The use of orthogonal components (OC) underlies  the construction of measuring elements of  modern protection and automation devices. In most microprocessor-based protections, the orthogonal component of the input signal is extracted using a discrete Fourier transform (DFT). The DFT disadvantages are its low speed, which is more than one period of the fundamental frequency, as well as the sensitivity to the free aperiodic component, which creates significant conversion errors depending on the time constant of its decay. Such a settling time of the true output signal is often unacceptable for the design of high-speed measuring devices. The paper proposes to form the OC of the equivalent signal according to the values of the cosine and sine OC of the fundamental harmonic, formed using the DFT by multiplying them by the resulting correction factor. The developed algorithm for the formation of orthogonal components of input signals in microprocessor protections is characterized by high speed in transient modes and it has wide functionality. So, the proposed digital device for forming the orthogonal components of an equivalent signal, in comparison with digital filter based on the DFT, has an increased operating speed both in the mode of occurrence of a short circuit and during the decay of the monitored signal, while maintaining the same characteristics as in the DFT in other modes. A block diagram of the proposed digital device for forming the OC of an equivalent signal has been developed, all blocks of which can be implemented on a microelectronic and microprocessor element base. A digital model of the specified device has been developed in the dynamic modeling system MatLab-Simulink in accordance with the structural diagram. As a result of the calculations, a significant (up to two times) increase in the performance of the proposed digital device for forming the OC in transient modes has been established in comparison with the shapers based on the DFT.

A method is proposed for the mechanical calculation of flexible wires of substation in the presence of one tap to an electrical apparatus located in the middle of the span, taking into account its real location. The technique takes into account the presence of tension insulators strings, different heights of the suspension of wires. The loads on the conductor and tap depend on the climatic regime and take into account wind and icy conditions, as well as temperature changes. The transition to another climatic regime is performed by solving the equation of state, taking into account the coefficients of the horizontal and vertical load of the given and initial regimes. Formulas are given for calculating load factors that take into account weight, wind and ice cover loads on wires and insulator strings, as well as the slope of the span. They are calculated for each climatic mode based on the actual location of the tap to the electrical apparatus and the forces from it to the busbar. It is shown that the calculation results are in good agreement with the proposed method and the computer program. Formulas are given for calculating the sag and horizontal deviations of the wires when the tap is located in the middle of the span. A method is proposed for calculating the components of the forces on the busbar from the tap, taking into account its real location in substation. Formulas for calculating these components are given for different variants of the tap orientation. Knowledge of the values of the components of concentrated forces from the tap allows to increase the accuracy of calculating the sag and tension of the substation wires. Formulas are given for calculating the coefficients of increasing the sag, taking into account the components of the forces from the tap.

Abstract. Preference is given to cable lines with  cross-linked polyethylene insulation in electrical networks with a nominal voltage of 10 kV during reconstruction of existing and construction of new industrial enterprises. The standard service life of such cables is at least 30 years (subject to the conditions of storage, transportation, installation and operation), and the actual one   is determined by the technical condition of the cable. The service life of a cable line depends on the state of its insulation, the aging of which occurs under the influence of several factors. Conventionally, all factors influencing one or another degree on the cable insulation resource can be divided into thermal, electromagnetic, climatic, mechanical and operational. The most significant reason for the insulation aging  is high temperature, which accelerates the reaction of thermo-oxidative destruction, during which high-molecular polymer compounds decompose. In fact, cables are operated at temperatures below the long-term permissible values, and, therefore, the aging of the insulation is slower, and the actual service life will be longer than the standard. At present, condition of the insulation is monitored with the use of high voltage tests related to destructive testing methods. When designing and operating cable lines, it is necessary to estimate the duration of the actual service life under various operating conditions. In theory, there are several expressions for calculating the service life of a cable line when exposed to temperature, humidity, electric field and aggressive environments, but all of them are not applicable in practice due to the presence of a large number of coefficients whose values are unknown. The paper presents an analytical expression obtained for determining the service life of power electric cables, taking into account the aging of the insulation under the influence of temperature and electric field.

