TELKOM
NIKA
, Vol.12, No
.3, Septembe
r 2014, pp. 5
63~580
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v12i3.94
563
Re
cei
v
ed Fe
brua
ry 29, 20
14; Re
vised
May 19, 20
14
; Accepte
d
Ju
ne 13, 201
4
A Review of Current Control Strategy for Single-Phase
Grid-Connected Inverters
Peng Mao
*1,2
, Mao Zhang
1
, Saihua Cui
2
, Weiping Zhang
1,2
, Bong-H
w
a
n
K
w
o
n
3,
1
School of Info
rmation a
nd El
ectronics, Be
i
j
i
ng Institute of T
e
chnolog
y, C
h
in
a
2
School of Info
rmation En
gin
e
e
rin
g
, North Ch
ina U
n
ivers
i
t
y
of
T
e
chnol
og
y,
Chin
a
3
Department o
f
Electronic an
d Electrica
l
En
gin
eeri
ng, Poh
ang U
n
ivers
i
t
y
of Science a
n
d
T
e
chnol
og
y,
Korea
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: maope
ng@
n
c
ut.edu.cn
A
b
st
r
a
ct
T
h
is pap
er giv
e
s an
overvi
ew
of the
mai
n
cu
rr
ent contro
l strategy for si
ngl
e
-
phas
e gri
d
-co
nnecte
d
inverters. T
he
mo
de
l of the
p
o
w
e
r circuit is f
i
rst discu
ss
ed.
T
hen, a cl
assifi
cation
of curre
nt control strat
e
g
y
in statio
nary r
e
ferenc
e fra
m
e foll
ow
s.
T
h
is is conti
n
u
ed
by a d
i
scussi
o
n
of curre
nt co
ntrol structures
for
singl
e ph
ase
grid-co
n
n
e
cted
inverters an
d
the possi
b
iliti
e
s of imple
m
entatio
n in st
ation
a
ry refere
nc
e
frames. T
he ot
her no
n-
mai
n
s
t
ream r
egu
lato
rs w
e
re
also i
n
troduc
ed. F
u
r
t
her on, both t
he
mod
e
l of the
pow
er circ
uit
and
curre
nt c
ontrol
strategy
in
rotati
ng
refe
re
n
c
e fram
e we
re
fo
cu
se
d o
n
a
s
wel
l
.
Th
e
overvi
ew
of control strategy
for single-
ph
ase
gri
d
-con
n
e
cted inv
e
rter
s and the
i
r adva
n
tag
e
s a
n
d
disa
dvant
ages
w
e
re conclu
de
d in this pa
per.
Ke
y
w
ords
: singl
e-ph
ase gri
d
-con
necte
d in
verters, curren
t
control strategy, stati
onary referenc
e
frame,
rotating reference fram
e
1. Introduc
tion
No
wday
s, fossil fuel is th
e main ene
rgy supplie
r o
f
the world
w
i
de economy,
but th
e
recognitio
n
of it as being a major ca
use
of env
ironm
ental pro
b
lem
s
makes the
manki
nd to look
for alternative
re
sou
r
ces i
n
power
gene
ration.
Moreov
er, the d
a
y-b
y
-day in
cre
a
sing dem
and f
o
r
energy
can
create
proble
m
s fo
r th
e p
o
we
r
distri
but
ors,
like g
r
id
instability a
n
d
even
outa
g
e
s.
The n
e
cessit
y of prod
uci
n
g more e
nerg
y
combi
ned
with the i
n
terest in
cle
an t
e
ch
nolo
g
ies
yields
in an increa
sed develo
p
m
ent of powe
r
dist
rib
u
tion sy
stem
s usin
g rene
wable e
n
e
rgy.
Among the
rene
wa
ble e
nergy
sou
r
ces, t
he pho
tovoltaic (PV
)
tech
nology
gains
accepta
n
ce
as
a
way of
maintaini
n
g
and
im
p
r
ovi
ng living
sta
ndards with
o
u
t harming
the
environ
ment.
