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Data-driven models analyze power grids under incomplete physical information,and their accuracy has been mostly validated empirically using certain trainingand testing datasets. This paper explores error bounds for data-driven modelsunder all possible training and testing scenarios, and proposes an evaluationimplementation based on Rademacher complexity theory. We answer key questionsfor data-driven models: how much training data is required to guarantee acertain error bound, and how partial physical knowledge can be utilized toreduce the required amount of data. Our results are crucial for the evaluationand application of data-driven models in power grid analysis. We demonstratethe proposed method by finding generalization error bounds for twoapplications, i.e. branch flow linearization and external network equivalentunder different degrees of physical knowledge. Results identify how the boundsdecrease with additional power grid physical knowledge or more training data.

Bounding Regression Errors in Data-driven Power Grid Steady-state Models