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Energy-optimal current distribution in an electrical network – controlling by the differential or the integral systems

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Języki publikacji
EN
Abstrakty
EN
In the complex RLC network, apart from the currents flows arising from the normal laws of Kirchhoff, other distributions of current, resulting from certain optimization criteria, may also be received. This paper is the development of research on distribution that meets the condition of the minimum energy losses within the network called energy-optimal distribution. Optimal distribution is not reachable itself, but in order to trigger it off, it is necessary to introduce the control system in current-dependent voltage sources vector, entered into a mesh set of a complex RLC network. For energy-optimal controlling, to obtain the control operator, the inversion of R(s) operator is required. It is the matrix operator and the dispersive operator (it depends on frequency). Inversion of such operators is inconvenient because it is algorithmically complicated. To avoid this the operator R(s) is replaced by the R’ operator which is a?matrix, but non-dispersive one (it does not depend on s). This type of control is called the suboptimal control. Therefore, it is important to make appropriate selection of the R’ operator and hence the suboptimal control. This article shows how to implement such control through the use of matrix operators of multiple differentiation or integration. The key aspect is the distribution of a single rational function H(s) in a series of ‘s’ or ‘s1’. The paper presents a new way of developing a given, stable rational transmittance with real coefficients in power series of ‘s/s1. The formulas to determine values of series coefficients (with ‘s/s1’) have been shown and the conditions for convergence of differential/integral operators given as series of ‘s/s1’ have been defined.
Rocznik
Strony
613--620
Opis fizyczny
Bibliogr. 15 poz., rys.
Twórcy
  • Cracow University of Technology, Faculty of Electrical and Computer Engineering, 24 Warszawska St., 31-155 Cracow, Poland
autor
  • Cracow University of Technology, Faculty of Electrical and Computer Engineering, 24 Warszawska St., 31-155 Cracow, Poland
autor
  • Cracow University of Technology, Faculty of Electrical and Computer Engineering, 24 Warszawska St., 31-155 Cracow, Poland
Bibliografia
  • [1] C.A. Desoer, “The maximum power transfer theorem for n-ports". IEEE Trans., vol. CT-20, 228.230, (1979).
  • [2] R.A. Rohrer, "Optimal matching: A new approach to the matching problem for real invariant one port networks". IEEE Trans., vol. CT-15, 118.124, (1968).
  • [3] M. Siwczyński, A. Drwal, and S. .aba, "Minimum-energetic sinusoidal signals distribution in electrical circuits", Wiadomości Elektrotechniczne, no. 9, 22.25 (2014), [in Polish].
  • [4] L.S. Czarnecki, "Discussion on a uniform concept of reactive power of nonsinusoidal currents in a time-domain", Przegląd Elektrotechniczny, vol. 85, no. 6, 164.166, (2009).
  • [5] A.P. Rens, "Validation of popular nonsinusoidal power theories for the analysis and management of modern power systems", North-West University, Potchefstroom Campus, 2006.
  • [6] J. Walczak, and M. Pasko, "The minimization of losses of active power and the symmetrization of power flow in the nonsinusoidal systems”, Jakość i Użytkowanie Energii Elektrycznej, vol. 5, no. 1, 55‒59, (1999), [in Polish].
  • [7] L.S. Czarnecki, “Currents’ Physical Components (CPC) concept: a fundamental for power theory”. Przegląd Elektrotechniczny, vol. 84, no. 6, 28‒37, (2008).
  • [8] M. Siwczyński, A. Drwal, and S. Żaba, “Energy-optimal current distribution in a complex linear electrical network with pulse or periodic voltage and current signals. Optimal control”, Bull. Pol. Ac.: Tech., 64 (1), 45‒50, (2016).
  • [9] M. Siwczyński, A. Drwal, and S. Żaba, “Energy-optimal current distribution in a complex linear electrical network with pulse or periodic voltage and current signals. Suboptimal control”. Measurement Automation Monitoring, vol. 62, no. 4, 125‒128, (2016).
  • [10] M.A. Krasnosielskij, F.A. Lipszyc, and A.V. Sobolev, “Pozitywnyje liniejnyje sistiemy”. Science, Moscow, 1985, [in Russian].
  • [11] E.N. Rosenvasser and S. K. Volovodov, “Operatornyje mietody i kolebatielnyje processy”. Science, Moscow, 1985, [in Russian].
  • [12] D.V. Lee, “On the power-series expansion of a rational function”, Acta Arithmetica, vol. 57, no. 3, 229‒255, (1992).
  • [13] P.B. Laval, “Representation of functions as power series”, Kennesaw State University, USA, 2008.
  • [14] A. Straub, “Multivariate apery numbers and supercongruences of rational functions”. Algebra Number Theory, no. 8, 1985‒2007, (2014).
  • [15] M. Houben, “Congruences for Coefficiences of Power Series Expansions of Rational Functions”. Utrecht University, Niederlads, 2016.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
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