Abs ac — Di ec Powe Con ol (DPC) echnique has been
widely used as con ol s a egy o h ee-phase powe ec i ie s
due o i s simplici y and good pe o mance. The DPC uses he
ins an aneous ac i e and eac i e powe o con ol he powe
con e e , he con olle design has been p oposed as a di ec
con ol wi h a look up able (LUT), and in ecen wo ks, as an
indi ec con ol wi h an inne con ol loop wi h p opo ional plus
in eg al con olle s o he ins an aneous ac i e and eac i e
powe e o s. In his pape a model-based DPC o h ee-phase
powe con e e s is designed, ob aining exp essions o he inpu
con ol signal which allow o design an adap i e con ol law
minimizing he e o s in oduced by he pa ame e s unce ain ies
as he smoo hing induc o alue o he g id equency. Con olle
design p ocess, s abili y s udy o he sys em and expe imen al
esul s o a synch onous h ee-phase powe ec i ie p o o ype
a e p esen ed o alida e he p oposed con olle .
Index Te ms— Adap i e con ol, di ec powe con ol, powe
ac o co ec ion, powe quali y, h ee-phase powe con e e s.
I. INTRODUCTION
owe ec i ie s a e well-known powe sys ems o
indus ial applica ions as DC-bus supply o h ee-phase
ec o -con olled PWM in e e s and DC-Loads and o he
in eg a ion o enewable ene gy applica ions. No con olled
h ee-phase ec i ie s ha e been widely used due o i s
eliabili y, obus ness and low cos , a he expense o
in oducing ene gy losses in he ansmission line and
ha monic cu en s in o he g id ha no ul il he new s anda ds
o he elec ic g id, IEEE-519 o USA and IEC 61000-3-2
and 61000-3-4 o Eu ope [1]-[4]. Due o hese ac s new
powe con e e opologies and hei con ol s a egies
ul illing wi h hese s anda ds ha e been de eloped and
s udied in ecen yea s [5]-[18]. Among hese opologies,
PWM egene a i e ec i ie s (Fig. 1) ha e some ex a
ad an ages as: bidi ec ional powe low, almos sinusoidal
Manusc ip ecei ed Ap il 23, 2007. Accep ed o publica ion No embe
21, 2007. This wo k was suppo ed in pa by he Andalusian Go e nmen
unde g an TIC-1172.
Copy igh (c) 2007 IEEE. Pe sonal use o his ma e ial is pe mi ed.
Howe e , pe mission o use his ma e ial o any o he pu poses mus be
ob ained om he IEEE by sending a eques o pubs-pe [email protected] g.
S.Vazquez, J. A. Sanchez, J. M. Ca asco, J. I. Leon, E. Gal an a e wi h
he Depa men o Elec onic Enginee ing, Uni e si y o Se ille, 41092
Se ille, Spain (e-mail: s azquez@g e.esi.us.es).
cu en s, nea uni y powe ac o and egula ion o dc-link
ol age. Due o hese ac s he con ol o hese powe sys ems
is cu en ly one objec i e o he esea che s. One o he mos
e icien con ol s a egies o his sys em is Di ec Powe
Con ol (DPC). DPC con ol s a egy lies on he ins an aneous
eac i e powe heo y in oduced by Akagi e al. [19] and is
based on he e alua ion o he ac i e and eac i e
ins an aneous powe e o s alues and he ol age ec o
posi ion [20] o he Vi ual-Flux ec o posi ion [21] wi hou
any in e nal con ol loop o he cu en s. The basic idea o
DPC is o choose he bes s a e o he powe swi ches among
he eigh possible s a es in o de o main ain he DC-Link
ol age cons an , and o keep he uni y powe ac o . The
ec o selec ion is made h ough a Look Up Table (LUT),
whe e he inpu a iables a e he ol age g id ec o posi ion
and he ins an aneous ac i e and eac i e powe e o s. This
con olle has he beha iou o a bang-bang con olle , so he
au ho s usually include a hys e esis band in o de o educe he
con olle gain. One d awback o his DPC con olle is ha i
has no a cons an swi ching equency and in o de o
o e come his ac Pulse Wid h Modula ion (PWM) and Space
Vec o Modula ion (SVM) wi h cons an swi ching equency
ha e been in oduced [22]-[27]. Howe e he main d awback
o DPC is he high gain o he con olle , and as consequence,
he alues o he inpu induc o s ha e o be e y la ge o
a enua e he cu en ipple, inc easing he cos , size and
weigh o he sys em. In o de o educe he inpu induc o s
alues, LCL il e s ha e been p oposed o connec he powe
con e e o he g id [28]-[30]. Tha solu ion has he d awback
o he il e esonance so i has o be well s udied. Besides,
ecen ly wo ks ha e in oduced p edic i e con ol s a egies
o he DPC [31]-[32].
