  For power grids predominantly featuring large synchronous generators (SGs),
there exists a significant body of work bridging optimization and control
tasks. A generic workflow in such efforts entails: characterizing the steady
state of control algorithms and SG dynamics; assessing the optimality of the
resulting operating point with respect to an optimal dispatch task; and
prescribing control parameters to ensure that (under reasonable ambient
perturbations) the considered control nudges the system steady state to
optimality. Well studied instances of the aforementioned approach include
designing: i) automatic generation control (AGC) participation factors to
ensure economic optimality, and ii) governor frequency-droop slopes to ensure
power sharing. Recognizing that future power grids will feature a diverse mix
of SGs and inverter-based resources (IBRs) with varying control structures,
this work examines the different steps of the optimization-control workflow for
this context. Considering a representative model of active power-frequency
dynamics of IBRs and SGs, a characterization of steady state is put forth (with
and without secondary frequency control). Conditions on active-power droop
slopes and AGC participation factors are then derived to ascertain desired
power sharing and ensure economically optimal operation under varying power
demands.
