title: ÐÐµÑÐ¾Ð´ Ð²ÐµÐºÑÐ¾ÑÐ½ÑÑ ÑÑÐ½ÐºÑÐ¸Ð¹ ÐÑÐ¿ÑÐ½Ð¾Ð²Ð° Ð´Ð»Ñ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ ÑÐ½ÐµÑÐ³Ð¾ÑÐ¸ÑÑÐµÐ¼
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Lyapunov vector function method for analyzing the invariability of electric energy systems
Creators: name: ÐÐ°ÑÐ°ÐºÑÐ¸ÐµÐ²Ð°, ÐÐµÑÐ°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: Ð­Ð½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¸Ðµ ÑÐ¸ÑÑÐµÐ¼Ñ
Ð¡Ð»Ð¾Ð¶Ð½ÑÐµ ÑÐ¸ÑÑÐµÐ¼Ñ
Ð¤ÑÐ½ÐºÑÐ¸Ð¸ (Ð¼Ð°Ñ.) ÐÑÐ¿ÑÐ½Ð¾Ð²Ð°
Ð´ÐµÐºÐ¾Ð¼Ð¿Ð¾Ð·Ð¸ÑÐ¸Ñ
Ð°Ð³ÑÐµÐ³Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
decomposition
aggregation

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð°Ð½Ð°Ð»Ð¸Ð·Ñ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð¼Ð°Ð¶Ð¾ÑÐ¸ÑÑÑÑÐ¸Ñ ÑÐ¸ÑÑÐµÐ¼, ÑÐ¸Ð½ÑÐµÐ·Ð¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ Ð´Ð»Ñ ÑÐ»Ð¾Ð¶Ð½ÑÑ Ð¼Ð°ÑÐ¸Ð½Ð½ÑÑ ÑÐ½ÐµÑÐ³Ð¾ÑÐ¸ÑÑÐµÐ¼, Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ Ð²ÐµÐºÑÐ¾ÑÐ½ÑÑ ÑÑÐ½ÐºÑÐ¸Ð¹ ÐÑÐ¿ÑÐ½Ð¾Ð²Ð°. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ñ ÑÐ°Ð±Ð¾ÑÑ: 1. ÐÐ·ÑÑÐµÐ½Ð¸Ðµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° ÑÐ¸Ð½ÑÐµÐ·Ð° Ð¼Ð°Ð¶Ð¾ÑÐ¸ÑÑÑÑÐ¸ÐµÐ¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ Ð²ÐµÐºÑÐ¾ÑÐ½ÑÑ ÑÑÐ½ÐºÑÐ¸Ð¹ ÐÑÐ¿ÑÐ½Ð¾Ð²Ð°. 2. ÐÐµÐºÐ¾Ð¼Ð¿Ð¾Ð·Ð¸ÑÐ¸Ñ ÑÐ»Ð¾Ð¶Ð½Ð¾Ð¹ ÑÐ½ÐµÑÐ³Ð¾ÑÐ¸ÑÑÐµÐ¼Ñ. 3. ÐÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ ÑÑÐ»Ð¾Ð²Ð¸Ð¹ ÑÐºÑÐ¿Ð¾Ð½ÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð´Ð»Ñ Ð¸Ð·Ð¾Ð»Ð¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ Ð¿Ð¾Ð´ÑÐ¸ÑÑÐµÐ¼ Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð¹ ÑÐ½ÐµÑÐ³Ð¾ÑÐ¸ÑÑÐµÐ¼Ñ. 4. ÐÐ¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ Ð¼Ð°Ð¶Ð¾ÑÐ°Ð½ÑÑ Ð¸ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ ÑÑÐ»Ð¾Ð²Ð¸Ð¹ ÐµÐµ ÑÑÑÐµÑÑÐ²Ð¾Ð²Ð°Ð½Ð¸Ñ Ð´Ð»Ñ Ð°Ð³ÑÐµÐ³Ð°ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¹ ÑÐ½ÐµÑÐ³Ð¾ÑÐ¸ÑÑÐµÐ¼Ñ. 5. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð¼Ð°Ð¶Ð¾ÑÐ¸ÑÑÑÑÐµÐ¹ ÑÐ¸ÑÑÐµÐ¼Ñ. 6. Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÐµÑÐ¿ÐµÑÐµÐ½Ð¸Ñ, Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð¼Ð°Ð¶Ð¾ÑÐ¸ÑÑÑÑÐµÐ¹ ÑÐ¸ÑÑÐµÐ¼Ñ Ð´Ð»Ñ n-Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð¹ ÑÐ½ÐµÑÐ³Ð¾ÑÐ¸ÑÑÐµÐ¼Ñ Ñ Ð·Ð°Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÑÑÑÐºÑÑÑÐ¾Ð¹ ÑÐ²ÑÐ·Ð¸. