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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2409.04399 |
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| _version_ | 1866913897100869632 |
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| author | Bouterakos, Andreas Tzounas, Georgios |
| author_facet | Bouterakos, Andreas Tzounas, Georgios |
| contents | The paper focuses on the numerical stability and accuracy of implicit time-domain integration (TDI) methods when applied for the solution of a power system model impacted by time delays. Such a model is generally formulated as a set of delay differential algebraic equations (DDAEs) in non index-1 Hessenberg form. In particular, the paper shows that numerically stable ordinary differential equation (ODE) methods, such as the trapezoidal and the Theta method, can become unstable when applied to a power system that includes a significant number of delayed variables. Numerical stability is discussed through a scalar test delay differential equation, as well as through a matrix pencil approach that accounts for the DDAEs of any given dynamic power system model. Simulation results are presented in a case study based on the IEEE 39-bus system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04399 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of the Theta Method for Systems with Multiple Time-Delayed Variables Bouterakos, Andreas Tzounas, Georgios Systems and Control The paper focuses on the numerical stability and accuracy of implicit time-domain integration (TDI) methods when applied for the solution of a power system model impacted by time delays. Such a model is generally formulated as a set of delay differential algebraic equations (DDAEs) in non index-1 Hessenberg form. In particular, the paper shows that numerically stable ordinary differential equation (ODE) methods, such as the trapezoidal and the Theta method, can become unstable when applied to a power system that includes a significant number of delayed variables. Numerical stability is discussed through a scalar test delay differential equation, as well as through a matrix pencil approach that accounts for the DDAEs of any given dynamic power system model. Simulation results are presented in a case study based on the IEEE 39-bus system. |
| title | Stability of the Theta Method for Systems with Multiple Time-Delayed Variables |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2409.04399 |