Applica ions based on DPC ha e demons a ed ha i is a
simple and e icien con ol s a egy achie ing good dynamic
pe o mance and nea uni y powe ac o . Howe e he
smoo hing induc ances used o connec he powe con e e o
he g id a e s ill oo la ge, inc easing he cos , size and weigh
o he o al sys em and educing dynamics and ope a ion ange
o PWM ec i ie [33]. A con olle design based on he
sys em model can o e come his d awback op imizing he
powe sys em beha iou . Fu he mo e adap i e con ol
s a egies can be applied o minimize he e o s in oduced by
he pa ame e s unce ain ies as he induc o alue o he g id
equency.
A model-based Di ec Powe Con ol o Th ee-
Phase Powe Con e e s
Se gio Vazquez. S uden Membe , IEEE, Juan An onio Sanchez, Juan Manuel Ca asco, Membe ,
IEEE, Jose Ignacio Leon, Membe , IEEE, Edua do Gal an, Membe , IEEE
P
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2
This pape is o ganized as ollows: Fi s ly he disc e e
model o a h ee-phase wo-le el ec i ie is p esen ed.
Secondly, based on he sys em model he di ec powe con ol
law is de i ed, and an adap i e con ol law and he s abili y
s udy o he sys em a e p esen ed. In he las sec ion o he
pape expe imen al esul s a e included and analyzed in o de
o e i y he heo e ical s udy ha has been p esen ed in he
p e ious sec ions.
2
dc
V
a
i
c
i
b
i
an
cn
con
i
Load
i
cap
i
2
dc
V
bn
Fig. 1 Th ee-phase wo le el powe con e e .
II. MODEL OF THE SYSTEM
A h ee-phase wo le el powe con e e is depic ed in Fig.
1, whe e he neu al poin is deno ed by n. The sys em is
connec ed o he g id h ough smoo hing induc o s L, and i is
assumed ha a pu e esis i e load RL is connec ed a DC-Link
capaci o C. The sys em pa ame e s and a iables a e
desc ibed in Table 1.
TABLE 1
SYSTEM VARIABLES AND PARAMETERS
Va iable Desc ip ion
={ a b c}T Phase o neu al inpu ol age ec o
i ={ia ib ic}T Phase inpu cu en ec o
d
={
d
a
d
b
d
c}T Con ol inpu ec o
w
G id equency
L Smoo hing induc o
C Ou pu capaci o
RL Load esis ance
Vdc Ou pu capaci o ol age
The equa ions ha desc ibe he inpu cu en s dynamics and
he ou pu DC ol age dynamic can be de i ed om he sys em
model. Following he echnique p esen ed in [34], he sys em
model can be ob ained in he s a iona y αβ ame [23].
2
dc
di V
L
d
ab
abab
d
=×+ (1)
22
22
T
dcdcdc
L
VVV
d
Ci
d R
abab
d
æö
×=-
ç÷
èø (2)
T
Auu
abab
dd
éù
==
ëû
(3)
11
1
2
22
3
33
0
22
A
éù
--
êú
êú
=×
êú
-
êú
ëû
(4)
Equa ions (1) and (2) a e he disc e e model o he powe
con e e in
ab
coo dina es, he
ab
a iables can be
calcula ed as {·}
ab
=A{·}abc, whe e he ma ix A is de ined by
(4). In hese equa ions δαβ has been de ined as (3) and i is
assumed ha Vdc is always posi i e.
Fig. 2 shows he eigh possible s a es o he swi ches in he
ab
ame, and Table 2 summa izes he possible swi ch
posi ions in
ab
coo dina es.
TABLE 2
AVAILABLE SWITCH POSITIONS IN THE CONVERTER DISCRETE MODEL
S a e u
a
u
b
U0 0 0
U1
2
2
3
0
U2
2
3
2
U3
2
3
-
2
U4
2
2
3
- 0
U5
2
3
-
2
-
U6
2
3
2
-
U7 0 0
a
b
Fig. 2 Swi ch posi ions in
ab
ame.
The con ol objec i es o he h ee-phase powe con e e
a e he ollowing:
(i) The ins an aneous ac i e powe p and he ins an aneous
eac i e powe q should ack hei e e ence, p* and q*
espec i ely, which a e calcula ed in such way ha he
capaci o ou pu ol age is egula ed owa ds i s e e ence and
om he sou ce e minals only ins an aneous ac i e powe is
supplied [19].
