  Complex droop control, alternatively known as dispatchable virtual oscillator
control (dVOC), stands out for its unique capabilities in synchronization and
voltage stabilization among existing control strategies for grid-forming
converters. Complex droop control leverages the novel concept of ``complex
frequency'', thereby establishing a coupled connection between active and
reactive power inputs and frequency and rate-of-change-of voltage outputs.
However, its reliance on static droop gains limits its ability to exhibit
crucial dynamic response behaviors required in future power systems. To address
this limitation, this paper introduces \textit{dynamic complex-frequency
control}, upgrading static droop gains with dynamic transfer functions to
enhance the richness and flexibility in dynamic responses for frequency and
voltage control. Unlike existing approaches, the complex-frequency control
framework treats frequency and voltage dynamics collectively, ensuring
small-signal stability for frequency synchronization and voltage stabilization
simultaneously. The control framework is validated through detailed numerical
case studies on the IEEE nine-bus system, also showcasing its applicability in
multi-converter setups.
