Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
7, N
o
. 1
,
Mar
c
h
20
16
,
pp
. 66
~74
I
S
SN
: 208
8-8
6
9
4
66
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
/
IJPEDS
Perform
a
nce and Hi
gh Robustness
DPC f
o
r PWM Recti
f
ier
under Unstable V
DC
Bus
M
.
S. D
j
ebbar*
, H.
Bena
lla**
* Faculty
of
Eng
i
neer
ing Sciences, on
Electrical
Laborator
y
,
University
of
Tebes
s
a, Ager
ia
** Faculty
of
En
gineer
ing Sciences, on
Electr
i
cal
Laborator
y
,
University
Constantine1, Ag
eria
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Sep 28, 2015
R
e
vi
sed Dec 5,
2
0
1
5
Accepte
d Ja
n
3, 2016
This paper prop
oses a strateg
y
de c
ontrolling a static AC / D
C
converter
based on direct power control (
D
PC).
The insta
n
taneous ac
tiv
e and rea
c
tiv
e
power is contro
lled in such
a
wa
y
to
ensure
the PW
M rectif
ier with a
sinusoidal current absorption.
This cont
rol has
proven effectiv
e in terms of
reduction of to
tal harmonic distortion (T
HD) of
curren
t
absorbed. Offers
a
good control of
active and re
active power with an operation
at u
n
itar
y
power
factor
. The
test
of robustness carried
out and
th
e results have p
r
oven DPC
good perform
an
ce with
strong p
o
ssibilit
y
of d
e
integr
ate
it
into
the fi
eld of
high voltage and
high power
as
e
l
ec
tric
tr
act
ion.
Keyword:
Di
rect
po
wer
c
ont
rol
Power qu
ality
Pu
lse wid
t
h
mo
du
latio
n
Pwm
rectifier
Tot
a
l
ha
rm
oni
c di
st
o
r
t
i
o
n
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
oham
e
d Sal
a
h
Dje
b
bar
,
Facu
lty of En
gin
eering
Scien
ces,
on Electrical Laborat
o
ry,
Uni
v
ersity
of Tebessa
, Algeria,
C
onst
a
nt
i
n
e R
o
ad
, Te
bessa
1
2
0
0
2
,
Al
ge
ri
a.
Em
a
il: d
j
ebb
a
rcn
@
yah
o
o
.
fr
1.
INTRODUCTION
The
p
r
i
n
ci
pl
e
of
di
rect
co
nt
r
o
l
w
a
s
pr
o
pose
d
by
[
1
]
a
n
d
w
a
s l
a
t
e
r
devel
o
ped
f
o
r m
a
ny
appl
i
cat
i
o
ns
.
The
ob
ject
i
v
e
was t
o
el
i
m
i
n
at
e t
h
e bl
oc
k
of
m
odul
at
i
o
n a
n
d i
n
ner l
o
o
p
s
by
re
pl
aci
ng
a
swi
t
c
hi
n
g
t
a
bl
e wi
t
h
in
pu
ts erro
rs of activ
e an
d reactiv
e po
wer.
The fi
rst
ap
pl
i
cat
i
on de
vel
o
p
e
d was t
h
e co
nt
r
o
l
of
an electrical
m
achine, th
e control structure wa
s
kn
o
w
n
u
nde
r t
h
e n
a
m
e
C
ont
rol
Di
rect
T
o
rq
ue (
D
i
r
ect
T
o
r
que C
o
nt
r
o
l
,
D
T
C
)
.
In t
h
i
s
ca
se, t
h
e c
o
nt
rol
st
at
o
r
fl
u
x
a
n
d
t
h
e el
ect
rom
a
gnet
i
c
t
o
r
que
o
f
t
h
e
m
achi
n
e
wi
t
h
o
u
t
any
m
odul
at
i
o
n
bl
oc
k
[2]
.
The
n
, a sim
i
l
a
r t
echni
que cal
l
e
d Di
rect
Po
wer C
o
nt
r
o
l
(
D
i
r
ect
Po
wer
C
ont
r
o
l
,
D
P
C
)
was pr
o
pose
d
b
y
[4
] and
d
e
velo
p
e
d
later
b
y
[5
]
for a PWM rectifier co
ntro
l ap
p
lication
in ord
e
r t
o
i
m
p
r
o
v
e
t
h
e
q
u
ality o
f
the energy electrical network. In th
is case
,
the controlled variables are
the in
stan
tan
e
o
u
s activ
e an
d
reactive
po
we
r.
