Forecasting technical state and efficiency of electrical switching devices at electric complexes in oil and gas industry

This work is topical, since it allows predicting the physical state of the contact joints of low-voltage switching devices and to avoid their destruction, which occurs due to mechanical and chemical effects on the contacts during operation, leading to an increase in the transition resistance and overheating of the contacts. The following criteria were adopted as serviceability criteria for the contact connections of switching devices: the maximum temperature of their heating, the maximum value of the resistance of the pole of the device and its parts, as well as the excess of the temperature of the contact heated part over the ambient temperature. The authors obtained graphs of the dependence of the resistance value of the contact connections of magnetic starters and circuit breakers on the ambient temperature and load factor. The article determines the analytical dependence of the resistance of the magnetic starter contact connections on the ambient temperature. It also features mathematical models that take into account various operating conditions of switching devices, the input values of which are refined using regression analysis.


Introduction
During the operation contact connections of low-voltage switching devices are exposed to mechanical and chemical influences which lead to an increase in their transient resistance, and as a result, by the action of the load current, to their overheating and subsequent destruction. The development rate of defects depends on the design of the contact connection, its location and the intensity of external influences. The time-lag between defect occurrence and the emergency failure of contact is from several months to several years. The main control of contacts is the measurement of their transient resistance to direct current. Contact resistance is measured using M-246 micrometers. The ammetervoltmeter method measures resistance indirectly. The single bridge (Wheatstone bridge) and double bridge (Thomson bridge) methods are widely used [formula 1,2].
Electric thermometers, thermal candles, thermal stencils, and thermal indicators were used in the energy industry to control the contact connections of conducting parts before. Nowadays, thermal imagers are being successfully used for these purposes. Now there is a possibility not only to measure the temperature of individual points but also to observe the thermal conditions of electrical installations.
The heat amount released on defective contact depends on the square, the current flowing through it, the transient resistance, and the time. The thermal energy released when the current flows through the contact's transient resistance is transmitted as thermal radiation to the environment, to the conjugated conducting parts and insulating devices. The temperature of contact connections depends on many factors including the area of their surfaces, the heat transfer coefficients of conjugated conducting parts, and the environmental parameters (temperature). In the formula [2] heating temperature limit (excess of heat temperature above the ambient temperature) is adopted as the main criterion of contact connection's intactness at nominal current Inom and in formula [3] the value limit of phase (pole) resistance of the device and its parts. These two intactness criteria of switching devices are equivalent since the heating of contact connections occur before mentioned in formula [2] temperature by the flow of current load Il=Inom and energy released on the device resistance Rd, a power source of which is proportional to the resistance of conducting system.
The exceed of contact's heated part above the ambient temperature is acceptable as a criterion for evaluating the contact group's state.

Materials and methods
The estimated temperature excess is calculated from the current load Il and the nominal current Inom of the device: where tnorm is the normalized value of heating temperature excess for the controlled object (contact connection). The estimated calculated value of the contact resistance at the normal conversion temperature is calculated using this expression: m nom m norm where Rm is the measured resistance value at tm, [Om]; K is copper coefficient equal to 235; tnom is the nominal temperature equal to 40 °C [2]; tm is the ambient temperature at which the resistance measurements were made Rm, °C.
The electrical resistance of the contacts is calculated by the expression: where α is the temperature coefficient depending on conductor material; kl is the load factor of the switching device; Rnom is the nominal resistance of the contact groups [3].
The calculation is performed in the following order: -calculating the contact resistance Rm at ambient temperature tm=50 °C according to the expression (2): -contact resistances for other ambient temperature values are determined the same way; -for study the dependence of resistances on the load we determine the contacts resistance at kl=0.1 using the expression (3): -the resistance of the magnetic starter contacts at other values of the load factor is determined. For magnetic starters having the following nominal resistances of contact groups: 82.5; 33.0; 13.1 mOm; as well as for circuit breakers with the following nominal resistances 34.9; 27.9; 17.5 mOm; the calculation is made the same way [2].
Dependency graphs of contact connection's resistance value (magnetic starters and circuit breakers) on the ambient temperature and the load factor are shown in Fig. 1-4.
Predicting the development of a random process that reflects the functioning of a complex system should be preceded by statistical processing of experiment results to build a correlation field. Then, by using the correlation field we can find an empirical regression, which means to establish a quantitative relationship between the characteristics of the process. The next step is to approximate the ultimate empirical curve of regression. The simplest way of approximation of this curve is linear regression: The change γ is related to some change in the parameter x, but does not depend on the quantity of "parameter x has already accumulated". Using the principle of least squares it is easy to create a normal equation of linear regression [2]: Making simple transformations, we bring this system to this form β is a regression coefficient that can be easily calculated using determinants: α is a free regression term: The resulting expressions completely determine linear regression for a given sample. Equation (5) for the free term of the regression can be rewritten in the following way: The average point of the joint distribution of the quantities learnt always lies on the regression line [6].
For the determination of the regression line, it is enough to know only angular coefficient β. The fact that dependence studied is assumed to be linear allows using a sample correlation coefficient r for estimating the bond strength: The initial calculation is based on the dependence of the contact connections resistance of a magnetic starter from the ambient temperature (Table 1).

Results
The obtained expression is consistent with the analytical dependence of contact connections resistance of magnetic starter on the ambient temperature (Figures 1 and 5).
Analytical forecasting of changes in contact resistance of switching devices during operation. The work capacity of the switching device is determined by the resistance of its contacts Rc. We consider the function Rc(T) value of which changes continuously in the time interval T1=[t0, tn]. As a result, there are values of this function R0, R1,..., Ri, Rn on the interval T1 [2].  We can use the following expression to describe how the Rc parameter changes in this interval ; Toperating time, years; Rp =5Rnompermissible contact resistance [5].
The calculation is made in the following order [2]: -according to expressions (10, 11), we determine the character of the  Table 3.

Conclusions
During the analytical process of forecasting changes in contact groups resistance of low-voltage switching devices (magnetic starters and circuit breakers) under different operating conditions, mathematical models are obtained, the input values of which are refined using regression analysis. The change in contact connections resistance of the low-voltage devices is one of their technical condition characteristics and allows evaluating the efficiency of oil and gas industry equipment.