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The purpose of the article is to study the possibilities of preventing the imbalance caused by the stochastic nature of RES by regulating the electricity accumulation and the backup generator. The subject of the research is random processes of energy generation and consumption. The goal is achieved by a mathematical model construction in which the system parameters would be formalized and allow the choice of optimal options. The mathematical model uses random functions to obtain statistical estimates, and is implemented as sequential models of energy generation and consumption as an integrated random process. The models’ adequacy is confirmed by comparing the simulated and real indicators for a number of existing RES in Ukraine. The proposed approach made it possible to establish the presence of system parameters that minimize energy losses and consumption, reduce the probability of energy imbalance, and effectively use the reserve power. The proposed mathematical model allows determining the probability of various system states, it estimates the reliability of energy supply, and minimizes losses at the stages of designing a power system and planning its operating modes. The above estimates are typical for certain climatic conditions and modes of energy consumption, and are of a specific nature. The significance of the work lies in the fact that the proposed formulation of the problem makes it possible to adapt the mathematical model to various conditions, to find implicit dependencies between the technical parameters of the system and its indicators in order to find optimal solutions.

The article is dedicated to the study of random parameters describing the processes of electric energy consumption in power systems of different levels of localization. The objective of this research is to construct the mathematical model that adequately describes consumption modes as random processes. As experimental studies, we statistically processed the data on energy consumption of several settlements, regional and integrated energy systems of Ukraine for 2015-2017. The results obtained were used as the base for developing and testing the mathematical models. To achieve this goal, representations of the model parameters as random variables were used, and the results of simulation were compared with experimental data. The scatter of drift values is generally greater than volatility. When a group of consumers is combined or the size of the local power system increased, the spread of parameters expectedly decreases. The most significant result of the research is establishment of probability distribution laws for the parameters of the process of electric energy consumption. For the indicator of volatility, it can be considered as Gaussian. The drift index is well described by the Weibull distribution. We estimated the size of a random sampling of experimental data needed to obtain statistically stable results. Significance of the obtained results consists in establishing the degree of consistency of the actual data and random implementations of the simulation model, which proves adequacy of the proposed mathematical model and makes it possible to assess the real uncertainty of the process of balancing the power system.

The purpose of the research is to determine criteria and calculate optimal ratio of different renewable energy sources (RES) for hybrid systems, estimate the random component of power fluctuation and consider the opportunities for its minimization. As a subject of the study it is variable and poorly forecasted in a short-term prospect character of generated power can negatively affect modes of grid operation. This concerns stability of dynamic processes in the systems of power supply. To develop a mathematical model of these processes a number of factual data on the climatic parameters and energy consumption regimes during the joint operation of solar and wind stations was used. As an experimental study suggests, the initial data were collected and statistically processed. Based on the results, mathematical models were developed in the form of a composition of deterministic and stochastic components and theoretical studies on the search for optimal ratios of capacities of wind and solar power stations were carried out. The object of optimization in the work is the load variability. As a combined single criterion, it was proposed to use the coefficient of variation. The ratios of the wind and solar components of the power generation, considered in this study, has allowed us to determine variants with a minimal dispersion of RES generation or with a minimum ratio of dispersion to average generated power which depends on the average annual or seasonal weather conditions. As a rule, the share of wind power plants should be 10-40% of the total rated RES power, depending on the total share of RES.

In this paper, using the example of a two-mass calculation scheme, which can be used to describe the dynamic properties of many mechatronic systems with elastic elements, we present the results of research on finding control actions that provide compensation of dynamic errors based on solving the inverse dynamic problems according to a given law of change of the force in an elastic element. It is shown that the found control actions in the form of time dependences make it possible not to impose any restrictions on the methods of their technical implementation and thereby provide a comprehensive solution the problem of compensating for dynamic errors caused by elastic deformations of mechanical elements.

The article considers the analysis results of the occurrence frequency of genotypes and alleles of plasma, platelet and fibrinolytic hemostasis in full-term newborns with arterial and venous thrombosis of various localization. Gene polymorphisms were studied by real-time PCR in human DNA samples obtained from buccal epithelium and venous blood lymphocytes. The control group was a group of healthy full-term newborns from families without a thrombophilic history. Predictors of arterial and venous thrombosis in children are such as polymorphism of the plasminogen activator inhibitor gene PAI-1-675 4G/4G (OR=5,6 [2,3-13,8]), combinations of polymorphisms PAI-1-675 4G/4G + factor VII G10976A G/G (OR=5,8 [1,7-19,1]), combinations of polymorphisms PAI-1 -675 4G/4G + factor VII G10976A G/G + factor XIII Val34Leu G/G (% AR=61), fibrinogen FGB -455 G/A (OR=3,75 [1,4-9,4]) and integrin alpha 2 ITGA2 807 T/T (OR=15,56 [1,9-126,7]). Thus, the study of polymorphisms of the plasminogen activator inhibitor, fibrinogen, integrin alpha 2 can serve as one of the criteria for identifying a high-risk group for the development of arterial and venous thrombosis in newborns and should be taken into account when evaluating individual thrombophilia risk.