Features of asymmetric short circuit currents calculation in the elplek software product

In order to simplify the analysis of the electrical networks operation modes , specialized software tools for mathematical modeling of processes in them are used. There are many software products, but most of them are paid. To carry out research in complex power systems and obtain results in certain sections when performing practical and course work, as well as at certain stages of research, the authors actively use the free software product «Elplek», but in a deeper study of the software encountered certain features some parameters, which differ slightly from the generally accepted domestic method, which led to an error in the calculations in some versions of the schemes of power systems. The purpose of the research is to study the peculiarities of calculating the characteristics of asymmetric short circuits in the software product "Elplek" and to check the adequacy of the formed models. At the first stage, the object of research was chosen – this is a segment of the electrical network containing a small number of nodes and a theoretical calculation of the searched parameters of the short circuit mode in this segment of the electrical network was carried out. In the future, an approach was proposed on the task of parameters of elements in the software product "Elplek" and based on this approach, modeling was carried out as a result of which the results were obtained under the condition of the system's task, as sources of infinite power and calculations for the active part differ by 0.013%, and by reactive – 0.004%; subject to the task of the system, as sources of a certain power and calculations on the active part differ by 0.0046%, and on the jet - 0.0044%, which makes it possible to assert the feasibility of using the proposed approach in the analysis of indicators of emergency modes of complex schemes of electrical supply to consumers of certain segments of electric power systems. Features of calculation of characteristics of asymmetric short circuits in the Elplek software product are considered and the adequacy of the generated models is checked. Key words: power system segment modeling, Elplek software product, element parameter setting, single-phase short-circuit currents

Noise Processes in Discrete Communication Systems

This chapter focuses on noise processes in discrete communication systems. The problem with white Gaussian noise process discretization is that a strict definition implies that the noise has theoretically infinite power. Thus, it would be impossible to generate discrete noise, because the sampling theorem requires that the sampled signal must be physically realizable, that is, the sampled noise needs to have a finite power. To overcome this problem, noise entropy is defined as an additional measure of noise properties, and a truncated Gaussian probability density function is used. Adding entropy and truncated density to the definition of the noise autocorrelation and power spectral density functions allows mathematical modelling of the discrete noise source for both baseband and bandpass noise generators and regenerators. Noise theory and noise generators are essential for a theoretical explanation of the operation of digital and discrete communications systems and their design, simulation, emulation, and testing.

An Operator-Based Scheme for the Numerical Integration of FDEs

An operator-based scheme for the numerical integration of fractional differential equations is presented in this paper. The generalized differential operator is used to construct the analytic solution to the corresponding characteristic ordinary differential equation in the form of an infinite power series. The approximate numerical solution is constructed by truncating the power series, and by changing the point of the expansion. The developed adaptive integration step selection strategy is based on the controlled error of approximation induced by the truncation. Computational experiments are used to demonstrate the efficacy of the proposed scheme.

FILO OF ALEXANDRIA: DISCUSSION TOWARD THE LOGOS IN THE PHILOSOPHY OF EDUCATION

The article considers the influence of Greek philosophy on the ideas of the formation of the Hellenistic philosopher Philo of Alexandria. The object of study was the philosophical work of Philo. This study aimed to discover the ambiguity of the term logos as a central concept that defines in Philo's philosophy the relationship between God (the ideal creative teacher) and the world. In the works of Philo, the Logos appears as the highest, sub-divine, infinite power of the mind, which has no signs, but at the same time is identified with God. The transcendental nature of the Logos, embodied in the image of God's mind, in its paradoxical nature closely corresponds to holiness and higher wisdom. The research methodology is based on an interpretation that allows us to define the allegory and, therefore, the real meaning of Philo's philosophy, the central part of which is the philosophical reflection of the Holy Scriptures as the main source of education and the concept of Scripture, undergoing specific and simultaneously incomparable modifications. To identify these meanings, methods of systematization and hermeneutics are used. The result of the study is expressed in identifying various forms of embodiment and educational activity and the Logos.

One-relation languages and code generators

We investigate the open problem to characterize whether the infinite power of a given language is generated by an ω-code. In case the given language is a code (i.e. zero-relation language), the problem was solved. In this work, we solve the problem for the class of one-relation languages.

Features of autonomous and parallel operation of an asynchronous generator with a network of endless power in the current stage of EPS development

The article describes the use of asynchronous machines in generator mode to provide power to threephase consumers, as well as the features of autonomous and parallel operation of an asynchronous generator with an infinite power network. The use of static sources of reactive power allows widespread introduction of an asynchronous generator in the electric power system as a reliable source of active power.

Differentiation of the Mittag-Leffler Functions with Respect to Parameters in the Laplace Transform Approach

In this work, properties of one- or two-parameter Mittag-Leffler functions are derived using the Laplace transform approach. It is demonstrated that manipulations with the pair direct–inverse transform makes it far more easy than previous methods to derive known and new properties of the Mittag-Leffler functions. Moreover, it is shown that sums of infinite series of the Mittag-Leffler functions can be expressed as convolution integrals, while the derivatives of the Mittag-Leffler functions with respect to their parameters are expressible as double convolution integrals. The derivatives can also be obtained from integral representations of the Mittag-Leffler functions. On the other hand, direct differentiation of the Mittag-Leffler functions with respect to parameters produces an infinite power series, whose coefficients are quotients of the digamma and gamma functions. Closed forms of these series can be derived when the parameters are set to be integers.

Heat Transport Analysis in Rectangular Shields Using the Laplace and Poisson Equations

In the design of a building envelope, there is the issue of heat flow through the partitions. In the heat flow process, we distinguish steady and dynamic states in which heat fluxes need to be obtained as part of building physics calculations. This article describes the issue of determining the size of those heat fluxes. The search for the temperature field in a two-dimensional problem is common in building physics and heat exchange in general. Both numerical and analytical methods can be used to obtain a solution. Two methods were dealt with, the first of which was used to obtain the solution in the steady state and the other in the transient. In the steady state a method of initial functions, the basics of which were given by W.Z. Vlasov and A.Y. Lur’e was adopted. Originally MIF was used for analysis of the loads of a flat elastic medium. Since then it was used for solving concrete beams, plates and composite materials problems. Polynomial half-reverse solutions are used in the theory of a continuous medium. Here solutions were obtained by the direct method. As a result, polynomial forms of the considered temperature field were obtained. A Cartesian coordinate system and rectangular shape of the plate were assumed. The problem is governed by the Laplace equation in the steady state and Poisson in the transient state. Boundary conditions in the form of temperature (τ(x), t(y)) or/and flux (p(x), q(y)) can be provided. In the steady state the solution T(x, y) was assumed in the form of an infinite power series developed in relation to the variable y with coefficients Cn depending on x. The assumed solution was substituted into the Fourier equation and after expanding into the Taylor series the boundary condition for y = 0 and y = h was taken into account. From this condition the coefficient Cn can be calculated and, therefore, a closed solution for the temperature field in the plate.