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ Ð²ÐµÐºÑÐ¾ÑÐ½ÑÑ ÑÑÐ½ÐºÑÐ¸Ð¹ ÐÑÐ¿ÑÐ½Ð¾Ð²Ð° Ð±ÑÐ»Ð° Ð¿Ð¾Ð»ÑÑÐµÐ½Ð° Ð¼Ð°Ð¶Ð¾ÑÐ¸ÑÑÑÑÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ -Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð¹ ÑÐ½ÐµÑÐ³Ð¾ÑÐ¸ÑÑÐµÐ¼Ñ. ÐÐ»Ñ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð¼Ð°Ð¶Ð¾ÑÐ¸ÑÑÑÑÐµÐ¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð±ÑÐ»Ð° Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð° Ð¸Ð´ÐµÑ Ð´ÐµÐºÐ¾Ð¼Ð¿Ð¾Ð·Ð¸ÑÐ¸Ð¸ Ð¸ÑÑÐ¾Ð´Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ Ð½Ð° Ð¿Ð¾Ð´ÑÐ¸ÑÑÐµÐ¼Ñ Ñ Ð´Ð¸Ð°Ð³Ð¾Ð½Ð°Ð»ÑÐ½ÑÐ¼ Ð´Ð¾Ð¼Ð¸Ð½Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸ÐµÐ¼. ÐÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ðµ Ð´Ð°Ð½Ð½Ð¾Ð³Ð¾ ÑÑÐ»Ð¾Ð²Ð¸Ñ Ð¿Ð¾Ð·Ð²Ð¾Ð»Ð¸Ð»Ð¾ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°ÑÑ ÑÑÐ½ÐºÑÐ¸Ð¸ ÐÑÐ¿ÑÐ½Ð¾Ð²Ð°, Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð½ÑÐµ Ð´Ð»Ñ Ð¸Ð·Ð¾Ð»Ð¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ Ð¿Ð¾Ð´ÑÐ¸ÑÑÐµÐ¼ Ð² Ð¿Ð¾Ð´ÑÐ¸ÑÑÐµÐ¼Ð°Ñ ÑÐ¾ ÑÐ²ÑÐ·ÑÐ¼Ð¸.
description: The title of graduation thesis is Â« Lyapunov vector function method for analyzing the invariability of electric energy systems Â». This paper is devoted to stability analysis of majorizing systems synthesized for complex -machine power systems using the Lyapunov vector function method. Tasks were solved in the course of the work: 1. The study of the synthesis algorithm for the majorizing comparison model using the Lyapunov vector function method. 2. Decomposition of a complex power system. 3. Determination of the conditions of exponential stability for isolated subsystems of a multimachine system. 4. Creation of majorants and determination of the conditions of its existence for an aggregated energy system. 5. The study of the invariability of the majorizing system. 6. Software development, creation a majorizing system for an n-machine power system with a given communication structure. Overall, using the Lyapunov vector function method, the majoritarian comparison model of a multimachine system was obtained. The idea was proposed to decompose the original system into subsystems with diagonal dominance to create a majorizing model. Accomplishment of this condition make it possible to use the Lyapunov functions constructed for isolated subsystems in subsystems with connections.