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...
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| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/143661 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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