Representation of electricalmode in arc furnaces by a state change modeland determination of the possibilities of these states
Date
2018-02-01
Journal Title
Journal ISSN
Volume Title
Publisher
Lviv Politechnic Publishing House
Abstract
Опрацьовано математичні основи синтезу потоку
керуючих впливів, за якого оптимізується процес переве-
дення електричного режиму дугової сталеплавильної печі в
заданий стан в умовах, відповідних поточним станам печі
потоків збурень електричних режимів. Практичне
використання запропонованої математичної моделі зміни
станів дасть змогу оперативно синтезувати інтенсивність
потоку керуючих впливів, що дасть можливість отримати
оптимальну швидкодію регулювання динаміки пере-
хідного процесу зміни ймовірностей станів, і, тим самим,
досягти максимальної ймовірності знаходження елек-
тричного режиму в печі в необхідному електротехно-
логічно обґрунтованому стані.
It is the first paper where the electrical mode of an arc furnace (AF) is proposed to be considered as a state change. This work also proposes a methodology for calculating the time values of the probabilities of these states. The methodology is based on the representation of state-change processes by the Markov model of continuous time, discrete state (CDS) stochastic processes. The state of electrical mode in each phase of an arc furnace is identified by the value of arc current that can be set for a given melting period, may be in the range of permitted deviations, or may get to the range of large operational or emergency deviations. Assuming that the system goes from state to state under the action of the Poisson flows of events, the concept of intensity of disturbance flows, and the intensity of flows of control actions are introduced. This makes it possible to form a system of Kolmogorov differential equations to change the state probabilities of the AF electrical mode. The solution of the system results in obtaining time dependencies of change in state probabilities. When analyzing graphs of changes over time in the probabilities of AF electrical mode states, it is possible to choose the desired intensity of the flow of control actions, which ensures that the electrical mode is in a given state under the action of the corresponding disturbance flow.
It is the first paper where the electrical mode of an arc furnace (AF) is proposed to be considered as a state change. This work also proposes a methodology for calculating the time values of the probabilities of these states. The methodology is based on the representation of state-change processes by the Markov model of continuous time, discrete state (CDS) stochastic processes. The state of electrical mode in each phase of an arc furnace is identified by the value of arc current that can be set for a given melting period, may be in the range of permitted deviations, or may get to the range of large operational or emergency deviations. Assuming that the system goes from state to state under the action of the Poisson flows of events, the concept of intensity of disturbance flows, and the intensity of flows of control actions are introduced. This makes it possible to form a system of Kolmogorov differential equations to change the state probabilities of the AF electrical mode. The solution of the system results in obtaining time dependencies of change in state probabilities. When analyzing graphs of changes over time in the probabilities of AF electrical mode states, it is possible to choose the desired intensity of the flow of control actions, which ensures that the electrical mode is in a given state under the action of the corresponding disturbance flow.
Description
Keywords
arc furnace, electrical mode, probability of the electrical mode state, Markov stochastic processes, intensity of disturbance flows, intensity of control actions
Citation
Lozynskyi O. Representation of electricalmode in arc furnaces by a state change modeland determination of the possibilities of these states / Orest Lozynskyi, Andryi Lozynskyi, Yaroslav Paranchuk // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2018. — Vol 8. — No 1. — P. 26–30.