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(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: ?X50 is the deviation of X50 value from base value of short-circuit transformer inductance Х0;
?conf 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 (?Хs-c = +0,2–0,3 % with the confidence interval (accuracy) of the measurements (?conf = 0,1 %). Value ?Хs-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 ?conf (1.12–1.25) for the measurements of Хs-c can be used also in the case of calculation ?conf for the deviations ?Хs-c in the course of transformer testing for withstand to short-circuit current. The value of ?conf for the deviations ?Хs-c, determined on (1.26), does not exceed the value of ?conf for ?Хs-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 ?Хs-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 Хs-c with the aid of the confidence interval of measurements ?conf during the 25MVA/220 kV transformer testing.
Advantage of the proposed in this chapter method one can see well in the case of changing Хs-c in the third, and then in the fourth final shot from +0,22 % to 0,34 %, when the value of confidence interval with the normal distribution ?conf =
(no shaded rectangles in Figure 6) the significance of the obtained deviations does not give to estimate, since confidence intervals ?conf of third and fourth shots are overlapped. This can lead to the false conclusion that change ?Хs-c = +0,12 % from the third to the fourth shot insignificant and is connected only with the influence of measurement error.
The procedure of determination of ?conf, which presented in (1.13–1.26), allows to obtain the significant deviation of ?Хs-c with its change from the third short-circuit shot to the fourth short-circuit shot, having ?conf = 0,05 % for “Chapeau” distribution.
The obtained result is confirmed by the 25MVA/220 kV transformer dismantling at the manufacturing plant, when untwisting the regulating winding (RW) of transformer was discovered. Therefore, the proposed method is more reliable and can be recommending for the introduction on other short-circuit testing laboratories and in the operation in the power systems during the measurement of short-circuit inductance or impedance [by 3–4].
In addition to examined method, which makes it possible to obtain significant deviations of ?Хs-c with the aid of the correct calculation of ?conf, it follows to add that in the case of obtaining the insignificant deviations (as in Figure 6) from the first short-circuit shot to the second short-circuit shot and from second to the third short-circuit shot it is possible to consider significant deviation ?Хs-c = +0,17 % (0,22 % – 0,05 % = 0,17 %) from first to the third final short-circuit shot.
In addition to this, in the case of the intersection of the zones of confidence intervals ?conf between the first (?Хs-c = +0,05 %) and the second short-circuit shot (?Хs-c = +0,16 %) at point +0,11 % it is possible to consider this as one significant deviation ?Хs-c = +0,11 % with the confidence interval ?conf =
, since between the second and the third short-circuit shot also occurs insignificant deviation (Figure 6) [by 10–14].
From Figure 5 follow that zones of confidence interval ?conf of measurement short-circuit inductance Хs-c of the adjacent on the time short-circuit shot (for example, 2-nd short-circuit shot and 3-d short-circuit shot) can intersect between themselves: ?Хs-c2 = +0,16 % (?conf2 =
) and ?Хs-c3 = +0,22 % (?conf2 =
).
This “imposition” of measurement confidence interval is inadmissible, since in certain cases this hampers the estimation of winding condition state of transformer: if this deviation ?Хs-c insignificantly, i.e. it is connected with a measurement error, then of changes in the windings does not occur; but if it significantly, i.e. it corresponds to the development of residual deformations in the windings, then it must be considered for evaluating the winding condition state in order not to bring it to the destruction [5–14].
Example. During the short-circuit testing of two accordingly switch reactors of the type ROST-700 in the course of measurements by ADC of short-circuit inductance there was identified “Chapeau” type distribution.
The value of resulting of measurement root-mean-square deviation comprised:
= 0,02693 %; the value of the quantile coefficient t = 1,8143; the confidence interval of a measurement random error comprised ?conf = 0,052 % with the number of measurements of n = 572.
The obtained value ?conf = 0,052 % is lower than stipulated level of error +-0,1 %, which confirms the high accuracy of the determination of short-circuit inductance deviation in the proposed device – Smart Grid Monitoring System [by 1–9, 15–26].
1.9. Conclusion
The most important element of “intellectual of networks” (Smart Grid) are the systems of monitoring the parameters of electrical of equipment.
