MODELS OF THE COMPUTER INTELLECTUALIZATION OPTIMAL STRATEGY OF THE POWER SUPPLY FAST-FLOWING TECHNOLOGICAL PROCESSES OF THE RAILWAYS TRACTION SUBSTATIONS

Based on analysis of the problem of the power supply networks of railways innovative transformation, the direction of research is substantiated related to organization of the optimal strategy of computerized intellectualization of the power supply processes to the railways traction substations. The logical structure of a distributed computer environment developed in the form of graph, which adequately reflects the topology of the organization of the power supply system. A differential mathematical model of the computer architecture of the power supply control is proposed. An intelligent method for finding the optimal strategy for the intellectualization of the power supply processes was proposed to guarantee the specified indicators of the optimal functioning of individual nodes and segments of the power supply management computer network


ISSN 1335-4205 (print version) ISSN 2585-7878 (online version)
can be achieved by mutual integration of the intellectual resources of managers and modern capabilities of almost unlimited performance of distributed computing [3].
This fact led to creation of a new class of mathematical models and methods of intelligent information processing, as a basis for creation of the intelligent computer systems [3][4][5][6]. For example, in [7] a method was proposed based on use of simplified calculations of state of a train as a controlled system without the use of differential equations of motion, which can significantly increase the speed of calculations. This, in turn, will solve the problem of finding the optimal control in real time, taking into account the changing conditions during the movement of the train. To implement this method of calculation, a simplified model of the train was used as a controlled system.

Introduction
Computer systems and networks are the main component in functioning of business, government organizations, military institutions, health systems, education and science. In the process of managing the complex energy and social systems that operate in normal and abnormal modes, there is a need for registration, storage and processing of large amounts of information and formation of the control actions. National competitiveness depends, first of all, on the procedures for conducting, in real time, information analysis and decision-making of flexible management of production or social facilities.
The experience of using information technology in the management of complex systems has shown that many of the limitations in solving the real problems are significantly reduced by adding intelligence to computer systems, or modelling intelligent control procedures [1][2]. Moreover, in many cases, classical methods are ineffective for many practical problems of production and business since it is impossible to accurately describe reality when creating a management model.
A study of evolution of the computer networks and systems development for managing complex objects showed that the maximum efficiency of their functioning of mathematical models and methods for analyzing and evaluating the optimal functioning of individual nodes and segments of intelligent computer networks for controlling the fast-flowing power supply technological processes.

Aim formulation
The aim of the work is the organization of an optimal computerization strategy for the fast-flowing technological processes of power supply lines by developing mathematical models and methods of increased intellectual complexity and dimensionality of analysis and assessment of the conditions for optimal functioning of individual nodes and segments of a distributed computer-based power management network.

The main research material
Distributed railway power supply systems represent a hierarchical system, the basic level of which is the level of traction substations as the basis for minimizing the system-wide costs, optimizing power consumption and transportation reliability. The emergence of promising areas of innovation and investment transformation of railway power supply systems has contributed to development of a new class of intelligent computer networks for optimal control of power supply systems. The organization of intelligent systems requires comprehensive research in the subject area, to create a new model of the optimal strategy for intellectualization of a wide range of technological processes of the power supply systems. The implementation of an adequate reflection of the distributed architecture of transport [1,6]. In [8], to improve energy efficiency, the possibility of using Smart Grid in urban transport conditions was considered. Thanks to the Smart Grid solutions, traction power systems are no longer passive energy consumers. They become a dynamic link in the power system. In electric transport systems, energy islands can be created that serve as elements of modern smart power systems [9]. In work [10], the solution to the scientific problem of increasing the energy efficiency of DC traction systems by the development of distributed power systems that fit into the existing infrastructure to ensure high-speed traffic, which is necessary for electric transport, is considered. Thus, in the scientific works there is a promising direction of research aimed at developing mathematical models for the traction power supply systems and methods that combine human intelligence and the computer environment. A new class of computer intelligent systems has appeared that is focused on the integrated intellectualization of a set of procedures for the operational and strategic management of the fastflowing technological processes of energy supply and power consumption. This fact stimulated the emergence of new analytical and intelligent technologies, which, based on certain models, algorithms, and mathematical theorems, allow, according to known data, to estimate the values of unknown characteristics and parameters of a complex object of study [6,[11][12][13]. It became apparent that a qualitatively new set of intelligent traction power supply systems could be obtained by forming a deep mutual integration of topology of the power grid infrastructure of the power supply system and architecture of a distributed computer network. At the same time, truly little attention is paid to the previously unresolved parts of the problem of innovative transformation of traction electric lines -creation

