Algorithmic Construction of Lyapunov Functions for Power System Stability Analysis.
We present a methodology for the algorithmic construction of Lyapunov functions for the transient stability analysis of classical power system models. The proposed methodology uses recent advances in the theory of positive polynomials, semidefinite programming, and sum of squares decomposition, whic...
| Egile Nagusiak: | , , |
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| Formatua: | Journal article |
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2013
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| _version_ | 1826280429271908352 |
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| author | Anghel, M Milano, F Papachristodoulou, A |
| author_facet | Anghel, M Milano, F Papachristodoulou, A |
| author_sort | Anghel, M |
| collection | OXFORD |
| description | We present a methodology for the algorithmic construction of Lyapunov functions for the transient stability analysis of classical power system models. The proposed methodology uses recent advances in the theory of positive polynomials, semidefinite programming, and sum of squares decomposition, which have been powerful tools for the analysis of systems with polynomial vector fields. In order to apply these techniques to power grid systems described by trigonometric nonlinearities we use an algebraic reformulation technique to recast the system's dynamics into a set of polynomial differential algebraic equations. We demonstrate the application of these techniques to the transient stability analysis of power systems by estimating the region of attraction of the stable operating point. An algorithm to compute the local stability Lyapunov function is described together with an optimization algorithm designed to improve this estimate. |
| first_indexed | 2024-03-07T00:13:35Z |
| format | Journal article |
| id | oxford-uuid:7a13e06c-2c66-45fb-a556-f4dac8a4dda1 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:13:35Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:7a13e06c-2c66-45fb-a556-f4dac8a4dda12022-03-26T20:41:31ZAlgorithmic Construction of Lyapunov Functions for Power System Stability Analysis.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7a13e06c-2c66-45fb-a556-f4dac8a4dda1Symplectic Elements at Oxford2013Anghel, MMilano, FPapachristodoulou, AWe present a methodology for the algorithmic construction of Lyapunov functions for the transient stability analysis of classical power system models. The proposed methodology uses recent advances in the theory of positive polynomials, semidefinite programming, and sum of squares decomposition, which have been powerful tools for the analysis of systems with polynomial vector fields. In order to apply these techniques to power grid systems described by trigonometric nonlinearities we use an algebraic reformulation technique to recast the system's dynamics into a set of polynomial differential algebraic equations. We demonstrate the application of these techniques to the transient stability analysis of power systems by estimating the region of attraction of the stable operating point. An algorithm to compute the local stability Lyapunov function is described together with an optimization algorithm designed to improve this estimate. |
| spellingShingle | Anghel, M Milano, F Papachristodoulou, A Algorithmic Construction of Lyapunov Functions for Power System Stability Analysis. |
| title | Algorithmic Construction of Lyapunov Functions for Power System Stability Analysis. |
| title_full | Algorithmic Construction of Lyapunov Functions for Power System Stability Analysis. |
| title_fullStr | Algorithmic Construction of Lyapunov Functions for Power System Stability Analysis. |
| title_full_unstemmed | Algorithmic Construction of Lyapunov Functions for Power System Stability Analysis. |
| title_short | Algorithmic Construction of Lyapunov Functions for Power System Stability Analysis. |
| title_sort | algorithmic construction of lyapunov functions for power system stability analysis |
| work_keys_str_mv | AT anghelm algorithmicconstructionoflyapunovfunctionsforpowersystemstabilityanalysis AT milanof algorithmicconstructionoflyapunovfunctionsforpowersystemstabilityanalysis AT papachristodouloua algorithmicconstructionoflyapunovfunctionsforpowersystemstabilityanalysis |