*
*
0
pp
qq
®
®®
(5)
Thus, DPC con ols indi ec ly he cu en s p o ided by he
sou ce h ough he alues o he ins an aneous ac i e and
eac i e powe .
(ii) The capaci o ou pu ol age should be egula ed
owa ds i s e e ence.
*
dcdc
VV
® (6)
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3
III. CONTROL DESIGN
The p oposed con olle o he sys em (1)-(2) is composed
o an ins an aneous powe acking (inne ) loop and a ol age
egula ion (ou e ) loop. In wha ollows is desc ibed he design
o he wo con ol s ages.
A. Ins an aneous powe acking loop
The objec i e o he inne con ol loop is o gua an ee
acking o p and q owa ds hei e e ences. The
ins an aneous ac i e powe e e ence, p*, is he ou pu o he
ou e con ol loop, and is calcula ed in o de o achie e DC-
Link ol age egula ion. The ins an aneous eac i e powe
e e ence, q*, is made ze o in o de o achie e uni y powe
ac o .
In [23], i is shown ha in he known pa ame e s case, and
assuming ha inpu ol ages a e balanced and wi hou
ha monic con en , he ins an aneous ac i e powe i s de i a e
o e he ime, .
p, and he ins an aneous eac i e powe i s
de i a e o e he ime, .
q, a e exp essed espec i ely as
2
12
Tdc
V
Lq
Lp
ababab
ab
wd
æö
æö
ç÷
ç÷
=+-
ç÷
ç÷
ç÷
èø
èø
& (7)
2
2
TT dc J
V
Lq JLp
ab
abab
ab
dw
æö
ç÷
=--
ç÷
èø
& (8)
Now he locus o
dab
poin s whe e (7) and (8) a e made
equal o he cons an s k1 and k2 espec i ely can be calcula ed.
(
)
12
11
2
2
pk
dc
Lq kcJ
V
ab
ababab
ab
dw
=
=+-+
& (9)
( )
2
22
2
2
qk
dc
J
Lpkc
V
ab
abab
ab
dw
=
=-++
& (10)
Equa ion (9) is he ec o ial ep esen a ion o a s aigh line
in he
ab
ame, whe e c1J
ab
desc ibes he di ec ion o he
line, and c1 is an a bi a y cons an . This line is he se o
alues o δαβ ha makes .
p equal o he cons an k1, and spli s
he alpha-be a plane in wo egions, alues o δαβ abo e (9)
make .
p smalle han k1, while alues o δαβ below (9) make .
p
la ge han k1.
Equa ion (10) ep esen s he same idea o he eac i e
powe i s ime de i a e, whe e c2
ab
desc ibes he di ec ion
o he line, and c2 is an a bi a y cons an .
2
qk
ab
d
=
&
also spli s he
alpha-be a plane in wo egions, alues o δαβ abo e (10) make
.
q la ge han k2, while alues o δαβ below (10) make .
q smalle
han k2.
Fig. 3 shows he alpha-be a ame egions whe e .
p and .
q
a e enclosed o ce ain alues.
When cons an s k1 and k2 a e made equal o ze o equa ions
(9) and (10) a e espec i ely ans o med in he ollowing
exp essions [23]
(
)
2
0
1
2
2
p
dc
Lq cJ
V
ab
ababab
ab
dw
=
=++
& (11)
( )
0
2
2
2
q
dc
J
Lpc
V
ab
abab
ab
dw
=
=-+
& (12)
These wo s aigh lines spli he alpha-be a ame in ou
quad an s as i is shown in Fig. 4. Each zone is cha ac e ized
by he sign o he ins an aneous ac i e and eac i e powe i s
de i a e o e he ime, so when he sys em is wo king inside
one o hem he ins an aneous ac i e and/o he eac i e powe
can inc ease o diminish acco ding which wo k a ea is. The
in e sec ion poin be ween hese wo s aigh lines can be
calcula ed as
22
22
1
eq
cc
LqLp
J
VV
ababab
abab
ww
d
æöæö
ç÷ç÷
=+-
ç÷ç÷
èøèø
(13)
a
b
ab
Fig. 3 Bounda y limi s o he ins an aneous ac i e and eac i e powe i s
ime de i a e.
ab
eq
ab
d
0
0
p
q
<
<
&
&
0
p
ab
d
=
&
0
q
ab
d
=
&
0
0
p
q
>
<
&
&
0
0
p
q
<
>
&
&
0
0
p
q
>
>
&
&
a
b
Fig. 4 Equilib ium poin in s eady s a e
d
eq
ab
ep esen s he equilib ium poin o he sys em in s eady
s a e due o in his poin he ins an aneous ac i e and eac i e
powe demanded by he powe con e e o he powe supply
do no inc ease o diminish, and he e o e, a his poin , he
ins an aneous ac i e and eac i e powe demanded by he
powe con e e emain cons an s.
