Small-Signal Stability of Microgrids in DAE form under DoS Attacks with Contraction Analysis

This paper studies the small-signal stability of a distributed secondary controlled islanded AC microgrid under Denial-of-Service attacks in a semi-explicit nonlinear differential-algebraic equation form using contraction theory. Based on norm-2 matrix measurement of system generalized unreduced Jacobian, the stable region comprising two stable equilibrium states is determined by establishing relationship between secondary controller parameter and DoS attack duration factor. A numerical test in a 9-bus inverter-based microgrid is conducted for performance evaluation. The result shows the proposed method can find a sufficient condition for constructing stable regions under various DoS attack durations.