Th
us, th
ere are two
d
i
fferen
t
typ
e
s o
f
po
wer
d
i
rect co
n
t
ro
l stru
ctu
r
es
p
r
op
o
s
ed in
th
e literatu
re. On
t
h
e
o
n
e ha
nd
, refe
rences
[
4
]
,
[5]
pre
s
ent
a
no
n
l
i
n
ea
r
c
o
n
t
rol
vari
abl
e
s
w
i
t
c
hi
n
g
fre
qu
ency
, bet
t
e
r k
n
o
w
n
un
de
r t
h
e
nam
e
DPC
cl
assi
c,
on t
h
e ot
her
ha
nd i
n
[
6
]
,
t
h
e a
u
t
h
or
pr
o
p
o
s
es
t
o
associ
at
e t
h
e pri
n
ci
pl
e D
P
C
wi
t
h
a p
u
l
s
e
wi
dt
h
of
vect
or
m
odul
at
i
o
n
(S
VM
)
i
n
or
de
r t
o
obt
ai
n a c
o
nst
a
nt
swi
t
c
hi
n
g
fre
q
u
ency
wi
t
h
o
u
t
t
h
e
us
e
of
a s
w
i
t
c
hi
n
g
t
a
bl
e.
Tw
o t
echni
que
s fo
r pe
rf
orm
i
ng t
h
e cal
cul
a
t
i
on
of i
n
st
a
n
t
a
neo
u
s
po
wer
wi
t
h
o
u
t
sen
s
o
r
s have
be
e
n
pr
o
pose
d
.
Th
e fi
rst techniq
u
e
p
r
op
o
s
ed
in
th
is p
a
p
e
r
will b
e
th
e subj
ect of our work
[4
], [7
], [8
] esti
m
a
tes th
e
main
s v
o
ltag
e
s fro
m
th
e v
a
lu
es
o
f
th
e vo
ltag
e
o
f
th
e con
v
e
rter and
the RL filter (V-DPC
) and
estab
lish
co
nfigu
r
ation
s
DPC b
a
sed
o
n
th
e
po
sition
o
f
th
e
vo
ltag
e
v
e
cto
r
in
t
h
e
statio
n
a
ry
α
-
β
re
fer
e
nce.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
:
66
–
7
4
67
The sec
o
nd
t
echni
que
,
devel
o
ped
i
n
[5]
,
[
6
]
,
[9]
,
[
10]
, t
h
e
aut
h
ors
p
r
o
p
o
s
e
t
h
e est
i
m
ati
on
of
vi
rt
ual
flux
as a m
e
th
o
d
fo
r esti
m
a
ti
n
g
n
e
t
w
ork voltag
e
s fro
m
th
e vo
ltag
e
s
o
f
t
h
e con
v
e
rter and
th
e R
L
filter, (VF-
DPC)
.
Thi
s
c
ont
rol
s
t
rat
e
gy
ass
u
re
s dec
o
u
p
l
e
s c
ont
ro
l
o
f
activ
e an
d reactive po
wer,
wh
ile ab
so
rb
i
ng
sin
u
s
o
i
d
a
l curren
ts, en
su
ring
o
p
e
ration
o
f
t
h
e PW
M Rectifier as a clean
en
erg
y
qu
ality with
v
e
ry l
o
w THD
and power fact
or equal to unity [11].
We no
te at th
e en
d
,
t
h
at th
e essen
tial ai
m
o
f
th
is work
is h
i
g
h
ligh
t
ed
t
h
e im
p
o
r
tan
ce of th
is strateg
y
in
term
s o
f
qu
ality o
f
electric
p
o
wer an
d in
t
e
rm
s o
f
rob
u
stn
e
ss
p
r
ov
en
b
y
th
e
h
i
gh
p
e
rform
a
n
ce d
e
v
e
l
o
p
e
d.
2.
PRINCIPLE FUNCTIONING OF
THE
DPC
The (DPC) is
base
d on the direct control of ac
tive and
reactive powe
r in
a PW
M rectifier. Th
e
errors
betwee
n the refere
nce
values
of the instanta
neous a
c
tive and r
eact
ive powe
r and their
m
easure
s
are
in
trodu
ced in
t
w
o h
y
steresis
co
m
p
arato
r
s,
wh
ich
d
e
term
ine,
usi
n
g a s
w
i
t
chboard a
n
d t
h
e
value
of the
sector
whe
r
e t
h
e m
a
ins v
o
l
t
a
ge a
r
e l
o
cat
ed, t
h
e s
w
i
t
c
hi
ng
st
at
us
of
t
h
e sem
i
condu
ct
or. T
h
e
v
o
l
t
a
ge'
s
l
o
o
p
o
f
t
h
e
DC
bus
i
s
a
d
just
e
d
wi
t
h
a P
I
c
o
rr
ect
or,
i
n
o
r
de
r
t
o
c
ont
ro
l t
h
e er
ro
r b
e
t
w
een t
h
e sen
s
ed
vo
ltag
e
(
c
on
tinu
ous)
an
d
its refere
nce
.
The
refe
rence
reactive
power is directly impos
ed ze
r
o
f
o
r
a cu
rre
nt
'
s
si
nus
oi
dal
abs
o
r
p
t
i
o
n
o
n
a
sou
r
ce
vol
t
a
ge
su
pp
ose
d
t
o
b
e
si
nus
oi
d
a
l
,
i
n
o
r
der e
n
s
u
re
th
e
ru
nn
ing
of
th
e rectifier with
a u
n
itary p
o
wer
factor.Figure (1) s
h
ows the
ov
erall con
f
i
g
uratio
n
of th
e d
i
rect co
n
t
ro
l o
f
p
o
wer app
lied
to
th
e rectifier. It is
anal
o
g
o
u
s
t
o
t
h
at
of
t
h
e
di
rect
t
o
r
que
co
nt
r
o
l
(DTC
)
of
i
n
du
ct
i
on m
achi
n
es
[
12]
,
[
13]
.
