Suppression of Chaotic Oscillations in Small Energy Systems
The paper considers the suppression of chaotic oscillations in small energy systems that occur in emergency modes and lead to the phenomenon of voltage collapse, which corresponds to the process of voltage drop in the network, which can be accompanied by a complete shutdown of the affected area. The...
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| Format: | Article |
| Language: | Russian |
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Belarusian National Technical University
2022-08-01
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| Series: | Izvestiâ Vysših Učebnyh Zavedenij i Ènergetičeskih ob Edinennij SNG. Ènergetika |
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| Online Access: | https://energy.bntu.by/jour/article/view/2179 |
| _version_ | 1797879772117729280 |
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| author | V. N. Shashikhin J. M. Goryacheva S. V. Budnik |
| author_facet | V. N. Shashikhin J. M. Goryacheva S. V. Budnik |
| author_sort | V. N. Shashikhin |
| collection | DOAJ |
| description | The paper considers the suppression of chaotic oscillations in small energy systems that occur in emergency modes and lead to the phenomenon of voltage collapse, which corresponds to the process of voltage drop in the network, which can be accompanied by a complete shutdown of the affected area. The paper also presents a method that has been developed and that allows changing the spectrum of Lyapunov’s characteristic indicators and converting chaotic oscillations in a small power system to regular dynamic modes. The method of synthesis of control actions is based on the theorem of topological equivalence of hyperbolic nonlinear systems and their linearized models as well as on and the use of numerical integration of nonlinear differential equations describing the behavior of power systems in order to construct a phase portrait and calculate Lyapunov’s characteristic exponents. The results of the work consist in the synthesis of feedback, which ensures the formation of a spectrum of Lyapunov’s characteristic indicators with negative values. The suppression of chaotic regimes occurs by forming a spectrum of negative Lyapunov’s characteristic indicators in a closed system. The parameters of the regulator in the feedback circuit are determined using the modal control method based on the solution of the matrix algebraic Sylvester equation. The solution of the problem of transition from a chaotic regime to a regular movement in a small power system is considered. To test the operability of the proposed method of chaos suppression, the spectrum of Lyapunov’s characteristic indicators is calculated and trajectories in the phase space of the initial nonlinear system and the system with control action are constructed. For energy systems with chaotic dynamics, synthesized feedback makes it possible to suppress chaotic fluctuations and switch to regular modes, thereby preventing the occurrence of emergency modes. |
| first_indexed | 2024-04-10T02:52:33Z |
| format | Article |
| id | doaj.art-dbbda17df62240e69ce2d6a093cb372c |
| institution | Directory Open Access Journal |
| issn | 1029-7448 2414-0341 |
| language | Russian |
| last_indexed | 2024-04-10T02:52:33Z |
| publishDate | 2022-08-01 |
| publisher | Belarusian National Technical University |
| record_format | Article |
| series | Izvestiâ Vysših Učebnyh Zavedenij i Ènergetičeskih ob Edinennij SNG. Ènergetika |
| spelling | doaj.art-dbbda17df62240e69ce2d6a093cb372c2023-03-13T07:41:52ZrusBelarusian National Technical UniversityIzvestiâ Vysših Učebnyh Zavedenij i Ènergetičeskih ob Edinennij SNG. Ènergetika1029-74482414-03412022-08-0165433134010.21122/1029-7448-2022-65-4-331-3401816Suppression of Chaotic Oscillations in Small Energy SystemsV. N. Shashikhin0J. M. Goryacheva1S. V. Budnik2Санкт-Петербургский политехнический университет Петра ВеликогоСанкт-Петербургский политехнический университет Петра ВеликогоСанкт-Петербургский политехнический университет Петра ВеликогоThe paper considers the suppression of chaotic oscillations in small energy systems that occur in emergency modes and lead to the phenomenon of voltage collapse, which corresponds to the process of voltage drop in the network, which can be accompanied by a complete shutdown of the affected area. The paper also presents a method that has been developed and that allows changing the spectrum of Lyapunov’s characteristic indicators and converting chaotic oscillations in a small power system to regular dynamic modes. The method of synthesis of control actions is based on the theorem of topological equivalence of hyperbolic nonlinear systems and their linearized models as well as on and the use of numerical integration of nonlinear differential equations describing the behavior of power systems in order to construct a phase portrait and calculate Lyapunov’s characteristic exponents. The results of the work consist in the synthesis of feedback, which ensures the formation of a spectrum of Lyapunov’s characteristic indicators with negative values. The suppression of chaotic regimes occurs by forming a spectrum of negative Lyapunov’s characteristic indicators in a closed system. The parameters of the regulator in the feedback circuit are determined using the modal control method based on the solution of the matrix algebraic Sylvester equation. The solution of the problem of transition from a chaotic regime to a regular movement in a small power system is considered. To test the operability of the proposed method of chaos suppression, the spectrum of Lyapunov’s characteristic indicators is calculated and trajectories in the phase space of the initial nonlinear system and the system with control action are constructed. For energy systems with chaotic dynamics, synthesized feedback makes it possible to suppress chaotic fluctuations and switch to regular modes, thereby preventing the occurrence of emergency modes.https://energy.bntu.by/jour/article/view/2179бифуркацияхаосстабилизациямалая энергосистемауправлениеколебанияпараметрыхарактеристические показатели ляпуноваметод синтеза |
| spellingShingle | V. N. Shashikhin J. M. Goryacheva S. V. Budnik Suppression of Chaotic Oscillations in Small Energy Systems Izvestiâ Vysših Učebnyh Zavedenij i Ènergetičeskih ob Edinennij SNG. Ènergetika бифуркация хаос стабилизация малая энергосистема управление колебания параметры характеристические показатели ляпунова метод синтеза |
| title | Suppression of Chaotic Oscillations in Small Energy Systems |
| title_full | Suppression of Chaotic Oscillations in Small Energy Systems |
| title_fullStr | Suppression of Chaotic Oscillations in Small Energy Systems |
| title_full_unstemmed | Suppression of Chaotic Oscillations in Small Energy Systems |
| title_short | Suppression of Chaotic Oscillations in Small Energy Systems |
| title_sort | suppression of chaotic oscillations in small energy systems |
| topic | бифуркация хаос стабилизация малая энергосистема управление колебания параметры характеристические показатели ляпунова метод синтеза |
| url | https://energy.bntu.by/jour/article/view/2179 |
| work_keys_str_mv | AT vnshashikhin suppressionofchaoticoscillationsinsmallenergysystems AT jmgoryacheva suppressionofchaoticoscillationsinsmallenergysystems AT svbudnik suppressionofchaoticoscillationsinsmallenergysystems |