Differential equations of a nonlinear multipolar element

A method for forming nonlinear diffe­rential equations of a multipololar element, which connect its independent pole currents and independent polar voltages, is proposed. The difficulty of the analysis is that some of the internal and external unknowns may be under the symbol of differentiation. The starting infor­mation for this formation is the common differential equations of the system of internal and external currents and voltages. The method is demonstrated on the case of formation of the corresponding differential equations of the system as such that is formed by bipolar elements. The analysis is significantly simplified in the presence of internal D-dege­nerations of the system or resistive circuits.

  1. B.I. Blazhkevich, Fundamentals of the theory of linear electric circuits. K., 1964 (Ukrainian).
  2. L. O.Chua, Min-Lin Peng, Machine analysis of elec­tronic circuits (translated from Engl.), Moscow: "Mir", 1980 (Russian).
  3. V.Tchaban, Electromagnetic processes. ­– L .: "Space M", 2017 (Ukrainian)
  4. Tchaban V. Mathematical modeling in electrical engineering. – L.: T. Soroka’s Publishing House, 2010 (Ukrainian).
  5. Tchaban V. Fundamentals of the theory of transients of electromachine systems. – L .: "Higher school", 1980 (Russian)