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4
The ollowing equa ions de ine he alues o ins an aneous
ac i e powe e o , ~
p, and ins an aneous eac i e powe e o ,
~
q, espec i ely.
*
*
ppp
qqq
=-
=-
%
%
(14)
The powe swi ches s a e should be chosen among he
disc e e possible s a es inside a selec ion a ea de ined by he
sign o he ins an aneous ac i e and eac i e powe e o .
Table 3 shows he selec ion a ea as a unc ion o he sign o
ins an aneous powe e o s.
This basic selec ion algo i hm has he ollowing d awbacks:
1) The possible powe swi ches s a e is no always unique,
i.e. he e is mo e han one possible s a e o he powe
swi ches inside he selec ion a ea. Fig. 5 shows a possible
si ua ion whe e in a ea A2 he e a e i e possible s a e
ec o s.
2) The powe swi ches s a e is no always de ined inside he
selec ion a ea. Fig. 5 shows a possible si ua ion whe e in
a ea A4 he e is no any s a e ec o .
TABLE 3
SELECTION AREA AS FUNTION OF THE INSTANTANEOUS POWER ERRORS
~
p ~
q A ea
>0 >0 A1
>0 <0 A4
<0 >0 A2
<0 <0 A3
U0U7 U1
U2U3
U5 U6
U4
A2
A3
A4
A1
0
0
p
q
<
<
&
&
A1
0
0
p
q
>
<
&
&
A2
0
0
p
q
<
>
&
&
A4
0
0
p
q
>
>
&
&
A3
0
p
ab
d
=
&
0
q
ab
d
=
&
a
b
ab
Fig. 5 Powe swi ches s a es a iable in each selec ion a ea.
To o e come hese d awbacks in he basic selec ion
algo i hm is necessa y o de ine a ec o e e ence ha is
always in he app op ia e selec ion a ea, and o gene a e his
e e ence ec o wi h a modula ion echnique wi h a cons an
swi ching equency as PWM o SVM. I is possible o de ine
such a ec o e e ence aking in o accoun he equilib ium
poin
d
eq
ab
ec o alue and he in ol ed selec ion a ea. The
e e ence ec o can be calcula ed as a composi ion o he
d
eq
ab
ec o , a p opo ional ec o o
ab
and a p opo ional ec o
o J
ab
. As a unc ion o he selec ion a ea, hese wo las
ec o s a e added o sub ac ed o he
d
eq
ab
ec o o gene a e
he e e ence ec o . In wha ollows i is p esen ed how he
e e ence ec o is composed o each selec ion a ea. Besides,
a ec o diag am including he e e ence ec o and i s
componen s is shown in o de o demons a e ha he
p oposed e e ence ec o de ini ion is co ec and ha he
de ined e e ence ec o is loca ed inside he app op ia e
selec ion a ea.
Fo ins ance, he e e ence ec o in he selec ion a ea A1 is
de ined as ollows, whe e k1 and k2 a e de ined as posi i e
alues, ensu ing ha he e e ence ec o is loca ed inside he
selec ion a ea A1.
12
eq
k kJ
abababab
dd
D
=+×+ (15)
Fig. 6 shows how e e ence ec o
d
ab is composed, and
shows ha a e e ence ec o de ined as (15) is always inside
he selec ion a ea A1. Due o his ac he p oposed e e ence
ec o p o ides he necessa y con ol ac ion o achie e he
con ol objec i es, i.e., o educe he ins an aneous ac i e
powe and o educe he ins an aneous eac i e powe d awn
om he g id.
ab
d
eq
ab
d
ab
k
1
ab
J k
2
0
0
p
q
<
<
&
&
0
0
p
q
>
<
&
&
0
0
p
q
<
>
&
&
0
0
p
q
>
>
&
&
0
p
ab
d
=
&
0
q
ab
d
=
&
a
b
ab
Fig. 6 Re e ence ec o o selec ion a ea A1.
Using he same concep s i is possible o de ine he
e e ence ec o
d
ab o each a ea. The p oposed algo i hm o
calcula e he e e ence ec o has he ollowing s eps:
1) Calcula e ~
p, and ~
q.
2) Se he selec ion a ea.
3) Calcula e he e e ence ec o
Table 4 summa izes he p oposed algo i hm o calcula e he
e e ence ec o .