The numbe
r of PV installations ha
s a
n
exponentia
l growth, mai
n
ly due to th
e
govern
m
ent
s and utility compani
es th
at supp
ort
progra
m
s that
focu
s on gri
d
-conn
ecte
d PV
system
s. Be
sides thei
r lo
w efficien
cy, th
e controllabili
ty of
grid
-con
necte
d PV
systems
is their
main d
r
a
w
ba
ck. A
s
a
co
n
s
eq
uen
ce, th
e cu
rrent
co
ntrolle
r play
s a majo
r
role
. Therefore, t
he
control strate
gies b
e
come
of high intere
st.
This
pape
r gi
ves an
overvi
ew of the
mai
n
cu
rr
ent con
t
rol strategy f
o
r
single
-
p
h
a
s
e g
r
id
-
con
n
e
c
ted in
verters. The
model of
the
power
circuit
is first di
sc
ussed. Th
en, a
cla
ssifi
cation
of
curre
n
t control st
rategy i
n
stationa
ry referen
c
e
fram
e
follows. T
h
is is
co
ntinue
d
by a di
scu
ssi
on
of cu
rre
nt co
ntrol
stru
ctures fo
r si
ngle
pha
se
g
r
id
-conne
cted i
n
verters a
nd th
e po
ssi
bilities of
impleme
n
tation in
stationa
ry refe
ren
c
e f
r
ame
s
. Th
e o
t
her n
on-mai
n
stre
am
regu
lators were
al
so
introdu
ce
d. Furthe
r on, b
o
th the mod
e
l of the
power
circuit a
nd cu
rrent control
strateg
y
in
rotating refe
rence frame
were focu
se
d
on as well.
The overvie
w
of control strategy for sin
g
le-
pha
se
grid
-co
nne
cted i
n
verters and
thei
r advanta
g
e
s
and
disadvan
tages were
concl
ude
d in
this
pape
r.
2. The Model
Of The Po
w
e
r Circuit
The full
brid
ge top
o
logy
with the i
n
d
u
ct
or L,
con
necte
d b
e
tween th
e g
r
id
and th
e
inverter, is
prese
n
ted in Fi
gure
1. The
cap
a
cito
r Ci,
in the stru
ctu
r
e inp
u
t, represe
n
ting the
DC
voltage
sou
r
ce, and
a
current sou
r
ce Ii,
that ca
n
be
ei
ther th
e o
u
tp
ut of the
DC-DC conve
r
ter or
an array of photovoltaic p
anel
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 56
3 – 580
564
Figure 1. Full bridg
e
inverte
r
The output current
i
s
cont
rolled
by
im
p
o
sin
g
the
de
rivative of the
cu
rrent th
ro
ugh th
e
indu
ctor, or,
put differently
, by imposing
the volt
age across the in
ducto
r L. In this ma
nne
r, the
stru
cture of the co
nverte
r
sho
w
n in Fi
g
u
re 2
c
an
be
represented,
without
lo
ss
of gene
rality, as
the controlled
voltage
so
urce Vi,
present
ed in
Fig
u
re
2, wh
ere the
l
i
nk i
ndu
cto
r
s
are
re
present
ed
by the induct
o
r L, Vo is the utility voltag
e, and iL is th
e output PV system cu
rrent
.
Figure 2. Simplified equival
ent inverter
ci
rcuit
In Figure 2,
the ene
rgy flow i
s
control
l
ed by
the
current iL. Ho
wever, thi
s
current is
defined by t
he differe
nce
of voltage betwe
en
the
sou
r
ces Vi
and Vo, app
lied acro
ss the
impeda
nce. In this
ca
se, a
s
the im
ped
a
n
ce i
s
a pu
re
indu
ctan
ce, the current
wil
l
be e
qual to t
h
e
integral of the
voltage acro
ss it.