Fi
gu
re
1.
P
W
M
rect
i
f
i
e
r c
o
n
t
rol
bl
oc
k
on
t
h
e net
w
o
r
k
(cl
a
s
s
i
cal
DPC
)
The t
e
nsi
o
n an
d t
h
e so
urce cu
rre
nt
s are
m
easure
d
an
d t
r
ans
f
orm
e
d by
t
h
e C
onc
or
di
a m
a
tri
x
, i
n
o
r
de
r t
o
m
ove
fr
om
a three-
p
h
ase
refe
renc
e
to a
fixe
d tw
o-
pha
se re
fre
nce.
(
α
,
β
).
c
b
a
v
v
v
v
v
2
3
2
1
2
3
2
1
0
1
3
2
c
b
a
i
i
i
i
i
2
3
2
1
2
3
2
1
0
1
3
2
(1
)
The
network
voltage is estimated by t
h
e e
xpression
(2)
dt
di
L
S
V
e
c
b
a
c
b
a
dc
c
b
a
,
,
,
,
,
,
.
(2
)
Th
e calcu
latio
n
o
f
th
e
po
wers, in
stan
tan
e
o
u
s activ
e an
d reactiv
e, is
g
i
v
e
n b
y
th
e fo
llowin
g
equ
a
tion
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Perfo
r
man
ce
an
d Hi
g
h
Ro
bu
stn
e
ss
DPC for
PWM Rectifier un
d
e
r Un
st
a
b
l
e V
DC
Bus
(M.S.
D
j
eb
ba
r)
68
a
c
c
a
b
a
c
a
c
b
c
b
a
dc
c
c
b
b
a
a
c
c
b
b
a
a
dc
i
dt
di
i
dt
di
L
i
i
S
i
i
S
i
i
S
U
q
i
dt
di
i
dt
di
i
dt
di
L
i
S
i
S
i
S
V
p
.
.
3
3
1
)
.
.
.
(
.
.
.
(3
)
Th
e
kn
owledge of th
e estim
a
t
ed
v
o
ltag
e
secto
r
is req
u
i
red
to
determ
in
e th
e
o
p
tim
al switch
i
n
g
statu
s
es. Fo
r
th
is, th
e
work p
l
an
(
α
,
β
) i
s
di
vi
ded i
n
t
o
12
sect
or
s.
These l
a
t
t
e
r c
a
nbe
de t
e
rm
i
n
ed by
t
h
e f
o
l
l
o
wi
n
g
rel
a
t
i
ons
hi
p:
[6
]
6
)
1
(
6
)
2
(
n
n
n
(4
)
Whe
r
e:
n= 1…
12
,
n i
s
t
h
e n
u
m
b
er of t
h
e sect
o
r
i
n
st
ant
a
ne
o
u
sl
y
det
e
rm
i
n
ed b
y
t
h
e t
h
e vol
t
a
ge vect
or'
s
pos
i
t
i
on w
h
i
c
h i
s
gi
ve
n
by
:
)
(
v
v
Arctg
(5
)
Fi
gu
re 2.
Pl
an
(
α
,
β
) di
vi
de
d
i
n
t
o
1
2
sect
ors
3.
CO
NTR
O
L O
F
DI
RECT
V
O
LTAGE
(V
DC
)
Co
m
p
arin
g
th
e in
stan
tan
e
o
u
s
activ
e p
o
w
er at a referen
ce
p
o
wer, th
is latter is o
b
t
ain
e
d b
y
th
e DC
v
o
ltag
e
co
n
t
rol b
l
o
c
k
at th
e cap
acito
r termin
als, wh
ere
we u
s
e a PI co
ntro
ller (Propo
rtio
n
a
l, in
tegrato
r
) t
o
cont
rol
t
h
e e
r
r
o
r
bet
w
een
t
h
e
sense
d
vol
t
a
ge
(co
n
t
i
n
uo
us
) a
n
d
re
fere
nce.
Wh
ilst to ach
iev
e
a
un
ity p
o
wer fact
o
r
, reactiv
e
powe
r re
ference is
directly im
pose
d
zero
.
Fi
gu
re
3.
Det
e
r
m
i
n
at
i
on o
f
p
o
w
ers
e
r
r
o
rs
(
Δ
p,
Δ
q)
Fig
u
re
4
.
Direct Vo
ltag
e
regu
latio
n
with
PI co
rrector
Fi
gu
re
4 s
h
ow
s t
h
e
reg
u
l
a
t
i
o
n
of t
h
e
DC
v
o
l
t
a
ge
by
a P
I
cont
rol
l
e
r.
