Solvability Regions of Affinely Parameterized Quadratic Equations
Name
1703.08881v1.pdf
Description
Accepted version
Size
415.11 KB
Format
Adobe PDF
Checksum (MD5)
1c13672108e60f132d8e022b45391daf
Author(s)
Dvijotham, Krishnamurthy
Nguyen, Hung
Turitsyn, Konstantin
Date Issued
January 2018
Journal
IEEE Control Systems Letters
Publisher
Institute of Electrical and Electronics Engineers
Citation
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.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution-Noncommercial-ShareAlike
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DOI of Published Version
https://doi.org/10.1109/lcsys.2017.2721380
