SYNC
NOUS MA
TERS IDENTIFICATION USING
TEST DATA
L
Jose Anthnio Jardim, E E E
Edson da Costa Bortoni, E E E
DEE-FEG-UNESP
bortoni@feg.unesp.br
PEA-POLI-USP
jardini@pea.usp.br
BRAZIL
Abstract - Titis work shows a computational
m e ~ o d o i ofor
~ 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 axis of interest only.
The direct axis load point can 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)be equal to the power
angle (6). In practice it can 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 LevenbergMArquardt Algorithm [5].
0-7803-39464/97/$10.00
0 1997 IEEE.
IL TRANSIENT PROCESS MODELING
The synchronous machine transient process modeling will
be made in three steps. The first takes into account only the
steady state, before the load rejection; the second analyse the
transient process after the rejection and in the former, a
composite of the previous results will be done in order to
obtain the complete behavior of the machine under a load
rejection [4]. In these analysis all the variables are in per
unit.
A. Steady State
In a three-phase system with perfectly symmetric voltages,
balanced loads, with no damping winding currents,
neglecting the armature resistance and taking the angular
speed (0)equal to 1 P.u., one can obtain the initial
conditions of the linkage fluxes for the direct and quadrature
axis:
where U is the terminal effective voltage and 6 is the angle
between the terminal voltage (reference) and the q-axis.
B. Transientprocess
Using a second order model to represent the direct axis of
a synchronous machines, one can obtain:
where L d is the direct axis synchronous inductance, L’d, L”&
T’& and T’’& are the direct axis transient and subtransient
inductances and open circuit time constants.
For a first order quadrature axis model and applying the
same procedure used for the direct axis, yields:
A y s = i,
I
. L, - (L, - L:). e- tlT$
1
(3)
where L, is the quadrature axis synchronous inductance,Yq
and T”, are the quadrature axis subtransient inductance and
the subtransient open circuit time constant.
WB1-1.1
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:
vd
+ A y d = -U- cos&
+id .[Ld- ( L -~ L:).
vdo
- ( ~ -h
1. e-t/TL
1
(4)
In the same way, for the quadrature axis:
= \yqo + Avs = U. sm6 + i, .
\y,
-t/T&
]
(5)
The equation of the voltage variation in a load rejection is:
U,
= U . sin(at - S) - i,
-id
kd-
.
I
. L,
( L -~cd).
- (L, - U;). e-t’T;o]
- cos(wt)
- (L: - vi).e-t’TL
1.
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.
au = au-1- h .
(10)
It is important to note that any identification method has
its performance improved if the iterative process begins with
adequate initial approximations for the unknown parameters.
In this 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 quadrature axis time constants,
avoiding the laborious graphical approximation.
(6)
lV.EXAMPLEOF APPLICATION
sin(ot)
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),one can obtain:
. .cs
-
Table I Rated- c
% = 9375 kVA
UN = 13.8 kV
1~=392A
(7)
In the other hand, when there is no direct axis current
component, results:
coscp~= 0.8
Vmc = 125 V
Imc = 368 A
It was not possible to determine the quadrature axis load
point, however, load rejection tests under an arbitraxy axis
and under the direct axis was made. Fig. 1 shows the
transient (la) and subtransient (Ib) response for the direct
These are the basic
to the load rejection axis. Fig. 2 shows the transient (za) and s u b w e n t (2b)
description and they could be used to identify the
responseforthearbitrary~.
synchronous machines parameters. Thus,two procedures are
proposed in order to simplify the identitication process, and A.
mcjsparameters
spread the use of load rejection tests:
U,
=U.sin(ot-6)-ip.
-tlT&
].cos(mt)
(8)
Determine all the synchronous machines parameter with a
load rejection under an arbitrary condition using (6); or,
0 Make a load rejection test in the direct axis, using (7) to
determine the direct axis parameters, and make another
load rejection under an arbitrary axis to calculate the
quadrature axis parameters with (8), using the previous
calculated direct axis parameters as constants.
