As a common interface circuit for renewable energy integrated into the power grid, the inverter is prone to work under a three-phase unbalanced weak grid. In this paper, the instability of grid-connected inverters under the unbalanced grid condition is investigated. First, a dual second-order generalized integrator phase-locked loop (DSOGI-PLL)-based inverter under balanced and unbalanced conditions is modeled. A fourth-order impedance model is established to describe its impedance characteristics under the unbalanced grid condition. To analyze this multi-input multi-output system, a simplified stability analysis method based on the generalized Nyquist stability criterion and matrix theory is proposed. Then, the influences of circuit and control parameters on the stability of the grid-connected inverter system under the unbalanced grid condition are investigated. Finally, the accuracy of the derived frequency-coupled impedance model is verified via simulations, and the effectiveness of the proposed simplified stability analysis method on the system stability analysis is verified via both simulations and hardware experiments.

For a grid-connected inverter (GCI) without AC voltage sensors connected to the weak grid, the occurrence of frequency variation diminishes the accuracy of the estimated grid voltage and also degrades the output performance of the GCI. To solve these problems, based on virtual flux (VF) estimator, an improved Newton-Raphson method-based finite position set- phase locked loop (INR-FPS-PLL) and a frequency-adaptive control strategy with a quasi proportion complex integral (QPCI) controller are proposed. In detail, to meet the requirement for rapid acquisition of grid frequency information under frequency variation, the INR-FPS-PLL with only 6 iterations is developed. This PLL has low calculation burden and fast convergence. Then, because frequency variation reduces the accuracy of the estimated grid voltage, according to the principle of VF estimation, a grid voltage estimation method based on frequency-adaptive double first-order low-pass filter (DFO-LPF) with compensation techniques is proposed. Furthermore, to solve the performance degradation of GCI caused by grid frequency variation, the resonant frequency of the QPCI controller is adjusted according to the frequency information obtained by the INR-FPS-PLL, so that the zero-steady-state tracking error of grid current is ensured under frequency variation. Finally, simulation and experimental results verify the effectiveness of the proposed strategies.

Pulse width modulators in the digital control system of the voltage source converter (VSC) are used to generate switching signals. However, their complex multi-frequency characteristics may lead to middle- and high-frequency oscillations. There are currently limited studies on the three-phase pulse width modulation (PWM) VSC considering modulator’s sideband harmonics, and the modeling methods proposed for other kinds of PWM converters are not applicable to the three-phase VSC. Therefore, to investigate the sideband harmonic stability of three-phase VSCs, the multiple Fourier series-based modeling method of the digital PWM modulator is proposed in this paper. First, the analytic expressions of switching signals when the modulator is perturbed by harmonics are derived based on the proposed method. Then, this paper summarizes the selection principles of the dominant harmonic components of the perturbed modulator. Finally, complex analytic expressions are simplified and approximated linearly to provide easy-to-use analytic results for other researchers. Then, based on the proposed modeling method, the impedance model of the VSC with a symmetric regular sampled SPWM modulator is derived. Based on the derived model, the influences of the key parameters on the system stability are investigated. Finally, the theoretical analysis results are validated through both simulations and hardware experiments.

The switching dynamics of control limiters have significantly exacerbated the transient instability risk of grid-forming (GFM) converters. However, the limiter-induced instability phenomena have not been explored extensively, and the dynamical nature has seldom been revealed due to modeling challenges and analytical method limitations. In this paper, transient instability induced by the combined effects of the current limiter and modulation limiter in the GFM converter is investigated based on the nonsmooth dynamical theory. The piecewise-smooth electromagnetic transient model of the GFM converter is first derived fully considering the switching effects of the limiters and inner loop dynamics. On this basis, the limiter-induced instability phenomena of the GFM converter under large disturbances are explored and found to be induced by hidden attractors. By bifurcation analysis, the evolution mechanism of the hidden attractors is revealed, and the parameter design guideline for the transient stability enhancement is summarized. Furthermore, the multistability phenomenon that hidden attractors coexist with a stable equilibrium is reported. Due to the fractal structure of the basins of attraction, the transient behaviors of the GFM converter are sensitive to the disturbance and lack predictability. Finally, the findings are verified by experiments.