Keywords
output LC-filter
nonlinear transformer
singularly-perturbed system
integral manifold
theorem of existence
reduction of order
How to Cite
Abstract
The object of study is the sinusoidal voltage source, that is composed of a frequency converter with an output LC-filter and a non-linear single-phase output transformer. A mathematical model of this source is constructed in the form of a nonlinear singularly perturbed system of differential equations. Conditions for the existence of an integral manifold in a system with a not - known -control in advance in general form are obtained. The possibility of decreasing the order of the mathematical model of this power source by means of an integral manifold in the form of a power series is shown. A synthesis of the control strategy is carried out by establishing a correspondence between the modulating function and the coefficients of the Lyapunov function. The results of modeling are presented. References 14, figures 2.
References
Voldek A.I. Electric Machines. L.: Ehnergiya, 1978. 832 p.
Demidovich B.P. Lectures on the mathematical theory of stability. М.: Nauka, 1967. 472 p.
Cunningham V. Introduction to the theory of nonlinear systems. M.–L.: Gosenergoizdat, 1962. 456 p.
Krishchenko A.P., Kavinov A.V. Stabilization of affinity systems. Differential equations. 2000. V. 36. No 11. Pp. 1482–1487.
Lomov S.A. Introduction to the general theory of singular perturbations. M.: Nauka. Main editorial office of phys.-math. Literature, 1981. 400 p.
Misak T.V. Stabilization of the output voltage of a single-phase power supply with a nonlinear output transformer. Pratsi Instytutu Elektrodynamiky NANU. 2017. Issue 46. Pp. 60–70.
Mitropolsky Yu.A., Lykova O.B. Integral manifolds in nonlinear mechanics. М.: Nauka. 1973. 512 p.
Mikhalsky V.M. Means of improving the quality of electricity at the input and output of frequency and voltage converters with pulse width modulation. K.: Institute of Electrodynamics of NAS of Ukraine, 2013. 340 p.
Naife A. Introduction to the methods of perturbations. М.: Mir, 1984. 534 p.
Pankiv V.I., Tankevich E.M., Lutchin M.M. Approximation of magnetization characteristics of current transformers. Pratsi Instytutu Elektrodynamiky NANU. 2014. Issue 37. Pp. 82–90.
Drunk B.E. Valve converters of electrical energy parameters. Electronics and control systems. 2012. No 1(31). Pp. 28–30.
Strygin V.A., Sobolev V.V. Separation of movements by the method of integral manifolds. М.: Nauka, 1988. 256 p.
Yazdani A., Iravani R. Voltage-Sourced Converters In Power Systems. Modeling, Control and Applications. Published by John Wiley & Sons, Inc., Hoboken, New Jersey, 2010. 463 p.
Zhang L.J., Sun C.Q., Sun J.B. A Nonlinear Model for Marine High-voltage Transformer. Applied Mechanics and Materials, Vols. 602–605. 2014. Pp. 2572–2576.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Copyright (c) 2017 T.V. Mysak