The quantities involved in the load rejection process was:
P 0 p.u.
Q, = -2.930 M v ~= -0.3125 p.u.
= 0.972 p.u.
U, =13416V
I, = 126.1 A
= 0.321 p.u.
U, =84OOV
= 0.609 p.u.
Po EOMW
The following typical values was adopted as initial guesses
for the time constants:
III. PARAMETERSIDENTIFICATION
The syncbronous machines parameters will be identified
in order to minimize the error between the theoretid model
(6, 7 or 8) and the experimental data obtained. The
henberg-hhquardt method [5] will be employed to
minimize the goodness function defined as:
TAo = 5 5 TJ0 = 0-05s
Applying (7), the refined parameters were obtained with
relative error smaller than 1%, after 6 iterations.
WB1-1.2
SUBTRANSIENT STATE
TRANSIENT STATE
0.00
2.00
4.00
Time
[SI
6.00
8.00
(4
0.00
10.00
-
Time [SI
"0°
0.90
1 .eo
7.20
2.00
@>
-
Fig. 1 LOAD REJECTION DLRECT A X I S
1
!
0.92
1
0.80
0.40
4
0.92
TRANSIENT STATE
i
0.84
o'88
....
0.80
I
I
0.m
0.88
'---STEADYSTATE
,
1
2.00
'
4.00
1
'
Time
(4
Ld = 1.1375 P.U.
p d = 0.1876 P.U.
L2 = 0.1074 D.U.
1
8.00
8.00
[SI
'
0.84
1
I
0.00
10.00
,
I
0.40
'
0.80
I
'
I
7
7.20
Time [SI
'
.oo
I
2.00
(b)
Fig. 2 - LOAD REJECTION - A R B m U R Y m s
Table III - Adjusted quamature axisparameters
T<, = 0.074s
Lq = 1.055 p a .
TAo = 49653 s
T;Io = 0.0222 s
L i = 0.1492 P.U.
-
6, = 23.11'
V. CONCLUSIONS
B. Quadrature axis parameters
The work showed a mathematical modeling of the load
rejection phenomena, allowing the parameter identification
with numerical methods. This technique avoids the
employment of a load angle meter, making possible its
generalizeduse. The identification process explores all the
transient, subtransient and steady state information, and not
only specified points, reducing the errors and conducting to
more representative parameters.
The electrical quantities are:
Po
= 2.810 MW
Qo = -1.770 M v
U, = 13390 V
I, = 143 A
U, = 11400
= 0.300 p.u.
~= -0.189 P.U.
= 0.970 p.u.
= 0.365 p.u.
= 0.826 p.u.
VI. REFERENCES
The power angle will be also identified. Its initial value was
obtained using the following approximation:
[11 IEEE std 1 15 A - "Test Procedures fa SynchronousMachines"
[2] F.P. de Melio; J.R Ribeiro; "Derivation of synchronous machine
parameters ffom tests" - IEEE T m on PAS- 96, n 4, pp 1211-1 218.
[3] F.P. de Mello; "Measurement of synchronous machine rotor angle from
analysis of zero sequence harmonic components of machine terminaI
voltage" IEEE Trans. on PWRD- 9, n 4, oct 1994, pp 1770-1777.
[4] T.H.Ling T.N. Wen; T.D. Sheng, L.J. Yu; "Mathematical model of
synchmnous machine in transient process" in ICEM88.
[5] W.H. Press;B.P. Flannq, S.A Tenkolsky; W.T. Vetterling ''Nuiuerical
Recipes in C"- CambridgeUnivmity Press, 1988. UK.
[6] Krause, P.C.; No& F.; Skvarenina, T.L.; Olive, D.W.; "The theory of
neglecting statortransients". IEEE Trans.on PAS- 98, No1, pp 141-148.
-
Using (S), after 7 iterations, the adjusted parameters with
relative error smaller than 1% parameters are:
WB1-1.3