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

TL;DR

This paper develops theoretical error bounds for data-driven power grid models, showing how physical knowledge and training data size influence model accuracy and generalization in various scenarios.

Contribution

It introduces a Rademacher complexity-based method to quantify error bounds, incorporating physical knowledge to reduce data requirements for power grid models.

Findings

Error bounds decrease with more physical knowledge.

Additional training data improves model generalization.

Method applied to branch flow linearization and network equivalence.

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, and proposes an evaluation implementation based on Rademacher complexity theory. We answer key 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. 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.