TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 10, Octobe
r 20
14, pp. 7143
~ 715
9
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.592
8
7143
Re
cei
v
ed Ma
rch 6, 2
014;
Re
vised June
21, 2014; Accepte
d
Jul
y
1
8
, 2014
A Review of Current Control Strategy for Single-Phase
Grid-Connected Inverters
Peng Mao*
1,2
, Mao Zhang
1
, Weiping Zhang
1,2
, Bong-H
w
a
n
K
w
o
n
3
1
School of Infor
m
ation a
nd El
e
c
tronics, Be
ij
in
g Institute of
T
e
chn
o
lo
g
y
, Chi
n
a
2
School of Infor
m
ation En
gi
ne
erin
g, North
Ch
ina U
n
ivers
i
t
y
of
T
e
chnol
og
y,
Chin
a
3
Departme
n
t of Electronic a
n
d
Electrical En
gi
neer
ing,
Po
han
g Univ
ersit
y
of Scienc
e an
d T
e
chn
o
lo
g
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 overv
i
ew
of
the mai
n
cu
rrent control str
a
tegy
for sing
l
e
-ph
a
se gri
d
-c
onn
ected
inverters. T
h
e
mo
de
l of the
p
o
w
e
r circuit is
first discu
ss
ed.
T
hen, a c
l
assifi
cation
of curre
nt control
strateg
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
inv
e
rters a
n
d
the
possi
bi
l
i
ti
es of
impl
e
m
e
n
tation
in
stati
onary
refere
nc
e
frames. T
he ot
her no
n-
mai
n
s
t
ream re
gu
lato
rs w
e
re
also i
n
troduc
ed. F
u
rther 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
o
v
e
r
vie
w
o
f
co
n
t
ro
l stra
te
g
y
fo
r sin
g
l
e
-
p
h
a
s
e
g
r
i
d
-co
nne
cte
d
i
n
ve
rte
r
s a
n
d
th
ei
r
a
d
v
an
ta
ge
s and
disa
dvant
ages
w
e
re conclu
de
d in this pa
per.
Ke
y
w
ords
:
singl
e-p
has
e g
r
id-con
necte
d i
n
verters, curre
nt
control strategy, station
a
ry
reference fra
m
e,
rotating reference fram
e
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
No
wday
s, fossil fuel i
s
the main ene
rgy
suppli
e
r o
f
the world
w
i
de economy,
but the
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 alte
rnative
re
so
urce
s in
po
we
r g
ene
ration.
Mo
reov
er, the
day
-b
y-day in
crea
sing d
e
man
d
f
o
r
energy can
create p
r
oble
m
s for the p
o
we
r dist
ri
but
ors, like grid
instability an
d even outag
es.
The n
e
cessit
y of pro
d
u
c
in
g mo
re
ene
rg
y combi
ned
with the
interest in
cl
ean 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 th
e
rene
wa
ble
e
nergy
so
urces, the
ph
o
t
ovoltaic
(PV) te
chn
o
logy
gain
s
accepta
n
ce as a way of
maintaining
and impr
ovi
ng living sta
ndards
witho
u
t harmin
g
the
environ
ment.
The numb
e
r of PV installations h
a
s a
n
expone
ntia
l growth, mai
n
ly due to the
govern
m
ent
s and utility compani
es th
at sup
port p
r
ogra
m
s th
at focu
s on
gri
d
-conn
ecte
d
PV
system
s. Besides thei
r low effi
ciency, the cont
rollabili
ty of
grid-co
n
necte
d PV system
s
is thei
r
main d
r
a
w
ba
ck. A
s
a
con
s
eq
uen
ce, th
e current
co
ntrolle
r pl
ays a maj
o
r rol
e
. Therefore,
the
control strate
gies b
e
come
of high intere
st.
This
pap
er
gi
ves a
n
ove
r
view
of the mai
n
cu
rrent con
t
rol
st
rategy
f
o
r singl
e-p
h
a
s
e grid
-
con
n
e
c
ted in
verters. The
model of
the power circuit is
first
di
scu
s
sed.
Th
en,
a cla
ssifi
cation of
curre
n
t control strategy in stationa
ry ref
e
ren
c
e
fra
m
e
follows. Thi
s
is continu
ed by a discu
ssi
on
of
cu
rrent co
ntrol stru
ctu
r
es
fo
r sin
g
le pha
se grid
-conne
cted
inv
e
rters and
th
e
po
ssibilitie
s
o
f
impleme
n
tation in stationa
ry refere
nce frame
s
.
