IEEE In e na ional Symposium on Indus ial Elec onics (ISlE 2009)
Seoul Olympic Pa k el, Seoul, Ko ea July 5-8, 2009
Modeling and Simula ion
o
Synch onous Machine
and i s beha iou agains Vol age Sags
Daniel Aguila ', Al a o Luna, Alejand o Rolan, Ge a do Vazquez
Elec ical Depa men
o
Enginee ing
Technical Uni e si y
o
Ca alonia
Colom 1- 08222-Te assa, Spain
'Con ac Au ho : [email p o ec ed]
Gus a o Ace edo
Elec ical Depa men
o
Enginee ing and
Powe Sys ems
Fede al Uni e si y
o
Pe nambuco (UFPE)
Reci e, Pe nambuco B azil
Abs ac - This
pape
s udies
he
e ec s o ol age sags (dips),
bo h
symme ical
and
unsymme ical,
on
he
h ee-phase
Synch onous
Machine
(SM).
The
as
majo i y
o
he
elec ical
powe
gene a ion
sys ems in
he
wo ld
is consis o
synch onous
gene a o s
coupled o
he
elec ical
ne wo k
hough
a
ans o me .
Vol age sags on SM cause speed
a ia ions,
cu en
and
o que
peaks
and
hence may cause
ipping
and
equipmen
damage.
The
consequences o ol age sags in
he
machine
beha iou
depends
on
di e en
ac o s such as i s
magni ude
(o
dep h),
du a ion
and
ini ial poin -on-wa e,
and
also on
he
pa ame e s
o
he
machine. In his s udy,
h ee
machines o
di e en
nominal
powe
ha e been used o
simula e
on MATLAB
he
e ec s
o
he
ol age sags on
he
machine
unde
speci ic
condi ions.
SM is essen ial in o de o ob ain a eliable analysis
o
s abili y
and dynamical pe o mance.
The aim
o
his pape is simula e he SM and analyze i s
beha iou agains ol age sags. Sec ion II p esen s he SM
model. Sec ion III shows he ol age sags classi ica ion.
Finally, based on he simula ions using MATLAB, ol age sags
e ec s on SM a e analyzed in Sec ion IV.
II.
SYNCHRONOUS
MACHINE
MODEL
In his pape he SM gene ic model is used conside ing i s
dynamic equa ions in he dq e e ence ame gi en by [6].
Dampe winding exis in bo h dand qaxis:
The o que T ) and he load angle J( ) (measu ed om
phaso
E.s
o phaso
~)
a e exp essed as:
I'(z) =
isq(MdFiF
+MdDiD)-isd(MqiQ)+ ...
... + (Ld-Lq
)isdi
sq (4)
This is an impo an angle because i is use ul o
analyzing he machine s abili y.
Th ee SM ha e been simula ed: a high-speed s eam u bine
gene a o (835MVA), a low-speed hyd o u bine gene a o
(325MVA), bo h ob ained om [6], and a small gene a o ,
whose a ed pa ame e s a e included in Table I.
Fo simplici y pu poses, his model does no include
sa u a ion. Ne e heless, i is impo an o emphasize ha some
ol age sags may cause sa u a ion; howe e his happens a e
he sag e ec , no du ing i . This means ha sa u a ion leads o
high cu en . Howe e , sa u a ion akes he machine as e
back in o he s eady s a e, which educes he ansien ime
a e he ol age sag. Fu he mo e, due o sa u a ion he e is no
a big a ia ion on he beha iou
o
he o que [7].
(3)
(5)
(1)
(2)
1.
INTRODUCTION
The elec ici y is he main sou ce
o
ene gy nowadays in ou
socie y. I is used o p o ide he ene gy needed o ope a ing a
g ea a ie y
o
indus ial p ocesses, ligh ing and anspo a ion
as well as o he in o ma ion and communica ion echnologies
[1]. The Synch onous Gene a o (SG) has been widely used o
his pu pose a ound he wo ld due o i s capabili y
o
gene a ing elec ici y in la ge scale powe plan s. In addi ion,
small synch onous gene a o s, in he kVA ange, a e o en used
as well in an isola ed sys em whe e he gene a o is d i en wi h
a small combus ion engine as a p ime-mo e . These can be
used as eme gency powe sou ces o hospi als, he mili a y
acili ies and in he indus y in case
o
a blackou . Mo eo e ,
he i s s wind u bines based on SG a e di ec ly coupled o he
g id ( ixed speed gene a ion sys ems), al hough he p og ess in
he s a ic con e e echnology, has ans o med his gene a ion
sys ems hough a iable speed ope a ion, allowing he
op imum powe e icien o a wide wind speed ange [2].