TABLE 4
REFERENCE VECTOR DEFINITION AS A FUNCTION OF THE SELECTION AREA.
1s S ep 2º S ep 3º S ep
~
p ~
q Selec ion A ea Re e ence Vec o
>0 >0 A1 12
eq
k kJ
abababab
dd
=+×+
>0 <0 A2 12
eq
k kJ
abababab
dd
=+×-
<0 >0 A3 12
eq
k kJ
abababab
dd
=-×+
<0 <0 A4 12
eq
k kJ
abababab
dd
=-×-
Re e ence Vec o de ini ion in Table 4 can be w i en in a
single equa ion, educing he algo i hm compu a ional cos , i
k1 and k2 alues a e espec i ely de ined as
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5
1
2
p
q
kkp
kkq
D
D
=×
=×
%
%
(16)
kp and kq a e de ined as a nonze o posi i e cons an s, and he
p oposed e e ence ec o can be calcula ed independen ly o
he selec ion a ea.
eq
pq
kp kqJ
abababab
dd
D
=+××+××
%%
(17)
Con olle (17) in closed-loop wi h he sys em dynamics (7)-
(8) p o ides he ollowing equa ions
2
2
2
2
dc
p
dc
q
V
Lp kp
V
Lq kq
ab
ab
=-×××
=-×××
&%
&%
(18)
Taking in o accoun ha in s eady s a e he ins an aneous
ac i e and eac i e e e ence powe a e cons an s hen
*
*
0
0
dp
Ld
dq
Ld
=
=
(19)
2
2
0
2
0
2
dc
p
dc
q
V
Lp kp
V
Lq kq
ab
ab
+×××=
+×××=
&
%%
&
%%
(20)
Equa ions (20) demons a e ha using he p oposed
e e ence ec o , he ins an aneous ac i e and eac i e powe
e o s end exponen ially o ze o and he sys em is s able.
Now an adap i e law wi h he aim o elimina e he e ec s o
he sys em pa ame e s unce ain ies, he smoo hing induc o
and he g id equency alue, is de i ed. In he h ee-phase
powe con e e he eac ance pa ame e , X, is he p oduc o
he smoo hing induc o alue and he g id equency.
XL
w
D
= (21)
ˆ
XXX
=-
%
(22)
ˆ
XX
=
&
&
%
(23)
Equa ion (22) de ines he e o be ween he ac ual alue o
he eac ance and i s es ima ed alue ^
X. Taking in o accoun
ha pa ame e X is assumed o be cons an o slowly a ian ,
equa ion (23) de ines he e o ime de i a e.
22
ˆˆ
22
ˆ
1
eq
dcdc
XqXp
J
VV
ababab
abab
d
æöæö
××
ç÷ç÷
=+-
ç÷ç÷
èøèø
(24)
ˆeq
pq
kp kqJ
abababab
dd
=+××+××
%%
(25)
Equa ion (24) is he exp ession o
d
eq
ab
as a unc ion o he
es ima ed pa ame e alue, and he p oposed con olle o he
h ee-phase powe con e e is ans o med in (25),
in oducing he new p oposed con olle in (7) and (8), he
exp essions o he powe e o s dynamics a e de i ed.
( )
2
ˆ
2
dc
p
V
Lp kpqXX
ab
=-×××+×-
&
%%
(26)
( )
2
ˆ
2
dc
q
V
Lq kqpXX
ab
=-×××-×-
&
%%
(27)
To de i e an adap i e law o econs uc pa ame e ^
X a
Lyapuno app oach is ollowed. Fo his pu pose a posi i e-
de ini e unc ion is p oposed, whe e pa ame e g is a posi i e
cons an ha ep esen s he adap a ion gain.
222
111
222
HLpLqX
g
=++
×
%
%% (28)
22
22 1
22
dcdc
pq
VV
H kp kqXpqqpX
abab g
æö
=--+-+
ç÷
èø
&
&%%
%%%% (29)
( )
ˆ
Xqppq
g
=×-×
&
%%
(30)
22
22
22
dcdc
pq
VV
H kp kq
abab
=-×××-×××
&
%%
(31)
The ime de i a e o (28) along he ajec o ies o (26) and
(27) is (29) which is made nega i e semide ini e by p oposing
(30) o econs uc he pa ame e ^
X. Finally he ime de i a e is
gi en by (31).
Following Lasalle´s heo em a gumen s i can be s a ed ha
~
p → 0 and ~
q → 0 as → ∞ asymp o ically. Mo eo e , om
(30) ~
p ≡ 0 and ~
q ≡ 0 imply ha ~
X is cons an . Acco ding o
(26) and (27) his cons an should be ze o. This gua an ees
con e gence o he es ima ed alue owa ds i s ac ual alue.