T
o
cont
rol
t
h
e cl
o
s
ed l
o
o
p
sy
st
e
m
, it
i
s
necessa
ry to choose the c
o
e
f
ficients
k
p
an
d ki
, in
th
is case we u
s
e t
h
e im
p
o
s
itio
n
m
e
t
h
od
o
f
th
e
po
les [6
]
,
[1
4]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
:
66
–
7
4
69
2
2
n
i
n
p
C
k
C
k
(6
)
4.
HYSTE
R
ESIS
CONT
ROL AND SWIT
CHING
TABL
E
The
hysteresis
control is t
o
keep active a
n
d reac
tiv
e in
st
an
tan
e
o
u
s power in
a
d
e
sired b
a
n
d
. Th
is
cont
rol
i
s
base
d o
n
t
w
o c
o
m
p
arat
ors t
h
at
u
s
e as i
nput
t
h
e erro
r si
g
n
al
bet
w
ee
n t
h
e r
e
fere
nce val
u
e
s
and
estim
a
ted values of active a
n
d reactiv
e power.
If t
h
e error
is growi
n
g and r
eache
d
t
h
e top level, t
h
e
hysteresis
co
n
t
ro
l ch
ang
e
s its o
u
t
pu
t to
'1
', o
n
t
h
e co
n
t
rary if th
e erro
r
sig
n
a
l reach
e
s
th
e lo
wer
b
a
nd, th
en
t
h
e
o
u
t
pu
t will
be s
w
i
t
c
he
d t
o
'
0
'
.
0
1
0
1
Sq
Sq
Sp
Sp
hq
q
q
hq
q
q
hp
p
p
hp
p
p
ref
ref
ref
ref
(7
)
The
dynam
i
cs of active a
n
d reactive
p
o
w
e
r can be gi
ve
n
as
f
o
l
l
o
ws
:
)
.
.
(
1
)
.
.
(
1
)
(
1
2
2
e
e
e
e
u
e
u
e
L
dt
dq
u
e
u
e
L
e
e
L
dt
dp
(
8
)
T
h
e
sy
nt
hesi
s
of
t
h
e
swi
t
c
hi
n
g
t
a
bl
e
i
s
base
d
o
n
t
h
e
si
g
n
s
o
f
de
ri
vat
i
v
es
of
act
i
v
e
an
d
react
i
v
e
po
we
r
in each sector. For each sector, the c
h
a
nge
of t
h
e reactive
powe
r is positive
for thre
e ve
ctors,
ne
gative
for three
vecto
r
s, a
nd ze
ro
fo
r V
0
, V
7
.
Th
e sign
o
f
chan
g
e
i
n
th
e acti
v
e power is
p
o
sitiv
e for fo
ur
v
ectors,
n
e
g
a
ti
v
e
fo
r t
w
o
or three
vectors. For e
x
am
ple, for th
e
first
sector, t
h
e ve
ctors that influence the si
gn
of c
h
a
nge
of a
c
tive and
reactiv
e
p
o
wer are su
mm
arize
d
in th
e
fo
llo
wi
n
g
tab
l
e
[15
]
:
Table 1.
First sector of
c
h
ange
of
active
a
n
d réactive powe
r
0
p
0
p
0
q
0
q
0
p
V
3
, V
4,
V
5
, V
0
V
1
, V
6
V
1,
V
2
, V
3
V
4,
V
5
, V
6
V
0
, V
7
Th
e sw
itch
i
ng
tab
l
e pr
opo
sed
f
o
r
all sect
o
r
s
is
p
r
e
s
en
t
e
d
in
th
e
t
a
b
l
e
b
e
lo
w
Tabl
e 2.
Al
l
se
ct
ors swi
t
c
hi
ng
t
a
bl
e
5.
SIM
U
LATI
O
N
AN
D I
N
TE
RPRET
A
TIO
N
Th
e sim
u
latio
n
was
p
e
rformed
to
con
f
irm
th
e th
eoretical stu
d
y
o
f
th
e
rectifier in
stati
c
m
o
d
e
an
d
check the
dyna
mic perform
a
nce of th
e con
t
ro
l of
po
wers. Param
e
ters u
s
ed in
sim
u
latio
n
are as
fo
llo
ws:
p
S
q
S
1
2
3
4
5
6
7
8
9
10
11
12
1 0
V
5
V
5
V
6
V
6
V
1
V
1
V
2
V
2
V
3
V
3
V
4
V
4
1 1
V
3
V
3
V
4
V
4
V
5
V
5
V
6
V
6
V
1
V
1
V
2
V
2
0 0
V
6
V
1
V
1
V
2
V
2
V
3
V
3
V
4
V
4
V
5
V
5
V
6
0 1
V
1
V
2
V
2
V
3
V
3
V
4
V
4
V
5
V
5
V
6
V
6
V
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Perfo
r
man
ce
an
d Hi
g
h
Ro
bu
stn
e
ss
DPC for
PWM Rectifier un
d
e
r Un
st
a
b
l
e V
DC
Bus
(M.S.
