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Relevance. The urgent task of technical and economic development of the northern and eastern regions of Russia is to provide reliable and efficient power supply to consumers, geographically located in remote, hard-to-reach areas. The use of hybrid energy systems with renewable energy sources is a promising way to solve this problem. A characteristic feature of the modes of hybrid systems, especially with a high level of fuel replacement, is the presence of ripples in charge-discharge currents of batteries used as energy storage devices. The operation of batteries in the mode of pulsed currents leads to rapid degradation of their characteristics and reduction in the service life, which leads to decrease in reliability of the power supply system and increase in the cost of generated electricity. A significant drawback of hybrid systems built according to well-known standard schemes is the inefficient use of the potential of primary renewable energy, which is especially critical for power systems geographically located in areas with severe climatic conditions. The article proposes technical solutions to eliminate the indicated problems. Aim of the study is to search for and develop technical solutions to improve the efficiency of hybrid energy systems with a high level of fuel substitution. Methods: mathematical and computer modeling using the Matlab/Simulink software environment. Results. We offer a new method of construction and control algorithm of the modes of hybrid energy systems, which provide increasing their reliability and energy efficiency. The results of the modeling and the operating modes of a hybrid power plant with a high level of fuel substitution are presented, which proves that the proposed method of construction and the control algorithm provides reliable and efficient control of the power balance of a hybrid power system in all possible operating conditions. The application of the proposed algorithm in a dual-circuit energy storage device provides 5,7 % reduction in the failure rate of the hybrid power system, increasing the operating life of the batteries by 50 %, more efficient use of renewable energy by 28 % compared with conventional methods of construction of hybrid plants.

Relevance. The urgent task of technical and economic development of the northern and eastern regions of Russia is to provide reliable and efficient power supply to consumers, geographically located in remote, hard-to-reach areas. The use of hybrid energy systems with renewable energy sources is a promising way to solve this problem. A characteristic feature of the modes of hybrid systems, especially with a high level of fuel replacement, is the presence of ripples in charge-discharge currents of batteries used as energy storage devices. The operation of batteries in the mode of pulsed currents leads to rapid degradation of their characteristics and reduction in the service life, which leads to decrease in reliability of the power supply system and increase in the cost of generated electricity. A significant drawback of hybrid systems built according to well-known standard schemes is the inefficient use of the potential of primary renewable energy, which is especially critical for power systems geographically located in areas with severe climatic conditions. The article proposes technical solutions to eliminate the indicated problems. Aim of the study is to search for and develop technical solutions to improve the efficiency of hybrid energy systems with a high level of fuel substitution. Methods: mathematical and computer modeling using the Matlab/Simulink software environment. Results. We offer a new method of construction and control algorithm of the modes of hybrid energy systems, which provide increasing their reliability and energy efficiency. The results of the modeling and the operating modes of a hybrid power plant with a high level of fuel substitution are presented, which proves that the proposed method of construction and the control algorithm provides reliable and efficient control of the power balance of a hybrid power system in all possible operating conditions. The application of the proposed algorithm in a dual-circuit energy storage device provides 5,7 % reduction in the failure rate of the hybrid power system, increasing the operating life of the batteries by 50 %, more efficient use of renewable energy by 28 % compared with conventional methods of construction of hybrid plants.

Relevance. The urgent task of the technical and economic development of the Northern and Eastern regions of Russia is to provide reliable and efficient power supply to consumers, geographically located in remote, hard-to-reach areas. The use of wind power plants is a promising way to solve this problem. The primary task of the design and feasibility study of the use of wind power plants is to predict changes in wind speeds at the site of the power plant installation. The stochastic nature of the wind and its spatiotemporal variability explain the high complexity of this problem, for the solution of which the methods of mathematical modeling are used. The known models of wind speed based on Markov chains, autoregressive moving-average and other discrete models do not allow varying the time step, which does not allow their use for simulation of operating modes of wind turbines and wind energy systems. The article proposes a model of wind speed based on the stochastic differential equation which eliminates this drawback. The aim of the study is to construct wind speed model based on fractional Ornstein–Uhlenbeck process with a periodic long-term mean, which provides modeling of static and dynamic modes of operation of a wind power plant at different time intervals. Methods: mathematical and computer modeling using Matlab/Simulink software environment. Results. The proposed model, in contrast to the known SDE-based models, is able to produce autocorrelated wind speed trajectories with long-term dependence, daily and monthly variations to perform more detailed simulation of the operating modes of wind turbines at different time intervals with the required time step. The model was tested using the data of climatic observations of wind speed obtained from electronic archive of the All-Russian Institute of Hydrometeorological Information. The model adequacy was evaluated by comparing characteristics of simulated wind speed trajectories with actual observations collected at 518 weather stations located on territory of Russia.

Relevance. The urgent task of the technical and economic development of the Northern and Eastern regions of Russia is to provide reliable and efficient power supply to consumers, geographically located in remote, hard-to-reach areas. The use of wind power plants is a promising way to solve this problem. The primary task of the design and feasibility study of the use of wind power plants is to predict changes in wind speeds at the site of the power plant installation. The stochastic nature of the wind and its spatiotemporal variability explain the high complexity of this problem, for the solution of which the methods of mathematical modeling are used. The known models of wind speed based on Markov chains, autoregressive moving-average and other discrete models do not allow varying the time step, which does not allow their use for simulation of operating modes of wind turbines and wind energy systems. The article proposes a model of wind speed based on the stochastic differential equation which eliminates this drawback. The aim of the study is to construct wind speed model based on fractional Ornstein–Uhlenbeck process with a periodic long-term mean, which provides modeling of static and dynamic modes of operation of a wind power plant at different time intervals. Methods: mathematical and computer modeling using Matlab/Simulink software environment. Results. The proposed model, in contrast to the known SDE-based models, is able to produce autocorrelated wind speed trajectories with long-term dependence, daily and monthly variations to perform more detailed simulation of the operating modes of wind turbines at different time intervals with the required time step. The model was tested using the data of climatic observations of wind speed obtained from electronic archive of the All-Russian Institute of Hydrometeorological Information. The model adequacy was evaluated by comparing characteristics of simulated wind speed trajectories with actual observations collected at 518 weather stations located on territory of Russia.