Now aking in o accoun ~
p and ~
q de ini ions and ha q* is
ze o wi h he aim o achie e uni y powe ac o , he pa ame e
^
X can be econs uc ed using exp ession
*
ˆ
Xqp
g
=-××
&
(32)
B. Vol age egula ion loop
The ou e con ol loop is designed o egula e he ou pu
capaci o ol age, his ol age should be main ained equal o
he DC-Vol age e e ence alue
*
dc
V
.
The ol age capaci o dynamic is de ined by (2), and
assuming ha ins an aneous powe dynamics a e much as e
han DC-Vol age dynamic hen i is possible o a i m ha
*
pp
@
and
0
q
@
, and he e o e (2) can be educed o
22
2
T
dcdc
L
VV
d
C i
d R
abab
æö
×=-
ç÷
èø (33)
F om Akagi´s powe heo y he ins an aneous ac i e powe
is de ined as T
p i
abab
= so he DC-Vol age dynamic equa ion
can be w i en as
22
2
æö
×=-
ç÷
èø
dcdc
L
VV
d
Cp
d R
(34)
Now, in o de o educe no a ion, wo new a iables a e
de ined as ollows
2
2
D
=
dc
V
z (35)
*
D
=-
%
zzz
(36)
whe e
z
%
ep esen s he e o and
*
z
is he new e e ence
de ined as
(
)
2
*
*
2
=dc
V
z (37)

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6
(
)
2
2
*
dc
V
*
p
*
0
q
=
p
ˆ
eq
ab
d
ab
d
s
K
b
s
aK
i
p+
+
q
kJ
ab
p
k
ab
2
2
dc
V
q
22
ˆˆ
22
1
dcdc
XqXp
J
VV
abab
abab
æöæö
××
ç÷ç÷
+-
ç÷ç÷
èøèø
*
qpd
g
-×
ò
X
ˆ
p
Fig. 7 Block diag am o he p oposed DPC con olle .
and in oducing hese news a iables in (34)
()
(
)
2
*
2dc
LL
V
dz
Czp
d RR
-×=+-
%
% (38)
No ice ha (38) is a simple i s -o de s able sys em, so a
p opo ional plus in eg al con olle would sol e he p oblem
since he pe u ba ion is an unknown cons an . Finally he
p oposed PI con olle o he ou e con ol loop is
*p
i
s
K
K
pzz
ss
=+
+
%%
(39)
whe e Kp, Ki and
s a e design pa ame e s and p*is he
e e ence alue o he ins an aneous ac i e powe . This
con olle includes a low pass il e in he p opo ional e m o
educe he high equency noise.
Summa izing, he inal exp essions o he p oposed
con olle a e gi en by he ollowing equa ions.
(i) Powe acking loop.
*
22
*
*
*
ˆ
ˆˆ
22
ˆ
1
ˆ
0
eq
dcdc
eq
pq
Xqp
XqXp
J
VV
kp kqJ
ppp
qqq
q
ababab
abab
abababab
g
d
dd
=-××
æöæö
××
ç÷ç÷
=+-
ç÷ç÷
èøèø
=+××+××
=-
=-
=
&
%%
%
%
(40)
(ii) Vol age egula ion loop.
*
*
p
i
s
K
K
pzz
ss
zzz
D
=+
+
=-
%%
%
(41)
Fig. 7 shows he block diag am o he p oposed DPC
con olle including he adap i e law.
I. EXPERIMENTAL RESULTS
In his sec ion expe imen al esul s a e shown in o de o
es he p oposed con olle using a p o o ype. Fo his pu pose
he h ee-phase wo-le el powe con e e o Fig. 8a has been
de eloped, wi h a digi al implemen a ion o he con ol
algo i hm ha has been execu ed in a TMS320VC33 loa ing
poin DSP homemade boa d. The expe imen consis s o a
load s ep a DC-Link om no-load o ull load o 9.375kW.
Fo his pu pose capaci o ol age e e ence has been
es ablished o 750V and a 60 Ohm esis i e load (Fig. 8b) has
been suddenly connec ed o he DC-Link. To assess he DPC
con olle wi h he adap i e law app oach, a compa a i e wi h
he DPC con olle wi hou he adap i e law has been ca ied
ou . Measu emen s o DC-Link ol age, phase ol ages and
cu en s, ha monic con en s o cu en s, ac i e powe , eac i e
powe and powe ac o , ha e been aken wi h a Fluke 434
powe quali y analyze . Table 5 shows he elec ical
pa ame e s o he powe con e e , DC-Link ol age e e ence,
swi ching and sampling equencies ha ha e been used in he
expe imen al se up.