D
j
eb
ba
r)
70
Power source:
RMS Vo
ltag
e
V
=
23
0 V
Frequency
f =
5
0
Hz
Inter
n
al
resisto
r
Rs =
1
m
Ω
,
Internal induct
or Ls
= 0.
1
m
H
Filter RL :
L
f
=14 m
H
, R
f
= 1.
5
Ω
Rectifier :
Three
-
phase
b
r
idge rectifier (
P
D
3
)
t
o
IGBT
Loa
d
:
Stora
g
e ca
pacity C=2m
F
Voltage
Refe
re
nce
V
DC
-ref
=
600 V
Ohm
i
c load
(R= 100
Ω
),
Inductiv
e lo
ad
(R=4
5, L =
5
0
m
H
)
, Cap
acitiv
e l
o
ad
(R=10
0
Ω
,
C
=
20
0
μ
F)
.
PI c
o
nt
rol
l
e
r
p
a
ram
e
t
e
rs and
hy
st
eresi
s
reg
u
l
at
ors:
Sam
p
l
i
ng fre
q
u
ency
C
o
nt
rol
l
er P
I
:
fe
=
10
0
kHz
B
a
nd
wi
dt
h of
hy
st
eresi
s
reg
u
l
at
ors:
h
p
= 1
μ
W, h
q
= 1
μ
VA
R
PI c
o
ntroller
p
a
ram
e
ters
: k
i
= 2
5
,
k
p
= 1
5.
1.
Perfor
mance
of the
DPC During
the
V
a
ri
ati
o
n
o
f
the D
C
Bus
All th
e
figu
res wh
ich fo
llows, sh
ows th
e respo
n
s
e
of t
h
e rectifier con
t
ro
lled
b
y
th
e
DPC wh
en
a
chan
ge
o
f
t
h
e
r
e
fere
nce
of
t
h
e
DC
b
u
s
vol
t
a
g
e
fr
om
60
0
V t
o
80
0
V
by
a
fi
xed
st
ep
o
f
10
0
V i
n
t
h
e
m
o
m
e
nt
s:
0.
4sec
on
ds a
n
d
0.
7sec
o
nds
.
Th
e v
a
l
u
e of
the r
e
f
e
r
e
n
ce th
en
d
e
scend
s
550 V
at ti
m
e
t =
1
s
eco
n
d
s
an
d
t
h
en
it go
es up
to
th
e v
a
lu
e
of 8
5
0
V st
art
i
ng f
r
o
m
t
= 1.6 seco
nd
s (fi
g
u
re 5
)
. T
h
e l
o
ad at
t
h
e out
p
u
t
of t
h
e rect
i
f
i
e
r i
s
of t
h
e i
nduct
i
v
e
typ
e
(R =
45
Ω
;
L =
5
0
m
H
),
r
e
m
a
i
n
s co
nst
a
n
t
du
ri
n
g
t
h
e
var
i
at
i
on o
f
V
DC
.
Fi
gu
re 5.
V
DC
an
d Ref
e
r
e
n
c
e
V
o
ltag
e
dur
ing an
ad
ju
sted
v
a
r
i
atio
n 600
V to
850
V
Fig
u
re
6
.
Vo
ltag
e
an
d lin
e cu
rren
t i
n
th
e in
terv
al Tim
e
0.
3s - 0.
8s
Th
is
v
a
riation
d
u
ring
t
h
e simu
latio
n ti
m
e
d
o
e
s
no
t affect
th
e qu
ality of t
h
e si
g
n
a
ls of t
h
e electrical
q
u
a
n
tities.It is
n
o
t
ed
th
at t
h
e
DPC
p
r
ov
id
es
a p
e
rsisten
t
con
t
ro
l du
ri
n
g
d
i
stu
r
b
a
n
c
es
o
f
t
h
e
DC bu
s
vo
ltag
e
,
des
p
i
t
e
t
h
ese
di
st
ur
ba
nces, t
h
e fi
gu
res
(6
and
7
)
s
h
o
w
t
h
at the s
o
urce
curre
n
t ha
s
a
sinusoi
d
al shape that
changes i
n
amplitude i
n
accorda
n
ce
with the refe
rence c
h
a
nge
s, harm
onic
distortion of
t
h
e curre
nt (Figure
8),
h
a
v
e
v
e
ry l
o
w v
a
l
u
e (1
.53
%
),
wh
ich
prov
i
d
es a cl
ean power source
for electric power
q
u
a
lity and
u
n
ity
po
we
r fact
or
(
F
i
g
u
r
e
9)
.
0
0.
5
1
1.5
2
0
100
200
300
400
500
600
700
800
900
1000
T i
m
e (
s
)
D
i
r
e
c
t
V
o
l
t a
g
e
(
V
)
V d
c
ref
V d
c
0.
3
0.
3
5
0.
4
0.
4
5
0.
5
0.
5
5
0.
6
0.
6
5
0.
7
0.
75
0.
8
-50
0
-40
0
-30
0
-20
0
-10
0
0
10
0
20
0
30
0
40
0
T
i
m
e
(
s
)
L
i
n
e
V
o
l
t
a
g
e
( V
)
L
i
n
e
C
u
r
r
e
n
t ( A
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
:
66
–
7
4
71
Fi
gu
re
7.