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S T A S I U K e t a l .
with the corresponding initial conditions written as follows:

Differential mathematical models
Based on the system of Equations (1), a differential mathematical model is synthesized for calculating, first of all, probability values P 0 (t), P 1 (t), P 2 (t), P 3 (t), P 4 (t), P 5 (t), P 6 (t), P 7 (t), P 8 (t), P 9 (t), P 10 (t). In this regard, the principles of the theory of differential transformations of Pukhov are applied, the fundamental concepts of which are represented by the following mathematical equations [14] where: P i (t) is the initial function that can be differentiated n-times and which has a number of corresponding restrictions, including its derivatives; P i (k) -differential T-images of the original function P i (t); H -a scale factor, the dimension of which coincides with the dimension of the argument t, as a rule, is selected on conditions on 0 ≤ t ≤ H the entire range of the function -the original P i (t); / -a symbol of correspondence between the function -the original P i (t) and its differential T -image Pi(k). Based on the direct differential transformation, which is to the left of / , a differentiated T-image of the function-original is formed -P i (t) as a discrete function P i (k), with integer argument k = 0,1,2, ....Based on the set of the T-discrete values of the integer argument function P i (k) k = 0,1,2.., using the inverse differential transformation, which is located to the right of the symbol / , one obtains the original functions P i (t). Note that for k = 0, according to Equation (2), for any instantaneous value t of each i-th parameter P i (t), the corresponding equality P i (t) = P i (k) holds. P i (t) -P i (k). Using the direct differential transformation one synthesizes a differential mathematical model focused on the study of network computing architecture [14]: the computer environment and the topology of the power supply system of the traction substation opens up the possibility of maximizing the managing efficiency of the fast-flowing technological processes of power consumption. The important issue in this case is the ability of computer architecture to control the electrical systems of traction substations in real time. To form models and criteria for computer intellectualization of technological processes for managing energy systems, the architecture of a local area network of power supply management at the level of traction substations is presented in the form of a graph, which reflects adequately the topology of the electric system. Graph of the logical architecture of the local computer network ( Figure 1) includes two types of topologiesa star and a circle. A fragment of a star topology includes a node φ 0 (t) -which is the central server of a computer network of a traction substation, a node φ 1 (t) -to organize a unified information environment for primary information and maintaining a database, a node φ 2 (t) -to exchange information within a corporate computer network railway power supply control, node φ 3 (t) -to exchange the information on Internet, node φ 4 (t) -is a server operational management and maintenance of a set of automated workstations for power supply management, monitoring of traction transformers, high-voltage circuit breakers and power equipment, as well as a φ 5 (t) node for organizing microprocessor and relay protection of the traction power line.
A segment of the circle graph topology includes a series of joint nodes φ 0 (t) φ 1 (t) φ 2 (t) φ 3 (t) φ 4 (t) φ 5 (t) considered above, as well as node φ 6 (t) -organization of commercial electricity metering at commercial tariffs differentiated by zones of the day, φ 7 (t) is the node for monitoring the parameters of the traction power supply system, node φ 8 (t) is for the intellectual processing of commercial and technological information. In addition, the topology under consideration includes nodes φ 9 (t), φ 10 (t) -a distributed local power management network at the highest level, that is the department of the railway power supply.
Assume that in the process of exchanging information between components of a computer network, the flow rate of applications is represented by the value λ i (t) and the intensity of the service flow of applications is determined by the following value β i (t). To analyse the computer architecture of the local network and determine the values of the probabilities P 0 (t), P 1 (t), P 2 (t), P 3 (t), P 4 (t), P 5 (t), P 6 (t), P 7 (t), P 8 (t), P 9 (t), P 10 (t) the graph is presented in the form of a Kolmogorov differential equation system with the corresponding initial conditions, which can be written in the following form [1][2]: , , dt dP t P t P t P t P t P t P t dt dP t P t P t Obtained in this way, at n = 2, the set of discrete P i (0); P i (1), P i (2) i = 1,2,...10 is substituted into the inverse mathematical dependence in Equation (2) is obtained in an analytical form, the probability values P 0 (t), P 1 (t), P 2 (t), P 3 (t), P 4 (t), P 5 (t), P 6 (t), P 7 (t), P 8 (t), P 9 (t), P 10  ; ; .