Fig. 8 Labo a o y p o o ype, om le o igh : a) Th ee-phase wo le el powe
con e e . b) Resis i e load o 60 W
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7
TABLE 5
ELECTRICAL AND CONTROL PARAMENTERS FOR THE EXPERIMENTAL SYSTEM.
Pa ame e Desc ip ion
Phase- o-neu al Vol age 230 V
Smoo hing induc ance 0.8 mH
DC-Link capaci o 7050 µF
Resis i e load 60Ω
DC-Link Re e ence Vol age 750 V
Swi ching equency 11.2 KHz
Sampling equency m 22.4 kHz
All he cons an s used in he p oposed con olle ha e been
adjus ed expe imen ally. This includes, Kp and Ki o he
ol age egula ion loop, kp and kq ha p o ide he necessa y
damping o he con olle , and he adap a ion gain g.
A. T ansien beha io
Fig. 9 shows DC-Link ol age ansien alue when load
s ep om ze o o ull load (9.375kW) is applied o DC-Link.
Fig. 9a shows ansien esponse when he p oposed non-
adap i e DPC con olle is applied and Fig. 9b when he
p oposed adap i e DPC con olle is used. I can be no iced
ha in bo h cases he ansien esponse is simila . DC-Link
ol age only dec eases 15 V a e he load is connec ed, and i s
e e ence is achie ed again only in 0.6s a e he load change,
so a good ol age egula ion is ensu ed.
Fig. 9 DC-Link ansien ol age du ing load s ep om ze o o ull load. a) o
he p oposed non-adap i e DPC con olle . b) o he p oposed adap i e DPC
con olle
Fig. 10 Ins an aneous ac i e powe ansien esponses when load s ep occu s,
om 50 % o ull load, o g = 1e-6. F om op o bo om: a) Ins an aneous
ac i e powe e e ence. b) Ins an aneous ac i e powe e o .
Fig. 10 shows he ins an aneous ac i e powe ansien
esponse when a load s ep om 50% o ull load occu s. F om
expe imen s i is obse ed ha he adap a ion gain pa ame e
does no ha e in luence in he dynamic and he beha io o he
ins an aneous ac i e powe , o his eason only he ansien
esponse when g = 1e-6 is shown. Fig. 10a shows he
ins an aneous ac i e powe e e ence alue and Fig. 10b he
ins an aneous ac i e powe e o when he p oposed adap i e
DPC con olle is used.
Compa ed wi h classic DPC, he ansien beha io is qui e
simila , due o when a load s ep akes place he alues o ~
p and
~
q become high and he ou pu o he con olle (40) is e y
close o he ec o chosen by he classic DPC. In Fig. 11 a
possible case, when p* and q* suddenly dec ease, is shown.
ab
d
eq
ab
d
p
kp
ab
%
q
kqJ
ab
%
0
p
ab
d
=
&
0
q
ab
d
=
&
a
b
ab
Fig. 11 Compa ison be ween he e e ence ec o s ob ained wi h he Classic
DPC (□) and he p oposed DPC (○) when he ac i e and eac i e
ins an aneous powe e e ences dec ease suddenly.
Fig. 12 Ins an aneous eac i e powe ansien esponses when load s ep
occu s, om 50 % o ull load, o di e en alues o g. F om op o bo om:
a) g = 0. b) g = 1e-8. c) g = 1e-6.
Fig. 13 Es ima ed alue ansien esponses when load s ep occu s, om 50 %
o ull load, o di e en alues o g. F om op o bo om: a) g = 1e-8. b) g =
1e-6.
Fig. 12 shows he ins an aneous eac i e powe ansien
esponse when a load s ep om 50% o ull load occu s. I can
be no iced ha he p oposed adap i e DPC con olle pe mi s
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8
o educe he eac i e powe consump ion. Fig. 12a shows he
ins an aneous eac i e powe when he p oposed non-adap i e
DPC is used, Fig. 12b and Fig. 12c show ins an aneous
eac i e powe when he p oposed adap i e DPC is used o
di e en alues o he adap a ion gain.
Fig. 13 shows he es ima ed alue ansien esponse when a
load s ep om 50% o ull load occu s. I can be no iced ha ^
X
ipple inc eases when he adap a ion gain is high. In he
expe imen s i is obse ed ha highe alues o g lead o
highe ipples ha make sys em uns able. Howe e , he
eac i e powe consump ion is lowe as g inc eases. The e o e,
due o his ac he adap a ion gain has o be chosen as high as
possible bu aking in o accoun he possible sys em ins abili y.
