Matrix coding enabled impact mitigation against primary false data injection attacks in cyber-physical microgrids

The impact mitigation against false data injection attacks (FDIAs) has become a prevailing topic in enhancing the cyber resilience of microgrids. In particular, the primary FDIA (PFDIA) injecting biases into the sensor channel of the primary controller can fake the real physical states and result in devastating control commands to the power conversion device. Nevertheless, existing impact mitigation schemes cannot handle the PFDIA due to the primary control's strict real-time requirement. Therefore, this paper proposes a time- and cost-efficient impact mitigation scheme against the PFDIA by alternately encoding the transmitted measurement with an invertible coding matrix. Specifically, when the PFDIA is detected by unknown input observers (UIOs), two additional half-downsampled UIOs, which only require simple multiplication, addition, and subtraction operations within each control cycle, will be triggered to obtain the residuals under encoded and unencoded data. The complete bias vector can be then reconstructed recursively from these two residuals, and the bias will be removed from the compromised data to eliminate the malicious attack impact. Based on the theoretical analysis of reconstruction performance, the coding matrix is optimised to minimise the system noises' impact on reconstruction accuracy subject to the reconstruction stability and the encoding's hiddenness from the adversary. Finally, extensive experimental studies are conducted to validate the effectiveness, superiority, robustness, and lightweightness of the proposed impact mitigation scheme.