The o
t
her non
-mai
nstre
a
m re
gu
lators
we
re al
so
introdu
ce
d. Furthe
r on, bo
th the model
of the
power ci
rcuit an
d cu
rre
nt
co
ntrol strategy
in
rotating reference frame
were focu
se
d
on as well.
The overvie
w
of control strategy for sin
g
le-
pha
se gri
d
-co
nne
cted inverters a
nd their advant
age
s
and di
sadva
n
t
ages
were concl
ude
d in this
pape
r.
2. The Model
of the Po
w
e
r Circuit
The full
bri
d
ge top
o
logy
with the
ind
u
ctor L,
co
n
necte
d b
e
tween th
e g
r
id
and
the
inverter, i
s
prese
n
ted in Fi
gure
1. The
capa
citor
C
i
, in the structu
r
e input, re
pre
s
entin
g the
DC
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046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 714
3
– 7159
7144
voltage sou
r
ce, and a cu
rrent sou
r
ce I
i
,
that can be ei
ther the outp
u
t of the DC-DC
conve
r
ter or
an array of photovoltaic p
anel
s.
Figure 1. Full Bridge Invert
er
The output
current is cont
rolled by imp
o
sin
g
the derivative of the
current thro
ugh the
indu
ctor, o
r
, put differently
, by imposin
g
the volt
age
across the i
n
ducto
r L. In t
h
is ma
nne
r, the
stru
cture of t
he converte
r
sho
w
n i
n
Fig
u
re
2 c
an b
e
rep
r
e
s
ente
d
, without lo
ss
of gene
rality, as
the cont
rolled
voltage sou
r
ce V
i
, pre
s
ent
ed in Figu
re
2, whe
r
e the l
i
nk ind
u
cto
r
s
are rep
r
e
s
ent
ed
by the induct
o
r L, V
o
is the utility
voltage, and i
L
is the output PV system current.
Figure 2. Simplified Equiva
lent Inverter
Circuit
In Figure
2, the ene
rgy flow is
co
ntrol
l
ed by the current i
L
. Ho
wev
e
r, thi
s
c
u
rr
ent is
defined by the differen
c
e
of
voltage betwe
en the
source
s V
i
and V
o
, appl
ied acro
ss t
he
impeda
nce. In this
ca
se, a
s
the imp
eda
nce i
s
a
pure
indu
ctan
ce, the current
wil
l
be eq
ual to t
he
integral of the
voltage acro
ss it.
As
V
o
is known, once it is the utility volta
ge itself, V
i
is imposed an
d therefo
r
e V
L
. Thus:
(2.1)
PWM define
s
a modul
ated sign
al co
mposed
of the rep
r
od
ucti
on of the modulatin
g
sign
al’s spe
c
trum,
wh
ose am
plitude
is
define
d
by the
mo
dulation,
ad
ded to
ha
rmonic
comp
one
nts of
frequ
en
cie
s
that are
mu
ltiples of
the
swit
chin
g fre
quen
cy. Igno
ring the
effect
of
the harm
oni
c compo
nent
s of the switchi
ng frequ
en
cy on voltage V
i
, once the in
ducto
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
sho
w
s the man
n
e
r
in
whi
c
h
the
co
nverter
allo
ws the voltag
e
to be impo
sed
across the in
ducto
r, as
sh
own in
the e
q
u
ivalent circui
t of Figure 2.
Figure 3. Block
Diag
ram o
f
the Simplified Equivalent Circuit
()
()
()
Li
o
Vt
V
t
V
t
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TELKOM
NIKA
ISSN:
2302-4
046
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
)
7145
Indeed, the output cu
rre
n
t is
desi
r
e
d
to be a mirro
r of V
o
as expre
ssed in (2.2).