B. S eady s a e beha io
Fig. 14(a,b) shows he phase cu en s achie ed wi h he
p oposed non-adap i e DPC con olle , i can be no iced ha
low cu en s dis o ion is achie ed, in ac i s o al ha monic
dis o ion alue (THD) is 3.0% (Fig. 15a). Howe e he
cu en is leading he ol age and he powe ac o alue is
0.99 capaci i e as can be seen in Fig. 15b.
Fig. 14 Phase ol ages and cu en s o he p oposed non-adap i e DPC
con olle . Le o Righ : a) Phase c ol age and cu en . b) a, b and c phase
cu en .
Fig. 15 F om op o bo om: a) Cu en s ha monic con en o he p oposed
non-adap i e DPC con olle . b) Ac i e and eac i e powe and powe ac o
o he p oposed non-adap i e DPC con olle .
Fig. 16(a,b) shows he phase cu en s deli e ed by he
powe con e e when he p oposed adap i e DPC con olle is
used. I can be no iced ha in spi e o he limi ed smoo hing
induc ance alue (0.8mH) he cu en ipple is small and he
cu en THD is only 3.2% (Fig. 17a). Mo eo e compa ed
wi h he phase cu en s achie ed wi h he non-adap i e DPC
con olle he ha monic con en o cu en s is o he same
o de . Besides uni y powe ac o alue is achie ed as can be
seen in Fig. 17b. Due o his ac less eac i e powe is d awn
om he g id, eac i e powe is d as ically educed in 75%
( om 1.14 kVA in Fig. 15b o 0.3 kVA in Fig. 17b) and
be e pe o mance is achie ed wi h he same powe con e e .
Fig. 18a shows he ec o diag am wi h he p oposed non-
adap i e DPC con olle and Fig. 18b shows he ec o
diag am wi h p oposed adap i e DPC con olle . I can be seen
ha due o pa ame e s unce ain ies when he non-adap i e
con ol law is used ol ages and cu en s a e shi ed (Fig. 18a).
Howe e , when he adap i e solu ion is adop ed, hese
pa ame e s unce ain ies a e a oided and ol age and cu en s
a e in phase almos pe ec ly (Fig. 18b), showing he g ea
ad an age o using adap i e con ol echniques.
Fig. 19 shows he ins an aneous eac i e powe alue in
s eady s a e o di e en alues o g. As i was p esen ed in
Fig. 12 o ansien ope a ion, he eac i e powe consump ion
dec eases when g inc eases.
Fig. 16 Phase ol ages and cu en s o he p oposed adap i e DPC con olle
(g = 1e-6). F om op o bo om: a) Phase c ol age and cu en . b) a, b and c
phase cu en .
Fig. 17 F om op o bo om: a) Cu en s ha monic con en o he p oposed
adap i e DPC con olle (g = 1e-6). b) Ac i e and eac i e powe and powe
ac o o he p oposed adap i e DPC con olle (g = 1e-6).
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9
Fig. 18 Vec o diag am. F om le o igh : a) Vec o diag am o he p oposed
non-adap i e DPC con olle . b) Vec o diag am o he adap i e DPC
con olle (g = 1e-6).
Fig. 19 Ins an aneous eac i e powe s eady s a e alues o ull load and
di e en alues o g. F om op o bo om: a) g = 0. b) g = 1e-8. c) g = 1e-6.
II. CONCLUSIONS
DPC s a egies a e simple and e icien con ol s a egies
ha can be applied o powe sys ems as powe ec i ie s
allowing he use o low cos mic op ocesso s o hei
implemen a ion. Howe e , some d awbacks associa ed o he
high g id connec ion induc ance alue a e p esen in his ype
o con ol echniques. The p oposed DPC s a egy based on
he sys em model pe mi s o make smoo h he high gain o
p e ious DPC echniques and consequen ly, pe mi s o
dec ease he smoo hing connec ion induc ance alue educing
he cos , size and weigh o he o al sys em and inc easing he
ope a ion ange o he powe con e e and imp o ing he
dynamics o he sys em. Expe imen s wi h a h ee-phase wo-
le el labo a o y p o o ype ha e been ca ied ou o illus a e
he good pe o mance o he p oposed con ol echnique.
Besides, adap i e echniques ha e been applied o o e come
p oblems associa e wi h sys em pa ame e s unce ain ies,
which leads he p oposed con olle o achie e uni y powe
ac o , p o iding a be e pe o mance o he o e all sys em.
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