  Due to the insufficient measurements in the distribution system state
estimation (DSSE), full observability and redundant measurements are difficult
to achieve without using the pseudo measurements. The matrix completion state
estimation (MCSE) combines the matrix completion and power system model to
estimate voltage by exploring the low-rank characteristics of the matrix. This
paper proposes a robust matrix completion state estimation (RMCSE) to estimate
the voltage in a distribution system under a low-observability condition.
Tradition state estimation weighted least squares (WLS) method requires full
observability to calculate the states and needs redundant measurements to
proceed a bad data detection. The proposed method improves the robustness of
the MCSE to bad data by minimizing the rank of the matrix and measurements
residual with different weights. It can estimate the system state in a
low-observability system and has robust estimates without the bad data
detection process in the face of multiple bad data. The method is numerically
evaluated on the IEEE 33-node radial distribution system. The estimation
performance and robustness of RMCSE are compared with the WLS with the largest
normalized residual bad data identification (WLS-LNR), and the MCSE.
