A spatial multi-scale reservoir computing framework for power flow analysis in power grids

With the ongoing evolution of modern power grids, power flow calculation, which is the cornerstone of power system analysis and operation, has become increasingly complex. While promising, existing data-driven methods struggle with key challenges: poor generalization in data-scarce scenarios, efficiency bottlenecks when integrating physical laws, and a failure to capture higher-order interactions within the grid. To address these challenges, this paper proposes a Spatial Multi-scale Reservoir Computing framework that seamlessly incorporates functional matrix and physical information to solve power flow calculation. The framework utilizes parallel readout layer parameters to construct the functional matrix and integrates physical information to create multi-scale information processing mechanism and readout constraints. By improving the reservoir computing model, the framework also combines the reservoir paradigm with the inherent physical characteristics of power grids while maintaining computational efficiency. Experimental results demonstrate that presented framework achieves exceptional performance across various IEEE bus systems, showcasing superior generalization in data-scarce scenarios, as well as improvement in computational speed, prediction accuracy, and robustness, while ensuring the feasibility of the output results.