cong 1997108
TRANSCRIPT
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SYNC NOUS MA TERS IDENTIFICATION USING
L
TEST
DATA
Edson
daCosta Bortoni,
EEE
Jose Anthnio Jardim, EEE
DEE-FEG-UNESP PEA-POLI-USP
BRAZIL
Abstract
Titis
work shows a computational
m e ~ o d o i o ~or the determination of synchronous
machines parameters
using
load rejection test data. The
quadrature
axis
parameters are obtained with a rejection
under an arbitrary reference, reducing the present
difficulties.
I INTRODUCTION
In the last decades, many methods have been developed
in
order to obtain synchronous machines parameters. Two of
then gained prominence due to their practice, low
risk
level
imposed to the machine under test and moreover, the quality
of the obtained data. One is the frequency response method
[11 and the other is the load rejection test [ 2 ] .
The frequency response test is carried out
by
applying
currents about 0.5 of the rated current., with frequencies
varying
in
the range from
0.001
Hz to 1000 Hz
The
rotor
must
be
properly positioned
in
order to obtain the direct and
quadrature
axis
parameters. Using the frequency response
data one can evaluate the operational reactances and
consequently determine the parameters and time constants
currently
used
in power
systems
studies.
The second method also allows the determination of direct
and quadrature axis parameters
by
executing load rejection
in two special operational points, where the components of
current do exists in the axi s of interest only.
The
dire t axis
load point c n
be
obtained under exciting
the machine as it
has
been synchronized to the system. The
machine must be running at negligible active power and
driving a considerable amount of reactive power from the
system to obtain non-saturated parameters and avoiding
undesirable overvoltages during the tests.
The process to locate the quadrature axis is not
so
hivial,
since one must find a loading point in which the absolute
value of the power factor angle 9)e equal to the power
angle 6).
In
practice it c n
be
found
after
successive load
rejections
with
different reactive powers, aiming to ” i z e
the field current variations. An alternative procedure
is
the
employment of a power angle meter [3]. These “ H i e s
can, sometimes, make
this
test impracticable.
This work will show that the data obtained with a load
rejection under an arbitrary reference is sufiicient to
detennine the transient parameters using numerical
methods.
The identification will
be
made
using
the Levenberg-
MArquardt Algorithm [ 5 ] .
ILTRANSIENT PROCESSMODELING
The synchronous machine transient process modelingw i l l
be made in three steps. The
first
takes into account only the
steady state, before the load rejection; the second
analyse
the
transient process after the rejection and
in
the former, a
composite of the previous results
will
be done
in
order to
obtain
the complete behavior
of
the machine under a load
rejection
[4].
In
these analysis all the variables are in per
unit.
A .
teady State
In a three-phase system with perfectly symmetric voltages,
balanced loads, with no damping winding currents,
neglecting the armature resistance and taking the angular
speed 0) qual to 1 P.u., one can obtain the initial
conditionsof the linkage fluxes for the
direct
and quadrature
axi s
where
U is
the terminal effective voltage and
6
is the angle
between the terminal voltage (reference) and the q-axis.
B Transientprocess
Using a second order model to represent the
dire t
axis
of
a synchronous machines, one c n obtain:
where L d is the
dire t
axis synchronous inductance,
L’d,
L”
T’& and T’’& are the direct axis transient and subtransient
inductancesand open
circuit time
constants.
For a first order quadrature axis model and applying the
same procedureused for the direct axis, yields:
1
lT
A y s
=
i, . L, - L,
- L:).
e
I
(3)
where L, is the quadratureaxis synchronous inductance,Yq
and T”, are the quadrature a x i s subtransient inductance and
the subtransient open circuit time constant.
0-7803-39464/97/$10.00
1997
EEE.
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C. Description of The Load Rejection Phenomena
The machine behavior
in
a load rejection transient process
can be obtained by composing the phenomena that occur
before and after to the load rejection. Thus, the linkage
flux
in the direct
axis
will be:
where yt and Yda) are the and dcuIztted d u e s
at the instant t a is parameter vector iterativelly calculated
by the following equation.
vd
vdo
+
A y d
= -U- cos
+id
.
d
-
L ~L:).
-
~ h
1
(4) au = au-1- h 10)
.
e-t/TL
In the same way, for the quadrature
axis:
It is important to note that any identification method has
its performance mproved if the iterative process
begins
with
-t/T&
]
( 5 ) adequate initial approximations for the unknown parameters.
