15 research outputs found
Implementation of Population Algorithms to Minimize Power Losses and Cable Cross-Section in Power Supply System
The article dues to the arrangement of the reactive power sources in the power grid to reduce the active power losses in transmission lines and minimize cable cross-sections of the lines. The optimal arrangement is considered from two points of view. In the first case, it is possible to minimize the active power losses only. In the second case, it is possible to change the cross-sections of the supply lines to minimize both the active power losses and the volume of the cable lines. The sum of the financial cost of the active power losses, the capital investment to install the deep reactive power compensation, and cost of the cable volume is introduced as the single optimization criterion. To reduce the losses, the deep compensation of reactive power sources in nodes of the grid are proposed. This optimization problem was solved by the Genetic algorithm and the Particle Swarm optimization algorithm. It was found out that the deep compensation allows minimizing active power losses the cable cross-section. The cost-effectiveness of the suggested method is shown. It was found out that optimal allocation of the reactive power sources allows increasing from 9% to 20% the financial expenses for the enterprise considered
Swarm intelligence algorithms for the problem of the optimal placement and operation control of reactive power sources into power grids
Deep reactive power compensation allows for reduction of active power losses in transmission lines of power supply systems. The efficiency of the compensation depends on the allocation of reactive power compensation units (RPCUs) at the nodes of a network. In general, investigations devoted to the study of optimal allocation of the compensation units have revealed that it is a static and deterministic optimization problem that can be solved by heuristic methods. However, in real systems, it is reasonable to consider such optimization problems, taking into account the dynamic and stochastic properties of the problems. These properties are the result of equipment failures and operational changes in technical systems. In addition, optimizing the allocation of the compensation units is the NP-hard multifactor problem. Under these circumstances, it is advisable to use the swarm intelligence algorithms. Swarm intelligence is a relatively new approach to solving the optimization problem, which takes inspiration from the behaviour of ants, birds, and other animals. Advantages of swarm algorithms are most evident if problems involve the dynamic or stochastic nature of the objective function and constraints. Contrary to a number of similar studies, this research considers the problem of the optimal allocation of compensation units as a dynamic problem, taking into account the possible random failures of the compensation equipment. The optimization problem has been solved by two Swarm Intelligence algorithms (the Particle Swarm optimization and the Artificial Bee Colony optimization) and Genetic algorithms. It has been aimed at comparing the effectiveness of the algorithms for solving such problems. It was found that swarm algorithms could be successfully applied in the operation control of compensation units in real-time. Β© 2017 WIT Press
