Analysis of Small Oscillations in Complex Electric Power Systems
ABSTRACT
In this article the mathematical model of complex regulated electric system in matrix form is developed. This mathematical model makes it possible to study the steady-state stability of a complex electrical system by determining the eigenvalues of the dynamics matrix. The model of an electrical system that reflects transient processes for small deviations is convenient, both algorithmically and computationally, in particular, in cases of their joint solution with steady-state equations—the equations of nodal voltages. The obtained results in the form of the eigenvalues of the matrix spectrum are qualitatively the same as the results of classical studies, which is a consequence of the adequacy of the proposed model and the correct reflection of the dynamic processes occurring in a real electrical system. In addition, the equations obtained are of independent importance for the analysis of various modes, including transient, electrical systems of any complexity.
Cite this paper
Kaxramon Raximovich, A. and Tokhir Farkhadovich, M. (2018) Analysis of Small Oscillations in Complex Electric Power Systems. Engineering, 10, 253-261. doi: 10.4236/eng.2018.105017.
References
   Abdellatif, B.M. (2018) Stability with Respect to Part of the Variables of Nonlinear Caputo Fractional Differential Equations. Mathematical Communications, 23, 119-126.
http://www.mathos.unios.hr/mc/index.php/mc/article/view/2326/526

   Klos, A. (2017) Mathematical Models of Electrical Network Systems: Theory and Applications—An Introduction. Springer International Publishing AG, Berlin.
https://doi.org/10.1007/978-3-319-52178-7

   Holali, K.D., Efimov, D. and Richard, J.-P. (2016) Interval Observers for Linear Impulsive Systems. 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2016), Monterey, 23-25 August 2016, 867-872.

   Kothari, D.P. and Nagrath, I.J. (2003) Modern Power System Analysis. McGraw Hill Education, New York.

   Misrihanov, M.Sh. (2004) Klassicheskie i novye metody analiza mnogomernyh dinamicheskih system [Classical and New Methods of Analysis of Multidimensional Dynamic Systems]. Energoatom Publishing, Moskow (In Russian).

   Allaev, K.R. and Mirzabaev, A.M. (2016) Matrichnye metody analiza malyh kolebaniy elektricheskih system [Matrix Methods for the Analysis of Small Oscillations of Electrical Systems]. Fan va texnologiya Publishing, Tashkent (In Russian).

   Gotman, V.I. (2007) Common Algorithm of Static Stability Estimation and Computation of Steady States of Power Systems, Power Engineering, 311, 127-130.
http://www.lib.tpu.ru/fulltext/v/Bulletin_TPU/2007/v311eng/i4/30.pdf

   Fazylov, H.F. and Nasyrov, T.H. (1999) Ustanovivshiesya rezhimi elektroenergeticheskih sistem i ih optimizaciya [Established Regimes of Electric Power Systems and Their Optimization]. Moliya Publishing, Tashkent (In Russian).

   Kovalenko, S., Sauhats, A., Zicmane, I. and Utans, A. (2016) New Methods and Approaches for Monitoring and Control of Complex Electrical Power Systems Stability. IEEE 16th International Conference on Environment and Electrical Engineering (EEEIC 2016), Florence, 7-10 June 2016, 270-275.

   Allaev, K.R., Mirzabaev, A.M., Makhmudov, T.F. and Makhkamov, T.A. (2015) Matrix Analysis of Steady-State Stability of Electric Power Systems. AASCIT Communications, 2, 74-81.

   Irwanto, M., et al. (2015) Improvement of Dynamic Electrical Power System Stability Using Riccati Matrix Method, Applied Mechanics and Materials, 793, 29-33.

   Anderson, P.M. and Fouad, A.A. (2003) Power System Control and Stability. 2nd Edition, Willey-Interscience A John Wiley & Sons Inc., Hoboken.

   Kunder, P. (1993) Power System Stability and Control. McGraw-Hill, Inc., New York.

   Pal, M.K. (2007) Power System Stability. Edison, New Jersey.

   MATLAB (2001) User’s Guide. Reference Guide. The Math Works, Inc., Natick.

   Wilkinson, J.H. (1988) The Algebraic Eigenvalue Problem. Clarendon Press, Oxford.

   Albertos, A.P. and Sala, A. (2007) Multivariable Control Systems. Springer, London.

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