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The dynamic response of power grids to small transient events or persistent stochastic disturbances influences their stable operation. This paper studies the effect of topology on the linear time-invariant dynamics of power networks. For a variety of stability metrics, a unified framework based on the H2 -norm of the system is presented. The proposed framework assesses the robustness of power grids to small disturbances and is used to study the optimal placement of new lines on existing networks as well as the design of radial (tree) and meshed (loopy) topologies for new networks. Although the design task can be posed as a mixed-integer semidefinite program (MI-SDP), its performance does not scale well with network size. Using McCormick relaxation, the topology design problem can be reformulated as a mixed-integer linear program (MILP). To improve the computation time, graphical properties are exploited to provide tighter bounds on the continuous optimization variables. Numerical tests on the IEEE 39-bus feeder demonstrate the efficacy of the optimal topology in minimizing disturbances.
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An MILP Approach for Distribution Grid Topology Identification using Inverter Probing
Although knowing the feeder topology and line impedances is a prerequisite for solving any grid optimization task, utilities oftentimes have limited or outdated information on their electric network assets. Given the rampant integration of smart inverters, we have previously advocated perturbing their power injections to unveil the underlying grid topology using the induced voltage responses. Under an approximate grid model, the perturbed power injections and the collected voltage deviations obey a linear regression setup, where the unknown is the vector of line resistances. Building on this model, topology processing can be performed in two steps. Given a candidate radial topology, the line resistances can be estimated via a least-squares (LS) fit on the probing data. The topology attaining the best fit can be then selected. To avoid evaluating the exponentially many candidate topologies, this two-step approach is uniquely formulated as a mixed-integer linear program (MILP) using the McCormick relaxation. If the recovered topology is not radial, a second, computationally more demanding MILP confines the search only within radial topologies. Numerical tests explain how topology recovery depends on the noise level and probing duration, and demonstrate that the first simpler MILP yields a tree topology in 90% of the cases tested.
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- Award ID(s):
- 1751085
- PAR ID:
- 10143338
- Date Published:
- Journal Name:
- IEEE Power Tech Conference
- Page Range / eLocation ID:
- 1 to 6
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/PTC.2019.8810900
