Modeling and Stability Analysis of Small Perturbations in Three-Phase LCL Grid-Connected Inverters

With the rapidly increasing penetration of renewable energy sources (photovoltaics and wind power), the modern electric grid is undergoing dominated by power inverters-interfaced resources. Consequently, their stability potentially challenges grid performances. When the grid strength is relatively weak, the phase-locked loop (PLL) within the grid-following (GFL) converter experiences disturbances in its output angle under small signal perturbations. Neglecting this disturbance may affect the accuracy of stability assessment. Hence, in this paper, the impedance model of GFL converters is initially derived by taking into account the PLL dynamics, based on the harmonic linearization theory. In combination with stability criteria, the adaptability of GFL converters under diverse grid strengths is explored, thereby uncovering the influence of the PLL bandwidth on system stability. Finally, a numerical model is established and validated through simulation results, demonstrating the correctness of the theoretical analysis.