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

• Autorzy: Siwczyński M. , Żaba S. , Drwal A.

Identyfikatory

DOI

10.24425/bpasts.2019.129659

• 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.

Słowa kluczowe

EN

principle of minimum energy losses; optimal control; suboptimal control; power series; operators of multiple differentiation or integration; decomposition of a rational function

PL

zasada minimalnych strat energii; optymalna kontrola; nieoptymalna kontrola

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2019
• Tom: Vol. 67, nr 3
• Strony: 613--620
• Opis fizyczny: Bibliogr. 15 poz., rys.

Twórcy

autor

Siwczyński M.

• Cracow University of Technology, Faculty of Electrical and Computer Engineering, 24 Warszawska St., 31-155 Cracow, Poland

autor

Żaba S.

• Cracow University of Technology, Faculty of Electrical and Computer Engineering, 24 Warszawska St., 31-155 Cracow, Poland

autor

Drwal A.

• Cracow University of Technology, Faculty of Electrical and Computer Engineering, 24 Warszawska St., 31-155 Cracow, Poland

Bibliografia

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• [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].
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• [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).
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• [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).