Application of swarm intelligence algorithms to energy management of prosumers with wind power plants
The paper considers the problem of optimal control of a prosumer with a wind power plant in smart grid. It is shown that control can be performed in non-deterministic conditions due to the impossibility of accurate forecasting of the generation from renewable plants. A control model based on a priority queue of logical rules with structural-parametric optimization is applied. The optimization problem is considered from a separate prosumer, not from the entire distributed system. The solution of the optimization problem is performed by three swarm intelligence algorithms. Computational experiments were carried out for models of wind energy systems on Russky Island and Popov Island (Far East). The results obtained showed the high effectiveness of the swarm intelligence algorithms that demonstrated reliable and fast convergence to the global extreme of the optimization problem under different scenarios and parameters of prosumers. Also, we analyzed the influence of accumulator capacity on the variability of prosumers. The variability, in turn, affects the increase of the prosumer benefits from the interaction with the external global power system and neighboring prosumers
Optimal Management of Energy Consumption in an Autonomous Power System Considering Alternative Energy Sources
This work aims to analyze and manage the optimal power consumption of the autonomous power system within the Pamir region of Republic of Tajikistan, based on renewable energy sources. The task is solved through linear programming methods, production rules and mathematical modeling of power consumption modes by generating consumers. It is assumed that power consumers in the considered region have an opportunity to independently cover energy shortage by installing additional generating energy sources. The objective function is to minimize the financial expenses for own power consumption, and to maximize them from both the export and redistribution of power flows. In this study, the optimal ratio of power generation by alternative sources from daily power consumption for winter was established to be hydroelectric power plants (94.8%), wind power plant (3.8%), solar photovoltaic power plant (0.5%) and energy storage (0.8%); while it is not required in summer due to the ability to ensure the balance of energy by hydroelectric power plants. As a result, each generating consumer can independently minimize their power consumption and maximize profit from the energy exchange with other consumers, depending on the selected energy sources, thus becoming a good example of carbon-free energy usage at the micro-and mini-grid level. Β© 2022 by the authors. Licensee MDPI, Basel, Switzerland
Improving accuracy and generalization performance of small-size recurrent neural networks applied to short-term load forecasting
