Constructing Convex Inner Approximations of Steady-State Security Regions
We propose a scalable optimization framework for estimating convex inner approximations of the steady-state security sets. The framework is based on Brouwer fixed point theorem applied to a fixed-point form of the power flow equations. It establishes a certificate for the self-mapping of a polytope...
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| Format: | Article |
| Language: | English |
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Institute of Electrical and Electronics Engineers
2024
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| Online Access: | https://hdl.handle.net/1721.1/155090 |
| _version_ | 1824458039632068608 |
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| author | Nguyen, Hung D. Dvijotham, Krishnamurthy Turitsyn, Konstantin |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Nguyen, Hung D. Dvijotham, Krishnamurthy Turitsyn, Konstantin |
| author_sort | Nguyen, Hung D. |
| collection | MIT |
| description | We propose a scalable optimization framework for estimating convex inner approximations of the steady-state security sets. The framework is based on Brouwer fixed point theorem applied to a fixed-point form of the power flow equations. It establishes a certificate for the self-mapping of a polytope region constructed around a given feasible operating point. This certificate is based on the explicit bounds on the nonlinear terms that hold within the self-mapped polytope. The shape of the polytope is adapted to find the largest approximation of the steady-state security region. While the corresponding optimization problem is nonlinear and non-convex, every feasible solution found by local search defines a valid inner approximation. The number of variables scales linearly with the system size, and the general framework can naturally be applied to other nonlinear equations with affine dependence on inputs. Test cases, with the system sizes up to 1354 buses, are used to illustrate the scalability of the approach. The results show that the approximated regions are not unreasonably conservative and that they cover substantial fractions of the true steady-state security regions for most medium-sized test cases. |
| first_indexed | 2024-09-23T10:43:47Z |
| format | Article |
| id | mit-1721.1/155090 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2025-02-19T04:19:33Z |
| publishDate | 2024 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | mit-1721.1/1550902024-12-21T06:05:53Z Constructing Convex Inner Approximations of Steady-State Security Regions Nguyen, Hung D. Dvijotham, Krishnamurthy Turitsyn, Konstantin Massachusetts Institute of Technology. Department of Mechanical Engineering We propose a scalable optimization framework for estimating convex inner approximations of the steady-state security sets. The framework is based on Brouwer fixed point theorem applied to a fixed-point form of the power flow equations. It establishes a certificate for the self-mapping of a polytope region constructed around a given feasible operating point. This certificate is based on the explicit bounds on the nonlinear terms that hold within the self-mapped polytope. The shape of the polytope is adapted to find the largest approximation of the steady-state security region. While the corresponding optimization problem is nonlinear and non-convex, every feasible solution found by local search defines a valid inner approximation. The number of variables scales linearly with the system size, and the general framework can naturally be applied to other nonlinear equations with affine dependence on inputs. Test cases, with the system sizes up to 1354 buses, are used to illustrate the scalability of the approach. The results show that the approximated regions are not unreasonably conservative and that they cover substantial fractions of the true steady-state security regions for most medium-sized test cases. 2024-05-29T19:14:26Z 2024-05-29T19:14:26Z 2019-01 2024-05-29T19:06:54Z Article http://purl.org/eprint/type/JournalArticle 0885-8950 1558-0679 https://hdl.handle.net/1721.1/155090 H. D. Nguyen, K. Dvijotham and K. Turitsyn, "Constructing Convex Inner Approximations of Steady-State Security Regions," in IEEE Transactions on Power Systems, vol. 34, no. 1, pp. 257-267, Jan. 2019. en 10.1109/tpwrs.2018.2868752 IEEE Transactions on Power Systems Creative Commons Attribution-Noncommercial-ShareAlike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers arxiv |
| spellingShingle | Nguyen, Hung D. Dvijotham, Krishnamurthy Turitsyn, Konstantin Constructing Convex Inner Approximations of Steady-State Security Regions |
| title | Constructing Convex Inner Approximations of Steady-State Security Regions |
| title_full | Constructing Convex Inner Approximations of Steady-State Security Regions |
| title_fullStr | Constructing Convex Inner Approximations of Steady-State Security Regions |
| title_full_unstemmed | Constructing Convex Inner Approximations of Steady-State Security Regions |
| title_short | Constructing Convex Inner Approximations of Steady-State Security Regions |
| title_sort | constructing convex inner approximations of steady state security regions |
| url | https://hdl.handle.net/1721.1/155090 |
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