As Vo is kn
o
w
n, on
ce it is
the utility voltage itself, Vi is impo
sed a
n
d therefo
r
e VL. Thus:
()
()
()
Li
o
Vt
V
t
V
t
(2.1)
PWM d
e
fine
s a
mod
u
lat
ed
signal
co
mposed
of the reprodu
cti
on of the
m
odulatin
g
sign
al’s
sp
e
c
trum,
who
s
e amplitud
e
is def
in
ed
by the mo
dulation, a
d
ded to h
a
rmonic
comp
one
nts
of frequ
en
cie
s
that a
r
e
mu
ltiples of
th
e
swit
chin
g fre
quen
cy. Igno
ring th
e effect of
the ha
rmo
n
ic co
mpo
nent
s
of the
switchi
ng frequ
en
cy
on voltage V
i
, once the inducto
r wo
rks
as
a lo
w p
a
ss filter for the
cu
rre
nt, the volt
age i
m
po
se
d
acro
ss the
i
ndu
ctor is re
pre
s
ente
d
si
mply
by (2.1). Fi
gu
re 3
sh
ows t
he ma
nne
r in
whi
c
h
the
converte
r allo
ws th
e voltag
e to be im
po
sed
across the in
ducto
r, as
sh
own in
the e
q
u
ivalent circui
t of Figure 2.
Indeed, the
output curre
n
t is de
sired
to be a
mi
rror
of Vo as expre
s
sed i
n
(2.2
).
Neverth
e
le
ss,
according to
(2.3), the in
ducto
r vo
ltag
e is the de
rivative of the current thro
ug
h
itself. Theref
ore, (2.4
) de
scrib
e
s the vol
t
age Vi, wh
ich, in effect, is define
d
by the control lo
op,
sho
u
ld p
r
e
s
e
n
t a sine, in o
r
de
r to null th
e effect
of Vo, and a co
sin
e
, which, by comp
ositio
n, will
be the re
sult
ing voltage imposed a
c
ro
ss the ind
u
ctor, therefore
,
guarante
e
in
g a sinu
soid
al
c
u
rrent. In prac
tice, at the grid frequenc
y
, the i
ndu
ct
or i
s
a very
small
rea
c
tan
c
e, cau
s
ing t
he
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
A Revie
w
of Curre
n
t Control Strategy fo
r Si
ngle-P
h
a
s
e Grid
-Conn
e
c
ted Inverte
r
s (Peng Mao
)
565
voltage d
r
op
across t
he in
ducto
r to
be
much
smalle
r than th
e utilit
y voltage. In
other
wo
rd
s,
the
sine of Vi do
minates th
e co
sine, de
mo
nstratin
g that
the deman
d
on the cu
rre
n
t loop is m
u
ch
more i
n
favor of annullin
g the "distu
rb
an
ce" of the
utili
ty voltage rather tha
n
to ef
fectively cont
rol
the output cu
rrent.
Figure 3. Block di
agram of
the
simplified
equivalent ci
rcuit.
(2.2)
(2.3)
(2.4)
3. The Curr
e
n
t Con
t
rol Strategy
Of The
In
v
e
rter In Stationar
y
R
e
ference Frame
In the cont
rol
strategy, an
internal
cu
rre
n
t l
oop an
d a
n
external l
o
o
p
to cont
rol t
he input
voltage are i
m
pleme
n
ted.
The voltage
loop defin
es
the amplitud
e of the refe
rence current
by
multiplying its co
ntrol
sig
n
a
l
by
a
“waveform”,
whi
c
h
can b
e
a
sa
m
p
le of th
e out
put voltage
o
r
a
digitally gene
rated si
nu
soi
d
, generati
ng
the output cu
rrent refe
ren
c
e.
3.1 Classic P
I
control str
a
teg
y
Figure 4
dem
onstrates ho
w the
cla
s
sic
PI contro
l st
rategy is i
m
pl
emented, i
n
whi
c
h Vi i
s
determi
ned
b
y
the
curre
n
t
error si
gnal
p
a
ssing
throug
h the
compe
n
s
ator.
The
e
r
ror
sig
nal i
s
th
e
differen
c
e bet
wee
n
a sam
p
le of the curre
n
t and its refe
ren
c
e.
Figure 4. Block di
agram of
classi
cal
PI control st
rateg
y
current loop
It is ob
se
rve
d
, however, t
hat the o
u
tp
ut vo
ltage V
o
app
ea
rs
as a di
sturb
a
n
c
e in the
simplified
tra
d
itional m
o
d
e
l. From
the
block
di
ag
ram, the
current sig
nal
error is
equ
al
to
()
()
(
)
Lr
e
f
L
et
i
t
i
t
. Since a
perfectly sinusoidal current to
t
he utility line i
s
a
desi
gn
goal, e must
naturally ap
p
r
oa
ch zero. So, there are two tas
ks
that PI-controller ha
s
to operate: tracking
referen
c
e current and
reje
cting disturban
ce voltage [1]
-
[2].
