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As the crucial interface of renewable energy integration, the stable operation of power converters under grid faults and external disturbances has become much more important. However, synchronization instability of grid-tied inverters has been found caused by the phase-locked loop (PLL) under some critical operating conditions, such as the grid voltage sag, current surge and transmission line faults. Owing to the strong nonlinearity, transient stability analysis of inverters with PLL becomes much more complicated under large-signal perturbations and weak grid condition. In this paper, the large-signal synchronization stability of grid-tied inverters is investigated from the energy perspective. Based on the structural resemblance between the PLL and synchronous generator, the energy function is constructed to estabilish a Port-Hamiltonian model for the grid-tied inverter. For the nonlinear inverter system, an explicit Hamiton-based stability criterion is developed for grid-tied converters according to the concept of dissipativity and LaSalle’s theorem. Moreover, the analytical stability boundary is acquired based on the proposed stability criterion and attraction region estimation, covering both controller parameters and grid parameters. To verify the effectiveness of the proposed analysis approach, extensive simulation and experimental results are presented. Compared with the conventional large-signal methods, the proposed Hamiton-based approach has explicit physical meaning and high accuracy.

Under transient disturbance, the grid-forming voltage-source converter may lose its synchronization with the grid, inducing sustained low-frequency oscillation in instantaneous power, current, and phase angle. The physical origin of such oscillations is found to be a homoclinic bifurcation in this article. Before the system runs into a homoclinic bifurcation, a stable equilibrium point (SEP) and a stable periodic orbit coexist. When a large transient disturbance is applied, the system exhibits a periodic orbit, which manifests itself as low-frequency oscillation. Moreover, after the homoclinic bifurcation, the periodic orbit subsides, and only a single attractor, the SEP, exists in the phase space. In this case, the grid-forming converter is able to resynchronize with the grid even under transient disturbances. Bifurcation diagrams are derived as the boundaries of stable operation in the parameter space, which serve as practical design guidelines to avoid sustained oscillations. Cycle-by-cycle simulations and laboratory experiments are performed to verify the analytical findings.

The grid-forming and grid-following controls are adopted in three-phase voltage source converters according to different grid conditions. However, the basic operation principle of the two kinds of control is different and will lead to the instability of the grid-connected system through various paths. In this article, the energy function model of the grid-forming and grid-following controlled converters are established and compared in detail. The influence of system parameters is studied, and the large-signal stability boundaries are derived through a general method. Moreover, compared to the grid-forming controlled converter, the grid-following converter will lose stability by exhibiting a varying damping coefficient transient. The equivalent damping coefficient can be used as a criterion of whether the grid-forming/following control is suitable for the weak/strong grid condition. The simulation and experiment results show the difference of the transient process and validate the control criterion for different grid strength under large-signal disturbance.

Interactions of identical inverters in weak grids have received wide attentions. However, in a practical wind farm, parameters of grid-side inverters and lengths of collecting lines are not completely the same. In this case, a multi-inverter system is not symmetric, and thus the interaction mechanism could be more complicated than that of identical inverters. To investigate the interaction mechanism of differently parameterized inverters, this paper proposes a clustering-based modeling method, in which inverters with identical parameters are classified as one group. The clustering-based model allows for efficient stability assessment using three low-order transfer function matrices, instead of a full-order dynamic model. The root locus analysis is applied in the clustering-based model for stability analysis. Results show that the interconnection of distinct groups of inverters deteriorates common current stability, but has no impact on interactive current stability. The simulation and rtlab-based experimental results validate the effectiveness of the proposed model and the interaction mechanism of differently parameterized inverters.