Small-Signal Stability Boundary of Heterogeneous Multi-Converter Power Systems Dominated By the Phase-Locked Loops' Dynamics

While renewable resources are increasingly integrated into the electric power system, the small-signal instability risk may be induced by grid-following converters using phase-locked loops (PLLs) for grid synchronization, especially in low short-circuit strength systems. The stability analysis complexity is further increased in such a heterogeneous multi-converter system (HMCS), where multiple converters may have different PLLs' control parameters provided by various vendors. To understand how the different PLLs' dynamics collectively affect the small-signal stability of the HMCS, we transform the HMCS into an equivalent homogeneous multi-converter system for the small-signal stability analysis. Then, we analytically derives the small-signal stability boundary condition of the HMCS dominated by the PLLs' dynamics (HMCS-DPLL). The derived stability boundary allows us to obtain analytical results about how the small-signal stability of the HMCS-DPLL is collectively affected by network structure, converter operating conditions, and different PLLs' control parameters. 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 the full-order models on a 9-converter heterogeneous system.