This paper presents an overview of the synchronization stability of converter-based resources under a wide range of grid conditions. The general grid-synchronization principles for grid-following and grid-forming modes are reviewed first. Then, the small-signal and transient stability of these two operating modes are discussed, and the design-oriented analyses are performed to illustrate the control impact. Lastly, perspectives on the prospects and challenges are shared.

The stationary-frame complex-valued frequencydomain modeling has been applied to characterize the frequencycoupling dynamics of three-phase converters. Yet, those models are generally derived through mathematical transformations of the linearized time-invariant models in the rotating dq-frame. A step-by-step modeling method with clear physical insight in the stationary frame is still missing. This article attempts to fill in the void by introducing a general stationary (αβ)-frame, threeport equivalent circuit model for the converter power stage, based on the direct linearization around time-periodic trajectories. The model not only reveals the frequency-coupling effect of the ac-dc dynamic interaction but also provides an explicit theoretical basis for incorporating the control dynamics. Moreover, the dependence of the frequency-coupling terms on the initial phase of the input voltage is pointed out. Considering the phase-dependent feature, a frequency scan method that can accurately measure the αβ-frame converter model is proposed. The measured frequency responses in both the nonlinear time-domain simulations and experimental tests validate the effectiveness of the frequency scan method and the theoretical analysis.

This paper presents a systematic evaluation on the impedance passivity of voltage-controlled voltage-source converters. The commonly used single-and dual-loop control structures with different linear controllers are compared extensively, considering the effect of the time delay involved in the control loop. A virtual impedance control, co-designed with different voltage control schemes, is then proposed to eliminate the negative output resistance till half of the sampling frequency, which improves the system stability for grid-forming converters in grid-connected applications. Both frequency-domain analysis and experimental results validate the theoretical findings.

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Small-signal instability issues of interconnected converter systems can be addressed by the impedance-based stability analysis method, where the impedance ratio at the point of common connection of different subsystems can be regarded as the open-loop gain, and thus the stability of the system can be predicted by the Nyquist stability criterion. However, the right-half plan (RHP) poles may be present in the impedance ratio, which then prevents the direct use of Nyquist curves for defining stability margins or forbidden regions. To tackle this challenge, this paper proposes a general rule of impedance-based stability analysis with the aid of Bode plots. The method serves as a sufficient and necessary stability condition, and it can be readily used to formulate the impedance specifications graphically for various interconnected converter systems. Experimental case studies validate the correctness of the proposed method.

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This article proposes a multifrequency admittance model for voltage-source converters with three-phase unbalanced grid voltages. The model is derived with multiple complex vectors and harmonic transfer functions, which is merely dependent on its own input voltage trajectory, and can accurately capture the frequency-coupling dynamics. The dynamic effects of both the basic synchronous-reference-frame phase-locked loop (PLL) and its alternative with a notch filter of the negative-sequence voltage component are compared. It is revealed that the notchfiltered PLL significantly weakens the frequency-coupling effects, which leads to a reduced order of the admittance model. The developed model is validated by a frequency scan, and the frequency-coupling effects impacted by different PLLs and voltage unbalance factors are verified by the experimental tests. Finally, a case study on stability analysis in unbalanced grids proves the significance of the model.

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