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A significant number of domestic and industrial boilers are in operation in Ukraine. Nitrogen oxides are the most dangerous among all combustion products that pollute the atmosphere, therefore, one should take some measures for decreasing the formation of nitrogen oxides during combustion. The studies were carried out at the boilers of low power (100 kW) with a tubular radiator and an open end. The studies in the furnaces of industrial steam boilers having a tubular radiator with a closed end have not been done. The numerical study results of the gaseous fuel combustion processes in the furnace of a DE-10/14 steam water-tube boiler are presented. The fuel-air mixture is formed by premixing the 15% part of the air with a primary burner twist factor n=2.4 and a secondary burner twist factor n=1.6, and an air excess factor αв=10. As a result of the studies, the temperature and velocity distributions of gases in the combustion chamber, the density of heat flows on the screen tubular surfaces, and the concentrations of the combustion components were determined. Flue gas recirculation in the volume of 80-100% is provided, and the reversible movement of combustion products towards the combustion front provides a reduction in the concentration of nitrogen oxides up to 123-125 mg/m3 at the furnace outlet. Disadvantages are the following: the formation of stagnant zones near the end of the secondary radiator. The optimum diameter of the tubular radiator equals to two burners diameters and tubular radiator is located at a distance of one meter from the burner cutoff.

The purpose of this work is the theoretical substantiation and development of a practical method for calculating the exchange fund of electrical equipment of an industrial enterprise. The purpose is achieved through the use of separate methods of queuing theory if the flow of applications for repairs and restoration are the simplest. It is confirmed by the results of statistical studies. Therefore, for the mathematical description of the repair problem the authors use the scheme [Mm; Ms; n], which corresponds to the process of death and reproduction. As a criterion for optimizing the exchange fund of electrical equipment it is proposed to use the zero probability waiting for the replacement of a faulty electrical component with a working from the exchange fund. For the case of the simplest flow of applications for service, the authors suggest to use the Peck and Hazelwood tables, which significantly simplify the calculation of the exchange fund for known failure rates and electrical equipment recoveries. For practical use of the proposed method, the authors have developed convenient forms for presenting initial data for calculating the exchange fund, and it is proposed to present the results of calculations in the form of several options for the optimal number of electrical equipment in the exchange fund depending on the accepted level of zero expectation probability, the number of elements from the exchange fund and their recovery time. The proposed method will optimize the exchange fund of electrical equipment and reduce the cost of its formation.

In this paper, we consider the problems related to measuring and analyzing the characteristics of partial discharges which are the main instrument for oil-filled high-voltage electrical equipment diagnosing. The experiments on recording of partial discharges in transformer oil have been carried out in the “point-plane” electrode system at alternating current. The instantaneous voltage and the apparent charge have been measured depending on the root-mean-square voltage and the phase angle of partial discharges. This paper aimes at carrying out a statistical analysis of the obtained experimental results, in particular, the construction of a parametric probabilistic model of the dependence of the partial discharge inception voltage distribution on the value of the root-mean-square voltage. It differs from usual discharges which occur in liquid dielectric materials in case of sharp inhomogeneous electrode system. It has been suggested that discharges of a different type are the discharges in gas bubbles that occur when partial discharges in a liquid emerge. This assumption is confirmed by the fact that the number of such discharges increases with increasing the root-meansquare voltage value. It is the main novelty of this paper. This corresponds to the nature of the occurrence of such discharges. After rejecting the observations corresponding to discharges in gas bubbles, a parametric probabilistic model has been constructed. The model obtained makes it possible to determine the probability of partial discharge occurrence in a liquid at a given value of the instantaneous voltage depending on the root-mean-square voltage. 

One of the most important informational components of control systems is the data of the static load characteristics of each transformer of the substation. Currently, the evaluation of real static characteristics of the load is determined generally by the following methods: computational, analytical, passive and active experiments. These methods exhibit significant disadvantages regarding accuracy and cost rating and encounter plenty of parameters that are difficult to formalize (including climatic factors). The purpose of this work is to reduce electric power losses at 110/220 kV substations by implementation of a new control system for power transformers. This goal has been achieved by using a fuzzy controller in the structure of the control system for power transformers of 110/220 kV tie substations. The presented solution is multi-functional and can be extended to a wide class of power facilities. The results of the simulation of the transformer voltage regulation process, performed in the MatLAB application environment, showed that the implementation of a new fuzzy controller structure had improved the efficiency of the substation power control system in forecasting and management (compared to classical solutions based on regression and probabilistic models). Herewith, the most accurate accounting of consumer load, the maximum use of equipment at the substation for voltage regulation at the points of release and a significant reduction of active power losses at the tie substations 110/220 kV (up to 12,12%) compared to already known solutions were observed.

In this paper, we study the inverse problem for a mixed loaded equation with the Riemann-Liouville and Caputo operator in a rectangular domain. A criterion for the uniqueness and existence of a solution to the inverse problem is established. The solution of the problem is constructed in the form of the sum of a series of eigenfunctions of the corresponding one-dimensional spectral problem. It is proved that the unique solvability of the inverse problem substantially depends on the choice of the boundary of a rectangular region. An example is constructed in which the inverse problem with homogeneous conditions has a nontrivial solution. Estimates are obtained that allow substantiating the convergence of series in the class of regular solutions of this equation and the stability of the solution of the inverse problem from boundary data. В данной работе изучается обратная задача для смешанного нагруженного уравнения с оператором Римана-Лиувилля в прямоугольной области. Установлен критерий единственности. Построено решение задачи в виде суммы ряда по собственным функциям соответствующей одномерной спектральной задачи. Доказано, что однозначная разрешимость обратной задачи существенным образом зависит от выбора границы прямоугольной области. Построен пример, в котором обратная задача с однородными условиями имеет нетривиальное решение. Получены оценки, позволяющие обоснование сходимости рядов в классе регулярных решений данного уравнения и устойчивость решения обратной задачи от граничных данных. Вестник КРАУНЦ. Физико-математические науки, Выпуск 2 2020

Consider the propagation of electromagnetic energy through multiconductor three-phase high-voltage transmission line with arbitrary number of conductors. The mathematical formulation of the problem represents the system of partial differential equations known as transmission line equations. When constructing the capacitance matrix of an electric line, it is necessary to solve the boundary problems for the Laplace equation with nonlocal boundary conditions. The aim of this research is to develop a new method for constructing a potential coefficients matrix, which allows us to express the voltage vector in the wires through the charge vector. The application of this method leads to the necessity of solving a boundary value problem for Laplace equations with nonlocal boundary conditions. A new type of non-local boundary conditions has been identified, which has not been previously investigated. The boundary conditions of this type are represented by the contour integral over the boundary of the region from an unknown potential. In the general case, the obtained problem does not have a unique solution. The theorem of existence and uniqueness of the solution for the boundary value problem for the Laplace equation with nonlocal boundary conditions is proved. However, the requirement that the potential on the wire surface is constant allows us to prove the existence and uniqueness of the solution for considered problem. In order to illustrate the application of the developed approach we have solved numerically the problem for the sector-shaped cable with three cores. The values of potential and capacitive coefficients obtained by calculation are given. The error of the values of the diagonal elements of the matrices of potential and capacitive coefficients is estimated as less than 0.1%.