Abstract: PMUs suffer from corrupted measurements such as data missing, false data and noise due to different factors such as communication contingency, cyber-attacks and electromagnetic interference. Existing phasor measurement unit (PMU) measurement recovery algorithms cannot simultaneously meet the requirements of high precision, rapid processing and adaptability to multiple scenarios. This paper proposed a measurement recovery algorithm based on the reduced nuclear norm, which used the high-dimensional and low-rank properties of PMU measurements to perform low-order singular value decomposition in the proposed algorithm, and extracted the principal components from the corrupted measurements. It could restore the measurements in multiple modes and different states of the system with high accuracy. In order to further reduce the recovery time consumption of large-scale power system measurements and speed up the iteration efficiency, the adaptive penalty factor and the distributed alternating direction method of multipliers (ADMM), framework were proposed to effectively limit the data recovery time at the level of seconds, which rendered its applicability in practical power systems.