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The assessment of the suitability of cables of 6–110 kW with XLPE insulation in comparison with cables of the same voltage but possessing paper-oil insulation has been fulfilled on the basis of the method of multi-objective optimization that makes it possible to account not only the quantitative characteristics (of reduced costs), but also qualitative ones. As an indicator of the reliability of the cable line the maximum mean time to failure (the value inversely proportional to the parameter of succession of failures), which is an order more for cable lines with XLPE insulation than for cable lines with paper insulation, is adopted. A comprehensive assessment of the convenience of installation of cable lines revealed that the installation of cable with XLPE insulation features a 1.2–1.6 times easier installation as compared to three-wire (voltage 10 kW) and 1.4 times easier installation as compared to single-core oil-filled cables (voltage of 110 kW). The efficacy of the cables 6–110 kW with XLPE insulation is proved on the basis on the method of multi-objective optimization, that took into account as the costs for the construction and operation of cable lines and the reliability of its operation, ease of its installation and other quality indicators. If the goals taken into account are considered as equally important, the polyethylene-insulated cables for a voltage of 10–110 kW is more efficient as compared to three-wire (voltage 10 kW) and solid (110 kW) cables with paper insulation. Herewith, the cost of the cable with XLPE insulation may exceed the cost of cable with paper insulation up to two times. If the most important aim is to provide the minimum reduced costs for the construction and operation of the cable line, the use of cables with XLPE insulation for voltage of 10 kW is most advisable in individual cases.

The assessment of the suitability of cables of 6–110 kV with XLPE insulation in comparison with cables of the same voltage but possessing paper-oil insulation has been fulfilled on the basis of the criterion of reduced costs. Thus, the comparison was undertaken between cables of various design and material of insulation: three-core paper insulated ones vs. three-core XLPE insulated ones; three-core paper-insulated ones vs. solid wires with XLPE insulation; single-core oil-filled cables of 110 kV with paper insulation vs. solid wires of 110 kV with XLPE insulation. The increase in long-term permissible current loads for cables with XLPE insulation because of the larger permissible temperature of heating in comparison with cables with paper-oil insulation complies with as would increase in the cross-sectional area of cable cores (equal to 0.61 from the original) and therefore reduces the cost of the cable by reducing the cost of manufacture of conductors. The reduced costs of the construction and operation of cable lines with XLPE insulation (accounting the increase in the cost of a cable 1.2 and 2 times as compared with the cost of a cable with three-core insulation), despite the decline in the cost of manufacture of conductors and the reduced annual operating costs (9 % and 17 % respectively of cable lines of voltage of up to 35 kV and 110 kV), occurred to be more than the reduced costs of the construction and operation of cable lines with paper insulation. Currently the cost of one meter of cable with XLPE insulation is less than the cost of cables of AAB, CASB, AASv types of a voltage of 10 kV with aluminium cores, that ensures their undeniable efficacy.

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.

In this article, the authors consider the possibility of using a hybrid energy storage system to even out the load profile of the enterprise. Solving the problem of rational use of energy storage taking into account the initial variable load schedule will significantly reduce not only the cost of electricity consumption by the enterprise, but also the costs of its production. Detailed characteristics of batteries with various types of electrolytes and supercapacitors are given. A model of the active scheme of a hybrid electric energy storage system consisting of a lithium-ion battery and a supercapacitor unit with the corresponding characteristics is presented. The model was carried out by using the SimPowerSystems software in MatLab. During the simulation, the temperature and the aging effects and of the batteries were not taken into account. The selfdischarge parameter of the battery was also not presented. As a result of the simulation, discharge characteristics of supercapacitors and batteries were obtained based upon which the expediency of their combined use for leveling load profiles of various types was substantiated. The paper presents the results of the simulation of operating modes of a hybrid energy storage device, combining the advantages of two types of energy storage devices, as well as a diagram of delivered power to the network, corresponding to the specified parameters. The paper provides a mathematical description of the increasing power by hybrid storage system resulting from the combined use of supercapacitors and batteries. The paper presents the dependence of the power increase ratio on the frequency and the pulse current duty ratio, which proves that the maximum possible output power of the hybrid storage system can be several times greater than the power of a single battery having the same parameters.

