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

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Abstract
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 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-siganl 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 stabiity 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.
Funding Information
  • National Natural Science Foundation of China (U2166204, 51922094)

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