With the surge in power demand and the accelerated deployment of smart grid construction, power systems have progressively transitioned into Cyber physical systems (CPS). While the capabilities for precise intelligent sensing of system states and control have significantly improved, the exposure of power cyber physical systems to the external cyberspace has continuously expanded. In this context, False data injection attacks targeting the information layer have become one of the most threatening cyber attack methods at present due to their characteristics of strong concealment and great destructiveness. In addressing this problem, this paper presents an active detection approach. First, from the perspective of attackers, an l2-norm-based attack cost optimization model is constructed, which is employed as a verification benchmark to uncover the security flaws of traditional passive defense systems in resisting FDIA. Second, from the the perspective of defenders, a partition-based active detection method utilizing random signals is further developed. This method employs the K-means clustering algorithm to partition large-scale systems into multiple subsystems based on electrical parameters, and then injects random signals into each subsystem and extracts these signals after information transmission. Unlike traditional residual norm detection methods, the proposed approach identifies attacks by leveraging covariance changes between the excitation signals and residuals. Finally, the effectiveness and low false positive rate of the method are validated in the IEEE 14-bus system.