The load forecasting of a coal mining enterprise is a complicated problem due to the irregular technological process of mining. It is necessary to apply models that can distinguish both cyclic components and complex rules in the energy consumption data that reflect the highly volatile technological process. For such tasks, Artificial Neural Networks demonstrate advanced performance. In recent years, the effectiveness of Artificial Neural Networks has been significantly improved thanks to new state-of-the-art architectures, training methods and approaches to reduce overfitting. In this paper, the Recurrent Neural Network architecture with a small-size model was applied to the short-term load forecasting of a coal mining enterprise. A single recurrent model was developed and trained for the entire four-year operational period of the enterprise, with significant changes in the energy consumption pattern during the period. This task was challenging since it required high-level generalization performance from the model. It was shown that the accuracy and generalization properties of small-size recurrent models can be significantly improved by the proper selection of the hyper-parameters and training method. The effectiveness of the proposed approach was validated using a real-case dataset. Β© 2020 by the authors. Licensee MDPI, Basel, Switzerland
Data Mining Applied to Decision Support Systems for Power Transformersβ Health Diagnostics
This manuscript addresses the problem of technical state assessment of power transformers based on data preprocessing and machine learning. The initial dataset contains diagnostics results of the power transformers, which were collected from a variety of different data sources. It leads to dramatic degradation of the quality of the initial dataset, due to a substantial number of missing values. The problems of such real-life datasets are considered together with the performed efforts to find a balance between data quality and quantity. A data preprocessing method is proposed as a two-iteration data mining technology with simultaneous visualization of objectsβ observability in a form of an image of the dataset represented by a data area diagram. The visualization improves the decision-making quality in the course of the data preprocessing procedure. On the dataset collected by the authors, the two-iteration data preprocessing technology increased the dataset filling degree from 75% to 94%, thus the number of gaps that had to be filled in with the synthetic values was reduced by 2.5 times. The processed dataset was used to build machine-learning models for power transformersβ technical state classification. A comparative analysis of different machine learning models was carried out. The outperforming efficiency of ensembles of decision trees was validated for the fleet of high-voltage power equipment taken under consideration. The resulting classification-quality metric, namely, F1-score, was estimated to be 83%. Β© 2022 by the authors.Ministry of Education and Science of the Russian Federation,Β MinobrnaukaThe research funding from the Ministry of Science and Higher Education of the Russian Federation (Ural Federal University Program of Development within the Priority-2030 Program) is gratefully acknowledged
ΠΠΎΠ²ΡΡΠ΅Π½ΠΈΠ΅ ΡΠΎΡΠ½ΠΎΡΡΠΈ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠΈ ΡΠΎΡΠΎΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΈΡ ΡΡΠ°Π½ΡΠΈΠΉ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² k-ΡΡΠ΅Π΄Π½ΠΈΡ ΠΈ k-Π±Π»ΠΈΠΆΠ°ΠΉΡΠΈΡ ΡΠΎΡΠ΅Π΄Π΅ΠΉ