Du ing he las yea s, he powe quali y has gained a g ea
impo ance in bo h indus y and in esea ch. The g id may
p esen many ypes
o
dis u bances, being he ol age sags he
mos common ones. A ol age sag is a sho -du a ion ( om
hal
cycle o 1 minu e) d op be ween 10% and 90% in he
magni ude
o
he ms ol age. The in e es in s udying his kind
o
dis u bances is mainly due o he p oblems ha hey cause in
he elec ical equipmen s [3].
The simula ion
o
he
SM's
beha iou unde ol age sags
pe mi s de ining di e en c i e ia o p o ec ing and p e en ing
po en ial damages in such machines, as well as he e ec s on
he powe supply in e up ions [4, 5]. Hence, a alid model o
978-1-4244-4349-9/09/$25.00 ©2009 IEEE
729
RAT
ED
DATAOF5KVASY
NCHRO
NO
US
MA
CHI
NE
RAT
ED
DATA
OF
325MVA SYN
CHRO
NO
US
MA
CHI
NE
TABLE I
RAT
ED
DATA
OF
835MVA SYN
CHRO
NO
US
MA
CHI
NE
SN=835MVA
N=60Hz
Spe
ed
=
3600
lmin
SN=325MVA
N=60Hz
Speed
=
112.5
lmin
SN=5kVA
N=60Hz
Speed
=
3600
lmin
UN=
26kV
H=5
.6s
1
pole
pai
UN=20kV
H=
7.5s
32
pole
pai s
UN=437V
H=3
.55s
1
pole
pai
cos qJN=0
.85
J=65.8x l O!Js2
cos p N=
0.85
J=35
.1x1(JJJs2
cos p N=0.85(j)
J=0.2498
Kg
m2
V
Fmax
=6.6901V
5kVA SM. This machine has winding dampe s on he dand q
axes, which educe he e ec s
o
hese dis u bances, hus he
machine synch onism is no los . Ne e heless, in lage
machines, such as he 325MVA, winding dampe s canno
a oid he synch onism los o dep hs (o du a ions) sag
de e mined.
On he o he hand, when unsymme ical sag is applied o he
SM, he machine beha iou is di e en o each six
unsymme ical sag ypes.
On he whole, he ansien wa e shape caused by ol age
sag depends on di e en ac o s such as i s dep h, du a ion,
ini ial poin -on-wa e and machine pa ame e s [8]. A b ie
desc ip ion
o
hese ac o s is gi en below.
Type A Type B
TABL
E"
SAGS
TYPESINE
QU
ATI
ON
FORM
(OBTAI
NED
FROM
BOLLE
N[4])
III. SAG CLASSIFICATION AND CHARACTERIZATION
Vol age sags can be ei he symme ical o unsymme ical,
depending on he causes. I he indi idual phase ol ages a e
equal and he phase ela ionship is 120°, he sag is
symme ical. O he wise, he sag is unsymme ical [8].
Acco ding o [3] ol age sags can be g ouped in o se en
ypes, deno ed as A, B, C,
0,
E, F and G. Table II shows hei
exp essions (whe e his he sag dep h) and Fig. 1 shows hei
phaso diag ams. The mos common causes
o
ol age sags a e
aul s, la ge ans o me ene gizing and la ge mo o s a ing.
Fig. I. Vol age sags ypes: Symme ical ( ype A) and unsymme ical ( ype B
- G). All sags ha e a dep h
o
50%. (Ob ain ed om [4])
In o de o simula e he beha iou
o
SM, in his pape i has
been conside ed ha he sag shape is ec angula , no phase
jump occu s and he sag ype does no change when he aul is
clea ed. Hence, he ol age sags will be de ined by hei dep h
h(0.1 S hS 0.9), hei du a ion
S
,and hei ini ial poin -on-
wa e l li [8].
IV.
VOL
TAGE SAGS EFFECTS
The mos ele an ol age sags e ec s on he SM beha iou
a e speed a ia ions, wi h possible loss
o
he synch onism,
cu en and o que peaks. The machine beha iou is di e en
when symme ical and unsymme ical sags a e p oduced in he
ne wo k.
