Small-signal Stability Boundary of Heterogenous Multi-converter Power Systems Dominated by Phase-locked Loop Dynamics

While renewable resources are increasingly integrated into the electric power grid, the small-signal instability risk may be induced by grid-following converters using phase-locked loops (PLLs) for grid synchronization, especially under weak grid conditions. The analysis of the instability mechanism is complex in a multi-converter system due to the dynamic interaction between PLL-based converters and the power network. The analysis complexity is further increased in a heterogeneous multi-converter system (HMCS), where all converters have different control configurations and parameters from different manufacturers. To understand how the different PLL dynamics collectively affect the stability of the HMCS, this paper analytically derives the small-signal stability boundary condition of the HMCS dominated by the PLL dynamics (HMCS-DPLL). The derived stability boundary allows us to obtain analytical results about how the stability of the HMCS-DPLL is affected by grid strength, converter operating conditions, different PLL control parameters and the interaction among different PLLs. Based on the stability boundary condition, a computationally efficient method is also proposed to identify the design rationality of PLL control parameters as well as the small-signal stability and stability margin of the HMCS-DPLL. The analytical results and proposed method are validated by modal analysis and electromagnetic transient simulation with detailed models on a 9-converter heterogeneous system.