The analysis of scientific papers devoted to the mathematical description of electric generators of reciprocating motion with permanent magnets demonstrated that the proposed mathematical models of this type of generators are based on the theory of magnetic circuits. Such mathematical models are based on a simplified representation of the magnetic system and the magnetic field in the form of a magnetic circuit with corresponding magnetic conductivities. However, unlike traditional rotary type electric machines, electric generators of reciprocating motion have a number of features, the omission of which in mathematical modeling causes the increase of the cost of their creation (due to the duration of the design and experimental refinement of the generators). Therefore, at the initial stages of electromagnetic calculation and solving optimization problems, it is necessary to use adequate mathematical models to improve the accuracy of calculations of the parameters of these generators. For this purpose, a mathematical model based on field theory can be used; however, its main drawback is the complexity of its application for solving optimization problems. In this regard, to improve the accuracy of calculations of the parameters of electric generators of reciprocating motion with permanent magnets, it is proposed to use refining coefficients (coefficients of scattering and buckling of the magnetic flux) in mathematical models based on the theory of magnetic circuits. The authors have developed refined electromagnetic models of electric generators of reciprocating motion with permanent magnets, which make it possible to obtain the main parameters of generators at the initial stages of electromagnetic calculation and when solving optimization problems with acceptable accuracy. A distinctive feature of the refined electromagnetic models of generators is the consideration of the scattering and buckling coefficients of the magnetic flux in the magnetic system that change during the simulation.

Thermal power plants remain one of the main sources of environmental pollution. The deterioration of the quality of traditional carbon-containing energy resources leads to the need to develop technologies for co-combustion of biofuel and coal at small and large power plants. The paper proposes the concept of using solid waste from tire recycling by adding to the composition of the mixed fuel “coal – wood waste” as a substitute for coal slag, which is formed during the utilization of worn-out tires by pyrolysis. The aim of the work was to determine the possibility of increasing the calorific value of wood pellets by co-firing with pyrolysis slag instead of coal without increasing the burden on the environment. At the same time, the following tasks have been set: to determine the lowest combustion heat of mixed fuels and assess its change when replacing coal with slag; to determine moisture content, total sulfur content, volatile matter yield, ash content of mixed fuels according to standard methods; to assess the change in these parameters when replacing coal with slag at the same component ratios; to determine the optimal ratios of components in mixed fuels, which will not increase the burden on the environment when replacing coal with pyrolysis slag. It has been determined that replacing coal with slag results in an increase in calorific value by 37–45 %, a decrease in ash content by 37–42 %, and an increase in the yield of volatile substances. At the same time, the sulfur content increases by 5.6–18 %. The use of traditional cleaning equipment is recommended in order to reduce the emission of sulfur dioxide. The research results make it possible to substantiate the possibility of replacing coal with slag in mixed fuels at certain ratios of components. A new direction of using solid products from recycling of rubber products, i.e. worn-out tires, has been proposed by the pyrolysis method in mixed fuels “slag-wood pellets” for small and medium-sized power plants.

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.

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 inT–scoordinates 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.

Nowadays the world energy system faces numerous transitions and shifts of the existing socio-technical regimes towards higher sustainability. Along with it, the sustainable transitions are often being postponed, slowed down or rejected to avoid negative externalities that could threaten the system stability. In this study, we aim to reach the deeper understanding of the externalities of energy transitions and the vulnerability of energy systems under the influence of negative externalities caused by sustainable energy transitions. Using the Externality theory (Baumol, Oates), Sociotechnical transition theory (Geels), as well as Energy sustainability Trilemma Method for the evaluation of the sustainability of energy systems we argue that such externalities need to be treated (internalized, avoided) by special policy measures other than common (classical) ways which may cause slowing down of sustainability transitions and make extra barriers for them. Transitions to more clean and low-carbon energy systems using energy technologies such as solar, wind, small hydro, biomass, waste management, e-vehicles are in the scope of this paper. It classifies the wide range of policy methods (classical and new) being applied separately and simultaneously, and analyses their application in energy policies designing aimed to combat negative externalities of energy sustainability transitions worldwide, so they might be minimized by properly tailored energy policy in each particular case.