Renewable energy sources (RES) are seen as a means of the fuel and energy complex carbon footprint reduction but the stochastic nature of generation complicates RES integration with electric power systems. Therefore, it is necessary to develop and improve methods for forecasting of the power plants generation using the energy of the sun, wind and water flows. One of the ways to improve the accuracy of forecast models is a deep analysis of meteorological conditions as the main factor affecting the power generation. In this paper, a method for adapting of forecast models to the meteorological conditions of photovoltaic stations operation based on machine learning algorithms was proposed and studied. In this case, unsupervised learning is first performed using the k-means method to form clusters. For this, it is also proposed to use studied the feature space dimensionality reduction algorithm to visualize and estimate the clustering accuracy. Then, for each cluster, its own machine learning model was trained for generation forecasting and the k-nearest neighbours algorithm was built to attribute the current conditions at the model operation stage to one of the formed clusters. The study was conducted on hourly meteorological data for the period from 1985 to 2021. A feature of the approach is the clustering of weather conditions on hourly rather than daily intervals. As a result, the mean absolute percentage error of forecasting is reduced significantly, depending on the prediction model used. For the best case, the error in forecasting of a photovoltaic plant generation an hour ahead was 9 %.ΠΠΎΠ·ΠΎΠ±Π½ΠΎΠ²Π»ΡΠ΅ΠΌΡΠ΅ ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠΈ ΡΠ½Π΅ΡΠ³ΠΈΠΈ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΠΊΠ°ΠΊ ΡΡΠ΅Π΄ΡΡΠ²ΠΎ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΠ³Π»Π΅ΡΠΎΠ΄Π½ΠΎΠ³ΠΎ ΡΠ»Π΅Π΄Π° ΡΠΎΠΏΠ»ΠΈΠ²Π½ΠΎ-ΡΠ½Π΅ΡΠ³Π΅ΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ°, ΠΏΡΠΈ ΡΡΠΎΠΌ ΡΡΠΎΡ
Π°ΡΡΠΈΡΠ΅ΡΠΊΠΈΠΉ Ρ
Π°ΡΠ°ΠΊΡΠ΅Ρ Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠΈ ΠΎΡΠ»ΠΎΠΆΠ½ΡΠ΅Ρ ΠΈΡ
ΠΈΠ½ΡΠ΅Π³ΡΠ°ΡΠΈΡ Ρ ΡΠ»Π΅ΠΊΡΡΠΎΡΠ½Π΅ΡΠ³Π΅ΡΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ ΡΠΈΡΡΠ΅ΠΌΠ°ΠΌΠΈ. ΠΡΠ° ΡΡΡΠ΅ΡΡΠ²Π΅Π½Π½Π°Ρ ΡΡΡΠ΄Π½ΠΎΡΡΡ ΠΎΠ±ΡΡΠ»ΠΎΠ²Π»ΠΈΠ²Π°Π΅Ρ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΡ ΡΠΎΠ·Π΄Π°Π²Π°ΡΡ ΠΈ ΡΠΎΠ²Π΅ΡΡΠ΅Π½ΡΡΠ²ΠΎΠ²Π°ΡΡ ΠΌΠ΅ΡΠΎΠ΄Ρ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠΈ ΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ°Π½ΡΠΈΠΉ, ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡΠΈΡ
ΡΠ½Π΅ΡΠ³ΠΈΡ ΡΠΎΠ»Π½ΡΠ°, Π²Π΅ΡΡΠ° ΠΈ Π²ΠΎΠ΄Π½ΡΡ
ΠΏΠΎΡΠΎΠΊΠΎΠ². ΠΠ°ΠΈΠ±ΠΎΠ»Π΅Π΅ Π²Π°ΠΆΠ½ΡΠΌ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ΠΌ, ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΠ²Π°ΡΡΠΈΠΌ ΠΏΠΎΠ²ΡΡΠ΅Π½ΠΈΠ΅ ΡΠΎΡΠ½ΠΎΡΡΠΈ ΠΏΡΠΎΠ³Π½ΠΎΠ·Π½ΡΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ, ΡΠ²Π»ΡΠ΅ΡΡΡ Π³Π»ΡΠ±ΠΎΠΊΠΈΠΉ Π°Π½Π°Π»ΠΈΠ· ΠΌΠ΅ΡΠ΅ΠΎΡΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ»ΠΎΠ²ΠΈΠΉ ΠΊΠ°ΠΊ Π³Π»Π°Π²Π½ΠΎΠ³ΠΎ ΡΠ°ΠΊΡΠΎΡΠ°, Π²Π»ΠΈΡΡΡΠ΅Π³ΠΎ Π½Π° Π²ΡΡΠ°Π±ΠΎΡΠΊΡ ΡΠ»Π΅ΠΊΡΡΠΎΡΠ½Π΅ΡΠ³ΠΈΠΈ. Π Π΄Π°Π½Π½ΠΎΠΉ ΡΠ°Π±ΠΎΡΠ΅ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ ΠΈ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ ΠΌΠ΅ΡΠΎΠ΄ Π°Π΄Π°ΠΏΡΠ°ΡΠΈΠΈ ΠΏΡΠΎΠ³Π½ΠΎΠ·Π½ΡΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ ΠΏΠΎΠ΄ ΠΌΠ΅ΡΠ΅ΠΎΡΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΡΠ»ΠΎΠ²ΠΈΡ ΡΠ°Π±ΠΎΡΡ ΡΠΎΡΠΎΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ°Π½ΡΠΈΠΉ Π½Π° Π±Π°Π·Π΅ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΠΌΠ°ΡΠΈΠ½Π½ΠΎΠ³ΠΎ ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ. ΠΡΠΈΒ ΡΡΠΎΠΌ Π²Π½Π°ΡΠ°Π»Π΅ Π²ΡΠΏΠΎΠ»Π½ΡΠ΅ΡΡΡ ΠΎΠ±ΡΡΠ΅Π½ΠΈΠ΅ Π±Π΅Π· ΡΡΠΈΡΠ΅Π»Ρ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ k-ΡΡΠ΅Π΄Π½ΠΈΡ
