Stability of electric power systems as the task of nonlinear mechanics

Abstract

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.