In microprocessor protections of electric power systems, the controlled information parameters of input signals are determined using their orthogonal components. To form these components, digital Fourier filters which have inertia are most widely used. As a result, transient modes of orthogonal components formation are accompanied by the appearance of a dynamic error. It consists of dynamic amplitude and phase errors, which can significantly affect the functioning of the corresponding measuring elements and cause the possibility of their excessive triggering during external short circuits and slowing down the triggering during internal short circuits. The reduction of the influence of these factors on the behavior of measuring elements is ensured by the use of high-speed shapers to isolate orthogonal components, as well as by compensating for dynamic phase error. The proposed method of forming orthogonal components of a signal with compensation for dynamic phase error is based on obtaining orthogonal Fourier components, followed by determining from their samples the calculated components that coincide or are shifted in phase relative to the orthogonal Fourier components, respectively, in steady-state and transient modes. The resulting orthogonal components with minimal dynamic phase errors are calculated in accordance with samples of calculated orthogonal components and Fourier components. The efficiency of the proposed solution was evaluated by a computational experiment using a digital model implemented in the MATLAB-Simulink dynamic modeling environment. At the same time, both sinusoidal input signals and complex ones with an aperiodic component and higher harmonics were used as test actions. As a result of the studies carried out, it has been found that the proposed method of compensation for dynamic phase error in the formation of orthogonal components is workable and effective for both sinusoidal and complex input signals. The developed compensation method reduces the dynamic phase error of digital Fourier filters by three to four times. 

Vibration and torque ripple of the permanent magnet generator axis cause excessive wearing up of the generator, noise, efficiency reduction. The article theoretically considers the possibility of eliminating the oscillation of the rotation torque of the permanent magnets generator at constant load due to mutual compensation of the interaction of coils with the field of permanent magnets in the case of certain symmetry of this field. This effect is called pi resonance. For a given class of model functions of the magnetic field density of permanent magnets, it is shown that full compensation occurs with a certain number of coils (N_s) and magnets (N_r), while for other combinations of {N_s, N_r} the interaction is in the nature of oscillations. Pi resonance tables are given for a number of model field density functions represented by Fourier series up to the fifth power. Pi resonance is primarily realized in the case of a small difference in the values of N_r and N_s, which corresponds to the location near the main diagonal of the pi resonance table, as well as at the values of N_r, Ns corresponding to prime numbers. The number of configurations {N_r, N_s} providing pi resonance (compensation of parasitic torques) is the largest for the sinusoidal magnetic flux density and decreases if the magnetic flux density function is approximated by a high-degree Fourier series. It is shown that in the absence of coil cores, pi resonance is possible at N_r = N_s. An additional possibility of pi resonance is shown when placing coils on opposite sides of the rotor. A simplified method of investigating the system (without integrating the equation for the induction current) is substantiated. The results can be used in the design of permanent magnets generators and motors.  

The article presents a two-dimensional finite element model of the magnetic field of a magnetic system of a synchronous electric machine with fractional gear windings. The specific features of the distribution of magnetic fluxes (main effect, edge effect, scattering) in the magnetic system have been revealed and equivalent circuits of the magnetic circuit of the electric machine under study have been constructed at different positions of the stator gear relative to the rotor poles. The necessity of taking into account the edge effect and the dependence of the scattering flux through the gears of the stator on the coordinate of the rotor position has been justified, which is reflected in the analytical model that has been developed for determining the scattering flux through the gears of the stator of a synchronous electric machine with a fractional gear winding. The adequacy of analytical expressions was verified by means of a numerical method (finite element method). The resulting calculation error is due to the assumptions made when construсting an equivalent circuit of the magnetic circuit of the electric machine under study. A slight discrepancy between the results of the analytical calculation and the numerical experiment shows that the proposed model makes it possible to solve the problem of quantifying the magnitude of the magnetic flux scattering through the gears of the stator with high accuracy. In addition, this ensures an accurate determination of the influence of the geometric parameters of the magnetic circuit on the nature of the change in the periodic function of the scattering flow through the stator gear in the shortest time, which is of an obvious practical significance. The presented analytical model can be used in the process of optimizing a synchronous electric machine with fractional gear windings.

The article deals with the district heating systems transition to intelligent systems by developing a united information system and obtaining a high level of controllability of the entire system. During the implementation of automated control systems of district heating, a number of information tasks of the lower level are being introduced, including the data collection for thermal and hydraulic modes of operation for monitoring, operational management and analysis of the effectiveness. One of the problems of intelligent systems is data collection and its further storage and processing. Methods for data collection for real energy facilities are considered and the usage of multi-level system with the allocation of the upper level in the cloud storage has been proposed. In addition to the currently implemented data collection scheme in automated control systems, a generalized method of data acquisition with the introduction of duplicate streams has been proposed to ensure their integrity. The paper presents the approaches to identifying the collected data, ensuring the stability of the collection process, reliability of data storage and their integrity. Role-based security model with a dedicated single certification authority helps to protect data. Approaches to further processing of the collected data are shown, differing in the way of parallel data processing. The next stage of development is global monitoring systems that will be aimed to prompt response at all levels. The accumulated data will allow bringing the operating systems to a new level through the use of tools such as forecasting and simulation modeling, which will allow creating digital twins of heat supply systems. The proposed data collection system will perform forecasting and modeling at a higher level, and, as a result, help in the formation of more balanced management decisions.