Π΄Π»Ρ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΊΠ»Π°ΡΡΠ΅ΡΠΎΠ². ΠΠ»Ρ ΡΡΠΎΠΉ Π·Π°Π΄Π°ΡΠΈ ΡΠ°ΠΊΠΆΠ΅ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ΠΎ ΠΈ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΎ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ Π°Π»Π³ΠΎΡΠΈΡΠΌΠ° ΠΏΠΎΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΠ°Π·ΠΌΠ΅ΡΠ½ΠΎΡΡΠΈ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π° ΠΏΡΠΈΠ·Π½Π°ΠΊΠΎΠ² Π΄Π»Ρ Π²ΠΈΠ·ΡΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΎΡΠ΅Π½ΠΊΠΈ ΡΠΎΡΠ½ΠΎΡΡΠΈ ΠΊΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΠΈ. ΠΠ°ΡΠ΅ΠΌ Π΄Π»Ρ ΠΊΠ°ΠΆΠ΄ΠΎΠ³ΠΎ ΠΊΠ»Π°ΡΡΠ΅ΡΠ° ΠΏΠΎΡΡΡΠΎΠ΅Π½Π° ΡΠ²ΠΎΡ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΌΠ°ΡΠΈΠ½Π½ΠΎΠ³ΠΎ ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ Π΄Π»Ρ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΎΠ² ΠΈΒ Π°Π»Π³ΠΎΡΠΈΡΠΌ k-Π±Π»ΠΈΠΆΠ°ΠΉΡΠΈΡ
ΡΠΎΡΠ΅Π΄Π΅ΠΉ Π΄Π»Ρ ΠΎΡΠ½Π΅ΡΠ΅Π½ΠΈΡ ΡΠ΅ΠΊΡΡΠΈΡ
ΡΡΠ»ΠΎΠ²ΠΈΠΉ Π½Π° ΡΡΠ°ΠΏΠ΅ ΡΠΊΡΠΏΠ»ΡΠ°ΡΠ°ΡΠΈΠΈ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΊ ΠΎΠ΄Π½ΠΎΠΌΡ ΠΈΠ· ΡΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΠΊΠ»Π°ΡΡΠ΅ΡΠΎΠ². ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ Π±ΡΠ»ΠΎ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΎ Π½Π° ΠΏΠΎΡΠ°ΡΠΎΠ²ΡΡ
ΠΌΠ΅ΡΠ΅ΠΎΡΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
Π΄Π°Π½Π½ΡΡ
Π·Π° ΠΏΠ΅ΡΠΈΠΎΠ΄ Ρ 1985 ΠΏΠΎ 2021 Π³. ΠΠ΄Π½ΠΎΠΉ ΠΈΠ· ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠ΅ΠΉ ΡΡΠΎΠ³ΠΎ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Π° ΡΠ²Π»ΡΠ΅ΡΡΡ ΠΊΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΡ ΠΌΠ΅ΡΠ΅ΠΎΡΡΠ»ΠΎΠ²ΠΈΠΉ Π½Π° ΡΠ°ΡΠΎΠ²ΡΡ
, Π° Π½Π΅ ΡΡΡΠΎΡΠ½ΡΡ
ΠΈΠ½ΡΠ΅ΡΠ²Π°Π»Π°Ρ
. ΠΒ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΡΡΠ΅Π΄Π½ΠΈΠΉ ΠΌΠΎΠ΄ΡΠ»Ρ ΠΎΡΠ½ΠΎΡΠΈΡΠ΅Π»ΡΠ½ΠΎΠΉ ΠΎΡΠΈΠ±ΠΊΠΈ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎ ΡΠ½ΠΈΠΆΠ°Π΅ΡΡΡ Π² Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΠΎΡΒ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΠΌΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ. ΠΠ»Ρ Π½Π°ΠΈΠ»ΡΡΡΠ΅Π³ΠΎ Π²Π°ΡΠΈΠ°Π½ΡΠ° ΠΎΡΠΈΠ±ΠΊΠ° ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠΈ ΡΠΎΡΠΎΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΡΠ°Π½ΡΠΈΠΈ Π½Π° ΡΠ°Ρ Π²ΠΏΠ΅ΡΠ΅Π΄ ΡΠΎΡΡΠ°Π²ΠΈΠ»Π° 9Β %
ΠΠΏΠ΅ΡΠ°ΡΠΈΠ²Π½ΠΎΠ΅ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠΊΠΎΡΠΎΡΡΠΈ Π²Π΅ΡΡΠ° Π΄Π»Ρ Π°Π²ΡΠΎΠ½ΠΎΠΌΠ½ΠΎΠΉ ΡΠ½Π΅ΡΠ³Π΅ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΡΡΠ°Π½ΠΎΠ²ΠΊΠΈ ΡΡΠ³ΠΎΠ²ΠΎΠΉ ΠΆΠ΅Π»Π΅Π·Π½ΠΎΠ΄ΠΎΡΠΎΠΆΠ½ΠΎΠΉ ΠΏΠΎΠ΄ΡΡΠ°Π½ΡΠΈΠΈ
Currently, the prospects of creating hybrid power assemblies using renewable energy sources, including wind energy, and energy storage systems based on hydrogen energy technologies are being considered. To control such an energy storage system, it is necessary to perform operational renewable sources generation forecasting, particularly forecasting of wind power assemblies. Their production depends on the speed and direction of the wind. The article presents the results of solving the problem of operational forecasting of wind speed for a hybrid power assembly project aimed at increasing the capacity of the railway section between Yaya and Izhmorskaya stations (Kemerovo region of the Russian Federation). Hourly data of wind speeds and directions for 15 years have been analyzed, a neural network model