On Stability of Time-Invariant Current Controlled Weak-Grid-Tied Inverters Considering Sinusoidal Pulsewidth Modulation Saturation and Parameter Uncertainties

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.