Smart Grid Monitoring System, which described in this chapter, were proposed to use together with quick-working protection against short-circuit regimes in transformer windings.
At the beginning of winding deformations, and also in the case of winding turn-to-turn internal short-circuit the value of inductance L is developed to increase, or to decrease.
Smart Grid Monitoring System and connected with it protection block were stopped the process of winding destruction.
Short-circuit inductance measurements by ADC there was identified “Chapeau” type distribution of random error.
The determination of confidence interval of measurement random error of short-circuit inductance deviation ?Хs-c by algorithm (1.12–1.26) makes to increase the accuracy of the conducted measurements and the reliability of Smart Grid Monitoring System’s work for the control of short-circuit inductance of power transformers and the reactors.
Smart Grid Monitoring System makes it possible to continuously control the state of power transformer windings without their turning off from the network, to achieve their protection in the case of the appearance of the winding deformations or their damage, and it ensures the high accuracy of the inductance measurement with the confidence interval value of the random error less than +0,1 %. This increases the reliability of operation and the continuity of the power supply of the electrical energy users.
Active Vocabulary of electrotechnical terms and verbs:
Information-measuring system – информационно-измерительная система,
monitoring system – система мониторинга,
Smart Grid – интеллектуальная («умная») сеть,
inductance – индуктивность,
autotransformer – автотрансформатор,
short-circuit – короткое замыкание,
short-circuit testing – испытание на стойкость при коротком замыкании,
accuracy – точность,
accuracy of diagnostic parameters – точность (измерений) диагностических параметров,
confidence interval of measurement – доверительный интервал измерений,
Frequency Response Analysis – (метод) частотного анализа,
transformer winding fault diagnostic – диагностика повреждений обмоток трансформатора,
Low Voltage Impulse method – метод низковольтных импульсов,
short-circuit inductive reactance measurement – измерение индуктивного сопротивления короткого замыкания,
voltage transformer (TV) – трансформатор напряжения,
current transformer (CT) – трансформатор тока;
high-voltage circuit breaker (HVCB) – высокольтный выключатель,
dissolved gas analysis (DGA) – анализ растворённых (в масле) газов,
analog-to-digital converters (ADC) – аналого-цифровой преобразователь,
Short-current Testing Laboratory (STL) – лаборатория (стенд) испытаний на стойкость при коротком замыкании,
to enter- входить,
to include – включать (в себя),
to determine – определять,
to show – показывать,
to prevent – предотвращать.
Exercise 1. Match the English words and word-combinations given below with Russian evuivalents:
equipment a) получать,
application b) появление,
check c) непрерывный,
transformer d) применение,
windings e) оборудование,
Scheme f) среднее (значение),
to decrease g) трансформатор,
continuous h) определение,
measuring i) распределение,
converter j) среднеквадратичное отклонение,
primary k) значимая (величина),
voltage o) проверка,
calculation p) преобразователь,
Average q) случайная ошибка,
root-mean-square deviation r) первичный,
distribution s) схема,
short-circuit regime t) уменьшать,
determination u) напряжение,
appearance v) вычисление (расчёт)
random error x) режим короткого замыкания,
to obtain y) обмотка,
significant z) измеренный,
Exercise 2. Find the antonyms and translate them:
Appearance, increase, scientific, slow digital protection, high-voltage, necessary, automated working place, unscientific, rapid digital protection, nonautomated working place, unnecessary, decrease, low-voltage, disappearance.
Exercise 3. Study the Active vocabulary. Insert the missing verbs from the list into the sentence and translate them:
The five-year investment program __________ the construction of 73 new substations.
The signal from the control block __________ the protection block (rapid digital protection).
The instantaneous value of inductance is ___________ in the assigned time interval.
The most important elements of “intellectual networks” (Smart Grid) ______ the systems of monitoring the parameters of electrical equipment.
The program allows ________ the average value of the inductance during each period.
Figure 2 _______ the real oscillograms of short-circuit current (Figure 2a), voltage (Figure 2b).
Quick-working protection _______ accidental destruction of the test object and increases the crash safety of the test.