When symme ical sag is applied o he SM he mos se e e
peaks occu a he beginning and a he end
o
he sags. Fig. 2
shows he ansien e ec s caused by symme ical sag on he
=hV
- G
I
J3
~b
=- - hV -
j-hV
2 2
I
J3
~b
=- - hV +
j-hV
2 2
Type C
=hV
-G
I
J3
~b
=-
-
V-
j - hV
2 2
1
J3
~b
=-
-
V+
j - hV
2 2
Type E
=V
-G
I
J3
~b
=
--hV
-
j-hV
2 2
I
J3
~b
=
--hV
+
j-hV
2 2
Type G
=
.!..(2
+
h)V
-G
3
~b
=
-
~
(
2
+
h)V
-j
~
hV
~b
=
-
~
(
2
+
h)V
+j
~
hV
=hV
- G
I
J3
~b
=-
-
V-
j - V
2 2
I
J3
~
b
=-
-
V+
j - V
2 2
Typ
eD
=hV
-G
1
./3
~b
=- - hV -
j-V
2 2
I
./3
~
b
=- - hV +
j-V
2 2
Type F
=hV
- G
Wh
e
e:
h=0.1 ... 0
.9
sag
dep h
V=UD
/./3
phas
e- o-g ound
ac ol age
730
A. Dep h In luence
The beha iou
o
he machine is a ec ed by he sag dep h.
Asudden d op in he ol age supply p oduces acu en peak a
beginning
o
sag and ano he peak cu en when he aul is
clea ed and he ol age is es o ed. A e eaching he i s peak
alue, an oscilla ion is p oduced wi h cons an equency
(o
he g id) and dec easing ampli ude. Bo h cu en peaks a e
mo e se e e
i
he sag is deepe . Fo all dep hs analyzed, he
same beha iou is obse ed. To que and ac i e
powe
ha e he
same beha iou .
imo
/1OCOOdJ
T/2+kT
T/2+kT
T/2+kT
lJli
0°
90°
A
C,E
B,D,F
Sag
ype
TABL E III
MOST
UNFAVORABLE SAG DURA
nO
N AND INITIAL POINT-ON-
WAVE
FOR
SYNCHRONOUS M ACHINE
B. Ini ial poin -on-wa e in luence
Ini ial poin -an-wa e is also impo an in he s udy
o
he sag
e ec s. Consequen ly,di e en aul angles cause di e en
e ec s on he beha iou
o
he SM. Fig. 5 show he o que
peaks e sus he ini ial poin -one-wa e on he s eam u bine
SM o sags ypes A, B, C, D, E and F. Fo all simula ions,
dep h sag is 10% and du a ion sag is h ee cycles. The cu en
peaks ha e a e y simila beha iou .
As can be deduced om his igu e, he wo s peaks occu
nea he ini ial-poin -wa e
o
90 deg ee o he sags ype B, D
and F, and o he sags ype C and E he mos un a ou able
peaks a e a ound 0deg ees. In addi ion, igu es show ha
i
he
sag is symme ical ( ype A), he ini ial poin -an-wa e has no
in luence on he powe and o que peaks.
Bo h he cu en and o que highes alues a e ob ained
when sag du a ion is
hal
ape iod plus any numbe
o
ull
pe iods (A =TI2 +kT whe e kis a in ege k=0,1,2
...
). Hence,
he
mos
se e e cu en
and
o que peaks a e p oduced by he
speci ic ini ial poin -an-wa e and sag du a ion
o
Table III.
Fig. 3. Dep h in luence: 835MVA SM o que agains asymme ical ol age
sag: ype A, h= 0.1 o 0.9,
/),./
= lOOms(6 cycles),
'/1
,= 15°
_hi"/
nm./_0 IdJ
FigA. Dep h in luence : 5kVA SM o que agains a symme ical ol age sag:
ypeA
,h
=O.1 o 0.9,/),./=
lOOms
,
'/1
,= 15°
400
00
".
~
200 ,
.Q a
".
~
';:;..
m-200 V
-400a0.05 0.1 0.15
Time [seconds]
~~
I
E I
a0.05 0.1 0.15 0.2 0.25
Time [seconds]
Fig. 2. 5kVA Synch onous Machine beha iou o a symme ical ol age
sag: ype A, h=OA,
/),./
= lOOms,'/I' = 15°
Fig. 3 shows o que
o
hyd o u bine gene a o agains
symme ical ol age sag whose dep h ange is om 10% o
90%. Sag du a ion is ixed on lOOms (six cycles) o all
simula ions done and he ini ial-pain -wa e is 15°. I is clea as
he impac on o que is mo e se e e
i
he sag is deepe . The
s eam u bine gene a o has a e y simila beha iou .
Ne e heless, as a as 5kYA machine is conce ned,cu en ,
o que and ac i e powe oscilla ions a e a enua ed by winding
dampe s, as shown in Fig. 4, whose simula ions ha e been
made se ing he sag du a ion on lOOms and he ini ial pain -
on-wa e on 15°. Bo h igu es a e he esul
o
ecu si e
simula ions unde speci ic condi ions men ioned abo e in o de
o analyze each ac o sepa a ely.
:,
' E . :
a0.05 0.1 0.15 0.2 0.25
Time [seconds]
,
::
~
.
~
'
~
.:» -100
-200a0.05 0.1 0.15 0.2 0.25
Time [seconds]
731
20 40 60 80 100 120 140 160 180
poin -an-wa e [de ee]
impac on cu en s s a o is mo e se e e i he sag is longe ,
when he ol age is es o ed. Figs. 6 and 7 shows he ansien
o
he angle Job ained
o
ecu si e simula ions keeping dep h
sag on 10% and ini ial poin -on wa e on 15 deg ees.
il===:
.~
o 20 40 60 80 100 120 140 160 180
poin -an-wa e [de ee]
!
l
~
===
2
-
1
o 20 40 60 80 100 120 140 160 180
poin -an-wa e [de ee]
!T===
=:
•
=:=1
o 20 40 60 80 100 120 140 160 180
poin -an-wa e [de ee]
i':
~
1
o m
~
00 00 100
1m
1~ 1M 100
poin -an-wa e [deg ee]
!
1
;
~
==
:
:
===:1
o m
~
00 00 100
1m
1
~
1M 100
poin -an-wa e [deg ee]
i':
~
-
'
1
o 20 40 60 80 100 120 140 160 180
poin -an-wa e [deg ee]
Fig.5. Ini ial poin -an-wa e in luence: 325MVA SM o que peaks o
sags
ypes
A, B, C, D, E and F
o
di e en ini ial poin -an-wa e.
Du a ion is h ee cycles and dep h is 10%: (alI sag ypes, h=0.1,
!J.{
=
50ms
,l Ii =0 ° o 180°)
C. Du a ion In luence
The angle Jis in luenced by he sag du a ion. An inc ease in
he sag du a ion leads an inc ease in he peak alue eached in
he oscilla ion ha occu s a e ol age eco e ing. I his peak
alue is e y la ge, Jis unable o e u n o i s s eady s a e alue
and hen he synch onism is los .
In e ms
o
o que and powe , simula ion esul s sugges ha
in sho es ol age sag, peak alues a e highe a he beginning
ha a e he ol age is es o ed. Simila ly, compa ing he
ansien s o di e en du a ion leng hs i can be seen ha he
Time{
'ocond/
Fig. 6. Du a ion in luence: 325MVA SM
<5
agains ansymme ical ol age
sag: ype A, h=0.1 ,
!!J.
=0 - 200ms, Ij j = 15°
Time
,ocond/
Fig. 7. Du a ion in luence: 5kVA SM
<5
agains an symme ical ol age sag:
ype A, h=0.1
,!!J.
=0 - 200ms, Ij j = 15°
V.
CO
NCLUSIONS
Synch onous machines play a e y impo an ole in he
s abili y o powe sys ems, since he as majo i y
o
he
elec ical powe gene a ion sys ems in he wo ld using his
machine.
Symme ical and unsymme ical ol age sag e ec s on
h ee-phase SM ha e been quali a i ely analyzed on h ee SM
o
di e en nominal powe . The simula ion
o
SM allows us o
unde s and i s pe o mance and o deduc i s beha iou agains
dis u bances in he powe supply.
Vol age sags e ec s on equipmen depend on di e en
elemen s such as sag cha ac e is ics (dep h, du a ion, poin -on-
wa e and ype o sag), equipmen and g id. Pa icula ly, he
mos ele an ol age sags e ec s on he SM a e cu en and
o que peaks and possible loss
o
synch onism. The e we e no
signi ican di e ences in he simula ion
o
he SM ope a ing as
mo o o gene a o .
The SM will con inue ha ing a wide applica ion in
indus ial p ocesses and powe gene a ion, o hei excellen
ea u es.
732
ACKNOWLEDGMENT
This esea ch wo k was suppo ed by he p ojec ENE2008-
06588-C04-03-ALT om he Spanish Minis y
o
Educa ion
and Science.
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[3] M. H.J. Bollen, Unde s anding Powe Quali y P oblems, IEEE P ess,
New Yo k, 1999
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o
Momen a y Vol age Dips on he Ope a ion
o
Induc ion and Synch onous Mo o s, IEEE, T ans. Indus y Applica ion,
Vol 26,
No.4,
July/Augus 1990.
[5] F. Ca lsson, 1. Engs om, C. Sada angani, To que a ia ion Tu ing and
a e Vol age Sags o a Synch onous Machine, EPE 2001.
[6] P. C. K ause, Analysis
o
Elec ic Machine y, McG aw-Hill, New Yo k,
1986.
[7] F. Ca lsson, Sa u a ion in Synch nous Machines due o Vol age Sags,
IEEE 2003.
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Symme ical and
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