Effective algorithm of calculating the static modes of nonlinear electromagnetic circuits

2013;
: pp. 107-112
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University
3
Lviv Polytechnic National University

Existing electromagnetic circuits are mostly non-linear, however known methods of analysis of the processes for those circuits do not meet modern requirements and it is the one of least developed parts of Theoretical Electric Engineering. Therefore the development of methods of analysis is an important issue. The article discusses the problem of developing the algorithm of calculation for static modes in nonlinear electromagnetic circuits with reactive elements under the influence of periodical disturbances. Those modes are dynamic and are described by the system of differential equations (DE). The solution of the system consists of periodic non-harmonic dependencies. The problem is solved by a numerical method as the boundary value problem of DE of the first order with periodic boundary conditions so that it is possible to get dependencies on the period of state variables without solving the problem in time domain.

  1. N. Boholiubov and Yu. Mytropolskyi, Asymptotic methods in the theory of nonlinear oscillations, Moscow, Russia: Science, 2005.. (Russian)
  2. N. Shydlovska, Analysis of non-linear electric circuits by small parameter method, Kyiv, Ukraine: Euroindex, 1999. (Ukraian)
  3. H. Pukhov, Approximate methods of mathematical modeling based on the usage of differential T-transformations, Kyiv, Ukraine: Naukova dumka, 1988. – 210 p. (Russian)
  4. L. Hlukhivskyi, Periodic nonlinear processes in Electrical Engineering (differential harmonic method and its software), Kyiv, Ukraine: Alpha PC, 2005.
  5. N. Shydlovska, V. Samoilenko, O. Kravchenko, and I. Kucheriava, “Comparative analysis of analytical and numerical methods of calculating nonlinear processes in electrical circuit”, Tekhnichna Elektrodynamika, no. 1, pp.3–6, Kyiv, Ukraine: Instytut elektrodynamiky, 2009.
  6. A. Samarskiy, Introduction to numerical methods, Moscow, Russia: Nauka, 1987. (Russian)
  7. V. Shamanskiy, Methods of numerical solving of boundary value problems on a computer, Кyiv, Ukraine: Naukova dumka, 1966. (Russian)
  8. I. Harasymiv, B. Mandziy, and O. Felyshtyn, Computer simulations of electrical and electronic devices, Lviv: Svit, 1991. (Russian).
  9. V. Malyar, “Main theses of spline-method of calculating periodic working modes of electric circuits”, Elektronika i Svyaz, no. 5, pp. 11-14, 1998. (Russian)