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fnom. is the nominal value of the frequency.
Lj meas. is the instantaneous value of inductance.
In the following block the average value of inductance during each period is calculated:
(1.10)
In the block of calculation of deviation, Laverage value during the period is compared with the base L0 value, and their difference is calculated:
(1.11)
where: L average is the average value of inductance during the period;
L0 is the base value of transformer inductance, determined from the preliminary experiment.
When winding deformations begin or in the case of winding turn-to-turn internal short-circuit, the value of inductance L tends to increase, or to decrease from one time period to the next period in case of irreversible destruction of the controlled power transformer windings.
Then, the signal from the control block enters the protection block (rapid digital protection), where a signal to switch off is formed in the high-voltage circuit breaker (B). After that Information-measuring system and the connected with it protection block stop the process of winding destruction [by 1–4].
This Smart Grid monitoring system is a perspective direction of diagnostics under operating voltage.
1.4. Inductance Calculations of 167 MVA/ 500/220 kV Autotransformer
Basing on the foregoing, the algorithm (1.1–1.11) was developed and now constitutes a special program for calculating instantaneous inductance L during electrodynamic test of the power transformer by short-circuit currents. The program allows determining the average value of the inductance during each period. This value is more significant in the case of damage to the coil (primary deformation, coil circuit). To evaluate the potential effectiveness of the monitoring system, the calculations of instantaneous and average values of inductance (L) were performed for the case of accidental and non-regime (ANR) due to damage during short-circuit testing at Power Testing Laboratory (Togliatti) of 167 MVA/ 500/220 kV autotransformer.
During short-circuit testing of 167 MVA/ 500/220 kV autotransformer at the second short-circuit shot, i.e., experience with 100 % value of the short-circuit current 0.2 sec duration according to the test program (time set by the conditions of experience – 10 periods of current, and regulated by high voltage thyristor valves), there has been actuation of transformer gas protection.
Audit and inspection with the lifting of transformer tank and inspection of the active part of autotransformer have revealed the presence of electrical damage to the regulation winding (RW) – turn-to-turn short circuit. Figure 2 shows the real oscillograms of short-circuit current (Figure 2a), voltage (Figure 2b), estimated the average curve of inductance for 10 periods (Figure 2c), the calculated curve instantaneous inductance (Figure 2d) in the second short-circuit shot. Change of the value of the inductance of the curves in Figure 2 shows that the electric damage of RW winding happened at the 4th period and continued to develop in the remaining periods of short-circuit shot.
Calculations of inductance values show that the application of Smart Grid monitoring system and quick-working protection would submit a command to turn off the high-voltage circuit breaker in the fourth period of current that is, taking into account the work of protection and circuit breaker (at least three periods, i.e., 0.06 seconds), cease the emergency process at the 7-th period of current. Thus one could reduce the damage of RW windings and the cost of its repair at the transformer manufacturer.
a)
b)
c) and d) Figure 2. Oscillograms of short-circuit current (Figure 2a), voltage (Figure 2b), estimated the average curve of inductance for 10 periods (Figure 2c), the calculated curve instantaneous inductance (Figure 2d) in the second short-circuit shot of 167 MVA/ 500/220 kV autotransformer.
1.5. Smart Grid Monitoring System for Short-Circuit Testing
Smart Grid Monitoring System for control of parameters of the transformer when tested for withstands to short-circuit currents, part of the quick-working protection, is discussed in [by 1–3].
Figure 3. Smart Grid Monitoring System for control of transformer parameters during short-circuit testing, which is a part of the quick-working protection. 1-power supply (network), 2-safety high-voltage circuit breaker, 3-test transformer, 4-synchronous short-circuiter, 5–7-capacitive voltage dividers, 8–9, the control block, 9 – voltage transformer, 10–12-current-measurement shunts, 14–22-the functional blocks of the inductance average value’s calculation of the deviation from the original value, 23-testing transformer in the secondary winding short-circuit mode.
Control of the average value of inductance Laverage for the period during the test allows fixing moment of the beginning of the emergency regime and reducing the scale of the accident if the tested transformer is timely disconnected. The Monitoring System provides a more accurate measurement of inductance and increases the reliability of the power transformer in case of dangerous deformations.
Quick-working protection prevents accidental destruction of the test object and increases the crash safety of the test (Figure 3) [by 1–5].
In Figure 3 the following details of the equipment are shown: 1-power supply (network), 2-safety high-voltage circuit breaker, 3-test transformer, 4-synchronous short-circuiter, 5–7-capacitive voltage dividers, 8–9, the control block, 9 – voltage transformer, 10–12-current-measurement shunts, 14–22-the functional blocks of the inductance average value’s calculation of the deviation from the original value, 23-testing transformer in the secondary winding short-circuit mode [1–5].
Consider the work of the monitoring system in Figure 3 with an example of the 400 MVA/220 kV transformer testing. Current and voltage oscillograms at the second short-circuit shot on the phase «C» of the 400 MVA/220 kV transformer are shown in Figure 4.
Figure 4. Current oscillogram (1) and voltage oscillogram (2) in the second short-circuit shot on the phase «C» of the 400 MVA/220 kV transformer.
Current oscillogram analysis shows that the value of aperiodical (shock) component of short-circuit current at the beginning of the short-circuit shot amounted to 12.8 kA, and through 10 periods after attenuation of aperiodical (shock) component at the end of the shot, then periodic component is only 10.2 kA.
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 1–4].
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 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 ?L 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)
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:
