As a common interface circuit for renewable energy integrated into the power grid, the inverter is prone to work under a three-phase unbalanced weak grid. In this paper, the instability of grid-connected inverters under the unbalanced grid condition is investigated. First, a dual second-order generalized integrator phase-locked loop (DSOGI-PLL)-based inverter under balanced and unbalanced conditions is modeled. A fourth-order impedance model is established to describe its impedance characteristics under the unbalanced grid condition. To analyze this multi-input multi-output system, a simplified stability analysis method based on the generalized Nyquist stability criterion and matrix theory is proposed. Then, the influences of circuit and control parameters on the stability of the grid-connected inverter system under the unbalanced grid condition are investigated. Finally, the accuracy of the derived frequency-coupled impedance model is verified via simulations, and the effectiveness of the proposed simplified stability analysis method on the system stability analysis is verified via both simulations and hardware experiments.

For a grid-connected inverter (GCI) without AC voltage sensors connected to the weak grid, the occurrence of frequency variation diminishes the accuracy of the estimated grid voltage and also degrades the output performance of the GCI. To solve these problems, based on virtual flux (VF) estimator, an improved Newton-Raphson method-based finite position set- phase locked loop (INR-FPS-PLL) and a frequency-adaptive control strategy with a quasi proportion complex integral (QPCI) controller are proposed. In detail, to meet the requirement for rapid acquisition of grid frequency information under frequency variation, the INR-FPS-PLL with only 6 iterations is developed. This PLL has low calculation burden and fast convergence. Then, because frequency variation reduces the accuracy of the estimated grid voltage, according to the principle of VF estimation, a grid voltage estimation method based on frequency-adaptive double first-order low-pass filter (DFO-LPF) with compensation techniques is proposed. Furthermore, to solve the performance degradation of GCI caused by grid frequency variation, the resonant frequency of the QPCI controller is adjusted according to the frequency information obtained by the INR-FPS-PLL, so that the zero-steady-state tracking error of grid current is ensured under frequency variation. Finally, simulation and experimental results verify the effectiveness of the proposed strategies.

To address the challenges of high-penetration renewables, hybrid systems utilizing Grid-forming voltage source converters (GFM-VSCs) and Grid-following voltage source converters (GFL-VSCs) have attracted significant attention. However, transient mode switching induced by current limiting in the GFM-VSC significantly reduces the stability margin of the hybrid systems. Addressing the challenge of accurately quantifying stability boundaries under switching-induced dynamics and coupling effects, this paper establishes the equivalent transient mathematical analysis model of the hybrid system. Subsequently, a systematic quantitative analysis method is proposed, which enables the accurate calculation of the critical clearing angle and critical clearing time by explicitly incorporating the transient mode switching of the GFM-VSC and the dynamic coupling effects. Based on the quantitative evaluation, the stability boundaries under varying control parameters and fault conditions are characterized. Furthermore, the interaction mechanism between the GFL-VSC and the GFM-VSC is unveiled, specifically how the dynamic variation of the virtual power angle difference and the current injection of the GFL-VSC impact the mode switching of the GFM-VSC. Finally, a transient synchronous stabilization enhancement strategy is proposed to facilitate the reversion of the GFM-VSC to its normal operating mode following a fault, with its effectiveness verified through simulations.