Ho
wever,
wh
en the refere
nce
cu
rrent is a di
re
ct sig
nal, ze
ro
ste
ady-state
error can b
e
se
cured by u
s
ing a
cla
ssi
c propo
rt
ional-integral (PI)
controller.
Wh
en the refe
re
nce
curre
n
t is a
sinu
soi
dal sig
nal, it would l
ead to stea
dy-state e
r
ror d
ue to finite gain at the grid frequ
en
cy.
()
2
s
i
n
(
)
L
It
I
t
()
()
2
c
o
s
(
)
L
L
di
t
Vt
L
L
I
t
dt
()
2
c
o
s
(
)
2
s
i
n
(
)
iR
M
S
R
M
S
Vt
L
I
t
V
t
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 56
3 – 580
566
3.2 Classic P
I
control str
a
teg
y
w
i
th fe
e
d
-fo
r
w
a
r
d
As the grid
voltage is m
easura
b
le, the fo
rwa
r
d fe
edba
ck cont
roller G
c
d is
use
d
to
redu
ce
stea
d
y
-state e
rro
r
of the cont
roll
er du
e to
the
finite gain of PI, as sho
w
n
in Figure 5. T
h
e
model of PWM is the k, an
d
2
ri
e
k
V
, Whe
r
e Vtri
is the pea
k o
f
the triangula
r
ca
rri
er si
gna
l and e2
is the input of
the PWM.
Figure 5. Block di
agram containi
n
g
the feed-fo
rward
controlle
r
From the pro
posed blo
ck
diagram
that contai
ns this
feed-fo
rward
controlle
r, it
can be
s
e
en that:
(3.1)
From
(3.1
), whe
n
G
c
d
=
1
/
k, the di
stu
r
ban
ce
from
Vo ca
n be
eliminated,
and if
()
i
p
k
kk
s
L
s
, then iL= iref,
identifying the accurate
cu
rre
nt cont
rol effect for iref.
PI control
wit
h
g
r
id volta
g
e
feed
-forwa
rd
is
comm
on
ly use
d
fo
r
current-cont
rol
l
ed PV
inverters, but
this solution
exhibits two
we
ll
kno
w
n
dra
w
ba
cks: n
o
t enou
gh a
b
ility of the PI
controlle
r to
tra
c
k a
sin
u
soi
dal
refe
rence
wi
thout
stea
dy-state
erro
r a
nd
poor di
sturb
ance
rejection
capability [3]-[5]. This i
s
due to the poor
perf
o
rmance of
t
he integral
action. Moreover;
this le
ad
s in
turn
to the
pre
s
en
ce
of
the g
r
id-volta
ge b
a
ckg
r
ou
nd h
a
rm
oni
cs in
the
cu
rrent
waveform. Thus, a poor THD of the
current will typicall
y be obtained.
3.3 The Prop
ortion
+Reso
nant(PR) reg
u
lator in sta
t
ionar
y
reference fram
e
3.3.1 Cosine
func
tion bas
e
d on the internal model principle
Ne
w stationa
ry
refe
re
nce frame co
ntrol
meth
o
d
that
is ba
sed
o
n
the i
n
tern
al
model
prin
ciple in control theo
ry. The method
introdu
ce
s a sine tran
sf
er functio
n
with a spe
c
if
ied
resona
nt fre
q
uen
cy into t
he
curre
n
t compen
sato
r.
Thus, th
e g
a
i
n of the
op
en-lo
op t
r
an
sfer
function
of the co
ntrol
syst
em goe
s
to i
n
finity at the re
son
ant fr
eq
u
ency, which
ensure
s
that
the
steady-state
errors in resp
onse to step
cha
nge
s in
a
referen
c
e si
g
nal at that fre
quen
cy re
du
ces
to z
e
ro.
Con
s
id
er th
e
control
syste
m
in
whi
c
h
th
e refere
nce i
nput
sign
al i
s
sin
u
soidal. B
a
se
d o
n
the intern
al
model p
r
in
cip
l
e [6], the co
mpen
sato
r wi
th a sin
u
soid
al tran
sfer fu
nction i
s
requ
ired.
