In microprocessor automation and relay protection systems, amplitude (effective) values and phase shifts of input signals are widely used as controlled parameters of electrical quantities. In most cases, they are determined by samples of one or two orthogonal components of the main harmony of these signals. In existing microprocessor systems, non-recursive digital Fourier filters are mainly used to form them. At a nominal frequency in the power system, the orthogonal components highlighted by these filters do not introduce additional errors into the amplitudes and phase shifts determined by them. In modes with frequency deviation from the nominal value, the number of input signal samples per period becomes a fractional number, and sampling turns into asynchronous one. For this reason, corresponding errors appear in the amplitude and phase of the signal. The main issue of their correction is the direct or indirect estimation of frequency. In this article, an indirect estimation of the instantaneous frequency is realized by the dynamic cosine of the angle of one sample, which is calculated from three adjacent numerical values of the cosine orthogonal component of the signal. The use of instantaneous frequency information in determining amplitudes and phase shifts allows for full correction of the corresponding errors. It should be noted, however, that in transient modes, due to the influence of various factors, the dynamic cosine is determined with large errors. This makes it impractical to correct amplitude and phase errors in these modes, limiting its use only to steady-state modes. For these modes, a functional algorithm for correcting the amplitude and phase errors of signals in microprocessor automation and relay protection systems when the frequency deviates from the nominal one is proposed and investigated. The results of the performed investigations showed that the developed correction algorithm provides almost complete elimination of the manifestation of amplitude and phase errors in steady-state modes in the frequency range of 47–52 Hz.

The article considers the result of simulation the values of the current technical condition of electrical equipment based on the developed mathematical models. The models are implemented through a software package. Before the simulation, 72 power supply circuits were analyzed, and it occurred that 50 supply circuits of responsible consumers are of the greatest interest for simulation. The simulated integral value of the current state varies depending on the amount of pieces of equipment being monitored. In the course of the study, for each of the circuits under consideration, a number of values were obtained that simulate the selective combination of the technical condition index, a hypothesis was also put forward that the distribution of the populations is normal, and the verification of the latter was carried out using the Pearson criterion. With an increase in the number of pieces of electrical equipment taken into account in the monitoring, the average value of the technical condition index decreases. This indicator provides a cumulative assessment of the technical condition of the entire power supply system being examined. Taking into account the technical condition index, the values of the probability of trouble-free operation of the power supply circuits of the relevant consumers in question have been obtained. The probability of trouble-free operation of the circuits of power supply systems under consideration decreases if the current technical condition of their elements is taken into account. The simulation and calculations results indicate the necessity of regularly monitoring the current technical condition of electrical equipment and regularly recalculating the values of reliability indicators for power supply circuits in order to make the most effective decision on putting electrical equipment into scheduled repair. In order to reduce the probability of failure of electrical equipment in power supply systems, regular technical condition assessments as well as scheduled maintenance and repair work are required, while in order to obtain a more accurate reliability assessment, additional information on the condition of the equipment should be involved, such as maintenance and repair data, as well as information about the defects detected. The data obtained in the article can be used to reduce the likelihood of equipment downtime, increase the frequency of maintenance and repair, and, as a result, reduce the negative effects of under-supply of electricity.

The purpose of the study was to develop an algorithm for the implementation of an accurate determination of the location and nature of insulation fault on the power supply line, which foundation is a mathematical model of the electrical network mode based on the theory of electrical circuits with distributed parameters. The achievement of this goal is based on the analysis and mathematical description of the replacement circuits of a distribution line with two power centers in the stationary mode with known propagation constants and wave impedances and in a fault mode. The equations of the model are described in detail, using the example of calculating typical modes of a 50 km long low-power distribution line with two power centers, it is demonstrated that it is possible to quickly, in the current time mode, obtain the coordinate of probable insulation fault and assess the degree of it, while an indication of an emergency mode was a voltage deviation at the outputs of the power centers. In general, the method for calculating the mode of the distribution line of an alternating current electric power system under consideration allows quick monitoring of damage or unauthorized connection of the load for the purpose of power take-off, while this technique is also suitable for analyzing a line with a single power supply center, and also makes it possible to quickly adjust the voltage of sources to control the load power at the required level. A promising area for further research may be the extension of the technique to branched lines with several load branches and power centers, which is typical, for example, for offshore electric power systems. In addition, a system for monitoring isolation and selective protection of branched loads can be built on the model under consideration.