Neverth
e
le
ss,
according to
(2.3), the i
n
ducto
r vo
ltag
e is the
deriv
ative
of the current thro
ug
h
itself. Therefore, (2.4) d
e
scrib
e
s th
e vol
t
age V
i
, whi
c
h, in effect, is defin
ed by
the co
ntrol lo
op,
s
h
ou
ld
pr
es
en
t a
s
i
n
e
,
in
or
d
e
r
to
nu
ll the
e
ffe
c
t
o
f
V
o
,
and a co
sine
,
whi
c
h,
by compo
s
ition, will
be the resulting voltage i
m
posed a
c
ro
ss th
e indu
ct
or, therefore,
guaranteei
n
g
a sin
u
soid
al
c
u
rrent. In prac
tice, at the grid
freq
uen
cy, the in
duct
o
r i
s
a
very
small
rea
c
tan
c
e,
cau
s
in
g th
e
voltage dro
p
across the in
ducto
r to be much
sma
lle
r than the utility voltage. In
other word
s, the
sine of
V
i
do
minates the
co
sine, d
e
mo
nstratin
g that
the de
mand
on the
curre
n
t loop i
s
m
u
ch
more
in favo
r of ann
ulling t
he "di
s
turb
an
ce" of th
e utili
ty voltage rat
her th
an to
effectively cont
rol
the output cu
rrent.
(2.2)
(2.3)
(2.4)
3. The Curr
e
n
t Con
t
rol Strategy
of the
In
v
e
rter in Station
a
r
y
Referenc
e Fram
e
In the
co
ntrol
strategy, an
inte
rnal
cu
rrent loo
p
and
an
extern
al
loop to
control the
inpu
t
voltage are i
m
pleme
n
ted.
The voltag
e
loop d
e
fine
s the amplitu
d
e
of the reference current
b
y
multiplying its cont
rol
sign
a
l
by a “wavef
orm”,
whi
c
h
can be
a
sam
p
le of the
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
PI Control Strategy
Figure 4 dem
onstrates h
o
w
the cla
s
sic
PI cont
rol st
rategy is imple
m
ented, in which V
i
is
determi
ned b
y
the current error si
gnal p
a
ssing thr
oug
h the comp
en
sator. Th
e error sig
nal is 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
Diag
ram o
f
Classica
l PI Control Strategy Curre
n
t Loop
It is ob
se
rve
d
, however,
that the out
put voltage
V
o
appea
rs
as a
di
sturb
ance in th
e
simplified
tra
d
itional m
o
d
e
l. Fro
m
the
blo
c
k di
a
g
ram, the
cu
rrent si
gnal
error is eq
ual
to
. Since a perfectly sinu
soi
dal cu
rrent
to the utility lin
e is a de
sign
goal, e
must natu
r
all
y
approa
ch zero. So, there
are two ta
sks that PI-cont
rolle
r has to operate: tracking
referen
c
e current and
reje
cting disturban
ce voltage [1-2].
Ho
wever, wh
en
the refe
re
nce cu
rrent
i
s
a dire
ct
si
g
nal,
ze
ro ste
ady-state
error can be
se
cured by u
s
ing a
cla
s
sic prop
ortion
al-integral
(PI) c
ontrolle
r. Wh
en the refe
re
nce
cu
rre
nt 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.
3.2. Classic
PI Control Strategy
w
i
th
Feed
-for
w
a
r
d
As the g
r
id v
o
ltage i
s
me
asu
r
abl
e, the
forward
feed
back
cont
roll
er G
cd
is
us
ed
to
r
e
d
u
c
e
steady-state
error of the controlle
r due
to the finite
g
a
in of PI, as
sho
w
n in Fig
u
re 5. The m
odel
()
2
s
i
n
(
)
L
I
tI
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
V
G
P
I
()
()
()
Lr
e
f
L
et
i
t
i
t
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 714
3
– 7159
7146
of PWM i
s
th
e k, a
nd
, Wh
ere V
tri
i
s
the
pea
k of the t
r
i
angul
ar
ca
rrie
r
si
gnal
and
e
2
is the
input of the PWM.
Figure 5. Block
Diag
ram
Containin
g
the Feed
-forwa
rd
Controll
er
From the
pro
posed blo
c
k
diagram
that
contai
ns thi
s
feed-fo
rward
controlle
r, it can b
e
s
e
en that:
(3.1)
From
(3.1
),
wh
en
G
cd
=1/k,
the
di
sturb
a
n
c
e
from V
o
can
be
elimin
a
t
ed, and
if
, then i
L
= i
ref
, identifying the
accurate
cu
rrent cont
rol effect for i
ref
.
