MATHEMATICAL MODEL OF THE PRIMARY MEASURING CONVERTER OF HUMIDITY TRANSFORMER OIL
Authors: Hraniak Valerii , Yemchyk Viktor , Kozhushko Oleksandr 
Published: January 2023

Today, the vast majority of technological processes, both production and agriculture, are based on the use of electric machines. Among which, a significant part of production equipment requires the use of electric motors, the power of which exceeds hundreds of kilowatts. Such electric machines have also become widespread as generating equipment, where they are an integral part of power plants, both using traditional energy sources (thermal power plants, nuclear power plants, etc.), and renewable (hydroelectric power plants, wind farms, etc.), where the unit power of a single electrical machine is usually higher than in other sectors of economy.
When operating such equipment, systems for monitoring a significant number of technological parameters are often used, and in real time it characterizes the modes of their operation. This approach makes it possible to increase the reliability of operation and, with a fairly high probability, to avoid large-scale man-made threats that can be caused by an emergency failure of power electric machines (including powerful electric generators), which are quite often accompanied by the destruction of supporting structures, structural elements of industrial premises and can pose a threat to the life and health of production personnel. But the use of even the most modern systems for monitoring the technical condition does not provide one hundred percent reliability, and when operating electrical machines with a nominal power of the order of units of MW Today, the vast majority of technological processes, both production and agriculture, are based on the use of electrical equipment. A similar situation occurs in the household sector, where we can also note a significant increase in energy consumption in recent decades. Given this, it is obvious the need to ensure the transfer of significant amounts of electricity, which is not possible without the use of transformers and power electric devices, the construction of the lion's share of which provides insulation of live parts and excess heat using transformer oil. Such equipment, in particular, includes: oil transformers, oil and low oil switches, which are characterized by a relatively low cost at sufficiently high rated currents and voltages.
One of the most significant disadvantages of this equipment is the need for constant monitoring of the condition of transformer oil, the physical properties of which largely determine the dielectric strength and overload capacity of the equipment as a whole. The mass fraction of moisture in the latter is one of the key indicators that determine its dielectric and thermally conductive properties. Therefore, the existing technical regulations for the operation of the latter provide for regular laboratory examination of the physical properties of the latter during the technical inspection of equipment, which usually requires quite a lot of time. In turn, this leads to an increase in economic losses associated with increasing the duration of planned maintenance work. Therefore, given the above, it is obvious that the development of new high-precision means of rapid measurement of transformer oil humidity is an urgent task of considerable practical interest.
The article presents a mathematical model of a transformer oil sample, which establishes an unambiguous relationship between its humidity and integral dielectric conductivity in the range of humidity changes from 0% to 0.6%, which corresponds to the allowable moisture content in the latter. It is shown that the obtained functional dependence of the integral dielectric constant on moisture within the investigated range has a monotonically increasing character. Also, the design of a high-frequency humidity sensor based on a band asymmetric wave-water wave was developed, in which the primary measuring conversion of humidity into the amplitude of the output electromagnetic wave is carried out. A mathematical model of such a sensor is developed and the transformation equation is obtained.
To confirm the adequacy of the theoretical conclusions, an experimental study was conducted, based on which it was found that the total relative error does not exceed 2%.