There are t
w
o alternative
s
for the si
n
e
tran
sf
er fu
nction. On
e is the Lapl
ace tran
sform
of a
co
sine fu
nct
i
on, and th
e other is that
of a sine fu
nct
i
on. They
are give
n
by
2
12
22
22
,
cc
s
GG
ss
.
0
1
1
()
(
)
()
()
re
f
i
pc
d
LL
i
p
k
kk
k
G
sk
is
i
V
k
sL
kC
sL
k
k
s
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
A Revie
w
of Curre
n
t Control Strategy fo
r Si
ngle-P
h
a
s
e Grid
-Conn
e
c
ted Inverte
r
s (Peng Mao
)
567
Comp
ared th
e Bode
dia
g
rams of G
c
1
a
nd G
c
2
in
Fig
u
re
6, It is ob
serve
d
that
G
c
1
ha
s a
sufficie
n
t am
ount of p
hase margin, 90
deg
ree, b
u
t the pha
se
m
a
rgin
of G
c
2
is only 0
de
g
r
ee.
Therefore, if Gc2 i
s
empl
oyed
for the
sinu
soi
dal int
e
rnal m
odel,
the feedba
ck control syst
em
woul
d proba
bly be highly
unde
rdam
p
ed. Therefore,
it is impo
rtant to note
that the co
sine
function, G
c
l, sho
u
ld be
ch
ose
n
for the sinusoidal
inte
rnal mo
del. In this pape
r, G
c
1 is
calle
d the
sine t
r
an
sfer function. T
h
e gain
of th
e sin
e
tra
n
sf
er fun
c
tion i
s
theo
reti
call
y infinite at the
resona
nt ang
ular fre
que
ncy; namely, th
e gain of the
l
oop tra
n
sfe
r
functio
n
goe
s
to infinity at g
r
id
freque
ncy
0
. Figure 7
sho
w
s the
blo
c
k diag
ram
of
the si
nu
soida
l
intern
al m
o
del G
c
1,
whe
r
e the inp
u
t and output
are u an
d y, resp
ectively; and the gain i
s
Ks [7].
Figure 6. Bode diagram of two tr
an
sfe
r
function
s, Gc1 and G
c
2
Figure 7. Block di
agram of
sinu
soid
al internal m
odel
Gc1 b
a
sed o
n
co
sine fun
c
tion
3.3.2 The se
cond orde
r generalized integra
t
or
for
a single sinu
soidal signal
The pa
pe
r propo
se
s the
concept
of int
egrato
r
s for
sinusoidal
sig
nals. Th
e co
nce
p
ts of
ideal integ
r
at
or for a
sin
g
le sin
u
soid
al sign
al
an
d a station
a
ry-fram
e
ide
a
l integrator for
sinu
soi
dal sig
nals a
r
e expl
ored [8].
Similar to the dire
ct sign
al case, for a
sin
u
soi
dal si
gnal
()
s
i
n
(
)
et
A
t
, the amplitude
integratio
n of
this sig
nal
can
be writte
n as
()
s
i
n
(
)
yt
A
t
t
. Defini
ng further an auxiliary
sign
al
()
c
o
s
(
)
xt
A
t
, the Lapla
c
e tran
sf
orm
s
of the three si
gnal
s a
r
e
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930
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 56
3 – 580
568
(3.2)
Then
an id
ea
l integrator fo
r a
singl
e si
n
u
soi
dal
sign
a
l
can
be
co
nfigure
d
a
s
sh
own i
n
Figure 8. It i
s
e
a
sy to
get
the result shown in
Figu
re 9
from
Fig
u
re
8 [9]. Th
e corre
s
po
nd
ing
stationa
ry-fra
me gene
rali
zed integr
ator
is sh
own in Figure 9(c).
The integ
r
ato
r
output co
ntains
not only the integratio
n of the input, but also an ad
di
tional negligi
b
le com
pon
e
n
t. The seco
nd
orde
r ge
neral
ized inte
grato
r
is shown in Figure 10,
wh
ere KI is the integral
con
s
t
ants [10]-[1
1
].
