Digital measuring elements in microprocessor protections of electrical installations are implemented mainly with the use of orthogonal components of input signals. To form orthogonal components in microprocessor protections, digital Fourier filters are most widely used, the action of which is al-ways inertial in transient modes. As a result, a dynamic error appears, changing over time and completely disappearing when a steady-state regime occurs. The dynamic error consists of amplitude and phase errors, which can significantly affect the functioning of digital measuring elements and create conditions for their excessive triggering during external short circuits and deceleration of triggering during internal short circuits. Therefore, it is advisable to compensate for the dynamic error, for which it is proposed to determine the amplitude and phase of the fundamental harmonic signal by specially formed orthogonal components. The proposed method of forming orthogonal components of the signal with compensation of dynamic amplitude and phase errors is based on the use of orthogonal components of the digital Fourier filter, followed by the determination of their samples of the final orthogonal components that coincide with the orthogonal components of Fourier in steady-state mode and shifted in phase relative to the latter in transient mode. The amplitude and phase of the signal with minimal dynamic phase errors are calculated from the samples of the final orthogonal components in the digital measuring element. In the dynamic modeling environment of MATLAB-Simulink-SimPowerSystems, a digital model is implemented, which includes a power system, a three-phase group of current transformers, a load, a short-circuit block, as well as a model of a digital measuring element implemented on the basis of the final orthogonal components. The operation of the digital model was checked using two types of test effects, viz. a sinusoidal signal with a frequency of 50 Hz, and a signal close to the real secondary current of a short-circuit current transformer. As a result of the calculations, it was found that digital measuring elements made on the basis of the proposed methodology made it possible to reduce the relative dynamic amplitude and phase errors by three to four times, as compared with the Fourier measuring element taken as a reference.

The paper proposes a method for optimizing the layout of offshore wind farms to increase their efficiency by reducing the effect of aerodynamic shading, minimizing electrical losses in cable lines of the system for receiving and transmitting electrical energy generated by wind turbines to the electrical grid of the power system. The task is reduced to determining several parameters that define the geometric dimensions and shape of the layout grid with pre-installed tur-bine locations. This approach, in contrast to the coordinate-wise search method, makes it possible to build symmetrical grid layouts of wind power plants, which in practice are more convenient in terms of maintenance and operation. Together with the optimization of the layout, the search for the optimal location of the offshore transformer substation and the synthesis of the scheme of cable joints between wind power plants has been carried out. To solve this problem, a heuristic algorithm was used to search for a minimum spanning tree with a restriction on the conductivity of connections, which made it possible to build realistic schemes and more adequately assess their technical and economic characteristics. As the results of testing the proposed methodology on the example of optimizing the layout of the Horns Rev 1 wind farm have shown, the use of this approach has reduced the cost of the electrical system by 10–12 %. This is 7–11 % higher than the result obtained by using the MST algorithm, which performs the construction of a circuit of cable joints of a simplified topology. The change in the size and shape of the boundaries of the wind farm site resulted in an increase in the estimated electricity generation by 2.3 % and a decrease in its cost by 4 %. When optimizing the layout of wind turbines within the fixed boundaries of the site, these indicators are improved by only 1 and 2 % as compared to the original scheme.

A number of requirements are imposed on installations associated with regulated DC sources, including low voltage and current ripple in the load, as well as a wide range of output current variation. Such installations are traditionally made on controlled rectifiers or pulse-width converters in which voltage ripples are always present. The paper considers a method for reducing the voltage ripple of powerful rectifiers for powering magnetic systems based on the insertion of a compensating voltage equal in magnitude and opposite in phase to the ripple voltage into the load circuit. The possibility of using ripple compensators connected in parallel and in series with the load, as well as methods of obtaining a compensating voltage is shown. Methods for obtaining compensating voltage are given. In order to exclude the magnetization of the ripple compensator transformer, it is proposed to use several versions of the compensating transformer and the inclusion of ripple compensators. Practical schemes of passive compensators (with a demagnetizing circuit and a bifilar winding) are analyzed. The problem of developing ripple compensators for multiphase rectifiers, as well as ways to solve it, is considered. Practical recommendations for choosing a core material and calculating a transformer are given. On the basis of the presented theoretical and practical considerations for the design of the ripple compensators, simulation models have been developed in the Simulink pack-age of the MATLAB program. A technique for studying ripple compensators using the simulation models of a symmetrical 12-pulse rectifier that has been developed is presented. The results of simulation of passive ripple compensators, performed in two versions, showed their effectiveness, while the scheme was relatively simple and economic costs were relatively low. Also, the time of setting the set current in the system in the presence of a ripple compensator increases by no more than 3 %, and the accuracy and stability of operation do not change.

