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 polytop...
| Κύριοι συγγραφείς: | , , |
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| Άλλοι συγγραφείς: | |
| Μορφή: | Journal Article |
| Γλώσσα: | English |
| Έκδοση: |
2020
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| Θέματα: | |
| Διαθέσιμο Online: | https://hdl.handle.net/10356/143661 |
| _version_ | 1826128283187544064 |
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| author | Nguyen, Hung D. Dvijotham, Krishnamurthy Turitsyn, Konstantin |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Nguyen, Hung D. Dvijotham, Krishnamurthy Turitsyn, Konstantin |
| author_sort | Nguyen, Hung D. |
| collection | NTU |
| 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 | 2024-10-01T07:22:25Z |
| format | Journal Article |
| id | ntu-10356/143661 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:22:25Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-10356/1436612020-09-15T08:47:13Z Constructing convex inner approximations of steady-state security regions Nguyen, Hung D. Dvijotham, Krishnamurthy Turitsyn, Konstantin School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Feasibility Inner Approximation 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. Nanyang Technological University Accepted version 2020-09-15T08:47:13Z 2020-09-15T08:47:13Z 2018 Journal Article Nguyen, H. D., Dvijotham, K., & Turitsyn, K. (2019). Constructing convex inner approximations of steady-state security regions. IEEE Transactions on Power Systems, 34(1), 257-267. doi:10.1109/TPWRS.2018.2868752 0885-8950 https://hdl.handle.net/10356/143661 10.1109/TPWRS.2018.2868752 1 34 257 267 en IEEE Transactions on Power Systems © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: https://doi.org/10.1109/TPWRS.2018.2868752 application/pdf |
| spellingShingle | Engineering::Electrical and electronic engineering Feasibility Inner Approximation 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 |
| topic | Engineering::Electrical and electronic engineering Feasibility Inner Approximation |
| url | https://hdl.handle.net/10356/143661 |
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