has been built, and a compact architecture of a multilayer perceptron has been proposed for short-term forecasting of wind speed and direction for 1 and 6 hours ahead. The model that has been developed allows minimizing the risks of overfitting and loss of forecasting accuracy due to changes in the operating conditions of the model over time. A specific feature of this work is the stability investigation of the model trained on the data of long-term observations to long-term changes, as well as the analysis of the possibilities of improving the accuracy of forecasting due to regular further training of the model on newly available data. The nature of the influence of the size of the training sample and the self-adaptation of the model on the accuracy of forecasting and the stability of its work on the horizon of several years has been established. It is shown that in order to ensure high accuracy and stability of the neural network model of wind speed forecasting, long-term meteorological observations data are required.Π Π½Π°ΡΡΠΎΡΡΠ΅Π΅ Π²ΡΠ΅ΠΌΡ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΠΏΠ΅ΡΡΠΏΠ΅ΠΊΡΠΈΠ²Ρ ΡΠΎΠ·Π΄Π°Π½ΠΈΡ Π³ΠΈΠ±ΡΠΈΠ΄Π½ΡΡ
ΡΠ½Π΅ΡΠ³Π΅ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΡΠ°Π½ΠΎΠ²ΠΎΠΊ Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ Π²ΠΎΠ·ΠΎΠ±Π½ΠΎΠ²Π»ΡΠ΅ΠΌΡΡ
ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠΎΠ² ΡΠ½Π΅ΡΠ³ΠΈΠΈ, Π² ΡΠΎΠΌ ΡΠΈΡΠ»Π΅ ΡΠ½Π΅ΡΠ³ΠΈΠΈ Π²Π΅ΡΡΠ°, ΠΈ ΡΠΈΡΡΠ΅ΠΌ Π½Π°ΠΊΠΎΠΏΠ»Π΅Π½ΠΈΡ ΡΠ½Π΅ΡΠ³ΠΈΠΈ Π½Π° Π±Π°Π·Π΅ ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΠΉ Π²ΠΎΠ΄ΠΎΡΠΎΠ΄Π½ΠΎΠΉ ΡΠ½Π΅ΡΠ³Π΅ΡΠΈΠΊΠΈ. ΠΠ»Ρ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΡΠ°ΠΊΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΠΎΠΉ Π½Π°ΠΊΠΎΠΏΠ»Π΅Π½ΠΈΡ ΡΠ½Π΅ΡΠ³ΠΈΠΈ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎ ΠΎΠΏΠ΅ΡΠ°ΡΠΈΠ²Π½ΠΎΠ΅ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠΈ ΠΎΡ Π²ΠΎΠ·ΠΎΠ±Π½ΠΎΠ²Π»ΡΠ΅ΠΌΡΡ
ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠΎΠ², Π² ΡΠ°ΡΡΠ½ΠΎΡΡΠΈ Π²Π΅ΡΡΠΎΠ²ΡΡ
ΡΠ½Π΅ΡΠ³Π΅ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΡΠ°Π½ΠΎΠ²ΠΎΠΊ. ΠΡ
Π²ΡΡΠ°Π±ΠΎΡΠΊΠ° Π·Π°Π²ΠΈΡΠΈΡ ΠΎΡ ΡΠΊΠΎΡΠΎΡΡΠΈ ΠΈ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π²Π΅ΡΡΠ°. Π ΡΡΠ°ΡΡΠ΅ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°ΡΠΈ ΠΎΠΏΠ΅ΡΠ°ΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΊΠΎΡΠΎΡΡΠΈ Π²Π΅ΡΡΠ° Π΄Π»Ρ ΠΏΡΠΎΠ΅ΠΊΡΠ° Π³ΠΈΠ±ΡΠΈΠ΄Π½ΠΎΠΉ ΡΠ½Π΅ΡΠ³Π΅ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΡΡΠ°Π½ΠΎΠ²ΠΊΠΈ, Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½Π½ΠΎΠΉ Π½Π° ΠΏΠΎΠ²ΡΡΠ΅Π½ΠΈΠ΅ ΠΏΡΠΎΠΏΡΡΠΊΠ½ΠΎΠΉ ΡΠΏΠΎΡΠΎΠ±Π½ΠΎΡΡΠΈ ΠΆΠ΅Π»Π΅Π·Π½ΠΎΠ΄ΠΎΡΠΎΠΆΠ½ΠΎΠ³ΠΎ ΡΡΠ°ΡΡΠΊΠ° ΠΌΠ΅ΠΆΠ΄Ρ ΡΡΠ°Π½ΡΠΈΡΠΌΠΈ Π―Ρ ΠΈ ΠΠΆΠΌΠΎΡΡΠΊΠ°Ρ (ΠΠ΅ΠΌΠ΅ΡΠΎΠ²ΡΠΊΠ°Ρ ΠΎΠ±Π»Π°ΡΡΡ Π ΠΎΡΡΠΈΠΉΡΠΊΠΎΠΉ Π€Π΅Π΄Π΅ΡΠ°ΡΠΈΠΈ). ΠΡΠΎΠ°Π½Π°Π»ΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Ρ ΠΏΠΎΡΠ°ΡΠΎΠ²ΡΠ΅ Π΄Π°Π½Π½ΡΠ΅ ΡΠΊΠΎΡΠΎΡΡΠ΅ΠΉ ΠΈ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠΉ Π²Π΅ΡΡΠ° Π·Π° 15 Π»Π΅Ρ, ΠΏΠΎΡΡΡΠΎΠ΅Π½Π° Π½Π΅ΠΉΡΠΎΡΠ΅ΡΠ΅Π²Π°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΈ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π° ΠΊΠΎΠΌΠΏΠ°ΠΊΡΠ½Π°Ρ Π°ΡΡ