The paper considers the suppression of chaotic oscillations in small energy systems that occur in emergency modes and lead to the phenomenon of voltage collapse, which corresponds to the process of voltage drop in the network, which can be accompanied by a complete shutdown of the affected area. The paper also presents a method that has been developed and that allows changing the spectrum of Lyapunov’s characteristic indicators and converting chaotic oscillations in a small power system to regular dynamic modes. The method of synthesis of control actions is based on the theorem of topological equivalence of hyperbolic nonlinear systems and their linearized models as well as on and the use of numerical integration of nonlinear differential equations describing the behavior of power systems in order to construct a phase portrait and calculate Lyapunov’s characteristic exponents. The results of the work consist in the synthesis of feedback, which ensures the formation of a spectrum of Lyapunov’s characteristic indicators with negative values. The suppression of chaotic regimes occurs by forming a spectrum of negative Lyapunov’s characteristic indicators in a closed system. The parameters of the regulator in the feedback circuit are determined using the modal control method based on the solution of the matrix algebraic Sylvester equation. The solution of the problem of transition from a chaotic regime to a regular movement in a small power system is considered. To test the operability of the proposed method of chaos suppression, the spectrum of Lyapunov’s characteristic indicators is calculated and trajectories in the phase space of the initial nonlinear system and the system with control action are constructed. For energy systems with chaotic dynamics, synthesized feedback makes it possible to suppress chaotic fluctuations and switch to regular modes, thereby preventing the occurrence of emergency modes.

The article presents an adaptive genetic algorithm developed by the authors, which makes it possible to optimize the topology of a power network with distributed generation. The optimization was based on bioinspired methods. The objects of the study were a 15-node circuit of a power net-work with photovoltaic stations and a 14-node IEEE augmented circuit with distributed generation sources (three wind farms and two photovoltaic plants). The simulation of the modes of electric power systems was performed using the Pandapower library for the Python programming language, which is in the public domain. Three types of electric load of consumers were considered, reflecting the natures of electricity consumption in the nodes of real electric power systems, the results of numerical studies were presented. The proposed genetic algorithm used two different functions of interbreeding, the function of mutation, selection of the best individuals and mass mutation (complete population renewal). At the end of each iteration of the algorithm operation, statistical dependencies were de-rived that characterized its work: the best (minimal losses) and average adaptability in the population, a list of the best individuals throughout all iterations, etc. The verification was carried out in comparison with the results obtained by a complete search of possible radial configurations of the system, and it showed that the developed genetic algorithm had fast convergence, high accuracy and was able to work correctly with different configurations of electrical circuits, generation and load structures. The algorithm can be used in conjunction with renewable energy sources generation forecasting systems for the day ahead when planning the operating modes of power units in order to minimize the costs of covering electricity losses and improve the quality of electricity supplied.

The article presents the results of computational and experimental studies of thermochemical conversion of wood biomass to obtain liquid pyrolysis products taking into account their cooling rate. The method of calculating the optimal operating parameters (temperature and cooling rate) of the techno-logical process is presented. An expression is proposed to determine the consumption of wood raw materials depending on the temperature of the thermochemical conversion process. It is noted that the mass yield of liquid pyrolysis products from the reactor poorly depends on temperature and is approximately 0.45 in the range from 573 to 923 K. To assess the effect of the cooling rate of liquid pyrolysis products, a third-order differential equation was used for a model limited by the reaction rate. It has been shown that when liquid pyrolysis products are cooled, the degree of their conversion tends to a certain value other than 1 (depending on the cooling rate). Calculated data on the dependence of the degrees of conversion of liquid wood pyrolysis products on time at different cooling rates and temperatures of thermochemical conversion of biomass have been obtained. It has been established also that the ratio of the mass yield of cooled liquid pyrolysis products to the initial loading of the pyrolysis reactor makes it possible to find optimal cooling conditions for the primary products of biomass pyrolysis carried out at certain temperatures. Graphs of the dependence of this parameter on the temperature of the thermochemical conversion of wood biomass for different cooling rates of liquid pyrolysis products are presented. It is shown that the maximum possible yield of liquid products is provided at a reactor temperature of 923–973 K and a cooling rate of 700000–1200000 degrees/min. However, achieving such cooling rates is rather a difficult technical task. Therefore, more limited temperature 773–800 K is accepted, at which a practically realizable cooling rate of primary biomass de-composition products is achieved.

As in the whole world, there are regions in Russia that experience heat supply difficulties, mainly due to the high cost of fossil fuel as well as to growth of energy resources cost and polluting emissions. In this regard, search for solutions which would provide energy saving with an increase of energy, commercial and ecological efficiency of modern heat supply systems is becoming vitally important today. One of them is the development and use of special types of energy including renewable energy sources, wind energy in particular. Accordingly, the paper presents one of the possible solutions to the heat supply problem which are directed at meeting the whole region’s heat demand through the joint use of wind power plants with a boiler room operating on fuel oil. The study assessed the efficiency of constructing of wind power plants with a total capacity of 1.7 MW for the heat supply needs of a settlement, which is located on the Barents Sea coast in Russia. The selected area is characterized by an average annual wind speed of 7.0 m/s and a long heating period (9–10 months a year). The assessment showed that the wind power plant construction is financially reasonable, as additional profit can be generated by the end of the wind power plants scheduled service life that make up the half of primary investments. The results obtained in the paper are expected to make up for the lack of information on the feasibility of wind power plants construction for the heat supply needs, which is very useful for other countries that have similar areas experiencing various heat supply difficulties.