The active development of the mobile platforms sector such as smartphones, smart watches, fitness bracelets and other wearable electronic devices in the last 4 years has caused a huge growth of the market of mobile applications-services. Western countries are actively implementing mobile applications-services for household energy users. In Belarus, there is a positive dynamics in the number of active users of applications-services, every year it is possible to attract 7 % of unique customers. In the present paper the experience of implementation and operation of the mobile application for power systems is analyzed. The dynamics of the market of mobile applications-services has been traced: the amount of time spent by the person in interaction with the device was determined as well as the total expenditure of funds in the application at the moment; also, the growth of expenses within the applications was forecasted. The potential benefits for business and end-users of services from the implementation of mobile applications-services were demonstrated. Their properties, main qualities and advantages over traditional methods of “business – client” interaction are considered. A number of features needed for the successful functioning of the mobile application in the power system of Belarus are identified. The process of creating software for smart devices has been studied and the functionality needed by the mobile application for the power system has been proposed for attracting new users. A special algorithm for the launch and successful “life cycle” of a mobile application has been proposed. It allows to operate and develop mobile applications-services as efficiently as possible, as well as to avoid the most common errors at the stages of their development and launch. The implementation of a mobile application in the power system of the Republic of Belarus, in the long-term, will significantly increase customer loyalty, simplify interaction with users, make it possible to build new models of distribution of electricity, and, consequently, regulate the demand for energy resources.

In design activities, technical solutions are practiced, which provide for the use of different tension strings of insulators in a single span. The present paper considers the calculation of the sag and load factors for a span with two different tensioning insulator strings that are of identical suspension heights. The system of “the first tension insulators string – the wire – the second tension insulators string” was described by the equations of a parabola. A relationship has been established between the sag increase factor and the coefficients that take into account the presence of tensioning insulators strings. The resulting compact formula for sag increase is generally suitable for any combination of strings in a span. The coincidence of the calculation is shown for particular cases known from the literature. The formula for calculating the load factor for the equation of state was derived, taking into account the presence of different strings in the span. The reliability of the formula has been proved by the coincidence of results for particular cases of the arrangement of strings. The obtained expressions can be used both for vertical (weight and ice) loads and for horizontal (wind) ones. In the case of loads in two planes, the equation of state must take into account all the components when calculating the resulting reduced load on the wire along the inclined plane. Calculations were performed for different lengths of spans of switchgear with different wires and strings of insulators. A span with one and two tensioning strings of insulators, with the same suspension heights, in the absence of wind and ice is considered. The curves of the sagging wires to different strings have been plotted. It is demonstrated that when calculating sags and tensions, the difference between strings must not be neglected.

