The technique is proposed to improve the performance of the measuring element of microprocessor-based protection and its implementation is considered at the software level. Two factors mainly influence on the performance of the measuring elements of microprocessorbased protection of electrical installations. The first one is associated with the appearance of aperiodic and harmonic components in the measured signals due to transients and nonlinearity of the electrical installation elements, and the second–with the inertia of information processing algorithms, in particular–with analog and digital filtering. This leads to the fact that the signal determining time at the output of the measuring element is delayed to unacceptable values that in some cases makes the high-speed protection of electrical equipment ineffective. To solve this problem, it is proposed to form the output signal of the measuring element in the form of special equivalent signals, which are a function of the pre-calculated correction factor and orthogonal components of the controlled signal. In the MatLab-Simulink dynamic modeling environment a mathematical model of the developed measuring element has been implemented, as well as a model of the elements of the power system. Checking the functioning of the model of the measuring element was carried out with the use of 2 types of test effects, viz. a sinusoidal signal with a frequency of 50 Hz (idealized effect), as well as a signal close to the real secondary current of the current transformer in case of short circuit. Computational experiments carried out in relation to the current measuring element using harmonic and close-to-real test effects made it possible to reveal a significant (up to 2 times) increase in the performance of the proposed measuring element as compared to existing ones based on the implementation of the discrete Fourier transform.

The paper deals with a mixed problem for the telegraph equation well-known in electrical engineering and electronics, provided that the line is free from distortion. This problem is reduced to the analogous one for the one-dimensional inhomogeneous wave equation. Its solution can be found as the sum of the solution for a mixed homogeneous boundary value problem for the corresponding homogeneous wave equation and for the solution of a non-homogeneous wave equation with homogeneous boundary data and zero initial conditions. Solutions to both problems can be found by separating the variables in the form of a series of trigonometric functions of the line point with time-dependent coefficients. Such solutions are inconvenient for real application because they require calculation of a large number of integrals, and it is difficult to estimate the miscalculation. An alternative method for solving this problem is proposed, based on the use of special functions, viz. polylogarithms, which are complex power-series with power coefficients converging in a unit circle. The exact solution of the problem is expressed in the integral form via the imaginary part of the first-order polylogarithm on the unit circle, and the approximate one is expressed in the form of a finite sum via the real part of the dilogarithm and the imaginary part of the third-order polylogarithm. All these parts of the polylogarithms are periodic functions that have polynomial expressions of the corresponding powers on the segment of the length equal to the period. This makes it possible to effectively find an approximate solution to the problem. Also, a simple and convenient error estimate of the approximate solution of the problem is found. It is linear with respect to the step of splitting the line and the step of splitting the time range in which the problem is considered. The score is uniform along the length of the line at each fixed point of time. A concrete example of solving the problem according to the proposed mode is presented; graphs of exact and approximate solutions are constructed.

The thermal impact of cable power lines and structural materials of cables on the environment has been considered. A quantitative evaluation of the thermal impact of electrical cables with cross-linked polyethylene insulation on the environment was carried out using the Elcut program. Analysis of the temperature field near the loaded cable line of 10 kV demonstrated high values of soil temperature that negatively affects its redox potential and living organisms. To evaluate the environmental impact of electrical cable materials, an approach has been developed that takes into account not only the toxicity of the materials but also their volumetric content in the cable. Cable lines with cables with traditional paper-oil insulation cause more damage to the environment than cable lines with cables, insulated with crosslinked polyethylene. The environment, in turn, also has an impact on the electrical cables: the values of long-term permissible load currents depend on the ambient temperature (when laying cables in the open air, in an earthen trench or in cable rooms). The impact of solar radiation on the thermal conditions of the electric cable is estimated. A comparative analysis of the complex environmental impact of electric cables with traditional insulation and insulation of crosslinked polyethylene demonstrated that unarmored cable with crosslinked polyethylene insulation at a voltage of 10 kV (regardless of the type of its shell) causes less damage to the environment than the same traditional cable throughout the considered temperature range on their surfaces.