Figure 8. An ideal integ
r
ato
r
for a sin
g
le
sinu
soi
dal sig
nal
Figure 9. Signal pa
ssi
ng throu
gh an id
e
a
l integrato
r
22
2
2
22
22
22
2
2
22
2
2
22
22
co
s
s
i
n
co
s
s
i
n
()
(
)
(
)
co
s
s
i
n
()
cos
s
i
n
()
s
A
As
As
A
Ys
ss
s
s
s
s
AA
s
Es
ss
As
A
Xs
ss
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
A Revie
w
of Curre
n
t Control Strategy fo
r Si
ngle-P
h
a
s
e Grid
-Conn
e
c
ted Inverte
r
s (Peng Mao
)
569
Figure 10. Integrato
r
an
d the se
co
nd order ge
ne
ralized integrator
3.3.3 The Proportion
+Re
s
onan
t
(PR)
regulator
Form the
abo
ve con
c
lu
sion
s, it is expli
c
it
that both cosine fun
c
tion b
a
se
d on th
e intern
a
l
model p
r
in
cip
l
e, and the
se
con
d
orde
r g
ener
alized int
egrato
r
, have
the sa
me ex
pre
ssi
on
22
s
s
, but loo
k
in
g
at issu
es from different
views.
The
forme
r
, fro
m
the view poi
nt of fre
que
n
c
y
domain,
expl
ain h
o
w to g
e
t infinite g
a
i
n
at the
resonant f
r
equ
e
n
cy, which e
n
su
re
s th
at the
steady-state
errors in re
sp
onse to reference sinu
so
i
dal sign
al red
u
ce
s to ze
ro.
The latter, from
the view poin
t
of time domain, explain the integ
r
at
or
con
c
e
p
ts for
sinu
soi
dal si
g
nal, just like t
h
e
integrato
r
con
c
ept
s for dire
ct cu
rre
nt sig
nal.
We
call it,
,
reso
nant
reg
u
l
ator, an
d th
e Prop
ortio
n
+Re
s
ona
nt
(PR) current
controlle
r Gc1 is define
d
a
s
:
(3.3)
whe
r
e, KP and KI are the propo
rtion
a
l an
d
integral con
s
tants re
spe
c
tively.
In the ca
se
of current
co
ntrol for g
r
id
conn
ecte
d i
n
verter, the
curre
n
t error signal i
s
non
sinu
soid
al
, whi
c
h
co
ntains multiple
cu
rr
ent h
a
rmonics. F
o
r ea
ch
cu
rre
n
t ha
rmoni
c of
con
c
e
r
n, a
correspon
ding
re
son
ant re
gulator mu
st be installed. When the
multiple
current
harm
oni
cs a
r
e of con
c
e
r
n,
the co
rre
sp
o
nding
re
so
n
a
n
t regul
ator
should b
e
in
stalled. Re
so
n
ant
freque
nci
e
s
o
f
the reso
nan
t regulato
r
co
rre
sp
ond
to t
he freq
uen
ci
es of the con
c
erned
cu
rre
n
t
harm
oni
cs. T
he harmoni
c
comp
en
sato
r (HC) G
h
c i
s
d
e
fined a
s
bel
ow,
(3.4)
Comm
only; it is desi
gne
d to comp
ensate the
sele
cte
d
harm
oni
cs
3rd, 5th an
d 7th, as
they are the
most promine
n
t harmo
nics
in the curre
n
t spe
c
tru
m
.[12]-[14]
Usi
ng
(3.3),
(3.4), the tran
sfer fu
nctio
n
of
the ge
nera
lized
re
son
a
n
t
regul
ator
G
c
can
be
expre
s
sed a
s
(3.5)
Figure 11
sh
ows a mo
re d
e
tailed pi
cture of t
he stand
ard
controlle
r sch
eme of G
c
for the
singl
e-p
h
a
s
e
grid
-conn
ecte
d PV inverter (the
PWM mo
dulator i
s
inte
ntionally omitted).
