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Title: Constructing convex inner approximations of steady-state security regions
Authors: Nguyen, Hung D.
Dvijotham, Krishnamurthy
Turitsyn, Konstantin
Keywords: Engineering::Electrical and electronic engineering
Issue Date: 2018
Source: 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
Journal: IEEE Transactions on Power Systems 
Abstract: 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.
ISSN: 0885-8950
DOI: 10.1109/TPWRS.2018.2868752
Rights: © 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:
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:EEE Journal Articles

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