The information security risk of power systems has increased sharply due to the deep integration of information system and power physical system, where false data injection attack(FDIA) is a kind of the highly concealed and threatening cyber attacks for modern power system. Firstly, in this paper, to detect FDIA more accurately or efficiently, the problem of FDIA detection is transformed into the matrix separation problem based on proximal exchange-based alternating direction method of multipliers (PE-ADMM) and non-convex robust principal component analysis (NcRPCA). The two FDIA detection methods above have advantages in detection accuracy and computational efficiency respectively, but they are deficient in the other hand. Secondly, to improve the overall performance of FDIA detection on matrix separation, a novel FDIA detector on NcRPCA is proposed, where the proximal algorithm adopted in PE-ADMM is introduced to estimate disturbances, which can provide dynamic basis for adaptive setting of detection threshold. Finally, the experimental results of power systems show that the proposed FDIA detector has better robustness to noise and the overall detection performance is the best among six FDIA detection methods.