Читать книгу English Original Reader for Technical Students. Power transformers: short-circuit testing, monitoring systems (Smart Grid) - Александр Юрьевич Хренников - Страница 9

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 isn’t 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 (1.12–1.14), 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 error’s distribution of measurement:

(1.23)

where: Δэ – entropy error from (20);

is the root-mean-square deviation (RMSD) from (1.16).