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The National Academy of Sciences of Ukraine

The Institute of Electrodynamics

About Institute



V. M. Avramenko
Institute of Electrodynamics of the National Academy of Sciences of Ukraine,
Peremohy, 56, Kyiv-57, 03680, Ukraine,
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It is showed that the analytical methods of nonlinear mechanics, developed in Soviet Union in 30th of the last century, are adequate the task of stability of large electric power pools as substantially nonlinear dynamic systems. Equation of mechanical motion of the rotor inertia masses of turbine and generator is basic equation of dynamics of the electric power system. Its non-linearity in combination with the automatic regulators of power of turbine and excitation of synchronous generator results in formation of the nonlinear nonautonomous dynamic system. N.M. Krylov, N.N. Bogolyubov developed the theory of doing middle, which allows with the set error to find an analytical decision for the nonlinear system. Actually the same method is used for numeral integration of motion equations of synchronous generators for the analysis of EPS stability, but it requires effective organization of joint decision of the system of differential and algebraic equations which form the model of EPS dynamics. Simulation, executed for the real mode of UPS of Ukraine, which was additionally made heavier, showed that at certain terms (for example, repair mode), in accordance with predictions of the nonlinear systems theory, small disturbances can cause an autooscillations in the automatically controlled dynamic system. References 7, figures 8.
Key words: stability, electric power system, nonlinear mechanics, simulation method.

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2. Andronov A.A, Vitt A.A., Haikin S.E.. Theory of Oscillations. Moskva: Nauka, 1981. 568 p. (Rus)
3. Kyrylenko O.V., Butkevych O.F., Rybina O.B. Low-frequency oscillations of operating conditions of united power systems and prevention of system failure. Pratsi Instytutu Elektrodynamiky NAN Ukrainy. 2014. Vyp. 38. P. 30–39. (Ukr)
4. Krylov N.M., Bogoliubov N.N.. Introduction to nonlinear mechanics. Publishing house of AN USSR. Kiev, 1937. 403 p. (Rus)
5. O.S. Yandulskyi O.S., Marchenko A.A., Matsejko V.V.. Investigation of the properties of low-frequency oscillations based on synchronized vector measurements. Tekhnichna Elektrodynamika. 2014. № 5. P. 74–76. (Ukr)
6. Kundur P., Paserba J., Ajjarapu V. Definition and Classification of Power System Stability. IEEE Transactions on power systems. 2004. Vol. 19. № 2. P. 1387–1401.
7. Pavlovskyi V., Lukianenko L., Lenga O., Lambillon V., Rese L. Analysis of electromechanical oscillation in the IPS of Ukraine using eurostag and digsilent powerfactory software tools. Tekhnichna Elektrodynamika. 2015. № 5. P. 42–51. (Ukr)