Convolutional tensor completion-based DSSE under high DER penetration and abnormal measurements

Unlike transmission systems with sufficient observability and complete network information, distribution networks face persistent challenges such as noisy measurements, limited observability, and incomplete or uncertain topology. Traditional distribution system state estimation (DSSE) methods rely heavily on explicit network models (that is, feeder connectivity and line parameters), whereas existing canonical polyadic (CP)-based tensor completion approaches are limited by purely multilinear representations under distributed energy resource (DER)-related operating variability and measurement anomalies. To address these challenges, this paper proposes ConvCP, a self-supervised tensor completion framework for DSSE in which convolutional learning is embedded within the CP decomposition structure and operates without explicit network models. The method captures nonlinear dependencies through refined factor matrices and improves DSSE accuracy and robustness under diverse missing data scenarios, high levels of DER penetration, abnormal measurements, and suboptimal choices of tensor rank. Furthermore, given the high cost and limited deployment of phasor measurement units (PMUs) in distribution networks, the proposed approach is evaluated under limited-observability conditions with sparse voltage phasor measurements and less stringent phase-angle accuracy requirements than PMU-class measurements. Extensive studies are conducted on an IEEE 123-bus system and a realistic low-voltage distribution network to demonstrate the effectiveness of the proposed approach.