title: ÐÐµÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ ÑÐ½ÐµÑÐ³Ð¾ÑÐ¸ÑÑÐµÐ¼Ñ Ð¡ÐµÐ²ÐµÑÐ¾-ÐÐ°Ð¿Ð°Ð´Ð° Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐ¸Ð½Ñ ÑÐ¾Ð½Ð¸Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ Ð²ÐµÐºÑÐ¾ÑÐ½ÑÑ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹
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: Verification of dynamic models of the North-West power system based on phasor measurement data
Creators: name: Ð¤ÑÑÑÐµÐ², ÐÐ¸ÐºÐ¸Ñ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: 2023
Subjects: ÑÐ¸ÑÑÐµÐ¼Ð° Ð¼Ð¾Ð½Ð¸ÑÐ¾ÑÐ¸Ð½Ð³Ð° Ð¿ÐµÑÐµÑ Ð¾Ð´Ð½ÑÑ ÑÐµÐ¶Ð¸Ð¼Ð¾Ð²
Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ
Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ðµ ÐÐ¸Ð»ÑÐ±ÐµÑÑÐ°-Ð¥ÑÐ°Ð½Ð³Ð°
Ð¼ÐµÑÐ¾Ð´ ÐÑÐ¾Ð½Ð¸
Ð¿Ð¾Ð´Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²ÐµÐ½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ Ð¸Ð´ÐµÐ½ÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸
wide area measurement system
dynamic model
Hilbert-Huang transform
Prony method
subspace identification methods

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÐ¸ Ð²ÐµÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ ÑÐ°ÑÑÐ¸ ÑÐ½ÐµÑÐ³Ð¾ÑÐ¸ÑÑÐµÐ¼Ñ Ð¡ÐµÐ²ÐµÑÐ¾-ÐÐ°Ð¿Ð°Ð´Ð° Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð² ÑÐ°ÑÑÐ¾ÑÐ½Ð¾Ð¹ Ð¾Ð±Ð»Ð°ÑÑÐ¸. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1. ÐÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐ°ÑÑÐ¾ÑÐ½Ð¾-Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° Ðº Ð´Ð°Ð½Ð½ÑÐ¼, Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÐ¼ Ð¾Ñ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¼Ð¾Ð½Ð¸ÑÐ¾ÑÐ¸Ð½Ð³Ð° Ð¿ÐµÑÐµÑÐ¾Ð´Ð½ÑÑ ÑÐµÐ¶Ð¸Ð¼Ð¾Ð² (Ð¡ÐÐÐ ). 2. ÐÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð² Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²Ðµ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ð¹ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¿Ð¾Ð´Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²ÐµÐ½Ð½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¸Ð´ÐµÐ½ÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸. 3. Ð¡Ð¾Ð·Ð´Ð°Ð½Ð¸Ðµ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÐ¿ÑÐ¾ÑÐµÐ½Ð½Ð¾Ð¹ ÑÑÐµÐ¼Ñ ÑÐ°ÑÑÐ¸ ÑÐ½ÐµÑÐ³Ð¾ÑÐ¸ÑÑÐµÐ¼Ñ Ð¡ÐµÐ²ÐµÑÐ¾-ÐÐ°Ð¿Ð°Ð´Ð°. 4. ÐÐµÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð²Ð¾ Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ð¹ Ð¸ ÑÐ°ÑÑÐ¾ÑÐ½Ð¾Ð¹ Ð¾Ð±Ð»Ð°ÑÑÐ¸. Ð ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ»Ð¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ñ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ ÑÐ°ÑÑÐ¾ÑÐ½Ð¾-Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð°, Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑÐ¸Ðµ Ð¾Ð¿ÑÐµÐ´ÐµÐ»Ð¸ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÑ ÑÐ¾ÑÑÐ°Ð²Ð»ÑÑÑÐ¸Ñ Ð¸ÑÑÐ¾Ð´Ð½Ð¾Ð³Ð¾ ÑÐ¸Ð³Ð½Ð°Ð»Ð° Ð² ÑÐ°ÑÑÐ¾ÑÐ½Ð¾Ð¹ Ð¾Ð±Ð»Ð°ÑÑÐ¸ â ÑÐ°ÑÑá½¹ÑÑ Ð¸ Ð·Ð°ÑÑÑÐ°Ð½Ð¸Ñ. Ð ÑÐ°ÐºÐ¸Ð¼ Ð¼ÐµÑÐ¾Ð´Ð°Ð¼ Ð¾ÑÐ½Ð¾ÑÑÑÑÑ Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¤ÑÑÑÐµ, ÐÐ¸Ð»ÑÐ±ÐµÑÑÐ°-Ð¥ÑÐ°Ð½Ð³Ð° Ð¸ Ð¼ÐµÑÐ¾Ð´ ÐÑÐ¾Ð½Ð¸. Ð¢Ð°ÐºÐ¶Ðµ Ð±ÑÐ»Ð¸ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ñ Ð¿Ð¾Ð´Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²ÐµÐ½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ Ð¸Ð´ÐµÐ½ÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸, Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑÐ¸Ðµ Ð¾Ð¿ÑÐµÐ´ÐµÐ»Ð¸ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÑ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð² Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²Ðµ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ð¹, Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑ ÑÐ¾Ð»ÑÐºÐ¾ Ð´Ð°Ð½Ð½ÑÐµ Ð¾Ñ Ð¡ÐÐÐ . ÐÐ¾Ð¼Ð¸Ð¼Ð¾ ÑÑÐ¾Ð³Ð¾, Ð±ÑÐ»Ð° ÑÐ¾Ð·Ð´Ð°Ð½Ð° Ð¼Ð¾Ð´ÐµÐ»Ñ Ð½Ð° ÑÐ·ÑÐºÐµ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ ÑÐ¸ÑÑÐµÐ¼ Modelica. ÐÐ´ÐµÐºÐ²Ð°ÑÐ½Ð¾ÑÑÑ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð±ÑÐ»Ð° Ð¿ÑÐ¾Ð²ÐµÑÐµÐ½Ð° Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð´Ð°Ð½Ð½ÑÑ Ð¾Ñ Ð¡ÐÐÐ  Ð¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð² ÑÐ°ÑÑÐ¾ÑÐ½Ð¾Ð¹ Ð¾Ð±Ð»Ð°ÑÑÐ¸.
description: This work is devoted to the study of the possibility of verifying dynamic models of a part of the North-West power system using parameters in the frequen-cy domain. Tasks that were solved in the course of the study: 1. Application of time-frequency analysis methods to data received from the wide area measurement system (WAMS). 2. Determining the parameters of the state-space dynamic model using subspace identification methods. 3. Creation of a dynamic model of the North-West energy system simplified scheme. 4. Verification of the obtained models using parameters in the time and fre-quency domains. In the course of the work, various methods of time-frequency analysis were investigated, which make it possible to determine the parameters of the original signal components in the frequency domain - frequency and damping. These methods include the Fourier transform, Hilbert-Huang transform and the Prony method. Subspace identification methods were also considered, which allow deter-mining the parameters of a statespace dynamic model using only data from the WAMS. In addition, a model was created in the Modelica dynamic systems de-scription language. Adequacy of the obtained models was checked using data from the WAMS and parameters in the frequency domain obtained during the analysis of said data.