A comparative analysis of the methods of approximate thermal calculation of the superheated steam condenser of the steam compression heat pump of the heat supply system is presented. The working substance of the heat pump and the condensing steam is the refrigerant R410a. When the single-zone method is applied, the condenser is calculated by one area with the inclusion of the heat of overheating in the heat of condensation and the use of the overheating coefficient. The two-zone method assumes the calculation of the condenser in two separate areas, viz. the cooling of superheated steam and its actual condensation. The approbation was carried out during a numerical study of a condenser of a low-temperature heat pump system for heating and hot water supply, with a heat exchange surface in the form of a spiral coil pipe in a pipe immersed in a heated liquid. In the first approach, the flow rate and temperature of the heated water are limited by the saturation temperature of the condensing refrigerant, regardless of the flow pattern of the working media. The method of two-zone calculation of the superheated steam condenser with a counter-current or cross-counter-current flow scheme of working media makes it possible to obtain real results of the temperature of the heated water that exceeds the temperature of the saturated refrigerant vapor, taking into account the flow rate of the heated water. In this case, the wall temperature in the cooling area is higher than the saturation temperature, and during condensation it is lower, which further confirms the adequacy of the presented technique. The use of a two-zone technique with a separate averaging of the physical properties of the working media in the areas of superheated steam and condensation cooling, as well as temperature pressures, provides a more accurate value of the heat exchange surface, which in the case under consideration is reduced to 20%. Based on the conducted studies, it is recommended to use a two-zone technique that makes it possible to obtain reliable data on the parameters of the superheated steam condenser.

A program that allows modeling, thermodynamically optimizing and performing exergetic analysis of more than a hundred different variations of the schemes of trigeneration turbine units based on low-boiling working fluids. With the aid of the program that had been developed, an exergetic analysis of six schemes of trigeneration turbine units on the organic Rankine cycle was performed, viz. on an overheated steam with a steam compression refrigeration unit; with an intermediate overheating of the working fluid and a steam compression refrigeration unit; on an overheated steam with a refrigeration unit with carbon dioxide production; with an intermediate overheating of the working fluid and a refrigeration unit with carbon dioxide production; on an overheated steam with a refrigeration unit with production carbon dioxide and cooling of the turbine condenser with liquid carbon dioxide; with intermediate overheating of the working fluid, a refrigeration unit with carbon dioxide production and cooling of the turbine unit condenser with liquid carbon dioxide. A gas turbine unit was used as an energy source for the above-mentioned schemes. The possibility of using the resulting liquid carbon dioxide to cool the condenser of a turbine unit on an organic Rankine cycle has been studied. A comparative analysis of two methods of obtaining cold (using a steam compression refrigeration unit and a refrigeration unit with carbon dioxide production) for use in trigeneration schemes has been carried out. The research was based on the method of exergetic analysis, the results of which are presented in the form of enlarged Grassmann – Shargut diagrams. A technical and economic analysis of the use of intermediate overheating in the organic Rankine cycle has been carried out, ozone-safe freon R245FA was used as the working fluid. Recommendations for the application of the studied trigeneration schemes on the organic Rankine cycle are formulated.  

Large-scale hydraulic engineering construction associated with the erection and operation of large dams and reservoirs has an impact on the ecosystem and physical and geographical characteristics of the construction area. In addition, during the passage of catastrophic floods and high waters, the danger of a hydrodynamic accident increases, i. e. overflow of reservoirs, overflow of masses over the ridge of an earthen dam and its destruction, accompanied by the formation of a closure channel and the outflow of an unsteady water flow through it into the lower reaches in the form of a breakthrough wave. The process of erosion of an underground dam due to the overflow of water over the ridge can be divided into two stages. During the first one, the lower slope is eroded, along which the water moves as if by a rapid current. The profile of the dam, initially trapezoidal, by the end of the erosion takes a shape close to triangular, and the ridge mark on the side of the upper slope remains constant. The second stage is characterized by an intensive reduction of the ridge; the dam quickly takes the form of a practical profile spillway, which persists until the end of erosion. At the same time, there is an intensive expansion of the closure channel. As the analysis showed, the existing mathematical models used to calculate the dynamics of the erosion of the dam, especially its first stage before the expansion of the closure channel, are not perfect. The article presents a refined methodology developed by the authors for modeling the process of erosion of ground dams during water overflow over the ridge. The calculations made in accordance with this methodology make it possible to construct a flow hydrograph in the location of the eroded dam. The methodology can be used in the development of project documentation at the first stage of dam design, as well as in determining the forecast quantitative and qualitative characteristics of the water regime of reservoirs.