Impedance-Circuit-Based Stability Analysis for PLL-Synchronized Voltage Source Converter in Weak Grid

Impedance models of voltage source converters (VSCs) have been extensively developed for stability analysis. However, conventional impedance models depict the VSC as an all-in-one transfer function, which neglects the interrelation of impedance elements with the control loop, thereby providing limited physical insight. To tackle this challenge, this article develops a novel impedance circuit model for phase-locked loop (PLL)-synchronized VSCs, which equivalently maps control algorithms (such as PLL, current control (CC), decoupling control, etc.) into circuit elements. This model offers a clear visualization of interactions among control loops and reveals the physical essence of the PLL-induced negative resistance and the coupling of the PLL dynamics to the operating point. By analyzing the discrete circuit elements, it is demonstrated that introducing virtual impedance via q-axis voltage feedforward and increasing CC proportional gain are equivalent. However, since the introduction of virtual impedance results in oscillations of the VSC at high-power level, a method for optimizing the CC control parameters to improve system stability is proposed. Experimental results validate the accuracy of the proposed method.