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Small-signal instability of grid-connected power converters may arise whenthe converters use a phase-locked loop (PLL) to synchronize with a weak grid.Commonly, this stability problem (referred as PLL-synchronization stability inthis paper) was studied by employing a single-converter system connected to aninfinite bus, which however, omits the impacts of power grid structure and theinteractions among multiple converters. Motivated by this, we investigate howthe grid structure affects PLL-synchronization stability of multi-convertersystems. By using Kron reduction to eliminate the interior nodes, an equivalentreduced network is obtained which contains only the converter nodes. Weexplicitly show how the Kron-reduced multi-converter system can be decoupledinto its modes. This modal representation allows us to demonstrate that thesmallest eigenvalue of the grounded Laplacian matrix of the Kron-reducednetwork dominates the stability margin. We also carry out a sensitivityanalysis of this smallest eigenvalue to explore how a perturbation in theoriginal network affects the stability margin. On this basis, we provideguidelines on how to improve the PLL-synchronization stability ofmulti-converter systems by PLL-retuning, proper placement of converters orenhancing some weak connection in the network. Finally, we validate ourfindings with simulation results based on a 39-bus test system.

Impacts of Grid Structure on PLL-Synchronization Stability of Converter-Integrated Power Systems