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The dynamic response of power grids to small transient events or persistentstochastic disturbances influences their stable operation. This paper studiesthe effect of topology on the linear time-invariant dynamics of power networks.For a variety of stability metrics, a unified framework based on the $H_2$-normof the system is presented. The proposed framework assesses the robustness ofpower grids to small disturbances and is used to study the optimal placement ofnew lines on existing networks as well as the design of radial (tree) andmeshed (loopy) topologies for new networks. Although the design task can beposed as a mixed-integer semidefinite program (MI-SDP), its performance doesnot scale well with network size. Using McCormick relaxation, the topologydesign problem can be reformulated as a mixed-integer linear program (MILP). Toimprove the computation time, graphical properties are exploited to providetighter bounds on the continuous optimization variables. Numerical tests on theIEEE 39-bus feeder demonstrate the efficacy of the optimal topology inminimizing disturbances.

Designing Power Grid Topologies for Minimizing Network Disturbances: An Exact MILP Formulation