English Original Reader for Technical Students. Power transformers: short-circuit testing, monitoring systems (Smart Grid). Александр Юрьевич Хренников
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СКАЧАТЬ style="font-size:15px;">      
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: 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 measurement’s 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 = +0,2–0,3 % 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 1–4].

      The given procedure of the determination of the confidence interval Δconf (1.12–1.25) 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 (1.13–1.15) 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”.

      Let us illustrate this based on the example of a change in the significance of a deviation of short-circuit inductance ΔХs-c from one shot to the next during the 25MVA/220 kV transformer testing for withstand to short-circuit currents (Figure 6).

      Figure 6. Example of a change in short-circuit inductance and the estimation of the significance of deviations СКАЧАТЬ