  This paper proposes a taxonomy of power converter control schemes based on
the recently proposed concept of complex frequency. This quantity captures
local frequency variations due to the change of both the phase angle and
amplitude of bus voltages and current injections. The paper derives the
analytical expressions of the link between complex power variations and complex
frequency of each converter controller as well as the identification of
critical control parameters. The main contribution of this work is to provide a
general framework that allows classifying converters synchronization mechanisms
and controllers. This framework also allows comparing converters with
synchronous machines. To validate the theoretical results, extensive
simulations are performed using a modified version of the WSCC 9-bus system.
Examples of how the theoretical formulations of the paper can be used to
improve power converter control in power system applications are showcased.
