An L1-and-L2-regularized nonnegative tensor factorization for power load monitoring data imputation

Abstract

As smart grid advance, Power Load Forecasting (PLF) has become a research hotspot. As the foundation of the forecasting model, the Power Load Monitoring (PLM) data takes on great importance due to its completeness, reliability and accuracy. However, monitoring equipment failures, transmission channel congestion and anomalies result in missing PLM data, which directly affects the performance of the PLF model. To address this issue, this paper proposes an L1-and-L2-Regularized Nonnegative Tensor Factorization (LNTF) model to impute PLM missing data. Its main idea is threefold: (1) combining L1 and L2 norms to achieve effective feature extraction and improve the model’s robustness; (2) incorporating two temporal-dependent linear biases to describe the fluctuations of PLM data; (3) adding nonnegative constraints to precisely define the nonnegativity of PLM data. Extensive empirical studies on two publicly real-world PLM datasets with 1,569,491 and 413,357 known entries and missing rates of 93.35% and 96.75% demonstrate that the proposed LNTF improves 14.04%, 59.31%, and 71.43% on average over the state-of-the-art imputation models in terms of imputation error, convergence rounds, and time cos, respectively. Its high computational efficiency and low imputation error make practical sense for PLM data imputation.