Document Type : Original Article

Authors

Department of Electrical Engineering, Faculty of Engineering, Shahrekord University

10.22111/ieco.2026.55000.1752

Abstract

In this paper, an adaptive observer-based cyber-attack detection and estimation problem is studied for smart grid under false data injection attack (FDIA). By invoking mathematical model of the smart grid, sliding mode observer (SMO) is proposed for estimating grid states and generating residual signal. By monitoring grid status, evaluating residual signal and comparing it with the appropriate threshold level, attack detection is done and alarm signal is generated. Upon alarm generation, attack estimation algorithm is activated to estimate the FDIA occurred at the vulnerable buses. In the proposed detection scheme, only the frequency deviations of the generator buses are required; also, no off-line learning phase and no prior knowledge about attack signal are required. Moreover, the proposed scheme is able to detect FDIA and exactly estimates the severity of the detected attack. The Lyapunov stability theorem is used to guarantee stability of the proposed state observer and the proposed attack estimation algorithm, separately. Simulation results for the IEEE six-bus network under single-point and multi-point FDIAs show that upon attack occurrence, the defined evaluation function exceeds from a defined threshold level, which makes attack detection after some milliseconds. Also, the reported mean square error shows that the proposed attack estimation strategy can precisely estimate the attack shape and severity and identify the under-attack bus.

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