ΠΈΡΠ΅ΠΊΡΡΡΠ° ΠΌΠ½ΠΎΠ³ΠΎΡΠ»ΠΎΠΉΠ½ΠΎΠ³ΠΎ ΠΏΠ΅ΡΡΠ΅ΠΏΡΡΠΎΠ½Π° Π΄Π»Ρ ΠΊΡΠ°ΡΠΊΠΎΡΡΠΎΡΠ½ΠΎΠ³ΠΎ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΊΠΎΡΠΎΡΡΠΈ ΠΈ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π²Π΅ΡΡΠ° Π½Π° 1 ΠΈ 6 Ρ Π²ΠΏΠ΅ΡΠ΅Π΄. Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½Π½Π°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΌΠΈΠ½ΠΈΠΌΠΈΠ·ΠΈΡΠΎΠ²Π°ΡΡ ΡΠΈΡΠΊΠΈ ΠΏΠ΅ΡΠ΅ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ ΠΈ ΠΏΠΎΡΠ΅ΡΠΈ ΡΠΎΡΠ½ΠΎΡΡΠΈ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈΠ·-Π·Π° ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡ ΡΡΠ»ΠΎΠ²ΠΈΠΉ ΡΠ°Π±ΠΎΡΡ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΠΎ Π²ΡΠ΅ΠΌΠ΅Π½Π΅ΠΌ. ΠΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΡ Π΄Π°Π½Π½ΠΎΠΉ ΡΡΠ°ΡΡΠΈ Π·Π°ΠΊΠ»ΡΡΠ°Π΅ΡΡΡ Π² ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΈ ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΠΈ ΠΌΠΎΠ΄Π΅Π»ΠΈ, ΠΎΠ±ΡΡΠ΅Π½Π½ΠΎΠΉ Π½Π° Π΄Π°Π½Π½ΡΡ
ΠΌΠ½ΠΎΠ³ΠΎΠ»Π΅ΡΠ½ΠΈΡ
Π½Π°Π±Π»ΡΠ΄Π΅Π½ΠΈΠΉ, ΠΊ Π΄ΠΎΠ»Π³ΠΎΡΡΠΎΡΠ½ΡΠΌ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡΠΌ, Π° ΡΠ°ΠΊΠΆΠ΅ Π°Π½Π°Π»ΠΈΠ·Π΅ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠ΅ΠΉ ΠΏΠΎΠ²ΡΡΠ΅Π½ΠΈΡ ΡΠΎΡΠ½ΠΎΡΡΠΈ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π·Π° ΡΡΠ΅Ρ ΡΠ΅Π³ΡΠ»ΡΡΠ½ΠΎΠ³ΠΎ Π΄ΠΎΠΎΠ±ΡΡΠ΅Π½ΠΈΡ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π½Π° Π²Π½ΠΎΠ²Ρ ΠΏΠΎΡΡΡΠΏΠ°ΡΡΠΈΡ
Π΄Π°Π½Π½ΡΡ
. Π£ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ Ρ
Π°ΡΠ°ΠΊΡΠ΅Ρ Π²Π»ΠΈΡΠ½ΠΈΡ ΡΠ°Π·ΠΌΠ΅ΡΠ° ΠΎΠ±ΡΡΠ°ΡΡΠ΅ΠΉ Π²ΡΠ±ΠΎΡΠΊΠΈ ΠΈ ΡΠ°ΠΌΠΎΠ°Π΄Π°ΠΏΡΠ°ΡΠΈΠΈ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π½Π° ΡΠΎΡΠ½ΠΎΡΡΡ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈ ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΡ Π΅Π΅ ΡΠ°Π±ΠΎΡΡ Π½Π° Π³ΠΎΡΠΈΠ·ΠΎΠ½ΡΠ΅ Π² Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΎ Π»Π΅Ρ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ Π΄Π»Ρ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΡ Π²ΡΡΠΎΠΊΠΎΠΉ ΡΠΎΡΠ½ΠΎΡΡΠΈ ΠΈ ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΠΈ Π½Π΅ΠΉΡΠΎΡΠ΅ΡΠ΅Π²ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΊΠΎΡΠΎΡΡΠΈ Π²Π΅ΡΡΠ° Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΡ Π΄Π°Π½Π½ΡΠ΅ ΠΌΠ½ΠΎΠ³ΠΎΠ»Π΅ΡΠ½ΠΈΡ
ΠΌΠ΅ΡΠ΅ΠΎΡΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
Π½Π°Π±Π»ΡΠ΄Π΅Π½ΠΈΠΉ
ΠΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΡ ΡΠΎΠΏΠΎΠ»ΠΎΠ³ΠΈΠΈ ΡΠ΅ΡΠΈ Ρ ΠΠΠ-Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠ΅ΠΉ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠ³ΠΎ Π°Π΄Π°ΠΏΡΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠ³ΠΎ Π³Π΅Π½Π΅ΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π°Π»Π³ΠΎΡΠΈΡΠΌΠ°
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.Π ΡΡΠ°ΡΡΠ΅ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠ°Π½Π½ΡΠΉ Π°Π²ΡΠΎΡΠ°ΠΌΠΈ Π°Π΄Π°ΠΏΡΠΈΠ²Π½ΡΠΉ Π³Π΅Π½Π΅ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ Π°Π»Π³ΠΎΡΠΈΡΠΌ, ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡΠΈΠΉ ΠΎΠΏΡΠΈΠΌΠΈΠ·ΠΈΡΠΎΠ²Π°ΡΡ ΡΠΎΠΏΠΎΠ»ΠΎΠ³ΠΈΡ ΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅ΡΠΈ Ρ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΠΉ Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠ΅ΠΉ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π±ΠΈΠΎΠΈΠ½ΡΠΏΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ². ΠΠ±ΡΠ΅ΠΊΡΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ β 15-ΡΠ·Π»ΠΎΠ²Π°Ρ ΡΡ
Π΅ΠΌΠ° ΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅ΡΠΈ Ρ ΡΠΎΡΠΎΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ ΡΡΠ°Π½ΡΠΈΡΠΌΠΈ ΠΈ 14-ΡΠ·Π»ΠΎΠ²Π°Ρ Π΄ΠΎΠΏΠΎΠ»Π½Π΅Π½Π½Π°Ρ ΡΡ
