The wide bandwidth of phase-locked loop (PLL) will increase the negative real part of the output impedance of the grid-connected inverter (GCI), thus destroying the stability of the weak grids. This article proposes a novel method to improve the system stability through decoupling the PLL and grid impedance. Initially, the coupling relationship between PLL and grid impedance is revealed. It can explain why the choice of PLL bandwidth and the grid impedance magnitude is limited. Then, the decoupling method is proposed where the primary control structure of GCI does not need to change and uses the structured voltage, the product of PCC voltage and grid admittance, as the improved input of PLL. The proposed method can achieve the full-frequency passive of the output impedance of GCI even if the PLL has high bandwidth and the impedance measurement error is up to 60%, which means the adverse stability effect of PLL on the system is eliminated. The theoretical analysis is verified by simulations and experiments.

The phase-locked loop (PLL)-caused couplings on the grid-connected converter (GCC) are strengthened by increasing its bandwidth and then incur synchronization instability. This article proposes a constant-coupling-effect-based PLL (CCE–PLL) to resolve the aforementioned issues. Initially, the feature of the PLL-caused couplings on GCC is explored. It exhibits that the couplings are varied along with the PLL bandwidth hence jeopardizing the system's stability. Subsequently, the CCE–PLL with a constant and low coupling regardless of its bandwidth on the GCC is proposed. It illustrates that the CCE–PLL bandwidth does not influence the GCC's impedance response, bringing the GCC and CCE–PLL can be designed separately. Last, the experiments confirm that using CCE–PLL, the system has high robustness against grid impedance variation, and the GCC is capable of injecting/absorbing 1.0 per unit active power in a very weak grid. Moreover, the system attains good anti-interference ability and transient performance under system disturbances thanks to the permission usage of the high CCE–PLL bandwidth.

The weak grids may be unstable due to the negative resistance behavior of the grid-connected inverter (GCI) caused by the synchronization unit with the Phase-Locked Loop (PLL). This paper proposes a passivity enhancement method to attain the positive output resistance of GCI in qq channel. Initially, the impedance decomposition is utilized to reveal the reason for the negative output resistance brought by PLL. Secondly, with decomposed impedance, a novel PLL by adding a pre-filter and an impedance phase regulator with a normalized amplitude to the input of traditional SRF-PLL is proposed. Afterward, the effect of the critical system parameters and GCI operating conditions on the GCI’s passivity is discussed based on the established small-signal impedance model. Theoretical analysis manifests that the proposed PLL does not affect the system’s stability under rectifier mode and brings the passivity of GCI’s output impedance in qq channel in broad system parameters under inverter mode. Lastly, the experiments are implemented, verifying that using the proposed PLL, the instability caused by the intersection between grid and GCI impedances is removed thanks to the passivity. And the system can operate at 1.0 per unit active power reference under the very-weak-grid conditions.

Grid-Connected Inverters (GCIs) with Voltage Harmonics Compensation function (VHCF) have been widely applied to ensure the quality of bus voltages in weak grids, while in the analysis and design process of VHCF-GCI, the influences of Phase-Locked Loop (PLL) are usually ignored. Covering this gap, the harmonic instability and harmonic amplification for VHCF-GCI considering the influence of PLL are explored. With the small-signal model of PLL, the mathematical descriptions of the influences of PLL dynamics on harmonic impedance control loop and current control loop are derived, and the small-signal output impedance of VHCF-GCI including the PLL dynamics is presented. Based on the impedance-based analysis, the stability and the harmonic suppression performance of VHCF-GCI with different parameters of stability margin and bandwidth for PLL are studied. The study results reveal that differing from the conventional conclusion that the PLL with high bandwidth and high stability margin ensures the stability for GCI in low-frequency domain, the PLL with high bandwidth and high stability margin brings about the instability and harmonic amplification for VHCF-GCI in harmonic-frequency domain. Thus, to attain stability and harmonic suppression performance of VHCF-GCI, the design approach for PLL parameters in a full-frequency range is presented. Lastly, the theoretical analysis is verified by simulation and experimental results.

Virtual synchronous generators (VSGs) are susceptible to transient instability, especially under large disturbances without equilibrium points (EPs). This paper proposes an additional frequency control to restore EPs and ensure transient stability. In this control, the damping effect is enhanced to improve the transient behavior, and the additional potential energy is introduced to restore EPs after detecting the transient instability characteristics of VSGs. Compared with previous stabilizing methods, the proposed method can address transient stability issues both with and without EPs, and it does not rely on any grid information. Simulations and experiments validate the effectiveness of this method.

This paper proposes a zero-tracking second-order generalized integrator-based frequency-locked loop (ZT-SOGI-FLL) with better dynamics and stability than conventional SOGI-FLL. Unlike the internal model principle, the ZT-SOGI-FLL reconstructs the input signal under frequency deviation by tracking the zeros. Also, it has the same compact structure as the conventional SOGI-FLL. A linearized model is then derived to show that the ZT-SOGI-FLL is always an over-damped or a critical-damper system. More importantly, the derived model proves that the ZT-SOGI-FLL has a larger damping factor and higher bandwidth than SOGI-FLL when the same SOGI gain is tuned. Finally, the input-to-state stability of ZT-SOGI-FLL is analyzed to support the high robustness to severe grid faults. Comparative experimental results show that the ZT-SOGI-FLL has a faster and smoother dynamic response with a higher stability margin than some commonly-used SOGI-based methods under grid faults.