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The National Academy of Sciences of Ukraine

The Institute of Electrodynamics

About Institute



T.V. Mysak
Institute of Electrodynamics of the National Academy of Sciences of Ukraine,
Peremohy, 56, Kyiv-57, 03680, Ukraine,
е-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it

The object of the study is a source of sinusoidal voltage, which has a solar cell, a PWM frequency converter and an output LC filter, and a nonlinear, single phase output transformer with an additional LC-filter on the output, which is connected to a single-phase non-autonomous consumer network. A mathematical description of this source, as an affine nonlinear singularly perturbed system of differential equations, is obtained, and a decreasing order is made. Conditions for the stability of an integral variety in a system with an unknown forward control in generalized form are obtained. The nonlinear reduced system is brought to a kind that allows us to apply a linear feedback control strategy. The use of the gradient method allowed us to obtain the Lyapunov function in the form of a quadratic form, whose coefficients are solvations of the linear system of algebraic equations. A condition in which the use of these coefficients guarantees the local asymptotic stability of the system is given. The results of the simulation, conducted taking into account the constraints affecting the technical feasibility of implementing the strategy of control, are presented. The spectral composition of the output voltage has been estimated for nominal and minimum load cases. References 21, figures 2.
Key words: frequency converter, saturation nonlinearity, integral manifold, singularly-perturbed system, stability, Lyapunov function.

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Received 25.10.2018