PI control wi
th grid voltage feed-fo
rward
is
comm
only used fo
r cu
rre
nt-con
trolled PV
inverters, b
u
t this
solutio
n
exhibits t
w
o
well
kn
own
dra
w
ba
cks:
n
o
t eno
ugh
a
b
ility of the
PI
controlle
r to track a sin
u
soi
dal refe
rence wi
tho
u
t steady-state
erro
r an
d p
oor di
sturba
nce
reje
ction
cap
ability [3-5]. This i
s
due t
o
the poo
r
p
e
rform
a
n
c
e o
f
the integral
action. Mo
re
over;
this lead
s in
turn to the pre
s
en
ce of
the
grid
-volta
ge ba
ckgro
u
nd harmoni
cs in the cu
rren
t
waveform. Thus, a poor THD of the
current will typicall
y be obtained.
3.3. The Proportion
+Res
onant
(PR) Regulato
r
in Station
a
r
y
Referenc
e Fram
e
3.3.1. Cosine
Function
Ba
sed on th
e Intern
al Mod
e
l Principle
Ne
w station
a
r
y reference
frame control met
hod that
is based on
the internal
model
prin
ciple in
control theo
ry. The method
introdu
ce
s a sine tra
n
sf
er functio
n
with a spe
c
ifie
d
resona
nt freq
uen
cy into the current co
mpen
sa
to
r. Thus, the gai
n of the open-loo
p
tran
sfer
function
of the co
ntrol
syst
em goe
s
to i
n
finity at the re
son
ant fr
eq
u
ency, which e
n
su
re
s that th
e
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 which th
e refe
ren
c
e
i
nput si
gnal
is sinu
soi
dal. B
a
se
d on
the
internal
mod
e
l pri
n
cipl
e [
6
], the com
p
ensator
wi
th
a sin
u
soidal
transfe
r fun
c
t
i
on is
re
quire
d.
There are t
w
o alternative
s
for the sine
transfe
r fun
c
tion. One i
s
the Lapla
c
e
transfo
rm of
a
co
sine fu
nct
i
on, and th
e othe
r is that
of a
sine fu
nct
i
on. They
are
given
by
.
Comp
ared th
e Bode
dia
g
rams of G
c1
a
nd
G
c2
i
n
Fig
u
re
6, It is ob
serve
d
that
G
c1
has a
sufficie
n
t am
ount of p
h
a
s
e ma
rgin, 9
0
deg
ree, b
u
t
the pha
se
m
a
rgin
of G
c2
i
s
o
n
ly 0 d
egree.
Therefore, if
G
c2
is em
plo
y
ed for the
sinusoidal i
n
te
rnal m
odel, t
he feed
ba
ck
control
syste
m
woul
d proba
bly be highly
unde
rda
m
p
ed. The
r
efore,
it is impo
rtant to note
that the co
sin
e
function, G
cl
, sho
u
ld b
e
ch
ose
n
for the
sinu
soi
dal int
e
rnal
mod
e
l.
In this p
ape
r, G
c1
is called the
sine t
r
an
sfer function.
Th
e gain
of th
e sin
e
tra
n
s
f
er func
tion is
theoretic
a
lly 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
2
ri
e
k
V
P
I
0
1
1
()
(
)
()
()
ref
i
pc
d
LL
i
p
k
kk
k
G
sk
is
i
V
k
sL
kC
sL
k
k
s
()
i
p
k
kk
s
L
s
2
12
22
22
G,
G
cc
s
ss
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TELKOM
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ISSN:
2302-4
046
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
)
7147
freque
ncy
=
.
Figure 7 sh
ows the block diag
ram of
the sinusoid
a
l internal m
odel G
c1
,
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 Diag
ram of
Tw
o T
r
an
sfer Function
s, G
c1
and G
c2
.
Figure 7. Block
Diag
ram o
f
Sinusoidal I
n
ternal M
odel
G
c1
based o
n
Cosi
ne Fun
c
tion
3.3.2. The Second Ord
e
r Gener
a
lized
Integra
t
or fo
r a Single Sinusoidal Signal
The p
ape
r p
r
opo
se
s the
concept of int
egrato
r
s for sinusoidal
sig
nals. T
he
co
nce
p
ts
of
ideal inte
grat
or for a
sin
g
le si
nu
soid
al sig
nal
a
n
d
a
stationa
ry-fram
e
ide
a
l integ
r
ator for
sinu
soi
dal sig
nals a
r
e expl
ored [8].
