Robust Direct Control of Voltage Amplitude and Phase Angle for Grid-Forming Inverters

Grid-forming inverters (GFMs) play a key role in ensuring stable operation of low-inertia and weak-grid systems. However, conventional control strategies based on dq/αβ cascaded loops suffer from performance limitations under large-signal disturbances and nonlinear operating conditions. This article proposes a novel amplitude–angle-based modeling and control framework for GFMs, where the inverter dynamics are directly expressed in terms of output voltage amplitude and phase angle, avoiding the conventional synchronous dq-frame transformation and cascaded voltage–current control loops. Based on this formulation, a super-twisting sliding mode controller is designed to directly regulate voltage amplitude and phase angle, ensuring strong robustness against parameter variations, nonlinearities, and grid disturbances. Experimental results for single and two-GFM islanded systems are carried out to demonstrate fast dynamic response, effective power-sharing performance, and robustness under parameter variations and large voltage/frequency reference changes. Furthermore, the proposed amplitude–angle formulation is intended to provide a general framework for the systematic design of advanced nonlinear control strategies for GFMs.