Zo
o
m
C
u
rrent
l
i
n
e
and
V
o
l
t
a
ge i
n
t
h
e
in
terv
al
o
f
time 0.75
s -
0
.
9
s
Fi
gu
re
8.
Tot
a
l
Ha
rm
oni
c Di
s
t
ort
i
o
n
of t
h
e l
i
ne
current
The instanta
ne
ous active and reactive powe
r follow
their
im
posed re
fere
nces with m
i
n
i
m
a
l erro
r
(Figure
s
10,
11 and 12),
whi
l
e the reactive powe
r is al
ways zero
.
By analyzin
g
th
e resu
lts, it is d
e
termin
ed
th
at th
e
D
P
C
pr
ov
id
es a
g
ood d
y
n
a
m
i
c o
f
the syste
m
an
d
keep
s its rob
u
stn
e
ss
d
e
sp
ite the i
m
p
o
s
ed
d
i
sup
tio
ns
on
the
refe
re
nc
e o
f
the
DC
b
u
s
.
Fi
gu
re 9.
Powe
r Fact
or
Figure 10.
Activ
e an
d Reactive po
wer
d
e
p
e
nd
ing
o
n
the va
riation
o
f
the
refe
rence
V
DC
Figu
re 1
1
. In
stantane
ou
s Active
P
o
wer
P (
W)
a
n
d
Refere
nce
(
P
re
f) d
u
ri
ng
the v
a
riation V
DC
Fi
gu
re 1
2
. In
st
ant
a
ne
ou
s
R
e
a
c
t
i
v
e
Po
we
r q
(
VAR
)
and
Refe
rence
(q
re
f
)
du
ri
n
g
t
h
e va
ri
at
i
on
V
DC
0.
75
0.
8
0.
8
5
0.
9
-500
-400
-300
-200
-100
0
100
200
300
400
T i
m
e
(
s
)
L
i
n
e V
o
l
t
a g e ( V
)
L
i
n
e C
u
r r e n
t
( A
)
0
5
10
15
20
25
0
10
20
30
40
50
60
70
80
90
10
0
R
a
n
k
H a
r
m
o
n
i
c
s
T
H
D I
=
1.
53
%
0
0.
5
1
1.5
2
2.
5
0
0.2
0.4
0.6
0.8
1
1.2
T i
m
e
(
s
)
0
0.5
1
1.
5
2
-5
000
0
5
000
10
000
15
000
20
000
T i
m
e
(
s
)
A
c
t
i
v
e
p o
w
e r
P
(
W
)
R
e a c
t
i
v
e
p o
w
e
r
Q
(
V
A
R
)
0
0.
5
1
1.
5
2
-4
-2
0
2
4
6
8
10
12
x 1
0
4
T
i
m
e
(
s )
I
n
s
t a
n
t a
n
e
o
u
s A
c
t i
v e
P
o
w
e
r
p
(
W
)
p
- ref
( W
)
p
( W
)
0
0.5
1
1.
5
2
-0
.
5
0
0.
5
1
1.
5
2
2.
5
3
3.
5
x 1
0
4
T
i
m
e
( s )
I
n
s
t a
n
t
a
n
e
o
u
s
R
e
a
c
t
i
v
e
P
o
w
e
r
q
q-
re
f
( V
A
R
)
q
(
VAR
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Perfo
r
man
ce
an
d Hi
g
h
Ro
bu
stn
e
ss
DPC for
PWM Rectifier un
d
e
r Un
st
a
b
l
e V
DC
Bus
(M.S.
D
j
eb
ba
r)
72
5.
2. Perf
orm
a
nces of the
DP
C Duri
n
g
a
L
o
a
d
Vari
ati
o
n
Fi
gu
re
1.
3
V
d
c
v
o
l
t
a
ge a
n
d
V
d
c_
ref
d
u
r
i
n
g a
n
l
o
a
d
Ch
ang
e
A
t
time t = 0.25
s an
d t = 0.75
s for
V
DC
=
60
0 V
Fi
gu
re
1
4
.
V
o
l
t
a
ges a
n
d l
i
n
e c
u
r
r
ent
For
a DC
vol
t
a
ge V
DC
=
6
0
0
V m
a
in
tain
ed
co
nstan
t
.
At
first ti
m
e
, th
e rectifier feed
s an
i
n
du
ctiv
e lo
ad
with
a
val
u
e R
= 4
5
Ω
; L = 5
0
m
H, we add
in
p
a
rallel in
th
e seco
nd
tim
e
t = 0
.
25
seco
nd
s, a
cap
acitiv
e lo
ad v
a
lu
e
(R
=
10
0
Ω
, C
= 200
μ
F), t
h
e
we ad
d at th
e ti
me t = 0
.
7
5
s a
resistiv
e lo
ad
of R =
10
0
Ω
.