Similar to the dire
ct si
gnal ca
se, for a sin
u
soidal sign
al
，
the
amplitude i
n
tegratio
n of thi
s
si
gnal
ca
n
be written a
s
. Defining fu
rt
her
an
auxiliary sig
n
a
l
,
the Lapla
c
e transf
o
rm
s
of the three si
gnal
s are:
(3.2)
Then
an id
ea
l integrator fo
r a
sin
g
le
sin
u
soi
dal
sign
a
l
can
be
conf
igure
d
a
s
sh
own i
n
Figure 8. It is ea
sy to g
e
t the re
sult
sh
own i
n
Fig
u
re 9 fro
m
Fig
u
re
8 [9]. Th
e co
rrespon
d
i
ng
stationa
ry-fra
me gen
eralized integ
r
ato
r
is sho
w
n
in F
i
gure
9(c). T
he integ
r
ato
r
output contai
ns
not only the integratio
n of the input, but also
an a
ddi
tional negli
g
ible com
pon
e
n
t. The se
co
nd
orde
r ge
neral
ized inte
grato
r
is
shown in Figure 10, wh
ere K
I
is the i
n
tegral
con
s
t
ants [10
-
11].
o
2
o
o
()
s
i
n
(
)
et
A
t
()
s
i
n
(
)
yt
A
t
t
()
c
o
s
(
)
xt
A
t
2
2
2
2
22
22
22
22
22
22
22
2
2
cos
s
in
c
o
s
s
i
n
()
(
)
(
)
co
s
s
i
n
()
cos
s
in
()
sA
A
s
A
s
A
Ys
ss
s
s
s
s
AA
s
Es
ss
As
A
Xs
ss
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ISSN: 23
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046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 714
3
– 7159
7148
Figure 8. An Ideal Integrato
r
for a Single
Sinusoi
dal Signal
Figure 9. Signal Passing T
h
rou
gh an Id
eal Integrato
r
Figure 10. Integrato
r
an
d the Seco
nd O
r
de
r Gen
e
rali
zed Integ
r
ato
r
3.3.3. The Proportion
+Re
s
onan
t
m (P
R) Regula
t
or
Form th
e ab
o
v
e con
c
lu
sio
n
s
, it is expli
c
it that both cosine fun
c
tion b
a
se
d on th
e i
n
ternal
model p
r
in
ci
ple, and th
e
se
con
d
ord
e
r ge
ne
ra
li
ze
d integrator,
have the
same exp
r
e
s
sio
n
, but looking
at issue
s
from different
vi
ews. The
former, fro
m
the view point of
freque
ncy
do
main, explai
n
how to g
e
t in
finite gain
at the resona
nt frequ
en
cy, wh
ich e
n
sures t
hat
the stea
dy-st
a
te errors in
respon
se to
referen
c
e
sin
u
s
oid
a
l sig
nal
redu
ce
s to
zero. Th
e latter,
from the view point of time
domai
n, expl
ain the integrat
or co
ncepts for sinu
soid
a
l
signal, just li
ke
the integrato
r
con
c
ept
s for
dire
ct cu
rre
nt sign
al.
We
call it,
,
reso
nant regu
lator, and th
e Propo
rtion
+Resona
nt (PR)
current
controlle
r G
c1
is define
d
as:
(
)
cos(
)
xt
A
t
22
s
()
s
i
n
(
)
et
A
t
22
s
s
()
s
i
n
(
)
y
t
At
t
()
c
o
s
(
)
et
A
t
22
s
s
()
s
i
n
(
)
et
A
t
22
s
()
c
o
s
(
)
yt
A
t
t
22
s
22
s
s
()
s
i
n
(
)
yt
A
t
t
()
c
o
s
(
)
et
A
t
22
s
s
()
s
i
n
(
)
et
A
t
22
s
co
s
()
s
i
n
A
yt
t
22
s
22
s
s
sin
()
s
i
n
A
yt
t
22
2
s
s
cos
()
c
o
s
(
)
s
i
n
A
yt
A
t
t
t
22
2
s
s
sin
()
s
i
n
(
)
s
i
n
A
yt
A
t
t
t
()
c
o
s
(
)
et
A
t
()
s
i
n
(
)
et
A
t
22
2
I
s
K
s
1
I
K
s
22
s
s
22
s
s
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
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
)
7149
(3.3)
Whe
r
e, K
P
and K
I
are the p
r
opo
rtion
a
l an
d integral
con
s
tants
re
spe
c
tively.