With the aid of mathematical and physical simulation the electromagnetic field distributions in the end zone of a powerful turbogenerator has been obtained. On the basis of the comparison of the axial component of the magnetic induction on the surface of the extreme package of the stator core of the large-scale physical and mathematical models with the data of the field experiment, conclusions are drawn about the reliability of the results obtained. The data of the simulation and the field experiment correspond to the same turbogenerator, which makes it possible to evaluate the correctness of the construction of the mathematical model. It is shown that physical modeling makes it possible to evaluate the regularities of the distribution of the electromagnetic field (without obtaining accurate quantitative indicators) and can be used for qualitative comparison of the effectiveness of various design solutions of the end zone of the stator. However, such models have not become widely used, since numerous studies are required to form meaningful and sufficiently detailed conclusions about the parameters and characteristics of the object, the design of the end zone of high-power generators is complex, and the calculation of three-dimensional models is time-consuming and even with modern computer technology is associated with a number of simplifying factors. In mathematical modeling, a sequential logical transition is applied from a simple model of the central part of the machine to a more complex model of the end zone using preliminary results, which makes it possible to obtain data on the distribution of the electromagnetic field in complex areas. With the help of specialized software, a model has been created that is quite flexible in terms of modifying individual components, characterized by accessibility, visibility and unlimited possibilities for experimentation, including predicting situations that have not previously occurred or can give unpredictable results. 

The paper analyzes the main techniques and technologies of oil fluid recovery in the context of energy consumption, significantly rising over the latest decade. It is recognized that the number of publications in the area of energy efficiency is growing steadily. Currently Russian oil and gas industry are facing the task of accelerating reduction of energy consumption while preserving, or even increasing, production rates. The task is complicated by the fact that the majority of deposits in Russia either have already entered (primarily, Volga-Ural region) or are now entering (West Siberia) their last stage of exploration, whereas new deposits in East Siberia are only being brought into production. Furthermore, a lot of new deposits, which provide for high recovery rates, are profitable a priori as at the first stage of exploration they do not need any artificial lift due to their free flow production without any oil well pumps. However, there is a significant share of new deposits with low-permeability reservoirs, which require either a system of reservoir pressure maintenance or periodic hydraulic fracturing. At the same time deposits at the late stages of exploration, apart from the use of pump units, systems of reservoir pressure maintenance and hydraulic fracturing, require regular repair and restoration, measures against salt and heavy oil sediments, mechanical impurities, flooding, etc., which all has a negative effect on well profitability. In order to solve these problems, the authors review existing methods and calculate specific energy consumption using various pump systems for hypothetical wells, varying in yield. According to the research results, it has been revealed that from the point of view of energy efficiency, it is desirable to equip low- and low-yield wells with sucker rod progressive cavity pump units, medium-yield ones – with electric progressive cavity pumps driven by permanent magnet motor, medium- and high-yield wells – with electric progressive cavity pumps or electric submersible pumps driven by permanent magnet motor, depending on the characteristics of the pumpedout oil fluid.

The mixed problem for the telegraph equation well-known in electrical engineering and electronics, provided that the line is free from distortions, is reduced to a similar problem for one-dimensional inhomogeneous wave equation. An effective way to solve this problem is based on the use of special functions – polylogarithms, which are complex power series with power coefficients, converging in the unit circle. The exact solution of the problem is expressed in integral form in terms of the imaginary part of the first-order polylogarithm on the unit circle, and the approximate one – in the form of a finite sum in terms of the real part of the dilogarithm and the imaginary part of the third-order polylogarithm. All the indicated parts of the polylogarithms are periodic functions that have polynomial expressions of the corresponding degrees on an interval of length in the period, which makes it possible to obtain a solution to the problem in elementary functions. In the paper, we study a mixed problem for the telegrapher’s equation which is well-known in applications. This problem of linear substitution of the desired function witha time-exponential coefficient is reduced to a similar problem for the Klein – Gordon equation. The solution of the latter can be found by dividing the variables in the form of a series of trigonometric functions of a line point with time-dependent coefficients. Such a solution is of little use for practical application, since it requires the calculation of a large number of coefficients-integrals and it is difficult to estimate the error of calculations. In the present paper, we propose another way to solve this problem, based on the use of special He-functions, which are complex power series of a certain type that converge in the unit circle. The exact solution of the problem is presented in integral form in terms of second-order He-functions on the unit circle. The approximate solution is expressed in the final form in terms of third-order He-functions. The paper also proposes a simple and effective estimate of the error of the approximate solution of the problem. It is linear in relation to the line splitting step with a time-exponential coefficient. An example of solving the problem for the Klein – Gordon equation in the way that has been developed is given, and the graphs of exact and approximate solutions are constructed.

