Fréchet Power-Scenario Distance: A Metric for Evaluating Generative AI Models across Multiple Time-Scales in Smart Grids

Abstract--Generative artificial intelligence (AI) models in smart grids have advanced significantly in recent years due to their ability to generate large amounts of synthetic data, which would otherwise be difficult to obtain in the real world due to confidentiality constraints. A key challenge in utilizing such synthetic data is how to assess the data quality produced from such generative models. Traditional metrics such as sample-wise Euclidean distance and distributional distances applied directly to raw generated data inadequately reflect higher-order temporal dependencies and cross-temporal relationships between real and synthetic series, and thus struggle to discriminate generative quality. In this work, we propose a novel metric based on the Fr echet Distance (FD) estimated between two datasets in a learned feature space. The proposed method assesses synthetic data quality via distributional comparisons in a feature space derived from a model tailored to the smart grid domain. Empirical results demonstrate the superiority of the proposed metric across downstream tasks and generative models, enhancing the reliability of data-driven decision-making in smart grid operations. ENERA TIVE models in the electric energy sector have been an active field of research in the past few years, thanks to their potential to create realistic and diverse scenarios for system planning, reliability assessment, and renewable energy integration--ultimately enhancing grid resilience and operational efficiency. These models, such as Generative Adversarial Networks (GANs), allow researchers to access much larger sets of synthetic data across multiple time scales that would otherwise be unavailable due to confidentiality constraints [1]. In contrast to traditional methods that involve creating synthetic power networks and subsequently using commercial-grade simulation software to generate electrical measurement variables [2], these generative approaches leverage a data-driven methodology.