Constructing Convex Inner Approximations of Steady-State Security Regions

Journal Article · 04 September 2018 · IEEE Transactions on Power Systems

DOI: https://doi.org/10.1109/TPWRS.2018.2868752 · OSTI ID:1468954

Nguyen, Hung Dinh ^[1]; Dvijotham, Krishnamurthy ^[2]; Turitsyn, Konstantin ^[1]

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1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
2. Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

Here, 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.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC05-76RL01830
• OSTI ID: 1468954
• Journal Information: IEEE Transactions on Power Systems, Vol. 34, Issue 1; ISSN 0885-8950
• Publisher: IEEECopyright Statement
• Country of Publication: United States
• Language: English