Raigul Tuleuova

Prof. Raigul Tuleuova


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31 October 2026 in Mathematics
Verified
Journal Article
Open access
PDF file
Assel AbdildayevaAssel Abdildayeva
Assel Abdildayeva
GTGuldana Taganova
Guldana Taganova
NSNurgul Shazhdekeyeva
Nurgul Shazhdekeyeva
RTRaigul Tuleuova
Raigul Tuleuova
AAAinagul Adiyeva
Ainagul Adiyeva
ZSZhansaya Sabirova
Zhansaya Sabirova
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.