The manuscript is devoted to the problem of improving the methods of analysis of transients processes in power lines of ultra-high voltage under normal and emergency operating modes.
In the thesis, the actual scientific tasks of improving the methods of analysis of transient processes in ultra-high voltage electrical networks under normal and emergency modes of work are formulated and solved, which will allow adequately to reproduce the real picture of the propagation of electromagnetic waves in power transmission lines and to investigate the influence of oscillating electromechanical processes of the moving contact of the circuit breaker on the transients processes in elements of electrical networks.
In the first section, the analysis of publications related to the study of transients processes in electrical systems based on variational approaches. The number of these publications was insignificant, and the analysis confirms the expediency of using variational approaches to the study of transients processes in these systems. Thus, scientists unanimously support the simulation of the arc with active resistance (arc conductivity). However, the works do not take into account the transient mechanical processes in the circuit breaker themselves in the implementation of switching, despite the fact that the rate of their flow is commensurate with the rate of transients in the elements of electrical networks. Analysis of approaches to solving the equation of the long line for the study of transients processes in power lines with distributed parameters showed that the above equation is solved for an idealized line (line without loss), or apply a circular equivalent line. Thus, the equation itself loses its physical essence, and therefore the improvement of methods for the study of transients processes in long power lines with distributed parameters is an urgent task.
In the second section of the dissertation work the theoretical foundations of the nonconservative Lagrangian are given. It is shown how it is possible to obtain equations of motion of inertial masses with a a non-rigid motion transmission, equations of electric circuits with concentrated parameters and equations of a long power line with distributed parameters on the basis of a single energy approach, which is based on the modified Hamilton-Ostrogradsky integral variational principle. The obtaining of the mentioned equations was carried out by minimizing the extended functional action of Hamilton-Ostrogradsky.
The third section is devoted to the study of non-switching transients processes in electrical networks. In particular, here, based on the interdisciplinary method of mathematical modeling, models of the line of constant current and two fragments of electrical networks of alternating current are constructed, the key element of which is a long transmission line with distributed parameters. The theory of the electromagnetic field and circular approaches are used in the formation of the extended action functional on Hamilton-Ostrogradsky. This approach made it possible using ordinary differential equations and partial differential equations to adequately reproduce the physical processes in the objects under study. It is proposed to use the boundary conditions of the second and third genera (Neumann and Poincare conditions) to solve the long line equation. On the basis of the developed mathematical models, the transient processes in the direct current line for the modes of operation on the equivalent active-inductive load, short circuit and non-working stroke are analyzed. Transient processes in characteristic fragments of electrical networks in short-circuit modes, which were preceded by the output of systems in the steady state, are investigated.
In the fourth section to account for the switching processes in electrical networks, based on the theory of Lagrange, the mathematical model of ultra-high voltage circuit breaker.
Key words: transients processes, ultra-high voltage circuit breaker, electrical net¬work, ultra-high voltage, mathematical model, principle of Hamilton-Ostrogradsky, equation of Euler-Lagrange, mechanism of the movement of circuit breaker contacts, long line.
