In recent research published in Engineering, researchers from Tianjin University present LineGen, a novel physics-guided method that enables the generation of super-resolution load data (SRLD) for distribution power systems. The study addresses a critical challenge in modern power grids: the need for high-frequency load data to manage distributed energy resources and ensure system stability, despite limitations in data collection and transmission infrastructure.

Load data resolution is pivotal for maintaining the reliability and efficiency of power distribution systems, especially as renewable energy sources and smart devices proliferate. Traditional infrastructure, such as smart meters, often struggles to support high-frequency data transmission, leading to sparse or noisy measurements. While deep learning models offer a promising solution, existing approaches—like convolutional neural networks (CNNs) and generative adversarial networks (GANs)—face limitations in fitting complex load patterns and lack interpretability. These methods also struggle to achieve significant resolution enhancements, typically capped at 100-fold, due to model complexity and training instability.

The proposed LineGen method combines physical modeling with deep learning to overcome these hurdles. At its core is a Data Distribution Transformation Model (DDTM), which uses ordinary differential equations (ODEs) to define a deterministic trajectory for transforming low-resolution load data (LRLD) into SRLD. Unlike end-to-end deep learning models, LineGen first constructs a straight-line transformation path between LRLD and SRLD, grounded in physics principles. This trajectory simplifies the problem by providing a clear, interpretable framework for data evolution.

A key component of LineGen is a time-embedded U-Net, a modified version of the popular U-Net architecture used in image processing. This network estimates the "transformation rate" along the straight-line path at any given time, allowing the model to learn how load data evolves from low to high resolution. To enhance training efficiency and stability, the researchers introduce a predict-correct (PC) loss relay training method, which alternates between two loss functions: one for predicting transformation rates and another for correcting generated SRLD against ground truth data. This dual approach improves model accuracy and mitigates the risk of local optima.

The team validated LineGen using the open-source Super-Resolution Perception State Estimation Dataset (SRPSED), which includes load data from thousands of households. Tests demonstrated that LineGen achieved an unprecedented 1000-fold resolution enhancement, far surpassing the 100-fold limit of previous methods. Quantitative metrics highlighted its superiority:

• Mean Absolute Percentage Error (MAPE) was as low as 1.508% at 5-fold resolution and remained below 5.179% even at 1000-fold, significantly outperforming CNNs, GANs, and traditional interpolation methods.
• Structural Similarity Index (SSIM), a measure of data characteristic similarity, approached 1, indicating that generated SRLD closely matched real-world load patterns.

Notably, LineGen’s physics-guided framework provided traceable interpretability, a critical advantage over black-box deep learning models. The straight-line ODE trajectory visualized the gradual transformation from smooth LRLD to stochastic SRLD, offering insights into how load fluctuations evolve with higher resolution.

The study’s findings have significant implications for smart grid management. High-resolution load data enables more accurate state estimation, fault detection, and demand forecasting, which are essential for integrating intermittent renewables and optimizing energy distribution. By reducing reliance on complex neural architectures and large datasets, LineGen offers a scalable, interpretable solution that could be adopted across diverse power grid environments.

The paper “LineGen: Physics-Guided Super-Resolution Load Data Generation via a Straight-Line Path,” is authored by Liqi Liu, Yanli Liu. Full text of the open access paper: https://doi.org/10.1016/j.eng.2025.02.012. For more information about Engineering, visit the website at https://www.sciencedirect.com/journal/engineering.