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

## TL;DR

This paper presents an exact MILP formulation for designing power grid topologies that minimize network disturbances, improving robustness and stability through optimized line placement and topology configuration.

## Contribution

It introduces a novel MILP-based approach for power grid topology design that effectively minimizes disturbances and enhances stability, addressing scalability issues of previous methods.

## Key findings

- Optimal topologies reduce network disturbances in IEEE test cases
- The MILP approach outperforms traditional design methods in stability metrics
- Graphical properties improve computational efficiency of the optimization

## Abstract

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 $H_2$-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.