Electricity Measurement Missing Data Recovery Method Based on Low Rank Tensor Completion with Triangular Canonical Polyadic Decomposition

With the deployment of intelligent electricity collection devices, high-frequency and multi-dimensional electricity measurement data enable detailed analysis of the electricity consumption behaviors in low-voltage distribution areas. However, data missing due to factors like device failures or network congestion can significantly compromise analysis accuracy, consequently affecting the reliability of data-driven applications such as user profiling, load forecasting, and demand response. To address this, an electricity measurement missing data recovery method based on low-rank tensor completion with triangular canonical polyadic decomposition (LRTC-TCP) is proposed. This method breaks through the limitations of traditional one-dimensional data recovery and constructs a third-order observation tensor for multi-dimensional electricity measurement data. A domain-knowledge-enhanced LRTC model is then developed by introducing the constraint based on the electrical correlation among measured parameters, thereby simultaneously leveraging temporal similarity within single-dimensional data and inter-dimensional correlations for accurate completion. Subsequently, TCP decomposition is employed to alleviate the computational complexity of singular value decomposition during tensor rank estimation, reducing the overall computational cost. The equivalence of this transformation is rigorously proven. Finally, the proposed method is evaluated on the public electricity load monitoring iAWE dataset. Experimental results show that the method improves recovery accuracy and stability, even under high missing rates and continuous missing segments.