The
abstract
on a theme of master's work
Our
goal is to improve the accuracy of
experimental
determination of the frequency characteristics of the conductivity of
the
stator windings of synchronous machines (SM) according to the
measurement of
the transient at sudden three phase short circuit on the findings of
the
electric machine.
The
urgency of this work lies in the fact that
the accuracy
of experimental determination of the parameters of the SM experiments a
sudden
three-phase short-circuit current (VKZ) by the method recommended by
force in
Ukraine and CIS countries, the industry standard GOST 10169-77
"Three-phase synchronous electric machines. Test methods "[2], in
some cases may be inadequate. In this context requires the development
of a new
experimental method for determining the set of electromagnetic
parameters of
the SM according to the experiments VKZ, which will reduce the error
due to the
exclusion of systematic errors inherent in the standard procedure.
Expected
practical results: the application of this
method will
receive the combined electromagnetic parameters in real operating
conditions of
CM with different degrees of saturation at a relatively small
investment of
time to stage experience, and without changing the working patterns of
the
unit.
Experimentation
sudden three phase short circuit (SSC) is recommended for the
experimental
determination of synchronous, transient and subtransient inductances on
the
longitudinal axis of the rotor synchronous machines (SM), as well as
the
corresponding time constants. The procedure for finding the values of these parameters is
regulated by a number of documents: the
recommendations of the International Electrotechnical Commission IEC
34-4 [1],
the U.S. standard IEEE 115 and in force in Ukraine and CIS countries, the industry
standard GOST
10169-77 "Three-phase synchronous electric machines. Test methods
"[2].
It
is known that methods for determining the electromagnetic parameters of
electric machines based on measurements of currents and voltages
recorded
during the experiment, have the error. These errors manifest themselves
as
variations of the calculated parameters and make it difficult to answer
the
question: attests whether it is incorrect theoretical assumptions in
the
development of computational algorithms, or the possibility of
non-registration
in the experiments required the profile with a specified accuracy.
Therefore,
he questions the accuracy of experimental determination of the
parameters of
the SM experiments SSC the subject of many studies [3 – 7].
The
basis of the standard [1, 2] techniques a simplified model, which in
addition
to the winding excitation (WE) accounts for only one damper circuit in
each of
the axes of magnetic symmetry of the rotor SM. It is assumed that the
damped
periodic component of the stator current at sudden three phase short
circuit is
not more than two electromagnetic time constants. Also accepted
assumption is
to neglect the second harmonic in the current circuit, and neglecting
the slow
rotation of the magnetic flux of cos-aperiodic component of the stator
current.
Theoretically, the existence of these components in the stator current
at SSC
was shown in [8].
The
authors of [3–5] by analyzing a standard methodology,
ascertain
the
spread even
when the automated determination of electromagnetic parameters (EMP) by
using a
PC and trying to establish its cause in making assumptions associated
with the
neglect present in the stator current at SSC component of the second
harmonic.
In this case, they do not examine the influence of slow rotation of the
aperiodic component.
In
[6, 7] the effect of these assumptions on the dispersion of
electromagnetic
fields is considered simultaneously. In this study, uses the concept of
the
authors of [9]. In line with this concept stages of the study are in
the
following definition of EMP:
– Select a
mathematical model of the process SSC;
– Development
of an
algorithm for finding the parameters;
– Conducting
an
idealized experiment, aimed at the calculation of the current change in
SSC on
a given EMP SM and reverse their determination based on the calculation
of the
transition process;
– A
comparative
analysis of original and derived from an idealized experiment to EMP.
If
the difference between the results determine the EMP in an idealized
experiment
satisfies a given accuracy, it testifies to the correctness of the
chosen
mathematical model, and hence its applicability to the real electric
cars.
Otherwise, it would indicate inconsistency models of real objects. Then
it is
necessary to clarify the model and produce a new definition of the
parameters
measured.
Applying
the approach
described in [9] the author [6, 7] as reasons for the
scatter – found influence admissible perturbations associated
with the
neglect of
the slow rotation of the aperiodic component and a simultaneous neglect
of the
second harmonic current SSC, which form the basis of the standard
method [2].
The
essence of [6, 7] reduces to the requirement of conducting experiments
SSC and
processing of raw data in such circumstances under which a model of SM
described by equation (1), the maximum corresponds to the real object.
In
particular, the proposed transition and subtransient inductances and
the
relevant time constants of changes in the periodic component of the
current is
determined separately from the currents in each phase, and then find
their
average. Time constant characterizing the change in ane-periodic
component, it
is recommended to determine the current in a "special stage", ie in
phase with an axis at the moment of closure coincides with the
longitudinal
axis of the rotor. In this case, the effect of slow rotation
aperiodic-electric
flux is negligible. To eliminate the influence of EMP on defined
current
harmonic parameters of the proposed transition and find the results of
measuring the current through a periodic time approximately equal, ie
beginning
at the time when the aperiodic component is damped.
In
these literary sources are not assessed the influence of parameters of
SM on
the transverse axis of the currents in phases at SSC. As shown in [8],
this
effect is always the case even when short-circuit from idling. This is
due to
the influence of resistances of rotor circuits. Furthermore, as already
pointingelk, in all cases it is assumed that SM but the field winding
has only
one damper circuit in each axis of symmetry of the rotor. Currently in
solving
a calculation of electromechanical transients have a tendency to
integrate
multicontour rotors. The current standard in Ukraine [2] provides in
Section 25
and claim 26 determination of electromagnetic parameters and frequency
characteristics based on the rotor of an arbitrary number of units.
