A sufficient condition for small-signal synchronization stability with applications to PLL-dominated oscillation mode analysis

Small-signal instability in a wide frequency range due to the dynamic interaction between converters and the AC grid has attracted wide attention in recent years. Various impedance/admittance-based analysis methods are frequently adopted to resolve such problems. However, the stability criterion of the heterogeneous multi-converter system is not visually straightforward with admittance-based methods, because the complex coupling between admittances makes the stability criterion very difficult to be reduced. To overcome the shortcomings of those methods, an eigenvalue-free small-signal stability criterion is proposed by introducing the numerical range and Gershgorin discs theorem into the admittance model of multi-converter systems. By using Gershgorin discs to cover the numerical range of the system frequency domain admittance matrix, a transfer function of a single-input and single-output (SISO) system with variable weights is induced to perform the eigenvalue-free small-signal stability criterion, which provides a simple sufficient condition for system stability. Moreover, the SISO system is a weighted sum of admittances of heterogeneous converters, which illustrates that the stability of a heterogeneous multi-converter system is a tradeoff for heterogeneous single-converter systems. Finally, the effectiveness of the proposed method is demonstrated through eigenvalue analysis and simulation results based on a multi-converter test system.