In the ca
se
of curre
n
t co
ntrol for g
r
id
con
necte
d i
n
verter, the
curre
n
t error signal i
s
non
sinu
soid
al
, which co
ntains m
u
ltiple
curr
e
n
t harmonics. Fo
r each cu
rre
n
t harm
oni
c of
con
c
e
r
n, a correspon
ding
reso
nant re
gulator mu
st
be installed
.
When the multiple cu
rrent
harm
oni
cs are of
con
c
e
r
n,
the
corre
s
po
nding
re
so
na
nt reg
u
lato
r should
be i
n
st
alled.
Reson
ant
freque
nci
e
s
o
f
the re
son
a
n
t
regulato
r
co
rre
sp
ond
to t
he fre
quen
ci
es of the
con
c
erned
cu
rre
n
t
harm
oni
cs. T
he harmoni
c
comp
en
sato
r (HC) G
hc
is d
e
fined a
s
bel
ow,
(3.4)
Comm
only; it is
de
signe
d t
o
compe
n
sate the
sele
cte
d
ha
rmo
n
ics
3
rd
, 5
th
and
7
th
, 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 tra
n
s
fer fu
nction
of the gen
era
lized
re
son
a
n
t
regulato
r
G
c
can
be
expre
s
sed a
s
:
(3.5)
Figure 11
sh
ows a mo
re d
e
tailed pi
cture of
the stan
d
a
rd
controlle
r scheme
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).
Figure 11. Standa
rd Controller Scheme
of G
c
The Bod
e
pl
ots of di
sturb
ance rej
e
ct
io
n
for the PI
and PR
co
ntrolle
rs
are
s
h
ow
n
in
F
i
gu
r
e
12
, w
h
e
r
e
:
ε
is cu
rrent
error a
nd the
grid voltag
e
V
o
is grid volt
age, con
s
ide
r
ed
as the di
sturb
ance for the system [14].
11
22
()
()
cP
I
P
h
c
s
Gs
K
K
K
G
s
s
22
3,
5
,
7
,
()
hc
Ih
hn
o
s
GK
sh
22
2
2
3,
5
,
7
,
()
()
cP
I
I
h
hn
o
ss
Gs
K
K
K
ss
h
0
()
()
re
f
o
i
s
Vs
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 714
3
– 7159
7150
Figure 12. Bode Plot of Disturban
ce
Rej
e
ction (cu
r
ren
t
erro
r ratio di
sturb
a
n
c
e
)
of the PR+HC,
P
and PR Curre
n
t Controll
ers
As it can be
obse
r
ved, a
r
oun
d the fundam
e
n
tal freque
ncy the
PR provide
s
140
dB
attenuation,
while th
e PI provide
s
o
n
ly 17dB. Mo
re
over a
r
ou
nd
the 5
th
and
7
th
harmo
nics t
he
situation
is e
v
en worst, th
e PR
attenu
ation b
e
in
g
1
25 dB
and
the PI atten
u
ation o
n
ly 8
dB.
More
over fro
m
Figu
re 1
2
, it is cl
ear
th
at the PI reje
ction
cap
abili
ty at 5
th
and
7
th
harm
oni
c
is
comp
arable
with that one
of a simple
proportio
nal
co
ntrolle
r, the in
tegral a
c
tion
being i
rrel
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 op
en loo
p
and cl
osed
loop freq
uen
cy re
sp
o
n
se
of the system
using P
R
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 Open-lo
op PR
Current Co
ntrol
System
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
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
)
7151
Figure 14. Bode Plot of Referen
c
e Sig
nal
to Gr
id Cu
rre
n
t Tran
sfer F
unctio
n
(cl
o
sed loop
)
3.3.4. The Da
mped PR Re
gulator
The PR re
g
u
lator, exhibi
t theoreticall
y
an
infinite
gain at the reso
nan
ce fre
quen
cy,
ensurin
g a n
early pe
rfe
c
t harm
oni
c eli
m
ination.
Ho
wever, the
re
alizatio
n of ideal ge
ne
rali
zed
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
dam
ped ge
ne
rali
zed integ
r
ator is propo
se
d in whi
c
h h
a
ve limited gai
n at the
resona
nce freque
ncy. Thi
s
configu
r
ati
on can
be
realized in
di
gital platform
s
with a
hig
h
accuracy an
d
,
moreove
r
, it is well suite
d
for
alleviating som
e
inst
ability proble
m
s identified
in
ideal integ
r
at
ors [16
-
1
8
].
