  This paper developed a novel control approach for the sparse and safe
frequency regulation for inverter intensive microgrids (MGs). In the scenario,
the inverters and external grids are expected to reach a synchronized desired
frequency under regulations. To this end, the active power set-point acting as
a control from a high-level controller is designed while considering two
important performance metrics "sparsity" and "safety", which are to reduce the
information exchange between controllers and ensure that the frequency keeps in
safety regions during the whole operation process. Our proposed control design
framework allows the sparse linear feedback controller (SLFC) to be unified
with a family of conditions for safe control using control barrier functions. A
quadratic programming (QP) problem is then constructed, and the real-time
control policy is obtained by solving the QP problem. Importantly, we also
found that the real-time control for each inverter depends on the cross-layer
communication network topology which is the union of the one between
controllers from SLFC and the one determined by the power flow network.
Furthermore, our approach has been validated through extensive numerical
simulations.
