A Two-Dimensional Dead-Zone Virtual Oscillator Control for Single-Phase Grid-Forming Grid-Connected Converters

Virtual oscillator control (VOC) is a time-domain strategy for regulating grid-forming converters by emulating the dynamics of nonlinear oscillator circuits. Among the three commonly used VOC types—Van der Pol, dead-zone, and Andronov-Hopf (AH) oscillators—only the AH oscillator generates harmonic-free waveforms, whereas the Van der Pol and dead-zone oscillators 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 converter-grid system under large grid disturbances. To address existing design limitations, a two-dimensional dead-zone (TDDZ) oscillator is proposed for the first time, combining harmonic-free oscillations with a bounded nonlinear gain. The harmonic-free attribute is achieved by coupling 2-D states to define the nonlinear forcing function. Meanwhile, the nonlinear gain is retained as bounded by setting the boundaries of nonlinear functions, accounting for both the inherent nonlinearity of the damping function and the nonlinearity introduced by the power regulation loop. Perturbation theory is utilized to demonstrate the harmonic-free attribute, and the small-gain theorem is applied to assess the global asymptotic large-signal stability of the TDDZ-based converter-grid system. The effectiveness of the proposed TDDZ oscillator is validated through simulation and experimental results.