Constructing Convex Inner Approximations of Steady-State Security Regions
Name
Constructing_Convex_Inner_Approximations_of_Steady-State_Security_Regions.pdf
Description
Accepted version
Size
687.82 KB
Format
Adobe PDF
Checksum (MD5)
1b28e7d8a57c4e034a6bce213339ef20
Author(s)
Nguyen, Hung D.
Dvijotham, Krishnamurthy
Turitsyn, Konstantin
Date Issued
January 2019
Journal
IEEE Transactions on Power Systems
Publisher
Institute of Electrical and Electronics Engineers
Citation
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.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-Noncommercial-ShareAlike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/tpwrs.2018.2868752
