Solvability Regions of Affinely Parameterized Quadratic Equations
Quadratic systems of equations appear in several applications. The results in this paper are motivated by quadratic systems of equations that describe equilibrium behavior of physical infrastructure networks like the power and gas grids. The quadratic systems in infrastructure networks are parameter...
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| Language: | English |
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Institute of Electrical and Electronics Engineers
2024
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| Online Access: | https://hdl.handle.net/1721.1/155096 |
| _version_ | 1824458203417542656 |
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| author | Dvijotham, Krishnamurthy Nguyen, Hung Turitsyn, Konstantin |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Dvijotham, Krishnamurthy Nguyen, Hung Turitsyn, Konstantin |
| author_sort | Dvijotham, Krishnamurthy |
| collection | MIT |
| description | Quadratic systems of equations appear in several applications. The results in this paper are motivated by quadratic systems of equations that describe equilibrium behavior of physical infrastructure networks like the power and gas grids. The quadratic systems in infrastructure networks are parameterized- the parameters can represent uncertainty (estimation error in resistance/inductance of a power transmission line, for example)or controllable decision variables (power outputs of generators,for example). It is then of interest to understand conditions on the parameters under which the quadratic system is guaranteed to have a solution within a specified set (for example, bounds on voltages and flows in a power grid). Given nominal values of the parameters at which the quadratic system has a solution and the Jacobian of the quadratic system at the solution i snon-singular, we develop a general framework to construct convex regions around the nominal value such that the system is guaranteed to have a solution within a given distance of the nominal solution. We show that several results from recent literature can be recovered as special cases of our framework,and demonstrate our approach on several benchmark power systems. |
| first_indexed | 2024-09-23T13:02:50Z |
| format | Article |
| id | mit-1721.1/155096 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2025-02-19T04:22:09Z |
| publishDate | 2024 |
| publisher | Institute of Electrical and Electronics Engineers |
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| spelling | mit-1721.1/1550962025-01-04T04:56:42Z Solvability Regions of Affinely Parameterized Quadratic Equations Dvijotham, Krishnamurthy Nguyen, Hung Turitsyn, Konstantin Massachusetts Institute of Technology. Department of Mechanical Engineering Quadratic systems of equations appear in several applications. The results in this paper are motivated by quadratic systems of equations that describe equilibrium behavior of physical infrastructure networks like the power and gas grids. The quadratic systems in infrastructure networks are parameterized- the parameters can represent uncertainty (estimation error in resistance/inductance of a power transmission line, for example)or controllable decision variables (power outputs of generators,for example). It is then of interest to understand conditions on the parameters under which the quadratic system is guaranteed to have a solution within a specified set (for example, bounds on voltages and flows in a power grid). Given nominal values of the parameters at which the quadratic system has a solution and the Jacobian of the quadratic system at the solution i snon-singular, we develop a general framework to construct convex regions around the nominal value such that the system is guaranteed to have a solution within a given distance of the nominal solution. We show that several results from recent literature can be recovered as special cases of our framework,and demonstrate our approach on several benchmark power systems. 2024-05-30T15:06:19Z 2024-05-30T15:06:19Z 2018-01 2024-05-30T14:56:56Z Article http://purl.org/eprint/type/JournalArticle 2475-1456 https://hdl.handle.net/1721.1/155096 K. Dvijotham, H. Nguyen and K. Turitsyn, "Solvability Regions of Affinely Parameterized Quadratic Equations," in IEEE Control Systems Letters, vol. 2, no. 1, pp. 25-30, Jan. 2018. en 10.1109/lcsys.2017.2721380 IEEE Control Systems Letters Creative Commons Attribution-Noncommercial-ShareAlike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers arxiv |
| spellingShingle | Dvijotham, Krishnamurthy Nguyen, Hung Turitsyn, Konstantin Solvability Regions of Affinely Parameterized Quadratic Equations |
| title | Solvability Regions of Affinely Parameterized Quadratic Equations |
| title_full | Solvability Regions of Affinely Parameterized Quadratic Equations |
| title_fullStr | Solvability Regions of Affinely Parameterized Quadratic Equations |
| title_full_unstemmed | Solvability Regions of Affinely Parameterized Quadratic Equations |
| title_short | Solvability Regions of Affinely Parameterized Quadratic Equations |
| title_sort | solvability regions of affinely parameterized quadratic equations |
| url | https://hdl.handle.net/1721.1/155096 |
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