It can
b
e
seen
fro
m
Fig
u
r
es (1
3, 14
,
1
5
) th
at d
e
sp
ite th
e variatio
n
of th
e
lo
ad
th
e
DC vo
ltag
e
is con
s
tan
t
, th
e
cur
r
ent
a
n
d t
h
e
v
o
l
t
a
ge s
o
urce
ha
ve a
si
n
u
soi
d
al
s
h
ape
and
have
a ze
ro phase shi
f
t. T
h
e a
c
tive powe
r e
v
olve
s
in
am
p
litu
d
e
with
th
e ch
an
g
e
o
f
th
e l
o
ad
,
while the reactive
powe
r is alway
s
zero.
Fig
u
r
e
15
.
A
c
tiv
e an
d Reactive po
w
e
r
du
r
i
ng th
e
change l
o
ad at
tim
e
t = 0.25 s
and t =
0.75s
for
V
DC
= 60
0 V
Figure
16. C
h
a
nge
the l
o
ad at
tim
e
t = 0.
25
s f
o
r
V
d
c =
6
0
0
V
an
d at ti
m
e
t = 0.75
s
f
o
r
V
DC
= 70
0V
5.
3. Perf
orm
a
nces of the
DP
C Duri
n
g
an Vari
ati
o
n of
t
h
e
D
C
B
u
s an
d
the
L
o
ad
It
i
s
n
o
t
e
d
fr
o
m
Fi
gures (
1
6,
1
7
,
18
) t
h
at
t
h
e passa
ge
of
t
h
e co
nt
i
n
u
o
u
s
v
o
l
t
a
ge
of
6
0
0
V t
o
7
0
0
V
at
ti
m
e
t = 0
.
5
s
an
d
t
h
e ch
an
g
e
o
f
th
e l
o
ad
to
t
h
e in
stan
t t = 0.25
s (R = 100
Ω
, C = 200
μ
F)
and t
= 0.
7
5
s
(R
=
10
0
Ω
), does
not affect the perform
a
n
ce of the DPC since the reactive
po
wer is always zero, the
current
main
tain
s its sh
ap
esinu
s
o
i
d
a
l an
d
evo
l
v
e
s
with
ch
an
ging load a
nd
Vdc, the curre
nt
pha
se shift / s
o
urce
vol
t
a
ge
i
s
ze
ro
,
an
d a
u
n
i
t
a
ry
po
we
r fact
or
.
The active
power am
plitude naturally reacts w
ith t
h
e load
current
draw a
n
d inc
r
eased V
DC
.
0
0.
1
0.
2
0.
3
0.4
0.5
0.
6
0.
7
0.
8
0.
9
1
0
100
200
300
400
500
600
700
T i
m
e
(
s
)
V d
c
re
f
(
V
)
V
d
c
(
V
)
0.65
0.
7
0.75
0.8
0.
85
-
400
-
300
-
200
-
100
0
10
0
20
0
30
0
40
0
50
0
T
i
m e
( s
)
L
i
n
e
V
o
l
t
a
g
e
(
V
)
L
i
n
e
C
u
r r
e
n
t
( A
)
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
-1000
0
1000
2000
3000
4000
5000
6000
7000
T i
m
e
(
s
)
A
c
t
i
v
e p o
w
e r ( W
)
R
e a c
t
i
v
e p o
w
e r ( V
A
R
)
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
0
10
0
20
0
30
0
40
0
50
0
60
0
70
0
80
0
T i
m
e
(
s
)
V d
c
re
f
( V
)
V
d
c
(
V )
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
:
66
–
7
4
73
Fig
u
re
17
.
Vo
ltag
e
an
d lin
e cu
rren
t
du
ri
n
g
th
e
vari
at
i
o
n
of
t
h
e l
o
a
d
a
n
d
V
DC
Fi
gu
re 1
8
. Act
i
v
e
a
n
d
R
eact
i
v
e
p
o
we
r de
pen
d
i
n
g on
th
eVariatio
n
l
o
ad
at tim
e t = 0
.
25
s
and
t = 0.7
5
s
fo
r
a V
DC
=
6
0
0
V
an
d
70
0
V
5.4. Comment
It rem
a
in
s to
p
o
i
n
t
ou
t at th
e en
d
th
at th
is su
bj
ect was ad
dressed
in
a way to
co
n
f
i
r
m
w
h
at h
a
s b
e
en
achi
e
ve
d by
t
h
e aut
h
o
r
s [
4
]
,
[5]
,
[
8
]
by
ad
di
n
g
a cont
ri
b
u
t
i
on
fr
om
us
whi
c
h i
s
t
o
im
pl
em
ent
t
echni
cal
of
co
n
t
ro
l
(DPC) h
i
g
h
p
e
rfo
r
man
ce, ch
aracterized
b
y
its robu
stn
e
ss, efficien
cy an
d stab
ility. Th
ese
per
f
o
r
m
a
nces were ac
hi
eve
d
and co
n
f
i
r
m
e
d t
h
r
o
ug
h t
h
e
vari
o
u
s di
st
u
r
ba
nces cr
eate
d
around the energy
sy
st
em
, by
changi
ng t
h
e l
o
a
d
and t
h
e
bus
vol
t
a
ge V
DC
. It remain
s to
b
e
said
th
at th
is work
is ch
aracterized
b
y
a co
nt
i
n
u
o
u
s
b
u
s
un
st
abl
e
ref
e
rence
d
u
ri
ng
t
h
e
vari
ous
t
e
st
ed
pr
o
pose
d
i
n
t
h
i
s
w
o
rk
,
wh
i
c
h i
s
di
ffe
rent
fr
om
t
h
e
de
vel
o
pe
d researc
h
w
o
r
k
and
de
vel
o
pe
d by
t
h
e
a
u
t
h
o
r
s m
e
nt
i
oned
a
b
o
v
e.
