On the Impact of Fault Ride-Through on Transient Stability of Autonomous Microgrids: Nonlinear Analysis and Solution

Fault ride-through (FRT) is essential for inverter-interfaced distributed generation (IIDG) units to protect semiconductor switches from being imposed to overcurrent conditions while the transients are securely passed. To this end, a current limiting strategy is adopted for IIDG units, mostly embedded in control loops, to limit the current within the withstand-able band and to make the IIDG units stay connected to the (micro) grid during the transient. However, the FRT/current limiting of grid-forming inverters affects the transient stability of the autonomous droop-based microgrids and may make them unstable, which yet has not been well-explored in the literature. This issue is considered in this work through a scrupulous observation of the second-order nonlinear differential equation describing the frequency-phase angle dynamics and investigating the problem through the Lyapunov theory. The Chetaev's instability theorem, which is developed based on the Lyapunov direct method, is used to explore the instability conditions due to the FRT. It is revealed that the phase angle variation, as a consequence of the current limiting, and the arbitrary/resistive transient impedance of grid-forming inverters make the system unstable. Numerical and time-domain results through MATLAB/Simulink platform prove the validity of the models.