A unified power-grid representation for reuse across network structures and computational tasks

Data-driven power-system models are typically developed for specific grids and computational tasks, but their performance can deteriorate markedly or even fail when network structures or analytical objectives change. This paper develops a unified grid representation that separates physical-grid description from downstream computation. A self-supervised encoder represents each grid as a variable number of fixed-dimensional node, branch and global vectors under a common latent description. Although pretrained only on systems with at most 270 buses, the frozen encoder transfers without adaptation to a 70,000-bus network, more than 250 times larger in bus count, while preserving 0.7919 bus-correspondence accuracy. The same representation supports four independently trained downstream tasks: power-flow calculation, reactive-power adjustment, operating-condition generation and transient-stability assessment. On the previously unseen 70,000-bus grid, power-flow calculation achieves mean errors of 0.108circ in phase angle and 3.8×10textsuperscript-6 p.u. in voltage magnitude. Reactive-power adjustment achieved a 75% PSASP-verified correction rate on the previously unseen 70,000-bus grid, while operating-condition generation delivered at least one PSASP-verified feasible state for 82.2% of requests on previously unseen 400--1,000-bus grid families. For transient-stability assessment, the frozen encoder achieves accuracy within 0.8 percentage points of full encoder adaptation under matched training conditions. These results demonstrate that a unified power-grid representation can be learned once and reused unchanged across structurally different power systems and heterogeneous computational tasks.