6.
CO
NCL
USI
O
N
The
DPC ca
n
cont
rol the ene
r
gy e
x
cha
n
ge
betwee
n
th
e rectifier and
th
e
electrical n
e
twork with a
po
we
r fact
o
r
equal
t
o
uni
t
y
wi
t
h
o
u
t
usi
ng
a vol
t
a
ge /
cu
r
r
ent
sen
s
o
r
.T
hi
s t
echni
q
u
e rel
i
es on co
nt
r
o
l
l
o
o
p
s
of
th
e in
stan
tan
e
o
u
s
po
wer and
no
t th
ose curren
t
s.Sim
u
lati
on
res
u
l
t
s
obt
ai
ned i
n
t
h
i
s
wo
rk s
h
ow
ed
t
h
at
t
h
e
di
rect
p
o
w
er c
ont
rol
of
gua
ra
nt
ee rel
i
a
bl
e c
ont
rol
,
st
a
b
l
e
and
ro
b
u
st
wi
t
h
hi
g
h
dy
nam
i
c
per
f
o
r
m
a
nce, d
e
spi
t
e
th
e d
i
srup
tion
s
th
at h
a
s suffered
t
h
e PWM
rectifier.Spect
ral analysis of
th
e lin
e cu
rren
t ob
tain
ed
b
y
th
is
co
n
t
ro
l strategy sh
ows t
h
at all h
a
rm
o
n
i
cs are attenu
ated
,
resu
ltin
g
i
n
a
very lo
w THD
v
a
lu
e
o
f
1.53%, well
b
e
low th
e v
a
l
u
es im
p
o
s
ed
b
y
in
tern
ation
a
l
no
rm
s (5
%).
The DPC provides
a quic
k
calcula
t
i
on
of
i
n
st
ant
a
ne
o
u
s
po
we
r t
h
at
al
l
o
ws
o
b
t
a
i
n
i
n
g
a ve
ry
hi
g
h
dy
nam
i
cs of t
h
e sy
st
em
. It
i
s
al
so
c
h
aracteri
zed by
sim
p
lic
ity,
not using ne
sted
loop
s
(
not tr
an
sf
or
m
a
tio
n
s
of
coo
r
di
nat
e
d
,
n
o
t
m
odul
at
o
r
)
.
The
resul
t
s
ob
t
a
i
n
ed a
r
e ve
r
y
pr
om
i
s
i
ng and
hi
gh
pe
rf
or
m
a
nce, w
h
i
c
h
ena
b
l
e
s t
h
i
s
t
echni
que
t
o
(DPC
), occ
upi
ed
a place of very
adva
nced Am
ong
t
h
e
te
c
hni
que
s used to im
prove power quality and
clean up
the electrical network
The Pe
rf
orm
a
nce de
vel
o
pe
d
by
t
h
e D
P
C
du
ri
n
g
t
h
e
var
i
ous t
e
st
s o
f
r
o
b
u
st
ness,
has
gi
ve
n t
o
t
h
i
s
t
echni
q
u
e
an
i
m
port
a
nt
pl
ace
i
n
t
h
e
fi
el
d
of
hi
g
h
vol
t
a
ges a
n
d
l
a
r
g
e
po
we
r
suc
h
a
s
el
ect
ri
c t
r
act
i
o
n
.
We
si
gnal
at
t
h
e en
d t
h
e
m
a
jor
di
sa
dv
an
t
a
ge o
f
t
h
e (
D
P
C
) i
s
t
h
at
t
h
e c
o
n
v
e
r
t
e
r s
w
i
t
c
hi
n
g
fre
que
ncy
i
s
n
o
t
c
onst
a
nt
.
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0.
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4
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5
0.
6
0.
7
0.
8
-
400
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300
-
200
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100
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T
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L i
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o
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)
L i
n
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u
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5
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6
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7
0.
8
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9
1
-1
00
0
0
10
00
20
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50
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60
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70
00
T i
m
e
(
s
)
A
c
t i v e
p o
w
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V
A
R
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J
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S
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208
8-8
6
9
4
Perfo
r
man
ce
an
d Hi
g
h
Ro
bu
stn
e
ss
DPC for
PWM Rectifier un
d
e
r Un
st
a
b
l
e V
DC
Bus
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D
j
eb
ba
r)
74
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