Identification of the Mathematical Model of Failure Frequency of Overhead Lines of Power System Main Grid

Авторы: Zubov N.E., Galiaskarov I.M., Ryabchenko V.N. Опубликовано: 10.09.2020
Опубликовано в выпуске: #3(132)/2020  
DOI: 10.18698/0236-3933-2020-3-100-111

Раздел: Информатика, вычислительная техника и управление | Рубрика: Системный анализ, управление и обработка информации  
Ключевые слова: overhead lines, accidents, failure frequency (flux parameter), discrete positive dynamic system, mathematical model, identification, matrix equation, compatibility condition, matrix zero divisors, generalized matrix inverse

Based on the analysis of accidents of 500 kV over-head lines of the main electric electrical grid of a wide region over a long-time-interval, the failure frequency (failure flux parameter) was determined under the influence of natural and socio-economic factors. It is proposed to consider the indicated failure rate as the output signal of a discrete positive dynamic system with many difficult formalizable inputs. To identify the mathematical model of a dynamic system, it is proposed to use the original method, the identifiability criterion of which is based on the compatibility condition of the linear matrix equation, and the numerical identification algorithm is based on the solution formula using zero-divisors and generalized inverse matrices. The method does not require a priori information about the parameters of the mathematical model of the electric electrical grid, does not involve solving the forecasting problem, and does not apply statistical calculations


[1] Galiaskarov I.M., Misrikhanov M.Sh., Ryabchenko V.N., et al. Once more about the recurrence of failures in the grid backbone networks. Elektrichestvo, 2019, no. 11, pp. 4--11 (in Russ.). DOI: https://doi.org/10.24160/0013-5380-2019-11-4-11

[2] Skopintsev V.A. Kachestvo elektroenergeticheskikh sistem: nadezhnost’, bezopasnost’, ekonomichnost’, zhivuchest’ [Quality of electrical power system: reliability, safety, cost-effectiveness, durability]. Moscow, Energoatomizdat Publ., 2009.

[3] Kalman R.E., Falb P.L., Arbib M.A. Topics in mathematical system theory. McGraw-Hill, 1969.

[4] Kailath T. Linear systems. Prentice Hall, 1980.

[5] Krasnoselskiy M.A., Lifshits E.A., Sobolev A.V. Pozitivnye lineynye sistemy. Metod polozhitel’nykh operatorov [Positive linear systems. Method of positive operators]. Moscow, Nauka Publ., 1985.

[6] Haddad W., Chellaboina V., Hui Q. Nonnegative and compartmental dynamical systems. Princeton Univ. Press, 2010.

[7] Solodovnikov V.V., ed. Teoriya avtomaticheskogo regulirovaniya. Kn. 3. Ch. 1. Tekhnicheskaya kibernetika. Teoriya nestatsionarnykh, nelineynykh i samonastraivayushchikhsya sistem avtomaticheskogo regulirovaniya [Theory of automated regulation. Vol. 3. P. 1. Technical cybernetics. Theory of non-stationary, non-linear and self-adjusting automatic control systems]. Moscow, Mashinostroenie Publ., 1969.

[8] Van Overschee P., De Moor B.L. Subspace identification for linear systems. Boston, MA, Springer, 2012. DOI: https://doi.org/10.1007/978-1-4613-0465-4

[9] Voevodin V.V., Kuznetsov Yu.A. Matritsy i vychisleniya [Matrixes and calculations]. Moscow, Nauka Publ., 1984.

[10] Zubov N.E., Mikrin E.A., Ryabchenko V.N. Matrichnye metody v teorii i praktike sistem avtomaticheskogo upravleniya letatel’nykh apparatov [Matrix methods in theory and practice of aircraft automatic control systems]. Moscow, BMSTU Publ., 2016.

[11] Zybin E.Yu. On identifiability of closed-loop linear dynamical systems under normal operating conditions. Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2015, no. 4 (166), pp. 160--170 (in Russ.).

[12] Zubov N.E., Mikrin E.A., Ryabchenko V.N., et al. Identification of a discrete system based on matrix zero dividers. Avtomatizatsiya. Sovremennye tekhnologii, 2017, no. 6, pp. 269--274 (in Russ.).

[13] Zubov N.E., Vorob’eva E. A., Mikrin EA., et al. Synthesis of stabilizing spacecraft control based on generalized Ackermann’s formula. J. Comput. Syst. Sci. Int., 2011, vol. 50, iss. 1, pp. 93--103. DOI: https://doi.org/10.1134/S1064230711010199

[14] Zubov N.E., Mikrin E.A., Misrikhanov M.Sh., et al. Stabilization of coupled motions of an aircraft in the pitch-yaw channels in the absence of information about the sliding angle: analytical synthesis. J. Comput. Syst. Sci. Int., 2015, vol. 54, iss. 1, pp. 93--103. DOI: https://doi.org/10.1134/S1064230715010153

[15] Zubov N.E., Mikrin E.A., Misrikhanov M.Sh., et al. Output control of the longitudinal motion of a flying vehicle. J. Comput. Syst. Sci. Int., 2015, vol. 54, iss. 5, pp. 825--837. DOI: https://doi.org/10.1134/S1064230715040140

[16] Zubov N.E., Mikrin E.A., Ryabchenko V.N., et al. Synthesis of control laws for aircraft lateral motion at the lack of data on the slip angle: analytical solution. Russ. Aeronaut., 2017, vol. 60, iss. 1, pp. 64--73. DOI: https://doi.org/10.3103/S106879981701010X

[17] Bronnikov A.M., Bukov V.N., Ryabchenko V.N., et al. Algebraic singularities of dynamic systems associated with zero divisors of their transfer matrices. J. Comput. Syst. Sci. Int., 2004, vol. 43, iss. 3, pp. 351--359.

[18] Zubov N.E., Lapin A.V., Mikrin E.A., et al. Output control of the spectrum of a linear dynamic system in terms of the Van der Woude method. Dokl. Math., 2017, vol. 96, iss. 2, pp. 457--460. DOI: https://doi.org/10.1134/S1064562417050179