Floquet Stability Analysis of Alternative Synchronization Strategies for Parallel Grid-following Distributed Generators

Nano-grids enable the integration of distributed generators (DGs) in small-scale contexts such as residential households. Such DGs typically utilize current regulators with a phase-locked-loop (PLL) to enable grid-following behavior, where synchronization can be achieved using two alternative strategies: direct-synchronization based on grid voltage measurements, or self-synchronization based on the current regulator outputs. This paper conducts a stability comparison between self- and direct-synchronization for a simplified nano-grid involving parallel single- and three-phase DG inverters. The combined system is modeled in the DQ-frame, enabling Jacobian linearization to be applied, resulting in a linear system with time-periodic coefficients. Floquet theory is then applied to the linearized model for stability analysis. The analytical predictions resulting from Floquet theory are validated with Altair PSIM simulation and experimental results, showing the benefits of self-synchronization.