Stepanov

pp. 38-49

In this paper, we toch upon the theme of computation of linear electrical circuits with reciprocal inductivity by the operator method, in accordance with the program of the course "Electrotechnics". This theme is either omitted or considered with inadequate substantiation in textbooks, without formulation of the rules of thransition to the operator substitution schemes. In our paper, we fill this gap and consider all variants of schemes with reciprocal inductivity for which a direct transition to equivalent operator schemes is possible. We formulate the conditions necessary for a such transition. The article should be helpful for teachers in explaining to the students the operator method of computation of electrical circuits.

pp. 288-301

We propose a method for determining the non-stable equilibria on a multidimensional sphere that can be used for the analysis of dynamical stability by the direct Lyapunov method, which, in turn, is used to control a system of synchronous generators. Our method is based on finding an extremum (a minimum) of Lyapunov function on a multidimensional sphere the center of which is a stable equilibrium. The radius of the sphere is enlarged until a non-stable equilibrium (a saddle point) appears. This allows to compute the critical value of Lyapunov function and to estimate the reserve stability. For the analysis of transient stability we use the Lyapunov function of energy type. The proposed method diminishes the computational expenses and improves reliability of the estimation of reserve transient stability of synchronous generators

To ensure reliable operation of electric power systems it’s necessary to analyze and evaluate the inventory of dynamic stability of synchronous generators under large perturbations. In this paper the authors consider a methodology for analysis and evaluation of dynamic stability a feature of which is sharing high quality (the method of Lyapunov functions) and numerical methods. The authors propose an approximation method with the use of the interpolation polynomial to reduce computational costs and to carry out more accurate calculation of the critical value of the Lyapunov function. This method can improve accuracy of results to assess dynamic stability and make a more grounded choice of states of power systems and configuration of emergency automation systems.