Mathematical Model of Empirical Distribution Law of Power Transformer Failure Due to Winding Damage

Abstract

The work is devoted to the identification of the law of distribution according to statistical data of failure of power transformers of 6–10 kV due to damage to their windings for a three-year period: from 2018 to 2020.

According to statistical data, it has been established that there is a tendency to reduce damage to power transformers by almost two times. But the number of these failures still remains quite large. The main cause of power transformers failure is damage to their windings, which accounts for 82.17 % of other causes. Therefore, the statistics that characterize the failure of power transformers due to damage to the windings were taken for research.

It was established that in 2018 and 2019, the largest number of damages to power transformer windings occurred in April—July with a peak in June, and in 2020, the maximum damages were recorded in November and December.

The prerequisite for building mathematical models for predicting the failure of power transformers due to the damage to the windings in order to ensure the necessary number of spare parts for their quick recovery is the study of the nature of the failure of transformers. The following methods were used to solve the tasks: passive experiment — to collect information about the failure of power transformers; statistical analysis — to build an empirical law of distribution.

After analyzing the view of the histogram of the variation series of the sample of failure of power transformers due to damage to the windings, a hypothesis was put forward about the logarithmic normal distribution law of the failure of transformers due to damage to the windings. Pearson's c²-test was used to check it. As a result of the study, the proposed hypothesis was confirmed. Using Student's tables and the c²-distribution table with a confidence probability of g² = 0.98, confidence intervals were determined for statistical estimates of the mean value, variance and root mean square deviation, which characterize the failure of power transformers due to damage to the windings.

With further research, it will be possible to build mathematical models for predicting the failure of power transformers due to damage to the windings.