t
a
ge cha
n
ges a
fre
q
u
ency
st
e
p
f
r
om
56
Hz
t
o
5
0
Hz. F
r
o
m
t
h
e Fi
gu
re
1
1
, i
t
can be co
ncl
u
d
e
d t
h
at
t
h
e des
i
gne
d PS
D d
q
-
P
LL m
e
t
hod
h
a
s excel
l
e
nt
st
eady
-
st
at
e per
f
o
rm
ance even
un
de
r
Evaluation Warning : The document was created with Spire.PDF for Python.