  A widely embraced approach to mitigate the dynamic degradation in low-inertia
power systems is to mimic generation response using grid-connected inverters to
restore the grid's stiffness. In this paper, we seek to challenge this approach
and advocate for a principled design based on a systematic analysis of the
performance trade-offs of inverter-based frequency control. With this aim, we
perform a qualitative and quantitative study comparing the effect of
conventional control strategies --droop control (DC) and virtual inertia (VI)--
on several performance metrics induced by $\mathcal L_2$ and $\mathcal
L_\infty$ signal norms. By extending a recently proposed modal decomposition
method, we capture the effect of step and stochastic power disturbances, and
frequency measurement noise, on the overall transient and steady-state behavior
of the system. Our analysis unveils several limitations of these solutions,
such as the inability of DC to improve dynamic frequency response without
increasing steady-state control effort, or the large frequency variance that VI
introduces in the presence of measurement noise. We further propose a novel
dynam-i-c Droop controller (iDroop) that overcomes the limitations of DC and
VI. More precisely, we show that iDroop can be tuned to achieve high noise
rejection, fast system-wide synchronization, or frequency overshoot (Nadir)
elimination without affecting the steady-state control effort share, and
propose a tuning recommendation that strikes a balance among these objectives.
Extensive numerical experimentation shows that the proposed tuning is effective
even when our proportionality assumptions are not valid, and that the
particular tuning used for Nadir elimination strikes a good trade-off among
various performance metrics.
