Application of Stochastic Differential Equations in Second-Order Electrical Circuits Analysis

• Autorzy: Kolářová E. , Brančík L.

Warianty tytułu

PL

Zastosowanie stochastycznych równań różnicowych w obwodach elektrycznych drugiego rzędu

• Języki publikacji: EN

Abstrakty

EN

The paper deals with an unconventional approach to the analysis of electrical circuits with randomly varying parameters based on stochastic differential equations (SDE). A response of the electrical circuit is computed in the form of a sample mean with a particular confidence interval to provide credible estimate of the result. The method is applied to get voltage and current responses of the second-order RLGC network excited from a voltage source with a noise term. The results are compared with the classical deterministic state-variable approach.

PL

W artykule przedstawiono niekonwencjonalna metodę analizy obwodu elektrycznego o przypadkowo zmienianych parametrach. Metoda bazuje na stochastycznych równaniach różnicowych SDE. Metodę sprawdzono na przykładzie określania napięcia i prądu w sieci drugiego rzędu RLGC zasilanej napięciem z szumami.

Słowa kluczowe

EN

stochastic differential equation; second-order electrical circuit; state variable

PL

równania stochastyczne; obwód elektryczny drugiego rzędu; analiza obwodów

• Wydawca: Wydawnictwo SIGMA-NOT
• Czasopismo: Przegląd Elektrotechniczny
• Rocznik: 2012
• Tom: R. 88, nr 7a
• Strony: 103--107
• Opis fizyczny: Bibliogr. 15 poz., tab., wykr.

Twórcy

autor

Kolářová E.

autor

Brančík L.

• Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 2848/8, 616 00 Brno, Czech Republic,

Bibliografia

• [1] Arnold, L., Stochastic Differential Equations: Theory and Applications, John Wiley & Sons, 1974.
• [2] Cyganowski, S., Kloeden, P., Ombach, J., From Elementary Probability to Stochastic Differential Equations with Maple, Springer-Verlag, 2002.
• [3] Øksendal, B., Stochastic Differential Equations, An Introduction with Applications, Springer-Verlag, 2000.
• [4] Kolářová, E., Statistical Estimates of Stochastic Solutions of RL Electrical Circuits, in Proceedings of the IEEE International Conference on Industrial Technology ICIT06, Mumbai (India): IEEE 2006, p. 2546-2550.
• [5] Kolářová, E., Modelling RL Electrical Circuits by Stochastic Diferential Equations, in Proceedings of International Conference on Computer as a Tool, Belgrade (Serbia and Montenegro): IEEE R8, 2005, p. 1236-1238.
• [6] Kolářová,E., The Brownian Bridge Process, in Proceedings of XXVII International Colloquium on the Management of Educational Process, Brno (Czech Republic): University of Defence 2009, p. 104-107.
• [7] Rahman, F., Parisa, N., A Stochastic Perspective of RL Electrical Circuit using Different Noise Terms. COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering. Vol. 30, No. 2, 2011, p. 812-822.
• [8] Cheng, C. K., Lillis, J., Lin, S., Chang, N., Interconnect Analysis and Synthesis, John Wiley & Sons, 2000.
• [9] Li, M. P., Jitter, Noise, and Signal Integrity at High-Speed, Prentice Hall, 2007.
• [10] Paul, C. R., Analysis of Multiconductor Transmission Lines, John Wiley & Sons, 2008.
• [11] Brančík, L., Ševčík , B. , Computer Simulation of Nonuniform MTLs via Implicit Wendroff and State-Variable Methods. Radioengineering, 2011, Vol. 20, No. 1, p. 221-227.
• [12] Brančík, L. Time and Laplace-Domain Methods for MTL Transient and Sensitivity Analysis. COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2011, Vol. 30, No. 4, p. 1205-1223.
• [13] Chung, C.Y., Wang, K.W., Tse, C.T., Niu, R., PSS Design by Probabilistic Sensitivity Indices, in Proceedings of the IEEE Power Engineering Society Summer Meeting, Chicago, IL (U.S.A), 2002, p. 997.
• [14] Jensen, H.A., Cifuentes, A.O., Probabilistic Sensitivity Analysis for the Dynamic Response of Electronic Systems: a Study of the Interactions of Molding Compound and Die Attach Adhesive, with Regards to Package Cracking, in Proceedings of 44th Electronic Components and Technology Conference, Washington, DC (U.S.A): 1994, p. 107-114.
• [15] Qinshu, H., Xinen, L., Shifu, X., A Fast Approximate Method for Parametric Probabilistic Sensitivity Estimation, in Proceedings of the 3rd International Conference on Advanced Computer Theory and Engineering ICACTE2010, Chengdu (China): 2010, p. V3-349 - V3-351.