Graph Neural Networks for Voltage Stability Margins with Topology Flexibilities

High penetration of distributed energy resources (DERs) changes the flows in power grids causing thermal congestions which are managed by real-time corrective topology switching. It is crucial to consider voltage stability margin (VSM) as a constraint when modifying grid topology. However, it is nontrivial to exhaustively search using AC power flow (ACPF) for all control actions with desired VSM. Sensitivity methods are used to solve this issue of 'power flow-free VSM estimation' to screen candidate control actions. However, due to the volatile nature of DERs, sensitivity methods do not perform well near nonlinear operating regions which is overcome by solving ACPF. Here, we propose a new VSM estimation method that performs well at nonlinear operating regions without solving ACPF. We achieve this by formulating the learning of graph neural networks like the matrix-free power flow algorithms. We empirically demonstrate how this similarity bypasses the inaccuracy issues and performs well on unseen operating conditions and topologies without further re-training. The effectiveness is demonstrated on a power network with realistic load and generation profiles, various generation mix, and large control actions. The benefits are showcased in terms of speed, reliability to identify insecure controls, and adaptability to unseen scenarios and grid topologies.