Load profile alignment based on optimal power consumption management is considered to be one of the main ways to ensure efficient operation of energy systems in the short-term planning. Alignment load profile with a view to reducing costs can be implemented with the aid of consumers’ involvement by administrative and economic measures. Administrative measures are associated with the forced restriction of consumer loads in certain intervals of the planning period. On one hand, these measures provide benefits to the power system by alignment load profile, and on the other hand, they cause detriment to consumers. Ultimately, in some cases, for the whole power system, the detriment may be greater than the benefits. Therefore, it is advisable to use administrative measures in conditions of shortage of power and electricity in the power system. Optimal planning of short-term regimes of power systems according to rigid load profile received after alignment can be carried out by traditional methods. The solution of such a problem ought to be initially carried out under conditions of non-rigid load profile resulting from the directive use of administrative and economic measures carried out with the help of specially developed models. In this regard, the paper proposes a mathematical model of the problem of optimizing load profile of regulated electricity consumers to be used for optimal planning of shortterm power system modes, an algorithm for optimal planning of a short-term power system mode with optimizing load profile of regulated power consumers. Also, algorithms are proposed for accounting for simple and functional constraints in the form of equalities and inequalities when optimizing load profile. The effectiveness of the described algorithm for optimizing the short-term mode of the power system, taking into account the optimal load control of adjustable electricity consumers, has been studied using the example of optimal coverage of the load profile of power system, which contains two consumers with adjustable load profile, and two TPPs. Based on the calculated-and-experimental studies, it was determined that the proposed mathematical model of the problem is adequate, while the developed algorithms for optimal planning of short-term power system modes with optimization of load profile of regulated electricity consumers and taking into account various types of limitations are of high computational qualities.

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.

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.

The first and one of the most important functions of management is planning. At the same time, in the current market conditions, the time for the implementation of this stage is very limited. In many ways, this applies to the oil and gas industry all the same. Due to the reduction of the resource base of the industry, the share of super-profitable projects has decreased significantly. Extraction of hard-to-recover oil and gas reserves is associated with active investment activities and with the need to introduce expensive technologies and equipment. The most common type of investment project associated with the geological and technical activities is being considered in the present paper. In order to increase the economic efficiency of the geological and technical activities it is proposed to implement an automated model at the stage of planning. This model, on the basis of the generalized geological, technological, statistical, macroeconomic and economic indicators, allows to solve quickly the following problems: of more precise and prompt planning the expenses on carrying out geological and technical actions; of defining minimum admissible profitable level of an oil flow rate after carrying out geological and technical actions; of determining the most economically justified duration of the overhaul of the well; of organizing the projects of geological and technical measures according to their attractiveness. As a result of the implementation of the automated model, an efficiency matrix for a particular field was compiled that determines the impact of the necessary investments and planned flow rate on the economic indicators of the project. The use of this matrix made it possible to exclude several inefficient geological and technical measures from the plan. The method of ranking based on the calculation of the integrated efficiency coefficient has been developed. On its basis, the issue of making optimal management decisions taking into account the impact of risk assessment in the case of projects with the same economic efficiency is solved.

CuInSe2 thin-film solar cells are promising materials for photovoltaic devices. One of the main tasks of researchers is to find ways to increase the solar cells efficiency. In this paper we propose an original structure of a thin-film solar cell based on a tandem connection of a photoelectric converter and a thermoelectric layer based on CuInSe2. The photoelectric converter consists of CuInSe2 and CdS layers. A 3D model of the proposed thin-film solar cell was implemented in the COMSOL Multiphysics environment with using the Heat Transfer module. The simulation was carried out taking into account the diurnal and seasonal variations of both the ambient temperature and the power density of the AM1.5 solar spectrum for the geographical coordinates of Minsk. The solar radiation power density of about 500 kW/m2 can be achieved by using concentrators. The temperature pattern and temperature gradients are calculated in each layer of the solar cell without and with the temperature stabilization of the substrate back side as well as without and with the thermal insulation of the substrate ends. Graphs of the temperature gradients of the thermoelectric layer and the temperature variations of the photoelectric converter of the solar cell are given. As a result of the simulation, it is shown how the uneven heating of both the surface of a thin-film solar cell and its layers occur under conditions of diurnal and seasonal variations of both the ambient temperature and the solar radiation power density. Under concentrated solar radiation exposure, the photoelectric converter surface can be heated up to 700 °C without temperature stabilization of the solar cell substrate. The operating temperature of the photoelectric converter was maintained at no more than 2.35 °C in January and at no more than 14.23 °C in July due to the temperature stabilization of the substrate back side of the proposed device. This made it possible to achieve an increase in the output power of the solar cell both by summing the photoand thermoelectric output voltages and by the concentration of solar radiation.