Zero-Shot Cross-Topology Generalization for DC Power Flow in Grids with High Renewable Penetration
5 affiliations
- 1Department of Software Engineering, International Engineering and Technological University, Almaty 050060, Kazakhstan
- 2Higher School of Information Technology and Engineering, Astana International University, Astana 010000, Kazakhstan
- 3Department of Mathematics and Methods of Teaching Mathematics, Faculty of Physics, Mathematics and Information Technology, Khalel Dosmukhamedov Atyrau University, Atyrau 060011, Kazakhstan
- 4Department of Fundamental Sciences, Faculty of Pedagogy, Yessenov University, Aktau 130000, Kazakhstan
- 5Department of Higher Mathematics, Saken Seifullin Kazakh Agrotechnical University, Astana 010000, Kazakhstan
Abstract
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.
Related
- Constraint-Embedded Fractal Self-Similar Generation of Synthetic Topologies for Receiving-End Power Grids with Rich Renewable Energy: A Hybrid Metaheuristic Approach
- Topology-aware HVT MTCMOS power gating for power–delay optimization of cascaded transmission-gate MUX and DEMUX
- Deep-learning side-channel analysis of embedded ML-KEM: Single-trace message recovery, cross-device generalization, and frequency-band leakage characterization
- In-Context Learning for Multi-Fidelity Multiscale Model Closure and Cross-Operator Out-Of-Distribution Generalization
- Rigorous nested cross-validation and external generalization-gap analysis of a machine-learning classifier for U-251 glioblastoma cytotoxicity
BibTeX
@article{abdildayeva2026zeroshot,
title = {{Zero-Shot Cross-Topology Generalization for DC Power Flow in Grids with High Renewable Penetration}},
author = {Assel Abdildayeva and Guldana Taganova and Nurgul Shazhdekeyeva and Raigul Tuleuova and Ainagul Adiyeva and Gulmira Nigmetova and Batikhan Urbissinova and Zhansaya Sabirova},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14213972},
url = {https://www.mdpi.com/2227-7390/14/21/3972},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Zero-Shot Cross-Topology Generalization for DC Power Flow in Grids with High Renewable Penetration
AU - Assel Abdildayeva
AU - Guldana Taganova
AU - Nurgul Shazhdekeyeva
AU - Raigul Tuleuova
AU - Ainagul Adiyeva
AU - Gulmira Nigmetova
AU - Batikhan Urbissinova
AU - Zhansaya Sabirova
PY - 2026
DA - 2026/10/31
JO - Mathematics
DO - 10.3390/math14213972
UR - https://www.mdpi.com/2227-7390/14/21/3972
AB - 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.
SN - 2227-7390
ER -