With the advancement of the "Dual Carbon" strategy, the distribution network is transitioning from a traditional unidirectional radial supply to an active distribution network with the participation of multiple distributed power sources. The distribution cloud master station, which collects data from various distributed power sources and achieves multi-source coordination, relies on a sparse communication network and is thus vulnerable to the threat of False Data Injection(FDI) malicious attacks. To counteract the generalized FDI threat with high-frequency and unbounded high-order derivatives, a fully distributed secondary resilient control strategy for active distribution networks is proposed. By leveraging high-order integral suppression coefficients, the FDI in control channels with bounded finite-order derivatives is suppressed. It is proven by the Lyapunov method that the proposed defense strategy can achieve Uniformly Ultimately Bounded(UUB) convergence for frequency regulation and has been verified on an improved IEEE 9-bus active distribution network.