22
s
s
11
22
()
()
cP
I
P
h
c
s
Gs
K
K
K
G
s
s
22
3,
5
,
7
,
()
hc
I
h
hn
o
s
GK
sh
22
2
2
3,
5
,
7
,
()
()
cP
I
I
h
hn
o
ss
Gs
K
K
K
ss
h
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 56
3 – 580
570
Figure 11. sta
ndard co
ntroll
er sche
me of Gc
Figure 12. Bode plot of dist
urba
nc
e rej
e
ction (cu
r
rent error ratio
disturban
ce
) of the PR+HC,
P
and PR curre
n
t controllers.
The Bode pl
ots of distu
r
b
ance reje
ctio
n
for the PI and PR
cont
rolle
rs a
r
e
s
h
ow
n
in
F
i
gu
r
e
12
, w
h
e
r
e
:
ε
is cu
rrent
error
and the
grid voltag
e
Vo is g
r
id volt
age, con
s
ide
r
ed
as the di
sturb
ance for the system [14].
As it ca
n be
observed,
a
r
oun
d the fu
ndam
e
n
tal freque
ncy the
PR provide
s
140 dB
attenuation,
while th
e PI provide
s
only 17 dB.
Mo
re
over a
r
ou
nd t
he 5th
and
7th ha
rmoni
cs
the
situation
is e
v
en worst, th
e PR attenu
ation b
e
ing
1
25 dB
an
d t
he PI atten
u
a
tion o
n
ly 8
dB.
More
over fro
m
Figure 12,
it is clea
r th
at the PI
reje
ction
capa
bili
ty at 5th and 7th harm
oni
c is
comp
arable
with that one
of a simple p
r
oportio
nal
co
ntrolle
r, the integral a
c
tion
being irrel
e
va
nt.
Thus it i
s
d
e
mon
s
trate
d
the supe
rio
r
ity of t
he P
R
c
o
ntroller
res
p
ec
t to the PI in terms of
harm
oni
c cu
rrent reje
ction.
The ope
n loo
p
and clo
s
e
d
loop frequ
en
cy respon
se
of the system
using PR
co
ntrolle
r
can b
e
se
en i
n
Figure 13 a
nd Figu
re 14
respe
c
tively [15].
Figure 13. Bode plot of ope
n-loo
p
PR current co
ntrol
system
0
()
()
re
f
o
i
s
Vs
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
A Revie
w
of Curre
n
t Control Strategy fo
r Si
ngle-P
h
a
s
e Grid
-Conn
e
c
ted Inverte
r
s (Peng Mao
)
571
Figure 14. Bode plot of refe
ren
c
e si
gnal t
o
grid current
transfe
r funct
i
on (cl
o
sed lo
op)
3.3.4 The da
mped PR re
gulator
The P
R
reg
u
lator, exhi
bi
t theoreti
c
all
y
an infinite
gain at th
e reso
nan
ce f
r
e
quen
cy,
ensurin
g a nearly perfe
ct harm
oni
c elimination.
Ho
wever, the re
alizatio
n of ideal gen
eralize
d
integrato
r
s i
s
sometim
e
s n
o
t po
ssi
ble
d
ue to finite
preci
s
ion
in di
gi
tal system
s,
and th
e g
a
in,
at
the resona
nce freque
ncy, is ea
sy to be affect
ed by the fluctuation
of the grid fre
quen
cy.
Thus, a d
a
m
ped ge
nerali
z
ed inte
grato
r
is propo
se
d
in which ha
ve limited gai
n at the
resona
nce fre
quen
cy. Thi
s
config
ur
atio
n
can
be
realized in
digital
pl
atforms with
a hig
h
a
c
cu
ra
cy
and, mo
re
over, it i
s
well
suite
d
for a
lleviati
ng
so
me in
stability pro
b
lem
s
i
d
entified in
id
eal
integrato
r
s [16]-[18].
(3.6)
Usi
ng th
e ba
nd-p
a
ss filte
r
s G
hc1
a
nd
G
hc
, w
h
ic
h ar
e e
x
p
r
ess
e
d in
(
3
.6)
,
th
e re
fe
r
e
nc
e
sign
al to grid
current tra
n
sfer functio
n
e
x
hibits both a
large
r
ban
d
w
idth an
d sm
aller ma
gnitu
de
dips.
