Electricity Data Quality Enhancement Strategy Based on Low-Rank Matrix Recovery

Electricity consumption data form the foundation for the efficient and reliable operation of smart grids and are a critical component for ensuring effective data mining. However, due to factors such as meter failures and extreme weather conditions, anomalies frequently occur in the data, which adversely impact the performance of data-driven applications. Given the near full-rank nature of low-voltage distribution area electricity consumption data, this paper employs clustering to enhance the low-rank property of the data. Addressing common issues such as missing data, sparse noise, and Gaussian noise in electricity consumption data, this paper proposes a multi-norm optimization model based on low-rank matrix theory. Specifically, the truncated nuclear norm is used as an approximation of matrix rank, while the L1-norm and F-norm are employed to constrain sparse noise and Gaussian noise, respectively. The model is solved using the Alternating Direction Method of Multipliers (ADMM), achieving a unified framework for handling missing data and noise processing within the model construction. Comparative experiments on both synthetic and real-world datasets demonstrate that the proposed method can accurately recover measurement data under various noise contamination scenarios and different distributions of missing data. Moreover, it effectively separates principal components of the data from noise contamination.