«Automation and Informatization of the fuel and energy complex»

Calculation of instantaneous and average availability coefficients of a complex energy system with a given accuracy

UDC: 004.052
DOI: -

Authors:

¹ National University of Oil and Gas "Gubkin University", Moscow, Russia

Keywords: homogeneous Markov process, system of linear differential equations, homogeneous Markov chain, instantaneous and average availability coefficients

Annotation:

When modeling complex energy systems, there often arises a situation that requires calculating the values of instantaneous and average availability coefficients, which are one of the main indicators of these systems reliability. The methods of the above-mentioned reliability indicators calculation are based on various computational procedures for solving a system of linear homogeneous differential equations. However, such procedures often have poor numerical stability, which means that it is difficult, or even impossible, to assess the accuracy of the results obtained. The authors of the article propose such transformation of the initial system of linear homogeneous equations that allows representing its solution that includes a certain exponential function. This exponential function application makes it possible to obtain a fairly simple analytical estimation of the solution absolute error of the system under consideration. Based on this analytical estimate, a numerically stable algorithm for solving a system of linear differential homogeneous equations is built, which allows estimating the values of the instantaneous and average readiness factors of a complex energy system with a given absolute error. Examples are given of a numerically stable algorithm application for calculating both the instantaneous and average readiness factors with a given absolute error. In particular, the example provides some calculation of the instantaneous readiness factor with an absolute error less than or equal to 107 and a comparison is made with the exact value of this factor.

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