The paper considers the main trends in the development of electric motors for electric vehicles and mobile robots, as well as trends in the development of modern methods for calculating power electronics and electric drives based on an artificial neural network. Aspects of the efficiency development of modern synchronous and brushless DC motors are presented. Based on the mathematical model of a brushless DC motor, the architecture of a control unit with a neural network controller is built. A proactive calculation of the neural network was carried out, and the rules for adjusting the weighting coefficients were determined. Based on proactive calculation, a PID controller with self-adjusting parameters using a neural network was built, as well as a block diagram of the PID control system was built on the basis of the BP neural network; also, a speed controller was built using MATLAB modules. Besides, an S-activation function was built as a controller of the BP neural network; the function was based on the mathematical description of the neural network of the control unit of a brushless DC motor. The paper shows in detail the installation of a demultiplexer for better distribution of the S-function output. The resulting neural network encapsulates the S-function of the weight function. Based on the results of the neural network research and analysis of the BP neural network algorithm, a control algorithm has been established that is used to control the PID controller and is encapsulated in the simulation system. The theoretical possibilities of calculation based on a feedback neural network for constructing a simulation model of adaptive control of a brushless DC motor are demonstrated.

In this study, the calculation and mathematical modelling of effective diffusion coefficient and activation energy in convective drying of a product were investigated. The shrinkage coefficient for different temperatures was also calculated. The effective diffusion coefficient was calculated using Fick’s law developed for finite cylindrical geometry. Using the effective diffusion coefficient equation for air temperatures of 45, 55 and 65 °C, the results were obtained as 2.02 ∙ 10^–10, 5.05 ∙ 10^–10 and 8.08 ∙ 10^–10 m²/s, respectively. The activation energy was calculated as 61.1 kJ/mol using the slope of the graph ln(D_ef)^–1/T. The product shrinkage coefficients at drying air temperatures of 45, 55 and 65 °C were found to be approximately 23, 32 and 40 %, respectively. In order to find the most suitable mesh structure of the model, a network independence study was carried out using average moisture content values with an accuracy of 0.001. Nonlinear simultaneous heat and mass transfer equations for 45, 55 and 65 °C dehumidifying air are solved by the finite element method (MATLAB) with initial and boundary conditions. The equations are solved with a tolerance value of 0.001 for thirty minutes time steps. The initial conditions used in the analyses and the thermophysical properties of the product are detailed in tables and graphs. The data obtained from the experimental and numerical solution were compared and it was seen that the results were compatible with each other. According to this result, a mathematical model expressing simultaneous heat and mass transfer can be used to predict the moisture and temperature distribution in the product during drying.

This article discusses the principles of organization and operation of mini-CHP plants on local fuels (LF) to the conditions of hydrogen and carbon-free energy. The analysis of literary sources on the current state of development of mini-CHP plants on LF in the structure of the country's energy balance revealed a number of issues related to their operation and construction that arose after the commissioning of the Belarusian NPP. It is noted that a potential way to develop such energy sources is to switch to multi-purpose product development based on the principles of operation of the energy hub, which will potentially reduce the dependence of the energy source on the operation of the Unified Energy System (UES). The analysis of open literature sources on the potential role of LF in the transition to carbon-free energy was carried out. In this context, the operation of a mini-CHP plant on LF is considered according to two scenarios, viz. recovery of CO₂ from combustion products, followed by purification to food grade and sale to direct consumers, as well as changing the operating modes of the energy source by means of the accumulation of excess electrical energy in the form of hydrogen during the operation of a mini-CHP plant in accordance with the thermal load of consumers. Based on archival data from an operating wood chip-fueled mini-CHP with an ORC module that was selected for research as an analog object, an assessment of the economic conditions for the development of mini-CHP plants on LF was made when integrating food-grade CO₂ extraction units or for the production and accumulation of hydrogen into their schemes. For food grade carbon dioxide production systems, a functional dependency has been built that allows for a preliminary estimate of the value of the simple payback period when integrated into the scheme. Under the accepted conditions for the study object, the simple payback period obtained using the built dependency was less than 3 years. For systems of accumulation of excess electrical energy in the form of hydrogen, 3 options of the organization of work were considered. Based on the research object, the presence of boundary conditions for the ratio of the minimum and maximum differentiated tariff for the purchase of electric energy of the UES has been determined, under which it is advisable to further consider the economic indicators of the project for integrating a module for accumulating electric energy in the form of hydrogen into the scheme of a mini-CHP plant on LP.