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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. [ABSTRACT FROM AUTHOR]

For the grid-connected inverter, grid voltage sag can be a typical phenomenon. From the prospective of safe and robust operation, the inverter should be stable when the grid voltage sag (or large disturbance) occurs. Although the inverter stability in this case has attracted considerable attentions, few studies have given suggestions on the system stability boundary and parameter design. To fill this gap, this article deeply discusses the large-signal stability of the system under different situations and reveals the quantified impact of the phase-locked loop (PLL) on the large-signal stability of the system based on the fundamental current-source model. The large-signal stability criterion and boundaries for grid voltage sags are established, which are instructive to the design of PLL parameters. Besides, a novel design guideline for the PLL parameters is proposed to ensure the robust operation of the system both under the steady-state and grid voltage sags, as well as to achieve good dynamic performance after large disturbance occurs. The theoretical, simulation, and experimental results show that the proposed stability boundary has certain accuracy and the PLL parameters design guideline can ensure the system stability both under steady-state and grid voltage sag conditions. [ABSTRACT FROM AUTHOR]

With the aim of reducing the number of sensors, this article investigates the single-sensor grid-following control for the LCL-filtered inverter system, and proposes an intuitive robust stability analysis method in the linear framework to handle power control and grid voltage variations in engineering practice. Specifically, through the use of a state-and-disturbance observer, the lumped-disturbance compensated suppression and nominal system full-state feedback technologies are equivalently realized. And the lumped-disturbance estimation carrying voltage phase information at the point of common coupling is further used as synchronization target of the phase-locked loop (PLL) to achieve grid-following control, and the resulting phase-shift is further corrected by accurate phase compensation. In addition, due to the nonlinear nature of the PLL and the power control and grid voltage variations, the system analysis is faced with the dilemma of complex nonlinear analysis or small-signal analysis without a fixed equilibrium point. In this case, a PLL small-signal model with bounded parameter perturbation characterizing power control and grid voltage variations is developed, and further incorporated into the output impedance modeling of the single-sensor grid-following controlled inverter. According to the edge theorem, the system stability in the studied uncertain region is analyzed via four edge output impedances, and appropriate control parameters are selected accordingly. Finally, the experimental results from a downscaled prototype are provided to verify the effectiveness of the proposed single-sensor grid-following control scheme. [ABSTRACT FROM AUTHOR]

In this article, the stability problem is investigated for a class of time-invariant current controlled LCL-type weak-grid-tied inverter (WGTI) system. Considering that the existing stability analysis methods rarely effectively handle the adverse effects of both sinusoidal pulsewidth modulation (SPWM) saturation and plant uncertainty, and the corresponding theoretical results are poor in accuracy and completeness, this article proposes an intuitive stability analysis method in Laplace-domain to ensure the system robustness against SPWM saturation and plant uncertainty. Specifically, the describing function (DF) is employed to characterize the averaged SPWM saturation nonlinear model in Laplace domain. By designing equivalent functions without the poles inside the right-half s-plane, the Nyquist criterion required by the DF is equivalently converted into the Hurwitz criterion of closed-loop characteristic polynomial with interval coefficients containing uncertain circuit parameters. Subsequently, by means of the Kharitonov’s theorem, the interval characteristic polynomial is transformed into four Kharitonov polynomials with fixed parameters that are easy to analyze. The state-and-disturbance-observer (SDO)-based current controlled WGTI system is adopted as a case of application study. In order to reduce the conservatism of the Kharitonov’s theorem applied here, a “pointwise” stability analysis on the grid impedance is implemented. Finally, the controller parameters are determined by stability region analysis with different grid impedance points, and the effectiveness of the proposed method is further verified by a series of steady-state and transient experiments. [ABSTRACT FROM AUTHOR]

Considering that the traditional linearization method cannot accurately analyze the grid-tied inverter (GTI) system with nonlinear nature, in the single-phase case, a novel nonlinear model for the GTI system considering nonlinear factors, including synchronous reference frame phase-locked loop (PLL) and duty-cycle saturation in pulsewidth modulation, is proposed, and the corresponding global asymptotic stability condition is given. Specifically, some system nonlinear factors, e.g., duty-cycle saturation phenomenon and Park (dq) transformation and cosine operation in second-order generalized integrator-based PLL (SOGI-PLL), are investigated, and their sector-bounded conditions are derived. In order to seek less conservative results, the system state of the SOGI-PLL is restructured such that the linear part of the PLL system can be stabilized. Then, the nonlinear state-space model with sector bounded for the whole GTI system is formulated. Furthermore, the deduced sector conditions are introduced into the derivation of the Lyapunov function by using the S-procedure lemma, and the global asymptotic stability condition of the inverter system is, thus, obtained. The system stability regions under different grid impedances, current references, and control parameters are further analyzed. Finally, the effectiveness of the proposed theories is fully supported by transient experimental results. [ABSTRACT FROM AUTHOR]

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. Modelings of single-inverter and multiple-inverter 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 the readers to design a proper PLL for DPGSs. [ABSTRACT FROM AUTHOR]

The performance of the grid-connected inverter was affected by the uncertainty of the grid conditions including the background distortion and the grid impedance. Typically, the feedforward of the grid voltage at the point of common coupling (PCC) highly suppressed the grid current harmonics caused by the grid voltage distortion; however, the PCC grid usually had a nonnegligible grid impedance, and the PCC voltage feedforward aroused serious grid current harmonics or instability. This study proposes a novel adaptive algorithm for the PCC voltage feedforward to work well with the varied grid impedance. In the proposal, the band-pass filters at the harmonic frequencies are used to detect the variation of the grid impedance as well as to facilitate the adaptive PCC voltage feedforward. It is not necessary to inject an additional harmonic to estimate the grid impedance. The basic principles as well as the realization and logic of the proposed algorithm are detailed, and some selected waveforms are provided to verify the superior performance. Compared with the typical robust design or adaptive control, the proposed algorithm does not have to sacrifice the dynamic or the harmonics rejection performance, or to use the on or offline grid impedance estimation. [ABSTRACT FROM PUBLISHER]

In this paper, the inverter output impedance is passivized for solving the harmonic and the stability problems in the multiparallel inverters. The harmonics are easily aroused because of the disturbances, and the system stability is challenged by the grid impedance. Based on the simplified equivalent impedance model, the two problems are analyzed in the low-frequency (LF) band and the high-frequency (HF) band, respectively. Aiming at improving the LF performance, the weighted-proportional grid voltage feedforward and the harmonic quasi-resonant controller with phase compensation are proposed. The dynamic performance is enhanced with an additional current reference generation scheme. In order to improve the HF performance, a novel digital phase lead filter which brings the system back to a minimum-phase case is proposed. By the proposed control method, the high modulus of each inverter output impedance Zo is guaranteed, while the phase angles of Zo over the entire frequency band are avoided to be lower than −90°. The experiments based on four-parallel inverters have been conducted to validate the effectiveness of the proposed control method. [ABSTRACT FROM PUBLISHER]