  In this letter, we study the nonlinear stability problem of converter-based
power systems, where the converter dynamics are governed by a complex droop
control. This complex droop control augments the well-known power-frequency
(p-f) droop control, and it proves to be equivalent to the state-of-the-art
dispatchable virtual oscillator control (dVOC). In this regard, it is
recognized as a promising grid-forming solution to address the high penetration
of converters in future power systems. In previous work, the global stability
of dVOC (i.e., complex droop control) has been proven by prespecifying a
nominal synchronous steady state. For a general case of non-nominal (i.e.,
drooped) synchronous steady states, however, the stability problem requires
further investigation. In this letter, we provide parametric conditions under
which a non-nominal synchronous steady state exists and the system is almost
globally asymptotically stable with respect to this non-nominal synchronous
steady state.