(3.6)
Usi
ng th
e b
a
nd-p
a
ss filters G
hc1
and
G
hc
, which a
r
e
expresse
d i
n
(3.6), th
e referen
c
e
sign
al to grid
curre
n
t tran
sfer functio
n
e
x
hibits both a
large
r
ba
nd
width an
d sm
aller ma
gnitu
de
dips.
3.3.5. The Optimum Dam
p
ed PR Reg
u
lator
Figure 14
sh
ows the Bo
d
e
diag
ram
of
the refe
ren
c
e
sign
al to the
grid
cu
rrent
transfe
r
function. A flat unity gain a
nd ze
ro pha
se are ob
se
rve
d
within the freque
ncy ra
ng
e of interest. In
that
ca
se,
a good referen
c
e-sig
nal
-tra
cking cap
abilit
y is expecte
d
.
However, th
is feature force
s
the referen
c
e
signal to be
a nearly p
e
rf
ect sin
u
soida
l
waveform
with an insig
n
ificant ha
rmo
n
i
c
conte
n
t. In fact, the flat un
ity-gain an
d zero p
h
a
s
e ch
ara
c
t
e
ri
st
ic
s sug
g
e
s
t
that the grid
cu
rre
n
t
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
s
ss
n
s
h
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 714
3
– 7159
7152
Figure 15. Th
e Optimum Damped P
R
Regulato
r
Paper [1
9-2
0
]
presents
a
curre
n
t co
ntrol sc
hem
e fo
r the si
ngle
p
hase gri
d
-co
nne
cted
PV inverter with the follo
wing inte
re
sting feature
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
n
t cont
rol
scheme. Fi
g
u
re
16 sho
w
s th
e Bode di
ag
ram of refe
re
nce
sign
al to grid
curre
n
t transf
e
r functio
n
Figure 16. Bode Dia
g
ra
m o
f
Referen
c
e S
i
gnal to Grid
Curre
n
t Tran
sfer Fu
nctio
n
(clo
se
d loop
)
As expe
cted,
the referen
c
e sign
al to grid
cu
rre
nt tra
n
sfer fu
nctio
n
behave
s
a
s
a low-
band
width b
and pa
ss filter tune
d to reso
nate at
the gri
d
freq
u
ency. Note t
hat the tran
sfer
function ma
g
n
itude and p
hase are 0 d
B
and 0
◦
at
50Hz, re
spe
c
tively, which sug
g
e
s
ts that
a
good tra
c
king
capability of the fundame
n
tal grid
voltage co
mpo
n
ent is achi
eved. Moreove
r
, a
signifi
cant a
d
d
itional atten
uation i
s
ob
served in
Fi
gu
re 16
in the
shape
of the four n
a
rro
w
di
ps
that are cent
ered at fre
q
u
enci
e
s of 15
0,
250, 350,
and 450
Hz, resp
ectively. This beh
avior
confirms that
the simple and accu
rate
sync
h
r
oni
zat
i
on method u
s
ed in the propo
sed control
scheme
will not introdu
ce
the harmo
ni
c co
ntent of
the referen
c
e
signal into t
he grid
cu
rre
nt.
More
over; the Bode plots of disturba
n
c
e rej
e
ctio
n
for the optimum dampe
d PR
regul
ator
co
n
t
rollers i
s
th
e sa
me a
s
Figure 12. T
hus it i
s
d
e
m
onst
r
ated t
he optim
um
PR
controlle
r ha
s sa
me supe
riority in term
s of harm
oni
c cu
rrent rej
e
ction. Mea
n
while; it is wo
rth
mentionin
g
that the PLL-based sy
n
c
h
r
oni
zing al
go
rithm is n
o
t use
d
in this
system
with the
optimum da
mped
P
R
reg
u
lator, so
th
e
com
putatio
n
a
l loa
d
is ne
ce
ssarily lo
wer d
ue to
wit
hout
p
r
oc
es
s
i
n
g
time
r
e
qu
ir
ed
to
c
o
mpu
t
e the PLL synchronizi
ng algo
ri
thm.
0
()
()
re
f
o
i
s
Vs
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