математичне моделювання

The article analyzes the publications, which shows that two approaches to the analysis of transients in long power lines with distributed parameters are popular today: based on simplified methods of solving the equation of a long line, or equivalent to the known equation of a long line by circuit substitution schemes. In applying the first approach, the authors do not take into account the running resistance, phase and interphase conductivities, calculating the usually mentioned processes by the known methods of D’Alembert and “wandering waves”.

The article analyzes scientific publications, which showed that for most part of the study transients processes in the long power lines with distributed parameters is carried out by equivalent to the known equation of a long line with distributed parameters by a circular equivalent, or solve this equation using simplified approaches. These approaches require deterministic boundary conditions to the long line equation, which is not always possible when modeling transients processes in electrical networks.

One of the key problems in the implementation of closed-loop control systems is to measure all states of a dynamic system, especially, when there are severe environmental conditions. Consequently, the use of certain types of sensors is impossible for technical or economic reasons. Also, in electromechanical systems, there are a lot of values that cannot be directly measured by physical sensors. Thus, mathematical algorithms named as observers and estimators are in use to calculate the states of the dynamic system utilizing math model and available set of sensors.

The article analyzes scientific publications, who showed that for the most part, the study of switching transients in electrical networks during automatic reclosing cycles of circuit breaker, are carried out without taking into account the influence of electromechanical processes in the mechanisms of circuit breaker contacts, despite the fact that the speed of their course is commensurate with the speed of the electromagnetic processes.

The mathematical model of an electromechanical system with an asynchronous generator with rotor’s current regulation by frequency converter with an autonomous voltage inverter controlled by current controllers has been described in the article.

On the basis of a generalized interdisciplinary (interdisciplinary) method of mathema- tical modeling, which is based on modifications of the integral variational principle of Ha- milton-Ostrogradsky, proposed mathematical model of the ultra-high voltage circuit-breaker the main emphasis of which is placed on modeling work the mechanism of moving his contacts.

The transient electromagnetic processes in the power generation system with turbo- generator and brushless excitation system in a mode of initial excitation of turbo-generator are analyzed in the article. The research was carried out in the hybrid system that combines a computer model of a power part with the real excitation controller. The influence of setting the automatic control system on quality of voltage regulation and generator excitation current regulation is analyzed.

The paper on the basis of interdisciplinary approaches presented mathematical model of the electric power system, a key element of which is the power line that connected substation “Zakhidnoukrayins’ka” — substation “Vinnyts’ka”. On this basis, the analysis of transients in the power line to single-line performance. Results transients are presented as figures which analyzed.

The article presents an analysis of automatic adjustment system of level liquid in the tank in case the use of frequency-controlled asynchronous electric pump unit. It is proved expediency and conditions of use P- and PI- regulator. The recommendations of settings regulators have given. These results of automatic adjustment control system of level are obtained by computer simulation using Matlab-Simulink.

The electromechanical and electromagnetic transient processes in a power generation system with turbo-generator and brushless excitation for main working regimes are analyzed in the article. An analysis has been carried out by means of developed with the use of the object-oriented method the mathematical and computer models that take into account non- linearity of synchronous machines and discreteness of semiconductor converters.