Research
questions of the mathematical model, laid the basis for a standard
methodology
for the definition of a set of electromagnetic parameters of the SM
based
multicontour rotor according to the experiments SSC in the literature
were not
considered.
Materials
and research results. We use a standard
methodology for
the analysis of the definition of a frequency response (FR)
conductivity of SM
from the stator winding leads to the above concept [9].
The
choice of a mathematical model to determine the electromagnetic
parameters and
vx, taking into account multi-contour of the rotor is given in [2]. In
accordance with paragraph 1.25 of GOST 10169-77 machine
parameters
on
the
longitudinal axis should be determined by the transfer function
representing
the envelope of the periodic variation of the armature current in the
experiment SSC. This component is defined as half the difference of
ordinates
of the upper and lower enve-containing phase current. Introducing the
periodic
component of the current sum of exponentials, the law of its changes
over time
can be described by the function
(1)where 
–
Set short-circuit
current
–
initial
value and decay time constant of k-th exponential component periodic
current; n
– the number of exponents, equal to the number of account.
Thus,
taking into account the variation multicontour rotor stator phase
current at SSC
has a form similar to (1), the only difference is that the periodic
component
of the current is not two but three – four (on the
recommendation
of
[2])
exhibitors. In accordance with standard procedure
transition–function
(3)
correspond to the following expressions for determining the
conductivity of vx
from the stator windings in the longitudinal axis of the rotor:
(2)or
(3)
where 
–
coefficient
of damping
of the k-exponential component:.
The parameters in
(3), determined in accordance with clause 25.1.1 [2] as follows:
(4)
(2)
that the locus of the complex conductivity of individual equivalent
rotor
circuits are circles whose diameters are determined by the initial
value niyami
respective exponential components, approximating periodic current
statistical
pa. Then on the basis of the frequency response can be given a
graphical
interpretation of the standard methods for determining the EMP of the
experiments SSC. Relevant construction shown in Figure 1.
From
the analysis of Figure 1, it follows that the standard method involves
the
determination of subtransient the inductive resistance, as resistance
machines
from the stator windings for an infinitely long slip of the rotor.
This
corresponds to the fact that the initial value of a periodic component
of fault
current determines the conductivity of SM during sliding. Consequently,
Currently,
the procedure for measuring the parameters of the regime in experiments
SSC realized,
as a rule, using an analog-digital converters (ADC) or by using
specialized
digital recorders and their subsequent processing by computer. However,
it uses
practically the same approach as for plotting the results of
measurement
waveforms manually, ie, periodic and aperiodic components are,
respectively, as
half the difference and half the sum of the envelope of the phase
currents [6,
7]. Approximation of periodic current is carried by the successive
selection
first transition (at the final stage of the transition process) and
then
subtransient (the initial portion of the transfer function after
subtracting
the already found in transition) components. Analysis of the parameters
of
equivalent circuits multiloop replacement of some industrial turbine
generators, indicates the presence of rotor circuits, electromagnetic
time
constants are less than half-synchronous frequency. Even if a periodic
component of the transient current measured in accordance with the
requirements
of the standard (the average value of periodic currents of three
phases), the
allocation of exponentials with time constants, commensurate with the
time
half-power frequency may not be possible. This is due to the fact that,
in this
case, the envelope of the experimental curve can be given not less than
0.0033
sec. Discretization of the current of each phase increases, while three
times
and is half the period of industrial frequency. Therefore, the need for
periodic current transient in three – four exponential
components
to
reduce
errors in determining the frequency characteristics in the region of
large slip
as background information in the experiments SSC should use vector
representing
the transient stator current. Sampling frequency of measurements of
phase
transient currents using digital recorders, in this case, it may be 5
kHz or
more.
Proximate
algorithm.
Can propose the
following algorithm
refines the definition of FR.
According
to the approximation of the modulus of the generalized stator current
vector
function (8), the initial values of
the coefficients
of exponential
decay
components of
the periodic current 
,
which represent the projections of the complex
conductivity of the rotor contours at s = – 1 on the
longitudinal
axis
of the
rotor.
Assuming that the
values 
correspond
to the slip s
= ∞, are the vectors of the
complex
conductivity at
s = – 1:
; 
Given
that the time constants found in the original vector or their
projections on
the longitudinal axis-ing unchanged, calculated the true values of the complex
conductivity of rotor circuits in sliding s = –
1):
Are the actual maximum values of conductivities rotor contours at s = ∞, that returns the diameter corresponds to the frequency characteristics:<
By
(2) is calculated vx conductivity of the stator windings of SM.
Frequency
characteristics for the generators MT-30 and TGV-200M, calculated using
an
improved algorithm in an idealized experiment, practically coincided
with the
source.
Conclusions. Based on the analytical
description
of the changes in the generalized vector of stator current for
three-phase
short circuit on the findings of synchronous machines, a new approach
to
experimental determination of the frequency characteristics of the
conductivities of the stator windings, which allows to specify a
standard
methodology recommended by GOST 10169-77.
REFERENCES
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Electrotechnical Commission (IEC) Standard. Rotating Electrical
Machines. Part
4: Methods for determining synchronous machines quantities from tests.
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Three-phase synchronous electric machines. Test methods. –
Moscow:
Publishing
House of Standards, 1984. – 78.
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