Models of optimal computer intellectualization strategy
Represented by Equations (6), the probability values P 0 (t), P 1 (t), P 2 (t), P 3 (t), P 4 (t), P 5 (t), P 6 (t), P 7 (t), P 8 (t), P 9 (t), P 10 (t) conditions of each node of the graph can be used to formulate a criterion for the optimal strategy of power supply control procedures, which can be written as [14] , , , t T P t dt i 1 0 1 2 Since each node of the local computer network operates in a conflict between the intensity of the application flow λ i (t) and the intensity of the application flow β i (t), the dominance in such conditions is the observance by the conflict subjects of the minimax principle [2,4]. Achievement of optimal functioning in each node of the computer network is possible by rational adherence to the strategy of formation of such values of service flow intensity β i (t) that minimize the fee , In the process of modelling the optimal strategy, it is likely to proceed from the condition for formation of such λ i (t) that maximize the fee ,   The initial conditions, under t = 0, k = 0 are represented P 0 (t = 0) = P 0 (0) = 1, respectively P i (t = 0) = P i (0) = 0. The differential mathematical model in Equation (3) is the basis for the formation, in an analytical form, of probabilities P 0 (t), P 1 (t), P 2 (t), P 3 (t), P 4 (t), P 5 (t), P 6 (t), P 7 (t), P 8 (t), P 9 (t), P 10 (t) state of nodes of a traction substation computer network.

Conclusions
1. Research was conducted on the problem of innovative transformation of railway power supply systems to create promising energy-saving technologies for the power consumption and the formation of the new knowledge. This direction of research is justified, related to formation of a qualitatively new set of intelligent power supply systems, which is achieved through deep mutual integration of the topology of the power grid infrastructure and the architecture of the distributed computer network for power supply management. 2. Based on the modern concept of the intelligent traction power supply systems' synthesis, a research direction has been formulated related to organization of an optimal strategy for computer intellectualization of the fast-flowing technological processes of power supply in traction substations of railways, by creating mathematical models and methods for determining the optimal functioning of individual nodes and segments of an intelligent computer network power management. 3. The logical structure of a distributed computer environment that adequately reflects the topology of the organization of the electric power supply system at the level of traction substations is proposed in the form of a graph, based on which a differential mathematical model of the computer architecture of the power supply control is formed and methods for determining, in an analytical form, the set of values of Obviously, subject to the fulfilment of mathematical dependencies in Equations (8), (9) , , , , [3,[11][12].
The strategy is to select the law of change in the flow of customer service intensity βi (t), which implements minimization of functional in Equation (10) with the stochastic intensity of the customer service flow λ i (t), within the appropriate limits. Therefore, in connection with the antagonism of the goals of the subjects of the information conflict, the dominant strategy for the optimal intellectualization of the fast technological processes will be a strategy based on the minimax principle, i.e. [3] , , , The minimax strategy in Equation (11) allows to minimize functional in Equation (7) even in the cases of the worst combination of flow intensities λ i (t) and β i (t). Using the direct differential transformation in Equation (2) Based on calculations of the corresponding set of T-discrete, P i (0); P i (1), P i (2), …, P i (k), according to Equation (3), the optimization procedure based on the differential spectrum can be implemented as follows. After substituting the aggregate discrete P i (0); P i (1); P i (2), …, P i (k) in Equation (12), the state model for the φ i (t)-th node of the local network, for i = 0, that is P 0 (k) k = 0,1,2,..., takes the form: The procedure for selecting the optimal strategies for the intensity of application flows i opt m and the flow of service intensity of applications i opt b of a functional * i H is linked with studying it to an extremum by substituting values of the corresponding discrete into Equation (12) P i (0); P i (1); P i (2);...(i = 1,2,...,10). It is known that the necessary conditions for existence of an extremum of a functional, according to the Kuhn-Tucker theorem, are conditions that allow us to determine the optimal strategy in the form [3,8] the optimal strategy for computer intellectualization of the power supply process to provide specified indicators for the optimal functioning of individual nodes and segments of an intelligent computer control network.