«Automation and Informatization of the fuel and energy complex»

A universal indicator of the quality of a complex energy system functioning

UDC: 004.052
DOI: -

Authors:

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

Keywords: homogeneous Markov process with "income", vector of marginal probabilities, stationary reliability indicators, penalty function, risk, stability problem

Annotation:

The process of a complex energy system wandering of over its possible states, mainly associated with the process of failures and restorations of its elements, is adequately described by a homogeneous Markov process with "income". Under these conditions, a stationary indicator of the quality of functioning of this system is proposed, which is a linear form that is a scalar product of the vector of marginal probabilities of a homogeneous Markov process with "income" and the vector of "income" per unit of time. This indicator is a universal one, since its various types are the main complex indicators of the quality of the energy system functioning. In this case, solving any applied problems with a universal indicator is a solution to similar problems for all its particular types. The problem of the universal indicator stability is solved. When solving any applied problems, methods of linear algebra and optimal control of a homogeneous Markov process with "income" are used. It is shown that the main types of the stationary indicator are the following complex indicators: 1) system readiness coefficient as well as other similar coefficients; 2) the "penalty" function associated with failure to fulfill the planned task and other similar functions; 3) the risk of falling into "negative" states characterizing emergency situations in the system. An example of an algorithmic solution of the problem of stationary indicator stability is given and a condition is indicated, under which this solution is the only one solution of a similar problem for all its particular types.

Bibliography:

1. Sukharev M.G., Karasevich A.M. Tekhnologicheskiy raschet i obespechenie nadezhnosti gazo- i nefteprovodov. – M.: Neft' i gaz, RGU nefti i gaza im. I.M. Gubkina, 2000. – 271 s.
2. Nadezhnost' sistem energetiki i ikh oborudovaniya / pod obshchey red. Yu.N. Rudenko. – M.: Nedra, 1994. – T. 1. – 473 s.; T. 3: v 2 kn. Kn. 2. – 287 s.
3. Polovko A.M., Gurov S.V. Osnovy teorii nadezhnosti. – 2-e izd., pererab. i dop. – SPb.: BKhV-Peterburg, 2006. – 702 s.
4. GOST R 27.102-2021. Nadezhnost' v tekhnike. Nadezhnost' ob"ekta. Terminy i opredeleniya. – Vved. 2022–01–01. – M.: Rossiyskiy in-t standartizatsii, 2021. – IV, 36 s.
5. Khovard R.A. Dinamicheskoe programmirovanie i markovskie protsessy. – M.: Sovetskoe radio, 1964. – 189 s.
6. Karmanov V.G. Matematicheskoe programmirovanie. – 3-e izd., pererab. i dop. – M.: Nauka, 1986. – 288 s.
7. Ito K. Veroyatnostnye protsessy. Vypusk 1. – M.: Izd-vo inostr. lit., 1960. – 133 s.
8. Rusev V.N., Skorikov A.V. Asimptotika riska strakhovaniya dlya trebovaniy, imeyushchikh raspredeleniya s "tyazhelymi khvostami" // Avtomatizatsiya i informatizatsiya TEK. – 2023. – № 11(604). – S. 35–40. – DOI: 10.33285/2782-604X-2023-11(604)-35-40