The development of electric power industry is accompanied by an increase in the number of consumers subjected to loads with nonlinear characteristics. The arising problem of the distortion of electrical energy that takes place when the mentioned consumers are in operation is partially solved by using means of improving the quality of electrical energy. The increase in the share of small generating plants that are placed in the nodes of consumers exacerbates the interaction of non-linear loads, forming additional parallel streams of electrical energy. Distorted electrical power is not an indication to account. Existing views on distorting power are amenable to criticism. In the well-known works, the proposals for the assessment of power using the quadratic norm and the quadratic norms of its components have been grounded. For the analysis of processes of formation the components of electrical power, a diagram of the simplest circuit containing a series-connected source of electromotive force, resistors and a diode is considered; also, the circuit was conditionally separated into a source and a consumer. The analysis of the power formation of each circuit element is performed with the use of the expression of current and voltage, as periodic functions represented by the trigonometric form of Fourier series. The power components are separated with the use of the known interaction of harmonic components of current and voltage of different orders. For the circuit elements, the power components formed by current and voltage harmonics of the same order are selected as well as power components formed by current and voltage harmonics of different orders, in which, in their turn, the power components are selected that have the same order as the first ones. The power formed by the action of the latter group is proposed to be attributed to the distorting power and to account its action by the corresponding quadratic norm. A numerical calculation has been performed with a use of the specified power component distribution. Time diagrams illustrate the process of interaction of the power components, which–in the case of the diode–leads to no change in power over time.

One-dimensional axis-symmetrical and plane-symmetrical problem of propagation of the combustion and displacement fronts in oil-containing layer in situ has been considered numerically. Two combustible components, viz. liquid (oil) and solid (kerogen, oil sorbate), were considered. The influence of the blast rate, liquid component viscosity, oxygen concentration in blasted air and heat losses (the width of the oil-containing layer) on the dynamics of the heat dissipation and displacement fronts is investigated. In the cylindrical system the oxidizer flow to the combustion front is reducing over time; and the shift-down of the maximum temperature from the solid combustion front to the oil displacement front takes place (the combustion front “jump”). The time of the “jump” may vary from tenths to hundreds of days and the distance of the shift, – up to 10 or more meters, depending on the parameters of the system. After the “jump”, the combustion rate and maximum temperature continue to deteriorate and after the period of time close to the time lapse before the “jump” the chemical reaction ceases. Herewith the transition of combustion to the liquid phase after the “jump” doesn’t influence notably on oils displacement front speed. The time of the “jump”, as well as the velocity of the mutual combustion (maximum temperature) front and displacement front removal nearly linearly depends on incoming gas blast rate and non-linearly – on oil viscosity. When viscosity is low, the displacement front rapidly runs away from the combustion front, time of the “jump” retards and the distance between the fronts at the instance of the “jump” may reach 10 m or more. The oxygen concentration in the gas being blasted influences significantly on the mutual dynamics of the combustion and displacement fronts since combustion front velocity is proportional to oxygen concentration and displacement front velocity is independent on it. Oxygen enrichment of the gas being blasted just after the “jump” may help localize the area of heat release (combustion) near the oil displacement front. The mentioned manipulation may be utilized for sustainability control of the displacement front. However for its practical implementation it is necessary to have information on concentration and temperature fields inside the layer, which may be obtained from indirect data and via modeling. The results of investigation may be utilized for development of technical projects of oil recovery via in-situ combustion.