In th is case, they could
be
obtained by using basic
relationships [2]. Typical values found in text books can
also be
wed as messes. ms technique will
be
employed for the direct and quadratureaxis time
constants
avoiding the laborious graphical approximation.
\y, =
\yqo
+Avs = U . sm6 + i, .
The equation of the voltage variation in a load rejection is:
U, =
U .
sin(at-
S)
- , . L,
L,
U;). e-t’T;o] cos(wt)
1
sin(ot)
lV.
EXAMPLE
OF APPLICATION
6)
-id .
kd
L ~cd .
-
L: -vi). -t’TL
The
proposed method
will be
applied to one rounded rotor
synchronous machine, the rated characteristics are presented
in Table
I.
m e n there is no ament component in the
axis
iq=Oand
M ,
ne c n
obtain:
. .
TableI
-
Rated c cs
coscp~ 0 8
= 9375kVA
(7) UN
=
13.8kV Vmc = 125 V
In
the other hand, when there is no direct axis current
1 ~ = 3 9 2 A Imc= 368
A
component, results:
It
w a s
not possible to determine the quadrature a x i s load
point, however, load rejection tests under an arbitraxy axis
and under the drect axis was made. Fig. 1 shows the
].cos(mt)
8)
-tlT&
U,
=U.s in(ot -6)- ip .
transient (la) and subtransient (Ib) response for the
direct
response for thearbi trary~ .
These
are
the
basic to the
load
rejection
ax i s
Fig. 2 shows the transient
za)
and s u b w e n t (2b)
description and they could be
used
to identify the
synchronous machines parameters.
Thus,
wo procedures are
proposed in order to simplify the identitication process, and
spread the use of load rejection tests:
A.
mcjsparameters
The quantities involved in the load rejection process was:
Determine
all
the synchronous machines parameter
with
a
load rejection under an rbitr ry condition
using (6);
or,
0 Make a load rejection test
in
the direct axis, using (7) to
determine the
direct ax is
parameters, and make another
load rejection
under an
arbitrary
a x i s
to calculate the
quadrature
axis
parameters with
8),
using the previous
calculated direct axis parameters
as
constants.
Po E O M W
Q = -2.930 M v ~
U, =13416V
I, = 126.1A
U,
=84OOV
P
0 p.u.
= -0.3125 p.u.
= 0.972 p.u.
= 0.321 p.u.
=
0.609
p.u.
III.
PARAMETERS
IDENTIFICATION
The
ollowing typical
values
was
adopted
as
initial
guesses
for the time constants:
TAo =
5
TJ0 = 0-05s
The syncbronous machines parameters will be identified
in order to minimize the error between the theoret id model
(6,
7 or 8) and the experimental data obtained. The
henberg-hhquardt method [5] will be employed to Applying 7), the refined parameters
were obtained with
minimize
the goodness function defined as:
relative error smallerthan 1%, after
6
iterations.
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SUBTRANSIENT STATE
TRANSIENT STATE
0 00 2 00
4 00
6 00
8 00 10.00
0.00
0 40
0.80
7.20
1
eo
2.00
Time [S Time
[S
4 @>
Fig.
1 LOAD
REJECTION
-
DLRECT
X I S
0 92
o 88
.84
TRANSIENT STATE
....
' - - -STEADYSTATE
I
0.80
I
1 1 1 1
0 m 2 00 4 00
8.00
8 00
10 00
Time [S
4
Fig. 2 -
LOAD
REJECTION
Ld
=
1.1375
P.U.
p d
=
0.1 876P.U.
L2
=
0.1074
D.U.
-
TAo
=
49653 s
T;Io
= 0.0222s
B. Quadrature
axis
parameters
The electrical quantities are:
Po
= 2.810MW
= 0.300 p.u.
U,
=
13390 V = 0.970p.u.
I,
=
143 A
= 0.365 p.u.
U =
11400
=
0.826
p.u.
The power anglewill be also identified.
Its
initial
value was
obtained
using the following approximation:
Qo
=
-1.770 M v ~
-0.189
P.U.
Using (S), after 7 iterations, the adjusted parameters with
relative error smallerthan 1 parameters are:
0° 1
0 90
.92
i .88
0.84 I I I I I
0.00
0 40 0 80 7 . 2 0 7 .oo
2 00
Time [S
(b)
- A R B m U R Y m s
Table
III
-Adjustedquamature
axis
parameters
Lq =
1.055
p a .
L i =
0.1492
P.U.
T