Π΅ΠΌΠ° IEEE Ρ ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠ°ΠΌΠΈ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΠΉ Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠΈ (ΡΡΠΈ Π²Π΅ΡΡΠΎΠ²ΡΠ΅ ΠΈ Π΄Π²Π΅ ΡΠΎΡΠΎΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΡΠ°Π½ΡΠΈΠΈ). ΠΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠ΅ΠΆΠΈΠΌΠΎΠ² ΡΠ»Π΅ΠΊΡΡΠΎΡΠ½Π΅ΡΠ³Π΅ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠΈΡΡΠ΅ΠΌ Π²ΡΠΏΠΎΠ»Π½Π΅Π½ΠΎ Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ Π½Π°Ρ
ΠΎΠ΄ΡΡΠ΅ΠΉΡΡ Π² ΠΎΡΠΊΡΡΡΠΎΠΌ Π΄ΠΎΡΡΡΠΏΠ΅ Π±ΠΈΠ±Π»ΠΈΠΎΡΠ΅ΠΊΠΈ Pandapower Π΄Π»Ρ ΡΠ·ΡΠΊΠ° ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ Python. Π Π°ΡΡΠΌΠΎΡΡΠ΅Π½Ρ ΡΡΠΈ ΡΠΈΠΏΠ° ΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ Π½Π°Π³ΡΡΠ·ΠΊΠΈ ΠΏΠΎΡΡΠ΅Π±ΠΈΡΠ΅Π»Π΅ΠΉ, ΠΎΡΡΠ°ΠΆΠ°ΡΡΠΈΠ΅ Ρ
Π°ΡΠ°ΠΊΡΠ΅Ρ ΠΏΠΎΡΡΠ΅Π±Π»Π΅Π½ΠΈΡ ΡΠ»Π΅ΠΊΡΡΠΎΡΠ½Π΅ΡΠ³ΠΈΠΈ Π² ΡΠ·Π»Π°Ρ
ΡΠ΅Π°Π»ΡΠ½ΡΡ
ΡΠ»Π΅ΠΊΡΡΠΎΡΠ½Π΅ΡΠ³Π΅ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠΈΡΡΠ΅ΠΌ, ΠΏΡΠΈΠ²Π΅Π΄Π΅Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΠΈΡΠ»Π΅Π½Π½ΡΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ. Π ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠΌ Π³Π΅Π½Π΅ΡΠΈΡΠ΅ΡΠΊΠΎΠΌ Π°Π»Π³ΠΎΡΠΈΡΠΌΠ΅ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½Ρ Π΄Π²Π΅ ΡΠ°Π·Π»ΠΈΡΠ½ΡΠ΅ ΡΡΠ½ΠΊΡΠΈΠΈ ΡΠΊΡΠ΅ΡΠΈΠ²Π°Π½ΠΈΡ, ΡΡΠ½ΠΊΡΠΈΠΈ ΠΌΡΡΠ°ΡΠΈΠΈ, ΠΎΡΠ±ΠΎΡΠ° Π»ΡΡΡΠΈΡ
ΠΈΠ½Π΄ΠΈΠ²ΠΈΠ΄ΠΎΠ² ΠΈ ΠΌΠ°ΡΡΠΎΠ²ΠΎΠΉ ΠΌΡΡΠ°ΡΠΈΠΈ (ΠΏΠΎΠ»Π½ΠΎΠ³ΠΎ ΠΎΠ±Π½ΠΎΠ²Π»Π΅Π½ΠΈΡ ΠΏΠΎΠΏΡΠ»ΡΡΠΈΠΈ). Π ΠΊΠΎΠ½ΡΠ΅ ΠΊΠ°ΠΆΠ΄ΠΎΠΉ ΠΈΡΠ΅ΡΠ°ΡΠΈΠΈ ΡΠ°Π±ΠΎΡΡ Π°Π»Π³ΠΎΡΠΈΡΠΌΠ° Π²ΡΠ²ΠΎΠ΄ΡΡΡΡ ΡΡΠ°ΡΠΈΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ, Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΠ·ΡΡΡΠΈΠ΅ Π΅Π³ΠΎ ΡΠ°Π±ΠΎΡΡ: Π»ΡΡΡΠ°Ρ (ΠΌΠΈΠ½ΠΈΠΌΠ°Π»ΡΠ½ΡΠ΅ ΠΏΠΎΡΠ΅ΡΠΈ) ΠΈ ΡΡΠ΅Π΄Π½ΡΡ ΠΏΡΠΈΡΠΏΠΎΡΠΎΠ±Π»Π΅Π½Π½ΠΎΡΡΡ Π² ΠΏΠΎΠΏΡΠ»ΡΡΠΈΠΈ, ΡΠΏΠΈΡΠΎΠΊ Π»ΡΡΡΠΈΡ
ΠΈΠ½Π΄ΠΈΠ²ΠΈΠ΄ΠΎΠ² Π½Π° ΠΏΡΠΎΡΡΠΆΠ΅Π½ΠΈΠΈ Π²ΡΠ΅Ρ
ΠΈΡΠ΅ΡΠ°ΡΠΈΠΉ ΠΈ Ρ. Π΄. ΠΠ΅ΡΠΈΡΠΈΠΊΠ°ΡΠΈΡ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΠ»Π°ΡΡ Π² ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΈ Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ°ΠΌΠΈ, ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΠΌΠΈ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΏΠΎΠ»Π½ΠΎΠ³ΠΎ ΠΏΠ΅ΡΠ΅Π±ΠΎΡΠ° Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΡ
ΡΠ°Π΄ΠΈΠ°Π»ΡΠ½ΡΡ
ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΠΉ ΡΠΈΡΡΠ΅ΠΌΡ, ΠΈ ΠΏΠΎΠΊΠ°Π·Π°Π»Π°, ΡΡΠΎ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠ°Π½Π½ΡΠΉ Π³Π΅Π½Π΅ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ Π°Π»Π³ΠΎΡΠΈΡΠΌ ΠΎΠ±Π»Π°Π΄Π°Π΅Ρ Π±ΡΡΡΡΠΎΠΉ ΡΡ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΡΡ, Π²ΡΡΠΎΠΊΠΎΠΉ ΡΠΎΡΠ½ΠΎΡΡΡΡ ΠΈ ΡΠΏΠΎΡΠΎΠ±Π΅Π½ ΠΊΠΎΡΡΠ΅ΠΊΡΠ½ΠΎ ΡΠ°Π±ΠΎΡΠ°ΡΡ ΠΏΡΠΈ ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΡΡ
ΡΡ
Π΅ΠΌ ΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ΅ΡΠ΅ΠΉ, ΡΡΡΡΠΊΡΡΡΠ°Ρ
Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠΈ ΠΈ Π½Π°Π³ΡΡΠ·ΠΊΠΈ. ΠΠ»Π³ΠΎΡΠΈΡΠΌ ΠΌΠΎΠΆΠ΅Ρ ΠΏΡΠΈΠΌΠ΅Π½ΡΡΡΡΡ ΡΠΎΠ²ΠΌΠ΅ΡΡΠ½ΠΎ Ρ ΡΠΈΡΡΠ΅ΠΌΠ°ΠΌΠΈ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΠΠ-Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠΈ Π½Π° ΡΡΡΠΊΠΈ Π²ΠΏΠ΅ΡΠ΅Π΄ ΠΏΡΠΈ ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ΅ΠΆΠΈΠΌΠΎΠ² ΡΠ°Π±ΠΎΡΡ ΡΠ½Π΅ΡΠ³ΠΎΠΎΠ±ΡΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΠΉ Ρ ΡΠ΅Π»ΡΡ ΠΌΠΈΠ½ΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΠΈΠ·Π΄Π΅ΡΠΆΠ΅ΠΊ Π½Π° ΠΏΠΎΠΊΡΡΡΠΈΠ΅ ΠΏΠΎΡΠ΅ΡΡ ΡΠ»Π΅ΠΊΡΡΠΎΡΠ½Π΅ΡΠ³ΠΈΠΈ ΠΈ ΡΠ»ΡΡΡΠ΅Π½ΠΈΡ ΠΊΠ°ΡΠ΅ΡΡΠ²Π° ΠΎΡΠΏΡΡΠΊΠ°Π΅ΠΌΠΎΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΡΠ½Π΅ΡΠ³ΠΈΠΈ