Bounding Regression Errors in Data-Driven Power Grid Steady-State Models

Abstract

Data-driven models analyze power grids under incomplete physical information, and their accuracy has been mostly validated empirically using certain training and testing datasets. This paper explores error bounds for data-driven models under all possible training and testing scenarios drawn from an underlying distribution, and proposes an evaluation implementation based on Rademacher complexity theory. We answer critical questions for data-driven models: how much training data is required to guarantee a certain error bound, and how partial physical knowledge can be utilized to reduce the required amount of data. Different from traditional Rademacher complexity that mainly addresses classification problems, our method focuses on regression problems and can provide a tighter bound. Our results are crucial for the evaluation and application of data-driven models in power grid analysis. We demonstrate the proposed method by finding generalization error bounds for two applications, i.e., branch flow linearization and external network equivalent under different degrees of physical knowledge. Results identify how the bounds decrease with additional power grid physical knowledge or more training data.