Zero-Shot Cross-Topology Generalization for DC Power Flow in Grids with High Renewable Penetration

This study examines zero-shot cross-topology generalization for DC power flow under varying load and renewable generation. A leakage-safe primary protocol uses 3500 physically generated IEEE-30 scenarios for development and internal evaluation, and 1000 IEEE-57 scenarios for external evaluation and reserve. Each bus is represented by 16 operating and topological features. The proposed KENO-Krylov operator combines bounded neural initialization, positive local preconditioning, explicit Kirchhoff residuals, and a 20-step Krylov/CG-like recurrence with a hard slack-bus constraint, using 2523 trainable parameters. On the locked IEEE-30 test, it achieves R2 = 0.999999 and angle MAE 0.00159°. On unseen IEEE-57, it retains R2 = 0.9440 and angle MAE 0.783°, but the median relative KCL residual remains 0.1433. Supplementary paired experiments quantify three renewable-generation regimes, external component ablations, and larger and radial networks. At the highest prescribed renewable scale, mean generation covers 49.63% and 53.25% of demand on IEEE-30 and IEEE-57. On 500 new IEEE-118 scenarios, angle MAE increases to 7.719° and median KCL to 0.974; radial stress tests reveal further accuracy limitations. Learned corrections slightly improve angle MAE over PCG-20, whereas convergent numerical solvers are more accurate and reused Cholesky factorization is faster in the measured setting. Nominal 90% uncertainty calibration does not transfer externally. The evidence supports comparative point-prediction transfer within the stated synthetic DC experiments, not universal topology generalization, operational security, or validity for nonlinear AC systems.