Benchmarking Nonlinear Oscillators for Grid-Forming Inverter Control

Virtual oscillator control (VOC) is a time-domain strategy that leverages the dynamics of nonlinear oscillator circuits for synchronizing and regulating grid-forming inverters. In this article, we examine a class of second-order circuits composed of a harmonic oscillator and nonlinear state-dependent damping that has found extensive interest in the context of VOC. We center our analysis on the Van der Pol, Dead-zone, and Andronov-Hopf oscillators; these are characterized by several distinguishing attributes but they all share the common structure noted above. Analytical methods based on averaging and perturbation theory are outlined to derive several performance metrics related to harmonic and dynamic properties of these oscillators under a unified framework. Our results reveal that the Andronov-Hopf oscillator is well suited for grid-forming inverter applications since it can yield harmonics-free waveforms without compromising dynamic performance. Analytical results are validated with numerical simulations and experiments, and a multiinverter hardware setup is used to illustrate a practical use case.