Dispatchable virtual oscillator control (dVOC) is widely studied for grid-forming, grid connected voltage-source converters due to its time-domain implementation of nonlinear oscillator dynamics. Large-signal stability analysis of dVOC is critical for reliable system operation. The prior small-gain theorem-based analysis provides only a sufficient condition and is conservative, as it neglects phase information and oversimplifies the nonlinear structure, which can potentially predict instability in stable cases with substantial margins. In this paper, we present a necessary and sufficient stability condition in the frequency domain that eliminates this conservativeness. Phase information is retained via complex transfer function representations of the system dynamics, and the nonlinear structure is precisely modeled within a bounded nonlinearity range. Based on the structural singular value criterion, a necessary and sufficient condition for the large-signal stability analysis of dVOC is derived, ensuring that predicted stability matches actual stability (sufficient condition), while any predicted instability implies the existence of at least one unstable operating case.