3.3.5 The optimum damped PR regula
t
or
Figure 14
sh
ows the Bo
d
e
diag
ra
m
of the refe
ren
c
e sig
nal to th
e grid
current
tran
sfer
function. A flat unity gain and ze
ro ph
ase are ob
se
rved within the
freque
ncy ran
ge of intere
st. In
that case, a good refere
n
c
e-sig
nal
-tra
cking capa
bilit
y is expected
.
Howeve
r, this feature force
s
the referen
c
e
signal to be
a nearly pe
rfect sin
u
soida
l
waveform with an insignif
i
cant ha
rmoni
c
conte
n
t. In fact, the flat unity-gain an
d zero p
h
a
s
e ch
ara
c
teri
stics
sug
g
e
s
t that the grid
cu
rre
nt
will track the f
undam
ental referen
c
e
sign
al and its ha
rmonics pe
rfe
c
tly.
1
11
22
1
22
3,
5
,
7
,
1
22
2
2
3,
5
,
7
,
1
2
()
()
2
2
2(
)
22
()
22
(
)
o
cP
I
P
h
c
oo
ho
hc
I
h
hn
ho
o
oh
o
cP
I
I
h
hn
oo
h
o
o
s
Gs
K
K
K
G
s
ss
ns
GK
sn
s
h
sn
s
Gs
K
K
K
ss
s
n
s
h
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 56
3 – 580
572
Figure 15. Th
e optimum da
mped PR reg
u
lator
Paper [1
9]-[2
0
] pre
s
ent
s a
curre
n
t co
ntrol
schem
e fo
r the
single
p
hase gri
d
-co
nne
cted
PV inverter
with the
follo
wing
interesti
ng featu
r
e
s
: 1) accu
rate synchro
n
ization with
the
grid
voltage; 2) lo
w ha
rmo
n
ic
content of the
grid
cu
rre
nt; and 3
)
lo
w computation
a
l
load. Figu
re
15
sho
w
s the p
r
opo
sed
cu
rre
nt control scheme. Fi
gu
re
16 sh
ows th
e Bode dia
g
ram of refe
re
nce
sign
al to grid
curre
n
t transf
e
r functio
n
Figure 16. Bode diag
ram of
refere
nce sig
nal to
grid current tran
sfe
r
functio
n
(cl
o
sed loop
)
As expe
cted,
the refere
nce sign
al to grid
cu
rrent transfe
r fun
c
tion beh
aves
as a lo
w-
band
width b
and pa
ss filter tune
d to resonate
at
the gri
d
frequ
ency. Note t
hat the tran
sfer
function
mag
n
itude a
nd p
hase a
r
e 0
d
B
and 0
◦
at
50 Hz
, res
p
ectively, whic
h
s
u
gges
ts
that
a
good
tra
cki
n
g
capability o
f
the funda
m
ental g
r
id
vol
t
age
comp
on
ent is
achiev
ed. Mo
reove
r
, a
signifi
cant a
d
d
itional atten
uation i
s
ob
served i
n
Fi
g.
16 in the
sha
pe of the fo
ur narro
w dip
s
t
hat
are cente
r
ed
at frequen
cie
s
of 150, 250
, 350, and
45
0Hz, respe
c
tively.
This behavior confirms
that the
simpl
e
and ac
curate synchroni
zation m
e
thod used i
n
the
prop
osed control scheme will
not introdu
ce
the harmoni
c co
ntent of the refe
ren
c
e
sign
al into the grid current
. Moreover; the
Bode plots of
disturb
a
n
c
e rejectio
n
for t
he optimum da
mped PR reg
u
lator controllers
is the
sam
e
as Fi
gure 1
2
. Thu
s
it is demo
n
strate
d the optim
u
m
PR contro
ller ha
s
sam
e
sup
e
rio
r
it
y
in t
e
rms of
h
a
r
m
onic
cu
rr
en
t
reject
io
n. Mean
while; it is wo
rth me
ntioning that th
e
PLL-b
a
sed synchroni
zing algorith
m
is not
used
in t
h
is
system
with the optim
um dam
ped
PR
regul
ator,
so
the
comp
utational l
oad
is n
e
cessa
r
il
y lowe
r d
u
e
to with
out
pro
c
e
ssi
ng ti
me
requi
re
d to co
mpute the PL
L synchro
n
izi
ng algo
rithm.
0
()
()
re
f
o
i
s
Vs
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