The calculated curve derivative from current and calculated inductance Ls-c curve of 400 MVA/220 kV transformer in the short-circuit shot on the phase «C» with 100 % of the value of the aperiodical (shock) short-circuit current are shown in Figure 5. Deviation of Ls-c amounted to +1.3 % in the short-circuit shot.
a)
b)
Figure 5. The calculated curve in the short-circuit shot on the phase «C» with 100 % of the value of the aperiodical (shock) short-circuit current of 400 MVA/220 kV transformer: a) derivative from current; b) calculated inductance Ls-c curve.
During the tests for withstands to short-circuit currents of 400 MVA/220 kV transformer, the following data were obtained:
values of voltage and current in short circuit shots,
the short-circuit inductance measurement results,
level of vibration in the short circuit shot,
LVI-testing data,
the results of chromatographic analysis of transformer oil dissolved gas (DGA).
Diagnostic data parameters allowed to complete the objective picture of the condition stste of 400 MVA/220 kV transformer during the tests for withstands to short-circuit currents [by 14].
1.6. An Accuracy of Diagnostic Parameter of Smart Grid Monitoring System
When Smart Grid Monitoring System is working, an important issue is the accuracy of main diagnostic parameter which characterizing the normal operation of power transformer the short-circuit inductance of the windings. Large error during the measurement of this parameter can lead to malfunctions of the device: false outages or, on the contrary, the protection isnt working when the inductance changed after the transformer or the reactor had been damaged. Therefore, it is proposed to introduce to the scheme of this device the block of the mathematical treatment of ΔL measurement.
The confidence interval of a random measurement error of transformer inductance was determined in the block of mathematical treatment of L measurements results by a specific algorithm.
Measured parameters I, U, P, F from the measured voltage transformers, capacitive voltage dividers, current-measurement shunts and frequency counter are input to the entrance of mathematical treatment block of measurement results, where at the entrance there are analog-to-digital converters (ADC), within which the following operations are performed by a special algorithm:
1) The value of short-circuit transformer inductance which is converted to a frequency 50 Hz, is calculated
(1.12)
Where Ii, Ui, Pi, Fi are the values of current, voltage, power and frequency which are measured by ADC during i- count.
2) The average value of short-circuit transformer inductance at the 50 Hertz frequency is calculated
(1.13)
together with the total average value, including the parameters of the I, U, P, F:
(1.14)
where: Xi values of the I, U, P, F, measured by ADC during i-counting,
n is the number of measurements.
3) The deviation of short-circuit inductance is calculated
(1.15)
where:X0 base value of short-circuit transformer inductance, determined by calculations according to the results of preliminary tests.
4) The root-mean-square deviation (RMSD) of the measurement results for each of the primary parameters of I, U, P, F is calculated;
5) The RMSD for the resultant of short-circuit inductance is calculated:
(1.16)
where:are the corresponding RMSD of the means of the measurement (ADC converters of current, voltage, power and frequency);
are the specific weights of errors in a general error in the result X50:
(1.17)
where: I, U, P, F are the primary measured parameters of the current, voltage, power and frequency.
6) The value of the fourth central moment of distributing the random error of measurement of inductance X50 is calculated:
(1.18)
where n is number of measurements;
Xi50 is the value of short-circuit inductance;
Xaverage50 is the average value of short-circuit inductance;
7) The value of antikurtosis and kurtosis
of the distribution of a random error of measurement (the coefficient of kurtosis measures the «peakedness» of a distribution) is calculated
(1.19)
where: is the RMSD value from expression (1.16);
M4 is the value of the fourth central moment of distribution from (1.18).
8) The value of an entropy error of measurement is calculated:
(1.20)
where: n is the number of measurements;
d is the width of the interval of the histogram of distribution definition as:
(1.21)
where: Xi50 and Xaverage50 are the values from (1.121.14), moreover the maximum significance of a deviation between them is taken;
m is the optimum number of class intervals of columns for constructing the histogram of distribution law of the random error:
(1.22)
whereis the antikurtosis of distribution from (1.19);
n is the number of measurements;
nj is the number of counting in j column of the histogram (j = 1., m).
9) Determined by d width of the interval of the histogram of distribution by (1.21);
10) Determined by m optimum number of class intervals of columns for constructing the histogram of distribution law of the random error on (1.22);
11) Calculated value of the entropy coefficient of random errors distribution of measurement:
(1.23)
where: Δэ entropy error from (20);
is the root-mean-square deviation (RMSD) from (1.16).
1.7. Determination of the Distribution Law of Measurement Random Error
12) The form of distribution law of measurement random error, the diagram of the topographic classification of the laws of distribution, values of antikurtosis and entropy coefficient К are determined.
13) The value of quantile coefficient for the concrete identified distribution is calculated:
Table 1.1.
14) The error in the determination of root-mean-square deviation (RMSD) of random error distribution is calculated:
(1.24)
where: is the kurtosis of distribution;
n is the number of measurements.
15) The value of the confidence interval of a random error of measurement of short-circuit transformer inductance is determined:
(1.25)
where: t is the quantile coefficient;
is the measurements root-mean-square deviation (RMSD) of X50 value.
16) Obtained result of measuring the deviation of short-circuit transformer inductance is derived to the printing in the following form:
(1.26)
where: ΔX50 is the deviation of X50 value from base value of short-circuit transformer inductance Х0;
Δconf is the value of the confidence interval of a random error of measurement of short-circuit transformer inductance from (1.25).
1.8. Сalculation of Confidence of Interval of Measurement Random Error during Short-Circuit Transformer Testing
In the case of the appearance of residual deformations in the windings of transformer-reactor electrical equipment (TREE) comes a gradual increase in the value of short-circuit transformer inductance.
The criterion of the evaluation of the threshold quantity of the deviation of short-circuit inductance, which corresponds to the beginning of the appearance of deformation, is value (ΔХs-c = +0,20,3 % with the confidence interval (accuracy) of the measurements (Δconf = 0,1 %). Value ΔХs-c = +1 % corresponds to the sufficiently serious deformations of the transformer windings [by 14].
The given procedure of the determination of the confidence interval Δconf (1.121.25) for the measurements of Хs-c can be used also in the case of calculation Δconf for the deviations ΔХs-c in the course of transformer testing for withstand to short-circuit current. The value of Δconf for the deviations ΔХs-c, determined on (1.26), does not exceed the value of Δconf for ΔХs-c, since utilized in (1.131.15) Xaverageand X0 are calculated from the samples n of the uniform the equal-point values xi, which have one and the same law of random error distribution in the type Chapeau.