Abstract
This paper examines the almost-sure asymptotic stability of coupled synchronous machines encountered in electrical power systems, under the effect of fluctuations in the interconnection system due to varying network conditions. A linearized multimachine model is assumed with one of the machines having negligible damping weakly coupled to the other machines with positive damping. Furthermore, the fluctuations are assumed to contain both harmonically varying and stochastically varying components. For small intensity excitations, the physical processes are approximated by a diffusive Markov process defined by a set of Itô equations. Results pertaining to the almost-sure asymptotic stability are derived using the maximal Lyapunov exponent obtained for the Itô equations. Assumptions made for the modeling and analysis are consistent with possible operating conditions in an electrical power system.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F. P. deMello and C. Concordia, 1969. IEEE Trans. Power Appar. Syst., pp. 316–329. Concepts of synchronous machine stability as affected by excitation control.
F. Kozin and S. Sugimoto, 1977. Proceedings of the Conference on Stochastic Differential Equations and Applications, ed: J. David Mason, Academic Press, New York. Relations between sample and moment stability for linear stochastic differential equations.
L. Arnold, 1984. SIAM J. of Applied Mathematics, Vol. 44, No. 4, pp. 793–802. A formula connecting sample and moment stability of linear stochastic systems.
R. Z. Khasminiskii, 1967. Theory of Probab, Appl., Vol. 12, pp. 144–147. Necessary and sufficient conditions for the asymptotic stability of linear stochastic systems.
L. Arnold and W. Kliemann, 1983. Probabilistic Analysis and Related Topics, Vol. 3, ed. A.T. Bharucha-Reid, Academic Press, New York, Qualitative theory of stochastic systems.
M. A. Pai, Energy Function Analysis for Power System Stability, Kulwer Academic Publisher, boston, 1989.
K. A. Laparo and G. L. Blankenship, 1985. IEEE Transactions on Circuits and Systems, Vol. 32, No. 2, pp. 177–184. A probabilistic mechanism for small disturbance instabilities in electric power systems.
G. C. Papanicolaou and W. Kohler, 1976. Communications in Mathematical Physics, Vol. 46, pp. 217–232. Asymptotic analysis of deterministic and stochastic equations with rapidly varying components.
N. Sri Namachchivaya and Y. K. Lin, 1988. Probabilistic Engineering Mechanics, Vol. 3, No. 3, pp. 159–167. Application of stochastic averaging for nonlinear systems with high damping.
E. Wong and M. Zakai, 1965. International Journal of Engineering Sciences, Vol. 3, pp. 213–229. On the relationship between ordinary and stochastic differential equations.
F. Kozin and S. Prodromou, 1971. SIAM Journal of Applied Mathematics, Vol. 21, pp. 413–424. Necessary and sufficient conditions for almost-sure sample stability of linear Itô equation.
K. Nishioka, 1976. Kodai Math. Sem. Rep., 27, pp. 211–230. On the stability of two dimensional linear stochastic systems.
R. Z. Khasminiskii, 1980. Stochastic Stability of Differential Equations. Sijthoff and Noordhoff.
R. L. Stratonovich, 1967. Topics in the Theory of Random Noise, Vol. II, Gordon and Breach.
N. Sri Namachchivaya, 1989. J. of Sound and Vibration, Vol. 132, pp. 301–314. Mean square stability of a rotating shaft under combined harmonic and stochastic excitations.
I. S. Gradshteyn and I.M. Ryzhik, 1980. Table of Integrals Series, and Products. Academic Press.
R.R. Mitchell and F. Kozin, 1979. SIAM J. of Applied Mathematics, Vol. 27, No. 4, pp. 571–606. Sample stability of second order linear differential equation with wide band noise coefficients.
J. A. Pinello and J. E. Van Ness, 1971. IEEE Transactions on Power Apparatus and Systems, Vol. PAS-90, pp. 1856–1862. Dynamic response of a large power system to a cyclic load produced by nuclear reactor.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag
About this paper
Cite this paper
Namachchivaya, N.S., Pai, M.A., Doyle, M. (1991). Stochastic approach to small disturbance stability in power systems. In: Arnold, L., Crauel, H., Eckmann, JP. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086677
Download citation
DOI: https://doi.org/10.1007/BFb0086677
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54662-7
Online ISBN: 978-3-540-46431-0
eBook Packages: Springer Book Archive