Since Smart-Islands (SIs) with advanced cyber-infrastructure are incredibly vulnerable to cyber-attacks, increasing attention needs to be applied to their cyber-security. False data injection attacks (FDIAs) by manipulating measurements may cause wrong state estimation (SE) solutions or interfere with the central control system performance. There is a possibility that conventional attack detection methods do not detect many cyber-attacks; hence, system operation can interfere. Research works are more focused on detecting cyber-attacks that target DC-SE; however, due to more widely uses of AC SIs, investigation on cyber-attack detection in AC systems is more crucial. In these regards, a new mechanism to detect injection of any false data in AC-SE based on signal processing technique is proposed in this paper. Malicious data injection in the state vectors may cause deviation of their temporal and spatial data correlations from their ordinary operation. The suggested detection method is based on analyzing temporally consecutive system states via wavelet singular entropy (WSE). In this method, to adjust singular value matrices and wavelet transforms' detailed coefficients, switching surface based on sliding mode controller are decomposed; then, by applying the stochastic process, expected entropy values are calculated. Indices are characterized based on the WSE in switching level of current and voltage for cyber-attack detection. The proposed detection method is applied to different case studies to detect cyber-attacks with various types of false data injection, such as amplitude, and vector deviation signals. The simulation results confirm the high-performance capability of the proposed FDIA detection method. This detection method's significant characteristic is its ability in fast detection (10 ms from the attack initiation); besides, this technique can achieve an accuracy rate of over 96.5%.INDEX TERMS Cyber-attack detection, wavelet transform, wavelet singular entropy, smart-island, false data injection attack, AC state.