The results of experimental and theoretical studies of the temperature state of the high- pressure cylinder (HPC) of the T-100-130 steam turbine for one of the start modes are presented. Taking into account the dependence of the coefficient of linear expansion on the temperature, the elongations of the individual sections of the casing under different temperatures and its total elongation after the turbine operation starts to correspond to the stationary operation mode have been found. The studies have shown that in the process of actuation the turbine there is a significant difference in temperature along the length of the HPC casing. In this case, the most intense heating occurs in the area from the second to the sixth section. The greatest temperature difference was observed in stationary operation at maximum temperature in the fifth section. Using the orthogonal method of L. V. Kantorovich, an approximate analytical solution of the thermal conductivity problem for a two-layer wall (turbine casing – thermal insulation) under inhomogeneous boundary conditions of the third kind is obtained. With the use of experimental data on the temperature state of the outer surface of the casing of the HPC by solving the inverse problem of thermal conductivity, the average heat transfer coefficients for the actuation period characterizing the intensity of heat transfer from steam to the casing have been found. On the basis of experimental data on the temperature change of any of the controlled parameters of the turbine over time, a theoretical method for predicting its change in a certain time range from the time of the its last measurement has been developed. The use of this method to predict the change in the temperature difference between the top and bottom of the HPC casing during the actuation showed that for a period of time equal to 3–5 minutes the forecast is fulfilled with high reliability.

The structural-parametric optimization of the automatic control system for power units (ACSPU) of 300 MW of Lukoml’skaya GRES (Lukoml Local Condensing Power Plant) in the mode of both the permanent and the variable superheated steam pressure upstream of the turbine is under consideration. During 1974–1979, eight units of the Lukoml’skaya GRES implemented the ACSPU with a leading boiler power control. At the moment, these systems no longer meet all the frequency control quality requirements. In 2016, the daily schedule of electric loads of the Belarusian power system was as follows: the basic part of the schedule of electric loads was covered by combined heat and power plants (CHP) and by mini-CHP (which are the least maneuverable of the power plants), the semi-peak part of it–by local condensing power plants (Lukoml’skaya GRES and Berezovskaya GRES), the peak part–by import electric energy from neighboring power systems. However, this year the first unit of the Belorussian NPP will be put into operation, while the second one–in 2020. After the launch of the Belorussian NPP, it will cover basic part of load curve; CPPs will cover the semi-peak part, while the peak part of load curve will be covered by local condensing power plants. Correspondingly, due to the alteration of the structure of daily schedule of electric loads of the Belarusian power system, it is necessary to improve the efficiency of power units of Lukoml’skaya GRES as well as of the entire Lukoml’skaya GRES in general. This can be achieved with the help of the method of parametric optimization of the typical ACSPU proposed in the present paper. As a result, the quality of control of power and pressure upstream of the turbine will be improved; the flow of fuel will be reduced, as well as the turbine regulation valve displacement; environmental performance of entire power plant will be improved, too. The proposed technique has been confirmed by the results of computer simulation of transient processes in the automatic control system under external and internal disturbances.

Minimization of consumption by the buildings during exploitation of energy resources produced of non-renewable energy sources is the main objective of modern energy efficient construction. Currently, there are two principal solutions to this issue: the use of renewable energy sources (such as solar energy, geothermal energy, etc.) and optimization of secondary energy consumption. The paper considers one of the main approaches of secondary energy consumption, which is advisable to use in residential buildings, viz. the use of heat of household drains. Taking into account the fact that in modern energy-efficient buildings a significant amount of energy is still spent on hot water supply, one of the options for optimizing this process is the reuse of waste water heat as the initial source of heating of cold water supplied to the building. The design and technological solution of the heat exchanger, which will make the most efficient use of waste water heat for heating cold tap water possible, is proposed. A characteristic feature of the heat exchanger is the providing a screw movement of waste water along the internal standpipe. At the same time, cold water moves evenly along its outer contour, gradually being heated up from household drains. The key problem of the considered design solution is the correct choice of the appropriate slope of the screw surface, which will ensure the maximum transfer of heat to cold water and at the same time provide a quality drain, eliminating the possibility of clogging and stagnation of small particles. In order to solve this problem an assessment of the existing theoretical and practical approaches to the provision of water flow in technological pipelines which allows determining the optimal value of the slope of the surface has been fulfilled.