The paper presents a thermodynamic analysis of secondary overheating in turbo-expander plants on low-boiling working fluids. The possibility of optimizing the parameters of the working fluid in a secondary stem superheater has been studied. The research was carried out for two typical turbo-expander cycles: with a heat exchanger at the outlet of the turbo-expander, intended for cooling an overheated low-boiling working fluid, and without a heat exchanger. Cycles in T–s coordinates were constructed for the studied schemes. The influence of pressure and temperature in the intermediate superheater on the exergetic efficiency of the turbo-expander unit was studied. Thus, the dependences of the exergetic efficiency and losses on the elements of the turbo-expander cycle are obtained when the temperature of the working fluid changes and pressure of the working fluid not changes in the intermediate superheater, and when the pressure changes and the temperature does not change. As a low-boiling working fluid, the ozone-safe freon R236EA is considered, which has a “dry” saturation line characteristic, zero ozone layer destruction potential, and a global warming potential equal to 1370. It has been determined that increasing the parameters of the low-boiling working fluid in front of the low-pressure turbo expander (regardless of the scheme of the turbo expander cycle) does not always cause an increase in the exergetic efficiency. Thus, overheating of the working fluid at a pressure exceeding the critical pressure causes a positive exergetic effect, but for each temperature there is an optimal pressure at which the efficiency will be maximum. At a pressure below the critical pressure, overheating leads to a decrease in the exergetic efficiency, and the maximum exergetic effect is achieved in the absence of a secondary steam superheater. All other things being equal, a turbo-expander cycle with a heat exchanger is more efficient than without it over the entire temperature range and pressure of the low-boiling working fluid under study.

Localizing safety systems are provided to contain radioactive substances in an accident and attenuate ionizing radiation at a modern nuclear power plant. Together with radioactive substances, hydrogen is also retained, which is formed during the decomposition of the primary coolant. The accumulation of hydrogen in the presence of oxygen from the atmosphere in the accident localization zone carries the danger of the formation of flammable and explosive concentrations of these components. Nuclear power plant (NPP) deigns with water-water energetic reactor (WWER) provides for a hydrogen removal system including passive catalytic hydrogen recombiners. The device capacity  is confirmed experimentally under reference conditions (lean air-hydrogen mixture, pressure and temperature close to normal, no interference with gas exchange). Capacity is an important safety parameter. In the event of an accident, conditions inside the ealed enclosure of the localizing system of NPP with WWER can  differ from the reference  ones and affect the capacity.  On the basis of calculations, the operation of recombiners with lack of  oxygen  and with hindered  gas exchange has been investigated in the paper. The decrease in capacity with lack of oxygen reaches 50 %, which is mainly  caused by an increase in underburning. Compared to the reference conditions, the effect is more pronounced in the event of an accident – 60–70 %. The hindered gas exchange is modeled by a decrease in the height of recombiner traction channel. This case can be reduced to the placement of the device in cramped conditions and the effect of the atmosphere speed inside the enclosure. Regardless of the hydrogen concentration, the operating characteristic of the device remains linear, with a two-fold decrease in height leads to a decrease in capacity by 20 %. The results can be used to substantiate the safety of NPPs with WWER and to review on the safety subtantiation of power units.