A Two-Dimensional Dead-Zone Virtual Oscillator Control for Single-Phase Inverters

Virtual oscillator control (VOC) is a time-domain strategy for regulating grid-forming inverters, with three commonly used types: Van der Pol, dead-zone, and Andronov-Hopf oscillators. Among them, only the Andronov-Hopf oscillator generates harmonic-free waveforms, while the others introduce harmonic content. However, the dead-zone oscillator uniquely features a bounded nonlinear gain, which is essential for ensuring global asymptotic large-signal stability in the VOC-based inverter-grid system under grid disturbances. To address existing design limitations, a two-dimensional dead-zone (TDDZ) oscillator is proposed, combining harmonic-free oscillations with a bounded nonlinear gain. The harmonic-free attribute is achieved by coupling two-dimensional states to define the nonlinear forcing function, while the bounded nonlinear gain is realized by setting the boundaries of nonlinear functions. Perturbation theory is utilized to demonstrate the harmonic-free attribute, and the small-gain theorem is applied to ensure the large-signal stability. The effectiveness of the TDDZ oscillator is validated through simulation and experimental results.