Tariffs for energy and energy resources are the main factors determining the sustainable development of the economy. The aim of the paper is to determine and compare the dynamics evolution of the tariffs for thermal energy and the evolution of the gross domestic product (GDP).The data on the heat consumption and tariff change in the city of Chisinau were examined in monetary terms and in relative units compared to the base year 2009. The higher the tariffs, the more part of the GDP, characterized in the economy by the volume of "Output", is spent on "Intermediate consumption (PP)". The difference between "Output" and "Intermediate consumption" volumes is the "gross added value (VAB)", which is the main component of GDP. The analysis of the changes in the real GDP volume of the Republic of Moldova and the increase of the tariffs for the years 2009-2017 (taking into account the GDP forecast for 2018) show that the increase in the tariffs for thermal energy significantly exceeded the real GDP growth. Considering that the planned GDP growth is 4,7% and taking into account the change in the consumer price index (inflation rate), the calculated reduction of the thermal energy tariff in Chisinau is estimated at 28% compared to the existing value, so to 803 lei / Gcal compared to the currently regulated value of 1122 lei / Gcal. The conclusion was reached on the opportunity of applying the proposed methodology to justify current tariffs and in the near future not only extends to thermal energy tariffs, but also for other types of energy, material resources and services in the field of production and social sphere.

Tariffs for energy and energy resources are the main factors determining the sustainable development of the economy. The aim of the paper is to determine and compare the dynamics evolution of the tariffs for thermal energy and the evolution of the gross domestic product (GDP).The data on the heat consumption and tariff change in the city of Chisinau were examined in monetary terms and in relative units compared to the base year 2009. The higher the tariffs, the more part of the GDP, characterized in the economy by the volume of "Output", is spent on "Intermediate consumption (PP)". The difference between "Output" and "Intermediate consumption" volumes is the "gross added value (VAB)", which is the main component of GDP. The analysis of the changes in the real GDP volume of the Republic of Moldova and the increase of the tariffs for the years 2009-2017 (taking into account the GDP forecast for 2018) show that the increase in the tariffs for thermal energy significantly exceeded the real GDP growth. Considering that the planned GDP growth is 4,7% and taking into account the change in the consumer price index (inflation rate), the calculated reduction of the thermal energy tariff in Chisinau is estimated at 28% compared to the existing value, so to 803 lei / Gcal compared to the currently regulated value of 1122 lei / Gcal. The conclusion was reached on the opportunity of applying the proposed methodology to justify current tariffs and in the near future not only extends to thermal energy tariffs, but also for other types of energy, material resources and services in the field of production and social sphere.

The electric power system (EPS) is a large, multi-parameter, non-linear and dynamic system. The problem of calculation of relay protection (RP) settings has become more urgent nowadays. The situation is exacerbated by the active implementation of renewable energy sources, FACTS, etc., which significantly change the “traditional” EPS and their operating modes. The problem can be solved by deep analysis of functioning of main elements of RP devices in the specific operating conditions and revision of coefficients used in settings calculation. That can be done using RPs detailed mathematical models and modern EPS simulators. The results of the analysis will make it possible to formulate a new methodology for setting up RP. That is a final goal. In the framework of solving this problem, the novel approach for developing RPs’ detailed mathematical models is formulated and theoretically proved. On the basis of this approach, mathematical models of the system “instrumental transformer - auxiliary transformer - analog filter” (measuring part of digital transformer differential protection) for different types of auxiliary current transformers (active and passive) and filters (Butterworth, Chebyshev, Bessel) are developed. A comparative numerical analysis of their frequency and phase responses is carried out, including taking into account the magnetization of instrumental current transformers. Summarizing, the theoretical and practical studies presented in the article allows formulating requirements for RPs’ detailed mathematical models, which will be used in the further research. 

The electric power system (EPS) is a large, multi-parameter, non-linear and dynamic system. The problem of calculation of relay protection (RP) settings has become more urgent nowadays. The situation is exacerbated by the active implementation of renewable energy sources, FACTS, etc., which significantly change the “traditional” EPS and their operating modes. The problem can be solved by deep analysis of functioning of main elements of RP devices in the specific operating conditions and revision of coefficients used in settings calculation. That can be done using RPs detailed mathematical models and modern EPS simulators. The results of the analysis will make it possible to formulate a new methodology for setting up RP. That is a final goal. In the framework of solving this problem, the novel approach for developing RPs’ detailed mathematical models is formulated and theoretically proved. On the basis of this approach, mathematical models of the system “instrumental transformer - auxiliary transformer - analog filter” (measuring part of digital transformer differential protection) for different types of auxiliary current transformers (active and passive) and filters (Butterworth, Chebyshev, Bessel) are developed. A comparative numerical analysis of their frequency and phase responses is carried out, including taking into account the magnetization of instrumental current transformers. Summarizing, the theoretical and practical studies presented in the article allows formulating requirements for RPs’ detailed mathematical models, which will be used in the further research.