Bounding Machine Learning Model Errors in Power Grid Analysis

Machine learning methods analysis power grids under incomplete physical information, and their accuracy has been mostly validated empirically using excessive testing datasets. We explore error bounds for machine learning methods under all possible scenarios, and propose an evaluation implementation base on Rademacher complexity theory. We answer key questions in learning practices: how much training data is required to guarantee a certain bound on inaccuracy, and how partial physical knowledge can be utilized to reduce the required amount of data. Our results are crucial for the secure and explanatory application of data-driven methods in power grid analysis. We demonstrate the proposed method by finding generalization error bounds in branch flow linearization and external network equivalent under different degree of physical knowledge.