English Original Reader for Technical Students. Power transformers: short-circuit testing, monitoring systems (Smart Grid)

(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)

where

is 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: ?э – 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: