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Description of algorithms for balancing numerical matrices and theirdivision into hierarchical levels according to their type and complexity

Khanas Yuriy, Borecki Michał

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

2021

T. 11, nr 1

44--49

This article describes a set of algorithms for so-called balancing of numerical matrices, which were developed by the author. Each section consists of several algorithms that are divided into different levels. The order of these levels depended on the chronology of the creation of certain algorithms. Chronology also affected the complexity of these balancing algorithms, so it can be argued that the algorithms are described in order from the simplest level to the most complex. It is important to emphasize that the purpose of the article is to describe the actions on matrices that determine the balancing algorithm of a certain level, and practical application will be the next step.

Artykuł przedstawia autorskie algorytmy bilansowania macierzy. Każdy rozdział składa się z kilku algorytmów, które są rozdzielone na różne poziomy. Te poziomy są uporządkowane w zależności od chronologii ich stworzenia. Podobnie chronologia ma wpływ na złożoność algorytmów zbilansowania, w związku z tym można stwierdzać, że algorytmy są uszeregowana według stopnia złożoności. Niniejszy artykuł jest pierwszym etapem pokazującym sposób zbilansowania pewnego poziomu macierzy, natomiast kolejnym etapem będzie efekt praktyczny.

Main aspects influencing the evaluation of atmospheric overvoltages in high-voltage networks

Borecki Michał, Ciuba Maciej, Kharchenko Yevhen, Khanas Yuriy

Bulletin of the Polish Academy of Sciences. Technical Sciences

2021

Vol. 69, nr 1

art. no. e135838

The effectiveness of lightning protection on the power and distribution grid is a significant factor, which influences the power distribution reliability and the failure rate of system elements. As part of this article, a mathematical model will be presented, taking into account selected parameters that affect the assessment of the lightning hazard of an overhead line. The proposed model will consider the location of the object near the line and the adjustment of line conductor overhangs. Moreover, the mentioned mathematical model allows for analyzing the impact of considered parameters on the protection level of the power system, and transient overvoltages that occur in this system. The article contains also a detailed description of an effective and fast method to assess the lightning discharge impact on the power system with insufficient data. The introduced model was tested to verify the correctness of its operation by comparison of calculation results and functional data. High convergence of calculated and functional data and uncomplicated model structure ensure a wide range of applications for the proposed solution to easily prevent emergency situations in the power system. Furthermore, the described model gives the opportunity to assess the reduction of the range of selectivity zone associated with the power line, in conjunction with the impact of constructional peculiarities and a near object.