математичне моделювання

Наведено типові математичні моделі управління портфелями проектів з удоско- налення системи безпеки життєдіяльності (БЖД), сутність яких полягає у виборі такої оптимальної структури заходів, реалізація яких значно впливає на її ефективність за умови обмеженого обсягу виділених ресурсів для окремо взятої території чи їх групи, а також регіону загалом. Встановлено, що отримані результати числового експерименту в багатьох випадках не тільки збігаються з результатами реального розподілу фінансових ресурсів, але й у багатьох випадках є значно кращими від них.

Mathematical modeling of frequency-controlled dual-winding induction electric drives typically involves using mathematical circuit models to investigate transient and steady-state modes. Such models often disregard spatial harmonics. Spatial harmonics in machines refer to the harmonics of the distribution of the winding function within the machine stator slots. Mathematical models based on the method of finite element analysis are primarily used to study the influence of spatial harmonics on the stator current and electromagnetic torque of dual-winding machines.

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.