In the distributed power generation systems (DPGSs) based on the renewable energies, the stability and harmonics of the grid-connected inverter are seriously affected by the uncertainties of the grid at the point of common coupling (PCC). More importantly, as several inverters are usually tied at the PCC together, the interactions among the inverters and the grid impedance can cause more serious harmonics and instabilities at the low frequencies. Hence, the phase-locked loop (PLL) affecting the low-frequency behaviors must be considered. This study aims to provide a comprehensive study of the stability and harmonics of single-phase inverters in the weak grid. Modellings of single-inverter and multiple-inverters systems considering the PLL are established. The impacts of different PLLs on the low-order current harmonics and stability are then studied. It has been proved that the maximum ability of inverters in suppressing the low-order grid current harmonics closely relates to the PLL, even if a harmonic resonant controller and/or PCC voltage feedforward is used. Thus, using different PLLs yields quite different performances. Simulation and experimental results will be given to demonstrate the analysis which is helpful for readers to design a proper PLL for DPGSs.

For the grid-connected LCL-filtered inverter, the grid current feedback active damping (AD) can assure a desirable bandwidth and a good robustness against certain parameter variations by using a minimal number of sensors. However, the inverter performance was seriously endangered by non-ideal conditions at the point of common coupling (PCC), including background voltage distortions and grid impedance varying. The grid current AD could not work well for wide grid impedance variation. Hence, in this study, the robustness with such control is discussed and its relations with system parameters are derived through mathematic derivations. It is proved that, for the typical grid current AD control, a contradiction between high bandwidth and high robustness exists. On the basis of analyzing the reasons for the limitations of the typical control, a systematic approach for enhancing the robustness under complex grid conditions has been proposed. The proposed fundamental PCC voltage feedforward enhances the robustness while the proposed phase shaping compensator assures a higher robustness with a desired bandwidth. Comparative waveforms with the typical grid current AD control have been provided to verify the correctness of the analysis and the improvement of the proposed approach.

For single-phase grid-connected inverters, the second-order generalized integrator-based phase-locked loop (SOGI-PLL) is widely used for good harmonics attenuation and frequency adaptability. However, existing studies usually neglect the frequency feedback loop in the modeling and design process, and thus, the potential instability caused by the frequency feedback loop is not well explained. Besides, the improper design of SOGI-PLL can lead to the inverter instability both under ideal and weak grid conditions. Therefore, by fully considering the coupling of the frequency feedback loop, this article establishes an accurate model for SOGI-PLL. Furthermore, effects of different PLL parameters on behaviors of both the SOGI-PLL itself and the inverter are studied, based on which a graphical method for PLL parameters design is proposed. As proved, the frequency feedback loop can deteriorate the stability and performance of both SOGI-PLL itself and inverter system, especially if rapid transient is expected. The modeling method is also extended to the low-pass filter-SOGI-PLL and the improved parameters design is discussed. Experimental results verify the correctness of the proposed PLL model and the abovementioned analysis results. The proposed model is helpful to deeply reveal the instability mechanism and provides a reference for the PLL design under nonideal grid conditions.

For inverters, a phase-locked loop (PLL) is usually needed for the grid synchronization. Typically, for the single-phase inverters, the orthogonal-signal-generators based PLLs (e.g., delay-based PLL) can be used. However, if the grid at the point of common coupling (PCC) exhibits a large grid impedance, the inverter may not work well or even be unstable. In order to work satisfactorily in the very weak grid, this study aims to formulate a robust PLL. At first, by modeling the inverter output impedance and considering the frequency coupling effect, the stability of the typical delay-based PLL has been analyzed and the reason for the performance degradation has been explained. Then, based on analyzing the differences of PLL blocks under different PCC conditions, the robust PLL with the grid current feedforward is discussed. Compared with the typical PLL, the improvement of the system behaviors in the weak grid cases is mainly attributed to the extra term on the numerator of output impedance, which is introduced by the current feedforward of the proposed PLL. The selection of control parameters has been emphasized for maintaining the high robustness. At last, selected comparative waveforms have verified that the single-phase inverter can perform well even with the large grid impedance, without the grid impedance estimation.

This article presents a current control methodology equipped with a state and disturbance observer (SDO) to address the uncertain disturbance problem existing in an LCL-type single-phase grid-tied inverter system. In this methodology, disturbance feedforward compensation and full-state feedback of the combined proportional–integral (PI) regulator are utilized to provide more degrees of freedom for a robust design of the controller. In order to realize this technology without additional sensors, a reduced-order SDO is designed by decoupling the real inverter plant into a nominal model with lumped uncertainty and disturbance (LUD), making the estimation results more robust adaption for system uncertainty. Furthermore, the upper bound of the LUD is concerned and innovatively used to evaluate the size of the uncertainty region of the LUD estimated by the observer, which may be important to antidisturbance control. Other system performances, such as grid current distortion suppression and robust stability, are also analyzed. Finally, the effectiveness of the proposed control strategy is fully supported by simulation and experimental results.